An Initial Non-Equilibrium Porous-Media Model for CFD Simulation of Stirling Regenerators
Tew, Roy C.; Simon, Terry; Gedeon, David; Ibrahim, Mounir; Rong, Wei
2006-01-01
The objective of this paper is to define empirical parameters for an initial thermal non-equilibrium porous-media model for use in Computational Fluid Dynamics (CFD) codes for simulation of Stirling regenerators. The two codes currently used at Glenn Research Center for Stirling modeling are Fluent and CFD-ACE. The codes porous-media models are equilibrium models, which assume solid matrix and fluid are in thermal equilibrium. This is believed to be a poor assumption for Stirling regenerators; Stirling 1-D regenerator models, used in Stirling design, use non-equilibrium regenerator models and suggest regenerator matrix and gas average temperatures can differ by several degrees at a given axial location and time during the cycle. Experimentally based information was used to define: hydrodynamic dispersion, permeability, inertial coefficient, fluid effective thermal conductivity, and fluid-solid heat transfer coefficient. Solid effective thermal conductivity was also estimated. Determination of model parameters was based on planned use in a CFD model of Infinia's Stirling Technology Demonstration Converter (TDC), which uses a random-fiber regenerator matrix. Emphasis is on use of available data to define empirical parameters needed in a thermal non-equilibrium porous media model for Stirling regenerator simulation. Such a model has not yet been implemented by the authors or their associates.
Non-equilibrium model of two-phase porous media flow with phase change
Cueto-Felgueroso, L.; Fu, X.; Juanes, R.
2014-12-01
The efficient simulation of multi-phase multi-component flow through geologic porous media is challenging and computationally intensive, yet quantitative modeling of these processes is essential in engineering and the geosciences. Multiphase flow with phase change and complex phase behavior arises in numerous applications, including enhanced oil recovery, steam injection in groundwater remediation, geologic CO2 storage and enhanced geothermal energy systems. A challenge of multiphase compositional simulation is that the number of existing phases varies with position and time, and thus the number of state variables in the saturation-based conservation laws is a function of space and time. The tasks of phase-state identification and determination of the composition of the different phases are performed assuming local thermodynamic equilibrium. Here we investigate a thermodynamically consistent formulation for non-isothermal two-phase flow, in systems where the hypothesis of instantaneous local equilibrium does not hold. Non-equilibrium effects are important in coarse-scale simulations where the assumption of complete mixing in each gridblock is not realistic. We apply our model to steam injection in water-saturated porous media.
Indian Academy of Sciences (India)
Deepak Swami; P K Sharma; C S P Ojha
2014-12-01
In this paper, we have studied the behaviour of reactive solute transport through stratified porous medium under the influence of multi-process nonequilibrium transport model. Various experiments were carried out in the laboratory and the experimental breakthrough curves were observed at spatially placed sampling points for stratified porous medium. Batch sorption studies were also performed to estimate the sorption parameters of the material used in stratified aquifer system. The effects of distance dependent dispersion and tailing are visible in the experimental breakthrough curves. The presence of physical and chemical non-equilibrium are observed from the pattern of breakthrough curves. Multi-process non-equilibrium model represents the combined effect of physical and chemical non-ideality in the stratified aquifer system. The results show that the incorporation of distance dependent dispersivity in multi-process non-equilibrium model provides best fit of observed data through stratified porous media. Also, the exponential distance dependent dispersivity is more suitable for large distances and at small distances, linear or constant dispersivity function can be considered for simulating reactive solute in stratified porous medium.
Chapwanya, Michael
2010-01-01
This is a computational study of gravity-driven fingering instabilities in unsaturated porous media. The governing equations and corresponding numerical scheme are based on the work of Nieber et al. [Ch. 23 in Soil Water Repellency, eds. C. J. Ritsema and L. W. Dekker, Elsevier, 2003] in which non-monotonic saturation profiles are obtained by supplementing the Richards equation with a non-equilibrium capillary pressure-saturation relationship, as well as including hysteretic effects. The first part of the study takes an extensive look at the sensitivity of the finger solutions to certain key parameters in the model such as capillary shape parameter, initial saturation, and capillary relaxation coefficient. The second part is a comparison to published experimental results that demonstrates the ability of the model to capture realistic fingering behaviour.
Liu, Q
2016-01-01
In this paper, a multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is proposed for convection heat transfer in porous media under local thermal non-equilibrium (LTNE) condition. The model is constructed within the framework of the three-distribution-function approach: two temperature-based MRT-LB equations are proposed for the temperature fields of fluid and solid phases in addition to the MRT-LB equation of a density distribution function for the velocity field described by the generalized non-Darcy model. The thermal non-equilibrium effects are incorporated into the model by adding source terms into the temperature-based MRT-LB equations. Moreover, the discrete lattice effects are considered in the introduction of source terms into the temperature-based MRT-LB equations. The source terms accounting for the thermal non-equilibrium effects are simple and the model retains the inherent features of the standard LB method. Numerical results demonstrate that the proposed model can be served as an accura...
Kachalov, V. V.; Molchanov, D. A.; Sokotushchenko, V. N.; Zaichenko, V. M.
2016-11-01
At the present time, a considerable part of the largest dry gas reservoirs in Russia are found in the stage of declining production, therefore active exploitation of gas-condensate fields will begin in the coming decades. There is a significant discrepancy between the project and the actual value of condensate recovery factor while producing reservoir of this type, which is caused by insufficient knowledge about non-equilibrium filtration mechanisms of gas-condensate mixtures in reservoir conditions. A system of differential equations to describe filtration process of two-phase multicomponent mixture for one-, two- and three-dimensional cases is presented in this work. The solution of the described system was made by finite-element method in the software package FlexPDE. Comparative distributions of velocities, pressures, saturations and phase compositions of three-component mixture along the reservoir model and in time in both cases of equilibrium and non-equilibrium filtration processes were obtained. Calculation results have shown that system deviation from the thermodynamic equilibrium increases gas phase flow rate and reduces liquid phase flow rate during filtration process of gas-condensate mixture.
Non-equilibrium thermochemical heat storage in porous media
DEFF Research Database (Denmark)
Nagel, T.; Shao, H.; Singh, Ashok
2013-01-01
Thermochemical energy storage can play an important role in the establishment of a reliable renewable energy supply and can increase the efficiency of industrial processes. The application of directly permeated reactive beds leads to strongly coupled mass and heat transport processes that also...... compressible gas flow through a porous solid is presented along with its finite element implementation where solid-gas reactions occur and both phases have individual temperature fields. The model is embedded in the Theory of Porous Media and the derivation is based on the evaluation of the Clausius...
Non-equilibrium thermochemical heat storage in porous media
DEFF Research Database (Denmark)
Nagel, T.; Shao, H.; Singh, Ashok
2013-01-01
Thermochemical energy storage can play an important role in the establishment of a reliable renewable energy supply and can increase the efficiency of industrial processes. The application of directly permeated reactive beds leads to strongly coupled mass and heat transport processes that also...... compressible gas flow through a porous solid is presented along with its finite element implementation where solid-gas reactions occur and both phases have individual temperature fields. The model is embedded in the Theory of Porous Media and the derivation is based on the evaluation of the Clausius......-Duhem inequality. Special emphasis is placed on the interphase coupling via mass, momentum and energy interaction terms and their effects are partially illustrated using numerical examples. Novel features of the implementation of the described model are verified via comparisons to analytical solutions...
Numerical analysis of a non equilibrium two-component two-compressible flow in porous media
Saad, Bilal Mohammed
2013-09-01
We propose and analyze a finite volume scheme to simulate a non equilibrium two components (water and hydrogen) two phase flow (liquid and gas) model. In this model, the assumption of local mass non equilibrium is ensured and thus the velocity of the mass exchange between dissolved hydrogen and hydrogen in the gas phase is supposed finite. The proposed finite volume scheme is fully implicit in time together with a phase-by-phase upwind approach in space and it is discretize the equations in their general form with gravity and capillary terms We show that the proposed scheme satisfies the maximum principle for the saturation and the concentration of the dissolved hydrogen. We establish stability results on the velocity of each phase and on the discrete gradient of the concentration. We show the convergence of a subsequence to a weak solution of the continuous equations as the size of the discretization tends to zero. At our knowledge, this is the first convergence result of finite volume scheme in the case of two component two phase compressible flow in several space dimensions.
Trends in modeling of porous media combustion
Energy Technology Data Exchange (ETDEWEB)
Mujeebu, M. Abdul; Abdullah, M. Zulkifly [Porous Media Combustion Laboratory, School of Mechanical Engineering, Universiti Sains Malaysia, Engineering Campus, 14300 Nibong Tebal, Penang (Malaysia); Mohamad, A.A. [College of Engineering, Alfaisal University, Riyadh 11533, P.O. Box 50927 (Saudi Arabia); Bakar, M.Z. Abu [School of Chemical Engineering, Universiti Sains Malaysia, Engineering Campus, 14300 Nibong Tebal, Penang (Malaysia)
2010-12-15
Porous media combustion (PMC) has interesting advantages compared with free flame combustion due to higher burning rates, increased power dynamic range, extension of the lean flammability limits, and low emissions of pollutants. Extensive experimental and numerical works were carried out and are still underway, to explore the feasibility of this interesting technology for practical applications. For this purpose, numerical modeling plays a crucial role in the design and development of promising PMC systems. This article provides an exhaustive review of the fundamental aspects and emerging trends in numerical modeling of gas combustion in porous media. The modeling works published to date are reviewed, classified according to their objectives and presented with general conclusions. Numerical modeling of liquid fuel combustion in porous media is excluded. (author)
Zhang, Hong
2016-01-01
An adaptive moving mesh finite difference method is presented to solve two types of equations with dynamic capillary pressure term in porous media. One is the non-equilibrium Richards Equation and the other is the modified Buckley-Leverett equation. The governing equations are discretized with an adaptive moving mesh finite difference method in the space direction and an implicit-explicit method in the time direction. In order to obtain high quality meshes, an adaptive time-dependent monitor function with directional control is applied to redistribute the mesh grid in every time step, and a diffusive mechanism is used to smooth the monitor function. The behaviors of the central difference flux, the standard local Lax-Friedrich flux and the local Lax-Friedrich flux with reconstruction are investigated by solving a 1D modified Buckley-Leverett equation. With the moving mesh technique, good mesh quality and high numerical accuracy are obtained. A collection of one-dimensional and two-dimensional numerical experi...
Energy Technology Data Exchange (ETDEWEB)
Muthtamilselvan, M.; Prakash, D. [Bharathiar University, Coimbatore (Iran, Islamic Republic of); Doh, Deog Hee [Korea Maritime University, Busan (Korea, Republic of)
2014-09-15
This work is made to study the effect of local thermal non-equilibrium (LTNE) on transient MHD laminar boundary layer flow of viscous, incompressible nanofluid over a vertical stretching plate embedded in a sparsely packed porous medium. The flow in the porous medium is governed by simple Darcy model. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. Three temperature model is used to represent the local thermal non-equilibrium among the particle, fluid, and solid-matrix phases. By applying similarity analysis, the governing partial differential equations are transformed into a set of time dependent nonlinear coupled ordinary differential equations and they are solved by Runge-Kutta Fehlberg Method along with shooting technique. Numerical results of the boundary layer flow characteristics for the fluid, particle and solid phases are obtained for various combinations of the physical parameters. It is found that the thermal non-equilibrium effects are strongest when the fluid/particle, fluid/solid Nield numbers and thermal capacity ratios are small. Moreover, the amount of heat transfer is maximum in nanoparticles than that of fluid and solid phases because of enhancement of thermal conductivity in nanofluids.
Network models of dissolution of porous media
Budek, Agnieszka
2012-01-01
We investigate the chemical dissolution of porous media using a network model in which the system is represented as a series of interconnected pipes with the diameter of each segment increasing in proportion to the local reactant consumption. Moreover, the topology of the network is allowed to change dynamically during the simulation: as the diameters of the eroding pores become comparable with the interpore distances, the pores are joined together thus changing the interconnections within the network. With this model, we investigate different growth regimes in an evolving porous medium, identifying the mechanisms responsible for the emergence of specific patterns. We consider both the random and regular network and study the effect of the network geometry on the patterns. Finally, we consider practically important problem of finding an optimum flow rate that gives a maximum increase in permeability for a given amount of reactant.
A Particle Resistance Model for Flow through Porous Media
Institute of Scientific and Technical Information of China (English)
WU Jin-Sui; YIN Shang-Xian; ZHAO Dong-Yu
2009-01-01
A particle model for resistance of flow in isotropic porous media is developed based on the fractal geometry theory and on the drag force flowing around sphere.The proposed model is expressed as a function of porosity,fluid property,particle size,fluid velocity (or Reynolds number) and fractal characters Df of particles in porous media.The model predictions are in good agreement with the experimental data.The validity of the proposed model is thus verified.
Kulasiri, Don
2002-01-01
Most of the natural and biological phenomena such as solute transport in porous media exhibit variability which can not be modeled by using deterministic approaches. There is evidence in natural phenomena to suggest that some of the observations can not be explained by using the models which give deterministic solutions. Stochastic processes have a rich repository of objects which can be used to express the randomness inherent in the system and the evolution of the system over time. The attractiveness of the stochastic differential equations (SDE) and stochastic partial differential equations (SPDE) come from the fact that we can integrate the variability of the system along with the scientific knowledge pertaining to the system. One of the aims of this book is to explaim some useufl concepts in stochastic dynamics so that the scientists and engineers with a background in undergraduate differential calculus could appreciate the applicability and appropriateness of these developments in mathematics. The ideas ...
a Fractal Network Model for Fractured Porous Media
Xu, Peng; Li, Cuihong; Qiu, Shuxia; Sasmito, Agus Pulung
2016-04-01
The transport properties and mechanisms of fractured porous media are very important for oil and gas reservoir engineering, hydraulics, environmental science, chemical engineering, etc. In this paper, a fractal dual-porosity model is developed to estimate the equivalent hydraulic properties of fractured porous media, where a fractal tree-like network model is used to characterize the fracture system according to its fractal scaling laws and topological structures. The analytical expressions for the effective permeability of fracture system and fractured porous media, tortuosity, fracture density and fraction are derived. The proposed fractal model has been validated by comparisons with available experimental data and numerical simulation. It has been shown that fractal dimensions for fracture length and aperture have significant effect on the equivalent hydraulic properties of fractured porous media. The effective permeability of fracture system can be increased with the increase of fractal dimensions for fracture length and aperture, while it can be remarkably lowered by introducing tortuosity at large branching angle. Also, a scaling law between the fracture density and fractal dimension for fracture length has been found, where the scaling exponent depends on the fracture number. The present fractal dual-porosity model may shed light on the transport physics of fractured porous media and provide theoretical basis for oil and gas exploitation, underground water, nuclear waste disposal and geothermal energy extraction as well as chemical engineering, etc.
Modeling microbial processes in porous media
Murphy, Ellyn M.; Ginn, Timothy R.
The incorporation of microbial processes into reactive transport models has generally proceeded along two separate lines of investigation: (1) transport of bacteria as inert colloids in porous media, and (2) the biodegradation of dissolved contaminants by a stationary phase of bacteria. Research over the last decade has indicated that these processes are closely linked. This linkage may occur when a change in metabolic activity alters the attachment/detachment rates of bacteria to surfaces, either promoting or retarding bacterial transport in a groundwater-contaminant plume. Changes in metabolic activity, in turn, are controlled by the time of exposure of the microbes to electron acceptors/donor and other components affecting activity. Similarly, metabolic activity can affect the reversibility of attachment, depending on the residence time of active microbes. Thus, improvements in quantitative analysis of active subsurface biota necessitate direct linkages between substrate availability, metabolic activity, growth, and attachment/detachment rates. This linkage requires both a detailed understanding of the biological processes and robust quantitative representations of these processes that can be tested experimentally. This paper presents an overview of current approaches used to represent physicochemical and biological processes in porous media, along with new conceptual approaches that link metabolic activity with partitioning of the microorganism between the aqueous and solid phases. Résumé L'introduction des processus microbiologiques dans des modèles de transport réactif a généralement suivi deux voies différentes de recherches: (1) le transport de bactéries sous forme de colloïdes inertes en milieu poreux, et (2) la biodégradation de polluants dissous par une phase stationnaire de bactéries. Les recherches conduites au cours des dix dernières années indiquent que ces processus sont intimement liés. Cette liaison peut intervenir lorsqu
Non-equilibrium modelling of distillation
Wesselingh, JA; Darton, R
1997-01-01
There are nasty conceptual problems in the classical way of describing distillation columns via equilibrium stages, and efficiencies or HETP's. We can nowadays avoid these problems by simulating the behaviour of a complete column in one go using a non-equilibrium model. Such a model has phase
A volume-balance model for flow on porous media
Malaga, Carlos; Mandujano, Francisco; Becerra, Julian
2015-11-01
Volume-balance models are used by petroleum engineers for simulating multiphase and multicomponent flow phenomena in porous media and the extraction process in oil reservoirs. In these models, mass conservation equations and Darcy's law are supplemented by a balance condition for the pore and fluid volumes. This provides a pressure equation suitable for simulating a compressible flow within a compressible solid matrix. Here we present an alternative interpretation of the volume-balance condition that includes the advective transport within a consolidated porous media. We obtain a modified equation for the time evolution of the pressure field. Numerical tests for phase separation under gravity are presented for multiphase three dimensional flow in heterogeneous porous media. The authors acknowledge funding from Fondo Sectorial CONACYT-SENER grant number 42536 (DGAJ-SPI-34-170412-217).
Combinatorial model of solute transport in porous media
Institute of Scientific and Technical Information of China (English)
张妙仙; 张丽萍
2004-01-01
Modeling of solute transport is a key issue in the area of soil physics and hydrogeology. The most common approach (the convection-dispersion equation) considers an average convection flow rate and Fickian-like dispersion. Here,we propose a solute transport model in porous media of continuously expanding scale, according to the combinatorics principle. The model supposed actual porous media as a combinative body of many basic segments. First, we studied the solute transport process in each basic segment body, and then deduced the distribution of pore velocity in each basic segment body by difference approximation, finally assembled the solute transport process of each basic segment body into one of the combinative body. The simulation result coincided with the solute transport process observed in test. The model provides useful insight into the solute transport process of the non-Fickian dispersion in continuously expanding scale.
Fractal Derivative Model for Air Permeability in Hierarchic Porous Media
Directory of Open Access Journals (Sweden)
Jie Fan
2012-01-01
Full Text Available Air permeability in hierarchic porous media does not obey Fick's equation or its modification because fractal objects have well-defined geometric properties, which are discrete and discontinuous. We propose a theoretical model dealing with, for the first time, a seemingly complex air permeability process using fractal derivative method. The fractal derivative model has been successfully applied to explain the novel air permeability phenomenon of cocoon. The theoretical analysis was in agreement with experimental results.
Mathematical models of a diffusion-convection in porous media
Directory of Open Access Journals (Sweden)
Anvarbek M. Meirmanov
2012-06-01
Full Text Available Mathematical models of a diffusion-convection in porous media are derived from the homogenization theory. We start with the mathematical model on the microscopic level, which consist of the Stokes system for a weakly compressible viscous liquid occupying a pore space, coupled with a diffusion-convection equation for the admixture. We suppose that the viscosity of the liquid depends on a concentration of the admixture and for this nonlinear system we prove the global in time existence of a weak solution. Next we rigorously fulfil the homogenization procedure as the dimensionless size of pores tends to zero, while the porous body is geometrically periodic. As a result, we derive new mathematical models of a diffusion-convection in absolutely rigid porous media.
Lattice Boltzmann model for incompressible flows through porous media.
Guo, Zhaoli; Zhao, T S
2002-09-01
In this paper a lattice Boltzmann model is proposed for isothermal incompressible flow in porous media. The key point is to include the porosity into the equilibrium distribution, and add a force term to the evolution equation to account for the linear and nonlinear drag forces of the medium (the Darcy's term and the Forcheimer's term). Through the Chapman-Enskog procedure, the generalized Navier-Stokes equations for incompressible flow in porous media are derived from the present lattice Boltzmann model. The generalized two-dimensional Poiseuille flow, Couette flow, and lid-driven cavity flow are simulated using the present model. It is found the numerical results agree well with the analytical and/or the finite-difference solutions.
Dissipative particle dynamics model for colloid transport in porous media
Energy Technology Data Exchange (ETDEWEB)
Pan, W.; Tartakovsky, A. M.
2013-08-01
We present that the transport of colloidal particles in porous media can be effectively modeled with a new formulation of dissipative particle dynamics, which augments standard DPD with non-central dissipative shear forces between particles while preserving angular momentum. Our previous studies have demonstrated that the new formulation is able to capture accurately the drag forces as well as the drag torques on colloidal particles that result from the hydrodynamic retardation effect. In the present work, we use the new formulation to study the contact efficiency in colloid filtration in saturated porous media. Note that the present model include all transport mechanisms simultaneously, including gravitational sedimentation, interception and Brownian diffusion. Our results of contact efficiency show a good agreement with the predictions of the correlation equation proposed by Tufenkji and EliMelech, which also incorporate all transport mechanisms simultaneously without the additivity assumption.
Modelling of radon transport in porous media
van der Graaf, E.R.; de Meijer, R.J.; Katase, A; Shimo, M
1998-01-01
This paper aims to describe the state of the art of modelling radon transport in soil on basis of multiphase radon transport equations. Emphasis is given to methods to obtain a consistent set of input parameters needed For such models. Model-measurement comparisons with the KVI radon transport Facil
Modelling of radon transport in porous media
van der Graaf, E.R.; de Meijer, R.J.; Katase, A; Shimo, M
1998-01-01
This paper aims to describe the state of the art of modelling radon transport in soil on basis of multiphase radon transport equations. Emphasis is given to methods to obtain a consistent set of input parameters needed For such models. Model-measurement comparisons with the KVI radon transport Facil
Viscoelastic flow simulations in model porous media
De, S.; Kuipers, J. A. M.; Peters, E. A. J. F.; Padding, J. T.
2017-05-01
We investigate the flow of unsteadfy three-dimensional viscoelastic fluid through an array of symmetric and asymmetric sets of cylinders constituting a model porous medium. The simulations are performed using a finite-volume methodology with a staggered grid. The solid-fluid interfaces of the porous structure are modeled using a second-order immersed boundary method [S. De et al., J. Non-Newtonian Fluid Mech. 232, 67 (2016), 10.1016/j.jnnfm.2016.04.002]. A finitely extensible nonlinear elastic constitutive model with Peterlin closure is used to model the viscoelastic part. By means of periodic boundary conditions, we model the flow behavior for a Newtonian as well as a viscoelastic fluid through successive contractions and expansions. We observe the presence of counterrotating vortices in the dead ends of our geometry. The simulations provide detailed insight into how flow structure, viscoelastic stresses, and viscoelastic work change with increasing Deborah number De. We observe completely different flow structures and different distributions of the viscoelastic work at high De in the symmetric and asymmetric configurations, even though they have the exact same porosity. Moreover, we find that even for the symmetric contraction-expansion flow, most energy dissipation is occurring in shear-dominated regions of the flow domain, not in extensional-flow-dominated regions.
Modeling Transverse Chemotaxis in Porous Media
Porter, M. L.; Valdés-Parada, F. J.; Wood, B. D.
2009-12-01
The movement of microorganisms toward a chemical attractant (chemotaxis) has been shown to aid in subsurface contaminant degradation and enhanced oil recovery. However, chemotaxis is inherently a pore scale process that must be upscaled to arrive at continuum scale models for field applications. In this work, the method of volume averaging is used to upscale the microscale chemotactic microbial transport equations in order to obtain the corresponding macroscale models for the mass balance of bacteria and the chemical attractant to which they respond. As a first approach, cellular growth/death and consumption of the attractant by chemical reaction are assumed to be negligible with respect to convective and diffusive transport mechanisms. Two effective medium coefficients are introduced in the model, namely a total motility tensor and a total velocity vector. Under certain conditions, it is shown that the coefficients can differ considerably from the values corresponding to non-chemotactic transport. The model is validated by comparing the predicted transverse motility coefficients and concentration profiles to those measured within an engineered porous medium. For the concentration profiles, we introduced a lag that accounts for the difference between the arrival time of the microorganisms and the their chemotactic response to the attractant.
Martin, R.; Orgogozo, L.; Noiriel, C. N.; Guibert, R.; Golfier, F.; Debenest, G.; Quintard, M.
2013-05-01
computed by sending batteries of codes in a mass production procedure. Some constraints can now be provided for poro-elastic imaging at the scale of reservoirs, for CO2 storage monitoring or geophysical exploration. 1. Golfier F. et al., Biofilms in porous media: Development of macroscopic transport equations va volume averaging with closure for local mass equilibrium conditions, Advances in Water Resources, 32, 463-485 (2009). 2. Orgogozo L. et al., Upscaling of transport processes in porous media with biofilms in non-equilibrium conditions, Advances in Water Resources, 33(5), 585-600 (2010). 3. Davit Y. et al., Modeling non-equilibrium mass transport in biologically reactive porous media, Advances in Water Resources, 33, 1075-1093, (2010). 4. Davit Y. et al., Imaging biofilm in porous media using X-ray computed micro-tomography, Journal of Microscopy, 242(1), 15-25 (2010). 5. Noiriel C. et al., Upscaling calcium carbonate precipitation rates from pore to continuum scale, Chemical Geology, 318-319, 60-74 (2012).
Geometric Models for Isotropic Random Porous Media: A Review
Directory of Open Access Journals (Sweden)
Helmut Hermann
2014-01-01
Full Text Available Models for random porous media are considered. The models are isotropic both from the local and the macroscopic point of view; that is, the pores have spherical shape or their surface shows piecewise spherical curvature, and there is no macroscopic gradient of any geometrical feature. Both closed-pore and open-pore systems are discussed. The Poisson grain model, the model of hard spheres packing, and the penetrable sphere model are used; variable size distribution of the pores is included. A parameter is introduced which controls the degree of open-porosity. Besides systems built up by a single solid phase, models for porous media with the internal surface coated by a second phase are treated. Volume fraction, surface area, and correlation functions are given explicitly where applicable; otherwise numerical methods for determination are described. Effective medium theory is applied to calculate physical properties for the models such as isotropic elastic moduli, thermal and electrical conductivity, and static dielectric constant. The methods presented are exemplified by applications: small-angle scattering of systems showing fractal-like behavior in limited ranges of linear dimension, optimization of nanoporous insulating materials, and improvement of properties of open-pore systems by atomic layer deposition of a second phase on the internal surface.
Modeling of surfactant transport and adsorption in porous media
Energy Technology Data Exchange (ETDEWEB)
Chung, F.T.H.
1991-04-01
When surfactant solution is flowing in a reservoir formation, surfactants will be diluted by flow dispersion, retained in dead-end pores, adsorbed on rock surfaces, or precipitated due to ion exchange. The loss of surfactant will be detrimental to the performance of gas foam. Information of surfactant concentration profiles in reservoir formations is essential for gas foaming technique development. The major objective of this research is to investigate with mathematical models the transport and dynamic adsorption of surfactants in porous media. The mathematical models have taken into account the convection, dispersion, capacitance, and adsorption effects on concentrations of surfactants. Numerical methods and computer programs have been developed which can be used to match experimental results and to determine the characterization parameters in the models. The models can be included in foam simulation programs to calculate surfactant concentration profiles in porous media. A flow experimental method was developed to measure the effluent surfactant concentration, which will be used to determine the model parameters. Commercial foaming agent Alipal CD-128 was used in this study. Equilibrium adsorption and surfactant precipitation have been tested. Tracer solutions with a nonadsorbing solute such as dextrose and sucrose were used to determine the dispersion parameters for the experimental sandpack; thus, the adsorption of the surfactant in the test sand can be identified with an adequate model. 49 refs., 21 figs.
Diffuse-Interface Modelling of Flow in Porous Media
Addy, Doug; Pradas, Marc; Schmuck, Marcus; Kalliadasis, Serafim
2016-11-01
Multiphase flows are ubiquitous in a wide spectrum of scientific and engineering applications, and their computational modelling often poses many challenges associated with the presence of free boundaries and interfaces. Interfacial flows in porous media encounter additional challenges and complexities due to their inherently multiscale behaviour. Here we investigate the dynamics of interfaces in porous media using an effective convective Cahn-Hilliard (CH) equation recently developed in from a Stokes-CH equation for microscopic heterogeneous domains by means of a homogenization methodology, where the microscopic details are taken into account as effective tensor coefficients which are given by a Poisson equation. The equations are decoupled under appropriate assumptions and solved in series using a classic finite-element formulation with the open-source software FEniCS. We investigate the effects of different microscopic geometries, including periodic and non-periodic, at the bulk fluid flow, and find that our model is able to describe the effective macroscopic behaviour without the need to resolve the microscopic details.
Langevin model for reactive transport in porous media
Tartakovsky, Alexandre M.
2010-08-01
Existing continuum models for reactive transport in porous media tend to overestimate the extent of solute mixing and mixing-controlled reactions because the continuum models treat both the mechanical and diffusive mixings as an effective Fickian process. Recently, we have proposed a phenomenological Langevin model for flow and transport in porous media [A. M. Tartakovsky, D. M. Tartakovsky, and P. Meakin, Phys. Rev. Lett. 101, 044502 (2008)10.1103/PhysRevLett.101.044502]. In the Langevin model, the fluid flow in a porous continuum is governed by a combination of a Langevin equation and a continuity equation. Pore-scale velocity fluctuations, the source of mechanical dispersion, are represented by the white noise. The advective velocity (the solution of the Langevin flow equation) causes the mechanical dispersion of a solute. Molecular diffusion and sub-pore-scale Taylor-type dispersion are modeled by an effective stochastic advection-diffusion equation. Here, we propose a method for parameterization of the model for a synthetic porous medium, and we use the model to simulate multicomponent reactive transport in the porous medium. The detailed comparison of the results of the Langevin model with pore-scale and continuum (Darcy) simulations shows that: (1) for a wide range of Peclet numbers the Langevin model predicts the mass of reaction product more accurately than the Darcy model; (2) for small Peclet numbers predictions of both the Langevin and the Darcy models agree well with a prediction of the pore-scale model; and (3) the accuracy of the Langevin and Darcy model deteriorates with the increasing Peclet number but the accuracy of the Langevin model decreases more slowly than the accuracy of the Darcy model. These results show that the separate treatment of advective and diffusive mixing in the stochastic transport model is more accurate than the classical advection-dispersion theory, which uses a single effective diffusion coefficient (the dispersion
Review of permeability evolution model for fractured porous media
Institute of Scientific and Technical Information of China (English)
Jianjun Ma
2015-01-01
The ability to capture permeability of fractured porous media plays a significant role in several engi-neering applications, including reservoir, mining, petroleum and geotechnical engineering. In order to solve fluid flow and coupled flow-deformation problems encountered in these engineering applications, both empirical and theoretical models had been proposed in the past few decades. Some of them are simple but still work in certain circumstances;others are complex but also need some modifications to be applicable. Thus, the understanding of state-of-the-art permeability evolution model would help researchers and engineers solve engineering problems through an appropriate approach. This paper summarizes permeability evolution models proposed by earlier and recent researchers with emphasis on their characteristics and limitations.
Efficient algorithms for multiscale modeling in porous media
Wheeler, Mary F.
2010-09-26
We describe multiscale mortar mixed finite element discretizations for second-order elliptic and nonlinear parabolic equations modeling Darcy flow in porous media. The continuity of flux is imposed via a mortar finite element space on a coarse grid scale, while the equations in the coarse elements (or subdomains) are discretized on a fine grid scale. We discuss the construction of multiscale mortar basis and extend this concept to nonlinear interface operators. We present a multiscale preconditioning strategy to minimize the computational cost associated with construction of the multiscale mortar basis. We also discuss the use of appropriate quadrature rules and approximation spaces to reduce the saddle point system to a cell-centered pressure scheme. In particular, we focus on multiscale mortar multipoint flux approximation method for general hexahedral grids and full tensor permeabilities. Numerical results are presented to verify the accuracy and efficiency of these approaches. © 2010 John Wiley & Sons, Ltd.
An Introduction to Flow and Transport in Fractal Models of Porous Media: Part I
Cai, Jianchao; San José Martínez, Fernando; Martín, Miguel Angel; Perfect, Edmund
2014-09-01
This special issue gathers together a number of recent papers on fractal geometry and its applications to the modeling of flow and transport in porous media. The aim is to provide a systematic approach for analyzing the statics and dynamics of fluids in fractal porous media by means of theory, modeling and experimentation. The topics covered include lacunarity analyses of multifractal and natural grayscale patterns, random packing's of self-similar pore/particle size distributions, Darcian and non-Darcian hydraulic flows, diffusion within fractals, models for the permeability and thermal conductivity of fractal porous media and hydrophobicity and surface erosion properties of fractal structures.
Non-equilibrium modelling of arc plasma torches
Energy Technology Data Exchange (ETDEWEB)
Trelles, J P; Heberlein, J V R; Pfender, E [Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455 (United States)
2007-10-07
A two-temperature thermal non-equilibrium model is developed and applied to the three-dimensional and time-dependent simulation of the flow inside a dc arc plasma torch. A detailed comparison of the results of the non-equilibrium model with those of an equilibrium model is presented. The fluid and electromagnetic equations in both models are approximated numerically in a fully-coupled approach by a variational multi-scale finite element method. In contrast to the equilibrium model, the non-equilibrium model did not need a separate reattachment model to produce an arc reattachment process and to limit the magnitude of the total voltage drop and arc length. The non-equilibrium results show large non-equilibrium regions in the plasma-cold-flow interaction region and close to the anode surface. Marked differences in the arc dynamics, especially in the arc reattachment process, and in the magnitudes of the total voltage drop and outlet temperatures and velocities between the models are observed. The non-equilibrium results show improved agreement with experimental observations.
Modeling heterogeneous unsaturated porous media flow at Yucca Mountain
Energy Technology Data Exchange (ETDEWEB)
Robey, T.H. [Spectra Research Institute, Albuquerque, NM (United States)
1994-12-31
Geologic systems are inherently heterogeneous and this heterogeneity can have a significant impact on unsaturated flow through porous media. Most previous efforts to model groundwater flow through Yucca Mountain have used stratigraphic units with homogeneous properties. However, modeling heterogeneous porous and fractured tuff in a more realistic manner requires numerical methods for generating heterogeneous simulations of the media, scaling of material properties from core scale to computational scale, and flow modeling that allows channeling. The Yucca Mountain test case of the INTRAVAL project is used to test the numerical approaches. Geostatistical methods are used to generate more realistic representations of the stratigraphic units and heterogeneity within units is generated using sampling from property distributions. Scaling problems are reduced using an adaptive grid that minimizes heterogeneity within each flow element. A flow code based on the dual mixed-finite-element method that allows for heterogeneity and channeling is employed. In the Yucca Mountain test case, the simulated volumetric water contents matched the measured values at drill hole USW UZ-16 except in the nonwelded portion of Prow Pass.
Modeling and Simulations of Particulate Flows through Functionalized Porous Media
Li, Chunhui; Dutta, Prashanta; Liu, Jin
2016-11-01
Transport of particulate fluid through a functionalized porous material is of significant interest in many industrial applications, such as earth sciences, battery designs and water/air purifications. The entire process is complex, which involves the convection of fluid, diffusion of reactants as well as reversible chemical reactions at the fluid-solid interface In this work we present a convection-diffusion-reaction model and simulate the transport of particulate fluid through a functionalized porous media. The porous structures are generated and manipulated through the quartet structure generation set method. The Navier-Stokes with convection-diffusion equations are solved using the lattice Boltzmann method. The chemical reactions at the interface are modeled by an absorption-desorption process and treated as the boundary conditions for above governing equations. Through our simulations we study the effects of porous structures, including porosity, pore orientation, and pore size as well as the kinetic rates of surface reactions on the overall performance of removal efficiency of the species from the solution. Our results show that whole process is highly affected by both the porous structures and absorption rate. The optimal parameters can be achieved by proper design. This work is supported by NSF Grants: CBET-1250107 and CBET -1604211.
Joekar-Niasar, Vahid
2012-02-23
The capillary pressure-saturation (P c-S w) relationship is one of the central constitutive relationships used in two-phase flow simulations. There are two major concerns regarding this relation. These concerns are partially studied in a hypothetical porous medium using a dynamic pore-network model called DYPOSIT, which has been employed and extended for this study: (a) P c-S w relationship is measured empirically under equilibrium conditions. It is then used in Darcy-based simulations for all dynamic conditions. This is only valid if there is a guarantee that this relationship is unique for a given flow process (drainage or imbibition) independent of dynamic conditions; (b) It is also known that P c-S w relationship is flow process dependent. Depending on drainage and imbibition, different curves can be achieved, which are referred to as "hysteresis". A thermodynamically derived theory (Hassanizadeh and Gray, Water Resour Res 29: 3389-3904, 1993a) suggests that, by introducing a new state variable, called the specific interfacial area (a nw, defined as the ratio of fluid-fluid interfacial area to the total volume of the domain), it is possible to define a unique relation between capillary pressure, saturation, and interfacial area. This study investigates these two aspects of capillary pressure-saturation relationship using a dynamic pore-network model. The simulation results imply that P c-S w relation not only depends on flow process (drainage and imbibition) but also on dynamic conditions for a given flow process. Moreover, this study attempts to obtain the first preliminary insights into the global functionality of capillary pressure-saturation-interfacial area relationship under equilibrium and non-equilibrium conditions and the uniqueness of P c-S w-a nw relationship. © 2012 The Author(s).
Phase field modeling of partially saturated deformable porous media
Sciarra, Giulio
2016-09-01
A poromechanical model of partially saturated deformable porous media is proposed based on a phase field approach at modeling the behavior of the mixture of liquid water and wet air, which saturates the pore space, the phase field being the saturation (ratio). While the standard retention curve is expected still^ to provide the intrinsic retention properties of the porous skeleton, depending on the porous texture, an enhanced description of surface tension between the wetting (liquid water) and the non-wetting (wet air) fluid, occupying the pore space, is stated considering a regularization of the phase field model based on an additional contribution to the overall free energy depending on the saturation gradient. The aim is to provide a more refined description of surface tension interactions. An enhanced constitutive relation for the capillary pressure is established together with a suitable generalization of Darcy's law, in which the gradient of the capillary pressure is replaced by the gradient of the so-called generalized chemical potential, which also accounts for the "force", associated to the local free energy of the phase field model. A micro-scale heuristic interpretation of the novel constitutive law of capillary pressure is proposed, in order to compare the envisaged model with that one endowed with the concept of average interfacial area. The considered poromechanical model is formulated within the framework of strain gradient theory in order to account for possible effects, at laboratory scale, of the micro-scale hydro-mechanical couplings between highly localized flows (fingering) and localized deformations of the skeleton (fracturing).
Fractal and Multifractal Models Applied to Porous Media - Editorial
Given the current high level of interest in the use of fractal geometry to characterize natural porous media, a special issue of the Vadose Zone Journal was organized in order to expose established fractal analysis techniques and cutting-edge new developments to a wider Earth science audience. The ...
Non-Equilibrium Modeling of Arc Plasma Torches
Trelles, J P; Heberlein, J V R
2013-01-01
A two-temperature thermal non-equilibrium model is developed and applied to the three-dimensional and time-dependent simulation of the flow inside a DC arc plasma torch. A detailed comparison of the results of the non-equilibrium model with those of an equilibrium model is presented. The fluid and electromagnetic equations in both models are approximated numerically in a fully-coupled approach by a variational multi-scale finite element method. In contrast to the equilibrium model, the non-equilibrium model did not need a separate reattachment model to produce an arc reattachment process and to limit the magnitude of the total voltage drop and arc length. The non-equilibrium results show large non-equilibrium regions in the plasma - cold-flow interaction region and close to the anode surface. Marked differences in the arc dynamics, especially in the arc reattachment process, and in the magnitudes of the total voltage drop and outlet temperatures and velocities between the models are observed. The non-equilibr...
Non-equilibrium modelling of distillation
Wesselingh, J.A
This is a lecture on the way that we engineers model distillation. How we have done such modelling, how we would like to do it, and how far we have come at this moment. The ideas that I will be bringing forward are not my own. I owe them mostly to R. Krishna, R. Taylor, H. Kooijman and A. Gorak.
Non-equilibrium modelling of distillation
Wesselingh, J.A
1997-01-01
This is a lecture on the way that we engineers model distillation. How we have done such modelling, how we would like to do it, and how far we have come at this moment. The ideas that I will be bringing forward are not my own. I owe them mostly to R. Krishna, R. Taylor, H. Kooijman and A. Gorak. The
Modeling approaches to natural convection in porous media
Su, Yan
2015-01-01
This book provides an overview of the field of flow and heat transfer in porous medium and focuses on presentation of a generalized approach to predict drag and convective heat transfer within porous medium of arbitrary microscopic geometry, including reticulated foams and packed beds. Practical numerical methods to solve natural convection problems in porous media will be presented with illustrative applications for filtrations, thermal storage and solar receivers.
A Fractal Model for the Transverse Thermal Dispersion Conductivity in Porous Media
Institute of Scientific and Technical Information of China (English)
郁伯铭; 李建华
2004-01-01
A quasi-analytical model, i.e. the fractal model, for the transverse thermal dispersion conductivity in porous media is presented based on the fractal characteristics of tortuous flow paths/streamlines in porous media. The fractal dimension of tortuous flow paths, the spatial deviation velocity and the transverse thermal dispersion conductivity are derived. The proposed model is expressed as functions of the fractal dimension of tortuous flow paths/streamlines, Peclet number, porosity and structural parameters. The present results are compared with those from the existing correlation, and good agreement is found between the present model predictions and those from the existing correlation.
Fate and Transport of Graphene Oxide in Granular Porous Media: Experimental Results and Modeling
Gao, Bin
2014-05-01
Although graphene oxide (GO) has been used in many applications to improve human life quality, its environmental fate and behavior are still largely unknown. In this work, a range of laboratory experiments were conducted to explore the aggregation, deposition, and transport mechanisms of GO nano-sheets in porous media under various conditions. Stability experimental data showed that both cation valence and pH showed significant effect on the aggregation of GO sheets. The measured critical coagulation concentrations were in good agreement with the predictions of the extended Schulze-Hardy rule. Sand column experimental results indicated that deposition and transport of GO in porous media were strongly dependent on solution ionic strength. Particularly, GO showed high mobility under low ionic strength conditions in both saturated and unsaturated columns. Increasing ionic strength dramatically increased the retention of GO in porous media, mainly through secondary-minimum deposition. Recovery rates of GO in unsaturated sand columns were lower than that in saturated columns under the same ionic strength conditions, suggesting moisture content also played an important role in the retention of GO in porous media. Findings from the bubble column experiments showed that the GO did not attach to the air-water interface, which is consistent with the XDLVO predictions. Additional retention mechanisms, such as film straining, thus could be responsible to the reduced mobility of GO in unsaturated porous media. The breakthrough curves of GO in saturated and unsaturated columns could be accurately simulated by an advection-dispersion-reaction model.
A Lattice Boltzmann Model for Fluid-Solid Coupling Heat Transfer in Fractal Porous Media
Institute of Scientific and Technical Information of China (English)
CAI Jun; HUAI Xiu-Lan
2009-01-01
We report a lattice Boltzmann model that can be used to simulate fluid-solid coupling heat transfer in fractal porous media.A numerical simulation is conducted to investigate the temperature evolution under different ratios of thermal conductivity of solid matrix of porous media to that of fluid.The accordance of our simulation results with the solutions from the conventional CFD method indicates the feasibility and the reliability for the developed lattice Boltzmann model to reveal the phenomena and rules of fluid-solid coupling heat transfer in complex porous structures.
Adaptive multiresolution modeling of groundwater flow in heterogeneous porous media
Malenica, Luka; Gotovac, Hrvoje; Srzic, Veljko; Andric, Ivo
2016-04-01
Proposed methodology was originally developed by our scientific team in Split who designed multiresolution approach for analyzing flow and transport processes in highly heterogeneous porous media. The main properties of the adaptive Fup multi-resolution approach are: 1) computational capabilities of Fup basis functions with compact support capable to resolve all spatial and temporal scales, 2) multi-resolution presentation of heterogeneity as well as all other input and output variables, 3) accurate, adaptive and efficient strategy and 4) semi-analytical properties which increase our understanding of usually complex flow and transport processes in porous media. The main computational idea behind this approach is to separately find the minimum number of basis functions and resolution levels necessary to describe each flow and transport variable with the desired accuracy on a particular adaptive grid. Therefore, each variable is separately analyzed, and the adaptive and multi-scale nature of the methodology enables not only computational efficiency and accuracy, but it also describes subsurface processes closely related to their understood physical interpretation. The methodology inherently supports a mesh-free procedure, avoiding the classical numerical integration, and yields continuous velocity and flux fields, which is vitally important for flow and transport simulations. In this paper, we will show recent improvements within the proposed methodology. Since "state of the art" multiresolution approach usually uses method of lines and only spatial adaptive procedure, temporal approximation was rarely considered as a multiscale. Therefore, novel adaptive implicit Fup integration scheme is developed, resolving all time scales within each global time step. It means that algorithm uses smaller time steps only in lines where solution changes are intensive. Application of Fup basis functions enables continuous time approximation, simple interpolation calculations across
Forced Convection Heat Transfer in Plate Channels Filled with Packed Beds or Sintered Porous Media
Institute of Scientific and Technical Information of China (English)
姜培学; 李勐; 任泽霈
2002-01-01
In the present work, forced convection heat transfer in plate channels filled with metallic or non-metallic particles (packed beds) or sintered porous media is simulated numerically using a thermal non-equilibrium model. The numerical simulation results are compared with experimental data. The difference between convection heat transfer in packed beds and in sintered porous media and the effects of the boundary condition assumptions are investigated. The results show that the numerical simulation of convection heat transfer of air or water in packed beds using the local thermal non-equilibrium model and the variable porosity model agrees well with the experimental data. The convection heat transfer coefficient in sintered porous media is much higher than that in packed beds. In the numerical simulation of convection heat transfer in sintered porous media, the boundary conditions on the wall should be that the particle temperatures are equal to the fluid temperature.
General slip regime permeability model for gas flow through porous media
Zhou, Bo; Jiang, Peixue; Xu, Ruina; Ouyang, Xiaolong
2016-07-01
A theoretical effective gas permeability model was developed for rarefied gas flow in porous media, which holds over the entire slip regime with the permeability derived as a function of the Knudsen number. This general slip regime model (GSR model) is derived from the pore-scale Navier-Stokes equations subject to the first-order wall slip boundary condition using the volume-averaging method. The local closure problem for the volume-averaged equations is studied analytically and numerically using a periodic sphere array geometry. The GSR model includes a rational fraction function of the Knudsen number which leads to a limit effective permeability as the Knudsen number increases. The mechanism for this behavior is the viscous fluid inner friction caused by converging-diverging flow channels in porous media. A linearization of the GSR model leads to the Klinkenberg equation for slightly rarefied gas flows. Finite element simulations show that the Klinkenberg model overestimates the effective permeability by as much as 33% when a flow approaches the transition regime. The GSR model reduces to the unified permeability model [F. Civan, "Effective correlation of apparent gas permeability in tight porous media," Transp. Porous Media 82, 375 (2010)] for the flow in the slip regime and clarifies the physical significance of the empirical parameter b in the unified model.
Fractal and prefractal geometric models have substantial potential of contributing to the analysis of flow and transport in porous media such as soils and reservoir rocks. In this study, geometric and hydrodynamic parameters of saturated 3D mass and pore-solid prefractal porous media were characteri...
A non-equilibrium model for soil heating and moisture transport during extreme surface heating
Directory of Open Access Journals (Sweden)
W. J. Massman
2015-03-01
Full Text Available With increasing use of prescribed fire by land managers and increasing likelihood of wildfires due to climate change comes the need to improve modeling capability of extreme heating of soils during fires. This issue is addressed here by developing a one-dimensional non-equilibrium model of soil evaporation and transport of heat, soil moisture, and water vapor, for use with surface forcing ranging from daily solar cycles to extreme conditions encountered during fires. The model employs a linearized Crank–Nicolson scheme for the conservation equations of energy and mass and its performance is evaluated against dynamic soil temperature and moisture observations obtained during laboratory experiments on soil samples exposed to surface heat fluxes ranging between 10 000 and 50 000 W m−2. The Hertz–Knudsen equation is the basis for constructing the model's non-equilibrium evaporative source term. The model includes a dynamic residual soil moisture as a function of temperature and soil water potential, which allows the model to capture some of the dynamic aspects of the strongly bound soil moisture that seems to require temperatures well beyond 150 °C to fully evaporate. Furthermore, the model emulates the observed increase in soil moisture ahead of the drying front and the hiatus in the soil temperature rise during the strongly evaporative stage of drying. It also captures the observed rapid evaporation of soil moisture that occurs at relatively low temperatures (50–90 °C. Sensitivity analyses indicate that the model's success results primarily from the use of a temperature and moisture potential dependent condensation coefficient in the evaporative source term. The model's solution for water vapor density (and vapor pressure, which can exceed one standard atmosphere, cannot be experimentally verified, but they are supported by results from (earlier and very different models developed for somewhat different purposes and for different porous
Stochastic porous media equations
Barbu, Viorel; Röckner, Michael
2016-01-01
Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found. The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model". The book will be of interest to PhD students and researchers in mathematics, physics and biology.
Pore-network modeling of solute transport and biofilm growth in porous media
Qin, Chao Zhong; Hassanizadeh, S. Majid
2015-01-01
In this work, a pore-network (PN) model for solute transport and biofilm growth in porous media was developed. Compared to previous studies of biofilm growth, it has two new features. First, the constructed pore network gives a better representation of a porous medium. Second, instead of using a con
Calibrating the Shan-Chen lattice Boltzmann model for immiscible displacement in porous media
DEFF Research Database (Denmark)
Christensen, Britt Stenhøj Baun; Schaap, M.G.; Wildenschild, D.
2006-01-01
The lattice Boltzmann (LB) modeling technique is increasingly being applied in a variety of fields where computational fluid dynamics are investigated. In our field of interest, environmentally related flow processes in porous media, the use of the LB method is still not common. For the LB...
Pore-network modeling of solute transport and biofilm growth in porous media
Qin, Chao Zhong; Hassanizadeh, S. Majid
2015-01-01
In this work, a pore-network (PN) model for solute transport and biofilm growth in porous media was developed. Compared to previous studies of biofilm growth, it has two new features. First, the constructed pore network gives a better representation of a porous medium. Second, instead of using a
Yohan, D.; Gerald, D.; Magali, G.; Michel, Q.
2008-12-01
The general problem of transport and reaction in multiphase porous media has been a subject of extensive studies during the last decades. For example, biologically mediated porous media have seen a long history of research from the environmental engineering point of view. Biofilms (aggregate of microorganisms coated in a polymer matrix generated by bacteria) have been particularly examined within the context of bioremediation in the subsurface zone. Five types of models may be used to describe these kinds of physical system: 1) one-equation local mass equilibrium models when the assumption of local mass equilibrium is valid 2) two equations models when the assumption of local mass equilibrium is not valid 3) one equation non-equilibrium models 4) mixed models coupling equations solved at two different scales 5) one equation time-asymptotic models. In this presentation, we use the method of volume averaging with closure to extend the time- asymptotic model at the Darcy scale to the reactive case. Closure problems are solved for simple unit cells, and the macro-scale model is validated against pore-scale simulations.
Non-equilibrium model for catalytic distillation process
Institute of Scientific and Technical Information of China (English)
Feng WANG; Ning ZHAO; Junping LI; Fukui XIAO; Wei WEI; Yuhan SUN
2008-01-01
A new improved tri-diagonal method was developed for the non-equilibrium stage model of the catalytic distillation by coupling consumptive reaction coefficient. The reactions in the distillation column were divided into generative reaction and consumptive reac-tion. The non-equilibrium stage model was introduced for the catalytic distillation process of the dimethyl car-bonate (DMC) synthesis by urea methanolysis over solid based catalyst, and the improved tri-diagonal method was used to solve the model equations. Comparison of pre-dicted results with experiment data shows that the mean relative error of the yield of DMC was 3.78% under dif-ferent conditions such as different operating pressures and reaction temperatures. The improved tri-diagonal matrix method could avoid the negative values of the liquid com-positions during the calculations and restrain the fluc-tuation of compositions by slowing down the variations of the values in the iteration. The modeling results show that the improved tri-diagonal method was appropriate for system containing a wide range of boiling point com-ponents and a different rate of reactions.
Solute transport through porous media using asymptotic dispersivity
Indian Academy of Sciences (India)
P K Sharma; Teodrose Atnafu Abgaze
2015-08-01
In this paper, multiprocess non-equilibrium transport equation has been used, which accounts for both physical and chemical non-equilibrium for reactive transport through porous media. An asymptotic distance dependent dispersivity is used to embrace the concept of scale-dependent dispersion for solute transport in heterogeneous porous media. Semi-analytical solution has been derived of the governing equations with an asymptotic distance dependent dispersivity by using Laplace transform technique and the power series method. For application of analytical model, we simulated observed experimental breakthrough curves from 1500 cm long soil column experiments conducted in the laboratory. The simulation results of break-through curves were found to deviate from the observed breakthrough curves for both mobile–immobile and multiprocess non-equilibrium transport with constant dispersion models. However, multiprocess non-equilibrium with an asymptotic dispersion model gives better fit of experimental breakthrough curves through long soil column and hence it is more useful for describing anomalous solute transport through hetero-geneous porous media. The present model is simpler than the stochastic numerical method.
Laboratory Models of Thermal Convection in Porous Media
Cooper, C. A.; Breitmeyer, R.; Schumer, R.; Voepel, H.; Decker, D.
2011-12-01
Experiments have been conducted to measure the length and times scales of thermal plumes in laboratory porous media. A polycarbonate cell 1 m high x 75 cm wide x 2.54 cm deep filled with 3 mm glass beads is heated uniformly from the bottom using electrical heat tape. The heat tape is in direct contact with an aluminum alloy heat exchanger sandwiched between the two vertical plates, and a digital controller is used to maintain constant temperature. The upper boundary is kept at constant temperature by circulating cold water from a constant-temperature refrigerating bath through copper tubes in contact with the upper part of the cell. Flow is visualized by mixing a neutrally buoyant thermochromic liquid tracer in the working fluid (water and glycerin). TLCs are liquid crystals manufactured to change color as a function of temperature. Color change is repeatable and reversible with a response time to temperature change is less than 0.01 s. Image acquisition is done using a CCD camera, and three images are captured nearly simultaneously, each with a red, blue, or green filter over the camera lens. The three images are then combined to make a true color image. At each pixel in the image, hue is extracted and a calibration curve is developed to relate hue to temperature. In one experiment with a 10 degree C temperature difference between the upper and lower boundaries, the onset of convection began within 26 minutes, which is about half the time predicted by a scale analysis. The initial velocity of all plumes is on the order of 15 cm/hr, although some plumes stop moving before reaching the upper boundary of the cell. There are several reasons for plume deceleration: (1) As plumes travel vertically, they alter the initial temperature profile of the fluid such that the temperature field makes constant adjustments, which affects the dimensions, velocities, and interactions of the plumes; (2) adjacent plumes merge, resulting in a single larger plume; and (3) interactions
POD-Galerkin Model for Incompressible Single-Phase Flow in Porous Media
Wang, Yi
2017-01-25
Fast prediction modeling via proper orthogonal decomposition method combined with Galerkin projection is applied to incompressible single-phase fluid flow in porous media. Cases for different configurations of porous media, boundary conditions and problem scales are designed to examine the fidelity and robustness of the model. High precision (relative deviation 1.0 x 10(-4)% similar to 2.3 x 10(-1)%) and large acceleration (speed-up 880 similar to 98454 times) of POD model are found in these cases. Moreover, the computational time of POD model is quite insensitive to the complexity of problems. These results indicate POD model is especially suitable for large-scale complex problems in engineering.
A new multiple-relaxation-time lattice Boltzmann model for incompressible flows in porous media
Liu, Qing; He, Chao
2013-01-01
In this paper, a two-dimensional eight-velocity (D2Q8) multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is proposed for incompressible porous flows at the representative elementary volume scale based on the Brinkman-Forchheimer-extended Darcy formulation. In the MRT-LB model, newly defined equilibrium moments are employed to account for the porosity of the porous media, and the linear and nonlinear drag forces of the media are incorporated into the model by adding a forcing term to the MRT-LB equation in the moment space. The model is validated by simulating the 2D Poiseuille flow, Couette flow and lid-driven cavity flow in porous media. The numerical results are in excellent agreement with the analytical solutions and/or the well-documented data available in the literature.
A modified lattice Bhatnagar-Gross-Krook model for convection heat transfer in porous media
Wang, Liang; Guo, Zhaoli
2015-01-01
The lattice Bhatnagar-Gross-Krook (LBGK) model has become the most popular one in the lattice Boltzmann method for simulating the convection heat transfer in porous media. However, the LBGK model generally suffers from numerical instability at low fluid viscosities and effective thermal diffusivities. In this paper, a modified LBGK model is developed for incompressible thermal flows in porous media at the representative elementary volume scale, in which the shear rate and temperature gradient are incorporated into the equilibrium distribution functions. With two additional parameters, the relaxation times in the collision process can be fixed at a proper value invariable to the viscosity and the effective thermal diffusivity. In addition, by constructing a modified equilibrium distribution function and a source term in the evolution equation of temperature field, the present model can recover the macroscopic equations correctly through the Chapman-Enskog analysis, which is another key point different from pre...
Closure conditions for non-equilibrium multi-component models
Müller, S.; Hantke, M.; Richter, P.
2016-07-01
A class of non-equilibrium models for compressible multi-component fluids in multi-dimensions is investigated taking into account viscosity and heat conduction. These models are subject to the choice of interfacial pressures and interfacial velocity as well as relaxation terms for velocity, pressure, temperature and chemical potentials. Sufficient conditions are derived for these quantities that ensure meaningful physical properties such as a non-negative entropy production, thermodynamical stability, Galilean invariance and mathematical properties such as hyperbolicity, subcharacteristic property and existence of an entropy-entropy flux pair. For the relaxation of chemical potentials, a two-component and a three-component models for vapor-water and gas-water-vapor, respectively, are considered.
A Pore-Network Model of In-Situ Combustion in Porous Media
Energy Technology Data Exchange (ETDEWEB)
Lu, Chuan; Yortsos, Y.C.
2001-01-29
This report the use of dual pore networks (pores and solid sites) for modeling the effect of the microstructure on combustion processes in porous media is considered. The model accounts for flow and transport of the gas phase in the porespace, where convection predominates, and for heat transfer by conduction in the solid phase. Gas phase flow in the pore and throats is governed by Darcy's law.
A Twophase Multirate-Mass Transfer Model for Flow and Transport in Porous Media
Dentz, M.; Tecklenburg, J.; Neuweiler, I.; Carrera, J.
2015-12-01
We present an upscaled non-local model for two-phase flow and transport in highly heterogeneous porous media. The media under consideration are characterized by sharp contrasts in the hydraulic properties typical for fractured porous media, for example. A two-scale expansion gives an upscaled flow and transport formulation that models multiratemass transfer between mobile (fracture) and immobile (matrix) medium portions. The evolution of saturation due to viscous dominated flow in the mobile domain and mass exchange with the immobile zones through capillary countercurrent flow. The medium heterogeneity is mapped onto the mass transfer parameters, which are encoded in a memory functionthat describes the non-local flux between mobile and immobile zones. The upscaled model is parameterized by the medium heterogeneity and the distribution of hydraulic parameters. Breakthrough of the displaced fluidshows characteristic heavy tails due to fluid retention in immobile zones.
An advective volume-balance model for flow in porous media
Malaga, Carlos; Mandujano, Francisco; Becerra, Julian
2016-11-01
Volume-balance models are used by petroleum engineers to simulate multiphase and multicomponent flow phenomena in porous media and the extraction process in oil reservoirs. In these models, mass conservation equations and Darcy's law are supplemented by a balance condition for the pore and fluid volumes. This provides a pressure equation suitable for simulating a compressible flow within a compressible solid matrix. Here we present an alternative interpretation of the volume-balance condition that includes the advective transport within a consolidated porous media. We obtain a modified equation for the time evolution of the pressure field. Preliminary numerical tests of phase separation due to gravity suggest the model reproduces qualitatively the physical phenomena. Fondo Sectorial CONACYT-SENER Grant Number 42536 (DGAJ-SPI-34-170412-217).
Lattice Boltzmann model for incompressible axisymmetric thermal flows through porous media.
Grissa, Kods; Chaabane, Raoudha; Lataoui, Zied; Benselama, Adel; Bertin, Yves; Jemni, Abdelmajid
2016-10-01
The present work proposes a simple lattice Boltzmann model for incompressible axisymmetric thermal flows through porous media. By incorporating forces and source terms into the lattice Boltzmann equation, the incompressible Navier-Stokes equations are recovered through the Chapman-Enskog expansion. It is found that the added terms are just the extra terms in the governing equations for the axisymmetric thermal flows through porous media compared with the Navier-Stokes equations. Four numerical simulations are performed to validate this model. Good agreement is obtained between the present work and the analytic solutions and/or the results of previous studies. This proves its efficacy and simplicity regarding other methods. Also, this approach provides guidance for problems with more physical phenomena and complicated force forms.
Determination of a Pore Structure Parameter of Porous Media by Analysis of Percolation Network Model
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
According to the simulation of nitrogen sorption process in porous media with three-dimensional network model, and the analysis for such a process with percolation theory, a new method is proposed to determine a pore structure parameter－mean coordination number of pore network, which represents the connectivity among a great number of pores. Here the “chamber-throat” model and the Weibull distribution are used to describe the pore geometry and the pore size distribution respectively. This method is based on the scaling law of percolation theory after both effects of sorption thermodynamics and pore size on the sorption hysteresis loops are considered. The results show that it is an effective procedure to calculate the mean coordination number for micro- and meso-porous media.
Modeling Inflation Using a Non-Equilibrium Equation of Exchange
Chamberlain, Robert G.
