Quantitative Permeability Prediction for Anisotropic Porous Media
Sheng, Q.; Thompson, K. E.
2012-12-01
Pore-scale modeling as a predictive tool has become an integral to both research and commercial simulation in recent years. Permeability is one of the most important of the many properties that can be simulated. Traditionally, permeability is determined using Darcy's law, based on the assumption that the pressure gradient is aligned with the principal flow direction. However, a wide variety of porous media exhibit anisotropic permeability due to particle orientation or laminated structure. In these types of materials, the direction of fluid flow is not aligned with the pressure gradient (except along the principal directions). Thus, it is desirable to predict the full permeability tensor for anisotropic materials using a first-principles pore-scale approach. In this work, we present a fast method to determine the full permeability tensor and the principal directions using a novel network modeling algorithm. We also test the ability of network modeling (which is an approximate method) to detect anisotropy in various structures. Both computational fluid dynamics (CFD) methods and network modeling have emerged as effective techniques to predict rock properties. CFD models are more rigorous but computationally expensive. Network modeling involves significant approximations but can be orders-of-magnitude more efficient computationally, which is important for both speed and the ability to model larger scales. This work uses network modeling, with simulations performed on two types of anisotropic materials: laminated packings (with layers of different sized particles) and oriented packings (containing particles with preferential orientation). Pore network models are created from the porous media data, and a novel method is used to determine the permeability tensor and principal flow direction using pore network modeling. The method is verified by comparing the calculated principal directions with the known anisotropy and also by comparing permeability with values from CFD
Numerical investigation of nanoparticles transport in anisotropic porous media.
Salama, Amgad; Negara, Ardiansyah; El Amin, Mohamed; Sun, Shuyu
2015-10-01
In this work the problem related to the transport of nanoparticles in anisotropic porous media is investigated numerically using the multipoint flux approximation. Anisotropy of porous media properties is an essential feature that exists almost everywhere in subsurface formations. In anisotropic media, the flux and the pressure gradient vectors are no longer collinear and therefore interesting patterns emerge. The transport of nanoparticles in subsurface formations is affected by several complex processes including surface charges, heterogeneity of nanoparticles and soil grain collectors, interfacial dynamics of double-layer and many others. We use the framework of the theory of filtration in this investigation. Processes like particles deposition, entrapment, as well as detachment are accounted for. From the numerical methods point of view, traditional two-point flux finite difference approximation cannot handle anisotropy of media properties. Therefore, in this work we use the multipoint flux approximation (MPFA). In this technique, the flux components are affected by more neighboring points as opposed to the mere two points that are usually used in traditional finite volume methods. We also use the experimenting pressure field approach which automatically constructs the global system of equations by solving multitude of local problems. This approach facilitates to a large extent the construction of the global system. A set of numerical examples is considered involving two-dimensional rectangular domain. A source of nanoparticles is inserted in the middle of the anisotropic layer. We investigate the effects of both anisotropy angle and anisotropy ratio on the transport of nanoparticles in saturated porous media. It is found that the concentration plume and porosity contours follow closely the principal direction of anisotropy of permeability of the central domain. PMID:26212784
Numerical investigation of nanoparticles transport in anisotropic porous media
Salama, Amgad
2015-07-13
In this work the problem related to the transport of nanoparticles in anisotropic porous media is investigated numerically using the multipoint flux approximation. Anisotropy of porous media properties are an essential feature that exist almost everywhere in subsurface formations. In anisotropic media, the flux and the pressure gradient vectors are no longer collinear and therefore interesting patterns emerge. The transport of nanoparticles in subsurface formations is affected by several complex processes including surface charges, heterogeneity of nanoparticles and soil grain collectors, interfacial dynamics of double-layer and many others. We use the framework of the theory of filtration in this investigation. Processes like particles deposition, entrapment, as well as detachment are accounted for. From the numerical methods point of view, traditional two-point flux finite difference approximation cannot handle anisotropy of media properties. Therefore, in this work we use the multipoint flux approximation (MPFA). In this technique, the flux components are affected by more