2013-01-01
Inflation is a change in the prices of goods that takes place without changes in the actual values of those goods. The Equation of Exchange, formulated clearly in a seminal paper by Irving Fisher in 1911, establishes an equilibrium relationship between the price index P (also known as "inflation"), the economy's aggregate output Q (also known as "the real gross domestic product"), the amount of money available for spending M (also known as "the money supply"), and the rate at which money is reused V (also known as "the velocity of circulation of money"). This paper offers first a qualitative discussion of what can cause these factors to change and how those causes might be controlled, then develops a quantitative model of inflation based on a non-equilibrium version of the Equation of Exchange. Causal relationships are different from equations in that the effects of changes in the causal variables take time to play out-often significant amounts of time. In the model described here, wages track prices, but only after a distributed lag. Prices change whenever the money supply, aggregate output, or the velocity of circulation of money change, but only after a distributed lag. Similarly, the money supply depends on the supplies of domestic and foreign money, which depend on the monetary base and a variety of foreign transactions, respectively. The spreading of delays mitigates the shocks of sudden changes to important inputs, but the most important aspect of this model is that delays, which often have dramatic consequences in dynamic systems, are explicitly incorporated.macroeconomics, inflation, equation of exchange, non-equilibrium, Athena Project
Basic theories for strain localization analysis of porous media with rate dependent model
Institute of Scientific and Technical Information of China (English)
ZHANG Hongwu; QIN Jianmin
2005-01-01
This paper analyzes the interaction between two kinds of internal length scales when the rate dependent plasticity is introduced to a multiphase material model to study the dynamic strain localization phenomenon of saturated and partially saturated porous media. The stability analysis demonstrates that the enhanced porous media model preserves the well-posedness of the initial value problem for both axial and shear waves because an internal length scale parameter is introduced in the visco-plasticity model. On the other hand, the interaction between the length scale introduced by the rate dependent model and that naturally contained in the governing equations of fully and partially saturated model will take place. A basic method is presented to investigate the internal length scale of the multiphase porous media under the interaction of these two kinds of length scale parameters. Material stability analysis is carried out for a certain permeability from which the results of wave number domain with real wave speed are distinguished. A one dimensional example is given to illustrate the theoretical findings.
Phase-field modeling of fracture in variably saturated porous media
Cajuhi, T.; Sanavia, L.; De Lorenzis, L.
2017-08-01
We propose a mechanical and computational model to describe the coupled problem of poromechanics and cracking in variably saturated porous media. A classical poromechanical formulation is adopted and coupled with a phase-field formulation for the fracture problem. The latter has the advantage of being able to reproduce arbitrarily complex crack paths without introducing discontinuities on a fixed mesh. The obtained simulation results show good qualitative agreement with desiccation experiments on soils from the literature.
N'Doye, Ibrahima
2015-05-25
In this paper, a dynamical fractional viscoelastic fluids convection model in porous media is proposed and its chaotic behavior is studied. A preformed equilibrium points analysis indicates the conditions where chaotic dynamics can be observed, and show the existence of chaos. The behavior and stability analysis of the integer-order and the fractional commensurate and non-commensurate orders of a fractional viscoelastic fluids system, which exhibits chaos, are presented as well.
Study of Gas Flow Characteristics in Tight Porous Media with a Microscale Lattice Boltzmann Model
Zhao, Jianlin; Yao, Jun; Zhang, Min; Zhang, Lei; Yang, Yongfei; Sun, Hai; An, Senyou; Li, Aifen
2016-01-01
To investigate the gas flow characteristics in tight porous media, a microscale lattice Boltzmann (LB) model with the regularization procedure is firstly adopted to simulate gas flow in three-dimensional (3D) digital rocks. A shale digital rock and a sandstone digital rock are reconstructed to study the effects of pressure, temperature and pore size on microscale gas flow. The simulation results show that because of the microscale effect in tight porous media, the apparent permeability is always higher than the intrinsic permeability, and with the decrease of pressure or pore size, or with the increase of temperature, the difference between apparent permeability and intrinsic permeability increases. In addition, the Knudsen numbers under different conditions are calculated and the results show that gas flow characteristics in the digital rocks under different Knudsen numbers are quite different. With the increase of Knudsen number, gas flow in the digital rocks becomes more uniform and the effect of heterogeneity of the porous media on gas flow decreases. Finally, two commonly used apparent permeability calculation models are evaluated by the simulation results and the Klinkenberg model shows better accuracy. In addition, a better proportionality factor in Klinkenberg model is proposed according to the simulation results. PMID:27587293
Study of Gas Flow Characteristics in Tight Porous Media with a Microscale Lattice Boltzmann Model
Zhao, Jianlin; Yao, Jun; Zhang, Min; Zhang, Lei; Yang, Yongfei; Sun, Hai; An, Senyou; Li, Aifen
2016-09-01
To investigate the gas flow characteristics in tight porous media, a microscale lattice Boltzmann (LB) model with the regularization procedure is firstly adopted to simulate gas flow in three-dimensional (3D) digital rocks. A shale digital rock and a sandstone digital rock are reconstructed to study the effects of pressure, temperature and pore size on microscale gas flow. The simulation results show that because of the microscale effect in tight porous media, the apparent permeability is always higher than the intrinsic permeability, and with the decrease of pressure or pore size, or with the increase of temperature, the difference between apparent permeability and intrinsic permeability increases. In addition, the Knudsen numbers under different conditions are calculated and the results show that gas flow characteristics in the digital rocks under different Knudsen numbers are quite different. With the increase of Knudsen number, gas flow in the digital rocks becomes more uniform and the effect of heterogeneity of the porous media on gas flow decreases. Finally, two commonly used apparent permeability calculation models are evaluated by the simulation results and the Klinkenberg model shows better accuracy. In addition, a better proportionality factor in Klinkenberg model is proposed according to the simulation results.
Multiscale modeling of high contrast brinkman equations with applications to deformable porous media
Brown, Donald
2013-06-18
Simulating porous media flows has a wide range of applications. Often, these applications involve many scales and multi-physical processes. A useful tool in the analysis of such problems in that of homogenization as an averaged description is derived circumventing the need for complicated simulation of the fine scale features. In this work, we recall recent developments of homogenization techniques in the application of flows in deformable porous media. In addition, homogenization of media with high-contrast. In particular, we recall the main ideas of the homogenization of slowly varying Stokes flow and summarize the results of [4]. We also present the ideas for extending these techniques to high-contrast deformable media [3]. These ideas are connected by the modeling of multiscale fluid-structure interaction problems. © 2013 American Society of Civil Engineers.
Thermal conductivity of granular porous media: A pore scale modeling approach
Directory of Open Access Journals (Sweden)
R. Askari
2015-09-01
Full Text Available Pore scale modeling method has been widely used in the petrophysical studies to estimate macroscopic properties (e.g. porosity, permeability, and electrical resistivity of porous media with respect to their micro structures. Although there is a sumptuous literature about the application of the method to study flow in porous media, there are fewer studies regarding its application to thermal conduction characterization, and the estimation of effective thermal conductivity, which is a salient parameter in many engineering surveys (e.g. geothermal resources and heavy oil recovery. By considering thermal contact resistance, we demonstrate the robustness of the method for predicting the effective thermal conductivity. According to our results obtained from Utah oil sand samples simulations, the simulation of thermal contact resistance is pivotal to grant reliable estimates of effective thermal conductivity. Our estimated effective thermal conductivities exhibit a better compatibility with the experimental data in companion with some famous experimental and analytical equations for the calculation of the effective thermal conductivity. In addition, we reconstruct a porous medium for an Alberta oil sand sample. By increasing roughness, we observe the effect of thermal contact resistance in the decrease of the effective thermal conductivity. However, the roughness effect becomes more noticeable when there is a higher thermal conductivity of solid to fluid ratio. Moreover, by considering the thermal resistance in porous media with different grains sizes, we find that the effective thermal conductivity augments with increased grain size. Our observation is in a reasonable accordance with experimental results. This demonstrates the usefulness of our modeling approach for further computational studies of heat transfer in porous media.
Discrete Particle Model for Porous Media Flow using OpenFOAM at Intel Xeon Phi Coprocessors
Shang, Zhi; Nandakumar, Krishnaswamy; Liu, Honggao; Tyagi, Mayank; Lupo, James A.; Thompson, Karten
2015-11-01
The discrete particle model (DPM) in OpenFOAM was used to study the turbulent solid particle suspension flows through the porous media of a natural dual-permeability rock. The 2D and 3D pore geometries of the porous media were generated by sphere packing with the radius ratio of 3. The porosity is about 38% same as the natural dual-permeability rock. In the 2D case, the mesh cells reach 5 million with 1 million solid particles and in the 3D case, the mesh cells are above 10 million with 5 million solid particles. The solid particles are distributed by Gaussian distribution from 20 μm to 180 μm with expectation as 100 μm. Through the numerical simulations, not only was the HPC studied using Intel Xeon Phi Coprocessors but also the flow behaviors of large scale solid suspension flows in porous media were studied. The authors would like to thank the support by IPCC@LSU-Intel Parallel Computing Center (LSU # Y1SY1-1) and the HPC resources at Louisiana State University (http://www.hpc.lsu.edu).
A Geometry Model for Tortuosity of Flow Path in Porous Media
Institute of Scientific and Technical Information of China (English)
YU Bo-Ming; LI Jian-Hua
2004-01-01
@@ A simple geometry model for tortuosity of flow path in porous media is proposed based on the assumption that some particles in a porous medium are unrestrictedly overlapped and the others are not. The proposed model is expressed as a function of porosity and there is no empirical constant in this model. The model predictions are compared with those from available correlations obtained numerically and experimentally, both of which are in agreement with each other. The present model can also give the tortuosity with a good approximation near the percolation threshold. The validity of the present tortuosity model is thus verified.
Porous Media and Immersed Boundary Hybrid-Modelling for Simulating Flow in Stone Cover-Layers
DEFF Research Database (Denmark)
Jensen, Bjarne; Liu, Xiaofeng; Christensen, Erik Damgaard
2017-01-01
In this paper we present a new numerical modelling approach for coastal and marine applications where a porous media conceptual model was combined with a free surface volume-of-fluid (VOF) model and an immersed boundary method (IBM). The immersed boundary model covers the method of describing a s....... In this paper, the model is applied to investigate two practical cases in terms of a cover layer of stones on a flat bed under oscillatory flow at different packing densities, and a rock toe structure at a breakwater....
Pore-scale modeling of competitive adsorption in porous media.
Ryan, Emily M; Tartakovsky, Alexandre M; Amon, Cristina
2011-03-01
In this paper we present a smoothed particle hydrodynamics (SPH) pore-scale multicomponent reactive transport model with competitive adsorption. SPH is a Lagrangian, particle based modeling method which uses the particles as interpolation points to discretize and solve flow and transport equations. The theory and details of the SPH pore-scale model are presented along with a novel method for handling surface reactions, the continuum surface reaction (CSR) model. The numerical accuracy of the CSR model is validated with analytical and finite difference solutions, and the effects of spatial and temporal resolution on the accuracy of the model are also discussed. The pore-scale model is used to study competitive adsorption for different Damköhler and Peclet numbers in a binary system where a plume of species B is introduced into a system which initially contains species A. The pore-scale model results are compared with a Darcy-scale model to investigate the accuracy of a Darcy-scale reactive transport model for a wide range of Damköhler and Peclet numbers. The comparison shows that the Darcy model over estimates the mass fraction of aqueous and adsorbed species B and underestimates the mass fractions of species A. The Darcy-scale model also predicts faster transport of species A and B through the system than the pore-scale model. The overestimation of the advective velocity and the extent of reactions by the Darcy-scale model are due to incomplete pore-scale mixing. As the degree of the solute mixing decreases with increasing Peclet and Damköhler numbers, so does the accuracy of the Darcy-scale model. Copyright © 2010 Elsevier B.V. All rights reserved.
Multiphase flow in porous media using CFD
DEFF Research Database (Denmark)
Hemmingsen, Casper Schytte; Walther, Jens Honore
We present results from a new Navier-Stokes model for multiphase flow in porous media implemented in Ansys Fluent 16.2 [1]. The model includes the Darcy-Forchheimer source terms in the momentum equations and proper account for relative permeability and capillary pressure in the porous media...... to model both the non-porous and porous media using the same formulation....
Modeling of biological clogging in unsaturated porous media
Soleimani, Sahar; Van Geel, Paul J.; Isgor, O. Burkan; Mostafa, Mohamed B.
2009-04-01
A two-dimensional unsaturated flow and transport model, which includes microbial growth and decay, has been developed to simulate biological clogging in unsaturated soils, specifically biofilters. The bacterial growth and rate of solute reduction due to biodegradation is estimated using the Monod equation. The effect of microbial growth is considered in the proposed conceptual model that relates the relative permeability term for unsaturated flow to the microbial growth. Two applications of the model are presented in this study. Using the model, the clogging mechanism in different soils has been simulated. The results of the model indicate that the time to reach a clogged state is influenced by the hydraulic properties of the soil. Clogging is delayed in soils with higher saturated hydraulic conductivities, and higher porosities. For the relative permeability model proposed, higher van Genuchten n values lead to a delay in clogging. The model was also used to simulate the progressive clogging of a septic bed as the biomat initially forms at the up-gradient end of the distribution pipe, displacing wastewater infiltration and biomat formation further down-gradient over time.
Three-dimensional bioremediation modeling in heterogeneous porous media
Energy Technology Data Exchange (ETDEWEB)
Wheeler, M.F. [Rice Univ., Houston, TX (United States). Dept. of Mathematical Sciences; Roberson, K.R. [Pacific Northwest Lab., Richland, WA (United States); Chilakapati, A. [Rice Univ., Houston, TX (United States). Dept. of Chemical Engineering
1992-06-01
Recently Price University and Pacific Northwest Laboratory (PNL) have begun a collaborative research effort that involves laboratory, field, and simulation work directed toward validating remediation strategies, including both natural and in situ bioremediation at US Department of Energy (DOE) sites such as Hanford. Because of chemical, biological, geologic and physical complexities of modeling these DOE sites, one of the major simulation goals of the project is to formulate and implement accurate and efficient (parallel) algorithms for modeling multiphase/multicomponent mow and reactive transport. In this paper we first describe the physical problem that needs to be modeled. Because of the emergence of concurrent supercomputing, we propose accurate numerical algorithms that are based on operator-splitting in time and domain decomposition iterative techniques. In particular reference is made to the biodegradation of carbon tetrachloride.
Biophysical Interactions in Porous Media: an Integrated Experimental and Modelling Approach
Otten, W.; Baveye, P.; Falconer, R.
2012-12-01
A critical feature of porous media is that the geometry provides habitats of a complexity that is not seen above ground, offering shelter, food water and gasses to microorganisms, who's spatial and temporal dynamics are shaped by this microscopic heterogeneity. The microbial dynamics, including fungal and bacterial growth, in turn affect the geometry and the hydrological properties, shaping the pore architecture at short and long time scales, altering surface tension, and (partially) blocking pores, thereby affecting the flow paths of water through a structure. Crucially, the majority of these processes occur at microscopic scales with impact on larger scale ecological processes and ecosystem services. The complexity of these interacting processes and feed-back mechanisms at first may seem overwhelming. However, we show in this paper how with recent progress in experimental techniques, integrated with a modelling approach we can begin to understand the importance of microscopic heterogeneity on microbial dynamics. We will demonstrate this integrated approach for fungal dynamics in porous media such as soil through a combination of novel experimental tools and mathematical modelling. Using benchtop X-ray CT systems we present the finer detail of pore structure at scales relevant for microbial processes, and present our recent advances in the use of theoretical tools to rigorously characterise, and quantitatively describe this environment, and present the state-of-the art with respect to visualization of water in porous media. Severe challenges remain with studying the spatial distribution of microorganisms. We present how biological thin sectioning techniques offer a way forward to study the spatial distribution of fungi and bacteria within pore geometries. Through a series of detailed experiments we show how pathways, resulting from connected pore volumes and distribution of water within them, are preferentially explored during fungal invasion. We complement the
Modelling bioaugmentation in unsaturated porous media: The linuron herbicide example
DEFF Research Database (Denmark)
Owsianiak, Mikolaj; Dechesne, Arnaud; Binning, Philip John
2010-01-01
at various water saturation levels. A bacterium mineralizing linuron is heterogeneously distributed within a 3-D model domain in spherical hotspots of 2-mm diameter size. Diffusion and advection due to infiltration are the transport processes, and microbial growth follows first order kinetics. Without...... advection, a bead spacing distance of 5 mm at saturated conditions is required to achieve a bioremediation goal of 90% linuron mineralization in 1 year. The gas phase is an important parameter affecting the transport of linuron, however, linuron biodegradation is growth kinetics limited within a broad water...... saturation range. It is hypothesized that the selection of faster degraders can compensate for high amounts of required beads....
Institute of Scientific and Technical Information of China (English)
CAI; Ruixian(蔡睿贤); ZHANG; Na(张娜)
2002-01-01
Some algebraically explicit analytical solutions are derived for the anisotropic Brinkman model an improved Darcy model describing the natural convection in porous media. Besides their important theoretical meaning (for example, to analyze the non-Darcy and anisotropic effects on the convection), such analytical solutions can be the benchmark solutions to promoting the develop ment of computational heat and mass transfer. For instance, we can use them to check the accuracy,convergence and effectiveness of various numerical computational methods and to improve numerical calculation skills such as differential schemes and grid generation ways.
Physical modelling of elastic anisotropy in porous media
Energy Technology Data Exchange (ETDEWEB)
Furre, Anne-Kari
1997-12-31
During the last decades, anisotropy has become increasingly interesting in hydrocarbon prospecting. Knowledge of anisotropy in the subsurface can improve reservoir production and data interpretation. This thesis presents experimental studies of three different artificial anisotropic media: layered materials, isotropic matrix with stress-induced fractures, and layered media with controlled crack patterns at an oblique angle relative to layering. Layered media were constructed by varying grain size distributions for different layers, which resulted in acoustic and permeability anisotropy. The thin layer materials could be described by Backus modelling provided the wavelength was much larger than the layer periods. Frequency dependent scattering was observed for waves travelling normal to the layers. Saturated wave velocities were consistent with transverse isotropic Biot theory, but because the permeability anisotropy was small, no flow dependent attenuation anisotropy was observed. When sandstones were cemented under stress and then released, to simulate a vertical core or uplift process, predominantly horizontal cracks developed in the samples. On reloading to the cementing stress level, the velocities were below the initial values, which supports the theories of crack growth. In further triaxial tests on the same material a stress-dependent anisotropy occurred similar to what is often seen in natural samples taken from large depths. 70 refs., 200 figs., 56 tabs.
Modeling the co-transport of viruses and colloids in unsaturated porous media.
Seetha, N; Mohan Kumar, M S; Majid Hassanizadeh, S
2015-10-01
A mathematical model is developed to simulate the co-transport of viruses and colloids in unsaturated porous media under steady-state flow conditions. The virus attachment to the mobile and immobile colloids is described using a linear reversible kinetic model. Colloid transport is assumed to be decoupled from virus transport; that is, we assume that colloids are not affected by the presence of attached viruses on their surface. The governing equations are solved numerically using an alternating three-step operator splitting approach. The model is verified by fitting three sets of experimental data published in the literature: (1) Syngouna and Chrysikopoulos (2013) and (2) Walshe et al. (2010), both on the co-transport of viruses and clay colloids under saturated conditions, and (3) Syngouna and Chrysikopoulos (2015) for the co-transport of viruses and clay colloids under unsaturated conditions. We found a good agreement between observed and fitted breakthrough curves (BTCs) under both saturated and unsaturated conditions. Then, the developed model was used to simulate the co-transport of viruses and colloids in porous media under unsaturated conditions, with the aim of understanding the relative importance of various processes on the co-transport of viruses and colloids in unsaturated porous media. The virus retention in porous media in the presence of colloids is greater during unsaturated conditions as compared to the saturated conditions due to: (1) virus attachment to the air-water interface (AWI), and (2) co-deposition of colloids with attached viruses on its surface to the AWI. A sensitivity analysis of the model to various parameters showed that the virus attachment to AWI is the most sensitive parameter affecting the BTCs of both free viruses and total mobile viruses and has a significant effect on all parts of the BTC. The free and the total mobile viruses BTCs are mainly influenced by parameters describing virus attachment to the AWI, virus interaction
Nakshatrala, K B; Ballarini, R
2016-01-01
Geo-materials such as vuggy carbonates are known to exhibit multiple spatial scales. A common manifestation of spatial scales is the presence of (at least) two different scales of pores, which is commonly referred to as double porosity. To complicate things, the pore-network at each scale exhibits different permeability, and these networks are connected through fissure and conduits. Although some models are available in the literature, they lack a strong theoretical basis. This paper aims to fill this lacuna by providing the much needed theoretical foundations of the flow in porous media which exhibit double porosity/permeability. We first obtain a mathematical model for double porosity/permeability using the maximization of rate of dissipation hypothesis, and thereby providing a firm thermodynamic underpinning. We then present, along with mathematical proofs, several important mathematical properties that the solutions to the double porosity/permeability model satisfy. These properties are important in their...
Numerical simulation on ferrofluid flow in fractured porous media based on discrete-fracture model
Huang, Tao; Yao, Jun; Huang, Zhaoqin; Yin, Xiaolong; Xie, Haojun; Zhang, Jianguang
2017-06-01
Water flooding is an efficient approach to maintain reservoir pressure and has been widely used to enhance oil recovery. However, preferential water pathways such as fractures can significantly decrease the sweep efficiency. Therefore, the utilization ratio of injected water is seriously affected. How to develop new flooding technology to further improve the oil recovery in this situation is a pressing problem. For the past few years, controllable ferrofluid has caused the extensive concern in oil industry as a new functional material. In the presence of a gradient in the magnetic field strength, a magnetic body force is produced on the ferrofluid so that the attractive magnetic forces allow the ferrofluid to be manipulated to flow in any desired direction through the control of the external magnetic field. In view of these properties, the potential application of using the ferrofluid as a new kind of displacing fluid for flooding in fractured porous media is been studied in this paper for the first time. Considering the physical process of the mobilization of ferrofluid through porous media by arrangement of strong external magnetic fields, the magnetic body force was introduced into the Darcy equation and deals with fractures based on the discrete-fracture model. The fully implicit finite volume method is used to solve mathematical model and the validity and accuracy of numerical simulation, which is demonstrated through an experiment with ferrofluid flowing in a single fractured oil-saturated sand in a 2-D horizontal cell. At last, the water flooding and ferrofluid flooding in a complex fractured porous media have been studied. The results showed that the ferrofluid can be manipulated to flow in desired direction through control of the external magnetic field, so that using ferrofluid for flooding can raise the scope of the whole displacement. As a consequence, the oil recovery has been greatly improved in comparison to water flooding. Thus, the ferrofluid
Modelling multiphase flow inside the porous media of a polymer electrolyte membrane fuel cell
DEFF Research Database (Denmark)
Berning, Torsten; Kær, Søren Knudsen
2011-01-01
Transport processes inside polymer electrolyte membrane fuel cells (PEMFC’s) are highly complex and involve convective and diffusive multiphase, multispecies flow through porous media along with heat and mass transfer and electrochemical reactions in conjunction with water transport through...... an electrolyte membrane. We will present a computational model of a PEMFC with focus on capillary transport of water through the porous layers and phase change and discuss the impact of the liquid phase boundary condition between the porous gas diffusion layer and the flow channels, where water droplets can...
Multiphase porous media modelling: A novel approach to predicting food processing performance.
Khan, Md Imran H; Joardder, M U H; Kumar, Chandan; Karim, M A
2016-07-20
The development of a physics-based model of food processing is essential to improve the quality of processed food and optimize energy consumption. Food materials, particularly plant-based food materials, are complex in nature as they are porous and have hygroscopic properties. A multiphase porous media model for simultaneous heat and mass transfer can provide a realistic understanding of transport processes and thus can help to optimize energy consumption and improve food quality. Although the development of a multiphase porous media model for food processing is a challenging task because of its complexity, many researchers have attempted it. The primary aim of this paper is to present a comprehensive review of the multiphase models available in the literature for different methods of food processing, such as drying, frying, cooking, baking, heating, and roasting. A critical review of the parameters that should be considered for multiphase modelling is presented which includes input parameters, material properties, simulation techniques and the hypotheses. A discussion on the general trends in outcomes, such as moisture saturation, temperature profile, pressure variation, and evaporation patterns, is also presented. The paper concludes by considering key issues in the existing multiphase models and future directions for development of multiphase models.
Liu, Jianjun; Song, Rui; Cui, Mengmeng
2014-01-01
A novel approach of simulating hydromechanical coupling in pore-scale models of porous media is presented in this paper. Parameters of the sandstone samples, such as the stress-strain curve, Poisson's ratio, and permeability under different pore pressure and confining pressure, are tested in laboratory scale. The micro-CT scanner is employed to scan the samples for three-dimensional images, as input to construct the model. Accordingly, four physical models possessing the same pore and rock matrix characteristics as the natural sandstones are developed. Based on the micro-CT images, the three-dimensional finite element models of both rock matrix and pore space are established by MIMICS and ICEM software platform. Navier-Stokes equation and elastic constitutive equation are used as the mathematical model for simulation. A hydromechanical coupling analysis in pore-scale finite element model of porous media is simulated by ANSYS and CFX software. Hereby, permeability of sandstone samples under different pore pressure and confining pressure has been predicted. The simulation results agree well with the benchmark data. Through reproducing its stress state underground, the prediction accuracy of the porous rock permeability in pore-scale simulation is promoted. Consequently, the effects of pore pressure and confining pressure on permeability are revealed from the microscopic view. PMID:24955384
Wang, Shifang; Wu, Tao; Deng, Yongju; Zheng, Qiusha; Zheng, Qian
2016-08-01
Gas diffusion in dry porous media has been a hot topic in several areas of technology for many years. In this paper, a diffusivity model for gas diffusion in dry porous media is developed based on fractal theory and Fick’s law, which incorporates the effects of converging-diverging pores and tortuous characteristics of capillaries as well as Knudsen diffusion. The effective gas diffusivity model is expressed as a function of the fluctuation amplitude of the capillary cross-section size variations, the porosity, the pore area fractal dimension and the tortuosity fractal dimension. The results show that the relative diffusivity decreases with the increase of the fluctuation amplitude and increases with the increase of pore area fractal dimension. To verify the validity of the present model, the relative diffusivity from the proposed fractal model is compared with the existing experimental data as well as two available models of Bruggeman and Shou. Our proposed diffusivity model with pore converging-diverging effect included is in good agreement with reported experimental data.
Distribution of biofilm thickness in porous media and implications for permeability models
Ye, Shujun; Zhang, Yanhong; Sleep, Brent E.
2015-12-01
The distribution of biofilm thickness on individual sand grains in a two-dimensional sand-filled cell maintained under anaerobic conditions was investigated. The cell was inoculated with a mixed microbial culture fed with methanol. Concentrations of biomass attached to the sand and suspended in the water in the cell were determined by protein analysis. The biofilm thickness on individual sand grains was investigated with confocal laser scanning microscopy (CLSM), and was found to follow a normal distribution with a mean range of 59-316 μ and standard deviations of 30-77 μ. The bulk average permeability reduction factor is 8. To investigate the implications of the variability of biofilm thicknesses, four models were used to calculate reductions in porous media permeability. Taylor's model predicted a reduction by a factor ranging from 14 to 5,000 (from minimum to maximum mean biofilm thickness). Vandevivere's model predicted a reduction in permeability by a factor ranging from 769 to 3,846 (from minimum to maximum mean biofilm thickness). Seki's model did not give physically meaningful results in this study. Clement's model predicted reduction by a factor ranging from 1 to 1.14 over the range of biomass levels observed in the cell. Data on the statistical and normal distributions of biofilm thickness in porous media, and assessment of their implications with respect to different permeability models, could lead to better understanding of the extent of bioclogging associated with field implementation of bioremediation of contaminants in aquifers.
Parallel 3-d simulations for porous media models in soil mechanics
Wieners, C.; Ammann, M.; Diebels, S.; Ehlers, W.
Numerical simulations in 3-d for porous media models in soil mechanics are a difficult task for the engineering modelling as well as for the numerical realization. Here, we present a general numerical scheme for the simulation of two-phase models in combination with an material model via the stress response with a specialized parallel saddle point solver. Therefore, we give a brief introduction into the theoretical background of the Theory of Porous Media and constitute a two-phase model consisting of a porous solid skeleton saturated by a viscous pore-fluid. The material behaviour of the skeleton is assumed to be elasto-viscoplastic. The governing equations are transfered to a weak formulation suitable for the application of the finite element method. Introducing an formulation in terms of the stress response, we define a clear interface between the assembling process and the parallel solver modules. We demonstrate the efficiency of this approach by challenging numerical experiments realized on the Linux Cluster in Chemnitz.
Liu, Qing; He, Ya-Ling
2015-11-01
In this paper, a double multiple-relaxation-time lattice Boltzmann model is developed for simulating transient solid-liquid phase change problems in porous media at the representative elementary volume scale. The model uses two different multiple-relaxation-time lattice Boltzmann equations, one for the flow field and the other for the temperature field with nonlinear latent heat source term. The model is based on the generalized non-Darcy formulation, and the solid-liquid interface is traced through the liquid fraction which is determined by the enthalpy-based method. The present model is validated by numerical simulations of conduction melting in a semi-infinite space, solidification in a semi-infinite corner, and convection melting in a square cavity filled with porous media. The numerical results demonstrate the efficiency and accuracy of the present model for simulating transient solid-liquid phase change problems in porous media.
Liu, Qing
2015-01-01
In this paper, a double multiple-relaxation-time lattice Boltzmann model is developed for simulating transient solid-liquid phase change problems in porous media at the representative elementary volume scale. The model uses two different multiple-relaxation-time lattice Boltzmann equations, one for the flow field and the other for the temperature field with nonlinear latent heat source term. The model is based on the generalized non-Darcy formulation, and the solid-liquid phase change interface is traced through the liquid fraction which is determined by the enthalpy method. The model is validated by numerical simulations of conduction melting in a semi-infinite space, solidification in a semi-infinite corner, and convection melting in a square cavity filled with porous media. The numerical results demonstrate the efficiency and accuracy of the present model for simulating transient solid-liquid phase change problems in porous media.
A Two-Scale Reduced Model for Darcy Flow in Fractured Porous Media
Chen, Huangxin
2016-06-01
In this paper, we develop a two-scale reduced model for simulating the Darcy flow in two-dimensional porous media with conductive fractures. We apply the approach motivated by the embedded fracture model (EFM) to simulate the flow on the coarse scale, and the effect of fractures on each coarse scale grid cell intersecting with fractures is represented by the discrete fracture model (DFM) on the fine scale. In the DFM used on the fine scale, the matrix-fracture system are resolved on unstructured grid which represents the fractures accurately, while in the EFM used on the coarse scale, the flux interaction between fractures and matrix are dealt with as a source term, and the matrix-fracture system can be resolved on structured grid. The Raviart-Thomas mixed finite element methods are used for the solution of the coupled flows in the matrix and the fractures on both fine and coarse scales. Numerical results are presented to demonstrate the efficiency of the proposed model for simulation of flow in fractured porous media.
Seeking New Model Geometry to Predict the Fate and Transport of Colloids in Porous Media
Ma, H.; Johnson, W. P.
2008-12-01
Classic colloidal filtration theory (CFT) employed particle tracking approaches in Happel sphere-in-cell model to predict transport and deposition rates of colloids in clean bed porous media. It works well when an energy barrier to deposition is absent, but fails when repulsion exists between the colloid and the collecting surface. Past efforts in modifying CFT, e.g. including a sticking coefficient to account for effect of colloid-collector repulsion on deposition, have not yielded consistently successful predictions. Recent advances in understanding colloidal retention in porous media in the presence of an energy barrier demonstrated two important deposition mechanisms: 1) wedging/straining at grain-to-grain contacts; and 2) retention at secondary energy minima with sufficiently low flow (e.g. flow stagnation zones). These mechanisms are not considered in CFT, partly because the sphere-in-cell model on which CFT is based lacks the necessary pore geometry feature (e.g. grain-to-grain contacts). Here we explore new model geometries that utilize the fluid envelope feature from CFT, but also incorporate grain-to-grain contacts. This presentation describes the testing of these new model geometries in predicting colloidal deposition in the absence of an energy barrier, and then extends to conditions when repulsive energy barriers to deposition are present.
A generalized lattice Boltzmann model for flow through tight porous media with Klinkenberg's effect
Chen, Li; Kang, Qinjun; Hyman, Jeffrey De'Haven; Viswanathan, Hari S; Tao, Wen-Quan
2014-01-01
Gas slippage occurs when the mean free path of the gas molecules is in the order of the characteristic pore size of a porous medium. This phenomenon leads to the Klinkenberg's effect where the measured permeability of a gas (apparent permeability) is higher than that of the liquid (intrinsic permeability). A generalized lattice Boltzmann model is proposed for flow through porous media that includes Klinkenberg's effect, which is based on the model of Guo et al. (Z.L. Guo et al., Phys.Rev.E 65, 046308 (2002)). The second-order Beskok and Karniadakis-Civan's correlation (A. Beskok and G. Karniadakis, Microscale Thermophysical Engineering 3, 43-47 (1999), F. Civan, Transp Porous Med 82, 375-384 (2010)) is adopted to calculate the apparent permeability based on intrinsic permeability and Knudsen number. Fluid flow between two parallel plates filled with porous media is simulated to validate model. Simulations performed in a heterogeneous porous medium with components of different porosity and permeability indicat...
Analysis of 2D flow and heat transfer modeling in fracture of porous media
Guo, Chunsheng; Nian, Xianbo; Liu, Yong; Qi, Chao; Song, Jinsheng; Yu, Wenhe
2017-08-01
Heat and mass transfer between porous media and fluid is a complex coupling process, which is widely used in various fields of engineering applications, especially for natural and artificial fractures in oil and gas extraction. In this study, a new method is proposed to deal with the flow and heat transfer problem of steady flow in a fracture. The fluid flow in a fracture was described using the same method as Mohais, who considered a fracture as a channel with porous wall, and the perturbation method was used to solve the mathematical model. Unlike previous studies, the shear jump boundary condition proposed by Ochoa-Tapia and Whitaker was used at the interface between the fluid and porous media. The main methods were perturbation analysis and the application of shear jump boundary conditions. The influence of permeability, channel width, shear jump degree and effective dynamic viscosity on the flow and heat transfer in the channel was studied by analysing the analytical solution. The distribution of axial velocity in the channel with the change of the typical parameters and the sensitivity of the heat transfer was obtained.
Modeling the effectiveness of U(VI) biomineralization in dual-porosity porous media
Rotter, B. E.; Barry, D. A.; Gerhard, J. I.; Small, J. S.
2011-05-01
SummaryUranium contamination is a serious environmental concern worldwide. Recent attention has focused on the in situ immobilization of uranium by stimulation of dissimilatory metal-reducing bacteria (DMRB). The objective of this work was to investigate the effectiveness of this approach in heterogeneous and structured porous media, since such media may significantly affect the geochemical and microbial processes taking place in contaminated sites, impacting remediation efficiency during biostimulation. A biogeochemical reactive transport model was developed for uranium remediation by immobile-region-resident DMRB in two-region porous media. Simulations were used to investigate the parameter sensitivities of the system over wide-ranging geochemical, microbial and groundwater transport conditions. The results suggest that optimal biomineralization is generally likely to occur when the regional mass transfer timescale is less than one-thirtieth the value of the volumetric flux timescale, and/or the organic carbon fermentation timescale is less than one-thirtieth the value of the advective timescale, and/or the mobile region porosity ranges between equal to and four times the immobile region porosity. Simulations including U(VI) surface complexation to Fe oxides additionally suggest that, while systems exhibiting U(VI) surface complexation may be successfully remediated, they are likely to display different degrees of remediation efficiency over varying microbial efficiency, mobile-immobile mass transfer, and porosity ratios. Such information may aid experimental and field designs, allowing for optimized remediation in dual-porosity (two-region) biostimulated DMRB U(VI) remediation schemes.
Global-local nonlinear model reduction for flows in heterogeneous porous media
AlOtaibi, Manal
2015-08-01
In this paper, we combine discrete empirical interpolation techniques, global mode decomposition methods, and local multiscale methods, such as the Generalized Multiscale Finite Element Method (GMsFEM), to reduce the computational complexity associated with nonlinear flows in highly-heterogeneous porous media. To solve the nonlinear governing equations, we employ the GMsFEM to represent the solution on a coarse grid with multiscale basis functions and apply proper orthogonal decomposition on a coarse grid. Computing the GMsFEM solution involves calculating the residual and the Jacobian on a fine grid. As such, we use local and global empirical interpolation concepts to circumvent performing these computations on the fine grid. The resulting reduced-order approach significantly reduces the flow problem size while accurately capturing the behavior of fully-resolved solutions. We consider several numerical examples of nonlinear multiscale partial differential equations that are numerically integrated using fully-implicit time marching schemes to demonstrate the capability of the proposed model reduction approach to speed up simulations of nonlinear flows in high-contrast porous media.
Pore network modeling of drainage process in patterned porous media: a quasi-static study
Zhang, Tao
2015-04-17
This work represents a preliminary investigation on the role of wettability conditions on the flow of a two-phase system in porous media. Since such effects have been lumped implicitly in relative permeability-saturation and capillary pressure-saturation relationships, it is quite challenging to isolate its effects explicitly in real porous media applications. However, within the framework of pore network models, it is easy to highlight the effects of wettability conditions on the transport of two-phase systems. We employ quasi-static investigation in which the system undergo slow movement based on slight increment of the imposed pressure. Several numerical experiments of the drainage process are conducted to displace a wetting fluid with a non-wetting one. In all these experiments the network is assigned different scenarios of various wettability patterns. The aim is to show that the drainage process is very much affected by the imposed pattern of wettability. The wettability conditions are imposed by assigning the value of contact angle to each pore throat according to predefined patterns.
Energy Technology Data Exchange (ETDEWEB)
Cliffe, K.A.; Morris, S.T.; Porter, J.D. [AEA Technology, Harwell (United Kingdom)
1998-05-01
NAMMU is a computer program for modelling groundwater flow and transport through porous media. This document provides an overview of the use of the program for geosphere modelling in performance assessment calculations and gives a detailed description of the program itself. The aim of the document is to give an indication of the grounds for having confidence in NAMMU as a performance assessment tool. In order to achieve this the following topics are discussed. The basic premises of the assessment approach and the purpose of and nature of the calculations that can be undertaken using NAMMU are outlined. The concepts of the validation of models and the considerations that can lead to increased confidence in models are described. The physical processes that can be modelled using NAMMU and the mathematical models and numerical techniques that are used to represent them are discussed in some detail. Finally, the grounds that would lead one to have confidence that NAMMU is fit for purpose are summarised.
Regeneratively Cooled Porous Media Jacket
Mungas, Greg (Inventor); Fisher, David J. (Inventor); London, Adam Pollok (Inventor); Fryer, Jack Merrill (Inventor)
2013-01-01
The fluid and heat transfer theory for regenerative cooling of a rocket combustion chamber with a porous media coolant jacket is presented. This model is used to design a regeneratively cooled rocket or other high temperature engine cooling jacket. Cooling jackets comprising impermeable inner and outer walls, and porous media channels are disclosed. Also disclosed are porous media coolant jackets with additional structures designed to transfer heat directly from the inner wall to the outer wall, and structures designed to direct movement of the coolant fluid from the inner wall to the outer wall. Methods of making such jackets are also disclosed.
A Multiscale Diffuse-Interface Model for Two-Phase Flow in Porous Media
Roudbari, Mahnaz Shokrpour; Verhoosel, Clemens V
2016-01-01
In this paper we consider a multiscale phase-field model for capillarity-driven flows in porous media. The presented model constitutes a reduction of the conventional Navier-Stokes-Cahn-Hilliard phase-field model, valid in situations where interest is restricted to dynamical and equilibrium behavior in an aggregated sense, rather than a precise description of microscale flow phenomena. The model is based on averaging of the equation of motion, thereby yielding a significant reduction in the complexity of the underlying Navier-Stokes-Cahn-Hilliard equations, while retaining its macroscopic dynamical and equilibrium properties. Numerical results are presented for the representative 2-dimensional capillary-rise problem pertaining to two closely spaced vertical plates with both identical and disparate wetting properties. Comparison with analytical solutions for these test cases corroborates the accuracy of the presented multiscale model. In addition, we present results for a capillary-rise problem with a non-triv...
A fully-explicit discontinuous Galerkin hydrodynamic model for variably-satu- rated porous media
Institute of Scientific and Technical Information of China (English)
De MAET T.; HANERT E.; VANCLOOSTER M
2014-01-01
Groundwater flows play a key role in the recharge of aquifers, the transport of solutes through subsurface systems or the control of surface runoff. Predicting these processes requires the use of groundwater models with their applicability directly linked to their accuracy and computational efficiency. In this paper, we present a new method to model water dynamics in variably- saturated porous media. Our model is based on a fully-explicit discontinuous-Galerkin formulation of the 3D Richards equation, which shows a perfect scaling on parallel architectures. We make use of an adapted jump penalty term for the discontinuous-Galerkin scheme and of a slope limiter algorithm to produce oscillation-free exactly conservative solutions. We show that such an approach is particularly well suited to infiltration fronts. The model results are in good agreement with the reference model Hydrus-1D and seem promising for large scale applications involving a coarse representation of saturated soil.
A numerical method for a model of two-phase flow in a coupled free flow and porous media system
Chen, Jie
2014-07-01
In this article, we study two-phase fluid flow in coupled free flow and porous media regions. The model consists of coupled Cahn-Hilliard and Navier-Stokes equations in the free fluid region and the two-phase Darcy law in the porous medium region. We propose a Robin-Robin domain decomposition method for the coupled Navier-Stokes and Darcy system with the generalized Beavers-Joseph-Saffman condition on the interface between the free flow and the porous media regions. Numerical examples are presented to illustrate the effectiveness of this method. © 2014 Elsevier Inc.
Comolli, Alessandro; Hakoun, Vivien; Dentz, Marco
2017-04-01
Achieving the understanding of the process of solute transport in heterogeneous porous media is of crucial importance for several environmental and social purposes, ranging from aquifers contamination and remediation, to risk assessment in nuclear waste repositories. The complexity of this aim is mainly ascribable to the heterogeneity of natural media, which can be observed at all the scales of interest, from pore scale to catchment scale. In fact, the intrinsic heterogeneity of porous media is responsible for the arising of the well-known non-Fickian footprints of transport, including heavy-tailed breakthrough curves, non-Gaussian spatial density profiles and the non-linear growth of the mean squared displacement. Several studies investigated the processes through which heterogeneity impacts the transport properties, which include local modifications to the advective-dispersive motion of solutes, mass exchanges between some mobile and immobile phases (e.g. sorption/desorption reactions or diffusion into solid matrix) and spatial correlation of the flow field. In the last decades, the continuous time random walk (CTRW) model has often been used to describe solute transport in heterogenous conditions and to quantify the impact of point heterogeneity, spatial correlation and mass transfer on the average transport properties [1]. Open issues regarding this approach are the possibility to relate measurable properties of the medium to the parameters of the model, as well as its capability to provide predictive information. In a recent work [2] the authors have shed new light on understanding the relationship between Lagrangian and Eulerian dynamics as well as on their evolution from arbitrary initial conditions. On the basis of these results, we derive a CTRW model for the description of Darcy-scale transport in d-dimensional media characterized by spatially random permeability fields. The CTRW approach models particle velocities as a spatial Markov process, which is
Modelling Simultaneous transport of Bioreative Solutes and Microorganisms in Porous Media
Institute of Scientific and Technical Information of China (English)
Y.TAN; LIZHENGAO
1998-01-01
Recent years have the development of a number of mathematical models for the descrption of the simultaneous transport of microorganisms and bioreactive solutes in porous media.Most models are based on the advection-dispersion equation,with terms added to account for interactions with the surfaces of the soild matrix ,transformations and microbial activties.Those models based on the advection-dispersion equation have all been shown to represent laboratory experimental data adequately altough various assumption have been made concerning the pore-scale distribution of bacteria.This paper provides an overview o the recent work on modelling the trasport and fate of microorganisms and bioreactive solutes in prous media and examines the different assumptions regarding the pore scale distrbution of microorganisms.
ON THE FILTRATION OF NON-NEWTONIAN FLUID IN POROUS MEDIA WITH A MULTIPLE PARAMETER MODEL
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
A multiple parameter model to describe the Non-Newtonianproperties of fluid filtration in porous media is presented with regard to the pressure gradient expression in terms of the velocity of filtration, where the multiple parameters should be determined by measurements. Based on such a model, an analysis was furnished to deduce the formula for the rate of production of a oil well, and the governing equations for single phase Non-Newtonian fluid fritration. In order to examine the effects of model parameters, the governing equations were numerically solved with the method of cross-diagonal decomposition ZG method. It is found that, for constant rate of production, the power index n of the model influences the pressure distribution considerably, particularly in the vicinity of a single well. The well-bore pressure of Leibenzonian fluid is lower than that of the power-law fluid in the case of the same parameter B and the power index n = 0.5.
In situ bioremediation: A network model of diffusion and flow in granular porous media
Energy Technology Data Exchange (ETDEWEB)
Griffiths, S.K.; Nilson, R.H.; Bradshaw, R.W.
1997-04-01
In situ bioremediation is a potentially expedient, permanent and cost- effective means of waste site decontamination. However, permeability reductions due to the transport and deposition of native fines or due to excessive microorganism populations may severely inhibit the injection of supplemental oxygen in the contamination zone. To help understand this phenomenon, we have developed a micro-mechanical network model of flow, diffusion and particle transport in granular porous materials. The model differs from most similar models in that the network is defined by particle positions in a numerically-generated particle array. The model is thus widely applicable to computing effective transport properties for both ordered and realistic random porous media. A laboratory-scale apparatus to measure permeability reductions has also been designed, built and tested.
Modelling large-deforming fluid-saturated porous media using an Eulerian incremental formulation
Rohan, Eduard
2016-01-01
The paper deals with modelling fluid saturated porous media subject to large deformation. An Eulerian incremental formulation is derived using the problem imposed in the spatial configuration in terms of the equilibrium equation and the mass conservation. Perturbation of the hyperelastic porous medium is described by the Biot model which involves poroelastic coefficients and the permeability governing the Darcy flow. Using the material derivative with respect to a convection velocity field we obtain the rate formulation which allows for linearization of the residuum function. For a given time discretization with backward finite difference approximation of the time derivatives, two incremental problems are obtained which constitute the predictor and corrector steps of the implicit time-integration scheme. Conforming mixed finite element approximation in space is used. Validation of the numerical model implemented in the SfePy code is reported for an isotropic medium with a hyperelastic solid phase. The propose...
Wang, J. X.; Jia, P. Y.; Wang, Y. S.; Jiang, L.
2010-03-01
In this article, using Gibson-Ashby constitutive model, we suggest a new method for numerical investigation of forced convection heat transfer in porous foam metal, and try to consolidate the study for mechanical property and that for thermal characteristic. By available experimental data, we simulated to two cases, namely as the transfer in porous media for diameter is 0.6 mm and porosity is 0.402, and for diameter is 1.6 mm and porosity is 0.462. The result, from our constitutive model for single forced convection heat transfer, corresponds well with the experimental data. As for pressure drop prediction in porous is in good agreement with experiment, and the error is only 5% to 10%, but for transfer is less accurate, the error is about 20%, which is acceptable in practice. So it is done that constitutive model is used to simulate the transfer property.
Biofilm growth in porous media: experiments, computational modeling at the porescale, and upscaling
Peszynska, Malgorzata; Iltis, Gabriel; Schlueter, Steffen; Wildenschild, Dorthe
2015-01-01
Biofilm growth changes many physical properties of porous media such as porosity, permeability and mass transport parameters. The growth depends on various environmental conditions, and in particular, on flow rates. Modeling the evolution of such properties is difficult both at the porescale where the phase morphology can be distinguished, as well as during upscaling to the corescale effective properties. Experimental data on biofilm growth is also limited because its collection can interfere with the growth, while imaging itself presents challenges. In this paper we combine insight from imaging, experiments, and numerical simulations and visualization. The experimental dataset is based on glass beads domain inoculated by biomass which is subjected to various flow conditions promoting the growth of biomass and the appearance of a biofilm phase. The domain is imaged and the imaging data is used directly by a computational model for flow and transport. The results of the computational flow model are upscaled to...
Time domain numerical modeling of wave propagation in 2D heterogeneous porous media
Chiavassa, Guillaume
2010-01-01
This paper deals with the numerical modeling of wave propagation in porous media described by Biot's theory. The viscous efforts between the fluid and the elastic skeleton are assumed to be a linear function of the relative velocity, which is valid in the low-frequency range. The coexistence of propagating fast compressional wave and shear wave, and of a diffusive slow compressional wave, makes numerical modeling tricky. To avoid restrictions on the time step, the Biot's system is splitted into two parts: the propagative part is discretized by a fourth-order ADER scheme, while the diffusive part is solved analytically. Near the material interfaces, a space-time mesh refinement is implemented to capture the small spatial scales related to the slow compressional wave. The jump conditions along the interfaces are discretized by an immersed interface method. Numerical experiments and comparisons with exact solutions confirm the accuracy of the numerical modeling. The efficiency of the approach is illustrated by s...
Joshi, Nitin; Ojha, C. S. P.; Sharma, P. K.
2012-10-01
In this study a conceptual model that accounts for the effects of nonequilibrium contaminant transport in a fractured porous media is developed. Present model accounts for both physical and sorption nonequilibrium. Analytical solution was developed using the Laplace transform technique, which was then numerically inverted to obtain solute concentration in the fracture matrix system. The semianalytical solution developed here can incorporate both semi-infinite and finite fracture matrix extent. In addition, the model can account for flexible boundary conditions and nonzero initial condition in the fracture matrix system. The present semianalytical solution was validated against the existing analytical solutions for the fracture matrix system. In order to differentiate between various sorption/transport mechanism different cases of sorption and mass transfer were analyzed by comparing the breakthrough curves and temporal moments. It was found that significant differences in the signature of sorption and mass transfer exists. Applicability of the developed model was evaluated by simulating the published experimental data of Calcium and Strontium transport in a single fracture. The present model simulated the experimental data reasonably well in comparison to the model based on equilibrium sorption assumption in fracture matrix system, and multi rate mass transfer model.
Veldsink, J.W.; Damme, R.M.J. van; Versteeg, G.F.; Swaaij, W.P.M. van
1995-01-01
In the present study, mass transport accompanied by chemical reactions in porous media is studied according to the Fick model and the dusty-gas model. For mass transport accompanied by a chemical reaction in catalyst structures showing a plane, line, or point of symmetry, the approximate analytical
Image-based modeling of flow and reactive transport in porous media
Qin, Chao-Zhong; Hoang, Tuong; Verhoosel, Clemens V.; Harald van Brummelen, E.; Wijshoff, Herman M. A.
2017-04-01
Due to the availability of powerful computational resources and high-resolution acquisition of material structures, image-based modeling has become an important tool in studying pore-scale flow and transport processes in porous media [Scheibe et al., 2015]. It is also playing an important role in the upscaling study for developing macroscale porous media models. Usually, the pore structure of a porous medium is directly discretized by the voxels obtained from visualization techniques (e.g. micro CT scanning), which can avoid the complex generation of computational mesh. However, this discretization may considerably overestimate the interfacial areas between solid walls and pore spaces. As a result, it could impact the numerical predictions of reactive transport and immiscible two-phase flow. In this work, two types of image-based models are used to study single-phase flow and reactive transport in a porous medium of sintered glass beads. One model is from a well-established voxel-based simulation tool. The other is based on the mixed isogeometric finite cell method [Hoang et al., 2016], which has been implemented in the open source Nutils (http://www.nutils.org). The finite cell method can be used in combination with isogeometric analysis to enable the higher-order discretization of problems on complex volumetric domains. A particularly interesting application of this immersed simulation technique is image-based analysis, where the geometry is smoothly approximated by segmentation of a B-spline level set approximation of scan data [Verhoosel et al., 2015]. Through a number of case studies by the two models, we will show the advantages and disadvantages of each model in modeling single-phase flow and reactive transport in porous media. Particularly, we will highlight the importance of preserving high-resolution interfaces between solid walls and pore spaces in image-based modeling of porous media. References Hoang, T., C. V. Verhoosel, F. Auricchio, E. H. van
Jiang, Lanlan; Liu, Yu; Teng, Ying; Zhao, Jiafei; Zhang, Yi; Yang, Mingjun; Song, Yongchen
2017-01-01
The purpose of this work is to develop a permeability estimation method for porous media. This method is based on an improved capillary bundle model by introducing some pore geometries. We firstly carried out micro-CT scans to extract the 3D digital model of porous media. Then we applied a maximum ball extraction method to the digital model to obtain the topological and geometrical pore parameters such as the pore radius, the throat radius and length and the average coordination number. We also applied a random walker method to calculate the tortuosity factors of porous media. We improved the capillary bundle model by introducing the pore geometries and tortuosity factors. Finally, we calculated the absolute permeabilities of four kinds of porous media formed of glass beads and compared the results with experiments and several other models to verify the improved model. We found that the calculated permeabilities using this improved capillary bundle model show better agreement with the measured permeabilities than the other methods.
Nonlinear Dynamics of Ion Concentration Polarization in Porous Media: The Leaky Membrane Model
Dydek, E Victoria
2013-01-01
The conductivity of highly charged membranes is nearly constant, due to counter-ions screening pore surfaces. Weakly charged porous media, or "leaky membranes", also contain a significant concentration of co-ions, whose depletion at high current leads to ion concentration polarization and conductivity shock waves. To describe these nonlinear phenomena the absence of electro-osmotic flow, a simple Leaky Membrane Model is formulated, based on macroscopic electroneutrality and Nernst-Planck ionic fluxes. The model is solved in cases of unsupported binary electrolytes: steady conduction from a reservoir to a cation-selective surface, transient response to a current step, steady conduction to a flow-through porous electrode, and steady conduction between cation-selective surfaces in cross flow. The last problem is motivated by separations in leaky membranes, such as shock electrodialysis. The article begins with a tribute to Neal Amundson, whose pioneering work on shock waves in chromatography involved similar mat...
Coupled Hydromechanical Model of Two-Phase Fluid Flow in Deformable Porous Media
Directory of Open Access Journals (Sweden)
You-Seong Kim
2013-01-01
Full Text Available A model of solid-water-air coupling in triphasic mixtures is compared with solid-water coupling in biphasic mixtures with an application to partially saturated porous media. Based on thermodynamics, the mathematical framework governing the behavior of a partially saturated soil is derived using balance equations, and the numerical implementation and drainage tests of a soil column are carried out to validate the obtained formulations. The role of the air phase in the hydro-mechanical behavior of triphasic mixtures can be analyzed from the interactions among multiple phases for the constitutive behavior of a solid skeleton, and the triphasic mixture model can be applied in geotechnical engineering problems, such as CO2 sequestration and air storage in aquifers.
van Milligen, B Ph
2014-01-01
The dispersion of solute in porous media shows a non-linear increase in the transition from diffusion to advection dominated dispersion as the flow velocity is raised. In the past, the behavior in this intermediate regime has been explained with a variety of models. {We present and use a simplified numerical model which does not contain any turbulence, Taylor dispersion, or fractality. With it, we show that the non-linearity in the intermediate regime nevertheless occurs. Furthermore,} we show that that the intermediate regime can be regarded as a phase transition between random, diffusive transport at low flow velocity and ordered transport controlled by the geometry of the pore space at high flow velocities. This phase transition explains the first-order behavior in the intermediate regime. A new quantifier, the ratio of the amount of solute in dominantly advective versus dominantly diffusive pore channels, plays the role of `order parameter' of this phase transition. Taylor dispersion, often invoked to exp...
Pore-Scale Modeling of Navier-Stokes Flow in Distensible Networks and Porous Media
Sochi, Taha
2013-01-01
In this paper, a pore-scale network modeling method, based on the flow continuity residual in conjunction with a Newton-Raphson non-linear iterative solving technique, is proposed and used to obtain the pressure and flow fields in a network of interconnected distensible ducts representing, for instance, blood vasculature or deformable porous media. A previously derived analytical expression correlating boundary pressures to volumetric flow rate in compliant tubes for a pressure-area constitutive elastic relation has been used to represent the underlying flow model. Comparison to a preceding equivalent method, the one-dimensional Navier-Stokes finite element, was made and the results were analyzed. The advantages of the new method have been highlighted and practical computational issues, related mainly to the rate and speed of convergence, have been discussed.
Multi-scale Modeling of Compressible Single-phase Flow in Porous Media using Molecular Simulation
Saad, Ahmed Mohamed
2016-05-01
In this study, an efficient coupling between Monte Carlo (MC) molecular simulation and Darcy-scale flow in porous media is presented. The cell-centered finite difference method with a non-uniform rectangular mesh were used to discretize the simulation domain and solve the governing equations. To speed up the MC simulations, we implemented a recently developed scheme that quickly generates MC Markov chains out of pre-computed ones, based on the reweighting and reconstruction algorithm. This method astonishingly reduces the required computational time by MC simulations from hours to seconds. In addition, the reweighting and reconstruction scheme, which was originally designed to work with the LJ potential model, is extended to work with a potential model that accounts for the molecular quadrupole moment of fluids with non-spherical molecules such as CO2. The potential model was used to simulate the thermodynamic equilibrium properties for single-phase and two-phase systems using the canonical ensemble and the Gibbs ensemble, respectively. Comparing the simulation results with the experimental data showed that the implemented model has an excellent fit outperforming the standard LJ model. To demonstrate the strength of the proposed coupling in terms of computational time efficiency and numerical accuracy in fluid properties, various numerical experiments covering different compressible single-phase flow scenarios were conducted. The novelty in the introduced scheme is in allowing an efficient coupling of the molecular scale and Darcy scale in reservoir simulators. This leads to an accurate description of the thermodynamic behavior of the simulated reservoir fluids; consequently enhancing the confidence in the flow predictions in porous media.
Klatt, Michael A; Schröder-Turk, Gerd E; Mecke, Klaus
2017-07-01
Structure-property relations, which relate the shape of the microstructure to physical properties such as transport or mechanical properties, need sensitive measures of structure. What are suitable fabric tensors that quantify the shape of anisotropic heterogeneous materials? The mean intercept length is among the most commonly used characteristics of anisotropy in porous media, for example, of trabecular bone in medical physics. We analyze the orientation-biased Boolean model, a versatile stochastic model that represents microstructures as overlapping grains with an orientation bias towards a preferred direction. This model is an extension of the isotropic Boolean model, which has been shown to truthfully reproduce multi-functional properties of isotropic porous media. We explain the close relationship between the concept of intersections with test lines to the elaborate mathematical theory of queues, and how explicit results from the latter can be directly applied to characterize microstructures. In this series of two papers, we provide analytic formulas for the anisotropic Boolean model and demonstrate often overlooked conceptual shortcomings of this approach. Queuing theory is used to derive simple and illustrative formulas for the mean intercept length. It separates into an intensity-dependent and an orientation-dependent factor. The global average of the mean intercept length can be expressed by local characteristics of a single grain alone. We thus identify which shape information about the random process the mean intercept length contains. The connection between global and local quantities helps to interpret observations and provides insights into the possibilities and limitations of the analysis. In the second paper of this series, we discuss, based on the findings in this paper, short-comings of the mean intercept analysis for (bone-)microstructure characterization. We will suggest alternative and better defined sensitive anisotropy measures from integral
Modeling of flow and solidification of liquid water during unidirectional freezing in porous media
Saruya, Tomotaka; Rempel, Alan; Kurita, Kei
2014-05-01
Flow and phase change of liquid in porous media are fundamental processes in earth science and soil physics. Particularly in cold region or periglacial environment, the flow and solidification of pore water in the ground simultaneously occur and their collective interactions control the growth of ice lenses and upward displacement of surface called as frost heave. In the nucleation and growth of ice lenses, the homogeneous mixture of soil particles and pore water is transformed to the heterogeneous structure due to the water redistribution and the particle migration. Unfrozen water that is adsorbed to the particle surface or confined to capillary regions plays an important role in the formation of ice lenses and its behaviors have been investigated from a perspective of premelting dynamics (e.g., Worster and Wettlaufer 2006). In the porous media below the nominal melting temperature, intermolecular forces that act between particles and ice through the liquid thin film produce the net thermomolecular force that is responsible for the particle separation form the ice lenses(Dash et al. 2006). Although the mechanisms of ice lens formation have been investigated by many researchers, still large uncertainties remain and more experimental constraints are required. Here we present experimental results of ice lens formation, particularly focusing on the role of grain size and compare the model by Rempel et al (2004). We have performed the unidirectional freezing experiments using water-saturated glass beads that have uniform structures. Since the flow of water in porous media depends on the particles size and pore throat size (Darcy's law), we have prepared various sizes of glass beads from submicron to submillimeter. Our experiments reveal the clear relationships between the host particle sizes and nucleated location and lens thickness. Part of this work is already published in Saruya et al, PRE but we extended to smaller sized regime. We compared our experimental results
Nonequilibrium Physics and Phase-Field Modeling of Multiphase Flow in Porous Media
Energy Technology Data Exchange (ETDEWEB)
Juanes, Ruben [Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
2016-09-01
The overarching goal of this project was to develop a new continuum theory of multiphase flow in porous media. The theory follows a phase-field modeling approach, and therefore has a sound thermodynamical basis. It is a phenomenological theory in the sense that its formulation is driven by macroscopic phenomena, such as viscous instabilities during multifluid displacement. The research agenda was organized around a set of hypothesis on hitherto unexplained behavior of multiphase flow. All these hypothesis are nontrivial, and testable. Indeed, a central aspect of the project was testing each hypothesis by means of carefully-designed laboratory experiments, therefore probing the validity of the proposed theory. The proposed research places an emphasis on the fundamentals of flow physics, but is motivated by important energy-driven applications in earth sciences, as well as microfluidic technology.
El-Amin, Mohamed F.
2017-06-06
Recently, applications of nanoparticles have been considered in many branches of petroleum engineering, especially, enhanced oil recovery. The current paper is devoted to investigate the problem of nanoparticles transport in fractured porous media, numerically. We employed the discrete-fracture model (DFM) to represent the flow and transport in the fractured formations. The system of the governing equations consists of the mass conservation law, Darcy\\'s law, nanoparticles concentration in water, deposited nanoparticles concentration on the pore-wall, and entrapped nanoparticles concentration in the pore-throat. The variation of porosity and permeability due to the nanoparticles deposition/entrapment on/in the pores is also considered. We employ the multiscale time-splitting strategy to control different time-step sizes for different physics, such as pressure and concentration. The cell-centered finite difference (CCFD) method is used for the spatial discretization. Numerical examples are provided to demonstrate the efficiency of the proposed multiscale time splitting approach.
Sullivan, Eric
2013-01-01
Transport phenomena in porous media are commonplace in our daily lives. Examples and applications include heat and moisture transport in soils, baking and drying of food stuffs, curing of cement, and evaporation of fuels in wild fires. Of particular interest to this study are heat and moisture transport in unsaturated soils. Historically, mathematical models for these processes are derived by coupling classical Darcy's, Fourier's, and Fick's laws with volume averaged conservation of mass and energy and empirically based source and sink terms. Recent experimental and mathematical research has proposed modifications and suggested limitations in these classical equations. The primary goal of this thesis is to derive a thermodynamically consistent system of equations for heat and moisture transport in terms of the chemical potential that addresses some of these limitations. The physical processes of interest are primarily diffusive in nature and, for that reason, we focus on using the macroscale chemical potentia...
Application of the CE/SE Method to a Two-Phase Detonation Model in Porous Media
Institute of Scientific and Technical Information of China (English)
DONG He-Fei; HONG Tao; ZHANG De-Liang
2011-01-01
We extend the conservation-element and solution-element method to simulate a two-phase detonation model in porous media. The accuracy of the method is validated by calculating an inert compaction problem. The main characteristics of piston-driven detonation phenomena, including the compaction wave, the onset of combustion,and the transition to detonation, could be predicted successfully.
de Vries, Enno T.; Raoof, Amir; van Genuchten, Marinus Th.
2017-01-01
Many environmental and agricultural applications involve the transport of water and dissolved constituents through aggregated soil profiles, or porous media that are structured, fractured or macroporous in other ways. During the past several decades, various process-based macroscopic models have bee
Trautz, Andrew; Smits, Kathleen; Cihan, Abdullah; Illangasekare, Tissa
2013-04-01
Evaporation from bare soil is a key component of the hydrologic cycle and the process primarily responsible for governing water and energy exchanges between the land and atmosphere. Despite its importance, there is still a great deal of uncertainty associated with our current understanding of this complex multiphase phenomenon. A common approach when modeling the movement of liquid water, water vapor and heat in the soil immediately below the land-atmosphere interface is to assume that water vapor concentration in air is always in equilibrium with liquid water. However, this equilibrium assumption is called into question by experiments about liquid/gas phase change in porous media suggesting that the equilibrium establishment is not instantaneous; a volatilization or condensation time is observed at the macroscopic scale under certain conditions. Introduction of such a non-equilibrium mass transfer relationship is based on the Hertz-Knudsen equation (HKE) derived from the kinetic theory of gases. Multiple formulations have been presented to represent the rate of phase change between water and vapor, many relying on empirical fitting parameters due to limited experimental data. The purpose of this work is to perform an unbiased comparison between various conceptual and mathematical formulations for non-equilibrium phase change on evaporation and develop appropriate numerical models to be used in simulations. The key to such a comparison is the availability of accurate data. As such data at the scale of interest is not possible to obtain in field settings, a unique two-dimensional cell apparatus was developed. The test cell was equipped with a network of sensors for automated and continuous monitoring of soil moisture, soil and air temperature and relative humidity, and wind velocity to generate precision data. A fully-coupled numerical model to solve the governing equations for heat, liquid water and water vapor transport in soil was developed. The code implements a
Drainage equations and non-Darcian modelling in coarse porous media or geosynthetic materials
Bordier, C.; Zimmer, D.
2000-03-01
In coarse porous media, Darcy's law is not valid because of turbulence. Different alternative laws have been proposed like Forchheimer's or Izbash's law. In the present study, these two laws were experimentally investigated and have been shown to be equally suitable to describe the flow equation in different coarse materials, namely gravel materials and geosynthetic products. Izbash's law (v n=-λ ni) has been preferred to derive drainage equations because it is in continuity with Darcy's law and facilitates the development of an analytical solution. It has been introduced in Boussinesq's equation, which has been solved by a semi-analytical semi-numerical method. General equations for the drainage of coarse porous media have been derived and incorporated into the drainage model SIDRA, which predicts water-table elevations and drain flow rates for a given net recharge. This allows for comparison (i) between predicted Darcian and non-Darcian behaviours and (ii) between predicted drainage functionings of different coarse materials. Water-table elevations are shown to be much more sensitive to non-Darcian flow equation and to the hydraulic properties of the materials than drain flow rates. Response surface maps of an objective function based on the Nash criterion show that the water-table predictions are almost not sensitive to drainable porosity values. They also indicate that the two parameters of the Izbash flow equation ( λ and n) are dependent for water-table prediction. Based on this result a method is proposed to determine hydraulic properties and drainage systems yielding similar water-table elevations. The results can help choosing between classical granular materials and geocomposite products in drainage systems such as leachate collection systems of landfills.
Modelling the Complex Conductivity of Charged Porous Media using The Grain Polarization Model
Leroy, P.; Revil, A.; Jougnot, D.; Li, S.
2015-12-01
The low-frequency complex conductivity response of charged porous media reflects a combination of three polarization processes occuring at different frequency ranges. One polarization process corresponds to the membrane polarization phenomenon, which is the polarization mechanism associated with the back-diffusion of salt ions through different pore spaces of the porous material (ions-selective zones and zones with no selectivity). This polarization process generally occurs at the lowest frequency range, typically in the frequency range [mHz Hz] because it involves polarization mechanism occurring over different pore spaces (the relaxation frequency is inversely proportional to the length of the polarization process). Another polarization process corresponds to the electrochemical polarization of the electrical double layer coating the surface of the grains. In the grain polarization model, the diffuse layer is assumed to not polarize because it is assumed to form a continuum in the porous medium. The compact Stern layer is assumed to polarize because the Stern layer is assumed to be discontinuous over multiple grains. The electrochemical polarization of the Stern layer typically occurs in the frequency range [Hz kHz]. The last polarization process corresponds to the Maxwell-Wagner polarization mechanism, which is caused by the formation of field-induced free charge distributions near the interface between the phases of the medium. In this presentation, the grain polarization model based on the O'Konski, Schwarz, Schurr and Sen theories and developed later by Revil and co-workers is showed. This spectral induced polarization model was successfully applied to describe the complex conductivity responses of glass beads, sands, clays, clay-sand mixtures and other minerals. The limits of this model and future developments will also be presented.
Khanafer, Khalil; Cook, Keith; Marafie, Alia
2012-01-01
A numerical study was conducted to analyze fluid flow within hollow fiber membranes of the artificial lungs. The hollow fiber bundle was approximated using a porous media model. In addition, the transport equations were solved using the finite-element formulation based on the Galerkin method of weighted residuals. Comparisons with previously published work on the basis of special cases were performed and found to be in excellent agreement. A Newtonian viscous fluid model for the blood was used. Different flow models for porous media, such as the Brinkman-extended Darcy model, Darcy's law model, and the generalized flow model, were considered. Results were obtained in terms of streamlines, velocity vectors, and pressure distribution for various Reynolds numbers and Darcy numbers. The results from this investigation showed that the pressure drop across the artificial lung device increased with an increase in the Reynolds number. In addition, the pressure drop was found to increase significantly for small Darcy numbers.
Crevillén-García, D.; Wilkinson, R. D.; Shah, A. A.; Power, H.
2017-01-01
Numerical groundwater flow and dissolution models of physico-chemical processes in deep aquifers are usually subject to uncertainty in one or more of the model input parameters. This uncertainty is propagated through the equations and needs to be quantified and characterised in order to rely on the model outputs. In this paper we present a Gaussian process emulation method as a tool for performing uncertainty quantification in mathematical models for convection and dissolution processes in porous media. One of the advantages of this method is its ability to significantly reduce the computational cost of an uncertainty analysis, while yielding accurate results, compared to classical Monte Carlo methods. We apply the methodology to a model of convectively-enhanced dissolution processes occurring during carbon capture and storage. In this model, the Gaussian process methodology fails due to the presence of multiple branches of solutions emanating from a bifurcation point, i.e., two equilibrium states exist rather than one. To overcome this issue we use a classifier as a precursor to the Gaussian process emulation, after which we are able to successfully perform a full uncertainty analysis in the vicinity of the bifurcation point.
Biofilm growth in porous media: Experiments, computational modeling at the porescale, and upscaling
Peszynska, Malgorzata; Trykozko, Anna; Iltis, Gabriel; Schlueter, Steffen; Wildenschild, Dorthe
2016-09-01
Biofilm growth changes many physical properties of porous media such as porosity, permeability and mass transport parameters. The growth depends on various environmental conditions, and in particular, on flow rates. Modeling the evolution of such properties is difficult both at the porescale where the phase morphology can be distinguished, as well as during upscaling to the corescale effective properties. Experimental data on biofilm growth is also limited because its collection can interfere with the growth, while imaging itself presents challenges. In this paper we combine insight from imaging, experiments, and numerical simulations and visualization. The experimental dataset is based on glass beads domain inoculated by biomass which is subjected to various flow conditions promoting the growth of biomass and the appearance of a biofilm phase. The domain is imaged and the imaging data is used directly by a computational model for flow and transport. The results of the computational flow model are upscaled to produce conductivities which compare well with the experimentally obtained hydraulic properties of the medium. The flow model is also coupled to a newly developed biomass-nutrient growth model, and the model reproduces morphologies qualitatively similar to those observed in the experiment.
Modeling the effects of water content on TiO2 nanoparticles transport in porous media
Toloni, Ivan; Lehmann, François; Ackerer, Philippe
2016-08-01
The transport of manufactured titanium dioxide (TiO2, rutile) nanoparticles (NP) in porous media was investigated by metric scale column experiments under different water saturation and ionic strength (IS) conditions. The NP breakthrough curves showed that TiO2 NP retention on the interface between air and water (AWI) and the interface between the solid and the fluid (SWI) is insignificant for an IS equal to or smaller than 3 mM KCl. For larger IS, the retention is depending on the water content and the fluid velocity. The experiments, conducted with an IS of 5 mM KCl, showed a significantly higher retention of NP than that observed under saturated conditions and very similar experimental conditions. Water flow was simulated using the standard Richards equation. The hydrodynamic model parameters for unsaturated flow were estimated through independent drainage experiments. A new mathematical model was developed to describe TiO2 NP transport and retention on SWI and AWI. The model accounts for the variation of water content and water velocity as a function of depth and takes into account the presence of the AWI and its role as a NP collector. Comparisons with experimental data showed that the suggested modeled processes can be used to quantify the NPs retentions at the AWI and SWI. The suggested model can be used for both saturated and unsaturated conditions and for a rather large range of velocities.
An immersed boundary-lattice Boltzmann model for biofilm growth in porous media
Benioug, M.; Golfier, F.; Oltéan, C.; Buès, M. A.; Bahar, T.; Cuny, J.
2017-09-01
In this paper, we present a two-dimensional pore-scale numerical model to investigate the main mechanisms governing biofilm growth in porous media. The fluid flow and solute transport equations are coupled with a biofilm evolution model. Fluid flow is simulated with an immersed boundary-lattice Boltzmann model while solute transport is described with a volume-of-fluid-type approach. A cellular automaton algorithm combined with immersed boundary methods was developed to describe the spreading and distribution of biomass. Bacterial attachment and detachment mechanisms are also taken into account. The capability of this model to describe correctly the couplings involved between fluid circulation, nutrient transport and bacterial growth is tested under different hydrostatic and hydrodynamic conditions (i) on a flat medium and (ii) for a complex porous medium. For the second case, different regimes of biofilm growth are identified and are found to be related to the dimensionless parameters of the model, Damköhler and Péclet numbers and dimensionless shear stress. Finally, the impact of biofilm growth on the macroscopic properties of the porous medium is investigated and we discuss the unicity of the relationships between hydraulic conductivity and biofilm volume fraction.
Pore-Scale Modeling of Non-Newtonian Flow in Porous Media
Sochi, Taha
2010-01-01
The thesis investigates the flow of non-Newtonian fluids in porous media using pore-scale network modeling. Non-Newtonian fluids show very complex time and strain dependent behavior and may have initial yield stress. Their common feature is that they do not obey the simple Newtonian relation of proportionality between stress and rate of deformation. They are generally classified into three main categories: time-independent, time-dependent and viscoelastic. Two three-dimensional networks representing a sand pack and Berea sandstone were used. An iterative numerical technique is used to solve the pressure field and obtain the flow rate and apparent viscosity. The time-independent category is investigated using two fluid models: Ellis and Herschel-Bulkley. The analysis confirmed the reliability of the non-Newtonian network model used in this study. Good results are obtained, especially for the Ellis model, when comparing the network model results to experimental data sets found in the literature. The yield-stres...
Energy Technology Data Exchange (ETDEWEB)
Schunk, Peter Randall; Cairncross, Richard A. (Drexel University, Philadelphia, PA); Madasu, S. (Drexel University, Philadelphia, PA)
2004-03-01
This report summarizes research advances pursued with award funding issued by the DOE to Drexel University through the Presidential Early Career Award (PECASE) program. Professor Rich Cairncross was the recipient of this award in 1997. With it he pursued two related research topics under Sandia's guidance that address the outstanding issue of fluid-structural interactions of liquids with deformable solid materials, focusing mainly on the ubiquitous dynamic wetting problem. The project focus in the first four years was aimed at deriving a predictive numerical modeling approach for the motion of the dynamic contact line on a deformable substrate. A formulation of physical model equations was derived in the context of the Galerkin finite element method in an arbitrary Lagrangian/Eulerian (ALE) frame of reference. The formulation was successfully integrated in Sandia's Goma finite element code and tested on several technologically important thin-film coating problems. The model equations, the finite-element implementation, and results from several applications are given in this report. In the last year of the five-year project the same physical concepts were extended towards the problem of capillary imbibition in deformable porous media. A synopsis of this preliminary modeling and experimental effort is also discussed.
Experimental Investigation and Pore-Scale Modeling of Non-Newtonian Fluid Flow in Porous Media
Hauswirth, S.; Dye, A. L.; Miller, C. T.; Tapscott, C.; Schultz, P. B.
2015-12-01
Systems involving the flow of non-Newtonian fluids in porous media arise in a number of settings, including hydraulic fracturing, enhanced oil recovery, contaminant remediation, and biological systems. Development of accurate macroscale models of such systems requires an understanding of the relationship between the fluid and medium properties at the microscale and averaged macroscale properties. This study investigates the flow of aqueous solutions of guar gum, a major component of hydraulic fracturing fluids that exhibits Cross model rheological behavior. The rheological properties of solutions containing varying concentrations of guar gum were characterized using a rotational rheometer and the data were fit to a model relating viscosity to shear rate and concentration. Flow experiments were conducted in a porous medium-packed column to measure the pressure response during the flow of guar gum solutions at a wide range of flow rates and determine apparent macroscale viscosities and shear rates. To investigate the relationship between the fluid rheology, microscale physics, and the observed macroscale properties, a lattice Boltzmann pore scale simulator incorporating non-Newtonian behavior was developed. The model was validated, then used to simulate systems representative of the column experiments, allowing direct correlation of detailed microscale physics to the macroscale observations.
Dynamic non-equilibrium wall-modeling for large eddy simulation at high Reynolds numbers
Kawai, Soshi; Larsson, Johan
2013-01-01
A dynamic non-equilibrium wall-model for large-eddy simulation at arbitrarily high Reynolds numbers is proposed and validated on equilibrium boundary layers and a non-equilibrium shock/boundary-layer interaction problem. The proposed method builds on the prior non-equilibrium wall-models of Balaras et al. [AIAA J. 34, 1111-1119 (1996)], 10.2514/3.13200 and Wang and Moin [Phys. Fluids 14, 2043-2051 (2002)], 10.1063/1.1476668: the failure of these wall-models to accurately predict the skin friction in equilibrium boundary layers is shown and analyzed, and an improved wall-model that solves this issue is proposed. The improvement stems directly from reasoning about how the turbulence length scale changes with wall distance in the inertial sublayer, the grid resolution, and the resolution-characteristics of numerical methods. The proposed model yields accurate resolved turbulence, both in terms of structure and statistics for both the equilibrium and non-equilibrium flows without the use of ad hoc corrections. Crucially, the model accurately predicts the skin friction, something that existing non-equilibrium wall-models fail to do robustly.
Predicting the growth of glioblastoma multiforme spheroids using a multiphase porous media model.
Mascheroni, Pietro; Stigliano, Cinzia; Carfagna, Melania; Boso, Daniela P; Preziosi, Luigi; Decuzzi, Paolo; Schrefler, Bernhard A
2016-10-01
Tumor spheroids constitute an effective in vitro tool to investigate the avascular stage of tumor growth. These three-dimensional cell aggregates reproduce the nutrient and proliferation gradients found in the early stages of cancer and can be grown with a strict control of their environmental conditions. In the last years, new experimental techniques have been developed to determine the effect of mechanical stress on the growth of tumor spheroids. These studies report a reduction in cell proliferation as a function of increasingly applied stress on the surface of the spheroids. This work presents a specialization for tumor spheroid growth of a previous more general multiphase model. The equations of the model are derived in the framework of porous media theory, and constitutive relations for the mass transfer terms and the stress are formulated on the basis of experimental observations. A set of experiments is performed, investigating the growth of U-87MG spheroids both freely growing in the culture medium and subjected to an external mechanical pressure induced by a Dextran solution. The growth curves of the model are compared to the experimental data, with good agreement for both the experimental settings. A new mathematical law regulating the inhibitory effect of mechanical compression on cancer cell proliferation is presented at the end of the paper. This new law is validated against experimental data and provides better results compared to other expressions in the literature.
Ray, Nadja; Rupp, Andreas; Prechtel, Alexander
2017-09-01
Upscaling transport in porous media including both biomass development and simultaneous structural changes in the solid matrix is extremely challenging. This is because both affect the medium's porosity as well as mass transport parameters and flow paths. We address this challenge by means of a multiscale model. At the pore scale, the local discontinuous Galerkin (LDG) method is used to solve differential equations describing particularly the bacteria's and the nutrient's development. Likewise, a sticky agent tightening together solid or bio cells is considered. This is combined with a cellular automaton method (CAM) capturing structural changes of the underlying computational domain stemming from biomass development and solid restructuring. Findings from standard homogenization theory are applied to determine the medium's characteristic time- and space-dependent properties. Investigating these results enhances our understanding of the strong interplay between a medium's functional properties and its geometric structure. Finally, integrating such properties as model parameters into models defined on a larger scale enables reflecting the impact of pore scale processes on the larger scale.
An implicit numerical model for multicomponent compressible two-phase flow in porous media
Zidane, Ali; Firoozabadi, Abbas
2015-11-01
We introduce a new implicit approach to model multicomponent compressible two-phase flow in porous media with species transfer between the phases. In the implicit discretization of the species transport equation in our formulation we calculate for the first time the derivative of the molar concentration of component i in phase α (cα, i) with respect to the total molar concentration (ci) under the conditions of a constant volume V and temperature T. The species transport equation is discretized by the finite volume (FV) method. The fluxes are calculated based on powerful features of the mixed finite element (MFE) method which provides the pressure at grid-cell interfaces in addition to the pressure at the grid-cell center. The efficiency of the proposed model is demonstrated by comparing our results with three existing implicit compositional models. Our algorithm has low numerical dispersion despite the fact it is based on first-order space discretization. The proposed algorithm is very robust.
El-Amin, Mohamed
2012-09-03
Geological storage of anthropogenic CO2 emissions in deep saline aquifers has recently received tremendous attention in the scientific literature. Injected CO2 plume buoyantly accumulates at the top part of the deep aquifer under a sealing cap rock, and some concern that the high-pressure CO2 could breach the seal rock. However, CO2 will diffuse into the brine underneath and generate a slightly denser fluid that may induce instability and convective mixing. Onset times of instability and convective mixing performance depend on the physical properties of the rock and fluids, such as permeability and density contrast. The novel idea is to adding nanoparticles to the injected CO2 to increase density contrast between the CO2-rich brine and the underlying resident brine and, consequently, decrease onset time of instability and increase convective mixing. As far as it goes, only few works address the issues related to mathematical and numerical modeling aspects of the nanoparticles transport phenomena in CO2 storages. In the current work, we will present mathematical models to describe the nanoparticles transport carried by injected CO2 in porous media. Buoyancy and capillary forces as well as Brownian diffusion are important to be considered in the model. IMplicit Pressure Explicit Saturation-Concentration (IMPESC) scheme is used and a numerical simulator is developed to simulate the nanoparticles transport in CO2 storages.
Delay, Frederick; Porel, Gilles; Chatelier, Marion
2013-07-01
We present a modeling exercise of solute transport and biodegradation in a coarse porous medium widely colonized by a biofilm phase. Tracer tests in large laboratory columns using both conservative (fluorescein) and biodegradable (nitrate) solutes are simulated by means of a dual flowing continuum approach. The latter clearly distinguishes concentrations in a flowing porous phase from concentrations conveyed in the biofilm. With this conceptual setting, it becomes possible to simulate the sharp front of concentrations at early times and the flat tail of low concentrations at late times observed on the experimental breakthrough curves. Thanks to the separation of flow in two phases at different velocities, dispersion coefficients in both flowing phases keep reasonable values with some physical meaning. This is not the case with simpler models based on a single continuum (eventually concealing dead-ends), for which inferred dispersivity may reach the unphysical value of twice the size of the columns. We also show that the behavior of the dual flowing continuum is mainly controlled by the relative fractions of flow passing in each phase and the rate of mass transfer between phases. These parameters also condition the efficiency of nitrate degradation, the degradation rate in a well-seeded medium being a weakly sensitive parameter. Even though the concept of dual flowing continuum appears promising for simulating transport in complex porous media, its inversion onto experimental data really benefits from attempts with simpler models providing a rough pre-evaluation of parameters such as porosity and mean fluid velocity in the system.
2010-01-01
A numerical study was conducted to analyze fluid flow within hollow fiber membranes of the artificial lungs. The hollow fiber bundle was approximated using a porous media model. In addition, the transport equations were solved using the finite-element formulation based on the Galerkin method of weighted residuals. Comparisons with previously published work on the basis of special cases were performed and found to be in excellent agreement. A Newtonian viscous fluid model for the blood was use...
Numerical modelling of two phase flow with hysteresis in heterogeneous porous media
Energy Technology Data Exchange (ETDEWEB)
Abreu, E. [Instituto Nacional de Matematica Pura e Aplicada (IMPA), Rio de Janeiro, RJ (Brazil); Furtado, F.; Pereira, F. [University of Wyoming, Laramie, WY (United States). Dept. of Mathematicsatics; Souza, G. [Universidade do Estado do Rio de Janeiro (UERJ), RJ (Brazil)
2008-07-01
Numerical simulators are necessary for the understanding of multiphase flow in porous media in order to optimize hydrocarbon recovery. In this work, the immiscible flow of two incompressible phases, a problem very common in waterflooding of petroleum reservoirs, is considered and numerical simulation techniques are presented. The system of equations which describe this type of flow form a coupled, highly nonlinear system of time-dependent partial differential equations (PDEs). The equation for the saturation of the invading fluid is a convection-dominated, degenerate parabolic PDE whose solutions typically exhibit sharp fronts (i.e., internal layers with strong gradients) and is very difficult to approximate numerically. It is well known that accurate modeling of convective and diffusive processes is one of the most daunting tasks in the numerical approximation of PDEs. Particularly difficult is the case where convection dominates diffusion. Specifically, we consider the injection problem for a model of two-phase (water/oil) flow in a core sample of porous rock, taking into account hysteresis effects in the relative permeability of the oil phase. (author)
Modeling the Impact of Fracture Growth on Fluid Displacements in Deformable Porous Media
Santillán, D.; Cueto-Felgueroso, L.; Juanes, R.
2015-12-01
Coupled flow and geomechanics is a critical research challenge in engineering and the geosciences. The flow of a fluid through a deformable porous media is present in manyenvironmental, industrial, and biological processes,such as the removal of pollutants from underground water bodies, enhanced geothermal systems, unconventional hydrocarbon resources or enhanced oil recovery techniques. However, the injection of a fluid can generate or propagate fractures, which are preferential flow paths. Using numerical simulation, we study the interplay between injection and rock mechanics, and elucidate fracture propagation as a function of injection rate, initial crack topology and mechanical rock properties. Finally, we discuss the role of fracture growth on fluid displacements in porous media. Figure: An example of fracture (in red) propagated in a porous media (in blue)
Large scale flow visualization and anemometry applied to lab on chip models of porous media
Paiola, Johan; Bodiguel, Hugues
2016-01-01
The following is a report on an experimental technique allowing to quantify and map the velocity field with a very high resolution and a simple equipment in large 2D devices. A simple Shlieren technique is proposed to reinforce the contrast in the images and allow you to detect seeded particles that are pixel-sized or even inferior to it. The velocimetry technique that we have reported on is based on auto-correlation functions of the pixel intensity, which we have shown are directly related to the magnitude of the local average velocity. The characteristic time involved in the decorrelation of the signal is proportional to the tracer size and inversely proportional to the average velocity. We have reported on a detailed discussion about the optimization of relevant involved parameters, the spatial resolution and the accuracy of the method. The technique is then applied to a model porous media made of a random channel network. We show that it is highly efficient to determine the magnitude of the flow in each o...
Survey on Efficient Linear Solvers for Porous Media Flow Models on Recent Hardware Architectures
Directory of Open Access Journals (Sweden)
Anciaux-Sedrakian Ani
2014-07-01
Full Text Available In the past few years, High Performance Computing (HPC technologies led to General Purpose Processing on Graphics Processing Units (GPGPU and many-core architectures. These emerging technologies offer massive processing units and are interesting for porous media flow simulators may used for CO2 geological sequestration or Enhanced Oil Recovery (EOR simulation. However the crucial point is “are current algorithms and software able to use these new technologies efficiently?” The resolution of large sparse linear systems, almost ill-conditioned, constitutes the most CPU-consuming part of such simulators. This paper proposes a survey on various solver and preconditioner algorithms, analyzes their efficiency and performance regarding these distinct architectures. Furthermore it proposes a novel approach based on a hybrid programming model for both GPU and many-core clusters. The proposed optimization techniques are validated through a Krylov subspace solver; BiCGStab and some preconditioners like ILU0 on GPU, multi-core and many-core architectures, on various large real study cases in EOR simulation.
Directory of Open Access Journals (Sweden)
Qingdong Zeng
2015-10-01
Full Text Available Fluid-solid coupling is ubiquitous in the process of fluid flow underground and has a significant influence on the development of oil and gas reservoirs. To investigate these phenomena, the coupled mathematical model of solid deformation and fluid flow in fractured porous media is established. In this study, the discrete fracture model (DFM is applied to capture fluid flow in the fractured porous media, which represents fractures explicitly and avoids calculating shape factor for cross flow. In addition, the extended finite element method (XFEM is applied to capture solid deformation due to the discontinuity caused by fractures. More importantly, this model captures the change of fractures aperture during the simulation, and then adjusts fluid flow in the fractures. The final linear equation set is derived and solved for a 2D plane strain problem. Results show that the combination of discrete fracture model and extended finite element method is suited for simulating coupled deformation and fluid flow in fractured porous media.
Santoso, R. K.; Rachmat, S.; Putra, W. D. K.; Resha, A. H.; Hartowo, H.
2017-07-01
Understanding the transport and retention of iron oxide nanoparticles is critical in optimizing electromagnetic heating well stimulation. If the injected concentration or injection rate is too big, nanoparticles can build-up inside the pore throat, which can reduce the permeability of the reservoir. A numerical model has been created to describe the behavior of iron oxide nanoparticles in porous media. The model is coupling material balance equation and fluid flow in porous media equations. There are six parameters to be estimated through matching with experimental data: irreversible attachment rate, reversible attachment rate, irreversible attachment capacity, reversible attachment capacity, reversible detachment rate and permeability. All parameters were obtained directly through coreflooding result in previous study. We add Langmuir static isotherm test to limit the maximum adsorption capacity to provide a better estimation of concentration distribution. We use 1% NaCl solution as the base fluid and 45-50 mesh sand as the porous media. From the Langmuir static isotherm test, the maximum adsorption concentration is determined. Then, coreflooding is conducted using 10 ppm nanofluid and 12 cc/min injection rate. The proposed model is matched with the experimental data and its parameters are consistent with the maximum adsorption capacity provided from the test.
Non-equilibrium dynamical phases of the two-atom Dicke model
Energy Technology Data Exchange (ETDEWEB)
Bhattacherjee, Aranya B.
2014-09-12
In this paper, we investigate the non-equilibrium dynamical phases of the two-atom Dicke model, which can be realized in a two species Bose–Einstein condensate interacting with a single light mode in an optical cavity. Apart from the usual non-equilibrium normal and inverted phases, a non-equilibrium mixed phase is possible which is a combination of normal and inverted phase. A new kind of dynamical phase transition is predicted from non-superradiant mixed phase to the superradiant phase which can be achieved by tuning the two different atom–photon couplings. We also show that a dynamical phase transition from the non-superradiant mixed phase to the superradiant phase is forbidden for certain values of the two atom–photon coupling strengths. - Highlights: • We investigate the non-equilibrium dynamical phases of the two-atom Dicke model. • The dynamical phase diagram reveals a new kind of non-equilibrium mixed phase. • A new kind of dynamical phase transition is predicted from mixed phase to the superradiant phase. • In the dynamical phase diagram of the mixed phase, there are regions where the superradiant phase cannot exist.
Non-equilibrium STLS approach to transport properties of single impurity Anderson model
Rezai, Raheleh; Ebrahimi, Farshad
2014-04-01
In this work, using the non-equilibrium Keldysh formalism, we study the effects of the electron-electron interaction and the electron-spin correlation on the non-equilibrium Kondo effect and the transport properties of the symmetric single impurity Anderson model (SIAM) at zero temperature by generalizing the self-consistent method of Singwi, Tosi, Land, and Sjolander (STLS) for a single-band tight-binding model with Hubbard type interaction to out of equilibrium steady-states. We at first determine in a self-consistent manner the non-equilibrium spin correlation function, the effective Hubbard interaction, and the double-occupancy at the impurity site. Then, using the non-equilibrium STLS spin polarization function in the non-equilibrium formalism of the iterative perturbation theory (IPT) of Yosida and Yamada, and Horvatic and Zlatic, we compute the spectral density, the current-voltage characteristics and the differential conductance as functions of the applied bias and the strength of on-site Hubbard interaction. We compare our spectral densities at zero bias with the results of numerical renormalization group (NRG) and depict the effects of the electron-electron interaction and electron-spin correlation at the impurity site on the aforementioned properties by comparing our numerical result with the order U2 IPT. Finally, we show that the obtained numerical results on the differential conductance have a quadratic universal scaling behavior and the resulting Kondo temperature shows an exponential behavior.
Stochastic Modeling of Non-equilibrium Bedload Transport
Kuai, Z.; Tsai, C. W.
2009-05-01
Traditional stochastic bed load models aimed to solve for the equilibrium bedload transport rate by matching the rate of bed erosion with the rate of deposition. Bedload transport can be in nonequilibrium even under the steady flow condition, as the quantity of moving particles in the bedload layer may vary. In a nonequilibrium condition, the interchange of sediment particles occurs not only between the bedload layer and the bed surface, but also across the interface between bedload and suspended load. The proposed approach attempts to add a new bedload-suspended load interchange layer to a stochastic bedlod transport model based on the Markov chain. The bedload transport rate is the product of the total particle volume in saltation and the average saltating velocity. We can quantify the number of saltating particles by modeling the occupancy probabilities vector of particles staying in three states (i.e., bed surface, bedload layer, and the interchange layer between the bedload and the suspended load.). The new stochastic bedload relation is validated against existing bedload model. The sudden change of flow and/or sediment condition leads to changes in the transition probabilities. The influence of sudden changes in flow-sediment properties on the bedload transport rate is investigated in this preliminary study. It is found that the neglecting the exchange process between the bedload layer and the suspended layer may lead to non-negligible errors in bedload calculation when the flow and/or sediment conditions change.
Interaction of pressure and momentum driven flows with thin porous media: Experiments and modeling
Naaktgeboren, Christian
Flow interaction with thin porous media arise in a variety of natural and man-made settings. Examples include flow through thin grids in electronics cooling, and NOx emissions reduction by means of ammonia injection grids, pulsatile aquatic propulsion with complex trailing anatomy (e.g., jellyfish with tentacles) and microbursts from thunderstorm activity over dense vegetation, unsteady combustion in or near porous materials, pulsatile jet-drying of textiles, and pulsed jet agitation of clothing for trace contaminant sampling. Two types of interactions with thin porous media are considered: (i) forced convection or pressure-driven flows, where fluid advection is maintained by external forces, and (ii) inertial or momentum-driven flows, in which fluid motion is generated but not maintained by external forces. Forced convection analysis through thin permeable media using a porous continuum approach requires the knowledge of porous medium permeability and form coefficients, K and C, respectively, which are defined by the Hazen-Dupuit-Darcy (HDD) equation. Their determination, however, requires the measurement of the pressure-drop per unit of porous medium length. The pressure-drop caused by fluid entering and exiting the porous medium, however, is not related to the porous medium length. Hence, for situations in which the inlet and outlet pressure-drops are not negligible, e.g., for short porous media, the definition of Kand C via the HDD equation becomes ambiguous. This aspect is investigated analytically and numerically using the flow through a restriction in circular pipe and parallel plates channels as preliminary models. Results show that inlet and outlet pressure-drop effects become increasingly important when the inlet and outlet fluid surface fraction φ decreases and the Reynolds number Re increases for both laminar and turbulent flow regimes. A conservative estimate of the minimum porous medium length beyond which the core pressure-drop predominates over the
Modeling hyperelasticity in non-equilibrium multiphase flows
Hank, Sarah; Favrie, Nicolas; Massoni, Jacques
2017-02-01
The aim of this article is the construction of a multiphase hyperelastic model. The Eulerian formulation of the hyperelasticity represents a system of 14 conservative partial differential equations submitted to stationary differential constraints. This model is constructed with an elegant approach where the specific energy is given in separable form. The system admits 14 eigenvalues with 7 characteristic eigenfields. The associated Riemann problem is not easy to solve because of the presence of 7 waves. The shear waves are very diffusive when dealing with the full system. In this paper, we use a splitting approach to solve the whole system using 3 sub-systems. This method reduces the diffusion of the shear waves while allowing to use a classical approximate Riemann solver. The multiphase model is obtained by adapting the discrete equations method. This approach involves an additional equation governing the evolution of a phase function relative to the presence of a phase in a cell. The system is integrated over a multiphase volume control. Finally, each phase admits its own equations system composed of three sub-systems. One and three dimensional test cases are presented.
Mass transfer model of nanoparticle-facilitated contaminant transport in saturated porous media.
Johari, Wan Lutfi Wan; Diamessis, Peter J; Lion, Leonard W
2010-02-01
A one-dimensional model has been evaluated for transport of hydrophobic contaminants, such as polycyclic aromatic hydrocarbon (PAH) compounds, facilitated by synthetic amphiphilic polyurethane (APU) nanoparticles in porous media. APU particles synthesized from poly(ethylene glycol)-modified urethane acrylate (PMUA) precursor chains have been shown to enhance the desorption rate and mobility of phenanthrene (PHEN) in soil. A reversible process governed by attachment and detachment rates was considered to describe the PMUA binding in soil in addition to PMUA transport through advection and dispersion. Ultimately, an irreversible second-order PMUA attachment rate in which the fractional soil saturation capacity with PMUA was a rate control was found to be adequate to describe the retention of PMUA particles. A gamma-distributed site model (GS) was used to describe the spectrum of physical/chemical constraints for PHEN transfer from solid to aqueous phases. Instantaneous equilibrium was assumed for PMUA-PHEN interactions. The coupled model for PMUA and PHEN behavior successfully described the enhanced elution profile of PHEN by PMUA. Sensitivity analysis was performed to analyze the significance of model parameters on model predictions. The adjustable parameter alpha in the gamma-distribution shapes the contaminant desorption distribution profile as well as elution and breakthrough curves. Model simulations show the use of PMUA can be also expected to improve the release rate of PHEN in soils with higher organic carbon content. The percentage removal of PHEN mass over time is shown to be influenced by the concentration of PMUA added and this information can be used to optimize cost and time require to accomplish a desired remediation goal.
Modelling multiphase flow inside the porous media of a polymer electrolyte membrane fuel cell
DEFF Research Database (Denmark)
Berning, Torsten; Kær, Søren Knudsen
2011-01-01
Transport processes inside polymer electrolyte membrane fuel cells (PEMFC’s) are highly complex and involve convective and diffusive multiphase, multispecies flow through porous media along with heat and mass transfer and electrochemical reactions in conjunction with water transport through an el...
Indian Academy of Sciences (India)
Trishikhi Raychoudhury; Vikranth Kumar Surasani
2017-06-01
Retention of surface-modified nanoscale zero-valent iron (NZVI) particles in the porous media near the point of injection has been reported in the recent studies. Retention of excess particles in porous media can alter the media properties. The main objectives of this study are, therefore, to evaluate the effect of particle retention on the porous media properties and its implication on further NZVI particle transport under different flow conditions. To achieve the objectives, a one-dimensional transport model is developed by considering particle deposition, detachment, and straining mechanisms along with the effect of changes in porosity resulting from retention of NZVI particles. Two different flow conditions are considered for simulations. The first is a constant Darcy’s flow rate condition, which assumes a change in porosity, causes a change in pore water velocity and the second, is a constant head condition, which assumes the change in porosity, influence the permeability and hydraulic conductivity (thus Darcy’s flow rate). Overall a rapid decrease in porosity was observed as a result of high particle retention near the injection points resulting in a spatial distribution of deposition rate coefficient. In the case of constant head condition, the spatial distribution of Darcy’s velocities is predicted due to variation in porosity and hydraulic conductivity. The simulation results are compared with the data reported from the field studies; which suggests straining is likely to happen in the real field condition.
Modeling of the Transport and Retention of Fullerene C60 Aggregates in Porous Media
Li, Y.; Wang, Y.; Pennell, K.; Abriola, L.
2008-12-01
Buckminster fullerene (C60) has recently gained wide application in many commercial products. Given its widespread use, release of C60 into the environment during manufacture, transportation, and/or application is likely. Although C60 has negligible solubility in water, it is capable of acquiring charge and form highly stable nano-scale aggregates (nC60) in aqueous systems. In recent years, several laboratory research efforts have been devoted to studying the potential fate and transport of nC60 in porous media representative of the natural subsurface environment. Traditional clean-bed filtration theory is typically applied to analyze the experimental results. Far less attention has focused on the applicability of filtration theory to nC60 transport under different soil and solution conditions. In this work, we simulate column transport of nC60 under progressively more complex conditions and compare with laboratory observations. For nC60 transport in columns packed with Ottawa sand and simple electrolyte solutions, i.e. 1mM CaCl2 and 1mM NaCl, simulation results reveal that traditional clean-bed filtration theory is not sufficient to model the asymmetric breakthrough curves and relatively flat retention profiles observed in these systems. Modification of the filtration model, incorporating a maximum retention capacity term, can provide remarkably improved modeling results. The second application is for transport of nC60 in Ottawa sand coated with surfactant. The observed retention profiles in these experiments exhibit a hyper-exponential feature. Modeling results demonstrate that coupled simulation of both surfactant and nC60 transport is required to correctly capture the hyper-exponential retention profile in these systems. Finally, efforts to model the transport of nC60 in real soils, including Appling and Webster soils, are presented, suggesting that modification of filtration theory is also necessary in this case, to capture the shape of the observed retention
Morales-Casique, E.; Lezama-Campos, J. L.; Guadagnini, A.; Neuman, S. P.
2013-05-01
Modeling tracer transport in geologic porous media suffers from the corrupt characterization of the spatial distribution of hydrogeologic properties of the system and the incomplete knowledge of processes governing transport at multiple scales. Representations of transport dynamics based on a Fickian model of the kind considered in the advection-dispersion equation (ADE) fail to capture (a) the temporal variation associated with the rate of spreading of a tracer, and (b) the distribution of early and late arrival times which are often observed in field and/or laboratory scenarios and are considered as the signature of anomalous transport. Elsewhere we have presented exact stochastic moment equations to model tracer transport in randomly heterogeneous aquifers. We have also developed a closure scheme which enables one to provide numerical solutions of such moment equations at different orders of approximations. The resulting (ensemble) average and variance of concentration fields were found to display a good agreement against Monte Carlo - based simulation results for mildly heterogeneous (or well-conditioned strongly heterogeneous) media. Here we explore the ability of the moment equations approach to describe the distribution of early arrival times and late time tailing effects which can be observed in Monte-Carlo based breakthrough curves (BTCs) of the (ensemble) mean concentration. We show that BTCs of mean resident concentration calculated at a fixed space location through higher-order approximations of moment equations display long tailing features of the kind which is typically associated with anomalous transport behavior and are not represented by an ADE model with constant dispersive parameter, such as the zero-order approximation.
Non-equilibrium Monte Carlo dynamics of the Sherrington-Kirkpatrick mean field spin glass model
Baldassarri, Andrea
1996-01-01
We present a numerical study of the non-equilibrium dynamics of the Sherrington-Kirkpatrick model. We analize the overlap distribution between the configurations visited at the time t and in particular its scaling behaviour with the size of the system. We find two different non-equilibrium dynamical regimes. The first is a proper Out of Equilibrium Regime, that is the relevant regime for the dynamics of an infinite system. The second is an Intermediate Regime that separates the Out of Equilib...
The matrix model, a driven state variables approach to non-equilibrium thermodynamics
Jongschaap, R.J.J.
2001-01-01
One of the new approaches in non-equilibrium thermodynamics is the so-called matrix model of Jongschaap. In this paper some features of this model are discussed. We indicate the differences with the more common approach based upon internal variables and the more sophisticated Hamiltonian and GENERIC
Online Adaptive Local-Global Model Reduction for Flows in Heterogeneous Porous Media
Directory of Open Access Journals (Sweden)
Yalchin Efendiev
2016-06-01
Full Text Available We propose an online adaptive local-global POD-DEIM model reduction method for flows in heterogeneous porous media. The main idea of the proposed method is to use local online indicators to decide on the global update, which is performed via reduced cost local multiscale basis functions. This unique local-global online combination allows (1 developing local indicators that are used for both local and global updates (2 computing global online modes via local multiscale basis functions. The multiscale basis functions consist of offline and some online local basis functions. The approach used for constructing a global reduced system is based on Proper Orthogonal Decomposition (POD Galerkin projection. The nonlinearities are approximated by the Discrete Empirical Interpolation Method (DEIM. The online adaption is performed by incorporating new data, which become available at the online stage. Once the criterion for updates is satisfied, we adapt the reduced system online by changing the POD subspace and the DEIM approximation of the nonlinear functions. The main contribution of the paper is that the criterion for adaption and the construction of the global online modes are based on local error indicators and local multiscale basis function which can be cheaply computed. Since the adaption is performed infrequently, the new methodology does not add significant computational overhead associated with when and how to adapt the reduced basis. Our approach is particularly useful for situations where it is desired to solve the reduced system for inputs or controls that result in a solution outside the span of the snapshots generated in the offline stage. Our method also offers an alternative of constructing a robust reduced system even if a potential initial poor choice of snapshots is used. Applications to single-phase and two-phase flow problems demonstrate the efficiency of our method.
Online Adaptive Local-Global Model Reduction for Flows in Heterogeneous Porous Media
Efendiev, Yalchin R.
2016-06-07
We propose an online adaptive local-global POD-DEIM model reduction method for flows in heterogeneous porous media. The main idea of the proposed method is to use local online indicators to decide on the global update, which is performed via reduced cost local multiscale basis functions. This unique local-global online combination allows (1) developing local indicators that are used for both local and global updates (2) computing global online modes via local multiscale basis functions. The multiscale basis functions consist of offline and some online local basis functions. The approach used for constructing a global reduced system is based on Proper Orthogonal Decomposition (POD) Galerkin projection. The nonlinearities are approximated by the Discrete Empirical Interpolation Method (DEIM). The online adaption is performed by incorporating new data, which become available at the online stage. Once the criterion for updates is satisfied, we adapt the reduced system online by changing the POD subspace and the DEIM approximation of the nonlinear functions. The main contribution of the paper is that the criterion for adaption and the construction of the global online modes are based on local error indicators and local multiscale basis function which can be cheaply computed. Since the adaption is performed infrequently, the new methodology does not add significant computational overhead associated with when and how to adapt the reduced basis. Our approach is particularly useful for situations where it is desired to solve the reduced system for inputs or controls that result in a solution outside the span of the snapshots generated in the offline stage. Our method also offers an alternative of constructing a robust reduced system even if a potential initial poor choice of snapshots is used. Applications to single-phase and two-phase flow problems demonstrate the efficiency of our method.
Energy Technology Data Exchange (ETDEWEB)
Fang, Le [Laboratory of Mathematics and Physics, Ecole Centrale de Pékin, Beihang University, Beijing 100191 (China); Zhu, Ying [Laboratory of Mathematics and Physics, Ecole Centrale de Pékin, Beihang University, Beijing 100191 (China); National Key Laboratory of Science and Technology on Aero-Engine Aero-Thermodynamics, School of Energy and Power Engineering, Beihang University, Beijing 100191 (China); Liu, Yangwei, E-mail: liuyangwei@126.com [National Key Laboratory of Science and Technology on Aero-Engine Aero-Thermodynamics, School of Energy and Power Engineering, Beihang University, Beijing 100191 (China); Lu, Lipeng [National Key Laboratory of Science and Technology on Aero-Engine Aero-Thermodynamics, School of Energy and Power Engineering, Beihang University, Beijing 100191 (China)
2015-10-09
The non-equilibrium property in turbulence is a non-negligible problem in large-eddy simulation but has not yet been systematically considered. The generalization from equilibrium turbulence to non-equilibrium turbulence requires a clear recognition of the non-equilibrium property. As a preliminary step of this recognition, the present letter defines a typical non-equilibrium process, that is, the spectral non-equilibrium process, in homogeneous isotropic turbulence. It is then theoretically investigated by employing the skewness of grid-scale velocity gradient, which permits the decomposition of resolved velocity field into an equilibrium one and a time-reversed one. Based on this decomposition, an improved Smagorinsky model is proposed to correct the non-equilibrium behavior of the traditional Smagorinsky model. The present study is expected to shed light on the future studies of more generalized non-equilibrium turbulent flows. - Highlights: • A spectral non-equilibrium process in isotropic turbulence is defined theoretically. • A decomposition method is proposed to divide a non-equilibrium turbulence field. • An improved Smagorinsky model is proposed to correct the non-equilibrium behavior.
Variational Principle for Non-Equilibrium Steady States of the XX Model
Matsui, T
2003-01-01
We show that non-equilibrium steady states of the one dimensional exactly solved XY model can be characterized by the variational principle of free energy of a long range interaction and that they cannot be a KMS state for any C$^*$-dynamical system.
A Non-Equilibrium Sediment Transport Model for Coastal Inlets and Navigation Channels
2011-01-01
Navigation Channels Alejandro Sánchez† and Weiming Wu‡ ABSTRACT SANCHEZ, A. and WU, W., 2011. A Non-Equilibrium Sediment Transport Model...2009; accessed January 20, 2009). Nicholson, J.; Brøker, I.; Roelvink, J. A.; Price, D.; Tanguy, J. M., and Moreno , L., 1997. Intercomparison of
Aerosol dynamics in porous media
Ghazaryan, Lilya
2014-01-01
In this thesis, a computational model was developed for the simulation of aerosol formation through nucleation, followed by condensation and evaporation and filtration by porous material. Understanding aerosol dynamics in porous media can help improving engineering models that are used in various in
DEFF Research Database (Denmark)
Yuan, Hao; Shapiro, Alexander
There is a considerable and ongoing effort aimed at understanding the transport and the deposition of suspended particles in porous media, especially non-Fickian transport and non-exponential deposition of particles. In this work, the influential parameters in filtration models are studied...... to understand their effects on the non-Fickian transport and the non-exponential deposition. The filtration models are validated by the comparisons between the modelling results and the experimental data.The elliptic equation with distributed filtration coefficients may be applied to model non-Fickian transport...... and hyperexponential deposition. The filtration model accounting for the migration of surface associated particles may be applied for non-monotonic deposition....
Modelling non-equilibrium thermodynamic systems from the speed-gradient principle
Khantuleva, Tatiana A.; Shalymov, Dmitry S.
2017-03-01
The application of the speed-gradient (SG) principle to the non-equilibrium distribution systems far away from thermodynamic equilibrium is investigated. The options for applying the SG principle to describe the non-equilibrium transport processes in real-world environments are discussed. Investigation of a non-equilibrium system's evolution at different scale levels via the SG principle allows for a fresh look at the thermodynamics problems associated with the behaviour of the system entropy. Generalized dynamic equations for finite and infinite number of constraints are proposed. It is shown that the stationary solution to the equations, resulting from the SG principle, entirely coincides with the locally equilibrium distribution function obtained by Zubarev. A new approach to describe time evolution of systems far from equilibrium is proposed based on application of the SG principle at the intermediate scale level of the system's internal structure. The problem of the high-rate shear flow of viscous fluid near the rigid plane plate is discussed. It is shown that the SG principle allows closed mathematical models of non-equilibrium processes to be constructed. This article is part of the themed issue 'Horizons of cybernetical physics'.
Edrisi, Siroos; Bidhendi, Norollah Kasiri; Haghighi, Maryam
2017-01-01
Effective thermal conductivity of the porous media was modeled based on a self-consistent method. This model estimates the heat transfer between insulator surface and air cavities accurately. In this method, the pore size and shape, the temperature gradient and other thermodynamic properties of the fluid was taken into consideration. The results are validated by experimental data for fire bricks used in cracking furnaces at the olefin plant of Maroon petrochemical complexes well as data published for polyurethane foam (synthetic polymers) IPTM and IPM. The model predictions present a good agreement against experimental data with thermal conductivity deviating <1 %.
Hu, Mengsu; Rutqvist, Jonny; Wang, Yuan
2016-11-01
In this study, a numerical manifold method (NMM) model is developed to analyze flow in porous media with discrete fractures in a non-conforming mesh. This new model is based on a two-cover-mesh system with a uniform triangular mathematical mesh and boundary/fracture-divided physical covers, where local independent cover functions are defined. The overlapping parts of the physical covers are elements where the global approximation is defined by the weighted average of the physical cover functions. The mesh is generated by a tree-cutting algorithm. A new model that does not introduce additional degrees of freedom (DOF) for fractures was developed for fluid flow in fractures. The fracture surfaces that belong to different physical covers are used to represent fracture flow in the direction of the fractures. In the direction normal to the fractures, the fracture surfaces are regarded as Dirichlet boundaries to exchange fluxes with the rock matrix. Furthermore, fractures that intersect with Dirichlet or Neumann boundaries are considered. Simulation examples are designed to verify the efficiency of the tree-cutting algorithm, the calculation's independency from the mesh orientation, and accuracy when modeling porous media that contain fractures with multiple intersections and different orientations. The simulation results show good agreement with available analytical solutions. Finally, the model is applied to cases that involve nine intersecting fractures and a complex network of 100 fractures, both of which achieve reasonable results. The new model is very practical for modeling flow in fractured porous media, even for a geometrically complex fracture network with large hydraulic conductivity contrasts between fractures and the matrix.
Jazayeri Shoushtari, Seyed Mohammad Hossein; Cartwright, Nick
2016-11-01
This paper examines the influence of porous media deformation on water-table wave dispersion in an unconfined aquifer using a numerical model which couples Richards' equation to the poro-elastic model. The study was motivated by the findings of Shoushtari et al. (J Hydrol 533:412-440, 2016) who were unable to reproduce the observed wave dispersion in their sand flume data with either numerical Richards' equation models (assuming rigid porous media) or existing analytic solutions. The water-table wave dispersion is quantified via the complex wave number extracted from the predicted amplitude and phase profiles. A sensitivity analysis was performed to establish the influence of the main parameters in the poro-elastic model, namely Young's modulus (E) and Poisson's ratio (ν). For a short oscillation period (T = 16.4 s), the phase lag increase rate (k i) is sensitive to the chosen values of E and ν, demonstrating an inverse relationship with both parameters. Changes in the amplitude decay rate (k r), however, were negligible. For a longer oscillation period (T = 908.6 s), variations in the values of E and ν resulted in only small changes in both k r and k i. In both the short and long period cases, the poro-elastic model is unable to reproduce the observed wave dispersion in the existing laboratory data. Hence porous media deformation cannot explain the additional energy dissipation in the laboratory data. Shoushtari SMH, Cartwright N, Perrochet P, Nielsen P (2016) The effects of oscillation period on groundwater wave dispersion in a sandy unconfined aquifer: sand flume experiments and modelling. J Hydrol 533:412-440.
Jazayeri Shoushtari, Seyed Mohammad Hossein; Cartwright, Nick
2017-03-01
This paper examines the influence of porous media deformation on water-table wave dispersion in an unconfined aquifer using a numerical model which couples Richards' equation to the poro-elastic model. The study was motivated by the findings of Shoushtari et al. (J Hydrol 533:412-440, 2016) who were unable to reproduce the observed wave dispersion in their sand flume data with either numerical Richards' equation models (assuming rigid porous media) or existing analytic solutions. The water-table wave dispersion is quantified via the complex wave number extracted from the predicted amplitude and phase profiles. A sensitivity analysis was performed to establish the influence of the main parameters in the poro-elastic model, namely Young's modulus ( E) and Poisson's ratio ( ν). For a short oscillation period ( T = 16.4 s), the phase lag increase rate ( k i) is sensitive to the chosen values of E and ν, demonstrating an inverse relationship with both parameters. Changes in the amplitude decay rate ( k r), however, were negligible. For a longer oscillation period ( T = 908.6 s), variations in the values of E and ν resulted in only small changes in both k r and k i. In both the short and long period cases, the poro-elastic model is unable to reproduce the observed wave dispersion in the existing laboratory data. Hence porous media deformation cannot explain the additional energy dissipation in the laboratory data. Shoushtari SMH, Cartwright N, Perrochet P, Nielsen P (2016) The effects of oscillation period on groundwater wave dispersion in a sandy unconfined aquifer: sand flume experiments and modelling. J Hydrol 533:412-440.
Reactive transport modeling in variably saturated porous media with OGS-IPhreeqc
He, W.; Beyer, C.; Fleckenstein, J. H.; Jang, E.; Kalbacher, T.; Shao, H.; Wang, W.; Kolditz, O.
2014-12-01
Worldwide, sustainable water resource management becomes an increasingly challenging task due to the growth of population and extensive applications of fertilizer in agriculture. Moreover, climate change causes further stresses to both water quantity and quality. Reactive transport modeling in the coupled soil-aquifer system is a viable approach to assess the impacts of different land use and groundwater exploitation scenarios on the water resources. However, the application of this approach is usually limited in spatial scale and to simplified geochemical systems due to the huge computational expense involved. Such computational expense is not only caused by solving the high non-linearity of the initial boundary value problems of water flow in the unsaturated zone numerically with rather fine spatial and temporal discretization for the correct mass balance and numerical stability, but also by the intensive computational task of quantifying geochemical reactions. In the present study, a flexible and efficient tool for large scale reactive transport modeling in variably saturated porous media and its applications are presented. The open source scientific software OpenGeoSys (OGS) is coupled with the IPhreeqc module of the geochemical solver PHREEQC. The new coupling approach makes full use of advantages from both codes: OGS provides a flexible choice of different numerical approaches for simulation of water flow in the vadose zone such as the pressure-based or mixed forms of Richards equation; whereas the IPhreeqc module leads to a simplification of data storage and its communication with OGS, which greatly facilitates the coupling and code updating. Moreover, a parallelization scheme with MPI (Message Passing Interface) is applied, in which the computational task of water flow and mass transport is partitioned through domain decomposition, whereas the efficient parallelization of geochemical reactions is achieved by smart allocation of computational workload over
An Analysis on Groundwater Recharge by Mathematical Model in Inclined Porous Media.
Pathak, Shreekant P; Singh, Twinkle
2014-01-01
The present paper discusses the analysis of solution of groundwater flow in inclined porous media. The problem related to groundwater flow in inclined aquifers is usually common in geotechnical and hydrogeology engineering activities. The governing partial differential equation of one-dimensional groundwater recharge problem has been formed by Dupuit's assumption. Three cases have been discussed with suitable boundary conditions and different slopes of impervious incline boundary. The numerical as well as graphical interpretation has been given and its coding is done in MATLAB.
Wang, W.; Zehner, B.; Böttcher, N.; Goerke, U.; Kolditz, O.
2013-12-01
Numerical modeling of the two-phase flow process in porous media for real applications, e.g. CO2 storage processes in saline aquifers, is computationally expensive due to the complexity and the non-linearity of the observed physical processes. In such modeling, a fine discretization of the considered domain is normally needed for a high degree of accuracy, and it leads to the requirement of extremely high computational resources. This work focuses on the parallel simulation of the two-phase flow process in porous media. The Galerkin finite element method is used to solve the governing equations. Based on the overlapping domain decomposition approach, the PETSc package is employed to parallelize the global equation assembly and the linear solver, respectively. A numerical model based on the real test site Ketzin in Germany is adopted for parallel computing. The model domain is discretized with more than four million tetrahedral elements. The parallel simulations are carried out on a Linux cluster with different number of cores. The obtained speedup shows a good scalability of the current parallel finite element approach of the two-phase flow modeling in geological CO2 storage applications.
A Tightly Coupled Non-Equilibrium Magneto-Hydrodynamic Model for Inductively Coupled RF Plasmas
2016-02-29
effects are described based on a hybrid State-to-State (StS) approach. A multi-temperature formulation is used to account for thermal non-equilibrium...for Inductively Coupled Radio-Frequency (RF) Plasmas. Non Local Thermodynamic Equilibrium (NLTE) effects are described based on a hybrid State-to-State...usually obtained through quantum chemistry calculations51–56 or through phenomenological models providing a simplified descrip- tion of the kinetic
Raeini, Ali Q.; Bijeljic, Branko; Blunt, Martin J.
2017-07-01
A generalized network extraction workflow is developed for parameterizing three-dimensional (3D) images of porous media. The aim of this workflow is to reduce the uncertainties in conventional network modeling predictions introduced due to the oversimplification of complex pore geometries encountered in natural porous media. The generalized network serves as a coarse discretization of the surface generated from a medial-axis transformation of the 3D image. This discretization divides the void space into individual pores and then subdivides each pore into sub-elements called half-throat connections. Each half-throat connection is further segmented into corners by analyzing the medial axis curves of its axial plane. The parameters approximating each corner—corner angle, volume, and conductivity—are extracted at different discretization levels, corresponding to different wetting layer thickness and local capillary pressures during multiphase flow simulations. Conductivities are calculated using direct single-phase flow simulation so that the network can reproduce the single-phase flow permeability of the underlying image exactly. We first validate the algorithm by using it to discretize synthetic angular pore geometries and show that the network model reproduces the corner angles accurately. We then extract network models from micro-CT images of porous rocks and show that the network extraction preserves macroscopic properties, the permeability and formation factor, and the statistics of the micro-CT images.
Tecklenburg, Jan; Neuweiler, Insa; Carrera, Jesus; Dentz, Marco
2016-05-01
We study modeling of two-phase flow in highly heterogeneous fractured and porous media. The flow behaviour is strongly influenced by mass transfer between a highly permeable (mobile) fracture domain and less permeable (immobile) matrix blocks. We quantify the effective two-phase flow behavior using a multirate rate mass transfer (MRMT) approach. We discuss the range of applicability of the MRMT approach in terms of the pertinent viscous and capillary diffusion time scales. We scrutinize the linearization of capillary diffusion in the immobile regions, which allows for the formulation of MRMT in the form of a non-local single equation model. The global memory function, which encodes mass transfer between the mobile and the immobile regions, is at the center of this method. We propose two methods to estimate the global memory function for a fracture network with given fracture and matrix geometry. Both employ a scaling approach based on the known local memory function for a given immobile region. With the first method, the local memory function is calculated numerically, while the second one employs a parametric memory function in form of truncated power-law. The developed concepts are applied and tested for fracture networks of different complexity. We find that both physically based parameter estimation methods for the global memory function provide predictive MRMT approaches for the description of multiphase flow in highly heterogeneous porous media.
Negara, Ardiansyah
2015-05-01
Anisotropy of hydraulic properties of the subsurface geologic formations is an essential feature that has been established as a consequence of the different geologic processes that undergo during the longer geologic time scale. With respect to subsurface reservoirs, in many cases, anisotropy plays significant role in dictating the direction of flow that becomes no longer dependent only on driving forces like the pressure gradient and gravity but also on the principal directions of anisotropy. Therefore, there has been a great deal of motivation to consider anisotropy into the subsurface flow and transport models. In this dissertation, we present subsurface flow modeling in single and dual continuum anisotropic porous media, which include the single-phase groundwater flow coupled with the solute transport in anisotropic porous media, the two-phase flow with gravity effect in anisotropic porous media, and the natural gas flow in anisotropic shale reservoirs. We have employed the multipoint flux approximation (MPFA) method to handle anisotropy in the flow model. The MPFA method is designed to provide correct discretization of the flow equations for general orientation of the principal directions of the permeability tensor. The implementation of MPFA method is combined with the experimenting pressure field approach, a newly developed technique that enables the solution of the global problem breaks down into the solution of multitude of local problems. The numerical results of the study demonstrate the significant effects of anisotropy of the subsurface formations. For the single-phase groundwater flow coupled with the solute transport modeling in anisotropic porous media, the results shows the strong impact of anisotropy on the pressure field and the migration of the solute concentration. For the two-phase flow modeling with gravity effect in anisotropic porous media, it is observed that the buoyancy-driven flow, which emerges due to the density differences between the
Pore network and pore scale modeling of reactive transport in porous media
Adler, P. M.; Vu, T. M.; Varloteaux, C.; Bekri, S.
2012-12-01
The study of the evolution of a porous medium where a reactive fluid flows is conditioned by the accurate determination of three macroscopic parameters governing the solute displacement, namely the solute velocity, dispersion and mean reaction rate. Of course, a possible application of such studies is CO2 sequestration. This presentation proposes to approach the determination of these parameters by two different ways and to compare them; both are on the pore scale. In the first one called PNM (for pore-network model), a pore-network is extracted from micro tomography images of a real porous medium. This network is composed of spherical pores joined by circular tubes; it is used to calculate transport macroscopic parameters and porosity-permeability evolution during the reactive transport flow as functions of dimensionless numbers representing the reaction and flow rate regimes. The flow is calculated by using Kirchhoff laws. Transport is determined in the asymptotic regime where the solute concentration undergoes an exponential evolution with time. In the second approach called PSM (for pore scale model), the pore-network model is used as a three dimensional medium which is discretized by the Level Set Method. The Stokes equations are solved in order to determine the local flow field and the corresponding permeability. The solute concentration is obtained by solving the local convection-diffusion equation in the 3D pore-network; numerical dispersion is reduced by a Flux Limiting Scheme. Two different geometries of porous media are addressed by both numerical codes. The first pore-network geometry is used to validate the PNM assumptions, whereas the second pore-network is defined for a better understanding of the dominant solute distribution. One of the main results obtained with the first pore-network is the dependence of the concentration profile on the Péclet number Pe in the pore-bodies. When this number increases, one has to switch from an assumption of
From micro-scale 3D simulations to macro-scale model of periodic porous media
Crevacore, Eleonora; Tosco, Tiziana; Marchisio, Daniele; Sethi, Rajandrea; Messina, Francesca
2015-04-01
In environmental engineering, the transport of colloidal suspensions in porous media is studied to understand the fate of potentially harmful nano-particles and to design new remediation technologies. In this perspective, averaging techniques applied to micro-scale numerical simulations are a powerful tool to extrapolate accurate macro-scale models. Choosing two simplified packing configurations of soil grains and starting from a single elementary cell (module), it is possible to take advantage of the periodicity of the structures to reduce the computation costs of full 3D simulations. Steady-state flow simulations for incompressible fluid in laminar regime are implemented. Transport simulations are based on the pore-scale advection-diffusion equation, that can be enriched introducing also the Stokes velocity (to consider the gravity effect) and the interception mechanism. Simulations are carried on a domain composed of several elementary modules, that serve as control volumes in a finite volume method for the macro-scale method. The periodicity of the medium involves the periodicity of the flow field and this will be of great importance during the up-scaling procedure, allowing relevant simplifications. Micro-scale numerical data are treated in order to compute the mean concentration (volume and area averages) and fluxes on each module. The simulation results are used to compare the micro-scale averaged equation to the integral form of the macroscopic one, making a distinction between those terms that could be computed exactly and those for which a closure in needed. Of particular interest it is the investigation of the origin of macro-scale terms such as the dispersion and tortuosity, trying to describe them with micro-scale known quantities. Traditionally, to study the colloidal transport many simplifications are introduced, such those concerning ultra-simplified geometry that usually account for a single collector. Gradual removal of such hypothesis leads to a
Debbaut, Charlotte; Vierendeels, Jan; Siggers, Jennifer H; Repetto, Rodolfo; Monbaliu, Diethard; Segers, Patrick
2014-01-01
The hepatic blood circulation is complex, particularly at the microcirculatory level. Previously, 2D liver lobule models using porous media and a 3D model using real sinusoidal geometries have been developed. We extended these models to investigate the role of vascular septa (VS) and anisotropic permeability. The lobule was modelled as a hexagonal prism (with or without VS) and the tissue was treated as a porous medium (isotropic or anisotropic permeability). Models were solved using computational fluid dynamics. VS inclusion resulted in more spatially homogeneous perfusion. Anisotropic permeability resulted in a larger axial velocity component than isotropic permeability. A parameter study revealed that results are most sensitive to the lobule size and radial pressure drop. Our model provides insight into hepatic microhaemodynamics, and suggests that inclusion of VS in the model leads to perfusion patterns that are likely to reflect physiological reality. The model has potential for applications to unphysiological and pathological conditions.
Modeling the Impact of Deformation on Unstable Miscible Displacements in Porous Media
Santillán, D.; Cueto-Felgueroso, L.
2014-12-01
Coupled flow and geomechanics is a critical research challenge in engineering and the geosciences. The simultaneous flow of two or more fluids with different densities or viscosities through deformable media is ubiquitous in environmental, industrial, and biological processes, including the removal of non-aqueous phase liquids from underground water bodies, the geological storage of CO2, and current challenges in energy technologies, such as enhanced geothermal systems, unconventional hydrocarbon resources or enhanced oil recovery techniques. Using numerical simulation, we study the interplay between viscous-driven flow instabilities (viscous fingering) and rock mechanics, and elucidate the structure of the displacement patterns as a function of viscosity contrast, injection rate and rock mechanical properties. Finally, we discuss the role of medium deformation on transport and mixing processes in porous media.
Ilyasov, A. M.; Bulgakova, G. T.
2016-08-01
This paper describes a mathematical model of the main fracture isolation in porous media by water-based mature gels. While modeling injection, water infiltration from the gel pack through fracture walls is taking into account, due to which the polymer concentration changes and the residual water resistance factor changes as a consequence. The salutation predicts velocity and pressure fields of the non-Newtonian incompressible fluid filtration for conditions of a non-deformable formation as well as a gel front trajectory in the fracture. The mathematical model of agent injection into the main fracture is based on the fundamental laws of continuum mechanics conservation describing the flow of non-Newtonian and Newtonian fluids separated by an interface plane in a flat channel with permeable walls. The mathematical model is based on a one-dimensional isothermal approximation, with dynamic parameters pressure and velocity, averaged over the fracture section.
General multi-group macroscopic modeling for thermo-chemical non-equilibrium gas mixtures
Liu, Yen; Panesi, Marco; Sahai, Amal; Vinokur, Marcel
2015-04-01
This paper opens a new door to macroscopic modeling for thermal and chemical non-equilibrium. In a game-changing approach, we discard conventional theories and practices stemming from the separation of internal energy modes and the Landau-Teller relaxation equation. Instead, we solve the fundamental microscopic equations in their moment forms but seek only optimum representations for the microscopic state distribution function that provides converged and time accurate solutions for certain macroscopic quantities at all times. The modeling makes no ad hoc assumptions or simplifications at the microscopic level and includes all possible collisional and radiative processes; it therefore retains all non-equilibrium fluid physics. We formulate the thermal and chemical non-equilibrium macroscopic equations and rate coefficients in a coupled and unified fashion for gases undergoing completely general transitions. All collisional partners can have internal structures and can change their internal energy states after transitions. The model is based on the reconstruction of the state distribution function. The internal energy space is subdivided into multiple groups in order to better describe non-equilibrium state distributions. The logarithm of the distribution function in each group is expressed as a power series in internal energy based on the maximum entropy principle. The method of weighted residuals is applied to the microscopic equations to obtain macroscopic moment equations and rate coefficients succinctly to any order. The model's accuracy depends only on the assumed expression of the state distribution function and the number of groups used and can be self-checked for accuracy and convergence. We show that the macroscopic internal energy transfer, similar to mass and momentum transfers, occurs through nonlinear collisional processes and is not a simple relaxation process described by, e.g., the Landau-Teller equation. Unlike the classical vibrational energy
General multi-group macroscopic modeling for thermo-chemical non-equilibrium gas mixtures
Energy Technology Data Exchange (ETDEWEB)
Liu, Yen, E-mail: yen.liu@nasa.gov; Vinokur, Marcel [NASA Ames Research Center, Moffett Field, California 94035 (United States); Panesi, Marco; Sahai, Amal [University of Illinois, Urbana-Champaign, Illinois 61801 (United States)
2015-04-07
This paper opens a new door to macroscopic modeling for thermal and chemical non-equilibrium. In a game-changing approach, we discard conventional theories and practices stemming from the separation of internal energy modes and the Landau-Teller relaxation equation. Instead, we solve the fundamental microscopic equations in their moment forms but seek only optimum representations for the microscopic state distribution function that provides converged and time accurate solutions for certain macroscopic quantities at all times. The modeling makes no ad hoc assumptions or simplifications at the microscopic level and includes all possible collisional and radiative processes; it therefore retains all non-equilibrium fluid physics. We formulate the thermal and chemical non-equilibrium macroscopic equations and rate coefficients in a coupled and unified fashion for gases undergoing completely general transitions. All collisional partners can have internal structures and can change their internal energy states after transitions. The model is based on the reconstruction of the state distribution function. The internal energy space is subdivided into multiple groups in order to better describe non-equilibrium state distributions. The logarithm of the distribution function in each group is expressed as a power series in internal energy based on the maximum entropy principle. The method of weighted residuals is applied to the microscopic equations to obtain macroscopic moment equations and rate coefficients succinctly to any order. The model’s accuracy depends only on the assumed expression of the state distribution function and the number of groups used and can be self-checked for accuracy and convergence. We show that the macroscopic internal energy transfer, similar to mass and momentum transfers, occurs through nonlinear collisional processes and is not a simple relaxation process described by, e.g., the Landau-Teller equation. Unlike the classical vibrational energy
Dong, Chen
2011-01-01
A mathematical model for contaminant species passing through fractured porous media is presented. In the numerical model, we combine two locally conservative methods; i.e., the mixed finite-element (MFE) method and the finite-volume method. Adaptive triangle mesh is used for effective treatment of the fractures. A hybrid MFE method is employed to provide an accurate approximation of velocity fields for both the fractures and matrix, which are crucial to the convection part of the transport equation. The finite-volume method and the standard MFE method are used to approximate the convection and dispersion terms, respectively. The temporary evolution for the pressure distributions, streamline fields, and concentration profiles are obtained for six different arrangements of fractures. The results clearly show the distorted concentration effects caused by the ordered and disordered (random) patterns of the fractures and illustrate the robustness and efficiency of the proposed numerical model. © 2011 by Begell House Inc.
Two-Temperature Model of non-equilibrium electron relaxation: A Review
Singh, Navinder
2007-01-01
The present paper is a review of the phenomena related to non-equilibrium electron relaxation in bulk and nano-scale metallic samples. The workable Two-Temperature Model (TTM) based on Boltzmann-Bloch-Peierls (BBP) kinetic equation has been applied to study the ultra-fast(femto-second) electronic relaxation in various metallic systems. The advent of new ultra-fast (femto-second) laser technology and pump-probe spectroscopy has produced wealth of new results for micro and nano-scale electronic...
Two-Temperature Model of non-equilibrium electron relaxation: A Review
Singh, Navinder
2007-01-01
The present paper is a review of the phenomena related to non-equilibrium electron relaxation in bulk and nano-scale metallic samples. The workable Two-Temperature Model (TTM) based on Boltzmann-Bloch-Peierls (BBP) kinetic equation has been applied to study the ultra-fast(femto-second) electronic relaxation in various metallic systems. The advent of new ultra-fast (femto-second) laser technology and pump-probe spectroscopy has produced wealth of new results for micro and nano-scale electronic...
A non-equilibrium picture of the chemical freeze-out in hadronic thermal models
De Assis, Leonardo P G; Chiapparini, Marcelo; Hirsch, Luciana R; Delfino, Antonio
2012-01-01
Thermal models have proven to be an useful and simple tool used to make theoretical predictions and data analysis in relativistic and ultra-relativistic heavy ion collisions. A new version of these models is presented here, incorporating a non equilibrium feature to the description of the intermediate fireball state formed at the chemical freeze-out. Two different effective temperatures are attributed to the expanding fireball, regarding its baryonic and mesonic sectors. The proposal is not merely to include an additional degree of freedom to reach a better adjustment to the data, but to open a room in the model conception for considerations on the non-equilibrium scenario of the system evolution. A set of well consolidated data for particles production is used to validated the reformulated version of thermal models presented here. A rather good performance of the extended version was verified, both for the quality of particle ratio data fittings as well as for describing the asymptotic energy behavior of tem...
Chang, J.; Nakshatrala, K.
2014-12-01
It is well know that the standard finite element methods, in general, do not satisfy element-wise mass/species balance properties. It is, however, desirable to have element-wide mass balance property in subsurface modeling. Several studies over the years have aimed to overcome this drawback of finite element formulations. Currently, a post-processing optimization-based methodology is commonly employed to recover the local mass balance for porous media models. However, such a post-processing technique does not respect the underlying variational structure that the finite element formulation may enjoy. Motivated by this, a consistent methodology to satisfy element-wise local mass balance for porous media models is constructed using convex optimization techniques. The assembled system of global equations is reconstructed into a quadratic programming problem subjected to bounded equality constraints that ensure conservation at the element level. The proposed methodology can be applied to any computational mesh and to any non-locally conservative nodal-based finite element method. Herein, we integrate our proposed methodology into the framework of the classical mixed Galerkin formulation using Taylor-Hood elements and the least-squares finite element formulation. Our numerical studies will include computational cost, numerical convergence, and comparision with popular methods. In particular, it will be shown that the accuracy of the solutions is comparable with that of several popular locally conservative finite element formulations like the lowest order Raviart-Thomas formulation. We believe the proposed optimization-based approach is a viable approach to preserve local mass balance on general computational grids and is amenable for large-scale parallel implementation.
Rubino, J. G.; Holliger, K.
2010-12-01
The classical version of the theory of poro-elasticity assumes that wave-induced fluid movements at the macroscopic scale, as defined by the prevailing wavelengths, are the only causes of seismic velocity dispersion and attenuation in porous media. Correspondingly, the probed material is implicitly supposed to be homogeneous at the microscopic and mesoscopic scales and all poro-elastic moduli are real-valued and independent of frequency. By now, there is, however, consistent evidence to demonstrate that, on their own, the physical mechanisms of classical poro-elasticity are unable to account for the attenuation behavior inferred from seismic observations. There is also increasing evidence indicating that structural and/or compositional heterogeneity at the mesoscopic scale is likely to be capable of explaining much of the excess attenuation observed in real data. Numerical modeling of poro-elastic seismic wave propagation in general and in the presence of mesoscopic heterogeneities in particular is inherently difficult. For this reason, most available work on this topic considers simplified geometries, such as periodically layered, binary distribution of the physical properties of the rock frame and/or the saturating pore fluids or mixtures of two porous phases characterized by a single dominant length scale. While such models have greatly contributed to a better conceptual understanding and quantification of the observed attenuation of seismic waves in porous media, they are often inadequate to account for specific geological and/or petrophysical details of a given situation. A primary reason for this is that to a first approximation many, if not most, typical porous rocks are characterized by continuous, scale-invariant distributions of the hydraulic and elastic material parameters as well as by continuously varying saturation levels. Mesoscopic heterogeneity of this type is not amenable to direct numerical modeling and we therefore address this problem through a
Modeling research on the response of geoelectric fields in a porous media seepage process
Zhou, Haitao; Gong, Xulong; Sun, Qiang; Yao, Yahui; Zhang, Rui
2017-03-01
Water seepage in rock and soil is a main inducing factor of accidents in many engineering fields such as tunnel engineering, mineral resource exploitation, and rock slopes. Water migration in rock and soil can lead to abnormal geoelectric fields due to the effects of diffusion, adsorption, filtration, and oxidation. This makes it possible to research the seepage law in porous media by measuring the response of geoelectric fields in this process. In this work, we carry out a physical simulation experiment to study the geoelectric field response occurring in the water-migration process. By analyzing the response of first electric potential, spontaneous potentials, and exciting current, we find that both the spontaneous potential and exciting current can reflect the change of seepage flow during the water-infiltration process. The exciting current and first electric potential is applicable to the seepage research on heterogeneous rock and soil, for they can accurately determine the position and velocity of the seepage. Real-time apparent resistivity not only indicates the infiltration area but also reflects the relative water content, i.e., the seepage reached saturation along with the reduction of the apparent resistivity.
A tightly coupled non-equilibrium model for inductively coupled radio-frequency plasmas
Energy Technology Data Exchange (ETDEWEB)
Munafò, A., E-mail: munafo@illinois.edu; Alfuhaid, S. A., E-mail: alfuhai2@illinois.edu; Panesi, M., E-mail: mpanesi@illinois.edu [Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, Talbot Laboratory, 104 S. Wright St., Urbana, Illinois 61801 (United States); Cambier, J.-L., E-mail: jean-luc.cambier@us.af.mil [Edwards Air Force Base Research Laboratory, 10 E. Saturn Blvd., Edwards AFB, California 93524 (United States)
2015-10-07
The objective of the present work is the development of a tightly coupled magneto-hydrodynamic model for inductively coupled radio-frequency plasmas. Non Local Thermodynamic Equilibrium (NLTE) effects are described based on a hybrid State-to-State approach. A multi-temperature formulation is used to account for thermal non-equilibrium between translation of heavy-particles and vibration of molecules. Excited electronic states of atoms are instead treated as separate pseudo-species, allowing for non-Boltzmann distributions of their populations. Free-electrons are assumed Maxwellian at their own temperature. The governing equations for the electro-magnetic field and the gas properties (e.g., chemical composition and temperatures) are written as a coupled system of time-dependent conservation laws. Steady-state solutions are obtained by means of an implicit Finite Volume method. The results obtained in both LTE and NLTE conditions over a broad spectrum of operating conditions demonstrate the robustness of the proposed coupled numerical method. The analysis of chemical composition and temperature distributions along the torch radius shows that: (i) the use of the LTE assumption may lead to an inaccurate prediction of the thermo-chemical state of the gas, and (ii) non-equilibrium phenomena play a significant role close the walls, due to the combined effects of Ohmic heating and macroscopic gradients.
THERMAL NON-EQUILIBRIUM REVISITED: A HEATING MODEL FOR CORONAL LOOPS
Energy Technology Data Exchange (ETDEWEB)
Lionello, Roberto; Linker, Jon A.; Mikic, Zoran [Predictive Science, Inc., 9990 Mesa Rim Rd., Ste. 170, San Diego, CA 92121-2910 (United States); Winebarger, Amy R. [NASA Marshall Space Flight Center, ZP 13, Huntsville, AL 35812 (United States); Mok, Yung, E-mail: lionel@predsci.com, E-mail: linkerj@predsci.com, E-mail: mikicz@predsci.com, E-mail: amy.r.winebarger@nasa.gov, E-mail: ymok@uci.edu [Department of Physics and Astronomy, University of California, 4129 Reines Hall, Irvine, CA 92697 (United States)
2013-08-20
The location and frequency of events that heat the million-degree corona are still a matter of debate. One potential heating scenario is that the energy release is effectively steady and highly localized at the footpoints of coronal structures. Such an energy deposition drives thermal non-equilibrium solutions in the hydrodynamic equations in longer loops. This heating scenario was considered and discarded by Klimchuk et al. on the basis of their one-dimensional simulations as incapable of reproducing observational characteristics of loops. In this paper, we use three-dimensional simulations to generate synthetic emission images, from which we select and analyze six loops. The main differences between our model and that of Klimchuk et al. concern (1) dimensionality, (2) resolution, (3) geometrical properties of the loops, (4) heating function, and (5) radiative function. We find evidence, in this small set of simulated loops, that the evolution of the light curves, the variation of temperature along the loops, the density profile, and the absence of small-scale structures are compatible with the characteristics of observed loops. We conclude that quasi-steady footpoint heating that drives thermal non-equilibrium solutions cannot yet be ruled out as a viable heating scenario for EUV loops.
A parametrized non-equilibrium wall-model for large-eddy simulations
Hickel, Stefan; Bodart, Julien; Larsson, Johan
2015-01-01
Wall-models are essential for enabling large-eddy simulations (LESs) of realistic problems at high Reynolds numbers. The present study is focused on approaches that directly model the wall shear stress, specifically on filling the gap between models based on wall-normal ordinary differential equations (ODEs) that assume equilibrium and models based on full partial differential equations (PDEs) that do not. We develop ideas for how to incorporate non-equilibrium effects (most importantly, strong pressure-gradient effects) in the wall-model while still solving only wall-normal ODEs. We test these ideas using two reference databases: an adverse pressure-gradient turbulent boundary-layer and a shock/boundary-layer interaction problem, both of which lead to separation and re-attachment of the turbulent boundary layer.
Energy Technology Data Exchange (ETDEWEB)
Salehi, N.
1996-04-19
This study deals with the retention mechanisms of colloidal particles in porous media flows, and the subsequent reduction in permeability in the case of stable and non adsorbing colloids. It combines experimental results and modelling. This study has been realised with stable dispersion of monodispersed carboxylate polystyrene latexes negatively charged injected through negatively charged polycarbonate membranes having mono-sized cylindrical pores. The mean particle diameter is smaller than the mean pore diameter. Both batch and flow experiments in Nuclepore membranes have been done. The results of batch experiments have proved no adsorption of the colloidal latex particles on the surface of the Nuclepore membranes without flow at low salinity. In flow experiments at low particle concentration, only deposition on the upstream side of the membrane have been induced by hydrodynamic forces even for non adsorbing particles without creating any permeability reduction. The retention levels are zero at low and high Peclet numbers with a maximum at intermediate values. Partial plugging was observed at higher colloid concentration even at low salinity without any upstream surface deposition. The modelling of plugging processes is achieved by considering the particle concentration, fluid rate and ratio between the mean pore diameter and the mean particle diameter. This study can be particularly useful in the fields of water treatment and of restoration of lands following radioactive contamination. (author). 96 refs., 99 figs., 29 tabs.
Microscopic Simulation and Macroscopic Modeling for Thermal and Chemical Non-Equilibrium
Liu, Yen; Panesi, Marco; Vinokur, Marcel; Clarke, Peter
2013-01-01
This paper deals with the accurate microscopic simulation and macroscopic modeling of extreme non-equilibrium phenomena, such as encountered during hypersonic entry into a planetary atmosphere. The state-to-state microscopic equations involving internal excitation, de-excitation, dissociation, and recombination of nitrogen molecules due to collisions with nitrogen atoms are solved time-accurately. Strategies to increase the numerical efficiency are discussed. The problem is then modeled using a few macroscopic variables. The model is based on reconstructions of the state distribution function using the maximum entropy principle. The internal energy space is subdivided into multiple groups in order to better describe the non-equilibrium gases. The method of weighted residuals is applied to the microscopic equations to obtain macroscopic moment equations and rate coefficients. The modeling is completely physics-based, and its accuracy depends only on the assumed expression of the state distribution function and the number of groups used. The model makes no assumption at the microscopic level, and all possible collisional and radiative processes are allowed. The model is applicable to both atoms and molecules and their ions. Several limiting cases are presented to show that the model recovers the classical twotemperature models if all states are in one group and the model reduces to the microscopic equations if each group contains only one state. Numerical examples and model validations are carried out for both the uniform and linear distributions. Results show that the original over nine thousand microscopic equations can be reduced to 2 macroscopic equations using 1 to 5 groups with excellent agreement. The computer time is decreased from 18 hours to less than 1 second.
Energy Technology Data Exchange (ETDEWEB)
Oostrom, Mart (BATTELLE (PACIFIC NW LAB)); Lenhard, Robert J.(INEEL); Delshad, M; Robertson, S D.(Spirit 76, Midland, TX); M.Th. van Genuchten, F.J. Leij and L. Wu
1998-01-01
A critical component of all multiphase flow codes is how relationships among relative permeabilities, fluid saturations, and capillary pressures (i.e., k-S-P relations) are described. Models that are able to mimic fundamental fluid-flow processes to predict k S-P relations are preferable than extrapolating measured data points to estimate k-S-P relations because they may have greater utility and may be more consistent. Furthermore, different saturation-path histories may be simulated with a computer code than those measured in the k-S-P experiments. Because the geometry of the pore spaces in natural porous media is very complex and will likely never be precisely known to predict k-S-P behavior from fundamental relationships, k-S-P models are largely empirical. In this paper, an empirical model based on theoretical considerations is developed to predict hysteretic k-S-P relations in porous media in which the smaller pores are water-wet and the larger pores are oil-wet, i.e., mixed-w et. At high oil-water capillary pressures, the water saturation is modeled to approach the residual water saturation. At low oil-water capillary pressures (i.e., negative), the oil saturation is modeled to approach the residual oil saturation. Relative permeabilities are predicted using parameters that describe main-drainage S-P relations and accounting for the distribution of water and oil in the pore spaces of mixed-wet porous media. The proposed algebraic expressions are easy to implement in multiphase flow codes and can be used to predict k-S-P relations for any saturation-path history. In addition, the model is relatively easy to calibrate to porous media.
Evolution and non-equilibrium physics: A study of the Tangled Nature Model
Becker, Nikolaj; Sibani, Paolo
2014-01-01
We argue that the stochastic dynamics of interacting agents which replicate, mutate and die constitutes a non-equilibrium physical process akin to aging in complex materials. Specifically, our study uses extensive computer simulations of the Tangled Nature Model (TNM) of biological evolution to show that punctuated equilibria successively generated by the model's dynamics have increasing entropy and are separated by increasing entropic barriers. We further show that these states are organized in a hierarchy and that limiting the values of possible interactions to a finite interval leads to stationary fluctuations within a component of the latter. A coarse-grained description based on the temporal statistics of quakes, the events leading from one component of the hierarchy to the next, accounts for the logarithmic growth of the population and the decaying rate of change of macroscopic variables. Finally, we question the role of fitness in large-scale evolution models and speculate on the possible evolutionary role of rejuvenation and memory effects.
Non-Equilibrium Zeldovich-Von Neumann-Doring Theory and Reactive Flow Modeling of Detonation
Energy Technology Data Exchange (ETDEWEB)
Tarver, C M; Forbes, J W; Urtiew, P A
2002-05-02
This paper discusses the Non-Equilibrium Zeldovich - von Neumann - Doring (NEZND) theory of self-sustaining detonation waves and the Ignition and Growth reactive flow model of shock initiation and detonation wave propagation in solid explosives. The NEZND theory identified the non-equilibrium excitation processes that precede and follow the exothermic decomposition of a large high explosive molecule into several small reaction product molecules. The thermal energy deposited by the leading shock wave must be distributed to the vibrational modes of the explosive molecule before chemical reactions can occur. The induction time for the onset of the initial endothermic reactions can be calculated using high pressure, high temperature transition state theory. Since the chemical energy is released well behind the leading shock front of a detonation wave, a physical mechanism is required for this chemical energy to reinforce the leading shock front and maintain its overall constant velocity. This mechanism is the amplification of pressure wavelets in the reaction zone by the process of de-excitation of the initially highly vibrationally excited reaction product molecules. This process leads to the development of the three-dimensional structure of detonation waves observed for all explosives. For practical predictions of shock initiation and detonation in hydrodynamic codes, phenomenological reactive flow models have been developed. The Ignition and Growth reactive flow model of shock initiation and detonation in solid explosives has been very successful in describing the overall flow measured by embedded gauges and laser interferometry. This reactive flow model uses pressure and compression dependent reaction rates, because time resolved experimental temperature data is not yet available. Since all chemical reaction rates are ultimately controlled by temperature, the next generation of reactive flow models will use temperature dependent reaction rates. Progress on a
Towards a model of non-equilibrium binding of metal ions in biological systems.
Beardmore, James; Exley, Christopher
2009-02-01
We have used a systems biology approach to address the hitherto insoluble problem of the quantitative analysis of non-equilibrium binding of aqueous metal ions by competitive ligands in heterogeneous media. To-date, the relative proportions of different metal complexes in aqueous media has only been modelled at chemical equilibrium and there are no quantitative analyses of the approach to equilibrium. While these models have improved our understanding of how metals are used in biological systems they cannot account for the influence of kinetic factors in metal binding, transport and fate. Here we have modelled the binding of aluminium, Al(III), in blood serum by the iron transport protein transferrin (Tf) as it is widely accepted that the biological fate of this non-essential metal is not adequately described by experiments, invitro and insilico, which have consistently demonstrated that at equilibrium 90% of serum Al(III) is bound by Tf. We have coined this paradox 'the blood-aluminium problem' and herein applied a systems biology approach which utilised well-found assumptions to pare away the complexities of the problem such that it was defined by a comparatively simple set of computational rules and, importantly, its solution assumed significant predictive capabilities. Here we show that our novel computational model successfully described the binding of Al(III) by Tf both at equilibrium and as equilibrium for Al(Tf) was approached. The model predicted significant non-equilibrium binding of Al by ligands in competition with Tf and, thereby, provided an explanation of why the distribution of Al(III) in the body cannot be adequately described by its binding and transport by Tf alone. Generically the model highlighted the significance of kinetic in addition to thermodynamic constraints in defining the fate of metal ions in biological systems.
Entropy analysis on non-equilibrium two-phase flow models
Energy Technology Data Exchange (ETDEWEB)
Karwat, H.; Ruan, Y.Q. [Technische Universitaet Muenchen, Garching (Germany)
1995-09-01
A method of entropy analysis according to the second law of thermodynamics is proposed for the assessment of a class of practical non-equilibrium two-phase flow models. Entropy conditions are derived directly from a local instantaneous formulation for an arbitrary control volume of a structural two-phase fluid, which are finally expressed in terms of the averaged thermodynamic independent variables and their time derivatives as well as the boundary conditions for the volume. On the basis of a widely used thermal-hydraulic system code it is demonstrated with practical examples that entropy production rates in control volumes can be numerically quantified by using the data from the output data files. Entropy analysis using the proposed method is useful in identifying some potential problems in two-phase flow models and predictions as well as in studying the effects of some free parameters in closure relationships.
Non-equilibrium structure and dynamics in a microscopic model of thin film active gels
Head, D A; Gompper, G
2013-01-01
In the presence of ATP, molecular motors generate active force dipoles that drive suspensions of protein filaments far from thermodynamic equilibrium, leading to exotic dynamics and pattern formation. Microscopic modelling can help to quantify the relationship between individual motors plus filaments to the large-wavelength properties represented by "hydrodynamic" models. Here we present results of extensive numerical simulations of active gels where the motors and filaments are confined between two infinite parallel plates. Thermal fluctuations and excluded-volume interactions between filaments are included. A systematic variation of rates for motor motion, attachment and detachment, including a differential detachment rate from filament ends, reveals a range of non-equilibrium behaviour. Strong motor binding produces structured filament aggregates that we refer to as asters, bundles or layers, whose stability depends on motor speed and differential end-detachment. The gross features of the dependence of the...
Overshoot in biological systems modelled by Markov chains: a non-equilibrium dynamic phenomenon.
Jia, Chen; Qian, Minping; Jiang, Daquan
2014-08-01
A number of biological systems can be modelled by Markov chains. Recently, there has been an increasing concern about when biological systems modelled by Markov chains will perform a dynamic phenomenon called overshoot. In this study, the authors found that the steady-state behaviour of the system will have a great effect on the occurrence of overshoot. They showed that overshoot in general cannot occur in systems that will finally approach an equilibrium steady state. They further classified overshoot into two types, named as simple overshoot and oscillating overshoot. They showed that except for extreme cases, oscillating overshoot will occur if the system is far from equilibrium. All these results clearly show that overshoot is a non-equilibrium dynamic phenomenon with energy consumption. In addition, the main result in this study is validated with real experimental data.
Golinelli, Olivier; Mallick, Kirone
2006-10-01
The asymmetric simple exclusion process (ASEP) plays the role of a paradigm in non-equilibrium statistical mechanics. We review exact results for the ASEP obtained by the Bethe ansatz and put emphasis on the algebraic properties of this model. The Bethe equations for the eigenvalues of the Markov matrix of the ASEP are derived from the algebraic Bethe ansatz. Using these equations we explain how to calculate the spectral gap of the model and how global spectral properties such as the existence of multiplets can be predicted. An extension of the Bethe ansatz leads to an analytic expression for the large deviation function of the current in the ASEP that satisfies the Gallavotti-Cohen relation. Finally, we describe some variants of the ASEP that are also solvable by the Bethe ansatz.
Energy Technology Data Exchange (ETDEWEB)
Golinelli, Olivier [Service de Physique Theorique, CEA Saclay, 91191 Gif-sur-Yvette Cedex (France); Mallick, Kirone [Service de Physique Theorique, CEA Saclay, 91191 Gif-sur-Yvette Cedex (France)
2006-10-13
The asymmetric simple exclusion process (ASEP) plays the role of a paradigm in non-equilibrium statistical mechanics. We review exact results for the ASEP obtained by the Bethe ansatz and put emphasis on the algebraic properties of this model. The Bethe equations for the eigenvalues of the Markov matrix of the ASEP are derived from the algebraic Bethe ansatz. Using these equations we explain how to calculate the spectral gap of the model and how global spectral properties such as the existence of multiplets can be predicted. An extension of the Bethe ansatz leads to an analytic expression for the large deviation function of the current in the ASEP that satisfies the Gallavotti-Cohen relation. Finally, we describe some variants of the ASEP that are also solvable by the Bethe ansatz.
Nüske, Feliks; Wu, Hao; Prinz, Jan-Hendrik; Wehmeyer, Christoph; Clementi, Cecilia; Noé, Frank
2017-03-01
Many state-of-the-art methods for the thermodynamic and kinetic characterization of large and complex biomolecular systems by simulation rely on ensemble approaches, where data from large numbers of relatively short trajectories are integrated. In this context, Markov state models (MSMs) are extremely popular because they can be used to compute stationary quantities and long-time kinetics from ensembles of short simulations, provided that these short simulations are in "local equilibrium" within the MSM states. However, over the last 15 years since the inception of MSMs, it has been controversially discussed and not yet been answered how deviations from local equilibrium can be detected, whether these deviations induce a practical bias in MSM estimation, and how to correct for them. In this paper, we address these issues: We systematically analyze the estimation of MSMs from short non-equilibrium simulations, and we provide an expression for the error between unbiased transition probabilities and the expected estimate from many short simulations. We show that the unbiased MSM estimate can be obtained even from relatively short non-equilibrium simulations in the limit of long lag times and good discretization. Further, we exploit observable operator model (OOM) theory to derive an unbiased estimator for the MSM transition matrix that corrects for the effect of starting out of equilibrium, even when short lag times are used. Finally, we show how the OOM framework can be used to estimate the exact eigenvalues or relaxation time scales of the system without estimating an MSM transition matrix, which allows us to practically assess the discretization quality of the MSM. Applications to model systems and molecular dynamics simulation data of alanine dipeptide are included for illustration. The improved MSM estimator is implemented in PyEMMA of version 2.3.
An alternative order-parameter for non-equilibrium generalized spin models on honeycomb lattices
Sastre, Francisco; Henkel, Malte
2016-04-01
An alternative definition for the order-parameter is proposed, for a family of non-equilibrium spin models with up-down symmetry on honeycomb lattices, and which depends on two parameters. In contrast to the usual definition, our proposal takes into account that each site of the lattice can be associated with a local temperature which depends on the local environment of each site. Using the generalised voter motel as a test case, we analyse the phase diagram and the critical exponents in the stationary state and compare the results of the standard order-parameter with the ones following from our new proposal, on the honeycomb lattice. The stationary phase transition is in the Ising universality class. Finite-size corrections are also studied and the Wegner exponent is estimated as ω =1.06(9).
Non-equilibrium steady states in two-temperature Ising models with Kawasaki dynamics
Borchers, Nick; Pleimling, Michel; Zia, R. K. P.
2013-03-01
From complex biological systems to a simple simmering pot, thermodynamic systems held out of equilibrium are exceedingly common in nature. Despite this, a general theory to describe these types of phenomena remains elusive. In this talk, we explore a simple modification of the venerable Ising model in hopes of shedding some light on these issues. In both one and two dimensions, systems attached to two distinct heat reservoirs exhibit many of the hallmarks of phase transition. When such systems settle into a non-equilibrium steady-state they exhibit numerous interesting phenomena, including an unexpected ``freezing by heating.'' There are striking and surprising similarities between the behavior of these systems in one and two dimensions, but also intriguing differences. These phenomena will be explored and possible approaches to understanding the behavior will be suggested. Supported by the US National Science Foundation through Grants DMR-0904999, DMR-1205309, and DMR-1244666
A non-equilibrium thermodynamic model for tumor extracellular matrix with enzymatic degradation
Xue, Shi-Lei; Li, Bo; Feng, Xi-Qiao; Gao, Huajian
2017-07-01
The extracellular matrix (ECM) of a solid tumor not only affords scaffolding to support tumor architecture and integrity but also plays an essential role in tumor growth, invasion, metastasis, and therapeutics. In this paper, a non-equilibrium thermodynamic theory is established to study the chemo-mechanical behaviors of tumor ECM, which is modeled as a poroelastic polyelectrolyte consisting of a collagen network and proteoglycans. By using the principle of maximum energy dissipation rate, we deduce a set of governing equations for drug transport and mechanosensitive enzymatic degradation in ECM. The results reveal that osmosis is primarily responsible for the compression resistance of ECM. It is suggested that a well-designed ECM degradation can effectively modify the tumor microenvironment for improved efficiency of cancer therapy. The theoretical predictions show a good agreement with relevant experimental observations. This study aimed to deepen our understanding of tumor ECM may be conducive to novel anticancer strategies.
Non equilibrium dynamics of mixing, oscillations, and equilibration: A model study
Energy Technology Data Exchange (ETDEWEB)
Ho, Chiu Man; Boyanovsky, D.; Ho, C. M.
2006-12-22
The non-equilibrium dynamics of mixing, oscillations and equilibration is studied in a field theory of flavored neutral mesons that effectively models two flavors of mixed neutrinos, in interaction with other mesons that represent a thermal bath of hadrons or quarks and charged leptons. This model describes the general features of neutrino mixing and relaxation via charged currents in a medium. The reduced density matrix and the non-equilibrium effective action that describes the propagation of neutrinos is obtained by integrating out the bath degrees of freedom. We obtain the dispersion relations, mixing angles and relaxation rates of ``neutrino'' quasiparticles. The dispersion relations and mixing angles are of the same form as those of neutrinos in the medium, and the relaxation rates are given by $\\Gamma_1(k) = \\Gamma_{ee}(k) \\cos^2\\theta_m(k)+\\Gamma_{\\mu\\mu}(k)\\sin^2\\theta_m(k); \\Gamma_2(k)= \\Gamma_{\\mu\\mu}(k) \\cos^2\\theta_m(k)+\\Gamma_{ee}(k)\\sin^2\\theta_m(k) $ where $\\Gamma_{\\alpha\\alpha}(k)$ are the relaxation rates of the flavor fields in \\emph{absence} of mixing, and $\\theta_m(k)$ is the mixing angle in the medium. A Weisskopf-Wigner approximation that describes the asymptotic time evolution in terms of a non-hermitian Hamiltonian is derived. At long time $>>\\Gamma^{-1}_{1,2}$ ``neutrinos'' equilibrate with the bath. The equilibrium density matrix is nearly diagonal in the basis of eigenstates of an \\emph{effective Hamiltonian that includes self-energy corrections in the medium}. The equilibration of ``sterile neutrinos'' via active-sterile mixing is discussed.
Energy Technology Data Exchange (ETDEWEB)
Clement, T Prabhakar; Barnett, Mark O; Zheng, Chunmiao; Jones, Norman L
2010-05-05
DE-FG02-06ER64213: Development of Modeling Methods and Tools for Predicting Coupled Reactive Transport Processes in Porous Media at Multiple Scales Investigators: T. Prabhakar Clement (PD/PI) and Mark O. Barnett (Auburn), Chunmiao Zheng (Univ. of Alabama), and Norman L. Jones (BYU). The objective of this project was to develop scalable modeling approaches for predicting the reactive transport of metal contaminants. We studied two contaminants, a radioactive cation [U(VI)] and a metal(loid) oxyanion system [As(III/V)], and investigated their interactions with two types of subsurface materials, iron and manganese oxyhydroxides. We also developed modeling methods for describing the experimental results. Overall, the project supported 25 researchers at three universities. Produced 15 journal articles, 3 book chapters, 6 PhD dissertations and 6 MS theses. Three key journal articles are: 1) Jeppu et al., A scalable surface complexation modeling framework for predicting arsenate adsorption on goethite-coated sands, Environ. Eng. Sci., 27(2): 147-158, 2010. 2) Loganathan et al., Scaling of adsorption reactions: U(VI) experiments and modeling, Applied Geochemistry, 24 (11), 2051-2060, 2009. 3) Phillippi, et al., Theoretical solid/solution ratio effects on adsorption and transport: uranium (VI) and carbonate, Soil Sci. Soci. of America, 71:329-335, 2007
Mondal, P.; Krol, M.; Sleep, B. E.
2015-12-01
A wide variety of groundwater contaminants can be treated with nano-scale zero valent iron (nZVI). However, delivery of nZVI in the subsurface to the treatment zones is challenging as the bare nZVI particles have a higher tendency to agglomerate. The subsurface mobility of nZVI can be enhanced by stabilizing nZVI with polymer, such as carboxymethyl cellulose (CMC). In this study, numerical simulations were conducted to evaluate CMC stabilized nZVI transport behavior in porous media. The numerical simulations were based on a set of laboratory-scale transport experiments that were conducted in a two-dimensional water-saturated glass-walled sandbox (length - 55 cm; height - 45 cm; width - 1.4 cm), uniformly packed with silica sand. In the transport experiments: CMC stabilized nZVI and a non-reactive dye tracer Lissamine Green B (LGB) were used; water specific discharge and CMC concentration were varied; movements of LGB, and CMC-nZVI in the sandbox were tracked using a camera, a light source and a dark box. The concentrations of LGB, CMC, and CMC-nZVI at the sandbox outlet were analyzed. A 2D multiphase flow and transport model was applied to simulate experimental results. The images from LGB dye transport experiments were used to determine the pore water velocities and media permeabilities in various layers in the sand box. These permeability values were used in the subsequent simulations of CMC-nZVI transport. The 2D compositional simulator, modified to include colloid filtration theory (CFT), treated CMC as a solute and nZVI as a colloid. The simulator included composition dependent viscosity to account for CMC injection and mixing, and attachment efficiency as a fitting parameter for nZVI transport modeling. In the experiments, LGB and CMC recoveries were greater than 95%; however, CMC residence time was significantly higher than the LGB residence time and the higher CMC concentration caused higher pressure drops in the sandbox. The nZVI recovery was lower than 40
Xiong, Qingrong; Baychev, Todor G.; Jivkov, Andrey P.
2016-09-01
Pore network models have been applied widely for simulating a variety of different physical and chemical processes, including phase exchange, non-Newtonian displacement, non-Darcy flow, reactive transport and thermodynamically consistent oil layers. The realism of such modelling, i.e. the credibility of their predictions, depends to a large extent on the quality of the correspondence between the pore space of a given medium and the pore network constructed as its representation. The main experimental techniques for pore space characterisation, including direct imaging, mercury intrusion porosimetry and gas adsorption, are firstly summarised. A review of the main pore network construction techniques is then presented. Particular focus is given on how such constructions are adapted to the data from experimentally characterised pore systems. Current applications of pore network models are considered, with special emphasis on the effects of adsorption, dissolution and precipitation, as well as biomass growth, on transport coefficients. Pore network models are found to be a valuable tool for understanding and predicting meso-scale phenomena, linking single pore processes, where other techniques are more accurate, and the homogenised continuum porous media, used by engineering community.
DEFF Research Database (Denmark)
Scheffler, Gregor Albrecht; Plagge, Rudolf
2010-01-01
This paper addresses the modelling of hygric material coefficients bridging the gap between measured material properties and the non-linear storage and transport coefficients in the transfer equation. The conductivity approach and a bundle of tubes model are the basis. By extending this model...
Tufenkji, Nathalie
2006-12-01
Controlled laboratory-scale column deposition experiments were conducted using a well-characterized mutant of the Escherichia coli (E. coli) K12 strain to obtain insight into the mechanisms that give rise to the observed deviation from classical colloid filtration theory (CFT). Both the suspended effluent bacteria concentration and the spatial distribution of retained bacteria were systematically measured over a wide range of solution conditions using columns packed with spherical glass beads. Calculations of Derjaguin-Landau-Verwey-Overbeek (DLVO) interaction energies based on measured cell zeta potentials indicated that the bacteria should experience considerable repulsive interaction forces when approaching the glass bead surface. In spite of these predictions, bacterial adhesion was observed even at the lowest solution ionic strength investigated (3 mM) and increased with solution salt concentration. Comparison of these results with measurements obtained using model colloidal particles (polystyrene latex microspheres) and a different microbe (Cryptosporidium parvum) suggested that another non-DLVO-type interaction may be contributing to the observed deposition behavior. Furthermore, predictions based on a discrete dual deposition mode (DDM) model disagreed with measured fractions of released cells. Taken together, the experimental and modeling results suggest that the deposition behavior of bacteria in saturated porous media is influenced by additional interaction mechanism(s) or factors not considered in classical DLVO theory, such as local charge heterogeneities of the cell membrane and surface biomolecule-specific interactions.
Ali, Iftikhar
2016-01-01
Shale gas recovery has seen a major boom in recent years due to the increasing global energy demands; but the extraction technologies are very expensive. It is therefore important to develop realistic transport modelling and simulation methods, for porous rocks and porous media, that can compliment the field work. Here, a new nonlinear transport model for single phase gas flow in tight porous media is derived, incorporating many important physical processes that occur in such porous systems: continuous flow, transition flow, slip flow, Knudsen diffusion, adsorption and desorption in to and out of the rock material, and a correction for high flow rates (turbulence). This produces a nonlinear advection-diffusion type of partial differential equation (PDE) with pressure dependent model parameters and associated compressibility coefficients, and highly nonlinear apparent convective flux (velocity) and apparent diffusivity. An important application is to the determination of shale rock properties, such as porosity...
Evolution of fluid-fluid interface in porous media as the model of gas-oil fields
Directory of Open Access Journals (Sweden)
Cerasela-Iliana Calugaru
2003-06-01
Full Text Available This article proposes a generalized model for describing deformations of the mobile interface separating two immiscible weakly compressible fluids in a weakly deformable porous medium. It describes a gravity non-equilibrium processes, including evolution of the gravitational instability and can be reduced in two cases. This paper deals with the first case in which elastic perturbations are propagating much slower than gravity perturbations. The obtained model has analytical solutions and is applied to simulate the behavior of oil-gas or water-oil interface in oil-gas reservoirs.
Software package r{sup 3}t. Model for transport and retention in porous media. Final report
Energy Technology Data Exchange (ETDEWEB)
Fein, E. (ed.)
2004-07-01
In long-termsafety analyses for final repositories for hazardous wastes in deep geological formations the impact to the biosphere due to potential release of hazardous materials is assessed for relevant scenarios. The model for migration of wastes from repositories to men is divided into three almost independent parts: the near field, the geosphere, and the biosphere. With the development of r{sup 3}t the feasibility to model the pollutant transport through the geosphere for porous or equivalent porous media in large, three-dimensional, and complex regions is established. Furthermore one has at present the ability to consider all relevant retention and interaction effects which are important for long-term safety analyses. These are equilibrium sorption, kinetically controlled sorption, diffusion into immobile pore waters, and precipitation. The processes of complexing, colloidal transport and matrix diffusion may be considered at least approximately by skilful choice of parameters. Speciation is not part of the very recently developed computer code r{sup 3}t. With r{sup 3}t it is possible to assess the potential dilution and the barrier impact of the overburden close to reality.
Institute of Scientific and Technical Information of China (English)
邓英尔; 刘慈群
2003-01-01
A mathematical model of two-phase fluid nonlinear flow in the direction ofnormal of ellipse through low-permeability porous media was established according to anonlinear flow law expressed in a continuous function with three parameters, a massconservation law and a concept of turbulent ellipses. A solution to the model was obtainedby using a finite difference method and an extrapolation method. Formulas of calculatingdevelopment index not only before but also after water breaks through an oil well in thecondition of two-phase fluid nonlinear flow in the media were derived. An example wasdiscussed. Water saturation distribution was presented. The moving law of drainage frontwas found. Laws of change of pressure difference with time were recognized. Results showthat there is much difference of water saturation distribution between nonlinear flow andlinear flow; that drainage front by water moves faster, water breaks through sooner and theindex gets worse because of the nonlinear flow ; and that dimensionless pressure differencegets larger at the same dimensionless time and difficulty of oil development becomes biggerby the nonlinear flow . Thus, it is necessary that influence of nonlinear flow on developmentindexes of the oil fields be taken into account. The results provide water-floodingdevelopment of the oil fields with scientific basis.
Tecklenburg, Jan; Carrera, Jesus; Dentz, Marco
2016-01-01
We study modeling of two-phase flow in highly heterogeneous fractured and porous media. The flow behaviour is strongly influenced by mass transfer between a highly permeable (mobile) fracture domain and less permeable (immobile) matrix blocks. We quantify the effective two-phase flow behaviour using a multirate rate mass transfer (MRMT) approach. We discuss the range of applicability of the MRMT approach in terms of the pertinent viscous and capillary diffusion time scales. We scrutinize the linearization of capillary diffusion in the immobile regions, which allows for the formulation of MRMT in the form of a non-local single equation model. The global memory function, which encodes mass transfer between the mobile and the immobile regions, is at the center of this method. We propose two methods to estimate the global memory function for a fracture network with given fracture and matrix geometry. Both employ a scaling approach based on the known local memory function for a given immobile region. With the firs...
Qiu, Charmaine; Gao, Hui; Fan, Dimin; Jin, Yan; Wang, Lian-Ping
2008-11-01
Adequate understanding of the mechanism of colloid retention by soil porous media is essential to the prediction and monitoring of the transport of contaminants by groundwater in the subsurface environment. Preliminary studies reveal that pore-scale processes are governed by colloid-grain and colloid-colloid interactions. In this talk, we focus on the assessment of their effects using a computational approach. First, micro-scale viscous flow in a model porous medium, i.e., a square channel filled with spherical grains, is simulated by simultaneously applying a mesoscopic lattice Boltzmann equation and a Navier-Stokes based hybrid approach, for rigorous cross-validation of the simulated flow. Lagrangian tacking of individual colloids is then conducted by solving colloids equation of motion including local hydrodynamic effects and physicochemical forces. Analysis of colloid transport will encompass effects of flow straining, depth-dependent spatial distribution, and retention of colloids under different solution ionic strengths, flow speeds, and packing configurations. Comparison with parallel experimental results using confocal microscopy will be briefly discussed.
Leichsenring, Peter; Wallmersperger, Thomas
2017-03-01
Ionic hydrogels belong to the class of polyelectrolyte gels, also known as ionic gels. Their ability to swell or shrink under different environmental conditions such as change of pH, ion concentration or temperature make them promising materials for new sensoric or actuatoric devices. Numerical simulations play a crucial role for further developing hydrogel based devices. In the present contribution, a thermodynamically consistent continuum model based on the theory of porous media is derived. The governing field equations are solved on a one-dimensional domain by applying the finite element method. For the time discretization an Euler backward algorithm is implemented. The hydrogel swelling behavior is triggered by a chemical stimulus and is analyzed in space and time. Two mechanical configurations are considered: the hydrogel free swelling behavior and a mechanically clamped configuration, where the hydrogel swelling is hindered, are evaluated in detail. The presented results lead to a precise understanding of the chemo-electro-mechanical behavior and the driving pressure contributions.
State-to-state modeling of non equilibrium low-temperature atomic plasmas
Bultel, Arnaud; Morel, Vincent; Annaloro, Julien; Druguet, Marie-Claude
2017-03-01
The most relevant approach leading to a thorough understanding of the behavior of non equilibrium atomic plasmas is to elaborate state-to-state models in which the mass conservation equation is applied directly to atoms or ions on their excited states. The present communication reports the elaboration of such models and the results obtained. Two situations close to each other are considered. First, the plasmas produced behind shock fronts obtained in ground test facilities (shock tubes) or during planetary atmospheric entries of spacecrafts are discussed. We focused our attention on the nitrogen case for which a complete implementation of the CoRaM-N2 collisional-radiative model has been performed in a steady one-dimensional computation code based on the Rankine-Hugoniot assumptions. Second, the plasmas produced by the interaction between an ultra short laser pulse and a tungsten sample are discussed in the framework of the elaboration of the Laser-Induced Breakdown Spectroscopy (LIBS) technique. In the present case, tungsten has been chosen in the purpose of validating an in situ experimental method able to provide the elemental composition of the divertor wall of a tokamak like WEST or ITER undergoing high energetic deuterium and tritium nuclei fluxes.
Electrical characteristics of TIG arcs in argon from non-equilibrium modelling and experiment
Baeva, Margarita; Uhrlandt, Dirk; Siewert, Erwan
2016-09-01
Electric arcs are widely used in industrial processes so that a thorough understanding of the arc characteristics is highly important to industrial research and development. TIG welding arcs operated with pointed electrodes made of tungsten, doped with cerium oxide, have been studied in order to analyze in detail the electric field and the arc voltage. Newly developed non-equilibrium model of the arc is based on a complete diffusion treatment of particle fluxes, a generalized form of Ohm's law, and boundary conditions accounting for the space-charge sheaths within the magneto-hydrodynamic approach. Experiments have been carried out for electric currents in the range 5-200 A. The electric arc has been initiated between a WC20 cathode and a water-cooled copper plate placed 0.8 mm from each other. The arc length has been continuously increased by 0.1 mm up to 15 mm and the arc voltage has been simultaneously recorded. Modelling and experimental results will be presented and discussed.
Valence-bond non-equilibrium solvation model for a twisting monomethine cyanine
McConnell, Sean; McKenzie, Ross H.; Olsen, Seth
2015-02-01
We propose and analyze a two-state valence-bond model of non-equilibrium solvation effects on the excited-state twisting reaction of monomethine cyanines. Suppression of this reaction is thought responsible for environment-dependent fluorescence yield enhancement in these dyes. Fluorescence is quenched because twisting is accompanied via the formation of dark twisted intramolecular charge-transfer (TICT) states. For monomethine cyanines, where the ground state is a superposition of structures with different bond and charge localizations, there are two possible twisting pathways with different charge localizations in the excited state. For parameters corresponding to symmetric monomethines, the model predicts two low-energy twisting channels on the excited-state surface, which leads to a manifold of TICT states. For typical monomethines, twisting on the excited state surface will occur with a small barrier or no barrier. Changes in the solvation configuration can differentially stabilize TICT states in channels corresponding to different bonds, and that the position of a conical intersection between adiabatic states moves in response to solvation to stabilize either one channel or the other. There is a conical intersection seam that grows along the bottom of the excited-state potential with increasing solvent polarity. For monomethine cyanines with modest-sized terminal groups in moderately polar solution, the bottom of the excited-state potential surface is completely spanned by a conical intersection seam.
Cueto-Felgueroso, L.; Fu, X.; Juanes, R.
2016-12-01
The description of multicomponent flows with complex phase behavior remains an open challenge in pore-scale modeling. Darcy-scale general purpose simulators assume local thermodynamic equilibrium, and perform equation-of-state-based calculations to make phase equilibrium predictions; that is, to determine the phase volume fractions and their compositions from overall component mole fractions. What remains unclear is whether the thermodynamic equilibrium assumption is valid given the flow conditions, complex structure of the pore space and characteristic time scales for flow. Diffuse-interface theories of multiphase flow have recently emerged as promising tools to understand and simulate complex processes involving the simultaneous flow of two or more immiscible fluid phases. The common goal in these approaches is to formulate thermodynamically consistent stress tensors and mesoscale balance laws, including the impact of surface tension on the momentum balance, as well as properly tracking interfacial dynamics and mass transfer. We propose a phase-field model of multiphase, multicomponent flow, which we use to address the following research questions: What is the impact of the wetting conditions at the pore scale on upscaled descriptions of multiphase flow? What is the impact of the displacement dynamics, pore space structure and wetting conditions on the phase behavior of multicomponent mixtures? We finally investigate upscaling procedures to incorporate non-equilibrium phase behavior at the continuum scale.
Energy Technology Data Exchange (ETDEWEB)
Luigi, A.; Saputelli, B.; Carlas, M.; Canache, P.; Lopez, E. [DPVS Exploracion y Produccion (Venezuela)
1998-12-31
This study was designed to determine the activation energy ranges and frequency factor ranges in chemical reactions in heavy oils of the Orinoco Belt in Venezuela, in order to account for the kinetics of physical changes that occur in the morphology of gas-oil dispersion. A non-equilibrium reaction model was used to model foamy oil behaviour observed at SDZ-182 horizontal well in the Zuata field. Results showed that activation energy for the first reaction ranged from 0 to 0.01 BTU/lb-mol and frequency factor from 0.001 to 1000 l/day. For the second reaction the activation energy was 50x10{sub 3} BTU/lb-mol and the frequency factor 2.75x10{sub 1}2 l/day. The second reaction was highly sensitive to the modifications in activation energy and frequency factor. However, both the activation energy and frequency factor were independent of variations for the first reaction. In the case of the activation energy, the results showed that the high sensitivity of this parameter reflected the impact that temperature has on the representation of foamy oil behaviour. 8 refs., 2 tabs., 6 figs.
Non-Markovian Persistence at the PC point of a 1d non-equilibrium kinetic Ising model
Menyhard, N; Menyhard, Nora; Odor, Geza
1997-01-01
One-dimensional non-equilibrium kinetic Ising models evolving under the competing effect of spin flips at zero temperature and nearest neighbour spin exchanges exhibiting a parity-conserving (PC) phase transition on the level of kinks are investigated here numerically from the point of view of the underlying spin system. The dynamical persistency exponent $\\Theta$ and the exponent $lambda$ characterising the two-time autocorrelation function of the total magnetization under non-equilibrium conditions are reported. It is found that the PC transition has strong effect: the process becomes non-Markovian and the above exponents exhibit drastic changes as compared to the Glauber-Ising case.
2005-10-01
s/___________________________ MICHAEL R. UPDIKE , Lt Col, USAF Deputy Chief, Airbase Technologies Division This report is...Mechanics of Materials, 35, 2003, 1161-1176. 5. Burmeister, Louis C., Convective Heat Transfer, 2nd Edition, John Wiley & Sons, Inc., New York, 1993. 6...No. 8, 1995, 1387-1392. 11. Incropera, F.P., DeWitt, D.P., Fundamentals of Heat and Mass Transfer, 3rd Edition, John Wiley & Sons, Inc., New York
Resurgence flows in porous media
Adler, Pierre; Mityushev, Vladimir
2010-05-01
Porous media are generally described by the Darcy equation when the length scales are sufficiently large with respect to the pore scale. This approach is also applicable when the media are heterogeneous, i.e., when permeability varies with space which is the most common case. In addition, real media are very often fractured; for a long time, this complex physical problem has been schematized by the double porosity model devised by Barenblatt. More recently, these fractured media have been addressed with a detailed description of the fractures and of their hydrodynamic interaction with the surrounding porous medium. This approach will be briefly summarized and the main recent progress surveyed (2). There is another situation which occurs frequently in underground studies. One well is connected to a distant well while it is not connected to closer wells. Such a situation can only be understood if there is a direct link between the two connected wells and if this link has little if any hydrodynamic interaction with the porous medium that it crosses. This link can be a fracture or more likely a set of fractures. This phenomenon is called resurgence because of the obvious analogy with rivers which suddenly disappear underground and go out at the ground surface again. Similar ideas have already been developed in other fields. In Physics, random networks limited to nearest neighbors have been recently extended to small world models where distant vertices can be related directly by a link. The electrical testing of porous media by electrical probes located at the walls (electrical tomography) has been used frequently in Geophysics since it is a non-invasive technique; this classical technique corresponds exactly to the situation addressed here from a different perspective. Media with resurgences consist of a double structure (3). The first one which is continuous is described by Darcy law as usual. The second one models the resurgences by capillaries with impermeable walls
Davit, Y.
2012-07-26
In this work, we study the transient behavior of homogenized models for solute transport in two-region porous media. We focus on the following three models: (1) a time non-local, two-equation model (2eq-nlt). This model does not rely on time constraints and, therefore, is particularly useful in the short-time regime, when the timescale of interest (t) is smaller than the characteristic time (τ 1) for the relaxation of the effective macroscale parameters (i. e., when t ≤ τ 1); (2) a time local, two-equation model (2eq). This model can be adopted when (t) is significantly larger than (τ 1) (i.e., when t≫τ 1); and (3) a one-equation, time-asymptotic formulation (1eq ∞). This model can be adopted when (t) is significantly larger than the timescale (τ 2) associated with exchange processes between the two regions (i. e., when t≫τ 2). In order to obtain insight into this transient behavior, we combine a theoretical approach based on the analysis of spatial moments with numerical and analytical results in several simple cases. The main result of this paper is to show that there is only a weak asymptotic convergence of the solution of (2eq) towards the solution of (1eq ∞) in terms of standardized moments but, interestingly, not in terms of centered moments. The physical interpretation of this result is that deviations from the Fickian situation persist in the limit of long times but that the spreading of the solute is eventually dominating these higher order effects. © 2012 Springer Science+Business Media B.V.
A non-equilibrium ionization model of the Local Bubble (I)
de Avillez, Miguel A
2012-01-01
Aims. We present the first high-resolution non-equilibrium ionization simulation of the joint evolution of the Local Bubble (LB) and Loop I superbubbles in the turbulent supernova-driven interstellar medium (ISM). The time variation and spatial distribution of the Li-like ions Civ, Nv, and Ovi inside the LB are studied in detail. Methods. This work uses the parallel adaptive mesh refinement code EAF-PAMR coupled to the newly developed atomic and molecular plasma emission module E(A+M)PEC, featuring the time-dependent calculation of the ionization structure of H through Fe, using the latest revision of solar abundances. The finest AMR resolution is 1 pc within a grid that covers a representative patch of the Galactic disk (with an area of 1 kpc^2 in the midplane) and halo (extending up to 10 kpc above and below the midplane). Results. The evolution age of the LB is derived by the match between the simulated and observed absorption features of the Li-like ions Civ, Nv, and Ovi . The modeled LB current evolution...
Non-equilibrium relaxation in a two-dimensional stochastic lattice Lotka-Volterra model
Chen, Sheng; Täuber, Uwe C.
We employ Monte Carlo simulations to study a stochastic Lotka-Volterra model on a two-dimensional square lattice with periodic boundary conditions. There are stable states when the predators and prey coexist. If the local prey carrying capacity is finite, there emerges an extinction threshold for the predator population at a critical value of the predation rate. We investigate the non-equilibrium relaxation of the predator density in the vicinity of this critical point. The expected power law dependence between the relaxation time and predation rate is observed (critical slowing down). The numerically determined associated critical exponents are in accord with the directed percolation universality class. Following a sudden predation rate change to its critical value, one observes critical aging for the predator density autocorrelation function with a universal scaling exponent. This aging scaling signature of the absorbing state phase transition emerges at significantly earlier times than stationary critical power laws, and could thus serve as an advanced indicator of the population's proximity to its extinction threshold. This research is supported by the U. S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Science and Engineering under Award DE-FG02-09ER46613.
Non-equilibrium relaxation in a stochastic lattice Lotka-Volterra model
Chen, Sheng; Täuber, Uwe C.
2016-04-01
We employ Monte Carlo simulations to study a stochastic Lotka-Volterra model on a two-dimensional square lattice with periodic boundary conditions. If the (local) prey carrying capacity is finite, there exists an extinction threshold for the predator population that separates a stable active two-species coexistence phase from an inactive state wherein only prey survive. Holding all other rates fixed, we investigate the non-equilibrium relaxation of the predator density in the vicinity of the critical predation rate. As expected, we observe critical slowing-down, i.e., a power law dependence of the relaxation time on the predation rate, and algebraic decay of the predator density at the extinction critical point. The numerically determined critical exponents are in accord with the established values of the directed percolation universality class. Following a sudden predation rate change to its critical value, one finds critical aging for the predator density autocorrelation function that is also governed by universal scaling exponents. This aging scaling signature of the active-to-absorbing state phase transition emerges at significantly earlier times than the stationary critical power laws, and could thus serve as an advanced indicator of the (predator) population’s proximity to its extinction threshold.
Non-equilibrium relaxation in a stochastic lattice Lotka-Volterra model.
Chen, Sheng; Täuber, Uwe C
2016-04-19
We employ Monte Carlo simulations to study a stochastic Lotka-Volterra model on a two-dimensional square lattice with periodic boundary conditions. If the (local) prey carrying capacity is finite, there exists an extinction threshold for the predator population that separates a stable active two-species coexistence phase from an inactive state wherein only prey survive. Holding all other rates fixed, we investigate the non-equilibrium relaxation of the predator density in the vicinity of the critical predation rate. As expected, we observe critical slowing-down, i.e., a power law dependence of the relaxation time on the predation rate, and algebraic decay of the predator density at the extinction critical point. The numerically determined critical exponents are in accord with the established values of the directed percolation universality class. Following a sudden predation rate change to its critical value, one finds critical aging for the predator density autocorrelation function that is also governed by universal scaling exponents. This aging scaling signature of the active-to-absorbing state phase transition emerges at significantly earlier times than the stationary critical power laws, and could thus serve as an advanced indicator of the (predator) population's proximity to its extinction threshold.
Numerical modeling of two-phase high speed jet with non-equilibrium solid phase crystallization
Molchanov, A. M.; Yanyshev, D. S.; Bykov, L. V.
2016-11-01
The main purpose of the paper is to demonstrate that the Euler approach is fully applicable to the multiphase flows with discrete phase undergoing phase transitions. It is carried out using the example of a jet flow with aluminium oxide particles non-equilibrium crystallization. The jet is strongly underexpanded. The non-equilibrium molecular effects are being taken into account. The obtained results of the simulations are in good agreement with the works of the other authors. The developed Euler approach proved itself to be the most robust in flows with complex flow geometry.
First-principles modelling of scanning tunneling microscopy using non-equilibrium Green's functions
DEFF Research Database (Denmark)
Lin, H.P.; Rauba, J.M.C.; Thygesen, Kristian Sommer
2010-01-01
a novel STM simulation scheme based on non-equilibrium Green's functions (NEGF) and Wannier functions which is both accurate and very efficient. The main novelty of the scheme compared to the Bardeen and Tersoff-Hamann approaches is that the coupling to the infinite (macroscopic) electrodes is taken...
Phenrat, Tanapon; Song, Jee Eun; Cisneros, Charlotte M; Schoenfelder, Daniel P; Tilton, Robert D; Lowry, Gregory V
2010-06-15
Assessing the environmental transport and fate of manufactured nanoparticles (NPs) and potential exposure risks requires models for predicting attachment of NPs coated with organic macromolecules in porous media. The objective of this study was to determine the properties of coated nanoparticles that control their attachment behavior. Deposition data for a variety of nanoparticles with different types of anionic organic coatings, including natural organic matter (NOM)-coated latex and hematite nanoparticles, and poly(styrenesulfonate)-, carboxymethylcellulose-, and polyaspartate-coated hematite and titanium dioxide nanoparticles (80 data points), were used to develop an empirical correlation between measurable NP properties and their sticking coefficient (alpha) under a variety of electrolyte conditions and flow velocities. Available semiempirical correlations used to predict the attachment efficiency of electrostatically stabilized (uncoated) NPs overestimate the attachment efficiency of nanoparticles coated with NOM or synthetic polyelectrolytes because the correlations neglect electrosteric repulsions and the decreased friction afforded by such coatings that can inhibit attachment to surfaces. Adding a dimensionless parameter (N(LEK)) representing steric repulsions and the decreased friction force afforded by adsorbed NOM or anionic polyelectrolytes in the correlation significantly improves the correlation. This establishes the importance of including the adsorbed NOM- or polyelectrolyte layer properties for estimating the attachment efficiency of NPs in the environment. The form of N(LEK) suggests that limiting unintended transport and exposure to NPs could be achieved by using coatings with the smallest adsorbed mass and polymer density, shortest extended layer thickness, and largest molecular weight that would still afford the desired functionality of the coating.
Zheng, Fei; Gao, Yanwei; Sun, Yuanyuan; Shi, Xiaoqing; Xu, Hongxia; Wu, Jichun
2015-12-01
Understanding the migration of dense non-aqueous phase liquids (DNAPLs) in complex subsurface systems is important for evaluating contamination source zones and designing remediation schemes after spill events. Six sandbox experiments were performed to explore the individual effect of flow velocity, and the combined effect of flow velocity and layered lenses on a DNAPL (PCE) migration in porous media. DNAPL saturation was measured using a light transmission system, and saturation distribution was quantified by spatial moments. The experimental results show that large flow velocity significantly promotes lateral and vertical migration of the low-viscosity DNAPL, while when layered lenses exist, the infiltration rate decreases and horizontal spread increases. Migration processes were numerically simulated, and the modelling results tested against experimental results. Furthermore, migration of DNAPLs with different viscosities was simulated to explore the combined effects of flow velocity and geological heterogeneity. Simulation results show that enhanced heterogeneity makes low-viscosity DNAPLs migrate along preferential pathways, resulting in irregular DNAPL morphology. Layered lenses combined with heterogeneity complicate the effect of flow velocity on the migration of low-viscosity DNAPLs by changing percolation paths. Results also demonstrate that flow velocity exhibits relatively little influence on the migration of medium/high-viscosity DNAPLs, which is predominantly controlled by viscosity and heterogeneity. Enhanced heterogeneity has a larger effect on migration behavior. Findings indicate that the migration paths and position of the source zone could change significantly, due to the combined effect of groundwater flow velocity and geological heterogeneity; thus, comprehensive hydrogeological investigation is needed to characterize the source zone.
2-D Modeling of Nanoscale MOSFETs: Non-Equilibrium Green's Function Approach
Svizhenko, Alexei; Anantram, M. P.; Govindan, T. R.; Biegel, Bryan
2001-01-01
We have developed physical approximations and computer code capable of realistically simulating 2-D nanoscale transistors, using the non-equilibrium Green's function (NEGF) method. This is the most accurate full quantum model yet applied to 2-D device simulation. Open boundary conditions and oxide tunneling are treated on an equal footing. Electrons in the ellipsoids of the conduction band are treated within the anisotropic effective mass approximation. Electron-electron interaction is treated within Hartree approximation by solving NEGF and Poisson equations self-consistently. For the calculations presented here, parallelization is performed by distributing the solution of NEGF equations to various processors, energy wise. We present simulation of the "benchmark" MIT 25nm and 90nm MOSFETs and compare our results to those from the drift-diffusion simulator and the quantum-corrected results available. In the 25nm MOSFET, the channel length is less than ten times the electron wavelength, and the electron scattering time is comparable to its transit time. Our main results are: (1) Simulated drain subthreshold current characteristics are shown, where the potential profiles are calculated self-consistently by the corresponding simulation methods. The current predicted by our quantum simulation has smaller subthreshold slope of the Vg dependence which results in higher threshold voltage. (2) When gate oxide thickness is less than 2 nm, gate oxide leakage is a primary factor which determines off-current of a MOSFET (3) Using our 2-D NEGF simulator, we found several ways to drastically decrease oxide leakage current without compromising drive current. (4) Quantum mechanically calculated electron density is much smaller than the background doping density in the poly silicon gate region near oxide interface. This creates an additional effective gate voltage. Different ways to. include this effect approximately will be discussed.
Nield, Donald A
1992-01-01
This book provides a user-friendly introduction to the topic of convection in porous media The authors as- sume that the reader is familiar with the basic elements of fluid mechanics and heat transfer, but otherwise the book is self-contained The book will be useful both as a review (for reference) and as a tutorial work, suitable as a textbook in a graduate course or seminar The book brings into perspective the voluminous research that has been performed during the last two decades The field has recently exploded because of worldwide concern with issues such as energy self-sufficiency and pollution of the environment Areas of application include the insulation of buildings and equipment, energy storage and recovery, geothermal reservoirs, nuclear waste disposal, chemical reactor engineering, and the storage of heat-generating materials such as grain and coal Geophysical applications range from the flow of groundwater around hot intrusions to the stability of snow against avalanches
Nield, Donald A
2013-01-01
Convection in Porous Media, 4th Edition, provides a user-friendly introduction to the subject, covering a wide range of topics, such as fibrous insulation, geological strata, and catalytic reactors. The presentation is self-contained, requiring only routine mathematics and the basic elements of fluid mechanics and heat transfer. The book will be of use not only to researchers and practicing engineers as a review and reference, but also to graduate students and others entering the field. The new edition features approximately 1,750 new references and covers current research in nanofluids, cellular porous materials, strong heterogeneity, pulsating flow, and more. Recognized as the standard reference in the field Includes a comprehensive, 250-page reference list Cited over 2300 times to date in its various editions Serves as an introduction for those entering the field and as a comprehensive reference for experienced researchers Features new sections on nanofluids, carbon dioxide sequestration, and applications...
Modeling density-driven flow in porous media principles, numerics, software
Holzbecher, Ekkehard O
1998-01-01
Modeling of flow and transport in groundwater has become an important focus of scientific research in recent years. Most contributions to this subject deal with flow situations, where density and viscosity changes in the fluid are neglected. This restriction may not always be justified. The models presented in the book demonstrate immpressingly that the flow pattern may be completely different when density changes are taken into account. The main applications of the models are: thermal and saline convection, geothermal flow, saltwater intrusion, flow through salt formations etc. This book not only presents basic theory, but the reader can also test his knowledge by applying the included software and can set up own models.
Blessent, Daniela; Jørgensen, Peter R; Therrien, René
2014-01-01
We used the FRAC3Dvs numerical model (Therrien and Sudicky 1996) to compare the dual-porosity (DP), equivalent porous medium (EPM), and discrete fracture matrix diffusion (DFMD) conceptual models to predict field-scale contaminant transport in a fractured clayey till aquitard. The simulations show that the DP, EPM, and DFMD models could be equally well calibrated to reproduce contaminant breakthrough in the till aquitard for a base case. In contrast, when groundwater velocity and degradation rates are modified with respect to the base case, the DP method simulated contaminant concentrations up to three orders of magnitude different from those calculated by the DFMD model. In previous simulations of well-characterized column experiments, the DFMD method reproduced observed changes in solute transport for a range of flow and transport conditions comparable to those of the field-scale simulations, while the DP and EPM models required extensive recalibration to avoid high magnitude errors in predicted mass transport. The lack of robustness with respect to variable flow and transport conditions suggests that DP models and effective porosity EPM models have limitations for predicting cause-effect relationships in environmental planning. The study underlines the importance of obtaining well-characterized experimental data for further studies and evaluation of model key process descriptions and model suitability. © 2013, National Groundwater Association.
Macropore-mesopore model of water flow through aggregated porous media
Energy Technology Data Exchange (ETDEWEB)
Fong, L.; Appelbaum, H.R.
1980-12-01
A combined, one-dimensional, macropore-mesopore, hydrologic model was developed for simulating water flow through soils for analysis of data related to water and chemical flow in soils. Flows within the macroporous system as well as interactive flows between macroporous and mesoporous systems were modeled. Computer subroutines were written and incorporated into the existing one-dimensional Terrestrial Ecosystem Hydrologic Model (TEHM) developed at ORNL. Simulation showed that macropore flow effects are important during heavy precipitation and are more significant in soils of comparatively low hydraulic conductivity (5 to 10 cm/d). Increased drainage and decreased lateral flow result from the addition of the macropore model. The effect was more pronounced in soils of large macroporosity. Preliminary results indicate that the model is insensitive to geometrical properties of macropores.
Wehrer, Markus; Jaesche, Philipp; Totsche, Kai Uwe
2012-09-01
A quantitative knowledge of the fate of deicing chemicals in the subsurface can be provided by joint analysis of lab experiments with numerical simulation models. In the present study, published experimental data of microbial degradation of the deicing chemical propylene glycol (PG) under flow conditions in soil columns were simulated inversely to receive the parameters of degradation. We evaluated different scenarios of an advection-dispersion model including different terms for degradation, such as zero order, first order and inclusion of a growing and decaying biomass for their ability to explain the data. The general break-through behavior of propylene glycol in soil columns can be simulated well using a coupled model of solute transport and degradation with growth and decay of biomass. The susceptibility of the model to non-unique solutions was investigated using systematical forward and inverse simulations. We found that the model tends to equifinal solutions under certain conditions.
Development of models for fast fluid pathways through unsaturated heterogeneous porous media
Energy Technology Data Exchange (ETDEWEB)
Robey, T.H. [Spectra Research Inst., Albuquerque, NM (United States)
1994-11-01
The pre-waste-emplacement ground water travel time requirement is a regulatory criterion that specifies ground water travel time to the accessible environment shall be greater than 1,000 years. Satisfying the ground water travel time criterion for the potential repository at Yucca Mountain requires the study of fast travel path formation in the unsaturated zone and development of models that simulate the formation of fast paths. Conceptual models for unsaturated flow that have been used for total-systems performance assessment generally fall into the categories of composite-porosity or fracture models. The actual hydrologic conditions at Yucca Mountain are thought to lie somewhere between the extremes of these two types of models. The current study considers the effects of heterogeneities on composite-porosity models and seeks to develop numerical methods (and models) that can produce locally saturated zones where fracture flow can occur. The credibility of the model and numerical methods is investigated by using test data from the INTRAVAL project (Swedish Nuclear Inspectorate, 1992) to attempt to predict in-situ volumetric water content at specific locations in Yucca Mountain. Work based on the numerical methods presented in this study is eventually intended to allow the calculation of ground water travel times in heterogeneous media. 60 refs.
An Inverse Model of Three-Dimensional Flow and Transport in Heterogeneous Porous Media
Robinson, B. A.; Vrugt, J. A.; Yoon, H.; Zhang, C.; Werth, C. J.; Kitanidis, P. K.; Lichtner, P. C.; Lu, C.
2007-12-01
A three-dimensional flow and transport model was developed to simulate the results of a laboratory-scale experiment in which snapshots of concentration were obtained using magnetic resonance imaging (MRI) during the displacement of tracer through a 14 by 8 by 8 cm flow cell. The medium was deliberately constructed to be heterogeneous with a known spatial correlation structure using sand of five different grain-size distributions. The extremely well characterized flow cell and large, high-precision data set of concentrations during displacement make this a unique experiment for examining the validity of flow and transport models, and for exploring new methods for interpreting large data sets using advanced optimization algorithms. A transport model was constructed by solving the steady state flow equations using the Finite Element Heat and Mass (FEHM) code, using FEHM's particle tracking transport model for simulating tracer migration. The particle tracking model was selected so that precise estimates of the transport parameters could be obtained that are not corrupted by numerical dispersion; a large number of particles (typically one million) were required to provide accuracy. The inverse model included nine uncertain parameters, the five permeability values of the individual sand units, and four dispersion/diffusion parameters. The inverse problem was solved with AMALGAM and DREAM, two recently developed self-adaptive multimethod optimization algorithms. The computations were enabled by performing both the transport model and the optimization loop on a high-performance computing cluster. Computational results indicate that parameter estimates and increased understanding of the behavior of the system can be obtained, and significant improvements in the fit to the data over hand calibration can be achieved, using this inverse modeling approach. The study also illustrates that numerical methods that make effective use of high- performance computing resources and
Wehrer, Markus; Lissner, Heidi; Totsche, Kai
2013-04-01
A quantitative knowledge of the fate of deicing chemicals in the subsurface can be provided by analysis of laboratory and field experiments with numerical simulation models. In the present study, experimental data of microbial degradation of the deicing chemical propylene glycol (PG) under flow conditions in soil columns and field lysimeters were simulated to analyze the process conditions of degradation and to obtain the according parameters. Results from the column experiment were evaluated applying different scenarios of an advection-dispersion model using HYDRUS-1D. To reconstruct the data, different competing degradation models were included, i.e., zero order, first order and inclusion of a growing and decaying biomass. The general breakthrough behavior of propylene glycol in soil columns can be simulated well using a coupled model of solute transport and degradation with growth and decay of biomass. The susceptibility of the model to non-unique solutions was investigated using systematical forward and inverse simulations. We found that the model tends to equifinal solutions under certain conditions. Complex experimental boundary conditions can help to avoid this. Under field conditions, the situation is far more complex than in the laboratory. Studying the fate of PG with undisturbed lysimeters we found that aerobic and anaerobic degradation occurs simultaneously. We attribute this to the physical structure and the aggregated nature of the undisturbed soil material . This results in the presence of spatially disjoint oxidative and reductive regions of microbial activity and requires, but is not fully reflected by a dual porosity model. Currently, the numerical simulation of this system is in progress, considering several flow and transport models. A stochastic global search algorithm (DREAM-ZS) is used in conjuction with HYDRUS-1D to avoid local minima in the inverse simulations. The study shows the current limitations and potentials of modeling degradation
2012-03-01
this research as prescribed by the selected journal. Chapter III provides a summary of the primary findings discussed in the article, as well as...hydrophobic and hydrophilic collector surfaces (Song et al. 2011). The transport of uncoated AgNPs in porous media (glass beads and hematite ...coated glass beads) at acidic and basic pH was studied in column experiments. At pH levels lower than the point of zero charge of hematite , the affinity
Ferrage, Eric; Hubert, Fabien; Tertre, Emmanuel; Delville, Alfred; Michot, Laurent J; Levitz, Pierre
2015-06-01
Swelling clay minerals play a key role in the control of water and pollutant migration in natural media such as soils. Moreover, swelling clay particles' orientational properties in porous media have significant implications for the directional dependence of fluid transfer. Herein we investigate the ability to mimic the organization of particles in natural swelling-clay porous media using a three-dimensional sequential particle deposition procedure [D. Coelho, J.-F. Thovert, and P. M. Adler, Phys. Rev. E 55, 1959 (1997)]. The algorithm considered is first used to simulate disk packings. Porosities of disk packings fall onto a single master curve when plotted against the orientational scalar order parameter value. This relation is used to validate the algorithm used in comparison with existing ones. The ellipticity degree of the particles is shown to have a negligible effect on the packing porosity for ratios ℓ(a)/ℓ(b) less than 1.5, whereas a significant increase in porosity is obtained for higher values. The effect of the distribution of the geometrical parameters (size, aspect ratio, and ellipticity degree) of particles on the final packing properties is also investigated. Finally, the algorithm is used to simulate particle packings for three size fractions of natural swelling-clay mineral powders. Calculated data regarding the distribution of the geometrical parameters and orientation of particles in porous media are successfully compared with experimental data obtained for the same samples. The results indicate that the obtained virtual porous media can be considered representative of natural samples and can be used to extract properties difficult to obtain experimentally, such as the anisotropic features of pore and solid phases in a system.
A homogenization-based constitutive model for two-dimensional viscoplastic porous media
Danas, Kostas; Idiart, Martin I.; Ponte Castañeda, Pedro
2008-01-01
An approximate model based on the so-called 'second-order' nonlinear homogenization method is proposed to estimate the effective behavior of viscoplastic porous materials exhibiting transversely isotropic symmetry. The model is constructed in such a way that it reproduces exactly the behavior of a 'composite-cylinder assemblage' in the limit of in-plane hydrostatic loading, and therefore coincides with the hydrostatic limit of Gurson's criterion for plastic porous materials. As a consequence, the new model improves on earlier 'second-order' homogenization estimates, which have been found to be overly stiff at sufficiently high triaxialities and nonlinearities. The proposed model is compared with exact results obtained for a special class of porous materials with sequentially laminated microstructures. The agreement is found to be excellent for the entire range of stress triaxialities, and all values of the porosity and nonlinearity considered. To cite this article: K. Danas et al., C. R. Mecanique 336 (2008).
Modeling and simulation of nanoparticles transport in a two-phase flow in porous media
El-Amin, Mohamed
2012-01-01
In the current paper, a mathematical model to describe the nanoparticles transport carried by a two-phase flow in a porous medium is presented. Both capillary forces as well as Brownian diffusion are considered in the model. A numerical example of countercurrent water-oil imbibition is considered. We monitor the changing of the fluid and solid properties due to the addition of the nanoparticles using numerical experiments. Variation of water saturation, nanoparticles concentration and porosity ratio are investigated.
Solvable continuous-time random walk model of the motion of tracer particles through porous media.
Fouxon, Itzhak; Holzner, Markus
2016-08-01
We consider the continuous-time random walk (CTRW) model of tracer motion in porous medium flows based on the experimentally determined distributions of pore velocity and pore size reported by Holzner et al. [M. Holzner et al., Phys. Rev. E 92, 013015 (2015)PLEEE81539-375510.1103/PhysRevE.92.013015]. The particle's passing through one channel is modeled as one step of the walk. The step (channel) length is random and the walker's velocity at consecutive steps of the walk is conserved with finite probability, mimicking that at the turning point there could be no abrupt change of velocity. We provide the Laplace transform of the characteristic function of the walker's position and reductions for different cases of independence of the CTRW's step duration τ, length l, and velocity v. We solve our model with independent l and v. The model incorporates different forms of the tail of the probability density of small velocities that vary with the model parameter α. Depending on that parameter, all types of anomalous diffusion can hold, from super- to subdiffusion. In a finite interval of α, ballistic behavior with logarithmic corrections holds, which was observed in a previously introduced CTRW model with independent l and τ. Universality of tracer diffusion in the porous medium is considered.
Gao, Jinfang; Xing, Huilin; Tian, Zhiwei; Pearce, Julie K.; Sedek, Mohamed; Golding, Suzanne D.; Rudolph, Victor
2017-01-01
Injection of CO2 subsurface may lead to chemical reactivity of rock where CO2 is dissolved in groundwater. This process can modify pore networks to increase or decrease porosity through mineral dissolution and precipitation. A lattice Boltzmann (LB) based computational model study on the pore scale reactive transport in three dimensional heterogeneous porous media (sandstone consisting of both reactive and non-reactive minerals) is described. This study examines how fluid transport in porous materials subject to reactive conditions is affected by unsteady state local reactions and unstable dissolution fronts. The reaction of a calcite cemented core sub-plug from the Hutton Sandstone of the Surat Basin, Australia, is used as a study case. In particular, the work studies the interaction of acidic fluid (an aqueous solution with an elevated concentration of carbonic acid) with reactive (e.g. calcite) and assumed non-reactive (e.g. quartz) mineral surfaces, mineral dissolution and mass transfer, and resultant porosity change. The proposed model is implemented in our custom LBM code and suitable for studies of multiple mineral reactions with disparate reaction rates. A model for carbonic acid reaction with calcite cemented sandstone in the CO2-water-rock system is verified through laboratory experimental data including micro-CT characterization before and after core reaction at reservoir conditions. The experimentally validated model shows: (1) the dissolution of calcite cement forms conductive channels at the pore scale, and enables the generation of pore throats and connectivity; (2) the model is able to simulate the reaction process until the reaction equilibrium status is achieved (around 1440 days); (3) calcite constituting a volume of around 9.6% of the whole core volume is dissolved and porosity is consequently increased from 1.1% to 10.7% on reaching equilibrium; (4) more than a third of the calcite (constituting 7.4% of the total core volume) is unaffected
Measuring and modelling straining of Escherichia coli in saturated porous media.
Foppen, Jan Willem; van Herwerden, Manon; Schijven, Jack
2007-08-15
Though coliform bacteria are used worldwide to indicate fecal pollution of groundwater, the parameters determining the transport of Escherichia coli in aquifers are relatively unknown. We evaluated the occurrence of both straining and attachment of E. coli ATCC25922 in columns of ultra-pure, angular, saturated quartz sand. The column experiments were conducted over a wide range of porous medium sizes, column heights, input concentrations, and pore water flow velocities. Straining and attachment were examined by modelling the breakthrough curves (with HYDRUS 1D). In addition, model output was compared with measured strained and attached bacteria via column extrusion experiments (in which sand was extruded from the column and placed in excess water) and flow reversal experiments (in which the pore water flow direction was reversed, thereby dislodging strained bacteria). Our model consisted of an attachment rate coefficient and a straining rate coefficient; both of these decreased with transport distance. The straining rate coefficient also decreased in a Langmuirian way, in response to the filling of available pore space, which in turn depended on influent bacteria concentration, quartz grain diameter, and transport distance. The maximum strained fraction was 25-30% of total bacteria mass applied to the column; the maximum attached fraction was 30-35%. The fit between modelled and measured (strained and attached) bacteria masses was acceptable, as was the sensitivity of the model output to fitted parameter values. Our results lead to a new description for the time-dependent mass balance of strained bacteria, which entails using three fitting parameters. The results also imply that column experiments in combination with retention profiles (or various column lengths) are not enough to explain the retention processes in a column. Column extrusion and flow reversal experiments provide vital additional information on the occurrence and magnitude of straining. Our
A splitting technique for analytical modelling of two-phase multicomponent flow in porous media
DEFF Research Database (Denmark)
Pires, A.P.; Bedrikovetsky, P.G.; Shapiro, Alexander
2006-01-01
In this paper we discuss one-dimensional models for two-phase Enhanced Oil Recovery (EOR) floods (oil displacement by gases, polymers, carbonized water, hot water, etc.). The main result presented here is the splitting of the EOR mathematical model into thermodynamical and hydrodynamical parts....... The introduction of a potential associated with one of the conservation laws and its use as a new independent coordinate reduces the number of equations by one. The (n)x(n) conservation law model for two-phase n-component EOR flows in new coordinates is transformed into a reduced (n-1)x(n-1) auxiliary system...... containing just thermodynamical variables (equilibrium fractions of components, sorption isotherms) and one lifting equation containing just hydrodynamical parameters (phase relative permeabilities and viscosities). The algorithm to solve analytically the problem includes solution of the reduced auxiliary...
Numerical modeling of subsidence in saturated porous media: A mass conservative method
Asadi, Roza; Ataie-Ashtiani, Behzad
2016-11-01
In this paper, a second order accurate cell-centered finite volume method (FVM) is coupled with a finite element method (FEM) to solve the deformation of a saturated porous layer based on Biot's consolidation model. The proposed numerical technique is applied to the fully unstructured triangular grids to simulate actual geological formations. To reconstruct the pressure gradient at control volume faces, the diamond scheme is implemented as a multipoint flux approximation method. Also the least square algorithm is used to interpolate pressure at the vertices from the cell-center values. The stability of this numerical model is studied in comparison to the different FEMs through various examples. It is shown that, although the Taylor-Hood FEM has been introduced as a remedy for violation of the inf-sup condition, it does not entirely remove the non-physical oscillations. Contrary to the linear and Taylor-Hood FEMs, the proposed discretization model provides monotonic solution without imposing any restriction on the mesh or time step size. Compared to the mixed FEM, the method achieves local mass balance with fewer degrees of freedom. To couple the flow and mechanical sub-problems, the fixed-stress operator split is implemented as an iterative sequential method, due to its unconditional stability, accuracy and high rate of convergence. The accuracy of the proposed model is verified via a range of examples including analytical and numerical solutions. The performance of this methodology is assessed through modeling of subsidence in an aquifer-interbed system. This problem illustrates the capability of the model in providing stable solution in heterogeneous domains with complicated shapes.
de Vries, Enno T.; Raoof, Amir; van Genuchten, Martinus Th.
2017-07-01
Many environmental and agricultural applications involve the transport of water and dissolved constituents through aggregated soil profiles, or porous media that are structured, fractured or macroporous in other ways. During the past several decades, various process-based macroscopic models have been used to simulate contaminant transport in such media. Many of these models consider advective-dispersive transport through relatively large inter-aggregate pore domains, while exchange with the smaller intra-aggregate pores is assumed to be controlled by diffusion. Exchange of solute between the two domains is often represented using a first-order mass transfer coefficient, which is commonly obtained by fitting to observed data. This study aims to understand and quantify the solute exchange term by applying a dual-porosity pore-scale network model to relatively large domains, and analysing the pore-scale results in terms of the classical dual-porosity (mobile-immobile) transport formulation. We examined the effects of key parameters (notably aggregate porosity and aggregate permeability) on the main dual-porosity model parameters, i.e., the mobile water fraction (ϕm) and the mass transfer coefficient (α). Results were obtained for a wide range of aggregate porosities (between 0.082 and 0.700). The effect of aggregate permeability was explored by varying pore throat sizes within the aggregates. Solute breakthrough curves (BTCs) obtained with the pore-scale network model at several locations along the domain were analysed using analytical solutions of the dual-porosity model to obtain estimates of ϕm and α. An increase in aggregate porosity was found to decrease ϕm and increase α, leading to considerable tailing in the BTCs. Changes in the aggregate pore throat size affected the relative flow velocity between the intra- and inter-aggregate domains. Higher flow velocities within the aggregates caused a change in the transport regime from diffusion dominated to more
A new approach to model the spatiotemporal development of biofilm phase in porous media.
Bozorg, Ali; Sen, Arindom; Gates, Ian D
2011-11-01
Bacteria can exist within biofilms that are attached to the solid matrix of a porous medium. Under certain conditions, the biomass can fully occupy the pore space leading to reduced hydraulic conductivity and mass transport. Here, by treating biofilm as a growing, high-viscosity phase, a novel macroscopic approach to model biofilm spatial expansion and its corresponding effects on porous medium hydraulic properties is presented. The separate yet coupled flow of the water and biofilm phases is handled by using relative permeability curves that allow for biofilm movement within the porous medium and bioclogging effects. Fluid flow is governed by Darcy's law and component transport is set by the convection-diffusion equation reaction terms for each component. Here, the system of governing equations is solved by using a commercial multiphase flow reservoir simulator, which is used to validate the model against published laboratory experiments. A comparison of the model and experimental observations reveal that the model provides a reasonable means to predict biomass development in the porous medium. The results reveal that coupled flow of water and movement of biofilm, as described by relative permeability curves, is complex and has a large impact on the development of biomass and consequent bioclogging in the porous medium.
Mathematical modeling for laminar flow of power law fluid in porous media
Energy Technology Data Exchange (ETDEWEB)
Silva, Renato A.; Mesquita, Maximilian S. [Universidade Federal do Espirito Santo (UFES), Sao Mateus, ES (Brazil). Centro Universitario Norte do Espirito Santo. Dept. de Engenharias e Computacao
2010-07-01
In this paper, the macroscopic equations for laminar power-law fluid flow is obtained for a porous medium starting from traditional equations (Navier-Stokes). Then, the volume averaging is applied in traditional transport equations with the power-law fluid model. This procedure leads to macroscopic transport equations set for non-Newtonian fluid. (author)
Modelling and analysis of CVD processes in porous media for ceramic composite preparation
Lin, Y.S.; Burggraaf, A.J.
1991-01-01
A continuum phenomenological model is presented to describe chemical vapour deposition (CVD) of solid product inside porous substrate media for the preparation of reinforced ceramic-matrix composites [by the chemical vapour infiltration (CVI) process] and ceramic membrane composites (by a modified C
Upscaling transport of adsorbing solutes in porous media: pore-network modeling
Raoof, A.; Hassanizadeh, S.M.; Leijnse, A.
2010-01-01
The main objective of this research was to enhance our understanding of and obtain quantitative relation between Darcy-scale adsorption parameters and pore-scale flow and adsorption parameters, using a three-dimensional multidirectional pore-network model. This helps to scale up from a simplified bu
Forced imbibition in natural porous media: comparison between experiments and continuum models.
Riaz, Amir; Tang, Guo-Qing; Tchelepi, Hamdi A; Kovscek, Anthony R
2007-03-01
A well-characterized set of large-scale laboratory experiments is presented, illustrating forced imbibition displacements in the presence of irreducible wetting phase saturation in a cylindrical, homogeneous Berea sandstone rock. Experiments are designed to operate in the regime of compact microscopic flows and large-scale viscous instability. The distribution of fluid phases during the flow process is visualized by high-resolution computed tomography imaging. Linear stability analysis and high-accuracy numerical simulations are employed to analyze the ability of macroscopic continuum equations to provide a consistent approximation of the displacement process. The validity of the equilibrium relative permeability functions, which form the basis for the continuum model, is fundamentally related to the stability of the displacement process. It is shown that not only is the stable flow regime modeled accurately by existing continuum models, but the onset of instability as well as the initial unstable modes are also determined with reasonable accuracy for unstable flows. However, the continuum model is found to be deficient in the case of fully developed unstable flows.
Nurhandoko, Bagus Endar B.; Wardaya, Pongga Dikdya; Adler, John; Siahaan, Kisko R.
2012-06-01
Seismic wave parameter plays very important role to characterize reservoir properties whereas pore parameter is one of the most important parameter of reservoir. Therefore, wave propagation phenomena in pore media is important to be studied. By referring this study, in-direct pore measurement method based on seismic wave propagation can be developed. Porosity play important role in reservoir, because the porosity can be as compartment of fluid. Many type of porosity like primary as well as secondary porosity. Carbonate rock consist many type of porosity, i.e.: inter granular porosity, moldic porosity and also fracture porosity. The complexity of pore type in carbonate rocks make the wave propagation in these rocks is more complex than sand reservoir. We have studied numerically wave propagation in carbonate rock by finite difference modeling in time-space domain. The medium of wave propagation was modeled by base on the result of pattern recognition using artificial neural network. The image of thin slice of carbonate rock is then translated into the velocity matrix. Each mineral contents including pore of thin slice image are translated to velocity since mineral has unique velocity. After matrix velocity model has been developed, the seismic wave is propagated numerically in this model. The phenomena diffraction is clearly shown while wave propagates in this complex carbonate medium. The seismic wave is modeled in various frequencies. The result shows dispersive phenomena where high frequency wave tends to propagate in matrix instead pores. In the other hand, the low frequency waves tend to propagate through pore space even though the velocity of pore is very low. Therefore, this dispersive phenomena of seismic wave propagation can be the future indirect measurement technology for predicting the existence or intensity of pore space in reservoir rock. It will be very useful for the future reservoir characterization.
Dynamic pore-scale network model (PNM) of water imbibition in porous media
Li, J.; McDougall, S. R.; Sorbie, K. S.
2017-09-01
A dynamic pore-scale network model is presented which simulates 2-phase oil/water displacement during water imbibition by explicitly modelling intra-pore dynamic bulk and film flows using a simple local model. A new dynamic switching parameter, λ, is proposed within this model which is able to simulate the competition between local capillary forces and viscous forces over a very wide range of flow conditions. This quantity (λ) determines the primary pore filling mechanism during imbibition; i.e. whether the dominant force is (i) piston-like displacement under viscous forces, (ii) film swelling/collapse and snap-off due to capillary forces, or (iii) some intermediate local combination of both mechanisms. A series of 2D dynamic pore network simulations is presented which shows that the λ-model can satisfactorily reproduce and explain different filling regimes of water imbibition over a wide range of capillary numbers (Ca) and viscosity ratios (M). These imbibition regimes are more complex than those presented under drainage by (Lenormand et al. (1983)), since they are determined by a wider group of control parameters. Our simulations show that there is a coupling between viscous and capillary forces that is much less important in drainage. The effects of viscosity ratio during imbibition are apparent even under conditions of very slow flow (low Ca)-displacements that would normally be expected to be completely capillary dominated. This occurs as a result of the wetting films having a much greater relative mobility in the higher M cases (e.g. M = 10) thus leading to a higher level of film swelling/snap-off, resulting in local oil cluster bypassing and trapping, and hence a poorer oil recovery. This deeper coupled viscous mechanism is the underlying reason why the microscopic displacement efficiency is lower for higher M cases in water imbibition processes. Additional results are presented from the dynamic model on the corresponding effluent fractional flows (fw
Modeling reactive transport in deformable porous media using the theory of interacting continua.
Energy Technology Data Exchange (ETDEWEB)
Turner, Daniel Zack
2012-01-01
This report gives an overview of the work done as part of an Early Career LDRD aimed at modeling flow induced damage of materials involving chemical reactions, deformation of the porous matrix, and complex flow phenomena. The numerical formulation is motivated by a mixture theory or theory of interacting continua type approach to coupling the behavior of the fluid and the porous matrix. Results for the proposed method are presented for several engineering problems of interest including carbon dioxide sequestration, hydraulic fracturing, and energetic materials applications. This work is intended to create a general framework for flow induced damage that can be further developed in each of the particular areas addressed below. The results show both convincing proof of the methodologies potential and the need for further validation of the models developed.
The Meshfree Finite Volume Method with application to multi-phase porous media models
Foy, Brody H.; Perré, Patrick; Turner, Ian
2017-03-01
Numerical methods form a cornerstone of the analysis and investigation of mathematical models for physical processes. Many classical numerical schemes rely on the application of strict meshing structures to generate accurate solutions, which in some applications are an infeasible constraint. Within this paper we outline a new meshfree numerical scheme, which we call the Meshfree Finite Volume Method (MFVM). The MFVM uses interpolants to approximate fluxes in a disjoint finite volume scheme, allowing for the accurate solution of strong-form PDEs. We present a derivation of the MFVM, and give error bounds on the spatial and temporal approximations used within the scheme. We present a wide variety of applications of the method, showing key features, and advantages over traditional meshed techniques. We close with an application of the method to a non-linear multi-phase wood drying model, showing the potential for solving numerically challenging problems.
Two dimension porous media reconstruction using granular model under influence of gravity
Sundari, Pury; Fauzi, Umar; Irayani, Zaroh; Viridi, Sparisoma
2011-01-01
Modeling of pores generation in 2-D with granular grains using molecular dynamics method is reported in this work. Grains with certain diameter distribution are let falling due to gravity. Three configurations (larger diameter on top, smaller diameter on top, and mixed) and two kinds of mixture (same grains density and same grains mass) are used in the simulation. Mixture with heterogen density gives higher porosity than the homogen one for higher initial height, but change into opposite cond...
Energy Technology Data Exchange (ETDEWEB)
Xu, Tianfu; White, Stephen P.; Pruess, Karsten
1998-02-15
Pyrite (FeS{sub 2}) is one of the most common naturally occurring minerals that is present in many subsurface environments. It plays an important role in the genesis of enriched ore deposits through weathering reactions, is the most abundant sulfide mineral in many mine tailings, and is the primary source of acid drainage from mines and waste rock piles. The pyrite oxidation reaction serves as a prototype for oxidative weathering processes with broad significance for geoscientific, engineering, and environmental applications. Mathematical modeling of these processes is extremely challenging because aqueous concentrations of key species vary over an enormous range, oxygen inventory and supply are typically small in comparison to pyrite inventory, and chemical reactions are complex, involving kinetic control and microbial catalysis. We present the mathematical formulation of a general multi-phase advective-diffusive reactive transport model for redox processes. Two alternative implementations were made in the TOUGHREACT and TOUGH2-CHEM simulation codes which use sequential iteration and simultaneous solution, respectively. The simulators are applied to reactive consumption of pyrite in (1) saturated flow of oxidizing water, and (2) saturated-unsaturated flow in which oxygen transport occurs in both aqueous and gas phases. Geochemical evolutions predicted from different process models are compared, and issues of numerical accuracy and efficiency are discussed.
PHT3D-UZF: A reactive transport model for variably-saturated porous media
Wu, Ming Zhi; Post, Vincent E. A.; Salmon, S. Ursula; Morway, Eric; Prommer, H.
2016-01-01
A modified version of the MODFLOW/MT3DMS-based reactive transport model PHT3D was developed to extend current reactive transport capabilities to the variably-saturated component of the subsurface system and incorporate diffusive reactive transport of gaseous species. Referred to as PHT3D-UZF, this code incorporates flux terms calculated by MODFLOW's unsaturated-zone flow (UZF1) package. A volume-averaged approach similar to the method used in UZF-MT3DMS was adopted. The PHREEQC-based computation of chemical processes within PHT3D-UZF in combination with the analytical solution method of UZF1 allows for comprehensive reactive transport investigations (i.e., biogeochemical transformations) that jointly involve saturated and unsaturated zone processes. Intended for regional-scale applications, UZF1 simulates downward-only flux within the unsaturated zone. The model was tested by comparing simulation results with those of existing numerical models. The comparison was performed for several benchmark problems that cover a range of important hydrological and reactive transport processes. A 2D simulation scenario was defined to illustrate the geochemical evolution following dewatering in a sandy acid sulfate soil environment. Other potential applications include the simulation of biogeochemical processes in variably-saturated systems that track the transport and fate of agricultural pollutants, nutrients, natural and xenobiotic organic compounds and micropollutants such as pharmaceuticals, as well as the evolution of isotope patterns.
Experimental studies and model analysis of noble gas fractionation in porous media
Ding, Xin; Kennedy, B. Mack.; Evans, William C.; Stonestrom, David A.
2016-01-01
The noble gases, which are chemically inert under normal terrestrial conditions but vary systematically across a wide range of atomic mass and diffusivity, offer a multicomponent approach to investigating gas dynamics in unsaturated soil horizons, including transfer of gas between saturated zones, unsaturated zones, and the atmosphere. To evaluate the degree to which fractionation of noble gases in the presence of an advective–diffusive flux agrees with existing theory, a simple laboratory sand column experiment was conducted. Pure CO2 was injected at the base of the column, providing a series of constant CO2 fluxes through the column. At five fixed sampling depths within the system, samples were collected for CO2 and noble gas analyses, and ambient pressures were measured. Both the advection–diffusion and dusty gas models were used to simulate the behavior of CO2 and noble gases under the experimental conditions, and the simulations were compared with the measured depth-dependent concentration profiles of the gases. Given the relatively high permeability of the sand column (5 ´ 10−11 m2), Knudsen diffusion terms were small, and both the dusty gas model and the advection–diffusion model accurately predicted the concentration profiles of the CO2 and atmospheric noble gases across a range of CO2 flux from ?700 to 10,000 g m−2 d−1. The agreement between predicted and measured gas concentrations demonstrated that, when applied to natural systems, the multi-component capability provided by the noble gases can be exploited to constrain component and total gas fluxes of non-conserved (CO2) and conserved (noble gas) species or attributes of the soil column relevant to gas transport, such as porosity, tortuosity, and gas saturation.
An investigation of counter-current flow in porous media with history-dependent modeling
Li, G.; Grader, A. S.; Halleck, P. H.; Karpyn, Z. T.
2003-04-01
Counter-current fluid flow occurs in many reservoir processes. It is important to understand and model these processes in order to operate them effectively. Both drainage and imbibition processes exist simultaneously when counter-current flow occurs. It has thus proven difficult to model this type of flow, especially when fluid banks form. Previously, counter-current flow experiments have been done in glass bead packs and the spatial and temporal saturation distributions obtained with X-ray computed tomography (CT). In the current paper, a new saturation-history-dependent approach has been developed to simulate the experiments. Hysteresis in both capillary pressure and relative permeabilities is considered during the process of matching the simulation results to experimental data. Capillary pressure and relative permeabilities are extracted with the aid of a deterministic reservoir simulator. During the history matching process, a family of curves (called scanning curves) is constructed connecting the two branches of the capillary hystersis loop. Each grid block of the sample is assigned a different scanning curve according to its saturation history. Simulation of the experiments reproduced two-dimensional saturation distributions over time with good accuracy. Similar results could not be obtained with traditional simulation using only one capillary pressure curve. History-dependent modeling successfully predicted cross-diameter counter-current flow in a cylindrical geometry. The parameters used in the single capillary pressure method are the average of the parameters used in the history-dependent method. Total effective mobility controls the flow process, being smaller in counter-current flow than in co-current flow. Experiments documented in the literature that exhibited formation of fluid banks were also successfully simulated. We anticipate that application of this method will improve the prediction of full-scale fluid flow processes such as ground water
Wheeler, M.F.
2010-09-06
For many years there have been formulations considered for modeling single phase ow on general hexahedra grids. These include the extended mixed nite element method, and families of mimetic nite di erence methods. In most of these schemes either no rate of convergence of the algorithm has been demonstrated both theoret- ically and computationally or a more complicated saddle point system needs to be solved for an accurate solution. Here we describe a multipoint ux mixed nite element (MFMFE) method [5, 2, 3]. This method is motivated from the multipoint ux approximation (MPFA) method [1]. The MFMFE method is locally conservative with continuous ux approximations and is a cell-centered scheme for the pressure. Compared to the MPFA method, the MFMFE has a variational formulation, since it can be viewed as a mixed nite element with special approximating spaces and quadrature rules. The framework allows han- dling of hexahedral grids with non-planar faces by applying trilinear mappings from physical elements to reference cubic elements. In addition, there are several multi- scale and multiphysics extensions such as the mortar mixed nite element method that allows the treatment of non-matching grids [4]. Extensions to the two-phase oil-water ow are considered. We reformulate the two- phase model in terms of total velocity, capillary velocity, water pressure, and water saturation. We choose water pressure and water saturation as primary variables. The total velocity is driven by the gradient of the water pressure and total mobility. Iterative coupling scheme is employed for the coupled system. This scheme allows treatments of di erent time scales for the water pressure and water saturation. In each time step, we rst solve the pressure equation using the MFMFE method; we then Center for Subsurface Modeling, The University of Texas at Austin, Austin, TX 78712; mfw@ices.utexas.edu. yCenter for Subsurface Modeling, The University of Texas at Austin, Austin, TX 78712; gxue
Two dimension porous media reconstruction using granular model under influence of gravity
Sundari, Pury; Fauzi, Umar; Irayani, Zaroh; Viridi, Sparisoma
2012-06-01
Modeling of pores generation in 2-D with granular grains using molecular dynamics method is reported in this work. Grains with certain diameter distribution are let falling due to gravity. Three configurations (larger diameter in at upper layer, smaller diameter in at upper layer, and mixed) and two kinds of mixture (similar of grain density and mass) are used in the simulation. Mixture with heterogeneous density gives higher porosity than the homogeneous one for higher initial height, but change into opposite condition for lower initial height.
The Rain on Underground Porous Media Part Ⅰ: Analysis of a Richards Model
Institute of Scientific and Technical Information of China (English)
Christine BERNARDI; Adel BLOUZA; Linda EL ALAOUI
2013-01-01
The Richards equation models the water flow in a partially saturated underground porous medium under the surface.When it rains on the surface,boundary conditions of Signorini type must be considered on this part of the boundary.The authors first study this problem which results into a variational inequality and then propose a discretization by an implicit Euler's scheme in time and finite elements in space.The convergence of this discretization leads to the well-posedness of the problem.
Application of Stochastic Approaches to Modelling Suspension Flow in Porous Media
DEFF Research Database (Denmark)
Shapiro, Alexander; Yuan, Hao
2012-01-01
briefly discussed. The population balance models growing out of the Boltzmann-Smolukhowski formalism take into account the particle and the pore size distributions. A system of integral-differential kinetic equations for the particle transport is derived and averaged. The continuous-time random walk...... theory considers the distribution of the residence times of particles in pores. The transport equation derived in the framework of CTRW contains a convolution integral with a memory kernel accounting for the particle flight distribution. An important simplification of the CTRW formalism, its reduction...
Porous media geometry and transports
Adler, Pierre
1992-01-01
The goal of ""Porous Media: Geometry and Transports"" is to provide the basis of a rational and modern approach to porous media. This book emphasizes several geometrical structures (spatially periodic, fractal, and random to reconstructed) and the three major single-phase transports (diffusion, convection, and Taylor dispersion).""Porous Media"" serves various purposes. For students it introduces basic information on structure and transports. Engineers will find this book useful as a readily accessible assemblage of al the major experimental results pertaining to single-phase tr
Acid/base front propagation in saturated porous media: 2D laboratory experiments and modeling
Loyaux-Lawniczak, Stéphanie; Lehmann, François; Ackerer, Philippe
2012-09-01
We perform laboratory scale reactive transport experiments involving acid-basic reactions between nitric acid and sodium hydroxide. A two-dimensional experimental setup is designed to provide continuous on-line measurements of physico-chemical parameters such as pH, redox potential (Eh) and electrical conductivity (EC) inside the system under saturated flow through conditions. The electrodes provide reliable values of pH and EC, while sharp fronts associated with redox potential dynamics could not be captured. Care should be taken to properly incorporate within a numerical model the mixing processes occurring inside the electrodes. The available observations are modeled through a numerical code based on the advection-dispersion equation. In this framework, EC is considered as a variable behaving as a conservative tracer and pH and Eh require solving the advection dispersion equation only once. The agreement between the computed and measured pH and EC is good even without recurring to parameters calibration on the basis of the experiments. Our findings suggest that the classical advection-dispersion equation can be used to interpret these kinds of experiments if mixing inside the electrodes is adequately considered.
Abriola, Linda M.; Pinder, George F.
1985-01-01
A multiphase approach to the modeling of aquifer contamination by organic compounds is developed. This approach makes it possible to describe the simultaneous transport of a chemical contaminant in three physical forms: as a nonaqueous phase, as a soluble component of an aqueous phase, and as a mobile fraction of a gas phase. The contaminant may be composed of, at most, two distinct components, one of which may be volatile and slightly water soluble and the other of which is both nonvolatile and insoluble in water. Equations which describe this complex system are derived from basic conservation of mass principles by the application of volume averaging techniques and the incorporation of various constitutive relations and approximations. Effects of matrix and fluid compressibilities, gravity, phase composition, interphase mass exchange, capillarity, diffusion, and dispersion are all considered. The resulting mathematical model consists of a system of three nonlinear partial differential equations subject to two equilibrium constraints. These equations relate five unknowns: two capillary pressures and three mass fractions.
A partially open porous media flow with chaotic advection: towards a model of coupled fields.
Metcalfe, Guy; Lester, Daniel; Ord, Alison; Kulkarni, Pandurang; Trefry, Mike; Hobbs, Bruce E; Regenaur-Lieb, Klaus; Morris, Jeffery
2010-01-13
In nature, dissipative fluxes of fluid, heat and/or reacting species couple to each other and may also couple to deformation of a surrounding porous matrix. We use the well-known analogy of Hele-Shaw flow to Darcy flow to make a model porous medium with porosity proportional to local cell height. Time- and space-varying fluid injection from multiple source/sink wells lets us create many different kinds of chaotic flows and chemical concentration patterns. Results of an initial time-dependent potential flow model illustrate that this is a partially open flow, in which parts of the material transported by the flow remain in the cell forever and parts pass through with residence time and exit time distributions that have self-similar features in the control parameter space of the stirring. We derive analytically the existence boundary in stirring control parameter space between where isolated fluid regions can and cannot remain forever in the open flow. Experiments confirm the predictions.
Bayesian data assimilation for stochastic multiscale models of transport in porous media.
Energy Technology Data Exchange (ETDEWEB)
Marzouk, Youssef M. (Massachusetts Institute of Technology, Cambridge, MA); van Bloemen Waanders, Bart Gustaaf (Sandia National Laboratories, Albuquerque NM); Parno, Matthew (Massachusetts Institute of Technology, Cambridge, MA); Ray, Jaideep; Lefantzi, Sophia; Salazar, Luke (Sandia National Laboratories, Albuquerque NM); McKenna, Sean Andrew (Sandia National Laboratories, Albuquerque NM); Klise, Katherine A. (Sandia National Laboratories, Albuquerque NM)
2011-10-01
We investigate Bayesian techniques that can be used to reconstruct field variables from partial observations. In particular, we target fields that exhibit spatial structures with a large spectrum of lengthscales. Contemporary methods typically describe the field on a grid and estimate structures which can be resolved by it. In contrast, we address the reconstruction of grid-resolved structures as well as estimation of statistical summaries of subgrid structures, which are smaller than the grid resolution. We perform this in two different ways (a) via a physical (phenomenological), parameterized subgrid model that summarizes the impact of the unresolved scales at the coarse level and (b) via multiscale finite elements, where specially designed prolongation and restriction operators establish the interscale link between the same problem defined on a coarse and fine mesh. The estimation problem is posed as a Bayesian inverse problem. Dimensionality reduction is performed by projecting the field to be inferred on a suitable orthogonal basis set, viz. the Karhunen-Loeve expansion of a multiGaussian. We first demonstrate our techniques on the reconstruction of a binary medium consisting of a matrix with embedded inclusions, which are too small to be grid-resolved. The reconstruction is performed using an adaptive Markov chain Monte Carlo method. We find that the posterior distributions of the inferred parameters are approximately Gaussian. We exploit this finding to reconstruct a permeability field with long, but narrow embedded fractures (which are too fine to be grid-resolved) using scalable ensemble Kalman filters; this also allows us to address larger grids. Ensemble Kalman filtering is then used to estimate the values of hydraulic conductivity and specific yield in a model of the High Plains Aquifer in Kansas. Strong conditioning of the spatial structure of the parameters and the non-linear aspects of the water table aquifer create difficulty for the ensemble Kalman
Directory of Open Access Journals (Sweden)
Shreekant Pathak
2016-09-01
Full Text Available The approximate solution of imbibition phenomenon governed by non-linear partial differential equation is discussed in the present paper. Primary oil recovery process due to natural soil pressure, but in the secondary oil recovery process water flooding plays an important role. When water is injected in the injection well for recovering the reaming oil after primary oil recovery process, it comes to contact with the native oil and at that time the imbibition phenomenon occurs due to different viscosity. For the mathematical modelling, we consider the homogeneous porous medium and optimal homotopy analysis method has been used to solve the partial differential equation governed by it. The graphical representation of the solution is given by MATHEMATICA and physically interpreted.
Homogenized models for a short-time filtration in elastic porous media
Directory of Open Access Journals (Sweden)
Anvarbek M. Meirmanov
2008-01-01
Full Text Available We consider a linear system of differential equations describing a joint motion of elastic porous body and fluid occupying porous space. The rigorous justification, under various conditions imposed on physical parameters, is fulfilled for homogenization procedures as the dimensionless size of the pores tends to zero, while the porous body is geometrically periodic and a characteristic time of processes is small enough. Such kind of models may describe, for example, hydraulic fracturing or acoustic or seismic waves propagation. As the results, we derive homogenized equations involving non-isotropic Stokes system for fluid velocity coupled with two different types of acoustic equations for the solid component, depending on ratios between physical parameters, or non-isotropic Stokes system for one-velocity continuum. The proofs are based on Nguetseng's two-scale convergence method of homogenization in periodic structures.
Modeling and Diagnostics of Fuel Cell Porous Media for Improving Water Transport
Energy Technology Data Exchange (ETDEWEB)
Allen, Jeff; M' edici, Ezequiel
2011-07-01
When a fuel cell is operating at high current density, water accumulation is a significant cause of performance and component degradation. Investigating the water transport inside the fuel cell is a challenging task due to opacity of the components, the randomness of the porous materials, and the difficulty in gain access to the interior for measurement due to the small dimensions of components. Numerical simulation can provide a good insight of the evolution of the water transport under different working condition. However, the validation of those simulations is remains an issue due the same experimental obstacles associated with in-situ measurements. The discussion herein will focus on pore-network modeling of the water transport on the PTL and the insights gained from simulations as well as in the validation technique. The implications of a recently published criterion to characterize PTL, based on percolation theory, and validate numerical simulation are discussed.
Dissolution in anisotropic porous media: Modelling convection regimes from onset to shutdown
De Paoli, Marco; Zonta, Francesco; Soldati, Alfredo
2017-02-01
In the present study, we use direct numerical simulations to examine the role of non-isotropic permeability on solutal convection in a fluid-saturated porous medium. The dense solute injected from the top boundary is driven downwards by gravity and follows a complex time-dependent dynamics. The process of solute dissolution, which is initially controlled by diffusion, becomes dominated by convection as soon as fingers appear, grow, and interact. The dense solute finally reaches the bottom boundary where, due to the prescribed impermeable boundary, it starts filling the domain so to enter the shutdown stage. We present the entire transient dynamics for large Rayleigh-Darcy numbers, Ra, and non-isotropic permeability. We also try to provide suitable and reliable models to parametrize it. With the conceptual setup presented here, we aim at mimicking the process of liquid CO2 sequestration into geological reservoirs.
Time domain numerical modeling of wave propagation in 2D acoustic / porous media
Chiavassa, Guillaume
2011-01-01
Numerical methods are developed to simulate the wave propagation in 2D heterogeneous fluid / poroelastic media. Wave propagation is described by the usual acoustics equations (in the fluid medium) and by the low-frequency Biot's equations (in the porous medium). Interface conditions are introduced to model various hydraulic contacts between the two media: open pores, sealed pores, and imperfect pores. Well-possedness of the initial-boundary value problem is proven. Cartesian grid numerical methods previously developed in porous heterogeneous media are adapted to the present context: a fourth-order ADER scheme with Strang splitting for time-marching; a space-time mesh-refinement to capture the slow compressional wave predicted by Biot's theory; and an immersed interface method to discretize the interface conditions and to introduce a subcell resolution. Numerical experiments and comparisons with exact solutions are proposed for the three types of interface conditions, demonstrating the accuracy of the approach...
Directory of Open Access Journals (Sweden)
Birgit Weyand
2015-01-01
Full Text Available A three-dimensional computational fluid dynamics- (CFD- model based on a differential pressure laminar flow bioreactor prototype was developed to further examine performance under changing culture conditions. Cell growth inside scaffolds was simulated by decreasing intrinsic permeability values and led to pressure build-up in the upper culture chamber. Pressure release by an integrated bypass system allowed continuation of culture. The specific shape of the bioreactor culture vessel supported a homogenous flow profile and mass flux at the scaffold level at various scaffold permeabilities. Experimental data showed an increase in oxygen concentration measured inside a collagen scaffold seeded with human mesenchymal stem cells when cultured in the perfusion bioreactor after 24 h compared to static culture in a Petri dish (dynamic: 11% O2 versus static: 3% O2. Computational fluid simulation can support design of bioreactor systems for tissue engineering application.
Institute of Scientific and Technical Information of China (English)
HUANG; Guanhua; HUANG; Quanzhong; ZHAN; Hongbin
2005-01-01
The newly developed Fractional Advection-Dispersion Equation (FADE), which is FADE was extended and used in this paper for modelling adsorbing contaminant transport by adding an adsorbing term. A parameter estimation method and its corresponding FORTRAN based program named FADEMain were developed on the basis of Nonlinear Least Square Algorithm and the analytical solution for one-dimensional FADE under the conditions of step input and steady state flow. Data sets of adsorbing contaminants Cd and NH4+-N transport in short homogeneous soil columns and conservative solute NaCI transport in a long homogeneous soil column, respectively were used to estimate the transport parameters both by FADEMain and the advection-dispersion equation (ADE) based program CXTFIT2.1. Results indicated that the concentration simulated by FADE agreed well with the measured data. Compared to the ADE model, FADE can provide better simulation for the concentration in the initial lower concentration part and the late higher concentration part of the breakthrough curves for both adsorbing contaminants. The dispersion coefficients for ADE were from 0.13 to 7.06 cm2/min, while the dispersion coefficients for FADE ranged from 0.119 to 3.05 cm1.856/min for NaCI transport in the long homogeneous soil column. We found that the dispersion coefficient of FADE increased with the transport distance, and the relationship between them can be quantified with an exponential function. Less scale-dependent was also found for the dispersion coefficient of FADE with respect to ADE.
Fractal Analysis of Stress Sensitivity of Permeability in Porous Media
Tan, Xiao-Hua; Li, Xiao-Ping; Liu, Jian-Yi; Zhang, Lie-Hui; Cai, Jianchao
2015-12-01
A permeability model for porous media considering the stress sensitivity is derived based on mechanics of materials and the fractal characteristics of solid cluster size distribution. The permeability of porous media considering the stress sensitivity is related to solid cluster fractal dimension, solid cluster fractal tortuosity dimension, solid cluster minimum diameter and solid cluster maximum diameter, Young's modulus, Poisson's ratio, as well as power index. Every parameter has clear physical meaning without the use of empirical constants. The model predictions of permeability show good agreement with those obtained by the available experimental expression. The proposed model may be conducible to a better understanding of the mechanism for flow in elastic porous media.
Numerical approximation for a degenerate parabolic-elliptic system modeling flows in porous media
Directory of Open Access Journals (Sweden)
Rabah-Hacene Bellout
2012-11-01
Full Text Available We present a numerical scheme for the approximation of the system of partial differential equations of the Peaceman model for the miscible displacement of one fluid by another in a two dimensional porous medium. In this scheme, the velocity-pressure equations are treated by a mixed finite element discretization using the Raviart-Thomas element, and the concentration equation is approximated by a finite volume discretization using the Upstream scheme, knowing that the Raviart-Thomas element gives good approximations for fluids velocities and that the Upstream scheme is well suited for convection dominated equations. We prove a maximum principle for our approximate concentration more precisely $ 0leq c_h(x,tleq 1$ a.e. in $Omega_T $ as long as some grid conditions are satisfied - at the difference of Chainais and Droniou [6]who have only observed that their approximate concentration remains in $[0;1]$ (and such is the case for other proposed numerical methods; e.g., [21,22]. Moreover our grid conditions are satisfied even with very large time steps and spatial steps. Finally we prove the consistency of the proposed scheme and thus are assured of convergence. A numerical test is reported.
The slender bubble model for very slow degassing in porous media and cold production
Energy Technology Data Exchange (ETDEWEB)
Chraibi, M. [Total, Paris (France); Zaleski, S. [Society of Petroleum Engineers, London (United Kingdom)]|[Paris Univ., Paris (France); Franco, F. [Society of Petroleum Engineers, London (United Kingdom)]|[Total, Paris (France)
2008-10-15
Cold oil production leads to degassing of the light species and the formation of a bubbly phase. This is often referred to as the foamy oil effect and is particularly observed with heavy oils, combining high viscosity and asphaltenes. The presence and behaviour of a foamy-oil effect is critical to the cold production process. However, because a wide range of different petrophysical parameters and experimental factors interact in a complex manner, this process is not a well-understood production mechanism. This study focused on improving the understanding of the solution gas drive mechanism in primary heavy oil recovery. A Darcy-scale model was developed that took into account the basic physical phenomena of bubble nucleation, bubble growth by solute diffusion and expansion, and bubble mobilization. The relative permeability of the gas phase was replaced by an expression for the gas mobility with new physical effects related to capillarity, viscosity, gravity, and bubble geometry. The purpose was to fit the productions with a limited number of parameters, having physical meaning, independently from the depletion rate. The paper also presented several simplifications of the basic Darcy-scale equations, that enabled the production prediction in a much simpler manner than through full simulations. The full set of Darcy-scale equations were solved using a numerical solution. The formation of strong gradients of the gas phase saturation were shown to depend on gravity and viscosity. 12 refs., 4 figs.
Modeling Bimolecular Reactions and Transport in Porous Media Via Particle Tracking
Energy Technology Data Exchange (ETDEWEB)
Dong Ding; David Benson; Amir Paster; Diogo Bolster
2012-01-01
model simulates more accurately than the ADRE.
Ai, Cheng; Zhou, Jian; Zhang, Heng; Zhao, Xinbao; Pei, Yanling; Li, Shusuo; Gong, Shengkai
2016-01-01
The non-equilibrium solidification behaviors of five Ni-Al-Ta ternary model single crystal alloys with different Al contents were investigated by experimental analysis and theoretical calculation (by JMatPro) in this study. These model alloys respectively represented the γ' phase with various volume fractions (100%, 75%, 50%, 25% and 0%) at 900 °C. It was found that with decreasing Al content, liquidus temperature of experimental alloys first decreased and then increased. Meanwhile, the solidification range showed a continued downward trend. In addition, with decreasing Al content, the primary phases of non-equilibrium solidified model alloys gradually transformed from γ' phase to γ phase, and the area fraction of which first decreased and then increased. Moreover, the interdendritic/intercellular precipitation of model alloys changed from β phase (for 100% γ') to (γ+γ')Eutectic (for 75% γ'), (γ+γ')Eutectic+γ' (for 50% γ' and 25% γ') and none interdendritic precipitation (for 0% γ'), and the last stage non-equilibrium solidification sequence of model alloys was determined by the nominal Al content and different microsegregation behaviors of Al element.
Modeling magma flow in volcanic conduit with non-equilibrium crystallization
Yulia, Tsvetkova
2010-05-01
Modeling magma flow in volcanic conduit including with non -equilibrium crystallization There is a set of models of magma flow in volcanic conduits which predicts oscillations in magma discharge during extrusion of lava domes. These models neglect heating of surrounding rocks and use 1D approximation of the flow in the conduit. Here magma flow is investigated with an account of heat exchange between surrounding rocks and magma and different dependences viscosity on temperature and crystal concentration. Stick-slip conditions were applied at the wall. The flow is assumed to be quasi-static and quasi 1D. Only vertical component of velocity vector is present, thus, we do not consider horizontal momentum balance. At the top of the conduit the pressure is assumed to be fixed, chamber pressure changes according with magma influx and outflux. First set of simulation was made for the viscosity that depends on cross-section average crystal concentration and parabolic velocity profile. In earlier models that account for crystal growth kinetics the temperature was allowed to change only due to the release of latent heat of crystallization. Heat transfer leads to cooling of the outer parts of the conduit leading to high crystal contents and high magma viscosities. Changes in viscosity result in changes in discharge rate. For the non-isothermal case there is no motion during most part of the cycle and a portion of magma solidifies at the top of the conduit forming a plug. During repose period chamber pressure is growing due to influx of fresh magma, and magma discharge rate starts to increase. Influx of hot magma into the conduit leads to decrease in friction resulting in a jump in discharge rate that lead to depressurization of magma chamber. Discharge rate decreases and magma solidifies again. For isothermal model with the same parameters discharge rate monotonically tends to the value of Qin. Simulation reveal that crystal content changes significantly across the conduit
Energy Technology Data Exchange (ETDEWEB)
Wang, G.X.; Matthys, E.F. [Univ. of California, Santa Barbara, CA (United States). Dept. of Mechanical and Environmental Engineering
1995-12-31
A one-dimensional model including non-equilibrium phenomena was developed for surface melting and resolidification of both pure metals and binary alloys substrates. Non-equilibrium kinetics from crystal growth theory are introduced in the model to treat both non-equilibrium melting and resolidification. The modelled problem involves a moving boundary with both heat and solute diffusions and is solved by an implicit control volume integral method with solid/liquid interface immobilization by coordinate transformation. For illustration of the model applicability, the authors have analyzed laser surface melting of pure metals (Al, Cu, Ni, Ti) and dilute Al-Cu alloys, and some typical results are presented. The computation results show large solid overheating and melt undercooling which result from the high heat flux and the slow kinetics. The melt undercooling is maintained during most of the resolidification process and so is the high solidification rate. Complex interface velocity variations during the earlier stages of resolidification were obtained and result from interactions between various physical mechanisms. A strong effect of the solute on the interface velocity was also predicted.
Guo, L.; Huang, H.; Gaston, D.; Redden, G. D.; Fox, D. T.; Fujita, Y.
2010-12-01
to homogeneous and heterogeneous porous media, respectively. In 1D columns, calcium carbonate mineral precipitation was driven by urea hydrolysis catalyzed by urease enzyme, and in 2D flow cells, calcium carbonate mineral forming reactants were injected sequentially, forming migrating reaction fronts that are typically highly nonuniform. The RAT simulation results for the spatial and temporal distributions of precipitates, reaction rates and major species in the system, and also for changes in porosity and permeability, were compared to both laboratory experimental data and computational results obtained using other reactive transport simulators. The comparisons demonstrate the ability of RAT to simulate complex nonlinear systems and the advantages of fully coupled approaches, over de-coupled methods, for accurate simulation of complex, dynamic processes such as engineered mineral precipitation in subsurface environments.
Transport phenomena in porous media
Ingham, Derek B
1998-01-01
Research into thermal convection in porous media has substantially increased during recent years due to its numerous practical applications. These problems have attracted the attention of industrialists, engineers and scientists from many very diversified disciplines, such as applied mathematics, chemical, civil, environmental, mechanical and nuclear engineering, geothermal physics and food science. Thus, there is a wealth of information now available on convective processes in porous media and it is therefore appropriate and timely to undertake a new critical evaluation of this contemporary information. Transport Phenomena in Porous Media contains 17 chapters and represents the collective work of 27 of the world's leading experts, from 12 countries, in heat transfer in porous media. The recent intensive research in this area has substantially raised the expectations for numerous new practical applications and this makes the book a most timely addition to the existing literature. It includes recent major deve...
Sweijen, Thomas; Hartog, Niels; Marsman, Annemieke; Keijzer, Thomas J. S.
2014-06-01
Mercury is a contaminant of global concern. The use of elemental mercury in various (former) industrial processes, such as chlorine production at chlor-alkali plants, is known to have resulted in soil and groundwater contaminations worldwide. However, the subsurface transport behaviour of elemental mercury as an immiscible dense non-aqueous phase liquid (DNAPL) in porous media has received minimal attention to date. Even though, such insight would aid in the remediation effort of mercury contaminated sites. Therefore, in this study a detailed field characterization of elemental mercury DNAPL distribution with depth was performed together with two-phase flow modelling, using STOMP. This is to evaluate the dynamics of mercury DNAPL migration and the controls on its distribution in saturated porous media. Using a CPT-probe mounted with a digital camera, in-situ mercury DNAPL depth distribution was obtained at a former chlor-alkali-plant, down to 9 m below ground surface. Images revealing the presence of silvery mercury DNAPL droplets were used to quantify its distribution, characteristics and saturation, using an image analysis method. These field-observations with depth were compared with results from a one-dimensional two-phase flow model simulation for the same transect. Considering the limitations of this approach, simulations reasonably reflected the variability and range of the mercury DNAPL distribution. To further explore the impact of mercury's physical properties in comparison with more common DNAPLs, the migration of mercury and PCE DNAPL in several typical hydrological scenarios was simulated. Comparison of the simulations suggest that mercury's higher density is the overall controlling factor in controlling its penetration in saturated porous media, despite its higher resistance to flow due to its higher viscosity. Based on these results the hazard of spilled mercury DNAPL to cause deep contamination of groundwater systems seems larger than for any other
You, Zhi-Qiang; Mewes, Jan-Michael; Dreuw, Andreas; Herbert, John M.
2015-11-01
The Marcus and Pekar partitions are common, alternative models to describe the non-equilibrium dielectric polarization response that accompanies instantaneous perturbation of a solute embedded in a dielectric continuum. Examples of such a perturbation include vertical electronic excitation and vertical ionization of a solution-phase molecule. Here, we provide a general derivation of the accompanying polarization response, for a quantum-mechanical solute described within the framework of a polarizable continuum model (PCM) of electrostatic solvation. Although the non-equilibrium free energy is formally equivalent within the two partitions, albeit partitioned differently into "fast" versus "slow" polarization contributions, discretization of the PCM integral equations fails to preserve certain symmetries contained in these equations (except in the case of the conductor-like models or when the solute cavity is spherical), leading to alternative, non-equivalent matrix equations. Unlike the total equilibrium solvation energy, however, which can differ dramatically between different formulations, we demonstrate that the equivalence of the Marcus and Pekar partitions for the non-equilibrium solvation correction is preserved to high accuracy. Differences in vertical excitation and ionization energies are <0.2 eV (and often <0.01 eV), even for systems specifically selected to afford a large polarization response. Numerical results therefore support the interchangeability of the Marcus and Pekar partitions, but also caution against relying too much on the fast PCM charges for interpretive value, as these charges differ greatly between the two partitions, especially in polar solvents.
Liu, Q
2016-01-01
In this paper, a three-dimensional (3D) multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is presented for convection heat transfer in porous media at the representative elementary volume (REV) scale. The model is developed in the framework of the double-distribution-function (DDF) approach: an MRT-LB model of the density distribution function with the D3Q19 lattice (or D3Q15 lattice) is proposed to simulate the flow field based on the generalized non-Darcy model, while an MRT-LB model of the temperature distribution function with the D3Q7 lattice is proposed to simulate the temperature filed. The present model is employed to simulate mixed convection flow in a porous channel and natural convection in a cubical porous cavity. The numerical results demonstrate the effectiveness and accuracy of the present model in solving 3D convection heat transfer problems in porous media. The numerical results also demonstrate that the present model is approximately second-order accuracy in space. In addition, an ...
Fan, Zhengfeng; Liu, Jie
2016-10-01
We present an ion-electron non-equilibrium model, in which the hot-spot ion temperature is higher than its electron temperature so that the hot-spot nuclear reactions are enhanced while energy leaks are considerably reduced. Theoretical analysis shows that the ignition region would be significantly enlarged in the hot-spot rhoR-T space as compared with the commonly used equilibrium model. Simulations show that shocks could be utilized to create and maintain non-equilibrium conditions within the hot spot, and the hot-spot rhoR requirement is remarkably reduced for achieving self-heating. In NIF high-foot implosions, it is observed that the x-ray enhancement factors are less than unity, which is not self-consistent and is caused by assuming Te =Ti. And from this non-consistency, we could infer that ion-electron non-equilibrium exists in the high-foot implosions and the ion temperature could be 9% larger than the equilibrium temperature.
Ovaysi, S.; Piri, M.
2009-12-01
We present a three-dimensional fully dynamic parallel particle-based model for direct pore-level simulation of incompressible viscous fluid flow in disordered porous media. The model was developed from scratch and is capable of simulating flow directly in three-dimensional high-resolution microtomography images of naturally occurring or man-made porous systems. It reads the images as input where the position of the solid walls are given. The entire medium, i.e., solid and fluid, is then discretized using particles. The model is based on Moving Particle Semi-implicit (MPS) technique. We modify this technique in order to improve its stability. The model handles highly irregular fluid-solid boundaries effectively. It takes into account viscous pressure drop in addition to the gravity forces. It conserves mass and can automatically detect any false connectivity with fluid particles in the neighboring pores and throats. It includes a sophisticated algorithm to automatically split and merge particles to maintain hydraulic connectivity of extremely narrow conduits. Furthermore, it uses novel methods to handle particle inconsistencies and open boundaries. To handle the computational load, we present a fully parallel version of the model that runs on distributed memory computer clusters and exhibits excellent scalability. The model is used to simulate unsteady-state flow problems under different conditions starting from straight noncircular capillary tubes with different cross-sectional shapes, i.e., circular/elliptical, square/rectangular and triangular cross-sections. We compare the predicted dimensionless hydraulic conductances with the data available in the literature and observe an excellent agreement. We then test the scalability of our parallel model with two samples of an artificial sandstone, samples A and B, with different volumes and different distributions (non-uniform and uniform) of solid particles among the processors. An excellent linear scalability is
Chaynikov, S.; Porta, G.; Riva, M.; Guadagnini, A.
2012-04-01
We focus on a theoretical analysis of nonreactive solute transport in porous media through the volume averaging technique. Darcy-scale transport models based on continuum formulations typically include large scale dispersive processes which are embedded in a pore-scale advection diffusion equation through a Fickian analogy. This formulation has been extensively questioned in the literature due to its inability to depict observed solute breakthrough curves in diverse settings, ranging from the laboratory to the field scales. The heterogeneity of the pore-scale velocity field is one of the key sources of uncertainties giving rise to anomalous (non-Fickian) dispersion in macro-scale porous systems. Some of the models which are employed to interpret observed non-Fickian solute behavior make use of a continuum formulation of the porous system which assumes a two-region description and includes a bimodal velocity distribution. A first class of these models comprises the so-called ''mobile-immobile'' conceptualization, where convective and dispersive transport mechanisms are considered to dominate within a high velocity region (mobile zone), while convective effects are neglected in a low velocity region (immobile zone). The mass exchange between these two regions is assumed to be controlled by a diffusive process and is macroscopically described by a first-order kinetic. An extension of these ideas is the two equation ''mobile-mobile'' model, where both transport mechanisms are taken into account in each region and a first-order mass exchange between regions is employed. Here, we provide an analytical derivation of two region "mobile-mobile" meso-scale models through a rigorous upscaling of the pore-scale advection diffusion equation. Among the available upscaling methodologies, we employ the Volume Averaging technique. In this approach, the heterogeneous porous medium is supposed to be pseudo-periodic, and can be represented through a (spatially) periodic unit cell
Directory of Open Access Journals (Sweden)
Katalin Martinás
2007-02-01
Full Text Available A microeconomic, agent based framework to dynamic economics is formulated in a materialist approach. An axiomatic foundation of a non-equilibrium microeconomics is outlined. Economic activity is modelled as transformation and transport of commodities (materials owned by the agents. Rate of transformations (production intensity, and the rate of transport (trade are defined by the agents. Economic decision rules are derived from the observed economic behaviour. The non-linear equations are solved numerically for a model economy. Numerical solutions for simple model economies suggest that the some of the results of general equilibrium economics are consequences only of the equilibrium hypothesis. We show that perfect competition of selfish agents does not guarantee the stability of economic equilibrium, but cooperativity is needed, too.
Non-equilibrium Landauer transport model for Hawking radiation from a black hole
Nation, P. D.; Blencowe, M. P.; Nori, Franco
2012-03-01
We propose that the Hawking radiation energy and entropy flow rates from a black hole can be viewed as a one-dimensional (1D), non-equilibrium Landauer transport process. Support for this viewpoint comes from previous calculations invoking conformal symmetry in the near-horizon region, which give radiation rates that are identical to those of a single 1D quantum channel connected to a thermal reservoir at the Hawking temperature. The Landauer approach shows in a direct way the particle statistics independence of the energy and entropy fluxes of a black hole radiating into vacuum, as well as one near thermal equilibrium with its environment. As an application of the Landauer approach, we show that Hawking radiation gives a net entropy production that is 50% larger than that obtained assuming standard 3D emission into vacuum.
Nield, Donald A
2017-01-01
This updated edition of a widely admired text provides a user-friendly introduction to the field that requires only routine mathematics. The book starts with the elements of fluid mechanics and heat transfer, and covers a wide range of applications from fibrous insulation and catalytic reactors to geological strata, nuclear waste disposal, geothermal reservoirs, and the storage of heat-generating materials. As the standard reference in the field, this book will be essential to researchers and practicing engineers, while remaining an accessible introduction for graduate students and others entering the field. The new edition features 2700 new references covering a number of rapidly expanding fields, including the heat transfer properties of nanofluids and applications involving local thermal non-equilibrium and microfluidic effects. Recognized as the standard reference in the field Includes a comprehensive, 350-page reference list Cited over 5900 times to date in its various editions Serves as an introduction ...
Multiparticle collision dynamics in porous media
Matyka, Maciej
2016-01-01
We adopt the multiparticle collision dynamics method to simulate fluid flows in porous media. For this, the particle-level drag force is introduced into the original algorithm. The force hinder the flow resulting in global resistance and decrease of permeability. The extended algorithm is validated in the flow through fully porous channel with analytical solution. Basic properties of the solver are investigated including its dependency of permeability on model parameters.
On thermal explosion in porous media
Gordon, Peter
2010-06-01
We consider a model of thermal explosion in porous media which is a natural generalization of the well-known problem of self-ignition introduced by (Gelfand 1963 Am. Math. Soc. Trans. 29 295-381). We rigorously prove that, similar to the Gelfand-Barenblatt problem, the thermal explosion (finite time blow-up of all solutions for the problem with non-negative initial data) occurs exclusively due to the absence of a weak solution of the corresponding stationary problem.
Porous media: Analysis, reconstruction and percolation
DEFF Research Database (Denmark)
Rogon, Thomas Alexander
1995-01-01
Spatial structure of selected porous media has been analysed in terms of the two first spatial moments (i.e. porosity and autocorrelation). Having established directional isotropy in the three spatial planes, multiple geometrical features measured in 2-d are attempted generalized to 3-d using...... in binary fields. Percolation threshold of reconstructed porous media has been determined for different discretizations of a selected model correlation function. Also critical exponents such as the correlation length exponent v, the strength of the infinite network and the mean size of finite clusters have...... been determined. We have obtained results which indicate that the effect of spatial correlation does affect not only the percolation threshold but also the exponents with respect to the values known for random media. We have attempted to predict key percolation values for a continuous medium (i...
Convection with local thermal non-equilibrium and microfluidic effects
Straughan, Brian
2015-01-01
This book is one of the first devoted to an account of theories of thermal convection which involve local thermal non-equilibrium effects, including a concentration on microfluidic effects. The text introduces convection with local thermal non-equilibrium effects in extraordinary detail, making it easy for readers newer to the subject area to understand. This book is unique in the fact that it addresses a large number of convection theories and provides many new results which are not available elsewhere. This book will be useful to researchers from engineering, fluid mechanics, and applied mathematics, particularly those interested in microfluidics and porous media.
Natural thermal convection in fractured porous media
Adler, P. M.; Mezon, C.; Mourzenko, V.; Thovert, J. F.; Antoine, R.; Finizola, A.
2015-12-01
In the crust, fractures/faults can provide preferential pathways for fluid flow or act as barriers preventing the flow across these structures. In hydrothermal systems (usually found in fractured rock masses), these discontinuities may play a critical role at various scales, controlling fluid flows and heat transfer. The thermal convection is numerically computed in 3D fluid satured fractured porous media. Fractures are inserted as discrete objects, randomly distributed over a damaged volume, which is a fraction of the total volume. The fluid is assumed to satisfy Darcy's law in the fractures and in the porous medium with exchanges between them. All simulations were made for Rayleigh numbers (Ra) equilibrium with the medium), cubic boxes and closed-top conditions. Checks were performed on an unfractured porous medium and the convection cells do start for the theoretical value of Ra, namely 4p². 2D convection was verified up to Ra=800. The influence of parameters such as fracture aperture (or fracture transmissivity), fracture density and fracture length is studied. Moreover, these models are compared to porous media with the same macroscopic permeability. Preliminary results show that the non-uniqueness associated with initial conditions which makes possible either 2D or 3D convection in porous media (Schubert & Straus 1979) is no longer true for fractured porous media (at least for 50
Energy Technology Data Exchange (ETDEWEB)
Nordhaug, Hans Fredrik
2001-07-01
In reservoir problems we consider some or all of the following phases: Oil, gas, water and solid. The solid phase is normally assumed to be immobile and non-deforming, but in general this does not need to be the case. By multi phase flow we will mean the flow of oil, gas and water. The phases are categorized according to their different physical quantities. A hydrocarbon phase, may consist of different hydrocarbon components, e.g., the oil phase can contain several oil and gas types. In this work the components are neglected and only the phases are considered. A porous medium is any solid phase, e.g. sand stone, that is permeable. The flow in a porous medium takes place through connected pores in the rock. Regions on a larger scale that contain oil or gas are called reservoirs. The typical size of a reservoir is kilometers in each direction while the pore scale size is millimeters or less. Solving the Navier-Stokes equation at the pore scale to obtain the transport on a larger scale is not numerically feasible because of the huge difference in scales. Therefore, some averaging is necessary to go from the pore scale (micro scale) to the reservoir scale (macro scale). In this process the Navier-Stokes equations are replaced by macro scale equations that are solved for macro scale variables. The papers presented herein cover several topics in multi phase flow in porous media, and they address some central problems both on the micro scale as well as on the macro scale. In addition, operator splitting techniques have been developed for convection dominated non-linear transport equations.
Machado, Anaïs; Bodiguel, Hugues; Beaumont, Julien; Clisson, Gérald; Colin, Annie
2016-01-01
We study flows of hydrolized polyacrylamide solutions in two dimensional porous media made using microfluidics, for which elastic effects are dominant. We focus on semi-dilute solutions (0.1%–0.4%) which exhibit a strong shear thinning behavior. We systematically measure the pressure drop and find that the effective permeability is dramatically higher than predicted when the Weissenberg number is greater than about 10. Observations of the streamlines of the flow reveal that this effect coincides with the onset of elastic instabilities. Moreover, and importantly for applications, we show using local measurements that the mean flow is modified: it appears to be more uniform at high Weissenberg number than for Newtonian fluids. These observations are compared and discussed using pore network simulations, which account for the effect of disorder and shear thinning on the flow properties. PMID:27478522
Chaotic Mixing in Three Dimensional Porous Media
Lester, Daniel R; Borgne, Tanguy Le
2016-01-01
Under steady flow conditions, the topological complexity inherent to all random 3D porous media imparts complicated flow and transport dynamics. It has been established that this complexity generates persistent chaotic advection via a three-dimensional (3D) fluid mechanical analogue of the baker's map which rapidly accelerates scalar mixing in the presence of molecular di?usion. Hence pore-scale fluid mixing is governed by the interplay between chaotic advection, molecular di?usion and the broad (power-law) distribution of fluid particle travel times which arise from the non-slip condition at pore walls. To understand and quantify mixing in 3D porous media, we consider these processes in a model 3D open porous network and develop a novel stretching continuous time random walk (CTRW) which provides analytic estimates of pore-scale mixing which compare well with direct numerical simulations. We ?nd that chaotic advection inherent to 3D porous media imparts scalar mixing which scales exponentially with longitudi...
Finite volume hydromechanical simulation in porous media.
Nordbotten, Jan Martin
2014-05-01
Cell-centered finite volume methods are prevailing in numerical simulation of flow in porous media. However, due to the lack of cell-centered finite volume methods for mechanics, coupled flow and deformation is usually treated either by coupled finite-volume-finite element discretizations, or within a finite element setting. The former approach is unfavorable as it introduces two separate grid structures, while the latter approach loses the advantages of finite volume methods for the flow equation. Recently, we proposed a cell-centered finite volume method for elasticity. Herein, we explore the applicability of this novel method to provide a compatible finite volume discretization for coupled hydromechanic flows in porous media. We detail in particular the issue of coupling terms, and show how this is naturally handled. Furthermore, we observe how the cell-centered finite volume framework naturally allows for modeling fractured and fracturing porous media through internal boundary conditions. We support the discussion with a set of numerical examples: the convergence properties of the coupled scheme are first investigated; second, we illustrate the practical applicability of the method both for fractured and heterogeneous media.
Babakhani, Peyman; Fagerlund, Fritjof; Shamsai, Abolfazl; Lowry, Gregory V; Phenrat, Tanapon
2015-08-25
The solute transport model MODFLOW has become a standard tool in risk assessment and remediation design. However, particle transport models that take into account both particle agglomeration and deposition phenomena are far less developed. The main objective of the present study was to evaluate the feasibility of adapting the standard code MODFLOW/MT3D to simulate the agglomeration and transport of three different types of polymer-modified nanoscale zerovalent iron (NZVI) in one-dimensional (1-D) and two-dimensional (2-D) saturated porous media. A first-order decay of the particle population was used to account for the agglomeration of particles. An iterative technique was used to optimize the model parameters. The model provided good matches to 1-D NZVI-breakthrough data sets, with R (2) values ranging from 0.96 to 0.99, and mass recovery differences between the experimental results and simulations ranged from 0.1 to 1.8 %. Similarly, simulations of NZVI transport in the heterogeneous 2-D model demonstrated that the model can be applied to more complicated heterogeneous domains. However, the fits were less good, with the R (2) values in the 2-D modeling cases ranging from 0.75 to 0.95, while the mass recovery differences ranged from 0.7 to 6.5 %. Nevertheless, the predicted NZVI concentration contours during transport were in good agreement with the 2-D experimental observations. The model provides insights into NZVI transport in porous media by mathematically decoupling agglomeration, attachment, and detachment, and it illustrates the importance of each phenomenon in various situations. Graphical Abstract ᅟ.
Dual Transport Process for Targeted Delivery in Porous Media
Deng, W.; Fan, J.
2015-12-01
The targeted delivery in porous media is a promising technology to encapsulate the solute (i.e., the cargo) in colloid-like microcapsules (i.e., the carriers), transport the microcapsules in the targeted location in porous media, and then release the solute. While extensive literatures and applications about the drug delivery in human and animal bodies exist, the targeted delivery using similar delivery carriers in subsurface porous media is not well understood. The dual transport process study is an explorative study for the targeted delivery in porous media. While the colloid transport is dominated by the advection process and the solute transport is dominated by the advection-dispersion, the dual transport process is the process with the first step of carrier transport, which is dominated by advection, and then after the release of cargo, the transport of cargo is dominated by advection-dispersion. By applying the random walk particle tracking (RWPT) approach, we investigate how the carriers transport in porous media and how the cargo release mechanisms affect the cargo distribution for the targeted delivery in various patterns of porous media. The RWPT numerical model will be verified against the experimental results of dual transport process in packed-disk 2D micromodels. The understanding of the mechanism of dual transport process is crucial to achieve the potential applications of targeted delivery in improved oil and gas recovery, CO2 sequestration, environmental remediation, and soil biomediation.
Non-equilibrium phase transitions
Henkel, Malte; Lübeck, Sven
2009-01-01
This book describes two main classes of non-equilibrium phase-transitions: (a) static and dynamics of transitions into an absorbing state, and (b) dynamical scaling in far-from-equilibrium relaxation behaviour and ageing. The first volume begins with an introductory chapter which recalls the main concepts of phase-transitions, set for the convenience of the reader in an equilibrium context. The extension to non-equilibrium systems is made by using directed percolation as the main paradigm of absorbing phase transitions and in view of the richness of the known results an entire chapter is devoted to it, including a discussion of recent experimental results. Scaling theories and a large set of both numerical and analytical methods for the study of non-equilibrium phase transitions are thoroughly discussed. The techniques used for directed percolation are then extended to other universality classes and many important results on model parameters are provided for easy reference.
Energy Technology Data Exchange (ETDEWEB)
Ho, C.K.; Webb, S.W.
1996-05-01
A review of mechanisms, models, and data relevant to the postulated phenomenon of enhanced vapor-phase diffusion in porous media is presented. Information is obtained from literature spanning two different disciplines (soil science and engineering) to gain a diverse perspective on this topic. Findings indicate that while enhanced vapor diffusion tends to correct the discrepancies observed between past theory and experiments, no direct evidence exists to support the postulated processes causing enhanced vapor diffusion. Numerical modeling analyses of experiments representative of the two disciplines are presented in this paper to assess the sensitivity of different systems to enhanced vapor diffusion. Pore-scale modeling is also performed to evaluate the relative significance of enhanced vapor diffusion mechanisms when compared to Fickian diffusion. The results demonstrate the need for additional experiments so that more discerning analyses can be performed.
Liu, Gaisheng; Zheng, C.; Gorelick, S.M.
2007-01-01
This paper evaluates the dual-domain mass transfer (DDMT) model to represent transport processes when small-scale high-conductivity (K) preferential flow paths (PFPs) are present in a homogenous porous media matrix. The effects of PFPs upon solute transport were examined through detailed numerical experiments involving different realizations of PFP networks, PFP/matrix conductivity contrasts varying from 10:1 to 200:1, different magnitudes of effective conductivities, and a range of molecular diffusion coefficients. Results suggest that the DDMT model can reproduce both the near-source peak and the downstream low-concentration spreading observed in the embedded dendritic network when there are large conductivity contrasts between high-K PFPs and the low-K matrix. The accuracy of the DDMT model is also affected by the geometry of PFP networks and by the relative significance of the diffusion process in the network-matrix system. Copyright 2007 by the American Geophysical Union.
Tassis, Konstantinos; Yorke, Harold W; Turner, Neal
2011-01-01
We combine dynamical and non-equilibrium chemical modeling of evolving prestellar molecular cloud cores, and explore the evolution of molecular abundances in the contracting core. We model both magnetic cores, with varying degrees of initial magnetic support, and non-magnetic cores, with varying collapse delay times. We explore, through a parameter study, the competing effects of various model parameters in the evolving molecular abundances, including the elemental C/O ratio, the temperature, and the cosmic-ray ionization rate. We find that different models show their largest quantitative differences at the center of the core, whereas the outer layers, which evolve slower, have abundances which are severely degenerate among different dynamical models. There is a large range of possible abundance values for different models at a fixed evolutionary stage (central density), which demonstrates the large potential of chemical differentiation in prestellar cores. However, degeneracies among different models, compou...
Mu, Yaoming; Sungkorn, Radompon; Toelke, Jonas
2016-09-01
In this paper, we extend pore-morphology-based methods proposed by Hazlett (1995) and Hilpert and Miller (2001) to simulate drainage and imbibition in uniformly wetting porous media and add an (optional) entrapment of the (non-)wetting phase. By improving implementation, this method allows us to identify the statistical representative elementary volume and estimate uncertainty by computing fluid flow properties and saturation distributions of hundreds of subsamples within a reasonable time-frame. The method was utilized to study three different porous medium systems and results demonstrate that morphology-based pore-scale modeling is a viable approach to assess the representative elementary volume with respect to capillary dominated two-phase flow. The focus of this paper is the determination of the representative elementary volume for multiphase-flow properties for a digital representation of a rock.
Neuweiler, I.; Dentz, M.; Erdal, D.
2012-04-01
Infiltration into dry strongly heterogeneous media, such as fractured rocks, can often not be modelled by a standard Richards equation with homogeneous parameters, as the averaged water content is not in equilibrium with the averaged pressure. Often, double continua approaches are used for such cases. We describe infiltration into strongly heterogeneous media by a Richards model for the mobile domain, that is characterized by a memory kernel that encodes the local mass transfer dynamics as well as the geometry of the immobile zone. This approach is based on the assumption that capillary flow can be approximated as diffusion. We demonstrate that this approximation is in many cases justified. Comparison of the model predictions to the results of numerical simulations of infiltration into vertically layered media shows that the non-local approach describes well non-equilibrium effects due to mass transfer between high and low conductivity zones.
Energy Technology Data Exchange (ETDEWEB)
Park, Ik Kyu; Cho, Heong Kyu; Kim, Jong Tae; Yoon, Han Young; Jeong, Jae Jun
2007-12-15
A computational model for transient, 3 dimensional 2 phase flows was developed by using 'unstructured-FVM-based, non-staggered, semi-implicit numerical scheme' considering the thermally non-equilibrium droplets. The assumption of the thermally equilibrium between liquid and droplets of previous studies was not used any more, and three energy conservation equations for vapor, liquid, liquid droplets were set up. Thus, 9 conservation equations for mass, momentum, and energy were established to simulate 2 phase flows. In this report, the governing equations and a semi-implicit numerical sheme for a transient 1 dimensional 2 phase flows was described considering the thermally non-equilibrium between liquid and liquid droplets. The comparison with the previous model considering the thermally non-equilibrium between liquid and liquid droplets was also reported.
Cerminara, Matteo; Esposti Ongaro, Tomaso; Carlo Berselli, Luigi
2014-05-01
We have developed a compressible multiphase flow model to simulate the three-dimensional dynamics of turbulent volcanic ash plumes. The model describes the eruptive mixture as a polydisperse fluid, composed of different types of gases and particles, treated as interpenetrating Eulerian phases. Solid phases represent the discrete ash classes into which the total granulometric spectrum is discretized, and can differ by size and density. The model is designed to quickly and accurately resolve important physical phenomena in the dynamics of volcanic ash plumes. In particular, it can simulate turbulent mixing (driving atmospheric entrainment and controlling the heat transfer), thermal expansion (controlling the plume buoyancy), the interaction between solid particles and volcanic gas (including kinetic non-equilibrium effects) and the effects of compressibility (over-pressured eruptions and infrasonic measurements). The model is based on the turbulent dispersed multiphase flow theory for dilute flows (volume concentration <0.001, implying that averaged inter-particle distance is larger than 10 diameters) where particle collisions are neglected. Moreover, in order to speed up the code without losing accuracy, we make the hypothesis of fine particles (Stokes number <0.2 , i.e., volcanic ash particles finer then a millimeter), so that we are able to consider non-equilibrium effects only at the first order. We adopt LES formalism (which is preferable in transient regimes) for compressible flows to model the non-linear coupling between turbulent scales and the effect of sub-grid turbulence on the large-scale dynamics. A three-dimensional numerical code has been developed basing on the OpenFOAM computational framework, a CFD open source parallel software package. Numerical benchmarks demonstrate that the model is able to capture important non-equilibrium phenomena in gas-particle mixtures, such as particle clustering and ejection from large-eddy turbulent structures, as well
Duchemin, Ivan; Jacquemin, Denis; Blase, Xavier
2016-04-28
We have implemented the polarizable continuum model within the framework of the many-body Green's function GW formalism for the calculation of electron addition and removal energies in solution. The present formalism includes both ground-state and non-equilibrium polarization effects. In addition, the polarization energies are state-specific, allowing to obtain the bath-induced renormalisation energy of all occupied and virtual energy levels. Our implementation is validated by comparisons with ΔSCF calculations performed at both the density functional theory and coupled-cluster single and double levels for solvated nucleobases. The present study opens the way to GW and Bethe-Salpeter calculations in disordered condensed phases of interest in organic optoelectronics, wet chemistry, and biology.
Porous media fluid transport and pore structure
Dullien, F A L
1992-01-01
This book examines the relationship between transport properties and pore structure of porous material. Models of pore structure are presented with a discussion of how such models can be used to predict the transport properties of porous media. Portions of the book are devoted to interpretations of experimental results in this area and directions for future research. Practical applications are given where applicable, and are expected to be useful for a large number of different fields, including reservoir engineering, geology, hydrogeology, soil science, chemical process engineering, biomedica
Diffusion of oriented particles in porous media
Energy Technology Data Exchange (ETDEWEB)
Haber, René [Institut für Physik, Technische Universität Chemnitz, D-09107 Chemnitz (Germany); Centre for Nonlinear Studies, Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn (Estonia); Prehl, Janett [Institut für Physik, Technische Universität Chemnitz, D-09107 Chemnitz (Germany); Herrmann, Heiko [Centre for Nonlinear Studies, Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn (Estonia); Hoffmann, Karl Heinz, E-mail: hoffmann@physik.tu-chemnitz.de [Institut für Physik, Technische Universität Chemnitz, D-09107 Chemnitz (Germany)
2013-11-29
Diffusion of particles in porous media often shows subdiffusive behavior. Here, we analyze the dynamics of particles exhibiting an orientation. The features we focus on are geometrical restrictions and the dynamical consequences of the interactions between the local surrounding structure and the particle orientation. This interaction can lead to particles getting temporarily stuck in parts of the structure. Modeling this interaction by a particular random walk dynamics on fractal structures we find that the random walk dimension is not affected while the diffusion constant shows a variety of interesting and surprising features.
Systematic validation of non-equilibrium thermochemical models using Bayesian inference
Miki, Kenji
2015-10-01
© 2015 Elsevier Inc. The validation process proposed by Babuška et al. [1] is applied to thermochemical models describing post-shock flow conditions. In this validation approach, experimental data is involved only in the calibration of the models, and the decision process is based on quantities of interest (QoIs) predicted on scenarios that are not necessarily amenable experimentally. Moreover, uncertainties present in the experimental data, as well as those resulting from an incomplete physical model description, are propagated to the QoIs. We investigate four commonly used thermochemical models: a one-temperature model (which assumes thermal equilibrium among all inner modes), and two-temperature models developed by Macheret et al. [2], Marrone and Treanor [3], and Park [4]. Up to 16 uncertain parameters are estimated using Bayesian updating based on the latest absolute volumetric radiance data collected at the Electric Arc Shock Tube (EAST) installed inside the NASA Ames Research Center. Following the solution of the inverse problems, the forward problems are solved in order to predict the radiative heat flux, QoI, and examine the validity of these models. Our results show that all four models are invalid, but for different reasons: the one-temperature model simply fails to reproduce the data while the two-temperature models exhibit unacceptably large uncertainties in the QoI predictions.
Systematic validation of non-equilibrium thermochemical models using Bayesian inference
Energy Technology Data Exchange (ETDEWEB)
Miki, Kenji [NASA Glenn Research Center, OAI, 22800 Cedar Point Rd, Cleveland, OH 44142 (United States); Panesi, Marco, E-mail: mpanesi@illinois.edu [Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, 306 Talbot Lab, 104 S. Wright St., Urbana, IL 61801 (United States); Prudhomme, Serge [Département de mathématiques et de génie industriel, Ecole Polytechnique de Montréal, C.P. 6079, succ. Centre-ville, Montréal, QC, H3C 3A7 (Canada)
2015-10-01
The validation process proposed by Babuška et al. [1] is applied to thermochemical models describing post-shock flow conditions. In this validation approach, experimental data is involved only in the calibration of the models, and the decision process is based on quantities of interest (QoIs) predicted on scenarios that are not necessarily amenable experimentally. Moreover, uncertainties present in the experimental data, as well as those resulting from an incomplete physical model description, are propagated to the QoIs. We investigate four commonly used thermochemical models: a one-temperature model (which assumes thermal equilibrium among all inner modes), and two-temperature models developed by Macheret et al. [2], Marrone and Treanor [3], and Park [4]. Up to 16 uncertain parameters are estimated using Bayesian updating based on the latest absolute volumetric radiance data collected at the Electric Arc Shock Tube (EAST) installed inside the NASA Ames Research Center. Following the solution of the inverse problems, the forward problems are solved in order to predict the radiative heat flux, QoI, and examine the validity of these models. Our results show that all four models are invalid, but for different reasons: the one-temperature model simply fails to reproduce the data while the two-temperature models exhibit unacceptably large uncertainties in the QoI predictions.
Dynamic behaviour of reactive distillation tray columns described with a non-equilibrium cell model
Baur, R.; Taylor, R.; Krishna, R.
2001-01-01
In this paper we develop a generic, dynamic, nonequilibrium (NEQ) cell model for reactive distillation (RD) tray columns. The features of our model are (1) the use of Maxwell–Stefan equations for describing mass transfer between fluid phases, (2) the reaction is assumed to take place in the liquid
Kramer, K.; Werf, van der D.C.
2010-01-01
The environment is changing and so are forests, in their functioning, in species composition, and in the species’ genetic composition. Many empirical and process-based models exist to support forest management. However, most of these models do not consider the impact of environmental changes and for
Comparison of Vibrational Relaxation Modeling for Strongly Non-Equilibrium Flows
2014-01-01
145 .98 4396 V. Summary and Conclusions The form of two vibrational relaxation models that are commonly used in DSMC and CFD simula- tions have been...Technical Paper 3. DATES COVERED (From - To) Dec 2013 – Jan 2014 4. TITLE AND SUBTITLE Comparison of Vibrational Relaxation Modeling for Strongly Non...including experimental gas measurement techniques , shock layer vibration-dissociation coupling, and vibrational energy freezing in strong expansions
Asymptotics of the filtration problem for suspension in porous media
Directory of Open Access Journals (Sweden)
Kuzmina Ludmila Ivanovna
2015-01-01
Full Text Available The mechanical-geometric model of the suspension filtering in the porous media is considered. Suspended solid particles of the same size move with suspension flow through the porous media - a solid body with pores - channels of constant cross section. It is assumed that the particles pass freely through the pores of large diameter and are stuck at the inlet of pores that are smaller than the particle size. It is considered that one particle can clog only one small pore and vice versa. The particles stuck in the pores remain motionless and form a deposit. The concentrations of suspended and retained particles satisfy a quasilinear hyperbolic system of partial differential equations of the first order, obtained as a result of macro-averaging of micro-stochastic diffusion equations. Initially the porous media contains no particles and both concentrations are equal to zero; the suspension supplied to the porous media inlet has a constant concentration of suspended particles. The flow of particles moves in the porous media with a constant speed, before the wave front the concentrations of suspended and retained particles are zero. Assuming that the filtration coefficient is small we construct an asymptotic solution of the filtration problem over the concentration front. The terms of the asymptotic expansions satisfy linear partial differential equations of the first order and are determined successively in an explicit form. It is shown that in the simplest case the asymptotics found matches the known asymptotic expansion of the solution near the concentration front.
Non-equilibrium phase transition in a two-species driven-diffusive model of classical particles
Ghadermazi, Mohammad; Jafarpour, Farhad H.
2016-09-01
A two-species driven-diffusive model of classical particles is introduced on a lattice with periodic boundary condition. The model consists of a finite number of first class particles in the presence of a second class particle. While the first class particles can only hop forward, the second class particle is able to hop both forward and backward with specific rates. We have shown that the partition function of this model can be calculated exactly. The model undergoes a non-equilibrium phase transition when a condensation of the first class particles occurs behind the second class particle. The phase transition point and the spatial correlations between the first class particles are calculated exactly. On the other hand, we have shown that this model can be mapped onto a two-dimensional walk model. The random walker can only move on the first quarter of a two-dimensional plane and that it takes the paths which can start at any height and end at any height upper than the height of the starting point. The initial vertex (starting point) and the final vertex (end point) of each lattice path are weighted. The weight of the outset point depends on the height of that point while the weight of the end point depends on the height of both the outset point and the end point of each path. The partition function of this walk model is calculated using a transfer matrix method.
Modelling of non-equilibrium flow in the branched pipeline systems
Sumskoi, S. I.; Sverchkov, A. M.; Lisanov, M. V.; Egorov, A. F.
2016-09-01
This article presents a mathematical model and a numerical method for solving the task of water hammer in the branched pipeline system. The task is considered in the onedimensional non-stationary formulation taking into account the realities such as the change in the diameter of the pipeline and its branches. By comparison with the existing analytic solution it has been shown that the proposed method possesses good accuracy. With the help of the developed model and numerical method the task has been solved concerning the transmission of the compression waves complex in the branching pipeline system when several shut down valves operate. It should be noted that the offered model and method may be easily introduced to a number of other tasks, for example, to describe the flow of blood in the vessels.
Non-equilibrium Dynamics for a Widom-Rowlinson Type Model with Mutations
Friesen, Martin
2017-01-01
A dynamical version of the Widom-Rowlinson model in the continuum is considered. The dynamics is modelled by a spatial two-component birth-and-death Glauber process where particles, in addition, are allowed to change their type with density dependent rates. An evolution of states is constructed in terms of correlation function evolution in a certain Ruelle space. It is shown that such evolution provides the unique weak solution to the associated Fokker-Planck equation. Existence of a unique invariant measure and ergodicity with exponential rate is established. Vlasov scaling is performed and the chaos preservation property is shown.
Vellela, Melissa; Qian, Hong
2009-10-06
Schlögl's model is the canonical example of a chemical reaction system that exhibits bistability. Because the biological examples of bistability and switching behaviour are increasingly numerous, this paper presents an integrated deterministic, stochastic and thermodynamic analysis of the model. After a brief review of the deterministic and stochastic modelling frameworks, the concepts of chemical and mathematical detailed balances are discussed and non-equilibrium conditions are shown to be necessary for bistability. Thermodynamic quantities such as the flux, chemical potential and entropy production rate are defined and compared across the two models. In the bistable region, the stochastic model exhibits an exchange of the global stability between the two stable states under changes in the pump parameters and volume size. The stochastic entropy production rate shows a sharp transition that mirrors this exchange. A new hybrid model that includes continuous diffusion and discrete jumps is suggested to deal with the multiscale dynamics of the bistable system. Accurate approximations of the exponentially small eigenvalue associated with the time scale of this switching and the full time-dependent solution are calculated using Matlab. A breakdown of previously known asymptotic approximations on small volume scales is observed through comparison with these and Monte Carlo results. Finally, in the appendix section is an illustration of how the diffusion approximation of the chemical master equation can fail to represent correctly the mesoscopically interesting steady-state behaviour of the system.
A Multiphase First Order Model for Non-Equilibrium Sand Erosion, Transport and Sedimentation
Preziosi, Luigi; Bruno, Luca
2015-01-01
Three phenomena are involved in sand movement: erosion, wind transport, and sedimentation. This paper presents a comprehensive easy-to-use multiphase model that include all three aspects with a particular attention to situations in which erosion due to wind shear and sedimentation due to gravity are not in equilibrium. The interest is related to the fact that these are the situations leading to a change of profile of the sand bed.
Simulation of uncompressible fluid flow through a porous media
Energy Technology Data Exchange (ETDEWEB)
Ramirez, A. [Instituto Politecnico Nacional (SEPI-ESIQIE-IPN), Unidad Profesional Zacatenco, Laboratorio de Analisis Met. (Edif. ' Z' y Edif. ' 6' P.B.), Mexico City (Mexico)], E-mail: adaramil@yahoo.com.mx; Gonzalez, J.L. [Instituto Politecnico Nacional (SEPI-ESIQIE-IPN), Unidad Profesional Zacatenco, Laboratorio de Analisis Met. (Edif. ' Z' y Edif. ' 6' P.B.), Mexico City (Mexico); Carrillo, F. [Instituto Politecnico Nacional (SEPI-CICATA-IPN), Unidad Altamira Tamaulipas, Mexico (Mexico); Lopez, S. [Instituto Mexicano del Petroleo (I.M.P.-D.F.), Mexico (Mexico)
2009-02-28
Recently, a great interest has been focused for investigations about transport phenomena in disordered systems. One of the most treated topics is fluid flow through anisotropic materials due to the importance in many industrial processes like fluid flow in filters, membranes, walls, oil reservoirs, etc. In this work is described the formulation of a 2D mathematical model to simulate the fluid flow behavior through a porous media (PM) based on the solution of the continuity equation as a function of the Darcy's law for a percolation system; which was reproduced using computational techniques reproduced using a random distribution of the porous media properties (porosity, permeability and saturation). The model displays the filling of a partially saturated porous media with a new injected fluid showing the non-defined advance front and dispersion of fluids phenomena.
Boiling in porous media; Ebullition en milieux poreux
Energy Technology Data Exchange (ETDEWEB)
NONE
1998-03-11
This conference day of the French society of thermal engineers was devoted to the analysis of heat transfers and fluid flows during boiling phenomena in porous media. This book of proceedings comprises 8 communications entitled: `boiling in porous medium: effect of natural convection in the liquid zone`; `numerical modeling of boiling in porous media using a `dual-fluid` approach: asymmetrical characteristic of the phenomenon`; `boiling during fluid flow in an induction heated porous column`; `cooling of corium fragment beds during a severe accident. State of the art and the SILFIDE experimental project`; `state of knowledge about the cooling of a particulates bed during a reactor accident`; `mass transfer analysis inside a concrete slab during fire resistance tests`; `heat transfers and boiling in porous media. Experimental analysis and modeling`; `concrete in accidental situation - influence of boundary conditions (thermal, hydric) - case studies`. (J.S.)
Non-equilibrium entanglement in a driven many-body spin-boson model
Energy Technology Data Exchange (ETDEWEB)
Bastidas, Victor M; Reina, John H [Universidad del Valle, Departamento de Fisica, A. A. 25360, Cali (Colombia); Brandes, Tobias, E-mail: vicmabas@univalle.edu.c, E-mail: j.reina-estupinan@physics.ox.ac.u [Institut fuer Theoretische Physik, Technische Universitaet Berlin, Hardenbergstr. 36, 10623 Berlin (Germany)
2009-05-01
We study the entanglement dynamics in the externally-driven single-mode Dicke model in the thermodynamic limit, when the field is in resonance with the atoms. We compute the correlations in the atoms-field ground state by means of the density operator that represents the pure state of the universe and the reduced density operator for the atoms, which results from taking the partial trace over the field coordinates. As a measure of bipartite entanglement, we calculate the linear entropy, from which we analyze the entanglement dynamics. In particular, we found a strong relation between the stability of the dynamical parameters and the reported entanglement.
Non-equilibrium modeling of the PMSE Overshoot Effect revisited: A comprehensive study
Biebricher, Alexander; Havnes, Ove
2012-06-01
Numerical investigations of the Polar Mesosphere Summer Echoes (PMSE) Overshoot Effect have to date been undertaken under the premise of plasma neutrality and current equilibrium at any time. We find it necessary to revisit the calculations without these restrictions, since electrons and ions are attached to and absorbed by mesospheric dust particles at vastly different rates under PMSE conditions. We find that differences to earlier modeling might be so significant as to warrant further investigation. Furthermore, we conduct comprehensive studies of the PMSE Overshoot Effect and put the results in the context of experimental realities.
Spectral - Lagrangian methods for Collisional Models of Non - Equilibrium Statistical States
Gamba, Irene M
2007-01-01
We propose a new spectral Lagrangian based deterministic solver for the non-linear Boltzmann Transport Equation for Variable Hard Potential (VHP) collision kernels with conservative or non-conservative binary interactions.The method is based on symmetries of the Fourier transform of the collision integral, where the complexity in its computing is reduced to a separate integral over the unit sphere $S^2$. In addition, the conservation of moments is enforced by Lagrangian constraints. The resulting scheme is very versatile and adjusts in a very simple manner, to several cases that involve energy dissipation due to local micro-reversibility (inelastic interactions) or elastic model of slowing down process. Our simulations are benchmarked with the available exact self-similar solutions, exact moment equations and analytical estimates for homogeneous Boltzmann equation for both elastic and inelastic VHP interactions. Benchmarking of the simulations involves the selection of a time self-similar rescaling of the num...
Large deviation statistics of non-equilibrium fluctuations in a sheared model-fluid
Dolai, Pritha; Simha, Aditi
2016-08-01
We analyse the statistics of the shear stress in a one dimensional model fluid, that exhibits a rich phase behaviour akin to real complex fluids under shear. We show that the energy flux satisfies the Gallavotti-Cohen FT across all phases in the system. The theorem allows us to define an effective temperature which deviates considerably from the equilibrium temperature as the noise in the system increases. This deviation is negligible when the system size is small. The dependence of the effective temperature on the strain rate is phase-dependent. It doesn’t vary much at the phase boundaries. The effective temperature can also be determined from the large deviation function of the energy flux. The local strain rate statistics obeys the large deviation principle and satisfies a fluctuation relation. It does not exhibit a distinct kink near zero strain rate because of inertia of the rotors in our system.
Energy Technology Data Exchange (ETDEWEB)
Class, H.
2000-07-01
The author investigates the numeric simulation of physical processes in porous media. The development of the model and its components is described, and the model is validated by laboratory experiments. Differences from the discretization methods BOX and CVFE are discussed as well as the applicability of the multigrid method described for multicomponent approaches. [German] Bei der thermischen Sanierung NAPL-kontaminierter Standorte, z.B. durch Injektion von Wasserdampf und/oder Heissluft, treten nichtisotherme Mehrphasenprozesse auf, die in einem Modell durch eine Betrachtung der Stroemungs- und Transportprozesse als Mehrkomponentensystem beschrieben werden koennen. Dabei ist der Austausch thermischer Energie zwischen den Phasen untereinander und auch dem poroesen Medium selbst, wie auch der Uebergang von Massekomponenten zwischen den Phasen zu beruecksichtigen. Die vorliegende Arbeit behandelt die numerische Simulation derartiger physikalischer Vorgaenge in poroesen Medien. Ausgehend von der Problemstellung wird die Entwicklung eines konzeptionellen Modells (Kap. 2) sowie die Umsetzung der daraus resultierenden mathematischen Gleichungen und dazu erforderlichen Diskretisierungs- und Loesungsmethoden in numerische Algorithmen dargestellt (Kap. 3). Anschliessend wird in Kap. 4 die Faehigkeit des erstelten numerischen Modells ueberprueft, Problemstellungen in natuerlichen Systemen zu simulieren (Vergleich mit Laborexperimenten); ausserdem werden Unterschiede der Diskretisierungsverfahren BOX und CVFE sowie die Anwendbarkeit des in dieser Arbeit fuer Mehrkomponentenformulierungen erweiterten Mehrgitterverfahrens diskutiert. (orig.)
Abnormal grain growth: a non-equilibrium thermodynamic model for multi-grain binary systems
Svoboda, J.; Fischer, F. D.
2014-01-01
Abnormal grain growth as the abrupt growth of a group of the largest grains in a multi-grain system is treated within the context of unequal retardation of grain growth due to the segregation of solute atoms from the bulk of the grains into the grain boundaries. During grain boundary migration, the segregated solute atoms are dragged under a small driving force or left behind the migrating grain boundary under a large driving force. Thus, the solute atoms in the grain boundaries of large grains, exhibiting a large driving force, can be released from the grain boundary. The mobility of these grain boundaries becomes significantly higher and abnormal grain growth is spontaneously provoked. The mean-field model presented here assumes that each grain is described by its grain radius and by its individual segregation parameter. The thermodynamic extremal principle is engaged to obtain explicit evolution equations for the radius and segregation parameter of each grain. Simulations of grain growth kinetics for various conditions of segregation with the same initial setting (100 000 grains with a given radius distribution) are presented. Depending on the diffusion coefficients of the solute in the grain boundaries, abnormal grain growth may be strongly or marginally pronounced. Solute segregation and drag can also significantly contribute to the stabilization of the grain structure. Qualitative agreement with several experimental results is reported.
Lattice Boltzmann implementation for Fluids Flow Simulation in Porous Media
Directory of Open Access Journals (Sweden)
Xinming Zhang
2011-06-01
Full Text Available In this paper, the lattice-Boltzmann method is developed to investigate the behavior of isothermal two-phase fluid flow in porous media. The method is based on the Shan–Chen multiphase model of nonideal fluids that allow coexistence of two phases of a single substance. We reproduce some different idealized situations (phase separation, surface tension, contact angle, pipe flow, and fluid droplet motion, et al in which the results are already known from theory or laboratory measurements and show the validity of the implementation for the physical two-phase flow in porous media. Application of the method to fluid intrusion in porous media is discussed and shows the effect of wettability on the fluid flow. The capability of reproducing critical flooding phenomena under strong wettability conditions is also proved.
Permeability of mono- and bi-dispersed porous media
Directory of Open Access Journals (Sweden)
Kim S.J.
2013-04-01
Full Text Available In this study, the permeability of mono- and bi-dispersed porous media is considered. The effects of the particle size distribution and the packing structure of particles on the permeability are investigated experimentally and analytically. Both experimental and analytic results suggest that the particlesize distribution is close to the log-normal distribution, and the permeability of the mono-dispersed porous media quasi-linearly decreases as the range of the particle size distribution increases. On the other hand, the effect of packing structure of particles on the permeability is shown to be negligible.The permeability of the bidispersed porous media quasi-linearly decreases as the range of cluster size increases, and nearly independent of the particle size distribution. The present model is valid over the range of parameters typically found in heat transfer applications.
Heat Conduction and Characteristic Size of Fractal Porous Media
Institute of Scientific and Technical Information of China (English)
WANG Wei-Wei; HUAI Xiu-Lan; TAO Yu-Jia
2006-01-01
Based on fractal theory, two types of random Sierpinski carpets (RSCs) and their periodic structures are generated to model the structures of natural porous media, and the heat conduction in these structures is simulated by the finite volume method. The calculated results indicate that in a certain range of length scales, the size and spatial arrangement of pores have significant influence on the effective thermal conductivity, and the heat conduction presents the aeolotropic characteristic. Above the length scale, however, the influence of size and spatial arrangement of pores on the effective thermal conductivity reduces gradually with the increasing characteristic size of porous media, the aeolotropic characteristic is weakened gradually. It is concluded that the periodicity in structures of porous media is not equal to the periodicity in heat conduction.
Katzourakis, Vasileios; Chrysikopoulos, Constantinos
2016-04-01
The present work re-introduces ColloidFit, which is an autonomous, modular, multipurpose fitting software for dense colloid and biocolloid transport phenomena in porous media. The initial version of ColloidFit, introduced by Sim and Chrysikopoulos (1995), was substantially improved and combined with a relatively intuitive and easy to use graphical user interface. The re-introduced ColloidFit can simulate the migration of suspended colloid or biocolloid particles in one-dimensional, water saturated, homogeneous porous media with uniform flow, accounting for non-equilibrium attachment onto the solid matrix, as well as gravitational effects. Furthermore, the improved ColloidFit software employs a variety of non-equilibrium, linear and nonlinear models for the simulation of colloid attachment onto a solid matrix under batch experimental conditions. The re-introduced ColloidFit uses the state of the art fitting software "Pest" to estimate unknown model parameter values, together with their 95% confidence intervals. Pest is a model-independent parameter estimation software capable of adjusting model parameters, so that discrepancies between model-generated data and the corresponding experimental measurements are reduced to a user preselected minimum. The fitting process is graphed and displayed in real time. The user is allowed to overview every step of the fitting progress, and if needed to change the initial parameter values. The re-introduced ColloidFit software is expected to make the fitting process of colloid and biocolloid transport data, just a simple task.
El-Amin, Mohamed
2017-08-28
In this paper, the magnetic nanoparticles are injected into a water-oil, two-phase system under the influence of an external permanent magnetic field. We lay down the mathematical model and provide a set of numerical exercises of hypothetical cases to show how an external magnetic field can influence the transport of nanoparticles in the proposed two-phase system in porous media. We treat the water-nanoparticles suspension as a miscible mixture, whereas it is immiscible with the oil phase. The magnetization properties, the density, and the viscosity of the ferrofluids are obtained based on mixture theory relationships. In the mathematical model, the phase pressure contains additional term to account for the extra pressures due to fluid magnetization effect and the magnetostrictive effect. As a proof of concept, the proposed model is applied on a countercurrent imbibition flow system in which both the displacing and the displaced fluids move in opposite directions. Physical variables, including waternanoparticles suspension saturation, nanoparticles concentration, and pore wall/throat concentrations of deposited nanoparticles, are investigated under the influence of the magnetic field. Two different locations of the magnet are studied numerically, and variations in permeability and porosity are considered.
Sivasankar, P; Rajesh Kanna, A; Suresh Kumar, G; Gummadi, Sathyanarayana N
2016-07-01
pH and resident time of injected slug plays a critical role in characterizing the reservoir for potential microbial enhanced oil recovery (MEOR) application. To investigate MEOR processes, a multispecies (microbes-nutrients) reactive transport model in porous media was developed by coupling kinetic and transport model. The present work differs from earlier works by explicitly determining parametric values required for kinetic model by experimental investigations using Pseudomonas putida at different pH conditions and subsequently performing sensitivity analysis of pH, resident time and water saturation on concentrations of microbes, nutrients and biosurfactant within reservoir. The results suggest that nutrient utilization and biosurfactant production are found to be maximum at pH 8 and 7.5 respectively. It is also found that the sucrose and biosurfactant concentrations are highly sensitive to pH rather than reservoir microbial concentration, while at larger resident time and water saturation, the microbial and nutrient concentrations were lesser due to enhanced dispersion. Copyright © 2016 Elsevier Ltd. All rights reserved.
Duc, Linh Do; Horák, Vladimír; Kulish, Vladimir; Lukáč, Tomáš
2017-01-01
Carbon dioxide is widely used as the power gas in the gas guns community due to its ease of handling, storability at room temperature, and high vapor pressure depending only upon temperature, but not a tank size, as long as some liquid carbon dioxide remains in the tank. This high vapor pressure can be used as the pressurant, making it what is referred to as a self-pressurising propellant. However, as a two-phase substance, carbon dioxide does have its drawbacks: (1) vaporization of liquefied CO2 inside a tank when shooting rapidly or a lot causes the tank to get cool, resulting in pressure fluctuations that makes the gun's performance and accuracy worse, (2) solid carbon dioxide that is also known as dry ice can appear on the output valve of the tank while shooting and it can cause damage or slow the gun's performance down, if it works its way into some control components, including the barrel of the gun. Hence, it is crucial to obtain a scientific understanding of carbon dioxide behavior and further the discharge characteristics of a wide range of pressure-tank configurations. For the purpose of satisfying this goal, a comprehensive discharge mathematical model for carbon dioxide tank dynamics is required. In this paper, the possibility to develop an advanced non-equilibrium model of depressurization in two-phase fluids is discussed.
Chen, Sheng; Täuber, Uwe C.
2015-03-01
Spatially extended stochastic models for predator-prey competition and coexistence display complex, correlated spatio-temporal structures and are governed by remarkably large fluctuations. Both populations are characterized by damped erratic oscillations whose properties are governed by the reaction rates. Here, we specifically study a stochastic lattice Lotka-Volterra model by means of Monte Carlo simulations that impose spatial restrictions on the number of occupants per site. The system tends to relax into a quasi-stationary state, independent of the imposed initial conditions. We investigate the non-equilibrium relaxation between two such quasi-stationary states, following an instantaneous change of the predation rate. The ensuing relaxation times are measured via the peak width of the population density Fourier transforms. As expected, we find that the initial state only influences the oscillations for the duration of this relaxation time, implying that the system quickly loses any memory of the initial configuration. Research supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-FG02-09ER46613.
Park, Chang Min; Heo, Jiyong; Her, Namguk; Chu, Kyoung Hoon; Jang, Min; Yoon, Yeomin
2016-10-15
This study aims to provide insights into the mechanisms governing the deposition and retention of silver nanoparticles (AgNPs) in saturated porous media. Column experiments were conducted with quartz sand under saturated conditions to investigate the deposition kinetics of AgNPs, their mobility at different groundwater hardnesses (10-400 mg/L as CaCO3), and humic acid (HA, 0-50 mg/L as dissolved organic carbon [DOC]). An anionic surfactant, sodium dodecyl sulfate (SDS), was used as a dispersing agent to prepare a SDS-AgNPs suspension. The deposition kinetics of AgNPs were highly sensitive to the surfactant concentration, ionic strength, and cation type in solution. The breakthrough curves (BTCs) of SDS-AgNPs suggested that the transport and retention were influenced by groundwater hardness and HA. At low water hardness and high HA, high mobility of SDS-AgNPs was observed in saturated conditions. However, the retention of SDS-AgNPs increased substantially in very hard water with a low concentration of HA, because of a decreased primary energy barrier and the straining effect during the course of transport experiments. A modified clean-bed filtration theory and a two-site kinetic attachment model showed good fits with the BTCs of SDS-AgNPs. The fitted model parameters (katt and kstr) could be used successfully to describe that the retention behaviors were dominated by electrostatic and electrosteric repulsion, based on extended Derjaguin-Landau-Vaerwey-Overbeek calculations.
Theory of porous media - past and present
Energy Technology Data Exchange (ETDEWEB)
Boer, R. de [Essen Univ. (Germany). Inst. fuer Mechanik
1998-10-01
Porous solids filled with liquid or gas play an important role in engineering, e.g., in material science, petroleum industry, chemical engineering, and soil mechanics as well as in biomechanics. Although porous media are of considerable practical significance the description of their mechanical and thermodynamical behavior has been unsatisfactory for a long time. The theory to describe the complex thermodynamical behavior of such saturated porous solids has come to certain well-founded conclusions only recently. It is the goal of this paper to show the historical development of the porous media theory, which already started in the eighteenth century, formed in some areas by polemic disputes and tragic events in the lifes of the scientists involved. Furthermore, the current state of the research into this subject is discussed, whereby the state of the development of the material independent basic equations and the constitutive theory is illustrated. For a certain class of models general theorems, such as minimum and maximum problems, are derived and the uniqueness of solutions of boundary value problems is proved. (orig.)
Directory of Open Access Journals (Sweden)
Ignat Ignatov
2015-12-01
Full Text Available In this paper are submited data on the possibility of applying the coronal gas discharge effect (CGDE in modeling non-equilibrium conditions with gas electric discharge simulating conditions occurying in the primary atmosphere (electric sparks, lightning imitating S. Miller’s experiments. The physical basis and technique of visualization of gas discharge (GD glowing of water drops in alternating electric fields of high electrical voltage (5–30 kV and frequency (10–150 kHz, as well as the possible electrosynthesis of organic molecules from a mixture of inorganic substances as hydrogen (H2, methane (CH4, ammonia (NH3 and carbon monoxide (CO in aqueous solutions of water exposed under the electrical discharge, UV-radiation and thermal heating to t = +100 0C were examined. The colour coronal spectral gas discharge analysis was applied for investigation of water samples of various origin, the samples of hot mineral, sea and mountain water obtained from various water sources of Bulgaria.
Non-equilibrium thermodynamics
De Groot, Sybren Ruurds
1984-01-01
The study of thermodynamics is especially timely today, as its concepts are being applied to problems in biology, biochemistry, electrochemistry, and engineering. This book treats irreversible processes and phenomena - non-equilibrium thermodynamics.S. R. de Groot and P. Mazur, Professors of Theoretical Physics, present a comprehensive and insightful survey of the foundations of the field, providing the only complete discussion of the fluctuating linear theory of irreversible thermodynamics. The application covers a wide range of topics: the theory of diffusion and heat conduction, fluid dyn
Dynamic pressures in porous media
Balcerak, Ernie
2012-12-01
Understanding the relationship between fluid pressures and water content (saturation) in soils or other porous media can be important in a wide range of practical areas, including oil recovery, infiltration and flooding during extreme weather events, and environmental remediation. The relationship between fluid pressures and saturation in porous media has been reported to be dynamic—to depend on the flow rate as saturation changes. However, previous studies designed to understand the dynamic component of this relationship have been highly contradictory. To learn more, Hou et al. conducted experiments to quantify the relationship between pressure and rate of saturation change using a small-volume system with highly characterized fluid selective microsensors. Their analyses corrected for two often-overlooked experimental artifacts: gas pressure gradients and sensor response rate. When the researchers applied these corrections, they found that the dependence of pressure on the rate of saturation change may be much less significant than previously thought. (Water Resources Research, doi:10.1029/2012WR012434, 2012)
Upscaling of flow in porous media from a tracer perspective
Berentsen, C.W.J.
2003-01-01
Most of our knowledge of flow in porous media is obtained at the pore and the macro scale. For reservoir scale modelling it is not practical to model the flow at these fine scales. Considering the usual objectives (e.g. large scale flow pattern and production forecast) it is undesirable to have to g
Brine transport in porous media self-similar solutions
C.J. van Duijn (Hans); L.A. Peletier (Bert); R.J. Schotting
1996-01-01
textabstractIn this paper we analyze a model for brine transport in porous media, which includes a mass balance for the fluid, a mass balance for salt, Darcy's law and an equation of state, which relates the fluid density to the salt mass fraction. This model incorporates the effect of local volume
MECHANISM FOR VISCOELASTIC POLYMER SOLUTION PERCOLATING THROUGH POROUS MEDIA
Institute of Scientific and Technical Information of China (English)
ZHANG Li-juan; YUE Xiang-an
2007-01-01
The pore throat of porous media is modeled as a constricted channel or expanded channel. The flow of viscoelastic polymer solution in pore throat model is studied by numerical method. Relationship between pressure drop and flow rate is developed, viscoelasticity and throat size are found to be two main factors in high flow resistance. According to pore throat model, 2-D stochastic channel bundle is put forward to model porous media, which is composed of pore throat models in series - parallel connection with size and length accord to Haring - Greenkorn stochastic distribution. Percolation model of viscoelastic fluid is developed on the basis of Darcy equation and pressure drop vs. flow rate relation in 2-D stochastic channel bundle. Results indicate that the seepage ability of viscoelastic polymer solution decreases with the increase of viscoelasticity, injection rate, and heterogeneity as well as the decrease of mean pore size of porous media. The high pressure drop of viscoelastic fluid at the connection of pore to throat plays a great role in its anomalous high flow resistance through porous media.
Kusaba, Akira; Li, Guanchen; von Spakovsky, Michael R; Kangawa, Yoshihiro; Kakimoto, Koichi
2017-08-15
Clearly understanding elementary growth processes that depend on surface reconstruction is essential to controlling vapor-phase epitaxy more precisely. In this study, ammonia chemical adsorption on GaN(0001) reconstructed surfaces under metalorganic vapor phase epitaxy (MOVPE) conditions (3Ga-H and Nad-H + Ga-H on a 2 × 2 unit cell) is investigated using steepest-entropy-ascent quantum thermodynamics (SEAQT). SEAQT is a thermodynamic-ensemble based, first-principles framework that can predict the behavior of non-equilibrium processes, even those far from equilibrium where the state evolution is a combination of reversible and irreversible dynamics. SEAQT is an ideal choice to handle this problem on a first-principles basis since the chemical adsorption process starts from a highly non-equilibrium state. A result of the analysis shows that the probability of adsorption on 3Ga-H is significantly higher than that on Nad-H + Ga-H. Additionally, the growth temperature dependence of these adsorption probabilities and the temperature increase due to the heat of reaction is determined. The non-equilibrium thermodynamic modeling applied can lead to better control of the MOVPE process through the selection of preferable reconstructed surfaces. The modeling also demonstrates the efficacy of DFT-SEAQT coupling for determining detailed non-equilibrium process characteristics with a much smaller computational burden than would be entailed with mechanics-based, microscopic-mesoscopic approaches.
Coupled electric and transport phenomena in porous media
Li, Shuai
2014-01-01
The coupled electrical and transport properties of clay-containing porous media are the topics of interest in this study. Both experimental and numerical (pore network modeling) techniques are employed to gain insight into the macro-scale interaction between electrical and solute transport phenomena
Coupled electric and transport phenomena in porous media
Li, Shuai
2014-01-01
The coupled electrical and transport properties of clay-containing porous media are the topics of interest in this study. Both experimental and numerical (pore network modeling) techniques are employed to gain insight into the macro-scale interaction between electrical and solute transport phenomena
Colloid adhesive parameters for chemical heterogeneous porous media
A simple modeling approach was developed to calculate colloid adhesive parameters for chemically heterogeneous porous media. The area of the zone of electrostatic influence between a colloid and solid-water interface (Az) was discretized into a number of equally sized grid cells to capture chemical...
Percolation theory for flow in porous media
Hunt, Allen; Ghanbarian, Behzad
2014-01-01
This monograph presents, for the first time, a unified and comprehensive introduction to some of the basic transport properties of porous media, such as electrical and hydraulic conductivity, air permeability and diffusion. The approach is based on critical path analysis and the scaling of transport properties, which are individually described as functions of saturation. At the same time, the book supplies a tutorial on percolation theory for hydrologists, providing them with the tools for solving actual problems. In turn, a separate chapter serves to introduce physicists to some of the language and complications of groundwater hydrology necessary for successful modeling. The end-of-chapter problems often indicate open questions, which young researchers entering the field can readily start working on. This significantly revised and expanded third edition includes in particular two new chapters: one on advanced fractal-based models, and one devoted to the discussion of various open issues such as the role of d...
Shock Electrodeposition in Charged Porous Media
Han, Ji-Hyung
2015-01-01
It is shown that surface conduction in porous media can drastically alter the stability and morphology of electrodeposition at high rates, above the diffusion-limited current. Copper electrodeposits are visualized by scanning electron microscopy and energy dispersive spectroscopy in cellulose nitrate membranes, whose pores are coated with positive or negative charged polymers. Above the limiting current, surface conduction inhibits growth in the positive membrane and produces irregular dendrites, while it enhances growth and suppresses dendrites behind a deionization shock in the negative membrane. The discovery of uniform growth contradicts quasi-steady leaky membrane models, which are in the same universality class as unstable Laplacian growth, and indicates the importance of transient electro-diffusion or electro-osmotic dispersion. Shock electrodeposition could be exploited for high-rate recharging of metal batteries or manufacturing of metal matrix composite coatings.
Moortgat, Joachim; Firoozabadi, Abbas
2013-10-01
Numerical simulation of multiphase compositional flow in fractured porous media, when all the species can transfer between the phases, is a real challenge. Despite the broad applications in hydrocarbon reservoir engineering and hydrology, a compositional numerical simulator for three-phase flow in fractured media has not appeared in the literature, to the best of our knowledge. In this work, we present a three-phase fully compositional simulator for fractured media, based on higher-order finite element methods. To achieve computational efficiency, we invoke the cross-flow equilibrium (CFE) concept between discrete fractures and a small neighborhood in the matrix blocks. We adopt the mixed hybrid finite element (MHFE) method to approximate convective Darcy fluxes and the pressure equation. This approach is the most natural choice for flow in fractured media. The mass balance equations are discretized by the discontinuous Galerkin (DG) method, which is perhaps the most efficient approach to capture physical discontinuities in phase properties at the matrix-fracture interfaces and at phase boundaries. In this work, we account for gravity and Fickian diffusion. The modeling of capillary effects is discussed in a separate paper. We present the mathematical framework, using the implicit-pressure-explicit-composition (IMPEC) scheme, which facilitates rigorous thermodynamic stability analyses and the computation of phase behavior effects to account for transfer of species between the phases. A deceptively simple CFL condition is implemented to improve numerical stability and accuracy. We provide six numerical examples at both small and larger scales and in two and three dimensions, to demonstrate powerful features of the formulation.
Energy Technology Data Exchange (ETDEWEB)
Santos, Adriano dos; Barros, Paulo [Universidade Federal do Rio Grande do Norte (UFRN), Natal, RN (Brazil)
2008-07-01
An analytical model for transport of particulate suspensions in porous medium is discussed. The model takes microscopic rock characteristics into account and considers that size exclusion is the dominant particle retention mechanism. Analytical solutions for suspended and retained particle concentrations are obtained and the inverse problem is solved, allowing the filtration coefficients determination from experiments. The filtration coefficients for the proposed and the classical deep bed filtration models are calculated from experimental data available in the literature and the results are compared. Finally, it is shown that the proposed model tends to the classical deep bed filtration model when the particle retention probability tends to zero. (author)
Rohan, Eduard; Jonášová, Alena
2016-01-01
The paper deals with modeling the liver perfusion intended to improve quantitative analysis of the tissue scans provided by the contrast-enhanced computed tomography (CT). For this purpose, we developed a model of dynamic transport of the contrast fluid through the hierarchies of the perfusion trees. Conceptually, computed time-space distributions of the so-called tissue density can be compared with the measured data obtained from CT; such a modeling feedback can be used for model parameter identification. The blood flow is characterized at several scales for which different models are used. Flows in upper hierarchies represented by larger branching vessels are described using simple 1D models based on the Bernoulli equation extended by correction terms to respect the local pressure losses. To describe flows in smaller vessels and in the tissue parenchyma, we propose a 3D continuum model of porous medium defined in terms of hierarchically matched compartments characterized by hydraulic permeabilities. The 1D ...
Zhou, Jun; Li, Nianbei; Yang, Ronggui
2015-06-01
The electrons and phonons in metal films after ultra-short pulse laser heating are in highly non-equilibrium states not only between the electrons and the phonons but also within the electrons. An electrohydrodynamics model consisting of the balance equations of electron density, energy density of electrons, and energy density of phonons is derived from the coupled non-equilibrium electron and phonon Boltzmann transport equations to study the nonlinear thermal transport by considering the electron density fluctuation and the transient electric current in metal films, after ultra-short pulse laser heating. The temperature evolution is calculated by the coupled electron and phonon Boltzmann transport equations, the electrohydrodynamics model derived in this work, and the two-temperature model. Different laser pulse durations, film thicknesses, and laser fluences are considered. We find that the two-temperature model overestimates the electron temperature at the front surface of the film and underestimates the damage threshold when the nonlinear thermal transport of electrons is important. The electrohydrodynamics model proposed in this work could be a more accurate prediction tool to study the non-equilibrium electron and phonon transport process than the two-temperature model and it is much easier to be solved than the Boltzmann transport equations.
Wu, Ming; Wu, Jianfeng; Wu, Jichun
2017-10-01
When the dense nonaqueous phase liquid (DNAPL) comes into the subsurface environment, its migration behavior is crucially affected by the permeability and entry pressure of subsurface porous media. A prerequisite for accurately simulating DNAPL migration in aquifers is then the determination of the permeability, entry pressure and corresponding representative elementary volumes (REV) of porous media. However, the permeability, entry pressure and corresponding representative elementary volumes (REV) are hard to determine clearly. This study utilizes the light transmission micro-tomography (LTM) method to determine the permeability and entry pressure of two dimensional (2D) translucent porous media and integrates the LTM with a criterion of relative gradient error to quantify the corresponding REV of porous media. As a result, the DNAPL migration in porous media might be accurately simulated by discretizing the model at the REV dimension. To validate the quantification methods, an experiment of perchloroethylene (PCE) migration is conducted in a two-dimensional heterogeneous bench-scale aquifer cell. Based on the quantifications of permeability, entry pressure and REV scales of 2D porous media determined by the LTM and relative gradient error, different models with different sizes of discretization grid are used to simulate the PCE migration. It is shown that the model based on REV size agrees well with the experimental results over the entire migration period including calibration, verification and validation processes. This helps to better understand the microstructures of porous media and achieve accurately simulating DNAPL migration in aquifers based on the REV estimation.
Porta, G. M.; Ceriotti, G.; Thovert, J.-F.
2016-02-01
We compare the ability of various continuum-scale models to reproduce the key features of a transport setting associated with a bimolecular reaction taking place in the fluid phase and numerically simulated at the pore-scale level in a disordered porous medium. We start by considering a continuum-scale formulation which results from formal upscaling of this reactive transport process by means of volume averaging. The resulting (upscaled) continuum-scale system of equations includes nonlocal integro-differential terms and the effective parameters embedded in the model are quantified directly through computed pore-scale fluid velocity and pore space geometry attributes. The results obtained through this predictive model formulation are then compared against those provided by available effective continuum models which require calibration through parameter estimation. Our analysis considers two models recently proposed in the literature which are designed to embed incomplete mixing arising from the presence of fast reactions under advection-dominated transport conditions. We show that best estimates of the parameters of these two models heavily depend on the type of data employed for model calibration. Our upscaled nonlocal formulation enables us to reproduce most of the critical features observed through pore-scale simulation without any model calibration. As such, our results clearly show that embedding into a continuum-scale model the information content associated with pore-scale geometrical features and fluid velocity yields improved interpretation of typically available continuum-scale transport observations.
Finkel, Michael; Grathwohl, Peter; Cirpka, Olaf A.
2016-12-01
We present a semianalytical model for the transport of solutes being subject to sorption in porous aquifers. We couple a travel time-based model of advective transport with a spherical diffusion model of kinetic sorption in nonuniform material mixtures. The model is formulated in the Laplace domain and transformed to the time domain by numerical inversion. By this, three-dimensional transport of solutes undergoing mass transfer between aqueous and solid phases can be simulated very efficiently. The model addresses both hydraulic and reactive heterogeneity of porous aquifers by means of hydrofacies, which function as homogeneous but nonuniform subunits. The total exposure time to each of these subunits controls the magnitude of sorption effects, whereas the particular sequence of facies through which the solute passes is irrelevant. We apply the model to simulate the transport of phenanthrene in a fluvio-glacial aquifer, for which the hydrofacies distribution is known at high resolution, the lithological composition of each facies has been analyzed, and sorption properties of the lithological components are available. Taking the fully resolved hydrofacies model as reference, we evaluate different approximations referring to lower information levels, reflecting shortcomings in typical modeling projects. The most important feature for a good description of both the main breakthrough and tailing of phenanthrene is the nonuniformity of the porous medium. While spatial heterogeneity of chemical properties might be neglected without introducing a large error, an approximation of the facies' composition in terms of a uniform substitute material considerably compromises the quality of the modeling result.
Bachrata, A.; Fichot, F.; Quintard, M.; Repetto, G.; Fleurot, J.
2012-05-01
A generalized non local-equilibrium, three-equation model was developed for the macroscopic description of two-phase flow heat and mass transfer in porous media subjected to phase change. Six pore-scale closure problems were proposed to determine all the effective transport coefficients for representative unit cells. An improved model is presented in this paper with the perspective of application to intense boiling phenomena. The objective of this paper is to present application of this model to the simulation of reflooding of severely damaged nuclear reactor cores. In case of accident at a nuclear power plant, water sources may not be available for a long period of time and the core heats up due to the residual power. Any attempt to inject water during core degradation can lead to quenching and further fragmentation of the core material. The fragmentation of fuel rods and melting of reactor core materials may result in the formation of a "debris bed". The typical particle size in a debris bed might reach few millimeters (characteristic length-scale: 1 to 5 mm), which corresponds to a high permeability porous medium. The proposed two-phase flow model is implemented in the ICARECATHARE code, developed by IRSN to study severe accident scenarios in pressurized water reactors. Currently, the French IRSN has set up two experimental facilities to study debris bed reflooding, PEARL and PRELUDE, with the objective to validate safety models. The PRELUDE program studies the complex two phase flow of water and steam in a porous medium (diameter 180 mm, height 200 mm), initially heated to a high temperature (400°C or 700°C). The series of PRELUDE experiments achieved in 2010 constitute a significant complement to the database of high temperature bottom reflood experimental data. They provide relevant data to understand the progression of the quench front and the intensity of heat transfer. Modeling accurately these experiments required improvements to the reflooding model
Energy Technology Data Exchange (ETDEWEB)
Bachrata, A.; Fichot, F.; Quintard, M.; Repetto, G.; Fleurot, J. [Institut de Radioprotection et de Surete Nucleaire, Cadarache (France); Universite de Toulouse (France); INPT, UPS (France); IMFT - Institut de Mecanique des Fluides de Toulouse, Allee Camille Soula, F-31400 Toulouse (France) and CNRS (France); IMFT, F-31400 Toulouse (France); Institut de Radioprotection et de Surete Nucleaire, Cadarache (France)
2012-05-15
A generalized non local-equilibrium, three-equation model was developed for the macroscopic description of two-phase flow heat and mass transfer in porous media subjected to phase change. Six pore-scale closure problems were proposed to determine all the effective transport coefficients for representative unit cells. An improved model is presented in this paper with the perspective of application to intense boiling phenomena. The objective of this paper is to present application of this model to the simulation of reflooding of severely damaged nuclear reactor cores. In case of accident at a nuclear power plant, water sources may not be available for a long period of time and the core heats up due to the residual power. Any attempt to inject water during core degradation can lead to quenching and further fragmentation of the core material. The fragmentation of fuel rods and melting of reactor core materials may result in the formation of a {sup d}ebris bed{sup .} The typical particle size in a debris bed might reach few millimeters (characteristic length-scale: 1 to 5 mm), which corresponds to a high permeability porous medium. The proposed two-phase flow model is implemented in the ICARECATHARE code, developed by IRSN to study severe accident scenarios in pressurized water reactors. Currently, the French IRSN has set up two experimental facilities to study debris bed reflooding, PEARL and PRELUDE, with the objective to validate safety models. The PRELUDE program studies the complex two phase flow of water and steam in a porous medium (diameter 180 mm, height 200 mm), initially heated to a high temperature (400 deg. C or 700 deg. C). The series of PRELUDE experiments achieved in 2010 constitute a significant complement to the database of high temperature bottom reflood experimental data. They provide relevant data to understand the progression of the quench front and the intensity of heat transfer. Modeling accurately these experiments required improvements to the
Bourgeat, Alain; Smaï, Farid
2008-01-01
We derive a compositional compressible two-phase, liquid and gas, flow model for numerical simulations of hydrogen migration in deep geological repository for radioactive waste. This model includes capillary effects and the gas high diffusivity. Moreover, it is written in variables (total hydrogen mass density and liquid pressure) chosen in order to be consistent with gas appearance or disappearance. We discuss the well possedness of this model and give some computational evidences of its adequacy to simulate gas generation in a water saturated repository.
Energy Technology Data Exchange (ETDEWEB)
Paul Meakin; Alexandre Tartakovsky
2009-07-01
In the subsurface fluids play a critical role by transporting dissolved minerals, colloids and contaminants (sometimes over long distances), by mediating dissolution and precipitation processes and enabling chemical transformations in solution and at mineral surfaces. Although the complex geometries of fracture apertures, fracture networks and pore spaces may make it difficult to accurately predict fluid flow in saturated (single-phase) subsurface systems, well developed methods are available. The simulation of multiphase fluid flow in the subsurface is much more challenging because of the large density and/or viscosity ratios found in important applications (water/air in the vadose zone, water/oil, water/gas, gas/oil and water/oil/gas in oil reservoirs, water/air/non-aqueous phase liquids (NAPL) in contaminated vadose zone systems and gas/molten rock in volcanic systems, for example). In addition, the complex behavior of fluid-fluid-solid contact lines, and its impact on dynamic contact angles, must also be taken into account, and coupled with the fluid flow. Pore network models and simple statistical physics based models such as the invasion percolation and diffusion-limited aggregation models have been used quite extensively. However, these models for multiphase fluid flow are based on simplified models for pore space geometries and simplified physics. Other methods such a lattice Boltzmann and lattice gas models, molecular dynamics, Monte Carlo methods, and particle methods such as dissipative particle dynamics and smoothed particle hydrodynamics are based more firmly on first principles, and they do not require simplified pore and/or fracture geometries. However, they are less (in some cases very much less) computationally efficient that pore network and statistical physics models. Recently a combination of continuum computation fluid dynamics, fluid-fluid interface tracking or capturing and simple models for the dependence of contact angles on fluid velocity
Energy Technology Data Exchange (ETDEWEB)
Meakin, Paul; Tartakovsky, Alexandre M.
2009-01-01
In the subsurface fluids play a critical role by transporting dissolved minerals, colloids and contaminants (sometimes over long distances), by mediating dissolution and precipitation processes and enabling chemical transformations in solution and at mineral surfaces. Although the complex geometries of fracture apertures, fracture networks and pore spaces may make it difficult to accurately predict fluid flow in saturated (single-phase) subsurface systems, well developed methods are available. The simulation of multiphase fluid flow in the subsurface is much more challenging because of the large density and/or viscosity ratios found in important applications (water/air in the vadose zone, water/oil, water/gas, gas/oil and water/oil/gas in oil reservoirs, water/air/non-aqueous phase liquids (NAPL) in contaminated vadose zone systems and gas/molten rock in volcanic systems, for example). In addition, the complex behavior of fluid-fluid-solid contact lines, and its impact on dynamic contact angles, must also be taken into account, and coupled with the fluid flow. Pore network models and simple statistical physics based models such as the invasion percolation and diffusion-limited aggregation models have been used quite extensively. However, these models for multiphase fluid flow are based on simplified models for pore space geometries and simplified physics. Other methods such a lattice Boltzmann and lattice gas models, molecular dynamics, Monte Carlo methods, and particle methods such as dissipative particle dynamics and smoothed particle hydrodynamics are based more firmly on first principles, and they do not require simplified pore and/or fracture geometries. However, they are less (in some cases very much less) computationally efficient that pore network and statistical physics models. Recently a combination of continuum computation fluid dynamics, fluid-fluid interface tracking or capturing and simple models for the dependence of contact angles on fluid velocity
Seepage Characteristics Study on Power-Law Fluid in Fractal Porous Media
Directory of Open Access Journals (Sweden)
Meijuan Yun
2014-01-01
Full Text Available We present fractal models for the flow rate, velocity, effective viscosity, apparent viscosity, and effective permeability for power-law fluid based on the fractal properties of porous media. The proposed expressions realize the quantitative description to the relation between the properties of the power-law fluid and the parameters of the microstructure of the porous media. The model predictions are compared with related data and good agreement between them is found. The analytical expressions will contribute to the revealing of physical principles for the power-law fluid flow in porous media.
Samsó, Roger; García, Joan; Molle, Pascal; Forquet, Nicolas
2016-01-01
Horizontal subsurface Flow Constructed Wetlands (HF CWs) are biofilters planted with aquatic macrophytes within which wastewater is treated mostly through contact with bacterial biofilms. The high concentrations of organic carbon and nutrients being transported leads to high bacterial biomass production, which decreases the flow capacity of the porous material (bioclogging). In severe bioclogging scenarios, overland flow may take place, reducing overall treatment performance. In this work we developed a mathematical model using COMSOL Multiphysics™ and MATLAB(®) to simulate bioclogging effects in HF CWs. Variably saturated subsurface flow and overland flow were described using the Richards equation. To simplify the inherent complexity of the processes involved in bioclogging development, only one bacterial group was considered, and its growth was described using a Monod equation. Bioclogging effects on the hydrodynamics were taken into account by using a conceptual model that affects the value of Mualem's unsaturated relative permeability. Simulation results with and without bioclogging were compared to showcase the impact of this process on the overall functioning of CWs. The two scenarios rendered visually different bacteria distributions, flow and transport patterns, showing the necessity of including bioclogging effects on CWs models. This work represents one of the few studies available on bioclogging in variably saturated conditions, and the presented model allows simulating the interaction between overland and subsurface flow occurring in most HF CWs. Hence, this work gets us a step closer to being able to describe CWs functioning in an integrated way using mathematical models. Copyright © 2015 Elsevier Ltd. All rights reserved.
Multiphase flow in fractured porous media
Energy Technology Data Exchange (ETDEWEB)
Firoozabadi, A.
1995-02-01
The major goal of this research project was to improve the understanding of the gas-oil two-phase flow in fractured porous media. In addition, miscible displacement was studied to evaluate its promise for enhanced recovery.
DEFF Research Database (Denmark)
Christensen, Britt Stenhøj Baun
En kombination af eksperimentelt arbejde og numerisk modellering blev anvendt til undersøgelse af poreskala to-fase strømning i porøse medie systemer af sand og glasperler. Det eksperimentelle arbejde gjorde brug af den ikke-indtrængende og ikke-destruktive røntgenstråle billedmetode CT-teknik (C...
Escher, Joachim; Matioc, Bogdan-Vasile
2011-01-01
We prove global existence of nonnegative weak solutions to a degenerate parabolic system which models the interaction of two thin fluid films in a porous medium. Furthermore, we show that these weak solutions converge at an exponential rate towards flat equilibria.
Energy Technology Data Exchange (ETDEWEB)
Mukhopadhyay, Sumit; Sonnenthal, Eric L.; Spycher, Nicolas
2007-01-15
When hot radioactive waste is placed in subsurface tunnels, a series of complex changes occurs in the surrounding medium. The water in the pore space of the medium undergoes vaporization and boiling. Subsequently, vapor migrates out of the matrix pore space, moving away from the tunnel through the permeable fracture network. This migration is propelled by buoyancy, by the increased vapor pressure caused by heating and boiling, and through local convection. In cooler regions, the vapor condenses on fracture walls, where it drains through the fracture network. Slow imbibition of water thereafter leads to gradual rewetting of the rock matrix. These thermal and hydrological processes also bring about chemical changes in the medium. Amorphous silica precipitates from boiling and evaporation, and calcite from heating and CO2 volatilization. The precipitation of amorphous silica, and to a much lesser extent calcite, results in long-term permeability reduction. Evaporative concentration also results in the precipitation of gypsum (or anhydrite), halite, fluorite and other salts. These evaporative minerals eventually redissolve after the boiling period is over, however, their precipitation results in a significant temporary decrease in permeability. Reduction of permeability is also associated with changes in fracture capillary characteristics. In short, the coupled thermal-hydrological-chemical (THC) processes dynamically alter the hydrological properties of the rock. A model based on the TOUGHREACT reactive transport software is presented here to investigate the impact of THC processes on flow near an emplacement tunnel at Yucca Mountain, Nevada. We show how transient changes in hydrological properties caused by THC processes often lead to local flow channeling and saturation increases above the tunnel. For models that include only permeability changes to fractures, such local flow channeling may lead to seepage relative to models where THC effects are ignored. However
Energy Technology Data Exchange (ETDEWEB)
Mukhopadhyay, S.; Sonnenthal, E.L.; Spycher, N.
2007-01-15
When hot radioactive waste is placed in subsurface tunnels, a series of complex changes occurs in the surrounding medium. The water in the pore space of the medium undergoes vaporization and boiling. Subsequently, vapor migrates out of the matrix pore space, moving away from the tunnel through the permeable fracture network. This migration is propelled by buoyancy, by the increased vapor pressure caused by heating and boiling, and through local convection. In cooler regions, the vapor condenses on fracture walls, where it drains through the fracture network. Slow imbibition of water thereafter leads to gradual rewetting of the rock matrix. These thermal and hydrological processes also bring about chemical changes in the medium. Amorphous silica precipitates from boiling and evaporation, and calcite from heating and CO{sub 2} volatilization. The precipitation of amorphous silica, and to a much lesser extent calcite, results in long-term permeability reduction. Evaporative concentration also results in the precipitation of gypsum (or anhydrite), halite, fluorite and other salts. These evaporative minerals eventually redissolve after the boiling period is over, however, their precipitation results in a significant temporary decrease in permeability. Reduction of permeability is also associated with changes in fracture capillary characteristics. In short, the coupled thermal-hydrological-chemical (THC) processes dynamically alter the hydrological properties of the rock. A model based on the TOUGHREACT reactive transport software is presented here to investigate the impact of THC processes on flow near an emplacement tunnel at Yucca Mountain, Nevada. We show how transient changes in hydrological properties caused by THC processes often lead to local flow channeling and saturation increases above the tunnel. For models that include only permeability changes to fractures, such local flow channeling may lead to seepage relative to models where THC effects are ignored
Directory of Open Access Journals (Sweden)
Gian Paolo Beretta
2008-08-01
Full Text Available A rate equation for a discrete probability distribution is discussed as a route to describe smooth relaxation towards the maximum entropy distribution compatible at all times with one or more linear constraints. The resulting dynamics follows the path of steepest entropy ascent compatible with the constraints. The rate equation is consistent with the Onsager theorem of reciprocity and the fluctuation-dissipation theorem. The mathematical formalism was originally developed to obtain a quantum theoretical unification of mechanics and thermodinamics. It is presented here in a general, non-quantal formulation as a part of an effort to develop tools for the phenomenological treatment of non-equilibrium problems with applications in engineering, biology, sociology, and economics. The rate equation is also extended to include the case of assigned time-dependences of the constraints and the entropy, such as for modeling non-equilibrium energy and entropy exchanges.
Beretta, Gian P.
2008-09-01
A rate equation for a discrete probability distribution is discussed as a route to describe smooth relaxation towards the maximum entropy distribution compatible at all times with one or more linear constraints. The resulting dynamics follows the path of steepest entropy ascent compatible with the constraints. The rate equation is consistent with the Onsager theorem of reciprocity and the fluctuation-dissipation theorem. The mathematical formalism was originally developed to obtain a quantum theoretical unification of mechanics and thermodinamics. It is presented here in a general, non-quantal formulation as a part of an effort to develop tools for the phenomenological treatment of non-equilibrium problems with applications in engineering, biology, sociology, and economics. The rate equation is also extended to include the case of assigned time-dependences of the constraints and the entropy, such as for modeling non-equilibrium energy and entropy exchanges.
Flow of polymer fluids through porous media
Zami-Pierre, Frédéric; Davit, Yohan; Loubens, Romain de; Quintard, Michel
2016-01-01
Non-Newtonian fluids are extensively used in enhanced oil recovery. However, understanding the flow of such fluids in complex porous media remains a challenging problem. In the presented study, we use computational fluid dynamics to investigate the creeping flow of a particular non-Newtonian fluid through porous media, namely a power-law fluid with a newtonian behavior below a critical shear rate. We show that the nonlinear effects induced by the rheology only weakly impact the topological st...
Effects of CO2 on P-wave attenuation in porous media with micro-cracks: A synthetic modelling study
Ekanem, A. M.; Li, X. Y.; Chapman, M.; Main, I. G.
2016-12-01
The presence of CO2 in hydrocarbon reservoirs can cause significant changes in seismic wave properties. In turn these properties can be used to map CO2 saturation in hydrocarbon reservoirs or aquifers - either from natural sources or by injection from the surface. We present the results of a synthetic modelling study of the effects of supercritical CO2 saturation on P-wave attenuation in a medium consisting of four horizontal layers, including a target aquifer. The target aquifer is modelled fully by an effective medium containing pores saturated with brine and/or CO2 and randomly-aligned microcracks at different densities. The other layers are modelled solely by their bulk seismic velocities and densities. We first compute synthetic seismograms for a reference case where the third layer is completely isotropic with no cracks, no pores and no fluid saturation. We then calculate synthetic seismograms for finite crack densities of 0.01, 0.02 and 0.03 at varying degrees of CO2 saturation in the third layer. The results of our analysis indicate that attenuation is sensitive both to CO2 saturation and the crack density. For a given crack density, attenuation increases gradually with decreasing percentage of CO2 saturation and reaches a maximum at around 10% saturation. The induced attenuation increases with crack density and with offset. These observations hold out the potential of using seismic attenuation as an additional diagnostic in the characterisation of rock formations for a variety of applications, including hydrocarbon exploration and production, subsurface storage of CO2 or geothermal energy extraction.
Simulation of H2O-vapor and Brine-CO2 in porous media with a Lattice Boltzmann Model.
Schaap, M. G.
2014-12-01
This DOE-BES funded study is a collaboration between Oregon State University (led by Dr. Dorthe Wildenschild) and the University of Arizona to investigate pore-scale aspects of capillary trapping to enhance the efficiency of geological CO2 sequestration. For the purposes of this project it is important to correctly simulate the physical conditions under which super-critical CO2 will be present after injection into the host rock. This means that the LB model should be able to handle the pressures, densities, temperatures in deep geological media. A logical way of dealing with is is to combine a single-component LB model with and Equation of State (EOS) that describes the physical interrelations among pressure, temperature and density. Previously, we showed that the Peng-Robinson (PR) EOS provides an excellent fit to super-critical conditions for the pure CO2 system. However, it is necessary to consider multi-component systems as the super-critical CO2 will be present with brines of varying salinity. A natural extension to the work under is to also treat the brine with an EOS. The brine will of be in a sub-critical state and it is therefore important to find an EOS that can faithfully match the physical conditions of brine between temperatures of 300 and 400K and pressures between 7 and 30 MPa. This study will present a number of EOS alternatives that attempt to correctly capture the density of the liquid branch of the water system for relevant temperatures and pressures. We will also propose modifications that allow us to deal with different brine concentrations and compare LB modeled interfacial tension and viscosity with published data. As a secondary objective we investigate whether it is possible to match water-vapor systems under ambient surface conditions relevant for vadose zone transport. Support: DOE DE-FG02-11ER16278
Boufadel, Michel C.; Suidan, Makram T.; Venosa, Albert D.
1999-04-01
We present a formulation for water flow and solute transport in two-dimensional variably saturated media that accounts for the effects of the solute on water density and viscosity. The governing equations are cast in a dimensionless form that depends on six dimensionless groups of parameters. These equations are discretized in space using the Galerkin finite element formulation and integrated in time using the backward Euler scheme with mass lumping. The modified Picard method is used to linearize the water flow equation. The resulting numerical model, the MARUN model, is verified by comparison to published numerical results. It is then used to investigate beach hydraulics at seawater concentration (about 30 g l -1) in the context of nutrients delivery for bioremediation of oil spills on beaches. Numerical simulations that we conducted in a rectangular section of a hypothetical beach revealed that buoyancy in the unsaturated zone is significant in soils that are fine textured, with low anisotropy ratio, and/or exhibiting low physical dispersion. In such situations, application of dissolved nutrients to a contaminated beach in a freshwater solution is superior to their application in a seawater solution. Concentration-engendered viscosity effects were negligible with respect to concentration-engendered density effects for the cases that we considered.
Tosco, Tiziana; Gastone, Francesca; Sethi, Rajandrea
2014-10-01
In the present work column transport tests were performed in order to study the mobility of guar-gum suspensions of microscale zero-valent iron particles (MZVI) in porous media. The results were analyzed with the purpose of implementing a radial model for the design of full scale interventions. The transport tests were performed using several concentrations of shear thinning guar gum solutions as stabilizer (1.5, 3 and 4 g/l) and applying different flow rates (Darcy velocity in the range 1 · 10- 4 to 2 · 10- 3 m/s), representative of different distances from the injection point in the radial domain. Empirical relationships, expressing the dependence of the deposition and release parameters on the flow velocity, were derived by inverse fitting of the column transport tests using a modified version of E-MNM1D (Tosco and Sethi, 2010) and the user interface MNMs (www.polito.it/groundwater/software). They were used to develop a comprehensive transport model of MZVI suspensions in radial coordinates, called E-MNM1R, which takes into account the non Newtonian (shear thinning) rheological properties of the dispersant fluid and the porous medium clogging associated with filtration and sedimentation in the porous medium of both MZVI and guar gum residual undissolved particles. The radial model was run in forward mode to simulate the injection of MZVI dispersed in guar gum in conditions similar to those applied in the column transport tests. In a second stage, we demonstrated how the model can be used as a valid tool for the design and the optimization of a full scale intervention. The simulation results indicated that several concurrent aspects are to be taken into account for the design of a successful delivery of MZVI/guar gum slurries via permeation injection, and a compromise is necessary between maximizing the radius of influence of the injection and minimizing the injection pressure, to guarantee a sufficiently homogeneous distribution of the particles around the
El-Amin, M F; Sun, Shuyu; Salama, Amgad
2013-01-01
In this paper, we introduce a mathematical model to describe the nanoparticles transport carried by a two-phase flow in a porous medium including gravity, capillary forces and Brownian diffusion. Nonlinear iterative IMPES scheme is used to solve the flow equation, and saturation and pressure are calculated at the current iteration step and then the transport equation is soved implicitly. Therefore, once the nanoparticles concentration is computed, the two equations of volume of the nanoparticles available on the pore surfaces and the volume of the nanoparticles entrapped in pore throats are solved implicitly. The porosity and the permeability variations are updated at each time step after each iteration loop. Two numerical examples, namely, regular heterogeneous permeability and random permeability are considered. We monitor the changing of the fluid and solid properties due to adding the nanoparticles. Variation of water saturation, water pressure, nanoparticles concentration and porosity are presented graph...
Energy Technology Data Exchange (ETDEWEB)
Colwell, Frederick [Oregon State Univ., Corvallis, OR (United States); Wildenschild, Dorthe [Oregon State Univ., Corvallis, OR (United States); Wood, Brian [Oregon State Univ., Corvallis, OR (United States); Gerlach, Robin [Montana State Univ., Bozeman, MT (United States); Mitchell, Andrew [Montana State Univ., Bozeman, MT (United States); Redden, George [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2014-08-29
The goal for this research was to understand how best to add compounds to receptive microbial communities in porous media in order to achieve optimal calcite precipitation in a volumetrically significant space and to understand the physiological health of the cells that are responsible for the calcite precipitation. The specific objectives were to: (1) develop better tools for visually examining biofilms in porous media and calcium carbonate precipitation being mediated by microbes in porous media, and (2) demonstrate the effectiveness of using that tool within a flow cell model system.
Sanz-Prat, Alicia; Lu, Chuanhe; Amos, Richard T.; Finkel, Michael; Blowes, David W.; Cirpka, Olaf A.
2016-09-01
the two types of biomass at late times. Results obtained by mapping the exposure-time based results to the two-dimensional domain are compared with simulations based on the two-dimensional, spatially explicit advection-dispersion-reaction equation. Once quasi-steady state has been reached, we find a good agreement in terms of the chemical-compound concentrations between the two approaches inside the reactive zones, whereas the exposure-time based model is not able to capture reactions occurring in the zones with zero electron-donor release. We conclude that exposure-time models provide good approximations of nonlinear bio-reactive transport when transverse mixing is not the overall controlling process and all reactions are essentially restricted to distinct reactive zones.
Sanz-Prat, Alicia; Lu, Chuanhe; Amos, Richard T; Finkel, Michael; Blowes, David W; Cirpka, Olaf A
2016-09-01
the two types of biomass at late times. Results obtained by mapping the exposure-time based results to the two-dimensional domain are compared with simulations based on the two-dimensional, spatially explicit advection-dispersion-reaction equation. Once quasi-steady state has been reached, we find a good agreement in terms of the chemical-compound concentrations between the two approaches inside the reactive zones, whereas the exposure-time based model is not able to capture reactions occurring in the zones with zero electron-donor release. We conclude that exposure-time models provide good approximations of nonlinear bio-reactive transport when transverse mixing is not the overall controlling process and all reactions are essentially restricted to distinct reactive zones.
A 2-D FEM thermal model to simulate water flow in a porous media: Campi Flegrei caldera case study
Directory of Open Access Journals (Sweden)
V. Romano
2012-05-01
Full Text Available Volcanic and geothermal aspects both exist in many geologically young areas. In these areas the heat transfer process is of fundamental importance, so that the thermal and fluid-dynamic processes characterizing a viscous fluid in a porous medium are very important to understand the complex dynamics of the these areas. The Campi Flegrei caldera, located west of the city of Naples, within the central-southern sector of the large graben of Campanian plain, is a region where both volcanic and geothermal phenomena are present. The upper part of the geothermal system can be considered roughly as a succession of volcanic porous material (tuff saturated by a mixture formed mainly by water and carbon dioxide. We have implemented a finite elements approach in transient conditions to simulate water flow in a 2-D porous medium to model the changes of temperature in the geothermal system due to magmatic fluid inflow, accounting for a transient phase, not considered in the analytical solutions and fluid compressibility. The thermal model is described by means of conductive/convective equations, in which we propose a thermal source represented by a parabolic shape function to better simulate an increase of temperature in the central part (magma chamber of a box, simulating the Campi Flegrei caldera and using more recent evaluations, from literature, for the medium's parameters (specific heat capacity, density, thermal conductivity, permeability. A best-fit velocity for the permeant is evaluated by comparing the simulated temperatures with those measured in wells drilled by Agip (Italian Oil Agency in the 1980s in the framework of geothermal exploration. A few tens of days are enough to reach the thermal steady state, showing the quick response of the system to heat injection. The increase in the pressure due to the heat transport is then used to compute ground deformation, in particular the vertical displacements characteristics of the Campi Flegrei caldera
Directory of Open Access Journals (Sweden)
Zhiqiang Chen
2016-03-01
Full Text Available The hydro-mechanical coupling transport process of sand production is numerically investigated with special attention paid to the bonding effect between sand grains. By coupling the lattice Boltzmann method (LBM and the discrete element method (DEM, we are able to capture particles movements and fluid flows simultaneously. In order to account for the bonding effects on sand production, a contact bond model is introduced into the LBM-DEM framework. Our simulations first examine the experimental observation of “initial sand production is evoked by localized failure” and then show that the bonding or cement plays an important role in sand production. Lower bonding strength will lead to more sand production than higher bonding strength. It is also found that the influence of flow rate on sand production depends on the bonding strength in cemented granular media, and for low bonding strength sample, the higher the flow rate is, the more severe the erosion found in localized failure zone becomes.
Large scale flow visualization and anemometry applied to lab-on-a-chip models of porous media.
Paiola, Johan; Auradou, Harold; Bodiguel, Hugues
2016-08-01
The following is a report on an experimental technique that allows one to quantify and map the velocity field with very high resolution and simple equipment in large 2D devices. Illumination through a grid is proposed to reinforce the contrast in the images and allow one to detect seeded particles that are pixel-sized or even smaller. The velocimetry technique that we have reported is based on the auto-correlation functions of the pixel intensity, which we have shown are directly related to the magnitude of the local average velocity. The characteristic time involved in the decorrelation of the signal is proportional to the tracer size and inversely proportional to the average velocity. We have reported on a detailed discussion about the optimization of relevant involved parameters, the spatial resolution and the accuracy of the method. The technique is then applied to a model porous medium made of a random channel network. We show that it is highly efficient to determine the magnitude of the flow in each of the channels of the network, opening the door to the fundamental study of the flows of complex fluids. The latter is illustrated with a yield stress fluid, in which the flow becomes highly heterogeneous at small flow rates.
Huang, Y.; Shao, H.; Thullner, M.; Kolditz, O.
2014-12-01
In applications of Deep Geothermal reservoirs, thermal recovery processes, and contaminated groundwater sites, the multiphase multicomponent flow and transport processes are often considered the most important underlying physical process. In particular, the behavior of phase appearance and disappearance is the critical to the performance of many geo-reservoirs, and great interests exit in the scientific community to simulate this coupled process. This work is devoted to the modeling and simulation of two-phase, two components flow and transport in the porous medium, whereas the phase change behavior in non-isothermal conditions is considered. In this work, we have implemented the algorithm developed by Marchand, et al., into the open source scientific software OpenGeoSys. The governing equation is formulated in terms of molar fraction of the light component and mean pressure as the persistent primary variables, which leads to a fully coupled nonlinear PDE system. One of the important advantages of this approach is avoiding the primary variables switching between single phase and two phase zones, so that this uniform system can be applied to describe the behavior of phase change. On the other hand, due to the number of unkown variables closure relationships are also formulated to close the whole equation system by using the approach of complementarity constrains. For the numerical technical scheme: The standard Galerkin Finite element method is applied for space discretization, while a fully implicit scheme for the time discretization, and Newton-Raphson method is utilized for the global linearization, as well as the closure relationship. This model is verified based on one test case developed to simulate the heat pipe problem. This benchmark involves two-phase two-component flow in saturated/unsaturated porous media under non-isothermal condition, including phase change and mineral-water geochemical reactive transport processes. The simulation results will be
Thermal non-equilibrium in heterogeneous media
de Lemos, Marcelo J S
2016-01-01
This book presents, in a self-contained fashion, a series of studies on flow and heat transfer in porous media, in which distinct energy balances are considered for the porous matrix and for the permeating fluid. Detailed mathematical modeling is presented considering both volume and time averaging operators simultaneously applied to the governing equations. System involving combustion in the gaseous phase, moving bed and double-diffusion mechanism are analyzed. Numerical results are presented for each case. In the end, this book contains the description of a tool that might benefit engineers in developing and designing more efficient thermal equipment.
Wang, Dengjun; Jin, Yan; Jaisi, Deb P.
2015-11-01
The fate and transport of individual type of engineered nanoparticles (ENPs) in porous media have been studied intensively and the corresponding mechanisms controlling ENPs transport and deposition are well-documented. However, investigations regarding the mobility of ENPs in the concurrent presence of another mobile colloidal phase such as naturally occurring colloids (colloid-mediated transport of ENPs) are largely lacking. Here, we investigated the cotransport and retention of engineered hydroxyapatite nanoparticles (HANPs) with naturally occurring hematite colloids in water-saturated sand columns under environmentally relevant transport conditions, i.e., pH, ionic strength (IS), and flow rate. Particularly, phosphate oxygen isotope fractionation of HANPs during cotransport was explored at various ISs and flow rates to examine the mechanisms controlling the isotope fractionation of HANPs in abiotic transport processes (physical transport). During cotransport, greater mobility of both HANPs and hematite occurred at higher pHs and flow rates, but at lower ISs. Intriguingly, the mobility of both HANPs and hematite was substantially lower during cotransport than the individual transport of either, attributed primarily to greater homo- and hetero-aggregation when both particles are copresent in the suspension. The shapes of breakthrough curves (BTCs) and retention profiles (RPs) during cotransport for both particles evolved from blocking to ripening with time and from flat to hyperexponential with depth, respectively, in response to decreases in pH and flow rate, and increases in IS. The blocking BTCs and RPs that are flat or hyperexponential can be well-approximated by a one-site kinetic attachment model. Conversely, a ripening model that incorporates attractive particle-particle interaction has to be employed to capture the ripening BTCs that are impacted by particle aggregation during cotransport. A small phosphate oxygen isotope fractionation (≤ 1.8
Study of the effects of stress sensitivity on the permeability and porosity of fractal porous media
Tan, Xiao-Hua; Li, Xiao-Ping; Liu, Jian-Yi; Zhang, Lie-Hui; Fan, Zhou
2015-10-01
Flow in porous media under stress is very important in various scientific and engineering fields. It has been shown that stress plays an important role in effect of permeability and porosity of porous media. In this work, novel predictive models for permeability and porosity of porous media considering stress sensitivity are developed based on the fractal theory and mechanics of materials. Every parameter in the proposed models has clear physical meaning. The proposed models are evaluated using previously published data for permeability and porosity measured in various natural materials. The predictions of permeability and porosity show good agreement with those obtained by the available experimental data and illustrate that the proposed models can be used to characterize the flow in porous media under stress accurately.
Numerical Simulations of Heat Explosion With Convection In Porous Media
Allali, Karam; Bikany, Fouad; Taik, Ahmed; Volpert, Vitaly
2013-01-01
In this paper we study the interaction between natural convection and heat explosion in porous media. The model consists of the heat equation with a nonlinear source term describing heat production due to an exothermic chemical reaction coupled with the Darcy law. Stationary and oscillating convection regimes and oscillating heat explosion are observed. The models with quasi-stationary and unstationary Darcy equation are compared.
Numerical simulations of heat explosion with convection in porous media
Allali, Karam; Bikany, Fouad; Taik, Ahmed; Volpert, Vitaly
2015-01-01
International audience; In this article, we study the interaction between natural convection and heat explosion in porous media. The model consists of the heat equation with a nonlinear source term describing heat production due to an exothermic chemical reaction coupled with the Darcy law. Stationary and oscillating convection regimes and oscillating heat explosion are observed. The models with quasi-stationary and unstationary Darcy equation are compared.
An empirical correlation for isothermal parallel plate channel completely filled with porous media
Directory of Open Access Journals (Sweden)
Hamdan Mohammad O.
2013-01-01
Full Text Available This study reports a simple empirical correlation for friction factor and Nusselt number for laminar, steady state, hydraulically and thermally fully developed flow in isothermal parallel plate channel completely filled with porous media. The study is carried out using a finite difference numerical analysis. The Darcy-Brinkman-Forchheimer model is used to model the flow inside the porous media. The empirical correlations are developed to relate friction factor and Nusselt number to Darcy and Forchheimer coefficient.
Foam Transport in Porous Media - A Review
Energy Technology Data Exchange (ETDEWEB)
Zhang, Z. F.; Freedman, Vicky L.; Zhong, Lirong
2009-11-11
Amendment solutions with or without surfactants have been used to remove contaminants from soil. However, it has drawbacks such that the amendment solution often mobilizes the plume, and its movement is controlled by gravity and preferential flow paths. Foam is an emulsion-like, two-phase system in which gas cells are dispersed in a liquid and separated by thin liquid films called lamellae. Potential advantages of using foams in sub-surface remediation include providing better control on the volume of fluids injected, uniformity of contact, and the ability to contain the migration of contaminant laden liquids. It is expected that foam can serve as a carrier of amendments for vadose zone remediation, e.g., at the Hanford Site. As part of the U.S. Department of Energy’s EM-20 program, a numerical simulation capability will be added to the Subsurface Transport Over Multiple Phases (STOMP) flow simulator. The primary purpose of this document is to review the modeling approaches of foam transport in porous media. However, as an aid to understanding the simulation approaches, some experiments under unsaturated conditions and the processes of foam transport are also reviewed. Foam may be formed when the surfactant concentration is above the critical micelle concentration. There are two main types of foams – the ball foam (microfoam) and the polyhedral foam. The characteristics of bulk foam are described by the properties such as foam quality, texture, stability, density, surface tension, disjoining pressure, etc. Foam has been used to flush contaminants such as metals, organics, and nonaqueous phase liquids from unsaturated soil. Ball foam, or colloidal gas aphrons, reportedly have been used for soil flushing in contaminated site remediation and was found to be more efficient than surfactant solutions on the basis of weight of contaminant removed per gram of surfactant. Experiments also indicate that the polyhedral foam can be used to enhance soil remediation. The
2013-03-01
Aquatic Test Organisms.” Environmental Science & Technology , 44(24): 9571-9577. Kim, Y. S., Kim, J. S., Cho, H. S., Rha, D. S., Kim, J. M., Park, J. D...Wiesner, M. R. (2004). “Velocity effects on fullerene and oxide nanoparticle deposition in porous media.” Environmental Science & Technology , 38(16...nanoparticles in quartz sands under varying flow conditions.” Environmental Science & Technology , 42(19): 7174-7180. Mattison, N. T., O’Carroll, D. M
Study of the effects of stress sensitivity on the permeability and porosity of fractal porous media
Energy Technology Data Exchange (ETDEWEB)
Tan, Xiao-Hua, E-mail: xiaohua-tan@163.com; Li, Xiao-Ping; Liu, Jian-Yi; Zhang, Lie-Hui; Fan, Zhou
2015-10-16
Flow in porous media under stress is very important in various scientific and engineering fields. It has been shown that stress plays an important role in effect of permeability and porosity of porous media. In this work, novel predictive models for permeability and porosity of porous media considering stress sensitivity are developed based on the fractal theory and mechanics of materials. Every parameter in the proposed models has clear physical meaning. The proposed models are evaluated using previously published data for permeability and porosity measured in various natural materials. The predictions of permeability and porosity show good agreement with those obtained by the available experimental data and illustrate that the proposed models can be used to characterize the flow in porous media under stress accurately. - Highlights: • Predictive models for permeability and porosity of porous media considering stress sensitivity are developed. • The fractal theory and mechanics of materials are used in these models. • The predictions of permeability and porosity show good agreement with those obtained by the available experimental data. • The proposed models can be used to characterize the flow in porous media under stress accurately.
Simulations of premixed combustion in porous media
Diamantis, D. J.; Mastorakos, E.; Goussis, D. A.
2002-09-01
A numerical model for planar premixed flames of methane in ceramic porous media has been developed to improve the understanding of the structure of such flames. The model successfully reproduces experimental data for both single- and two-layer surface flames. The success is attributed to the detail given to the boundary conditions and the radiation modelling, which was done by solving the radiation transfer equation inside the porous medium without any simplifying models. Surface-stabilized flames yielded SL/SL01 and their energy balance was similar to that of a free flame, which implies that the burning velocity acceleration is due to the reactant preheat. The flame solutions were further analysed with concepts from the computational singular perturbation method to construct reduced mechanisms. For all types of combustion (surface or submerged), an almost identical ordering of chemistry timescales to free flames was found and previously developed reduced mechanisms for free flames were accurate also for the flames inside the porous medium. The results suggest that the thermal exchange between the two phases that is responsible for the flame behaviour remains decoupled from the fast part of the chemistry.
Determination of Effective Thermal Conductivity For Real Porous Media Using Fractal Theory
Institute of Scientific and Technical Information of China (English)
ChenYongping; ShiMingheng
1999-01-01
In this paper,using fractal theory,the geometric structure of real soil was described with ist section view and section particle area fractal dimension d of porous media was counted.The volumetric solid content and the relation between volumetric solid content and porous media particle arrangements as well as measure scale were obtainted.A heat conduction model was established and the effective thermal conductivity of real soil based on the volumetric solid content was calculated.
Study of the mechanisms of the flame propagation and stabilization in porous media
Institute of Scientific and Technical Information of China (English)
2008-01-01
The CH4/air premixed gas combustion processes in porous media were numerically studied using the two-temperature reacting fluid model with dispersions and detailed chemical reaction mechanism GRI 3.0. The mechanisms of the propagation and stabilization of submerge flames and surface flames in porous media were illuminated distinctly by considering the magnitude of the terms in the two energy equations, analyzing the sensibility of flame propagation speed to flame location, heat exchange coefficient between gas and solid, thermal conductivity and radiative extinction coefficient of porous media. It was concluded that the propagation mechanism of a submerged flame is similar to that of a free flame with an additional preheat zone and that the surface-flame propagation mechanism in porous media is similar to that of a free flame with heat loss in reaction zone.
Non-Equilibrium Thermodynamics in Multiphase Flows
Mauri, Roberto
2013-01-01
Non-equilibrium thermodynamics is a general framework that allows the macroscopic description of irreversible processes. This book introduces non-equilibrium thermodynamics and its applications to the rheology of multiphase flows. The subject is relevant to graduate students in chemical and mechanical engineering, physics and material science. This book is divided into two parts. The first part presents the theory of non-equilibrium thermodynamics, reviewing its essential features and showing, when possible, some applications. The second part of this book deals with how the general theory can be applied to model multiphase flows and, in particular, how to determine their constitutive relations. Each chapter contains problems at the end, the solutions of which are given at the end of the book. No prior knowledge of statistical mechanics is required; the necessary prerequisites are elements of transport phenomena and on thermodynamics. “The style of the book is mathematical, but nonetheless it remains very re...
Bijeljic, B.; Andrew, M. G.; Menke, H. P.; Blunt, M. J.
2013-12-01
Advances in X ray imaging techniques made it possible not only to accurately describe solid and fluid(s) distributions in the pore space but also to study dynamics of multi-phase flow and reactive transport in-situ. This has opened up a range of new opportunities to better understand fundamental physics at the pore scale by experiment, and test and validate theoretical models in order to develop predictive tools at the pore scale and use it for upscaling. Firstly, we illustrate this concept by describing a new methodology for predicting non-Fickian transport in millimeter-sized three-dimensional micro-CT images of a beadpack, a sandstone, and a carbonate, representing porous media with an increasing degree of pore-scale complexity. The key strategy is to retain the full information on flow and transport signature of a porous medium by using probability distribution functions (PDFs) of voxel velocities for flow, and both PDFs of particle displacements and PDFs of particle transit times between voxels for transport. For this purpose, direct-simulation flow and transport model is used to analyse the relationship between pore structure, velocity, and the dynamics of the evolving plume. The model predictions for PDFs of particle displacements obtained by the model are in excellent agreement with those measured on similar cores in nuclear magnetic resonance experiments. A key determinant for non-Fickian transport is the spread in velocity distribution in the pore space. Further, we present micro-CT imaging of capillary trapping of scCO2 at reservoir conditions in a range of carbonates and sandstones having different pore structure and demonstrate that substantial quantities of scCO2 can be trapped in the pore space. Higher residual scCO2 saturations are found in sandstones compared to carbonates. The trapped ganglia exhibit different distribution of size, related to the inherent structure of pore space. Pore structures with large, open pores that are well connected lead
Plume dynamics in heterogeneous porous media
Neufeld, Jerome A.; Huppert, Herbert E.
2008-11-01
Buoyancy driven flows in layered porous media are present in many geological settings and play an important role in the mixing of fluids, from the dispersal of pollutants in underground aquifers to enhanced oil recovery techniques and, of more recent importance, the sequestration of carbon dioxide (CO2). Seismic images of the rise of a buoyant CO2 plume at Sleipner in the North Sea indicate that these plumes are greatly influenced by a vertical array of thin lenses of relatively low permeability material. We model propagation of CO2 at each layer as a gravity current in a porous medium which propagates along, and drains through, a thin, low permeability seal. Drainage, driven both by hydrostatic pressure and the body force on the draining fluid, leads to an initial rapid advance followed by a gradual retreat of the current to a steady-state. By incorporating a vertical array of these single layer models we are able to capture the rise of the buoyant plume in layered reservoirs. We find that the plume is characterized by a broad head with a tail given by the steady state extent.
Particle retention in porous media: Applications to water injectivity decline
Energy Technology Data Exchange (ETDEWEB)
Wennberg, Kjell Erik
1998-12-31
This thesis studies the problem of migration and deposition of colloidal particles within porous media, theoretically and by computerized simulation. Special emphasis is put on the prediction of injectivity decline in water injection wells due to inherent particles in the injection water. The study of particle deposition within porous media requires a correct prediction of the deposition rate or filtration coefficient. A thorough review of the modeling approaches used in the past are combined with new ideas in order to arrive at an improved model for the prediction of the filtration coefficient. A new way of determining the transition time for the dominant deposition mechanism to change from internal deposition to external cake formation is proposed. From this fundamental theory, equations are given for water injectivity decline predictions. A computer program called WID for water injectivity decline predictions was developed. Using water quality, formation properties, injection rate/pressure and completion information as input, WID predicts decline in vertical and horizontal injection wells with openhole, perforated and fractured completions. The calculations agree fairly well with field data; in some cases the agreement is excellent. A poor match in a few cases indicates that more mechanisms may be responsible for injectivity decline than those presently accounted for by the simulator. The second part of the study deals with a theoretical investigation of the multi-dimensional nature of particle deposition in porous media. 112 refs., 100 figs., 9 tabs.
Fluid dynamics in porous media with Sailfish
Coelho, Rodrigo C. V.; Neumann, Rodrigo F.
2016-09-01
In this work we show the application of Sailfish to the study of fluid dynamics in porous media. Sailfish is an open-source software based on the lattice-Boltzmann method. This application of computational fluid dynamics is of particular interest to the oil and gas industry and the subject could be a starting point for an undergraduate or graduate student in physics or engineering. We built artificial samples of porous media with different porosities and used Sailfish to simulate the fluid flow through them in order to calculate their permeability and tortuosity. We also present a simple way to obtain the specific superficial area of porous media using Python libraries. To contextualise these concepts, we analyse the applicability of the Kozeny-Carman equation, which is a well-known permeability-porosity relation, to our artificial samples.
Fluid dynamics in porous media with Sailfish
Coelho, Rodrigo C V
2016-01-01
In this work we show the application of Sailfish to the study of fluid dynamics in porous media. Sailfish is an open-source software based on the lattice-Boltzmann method. This application of computational fluid dynamics is of particular interest to the oil and gas industry and the subject could be a starting point for an undergraduate or graduate student in physics or engineering. We built artificial samples of porous media with different porosities and used Sailfish to simulate the fluid flow through in order to calculate permeability and tortuosity. We also present a simple way to obtain the specific superficial area of porous media using Python libraries. To contextualize these concepts, we test the Kozeny--Carman equation, discuss its validity and calculate the Kozeny's constant for our artificial samples.
Raju, Ch. Narasimha; Chatterjee, Ashok
2016-01-01
The Anderson-Holstein model with Caldeira-Leggett coupling with environment is considered to describe the damping effect in a single molecular transistor (SMT) which comprises a molecular quantum dot (with electron-phonon interaction) mounted on a substrate (environment) and coupled to metallic electrodes. The electron-phonon interaction is first eliminated using the Lang-Firsov transformation and the spectral density function, charge current and differential conductance are then calculated using the non-equilibrium Keldysh Green function technique. The effects of damping rate, and electron-electron and electron-phonon interactions on the transport properties of SMT are studied at zero temperature.
Hsieh, Chi-Pan; Chiang, Cheng-Chin; Huang, Chiung-Wei
2016-05-01
The mechanisms of the strong inward rectification in inward rectifier K(+) (Kir) channels are controversial because the drop in electrical potential due to the movement of the blocker and coupling ions is insufficient to explain the steep voltage-dependent block near the equilibrium potential. Here, we study the "driving force"-dependent block in Kir channels with a novel approach incorporating concepts from the non-equilibrium thermodynamics of small systems, and computer kinetic simulations based on the experimental data of internal Ba(2+) block on Kir2.1 channels. The steep exponential increase in the apparent binding rate near the equilibrium potential is explained, when the encounter frequency is construed as the likelihood of transfer events down or against the electrochemical potential gradient. The exponent of flux ratio, nf=2.62, implies that the blockage of the internal blocker may be coupled with the outward transport of 2 to 3K(+) ions. The flux-coupled block in the single-file multi-ion pore can be demonstrated by the concentration gradient alone, as well as when the driving force is the electrochemical potential difference across the membrane.
de Avillez, M A; Breitschwerdt, D; Spitoni, E
2012-01-01
Using three-dimensional non-equilibrium ionization (NEI) hydrodynamical simulation of the interstellar medium (ISM), we study the electron density, $n_{e}$, in the Galactic disk and compare it with the values derived from dispersion measures towards pulsars with known distances located up to 200 pc on either side of the Galactic midplane. The simulation results, consistent with observations, can be summarized as follows: (i) the DMs in the simulated disk lie between the maximum and minimum observed values, (ii) the log derived from lines of sight crossing the simulated disk follows a Gaussian distribution centered at \\mu=-1.4 with a dispersion \\sigma=0.21, thus, the Galactic midplane =0.04\\pm 0.01$ cm$^{-3}$, (iii) the highest electron concentration by mass (up to 80%) is in the thermally unstable regime (200
Explosion propagation in inert porous media.
Ciccarelli, G
2012-02-13
Porous media are often used in flame arresters because of the high surface area to volume ratio that is required for flame quenching. However, if the flame is not quenched, the flow obstruction within the porous media can promote explosion escalation, which is a well-known phenomenon in obstacle-laden channels. There are many parallels between explosion propagation through porous media and obstacle-laden channels. In both cases, the obstructions play a duel role. On the one hand, the obstruction enhances explosion propagation through an early shear-driven turbulence production mechanism and then later by shock-flame interactions that occur from lead shock reflections. On the other hand, the presence of an obstruction can suppress explosion propagation through momentum and heat losses, which both impede the unburned gas flow and extract energy from the expanding combustion products. In obstacle-laden channels, there are well-defined propagation regimes that are easily distinguished by abrupt changes in velocity. In porous media, the propagation regimes are not as distinguishable. In porous media the entire flamefront is affected, and the effects of heat loss, turbulence and compressibility are smoothly blended over most of the propagation velocity range. At low subsonic propagation speeds, heat loss to the porous media dominates, whereas at higher supersonic speeds turbulence and compressibility are important. This blending of the important phenomena results in no clear transition in propagation mechanism that is characterized by an abrupt change in propagation velocity. This is especially true for propagation velocities above the speed of sound where many experiments performed with fuel-air mixtures show a smooth increase in the propagation velocity with mixture reactivity up to the theoretical detonation wave velocity.
Influence of Dispersion on Transport of Tracer through Unsaturated Porous Media
Directory of Open Access Journals (Sweden)
T Bunsri
2008-01-01
Full Text Available The dispersion phenomenon has resulted from the various water flow magnitude and direction in porous media. The dissolved tracer tends to spread due to dispersion and then travel time of tracer through the porous media increases. In unsaturated porous media, dispersion coefficient varies with non-linear Darcy’s velocity and the water content. These effects observed in both of the laboratory scale sand and soil columns (20 cm. The unsaturated infiltration column and tracer tests have been used to interpret the relationships between Darcy’s velocity and the water content together with the dispersion coefficient. However, the dispersivity coefficient cannot be measured directly, it has to determine from advection-dispersion equation (ADE, which can be used to model the tracer transport in unsaturated porous media. The model was used to describe the non-linear functions of water contents and dispersivities for both porous media. The simulations have been verified that the dispersion of tracer through soil is higher than sand column and also travel time of tracer through soil is longer than sand column. Even though, soil has very low degree of pore velocity, the high dispersivity is observed in the simulations. The water content and tracer concentration profiles reveal that the increase of dispersivity induces the increase of flow path distance and the decrease of pore velocity. The maximum dispersivity was observed when the water content of porous media is relatively low; this leads the maximum of spreading of tracer.
Transport of subsurface bacteria in porous media
Energy Technology Data Exchange (ETDEWEB)
Bales, R.C.; Arnold, R.G.; Gerba, C.P.
1995-02-01
The primary objective of this study was to develop tools with which to measure the advective transport of microorganisms through porous media. These tools were then applied to investigate the sorptive properties of representative microorganisms that were selected at random from the DOE`s deep subsurface collection of bacterial, maintained at Florida State University. The transport screening procedure that arose from this study was also used to investigate biological factors that affect the transport/sorption of biocolloids during their movement through porous media with the bulk advective flow.
Scaling effect of breakthroughcharacter in porous media
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Breakthrough phenomenon during fluids percolating through wet saturated porous layer is widely met in the study of heat and mass transfer in porous media. Breakthrough pressure (BP) is a characteristic pressure that indicates the intrinsic properties of seepage within porous media. Measuring results of BP for saturated narrow-sieved sand are reported here. The curve of BP varying with the height of porous layer was obtained. Experiment and analysis indicate that BP is independent of the height of particle packed layer if thick enough; however, when the height is less than a certain critical value, BP dimims hes with the decrease of the height according to a universal scaling law.
Convective mixing in homogeneous porous media flow
Ching, Jia-Hau; Chen, Peilong; Tsai, Peichun Amy
2017-01-01
Inspired by the flow processes in the technology of carbon dioxide (CO2) storage in saline formations, we modeled a homogeneous porous media flow in a Hele-Shaw cell to investigate density-driven convection due to dissolution. We used an analogy of the fluid system to mimic the diffusion and subsequent convection when CO2 dissolves in brine, which generates a heavier solution. By varying the permeability, we examined the onset of convection, the falling dynamics, the wavelengths of fingers, and the rate of dissolution, for the Rayleigh number Ra (a dimensionless forcing term which is the ratio of buoyancy to diffusivity) in the range of 2.0 ×104≤Ra≤8.26 ×105 . Our results reveal that the effect of permeability influences significantly the initial convective speed, as well as the later coarsening dynamics of the heavier fingering plumes. However, the total dissolved mass, characterized by a nondimensional Nusselt number Nu, has an insignificant dependence on Ra. This implies that the total dissolution rate of CO2 is nearly constant in high Ra geological porous structures.
Chen, Jiliang; Jiang, Fangming
2016-02-01
With a previously developed numerical model, we perform a detailed study of the heat extraction process in enhanced or engineered geothermal system (EGS). This model takes the EGS subsurface heat reservoir as an equivalent porous medium while it considers local thermal non-equilibrium between the rock matrix and the fluid flowing in the fractured rock mass. The application of local thermal non-equilibrium model highlights the temperature-difference heat exchange process occurring in EGS reservoirs, enabling a better understanding of the involved heat extraction process. The simulation results unravel the mechanism of preferential flow or short-circuit flow forming in homogeneously fractured reservoirs of different permeability values. EGS performance, e.g. production temperature and lifetime, is found to be tightly related to the flow pattern in the reservoir. Thermal compensation from rocks surrounding the reservoir contributes little heat to the heat transmission fluid if the operation time of an EGS is shorter than 15 years. We find as well the local thermal equilibrium model generally overestimates EGS performance and for an EGS with better heat exchange conditions in the heat reservoir, the heat extraction process acts more like the local thermal equilibrium process.
Evolution and non-equilibrium physics
DEFF Research Database (Denmark)
Becker, Nikolaj; Sibani, Paolo
2014-01-01
We argue that the stochastic dynamics of interacting agents which replicate, mutate and die constitutes a non-equilibrium physical process akin to aging in complex materials. Specifically, our study uses extensive computer simulations of the Tangled Nature Model (TNM) of biological evolution...
Moortgat, Joachim
2013-01-01
Numerical simulation of multiphase compositional flow in fractured porous media, when all the species can transfer between the phases, is a real challenge. Despite the broad applications in hydrocarbon reservoir engineering and hydrology, a compositional numerical simulator for three-phase flow in fractured media has not appeared in the literature, to the best of our knowledge. In this work, we present a three-phase fully compositional simulator for fractured media, based on higher-order finite element methods. To achieve computational efficiency, we invoke the cross-flow equilibrium (CFE) concept between discrete fractures and a small neighborhood in the matrix blocks. We adopt the mixed hybrid finite element (MHFE) method to approximate convective Darcy fluxes and the pressure equation. This approach is the most natural choice for flow in fractured media. The mass balance equations are discretized by the discontinuous Galerkin (DG) method, which is perhaps the most efficient approach to capture physical dis...
Energy Technology Data Exchange (ETDEWEB)
Pinson, F
2006-03-15
- This work deals with the macroscopic modeling of turbulence in porous media. It concerns heat exchangers, nuclear reactors as well as urban flows, etc. The objective of this study is to describe in an homogenized way, by the mean of a spatial average operator, turbulent flows in a solid matrix. In addition to this first operator, the use of a statistical average operator permits to handle the pseudo-aleatory character of turbulence. The successive application of both operators allows us to derive the balance equations of the kind of flows under study. Two major issues are then highlighted, the modeling of dispersion induced by the solid matrix and the turbulence modeling at a macroscopic scale (Reynolds tensor and turbulent dispersion). To this aim, we lean on the local modeling of turbulence and more precisely on the k - {epsilon} RANS models. The methodology of dispersion study, derived thanks to the volume averaging theory, is extended to turbulent flows. Its application includes the simulation, at a microscopic scale, of turbulent flows within a representative elementary volume of the porous media. Applied to channel flows, this analysis shows that even within the turbulent regime, dispersion remains one of the dominating phenomena within the macro-scale modeling framework. A two-scale analysis of the flow allows us to understand the dominating role of the drag force in the kinetic energy transfers between scales. Transfers between the mean part and the turbulent part of the flow are formally derived. This description significantly improves our understanding of the issue of macroscopic modeling of turbulence and leads us to define the sub-filter production and the wake dissipation. A
Energy Technology Data Exchange (ETDEWEB)
Chandesris, M
2006-12-15
This work deals with the numerical simulation of turbulent flows in the whole nuclear reactor core, using multi-scale approaches. First, a macroscopic turbulence model is built, based on a porous media approach, to describe the flow in the fuel assemblies part of the nuclear core. Then, we study the jump conditions that have to be applied at a free fluid/porous interface. A thorough analytical study is carried out for laminar flows. This study allows to answer some fundamental questions about the physical meaning of the jump conditions, the values of the jump parameters and the location of the interface. Using these results, jump conditions for turbulent flows are proposed. The model is then applied to the simulation of a turbulent flow in a simplified model of a reactor core. (author)
Transport of Graphene Oxide through Porous Media
Duster, T. A.; Na, C.; Bolster, D.; Fein, J. B.
2012-12-01
Graphene oxide (GO) is comprised of anisotropic nanosheets decorated with covalently-bonded epoxide, ketone, and hydroxyl functional groups on the basal planes, and carboxylic and phenolic functional groups at the edges. Individual GO nanosheets are generally two to three micrometers in width, with thicknesses depending on the degree of exfoliation and typically ranging from one to approximately 100 nanometers. As a result of this extraordinarily large surface area-to-mass ratio and the presence of numerous proton-active functional groups, GO nanosheets exhibit a tremendous capacity to adsorb metals and other contaminants from aqueous solutions and are thus often suggested for use in in situ remediation efforts. The potential importance of GO nanosheets as an adsorbent in soil and groundwater necessitates a detailed understanding of their mobility in environmental systems, but this topic remains largely unexplored. Hence, the objective of this study was to investigate the transport behavior of GO nanosheets through well-characterized saturated porous media. In this study, we used replicate glass columns packed with two different sand grain sizes, and within each treatment we varied pH (5.5 to 8.5), ionic strength (electrolyte composition (Na+ and Ca2+ salts), and GO nanosheet exfoliation extent (few-layered and many-layered) to determine the relative influence of both physical and electrochemical properties on GO nanosheet transport in these systems. The break-through of GO nanosheets from each treatment was continuously monitored using a flow-through quartz cuvette and UV-Vis absorbance at 230 nm. GO nanosheet transport through these systems was then modeled using distinct advection-dispersion equations to establish the relative influence of attachment, deposition, and detachment in the overall transport behavior, and a corresponding retardation coefficient was calculated for each treatment. Break-through curves displayed anomalous transport behavior, which was
Institute of Scientific and Technical Information of China (English)
姜利国; 梁冰
2011-01-01
Geochemical process is one of the fftost important factors influenced fluid movement, solute transport and heat transfer in porous media such as rock and soil. Based on the unsaturated soil theory established by Fredlund, in which the unsaturated soil porous media has been considered as a media which has four phases, assumed the effect of precipitation/dissolution to be an individual phase. With some hypotheses, the porosity and water content of porous media are modified by solute concentration, a new coupled relation between solute transport and hydraulic parameters has been built. The new relation updates the traditional coupled model in which the impact from solute field acts On seepage flow field by only density and viscosity. Here, a coupled model of multi-phases and multi components hydraulic-transport-thermal and geochemical processes in variable saturated porous media is established. Using a infiltrate experiment for reactive coal mine gangue in the laboratory, the coupled numerical model is tested. The results show that the water seepage velocity calculated from experiment matches well the outcome from numerical model which considered the precipitation/dissolution coupling variable. Thus the applicability of the numerical model is verified.%地球化学作用是影响岩土类多孔介质中流体流动、传质、传热的重要因素之一.基于Fredlund所提出的非饱和土四相理论,将地球化学作用所产生的溶解/沉淀视为一个独立相,在一定的假设基础上,利用溶质浓度对介质孔隙度、含水率进行修正,从而建立起传质过程与介质水力性质之间的关系,改进了传统模型中传质过程与流体密度、黏度之间单一的耦合关系；并以此为基础建立了考虑地球化学作用下饱和-非饱和介质中多组分、多相流体渗流场-浓度场-温度场耦合的数学模型.通过在实验室内对反应性煤矸石进行渗透实验的结果对笔者所建模型进行了验证,
Institute of Scientific and Technical Information of China (English)
王小锋; 朱维耀; 邓庆军; 刘启鹏; 隋新光; 娄钰; 高英; 张雪龄
2014-01-01
According to the mass conservation law, a dynamic network model which considers interaction between solid walls and liquid molecules was established. This model is on the basis of solid-liquid intermolecular force and in combination with the distribution characteristics of pore throats in porous media. The change in pore pressure at different time steps was simulated through the model. The influences of solid-liquid intermolecular force, pore throat radius and wettability on the saturation distribution of remaining oil and the permeability curve of water flooding phase were analyzed. The results show that when considering solid-liquid intermolecular force the saturation of residual oil increases, thus interaction between rock and fluid molecules cannot be ignored in the study of porous flow in porous media.%根据质量守恒定律，从固液分子力作用出发，结合岩心的孔喉分布特征，建立考虑固壁与流体分子作用的动态网络模型。利用模型模拟得到不同时间步的孔隙压力变化，分析了固液分子间力、喉道半径、润湿性等因素对剩余油饱和度分布和水驱相渗曲线的影响。研究结果表明，考虑固液分子间力作用时剩余油饱和度增大，岩石骨架与流体间的分子作用在多孔介质的孔隙流动中不可忽略。
Du, Liming; Xie, Maozhao
2011-06-01
A numerical study of Reciprocating Superadiabatic Combustion of Premixed gases in porous media (hereafter, referred to as RSCP) is performed. In this system the transient combustion of methane-air mixture is stabilized in a porous media combustor by periodically switching flow directions. The mass, momentum, energy and species conservation equations are solved using a two-dimensional control volume method. Local thermal non-equilibrium between the gas and the solid phases is considered by solving separate energy equations for the two phases and coupling them through a convective heat transfer coefficient. The porous media is assumed to emit, absorb and isotropically scatter radiation. The influences of the dominating operating parameters, such as filtration velocity, equivalence ratio and half cycle on the temperature profile, heat release rate, radiant flux, radiant efficiency and combustion efficiency are discussed. The results show that coupling calculating of flow field, combustion reaction and volume radiation of the optically thick media is successively achieved and heat radiation plays an important role in the overall performance of the burner. The temperature profile inside the RSCP combustor has a typical trapezoidal shape and the profile of radiation flux is similar to sinusoidal shape. Compared with the conventional premixed combustion in porous medium, combustion behavior in RSCP combustor is superior, such as better thermal structure and higher radiation efficiency and combustion efficiency.
Numerical Simulation on Fiber Ball Filter for Porous Media Model%多孔介质模型的纤维球过滤器数值模拟
Institute of Scientific and Technical Information of China (English)
赵军; 朱庆强; 范德顺
2012-01-01
In order to get the relationship among sludge retention, filtration rate and pressure drop in filtration and that among release of sludge retention, backwash rate and pressure drop in backwash process, a numerical simulation was established for the liquid flow field of different sludge retention within fiber ball filter by use of porous media mode. The results show that, in filtration process, the pressure drop rises linearly in the trend with the rise of sludge retention, and it closes to exponential increase with the rise of filtering rate.%用多孔介质模型对纤维球过滤器内不同截泥量下的液相流场进行数值模拟,得到在过滤过程中截泥量-过滤速度-压降之间的关系,在反洗过程中截泥释放量-反洗速度-压降之间的关系.结果表明:在过滤过程中压降随着截泥量的增加呈现近似线性增加,压降随着过滤速度的增加呈现近似指数增加的趋势.
Flow of particle suspensions through porous media
Energy Technology Data Exchange (ETDEWEB)
Vetter, O.J.; Kandarpa, V.; Harouaka, A.
1982-06-22
A new attempt is made to study the mechanisms of particle invasions into porous media. The following subjects are described: A critical survey of the literature indicating that the mechanism of particle invasions is not known in sufficient detail. The pros and cons of existing particle measuring devices are briefly described. Results from a new laboratory study on particle characterizations are given. The results of the laboratory studies on the flow of particle suspensions through porous media (up to 200 md) are discussed. The effects of flow rate and particle concentrations on the amount of damage (i.e., permeability impairment) and depth of penetration (from core inlet towards outlet) are particularly emphasized. Filter methods (e.g., using millipore filter) cannot be used to determine particle invasions into porous medium. Any predictions of the injection problems based on millipore (or any other filter) measurements are useless and should be discarded.
Lattice gas methods for predicting intrinsic permeability of porous media
Energy Technology Data Exchange (ETDEWEB)
Santos, L.O.E.; Philippi, P.C. [Santa Catarina Univ., Florianopolis, SC (Brazil). Dept. de Engenharia Mecanica. Lab. de Propriedades Termofisicas e Meios Porosos)]. E-mail: emerich@lmpt.ufsc.br; philippi@lmpt.ufsc.br; Damiani, M.C. [Engineering Simulation and Scientific Software (ESSS), Florianopolis, SC (Brazil). Parque Tecnologico]. E-mail: damiani@lmpt.ufsc.br
2000-07-01
This paper presents a method for predicting intrinsic permeability of porous media based on Lattice Gas Cellular Automata methods. Two methods are presented. The first is based on a Boolean model (LGA). The second is Boltzmann method (LB) based on Boltzmann relaxation equation. LGA is a relatively recent method developed to perform hydrodynamic calculations. The method, in its simplest form, consists of a regular lattice populated with particles that hop from site to site in discrete time steps in a process, called propagation. After propagation, the particles in each site interact with each other in a process called collision, in which the number of particles and momentum are conserved. An exclusion principle is imposed in order to achieve better computational efficiency. In despite of its simplicity, this model evolves in agreement with Navier-Stokes equation for low Mach numbers. LB methods were recently developed for the numerical integration of the Navier-Stokes equation based on discrete Boltzmann transport equation. Derived from LGA, LB is a powerful alternative to the standard methods in computational fluid dynamics. In recent years, it has received much attention and has been used in several applications like simulations of flows through porous media, turbulent flows and multiphase flows. It is important to emphasize some aspects that make Lattice Gas Cellular Automata methods very attractive for simulating flows through porous media. In fact, boundary conditions in flows through complex geometry structures are very easy to describe in simulations using these methods. In LGA methods simulations are performed with integers needing less resident memory capability and boolean arithmetic reduces running time. The two methods are used to simulate flows through several Brazilian reservoir petroleum rocks leading to intrinsic permeability prediction. Simulation is compared with experimental results. (author)
Time-fractional particle deposition in porous media
Xu, Jianping
2017-05-01
In the percolation process where fluids carry small solid particles, particle deposition causes a real-time permeability change of the medium as the swarm of particles propagates along the medium. Then the permeability change influences percolation and deposition behaviors as a feedback. This fact triggers memory effect in the deposition dynamics, which means the particulate transport and deposition behaviors become history-dependent. In this paper, we conduct the time-fractional generalization of the classical phenomenological model of particle deposition in porous media to incorporate the memory effect. We tested and compared the effects of employing different types of fractional operators, i.e. the Riemann-Liouville type, the Hadamard type and the Prabhakar type. Numerical simulation results show that the system behaviors vary according to the change of distinct memory kernels in an expected way. We then discuss the physical meaning of the time-fractional generalization. It is shown that different types of fractional operators unanimously ground themselves on the local-Newtonian time transformation in a complex system, which is equivalent to a class of history integrals. By the introduction of various memory kernels, it enables the model to more powerfully fit and approximate observed data. Further, the fundamental meaning of this work is not to show which fractional operator is ‘better’, but to argue collectively the legitimacy and practicality of a non-Markovian particle deposition dynamics in porous media, and in fact it is admissible to a bunch of memory kernels which differ greatly from each other in functional forms. Hopefully the presented generalized mass conservation formalism offers a broader framework to investigate transport problems in porous media.
Power exponential velocity distributions in disordered porous media
Matyka, Maciej; Koza, Zbigniew
2016-01-01
Velocity distribution functions link the micro- and macro-level theories of fluid flow through porous media. Here we study them for the fluid absolute velocity and its longitudinal and lateral components relative to the macroscopic flow direction in a model of a random porous medium. We claim that all distributions follow the power exponential law controlled by an exponent $\\gamma$ and a shift parameter $u_0$ and examine how these parameters depend on the porosity. We find that $\\gamma$ has a universal value $1/2$ at the percolation threshold and grows with the porosity, but never exceeds 2.
Bacteria transport through porous media. Annual report, December 31, 1984
Energy Technology Data Exchange (ETDEWEB)
Yen, T.F.
1986-09-01
The following five chapters in this report have been processed separately for inclusion in the Energy Data Base: (1) theoretical model of convective diffusion of motile and non-motile bacteria toward solid surfaces; (2) interfacial electrochemistry of oxide surfaces in oil-bearing sands and sandstones; (3) effects of sodium pyrophosphate additive on the ''huff and puff''/nutrient flooding MEOR process; (4) interaction of Escherichia coli B, B/4, and bacteriophage T4D with Berea sandstone rock in relation to enhanced oil recovery; and (5) transport of bacteria in porous media and its significance in microbial enhanced oil recovery.
Heat Explosion In Porous Media Using Radial Basis Functions
Directory of Open Access Journals (Sweden)
Allali Karam
2016-01-01
Full Text Available The paper is devoted to the numerical investigation of the interaction between natural convection and heat explosion in a fluid-saturated porous media in a rectangular domain. The model consists of Darcy equations for an incompressible fluid in a porous medium coupled with the nonlinear heat equation. Numerical simulations are performed using the radial basis functions method (RBFs. We study the bifurcation of the periodic oscillation of the response born by Hopf bifurcation. First, a symmetry-breaking bifurcations observed; then is followed by successive period-doubling bifurcations leading to chaos.
Energy Technology Data Exchange (ETDEWEB)
Cushman, J.H.; Madilyn Fletcher
2000-06-01
Dynamic microbial attachment/detachment occurs in subsurface systems in response to changing environmental conditions caused by contaminant movement and degradation. Understanding the environmental conditions and mechanisms by which anaerobic bacteria partition between aqueous and solid phases is a critical requirement for designing and evaluating in situ bioremediation efforts. This interdisciplinary research project, of which we report only the Purdue contribution, provides fundamental information on the attachment/detachment dynamics of bacteria in heterogeneous porous media. Fundamental results from the Purdue collaboration are: (a) development of a matched-index method for obtaining 3-D Lagrangian trajectories of microbial sized particles transporting within porous media or microflow cells, (b) application of advanced numerical methods to optimally design a microflow cell for studying anaerobic bacterial attachment/detachment phenomena, (c) development of two types of models for simulating bacterial movement and attachment/detachment in microflow cells and natural porous media, (d) application of stochastic analysis to upscale pore scale microbial attachment/detachment models to natural heterogeneous porous media, and (e) evaluation of the role nonlocality plays in microbial dynamics in heterogeneous porous media
Energy Technology Data Exchange (ETDEWEB)
Cushman, J.H.
2000-06-01
Dynamic microbial attachment/detachment occurs in subsurface systems in response to changing environmental conditions caused by contaminant movement and degradation. Understanding the environmental conditions and mechanisms by which anaerobic bacteria partition between aqueous and solid phases is a critical requirement for designing and evaluating in situ bioremediation efforts. This interdisciplinary research project, of which we report only the Purdue contribution, provides fundamental information on the attachment/detachment dynamics of bacteria in heterogeneous porous media. Fundamental results from the Purdue collaboration are: (a) development of a matched-index method for obtaining 3-D Lagrangian trajectories of microbial sized particles transporting within porous media or microflow cells, (b) application of advanced numerical methods to optimally design a microflow cell for studying anaerobic bacterial attachment/detachment phenomena, (c) development of two types of models for simulating bacterial movement and attachment/detachment in microflow cells and natural porous media, (d) application of stochastic analysis to upscale pore scale microbial attachment/detachment models to natural heterogeneous porous media, and (e) evaluation of the role nonlocality plays in microbial dynamics in heterogeneous porous media.
Direct numerical simulation of inertial flows in porous media
Apte, S.; Finn, J.; Wood, B. D.
2010-12-01
At modest flow rates (10 ≤ Re ≤ 300) through porous media and packed beds, fluid inertia can result in complex steady and unsteady recirculation regions, dependent on the local pore geometry. Body fitted CFD is a broadly used design and analysis tool for flows in porous media and packed bed type reactors. Unfortunately, the inherent complexities of porous media make unstructured mesh generation a difficult and time consuming step in the simulation process. To accurately capture the inertial dynamics using high-fidelity direct simulations, body fitted meshes must be high quality and sufficiently refined. We present methods to parameterize and simplify mesh generation for packed beds, with an eye toward obtaining efficient mesh independence for Reynolds numbers in the inertial and unsteady regimes. The crux of mesh generation for packed beds is dealing with sphere-sphere or sphere-wall contact points, where a geometric singularity exists. To handle the sphere-sphere and sphere-wall contact points, we use a fillet bridge model, in which every pair of contacting entities are bridged by a fillet, eliminating a small fluid region near the contact point. This results in a continuous surface mesh which does not require resizing of the spheres and can accommodate prism cells for improved boundary layer resolution. A second order accurate, parallel, incompressible flow solver [Moin and Apte, AIAA J. 2006] is used to simulate flow through three different sphere packings: a periodic simple cubic packing, a wall bounded hexagonal close packing, and a randomly packed tube. Mesh independence is assessed using several measures including Ergun pressure drop coefficients, viscous and pressure components of drag force, kinetic energy, kinetic energy dissipation and interstitial velocity profiles. The results of these test cases are used to determine the feasibility of accurate and very large scale simulations of flow through a randomly packed bed of 103 pores. Preliminary results
Adaptive mixed finite element methods for Darcy flow in fractured porous media
Chen, Huangxin
2016-09-21
In this paper, we propose adaptive mixed finite element methods for simulating the single-phase Darcy flow in two-dimensional fractured porous media. The reduced model that we use for the simulation is a discrete fracture model coupling Darcy flows in the matrix and the fractures, and the fractures are modeled by one-dimensional entities. The Raviart-Thomas mixed finite element methods are utilized for the solution of the coupled Darcy flows in the matrix and the fractures. In order to improve the efficiency of the simulation, we use adaptive mixed finite element methods based on novel residual-based a posteriori error estimators. In addition, we develop an efficient upscaling algorithm to compute the effective permeability of the fractured porous media. Several interesting examples of Darcy flow in the fractured porous media are presented to demonstrate the robustness of the algorithm.
Adaptive mixed finite element methods for Darcy flow in fractured porous media
Chen, Huangxin; Salama, Amgad; Sun, Shuyu
2016-10-01
In this paper, we propose adaptive mixed finite element methods for simulating the single-phase Darcy flow in two-dimensional fractured porous media. The reduced model that we use for the simulation is a discrete fracture model coupling Darcy flows in the matrix and the fractures, and the fractures are modeled by one-dimensional entities. The Raviart-Thomas mixed finite element methods are utilized for the solution of the coupled Darcy flows in the matrix and the fractures. In order to improve the efficiency of the simulation, we use adaptive mixed finite element methods based on novel residual-based a posteriori error estimators. In addition, we develop an efficient upscaling algorithm to compute the effective permeability of the fractured porous media. Several interesting examples of Darcy flow in the fractured porous media are presented to demonstrate the robustness of the algorithm.
Foam-oil interaction in porous media: implications for foam assisted enhanced oil recovery.
Farajzadeh, R; Andrianov, A; Krastev, R; Hirasaki, G J; Rossen, W R
2012-11-15
The efficiency of a foam displacement process in enhanced oil recovery (EOR) depends largely on the stability of foam films in the presence of oil. Experimental studies have demonstrated the detrimental impact of oil on foam stability. This paper reviews the mechanisms and theories (disjoining pressure, coalescence and drainage, entering and spreading of oil, oil emulsification, pinch-off, etc.) suggested in the literature to explain the impact of oil on foam stability in the bulk and porous media. Moreover, we describe the existing approaches to foam modeling in porous media and the ways these models describe the oil effect on foam propagation in porous media. Further, we present various ideas on an improvement of foam stability and longevity in the presence of oil. The outstanding questions regarding foam-oil interactions and modeling of these interactions are pointed out. Copyright © 2012 Elsevier B.V. All rights reserved.
Measurement of Interfacial Area Production and Permeability within Porous Media
Energy Technology Data Exchange (ETDEWEB)
Crandall, Dustin; Ahmadi, Goodarz; Smith, Duane H.
2010-01-01
An understanding of the pore-level interactions that affect multi-phase flow in porous media is important in many subsurface engineering applications, including enhanced oil recovery, remediation of dense non-aqueous liquid contaminated sites, and geologic CO2 sequestration. Standard models of two-phase flow in porous media have been shown to have several shortcomings, which might partially be overcome using a recently developed model based on thermodynamic principles that includes interfacial area as an additional parameter. A few static experimental studies have been previously performed, which allowed the determination of static parameters of the model, but no information exists concerning the interfacial area dynamic parameters. A new experimental porous flow cell that was constructed using stereolithography for two-phase gas-liquid flow studies was used in conjunction with an in-house analysis code to provide information on dynamic evolution of both fluid phases and gas-liquid interfaces. In this paper, we give a brief introduction to the new generalized model of two-phase flow model and describe how the stereolithography flow cell experimental setup was used to obtain the dynamic parameters for the interfacial area numerical model. In particular, the methods used to determine the interfacial area permeability and production terms are shown.
Directory of Open Access Journals (Sweden)
William T Bean
Full Text Available Species distributions are known to be limited by biotic and abiotic factors at multiple temporal and spatial scales. Species distribution models, however, frequently assume a population at equilibrium in both time and space. Studies of habitat selection have repeatedly shown the difficulty of estimating resource selection if the scale or extent of analysis is incorrect. Here, we present a multi-step approach to estimate the realized and potential distribution of the endangered giant kangaroo rat. First, we estimate the potential distribution by modeling suitability at a range-wide scale using static bioclimatic variables. We then examine annual changes in extent at a population-level. We define "available" habitat based on the total suitable potential distribution at the range-wide scale. Then, within the available habitat, model changes in population extent driven by multiple measures of resource availability. By modeling distributions for a population with robust estimates of population extent through time, and ecologically relevant predictor variables, we improved the predictive ability of SDMs, as well as revealed an unanticipated relationship between population extent and precipitation at multiple scales. At a range-wide scale, the best model indicated the giant kangaroo rat was limited to areas that received little to no precipitation in the summer months. In contrast, the best model for shorter time scales showed a positive relation with resource abundance, driven by precipitation, in the current and previous year. These results suggest that the distribution of the giant kangaroo rat was limited to the wettest parts of the drier areas within the study region. This multi-step approach reinforces the differing relationship species may have with environmental variables at different scales, provides a novel method for defining "available" habitat in habitat selection studies, and suggests a way to create distribution models at spatial and
Gelet, R.; Loret, B.; Khalili, N.
2012-07-01
The constitutive thermo-hydro-mechanical equations of fractured media are embodied in the theory of mixtures applied to three-phase poroelastic media. The solid skeleton contains two distinct cavities filled with the same fluid. Each of the three phases is endowed with its own temperature. The constitutive relations governing the thermomechanical behavior, generalized diffusion and transfer are structured by, and satisfy, the dissipation inequality. The cavities exchange both mass and energy. Mass exchanges are driven by the jump in scaled chemical potential, and energy exchanges by the jump in coldness. The finite element approximation uses the displacement vector, the two fluid pressures and the three temperatures as primary variables. It is used to analyze a generic hot dry rock geothermal reservoir. Three parameters of the model are calibrated from the thermal outputs of Fenton Hill and Rosemanowes HDR reservoirs. The calibrated model is next applied to simulate circulation tests at the Fenton Hill HDR reservoir. The finer thermo-hydro-mechanical response provided by the dual porosity model with respect to a single porosity model is highlighted in a parameter analysis. Emphasis is put on the influence of the fracture spacing, on the effective stress response and on the permeation of the fluid into the porous blocks. The dual porosity model yields a thermally induced effective stress that is less tensile compared with the single porosity response. This effect becomes significant for large fracture spacings. In agreement with field data, fluid loss is observed to be high initially and to decrease with time.
DuVal, Carter B.; Trembanis, Arthur C.; Skarke, Adam
2016-03-01
Ripple bedform response to near bed forcing has been found to be asynchronous with rapidly changing hydrodynamic conditions. Recent models have attempted to account for this time variance through the introduction of a time offset between hydrodynamic forcing and seabed response with varying success. While focusing on temporal ripple evolution, spatial ripple variation has been partly neglected. With the fingerprint algorithm ripple bedform parameterization technique, spatial variation can be quickly and precisely characterized, and as such, this method is particularly useful for evaluation of ripple model spatio-temporal validity. Using time-series hydrodynamic data and synoptic acoustic imagery collected at an inner continental shelf site, this study compares an adapted time-varying ripple geometric model to observed field observations in light of the fingerprint algorithm results. Multiple equilibrium ripple predictors are tested within the time-varying model, with the algorithm results serving as the baseline geometric values. Results indicate that ripple bedforms, in the presence of rapidly changing high-energy conditions, reorganize at a slower rate than predicted by the models. Relict ripples were found to be near peak-forcing wavelengths after rapidly decaying storm events, and still present after months of sub-critical flow conditions.
Institute of Scientific and Technical Information of China (English)
Farzam Safarzadeh MALEKI; Abdul A KHAN
2016-01-01
A high-resolution, 1-D numerical model has been developed in the discontinuous Galerkin framework to simulate 1-D flow behavior, sediment transport, and morphological evaluation under unsteady flow conditions. The flow and sediment concentration variables are computed based on the one-dimensional shallow water flow equations, while empirical equations are used for entrainment and deposition processes. The sediment transport model includes the bed load and suspended load components. New formulations for Harten-Lax-van Leer (HLL) and Harten-Lax-van Contact (HLLC) are presented for shallow water flow equations that include the bed load and suspended load fluxes. The computational results for the flow and morphological changes after two dam break events are compared with the physical model tests. Results show that the modified HLL and HLLC formulations are robust and can accurately predict morphological changes in highly unsteady flows.
A micropolar mixture theory of multi-component porous media
Institute of Scientific and Technical Information of China (English)
Lu HUANG; Cheng-gang ZHAO
2009-01-01
A mixture theory is developed for multi-component micropolar porous media with a combination of the hybrid mixture theory and the micropolar continuum theory.The system is modeled as multi-component micropolar elastic solids saturated with multicomponent micropolar viscous fluids. Balance equations are given through the mixture theory. Constitutive equations are developed based on the second law of thermodynamics and constitutive assumptions. Taking account of compressibility of solid phases,the volume fraction of fluid as an independent state variable is introduced in the free energy function,and the dynamic compatibility condition is obtained to restrict the change of pressure difference on the solid-fluid interface. The constructed constitutive equations are used to close the field equations. The linear field equations are obtained using a linearization procedure,and the micropolar thermo-hydro-mechanical component transport model is established. This model can be applied to practical problems,such as contaminant,drug,and pesticide transport. When the proposed model is supposed to be porous media,and both fluid and solid are single-component,it will almost agree with Eringen's model.
Ho, Clifford K
2006-01-01
This book presents a compilation of state-of-the art studies on gas and vapor transport processes in porous and fractured media. A broad set of models and processes are presented, including advection/diffusion, the Dusty Gas Model, enhanced vapor diffusion, phase change, coupled processes, solid/vapor sorption, and vapor-pressure lowering. Numerous applications are also presented that illustrate these processes and models in current problems facing the scientific community. This book fills a gap in the general area of transport in porous and fractured media; an area that has historically been dominated by studies of liquid-phase flow and transport. This book identifies gas and vapor transport processes that may be important or dominant in various applications, and it exploits recent advances in computational modeling and experimental methods to present studies that distinguish the relative importance of various mechanisms of transport in complex media.
Impact of pore size variability and network coupling on electrokinetic transport in porous media
Alizadeh, Shima; Bazant, Martin Z.; Mani, Ali
2016-11-01
We have developed and validated an efficient and robust computational model to study the coupled fluid and ion transport through electrokinetic porous media, which are exposed to external gradients of pressure, electric potential, and concentration. In our approach a porous media is modeled as a network of many pores through which the transport is described by the coupled Poisson-Nernst-Planck-Stokes equations. When the pore sizes are random, the interactions between various modes of transport may provoke complexities such as concentration polarization shocks and internal flow circulations. These phenomena impact mixing and transport in various systems including deionization and filtration systems, supercapacitors, and lab-on-a-chip devices. In this work, we present simulations of massive networks of pores and we demonstrate the impact of pore size variation, and pore-pore coupling on the overall electrokinetic transport in porous media.
ONSET CONDITION OF STRAIN LOCALIZATION IN MATRIX OF SATURATED POROUS MEDIA
Institute of Scientific and Technical Information of China (English)
ZHAO Ji-sheng; TAO Xia-xin; SHI Li-jing; OU Jin-ping
2005-01-01
Based on governing equations of saturated porous media and Liapunov's stability here, onset conditions matrix of porous media used by solid stress and Terzaghi's effective stress constitutive description under seepage flow state, are presented, which have different forms with different representation of the solid phase, matrix or skeleton, constitutive model of porous media. The main difference relates with how to describe the interaction between solid phase and liquid phase in constitutive model. The derived onset condition of strain localization under Terzaghi's effective stress description can be used to interpret different failure types, piping effect, landslides and mudflows, by means of the type and the magnitude ratio of relative movement between solid phase and liquid phase. Examples here illuminate the onset condition of how to work.
Monte Carlo simulation of a two-phase flow in an unsaturated porous media
Directory of Open Access Journals (Sweden)
Xu Peng
2012-01-01
Full Text Available Relative permeability is a significant transport property which describes the simultaneous flow of immiscible fluids in porous media. A pore-scale physical model is developed for the two-phase immiscible flow in an unsaturated porous media according to the statistically fractal scaling laws of natural porous media, and a predictive calculation of two-phase relative permeability is presented by Monte Carlo simulation. The tortuosity is introduced to characterize the highly irregular and convoluted property of capillary pathways for fluid flow through a porous medium. The computed relative permeabilities are compared with empirical formulas and experimental measurements to validate the current model. The effect of fractal dimensions and saturation on the relative permeabilities is also discussed
Pusateri, Elise Noel
An Electromagnetic Pulse (EMP) can severely disrupt the use of electronic devices in its path causing a significant amount of infrastructural damage. EMP can also cause breakdown of the surrounding atmosphere during lightning discharges. This makes modeling EMP phenomenon an important research effort in many military and atmospheric physics applications. EMP events include high-energy Compton electrons or photoelectrons that ionize air and produce low energy conduction electrons. A sufficient number of conduction electrons will damp or alter the EMP through conduction current. Therefore, it is important to understand how conduction electrons interact with air in order to accurately predict the EMP evolution and propagation in the air. It is common for EMP simulation codes to use an equilibrium ohmic model for computing the conduction current. Equilibrium ohmic models assume the conduction electrons are always in equilibrium with the local instantaneous electric field, i.e. for a specific EMP electric field, the conduction electrons instantaneously reach steady state without a transient process. An equilibrium model will work well if the electrons have time to reach their equilibrium distribution with respect to the rise time or duration of the EMP. If the time to reach equilibrium is comparable or longer than the rise time or duration of the EMP then the equilibrium model would not accurately predict the conduction current necessary for the EMP simulation. This is because transport coefficients used in the conduction current calculation will be found based on equilibrium reactions rates which may differ significantly from their non-equilibrium values. We see this deficiency in Los Alamos National Laboratory's EMP code, CHAP-LA (Compton High Altitude Pulse-Los Alamos), when modeling certain EMP scenarios at high altitudes, such as upward EMP, where the ionization rate by secondary electrons is over predicted by the equilibrium model, causing the EMP to short
Qazi, Sanjive; Beltukov, Aleksei; Trimmer, Barry A
2004-01-01
The first event in signal transduction at a synapse is the binding of transmitters to receptors. Because of rapidly changing transmitter levels this binding is unlikely to occur at equilibrium. We describe a mathematical approach that models complex receptor interactions in which the timing and amplitude of transmitter release are noisy. We show that exact solutions for simple bimolecular interactions and receptor transitions can be used to model complex reaction schemes by expressing them in sets of difference equations. Results from the difference equation method to describe binding and channel opening at extended time points compare well with standard solutions using ordinary differential equations. Because it is applicable to noisy systems we used the difference method to investigate the information processing capabilities of GABA receptors and predict how pharmacological agents may modify these properties. As previously demonstrated, the response to a single pulse of GABA is prolonged through entry into a desensitized state. During trains of stimuli the signal to noise ratio can change, and even increase progressively, but the overall transmitted fidelity of the signal decreases with increased driving frequency. The GABA modulator chlorpromazine (primarily affects agonist on and off rates) is predicated to increase receptor signal to noise ratio at all frequencies whereas pregnenolone sulfate (affects receptor desensitization) completely inhibits information transfer.
Mass Transfer and Porous Media (MTPM)
Energy Technology Data Exchange (ETDEWEB)
Rotenberg, B.; Marry, V.; Malikova, N.; Vuilleumier, R.; Giffaut, E.; Turq, P.; Robinet, J.C.; Diaz, N.; Sardini, P.; Goutelard, F.; Menut, D.; Parneix, J.C.; Sammartino, S.; Pret, D.; Coelho, D.; Jougnot, D.; Revil, A.; Boulin, P.F.; Angulo-Jaramillo, R.; Daian, J.F.; Talandier, J.; Berne, P.; Cochepin, B.; Trotignon, L.; Bildstein, O.; Steefel, C.; Lagneau, V.; Van der Lee, J.; Birchall, D.J.; Harrington, J.F.; Noy, D.J.; Sellin, P.; Bildstein, O.; Piault, E.; Trotignon, L.; Montarnal, P.; Deville, E.; Genty, A.; Le Potier, C.; Imbert, C.; Semete, P.; Desgree, P.; Fevrier, B.; Courtois, A.; Touze, G.; Sboui, A.; Roberts, J.E.; Jaffre, J.; Glaus, M.A.; Rosse, R.; Van Loon, L.R.; Matray, J.M.; Parneix, J.C.; Tinseau, E.; Pret, D.; Mayor, J.C.; Ohkubo, T.; Kikuchi, H.; Yamaguchi, M.; Alonso, U.; Missana, T.; Garcia-Gutierrez, M.; Patelli, A.; Siitari-Kauppi, M.; Leskinen, A.; Rigato, V.; Samper, J.; Dewonck, S.; Zheng, L.; Yang, Q.; Naves, A.; Dai, Z.; Samper, J.; Wolfsberg, A.; Levitt, D.; Cormenzana, J.L.; Missana, T.; Mingarro, M.; Schampera, B.; Dultz, S.; Riebe, B.; Samper, J.; Yang, Q.; Genty, A.; Perraud, D.; Poller, A.; Mayer, G.; Croise, J.; Marschall, P.; Krooss, B.; Matray, J.M.; Tanaka, T.; Vogel, P.; Lavanchy, J.M.; Enssle, C.P.; Cruchaudet, M.; Dewonck, S.; Descostes, M.; Blin, V.; Radwan, J.; Poinssot, C.; Mibus, J.; Sachs, S.; Devol-Brown, I.; Motellier, S.; Tinseau, E.; Thoby, D.; Marsal, F.; DeWindt, L.; Tinseau, E.; Pellegrini, D.; Bauer, A.; Fiehn, B.; Marquardt, Ch.; Romer, J.; Gortzen, A.; Kienzler, B
2007-07-01
This session gathers 48 articles (posters) dealing with: interlayer / micro-pore exchange of water and ions in clays: a molecular dynamics study; the multi-scale characterisation of mineral and textural spatial heterogeneities in Callovo-Oxfordian argilite and its consequence on solute species diffusion modelling; the diffusion of ions in unsaturated clay rocks: Theory and application to the Callovo- Oxfordian argillite; the porous media characterization with respect to gas transfer in Callovo Oxfordian argillite; the predictions on a 2-D cementation experiment in porous medium: intercomparison on the Comedie project; the large-scale gas injection test (LASGIT) at the Aespoe hard rock laboratory in Sweden; simulating the geochemical coupling between vitrified waste, canister and near-field on the alliances platform; toward radionuclide transport calculations on whole radioactive waste disposal with CAST3M platform; the experimental study of the water permeability of a partially saturated argillite; a mixed hexahedral finite elements for Darcy flow calculation in clay porous media; the diffusive properties of stainless steel filter discs before and after use in diffusion experiments with compacted clays; the structural organization of porosity in the Opalinus clay at the Mont Terri Rock Laboratory under saturated and unsaturated conditions; the evaluation of pore structure in compacted saturated Bentonite using NMR relaxometry; diffusion coefficients measurement in consolidated clays: a combination of micro-scale profiling and solid pore structure analyses; the numerical interpretation of in-situ DIR diffusion experiments on the Callovo- Oxfordian clay at the Meuse/Haute-Marne URL the identification of relative conductivity models for water flow and solute transport in unsaturated compacted Bentonite; diffusion experiments in Callovo- Oxfordian clay from the Meuse/Haute-Marne URL, France: experimental setup and data analyses; the transport in organo
Nonlinear Taylor dispersion in gravity currents in porous media
Szulczewski, Michael; Juanes, Ruben
2012-11-01
Taylor dispersion describes how a non-uniform flow can accelerate diffusive mixing between fluids by elongating the fluid-fluid interface over which diffusion acts. While Taylor dispersion has been extensively studied in simple systems such as Poiseuille and Couette flows, it is poorly understood in more complex systems such as porous-media flows. Here, we study Taylor dispersion in porous media during a gravity-driven flow using theory and simulations. We consider a simple geometry for physical insight: a horizontal, confined layer of permeable rock in which two fluids of different densities are initially separated by a vertical interface. We show that the flow exhibits a non-uniform velocity field that leads to Taylor dispersion at the aquifer scale. Unlike the classical model of Taylor dispersion, however, the diffusive mixing is coupled to the flow velocity because it reduces the lateral density gradient that drives the flow. This coupling causes the flow to continually decelerate and eventually stop completely. To model the flow, we develop a non-linear diffusion equation for the concentration of the more dense fluid, which admits an analytical similarity solution. We discuss applications of the model to CO2 sequestration.
Multiphase Flow in Porous Media
Kamyabi, Farad
2014-01-01
In the hydrocarbon reservoirs that are normally saturated with two or more fluids, in order for better description of the flowing fluids behaviors and rockfluid interaction, the concept of relative permeability and capillary pressure should be exploited. Brilliant by Petrell AS is an object-oriented (C++) multi-physics Computational Fluid Dynamics (CFD) package developed for simulation of flow. In the continuous process of improving the system, the aim of this work is to model the multi...
Mirjani, Fatemeh; Thijssen, Joseph M; Whitesides, George M; Ratner, Mark A
2014-12-23
This paper examines charge transport by tunneling across a series of electrically insulating molecules with the structure HS(CH2)4CONH(CH2)2R) in the form of self-assembled monolayers (SAMs), supported on silver. The molecules examined were studied experimentally by Yoon et al. (Angew. Chem. Int. Ed. 2012, 51, 4658-4661), using junctions of the structure AgS(CH2)4CONH(CH2)2R//Ga2O3/EGaIn. The tail group R had approximately the same length for all molecules, but a range of different structures. Changing the R entity over the range of different structures (aliphatic to aromatic) does not influence the conductance significantly. To rationalize this surprising result, we investigate transport through these SAMs theoretically, using both full quantum methods and a generic, independent-electron tight-binding toy model. We find that the highest occupied molecular orbital, which is largely responsible for the transport in these molecules, is always strongly localized on the thiol group. The relative insensitivity of the current density to the structure of the R group is due to a combination of the couplings between the carbon chains and the transmission inside the tail. Changing from saturated to conjugated tail groups increases the latter but decreases the former. This work indicates that significant control over SAMs largely composed of nominally insulating groups may be possible when tail groups are used that are significantly larger than those used in the experiments of Yoon et al.1.
Pepona, Marianna; Favier, Julien
2016-09-01
In this work, we propose a numerical framework to simulate fluid flows in interaction with moving porous media of complex geometry. It is based on the Lattice Boltzmann method including porous effects via a Brinkman-Forchheimer-Darcy force model coupled to the Immersed Boundary method to handle complex geometries and moving structures. The coupling algorithm is described in detail and it is validated on well-established literature test cases for both stationary and moving porous configurations. The proposed method is easy to implement and efficient in terms of CPU cost and memory management compared to alternative methods which can be used to deal with moving immersed porous media, e.g. re-meshing at each time step or use of a moving/chimera mesh. An overall good agreement was obtained with reference results, opening the way to the numerical simulation of moving porous media for flow control applications.
Institute of Scientific and Technical Information of China (English)
XU You-Sheng; LIU Yang; HUANG Guo-Xiang
2004-01-01
@@ Digital images (DI) and lattice Boltzmann method (LBM) are used to characterize the threshold dynamic parameters of porous media. Two-dimensional representations of the porous structure are reconstructed from segmentation of digital images obtained from a series of tiny samples. The threshold pressure gradients and threshold Péclet numbers are researched on seven test samples by using LBM. Numerical results are in agreement with that obtained by integrating Darcy's law. The results also indicate that fluids can flow through porous media only if the fluid force is large enough to overcome threshold pressure gradient in porous media. One synthetic case is used to further illustrate the applicability of the proposed technique. In addition, the dynamical rules in our model are local, therefore it can be run on parallel computers with well computational efficiency.
Effects of Heterogeneity on Transport of Graphene Oxide in Saturated and Unsaturated Porous Media
Dong, S.; Sun, Y.; Shi, X.; Wu, J.; Gao, B.
2015-12-01
Graphene oxide (GO) has received increasing attention in many fields with its wide applications and rapid growth in production. Therefore, it is expected that GO nanoparticles will inevitably be released into the subsurface and cause the environmental risk subsequently. In view of this, knowledge of the fate for GO in the vadose zone and groundwater systems is indispensable. So far most research has focused on the deposition and transport of GO nanoparticles in one-dimensional homogenous porous media; nonetheless, the complex heterogeneous system is extensively distributed in natural subsurface environment and may not be well represented by the homogeneous packed columns. However, little investigations have been directed toward understanding the transport of GO in heterogeneous porous media. The overarching objective of this study is to advance current understanding of GO transport in structured heterogeneous porous media. The saturated and unsaturated columns packed with different sand combinations and solution ionic strength, were used to examine the breakthrough behavior of GO in heterogeneous porous media. A two-domain model considering GO exchange between zones was developed to describe GO transport in structured, heterogeneous porous media. The experimental data indicate that volumetric moisture content and water flow are the critical factors that control GO transport in heterogeneous porous media. And higher ionic strength decrease the mobility of GO particles in both saturated and unsaturated heterogeneous pore media. Simulations of this two-domain nanoparticle transport model matched experimental breakthrough data well for all the experimental conditions. Experimental and model results show that under saturated conditions, both fast-flow and slow-flow domains affect colloid transport in heterogeneous media. Under unsaturated conditions, however, our results indicate that flows in the fast flow domain dominate the colloid transport and retention processes.
Equilibrium and transfer in porous media 2 transfer laws
Daïan, Jean-François
2014-01-01
A porous medium is composed of a solid matrix and its geometrical complement: the pore space. This pore space can be occupied by one or more fluids. The understanding of transport phenomena in porous media is a challenging intellectual task. This book provides a detailed analysis of the aspects required for the understanding of many experimental techniques in the field of porous media transport phenomena. It is aimed at studentsor engineers who may not be looking specifically to become theoreticians in porous media, but wish to integrate knowledge of porous media with their previous scientif
Influence of biofilms on transport properties in porous media
Davit, Y.
2015-12-01
Microbial activity and biofilm growth in porous media can drastically modify transport properties such as permeability, longitudinal and transverse dispersion or effective reaction rates. Understanding these effects has proven to be a considerable challenge. Advances in this field have been hindered by the difficulty of modeling and visualizing these multi-phase non-linear effects across a broad range of spatial and temporal scales. To address these issues, we are developing a strategy that combines imaging techniques based on x-ray micro-tomography with homogenization of pore-scale transport equations. Here, we review recent progress in x-ray imaging of biofilms in porous media, with a particular focus on the contrast agents that are used to differentiate between the fluid and biofilm phases. We further show how the 3D distribution of the different phases can be used to extract specific information about the biofilm and how effective properties can be calculated via the resolution of closure problems. These closure problems are obtained using the method of volume averaging and must be adapted to the problem of interest. In hydrological systems, we show that a generic formulation for reactive solute transport is based on a domain decomposition approach at the micro-scale yielding macro-scale models reminiscent of multi-rate mass transfer approaches.
Evaluation of liquid aerosol transport through porous media
Hall, R.; Murdoch, L.; Falta, R.; Looney, B.; Riha, B.
2016-07-01
Application of remediation methods in contaminated vadose zones has been hindered by an inability to effectively distribute liquid- or solid-phase amendments. Injection as aerosols in a carrier gas could be a viable method for achieving useful distributions of amendments in unsaturated materials. The objectives of this work were to characterize radial transport of aerosols in unsaturated porous media, and to develop capabilities for predicting results of aerosol injection scenarios at the field-scale. Transport processes were investigated by conducting lab-scale injection experiments with radial flow geometry, and predictive capabilities were obtained by developing and validating a numerical model for simulating coupled aerosol transport, deposition, and multi-phase flow in porous media. Soybean oil was transported more than 2 m through sand by injecting it as micron-scale aerosol droplets. Oil saturation in the sand increased with time to a maximum of 0.25, and decreased with radial distance in the experiments. The numerical analysis predicted the distribution of oil saturation with only minor calibration. The results indicated that evolution of oil saturation was controlled by aerosol deposition and subsequent flow of the liquid oil, and simulation requires including these two coupled processes. The calibrated model was used to evaluate field applications. The results suggest that amendments can be delivered to the vadose zone as aerosols, and that gas injection rate and aerosol particle size will be important controls on the process.
Mixing and reactions in multiphase flow through porous media
Jimenez-Martinez, J.; Le Borgne, T.; Meheust, Y.; Porter, M. L.; De Anna, P.; Hyman, J.; Tabuteau, H.; Turuban, R.; Carey, J. W.; Viswanathan, H. S.
2016-12-01
The understanding and quantification of flow and transport processes in multiphase systems remains a grand scientific and engineering challenge in natural and industrial systems (e.g., soils and vadose zone, CO2 sequestration, unconventional oil and gas extraction, enhanced oil recovery). Beyond the kinetic of the chemical reactions, mixing processes in porous media play a key role in controlling both fluid-fluid and fluid-solid reactions. However, conventional continuum-scale models and theories oversimplify and/or ignore many important pore-scale processes. Multiphase flows, with the creation of highly heterogeneous fluid velocity fields (i.e., low velocities regions or stagnation zones, and high velocity regions or preferential paths), makes conservative and reactive transport more complex. We present recent multi-scale experimental developments and theoretical approaches to quantify transport, mixing, and reaction and their coupling with multiphase flows. We discuss our main findings: i) the sustained concentration gradients and enhanced reactivity in a two-phase system for a continuous injection, and the comparison with a pulse line injection; ii) the enhanced mixing by a third mobile-immiscible phase; and iii) the role that capillary forces play in the localization of the fluid-solid reactions. These experimental results are for highly-idealized geometries, however, the proposed models are related to basic porous media and unsaturated flow properties, and could be tested on more complex systems.
Institute of Scientific and Technical Information of China (English)
Ruiheng WU; Xueyu RUAN; Hongbing ZHANG; T.Y.Hsu
2004-01-01
By combining the α/γ interface migration and the carbon diffusion at the interface in Fe-C alloys, a mathematical model is constructed to describe the mixed-control mechanism for proeutectoid ferrite formation from austenite. In this model, the α/γ interface is treated as non-equilibrium interface, i.e., the carbon concentration of austenite at γ/α interface is obtained through theoretical calculation, instead of that assumed as the local equilibrium concentration.For isothermal precipitation of ferrite in Fe-C alloys, the calculated results show that the rate of interface migration decreases monotonically during the whole process, while the rate of carbon diffusion from γ/α interface into austenite increases to a peak value and then decreases. The process of ferrite growth may be considered as composed of three stages: the period of rapid growth, slow growth and finishing stage. The results also show that the carbon concentration of austenite at γ/α interface could not reach the thermodynamic equilibrium value even at the last stage of ferrite growth.
Open problems in non-equilibrium physics
Energy Technology Data Exchange (ETDEWEB)
Kusnezov, D.
1997-09-22
The report contains viewgraphs on the following: approaches to non-equilibrium statistical mechanics; classical and quantum processes in chaotic environments; classical fields in non-equilibrium situations: real time dynamics at finite temperature; and phase transitions in non-equilibrium conditions.
Zoschke, Kristin; Engel, Christina; Börnick, Hilmar; Worch, Eckhard
2011-10-01
The adsorption of the taste and odour (T&O) compounds geosmin and 2-methylisoborneol (2-MIB) onto powdered activated carbon (PAC) has been studied under conditions which are typical for a drinking water treatment plant that uses reservoir water for drinking water production. The reservoir water as well as the pre-treated water (after flocculation) contains NOM that competes with the trace compounds for the adsorption sites on the carbon surface. Although the DOC concentrations in the reservoir water and in the pre-treated water were different, no differences in the competitive adsorption could be seen. By using two special characterisation methods for NOM (adsorption analysis, LC/OCD) it could be proved that flocculation removes only NOM fractions which are irrelevant for competitive adsorption. Different model approaches were applied to describe the competitive adsorption of the T&O compounds and NOM, the tracer model, the equivalent background compound model, and the simplified equivalent background compound model. All these models are equilibrium models but in practice the contact time in flow-through reactors is typically shorter than the time needed to establish the adsorption equilibrium. In this paper it is demonstrated that the established model approaches can be used to describe competitive adsorption of T&O compounds and NOM also under non-equilibrium conditions. The results of the model applications showed that in particular the simplified equivalent background compound model is a useful tool to determine the PAC dosage required to reduce the T&O compounds below the threshold concentration.
Dendrite Suppression by Shock Electrodeposition in Charged Porous Media
Han, Ji-Hyung; Wang, Miao; Bai, Peng; Brushett, Fikile R.; Bazant, Martin Z.
2016-06-01
It is shown that surface conduction can stabilize electrodeposition in random, charged porous media at high rates, above the diffusion-limited current. After linear sweep voltammetry and impedance spectroscopy, copper electrodeposits are visualized by scanning electron microscopy and energy dispersive spectroscopy in two different porous separators (cellulose nitrate, polyethylene), whose surfaces are modified by layer-by-layer deposition of positive or negative charged polyelectrolytes. Above the limiting current, surface conduction inhibits growth in the positive separators and produces irregular dendrites, while it enhances growth and suppresses dendrites behind a deionization shock in the negative separators, also leading to improved cycle life. The discovery of stable uniform growth in the random media differs from the non-uniform growth observed in parallel nanopores and cannot be explained by classic quasi-steady “leaky membrane” models, which always predict instability and dendritic growth. Instead, the experimental results suggest that transient electro-diffusion in random porous media imparts the stability of a deionization shock to the growing metal interface behind it. Shock electrodeposition could be exploited to enhance the cycle life and recharging rate of metal batteries or to accelerate the fabrication of metal matrix composite coatings.
Studies on dispersive stabilization of porous media flows
Energy Technology Data Exchange (ETDEWEB)
Daripa, Prabir, E-mail: prabir.daripa@math.tamu.edu; Gin, Craig [Department of Mathematics, Texas A& M University, College Station, Texas 77843 (United States)
2016-08-15
Motivated by a need to improve the performance of chemical enhanced oil recovery (EOR) processes, we investigate dispersive effects on the linear stability of three-layer porous media flow models of EOR for two different types of interfaces: permeable and impermeable interfaces. Results presented are relevant for the design of smarter interfaces in the available parameter space of capillary number, Peclet number, longitudinal and transverse dispersion, and the viscous profile of the middle layer. The stabilization capacity of each of these two interfaces is explored numerically and conditions for complete dispersive stabilization are identified for each of these two types of interfaces. Key results obtained are (i) three-layer porous media flows with permeable interfaces can be almost completely stabilized by diffusion if the optimal viscous profile is chosen, (ii) flows with impermeable interfaces can also be almost completely stabilized for short time, but become more unstable at later times because diffusion flattens out the basic viscous profile, (iii) diffusion stabilizes short waves more than long waves which leads to a “turning point” Peclet number at which short and long waves have the same growth rate, and (iv) mechanical dispersion further stabilizes flows with permeable interfaces but in some cases has a destabilizing effect for flows with impermeable interfaces, which is a surprising result. These results are then used to give a comparison of the two types of interfaces. It is found that for most values of the flow parameters, permeable interfaces suppress flow instability more than impermeable interfaces.
Studies of Tracer Dispersion and Fluid Flow in Porous Media
Energy Technology Data Exchange (ETDEWEB)
Rage, T.
1996-12-31
This doctoral thesis explores the connection between the topology of a porous medium and its macroscopic transport properties and is based on computerized simulation. In porous media, both diffusion and convection contribute to the dispersion of a tracer and their combined effect is emphasized. The governing equations are solved numerically, using finite differences and Monte Carlo technique. The influence of finite Reynolds number on the outcome of echo-experiments is discussed. Comparing experiments and simulations it is found that nonlinear inertial forces lead to a visible deformation of a returned tracer at surprisingly small Reynolds numbers. In a study of tracer dispersion and fluid flow in periodic arrays of discs it is demonstrated that the mechanisms of mechanical dispersion in periodic media and in natural (non-periodic) porous media are essentially different. Measurements of the percolation probability distribution of a sandstone sample is presented. Local porosity theory predicts that this simple geometric function of a porous medium is of dominant importance for its macroscopic transport properties. It is demonstrated that many aspects of transport through fractures can be studied by using simple but realistic models and readily available computer resources. An example may be the transport of hydrocarbon fluids from the source rock to a reservoir. 165 refs., 44 figs., 1 table
Computation of streaming potential in porous media: Modified permeability tensor
Bandopadhyay, Aditya; DasGupta, Debabrata; Mitra, Sushanta K.; Chakraborty, Suman
2015-11-01
We quantify the pressure-driven electrokinetic transport of electrolytes in porous media through a matched asymptotic expansion based method to obtain a homogenized description of the upscaled transport. The pressure driven flow of aqueous electrolytes over charged surfaces leads to the generation of an induced electric potential, commonly termed as the streaming potential. We derive an expression for the modified permeability tensor, K↔eff, which is analogous to the Darcy permeability tensor with due accounting for the induced streaming potential. The porous media herein are modeled as spatially periodic. The modified permeability tensor is obtained for both topographically simple and complex domains by enforcing a zero net global current. Towards resolving the complicated details of the porous medium in a computationally efficient framework, the domain identification and reconstruction of the geometries are performed using adaptive quadtree (in 2D) and octree (in 3D) algorithms, which allows one to resolve the solid-liquid interface as per the desired level of resolution. We discuss the influence of the induced streaming potential on the modification of the Darcy law in connection to transport processes through porous plugs, clays and soils by considering a case-study on Berea sandstone.
COUPLING SIMULATION OF SURFACE FLOW AND SUBSURFACE FLOW OVER POROUS MEDIA
Institute of Scientific and Technical Information of China (English)
ZHANG Pei-wen; LIU De-fu; SONG Yu-pu
2004-01-01
Mathematical model of water flow over porous media is developed, the computer program is compiled ,and an example is given to verify the validity of the model. The results of the calculation show that the model is very useful and worth going further study in practical engineering.
Dilution and reactive mixing in three-dimensional helical flows in porous media
Chiogna, Gabriele; Ye, Yu; Grathwohl, Peter; Cirpka, Olaf A.; Rolle, Massimo
2016-04-01
Dilution under steady-state flow and transport conditions in porous media occurs primarily by lateral mass exchange at the fringe of solute plumes.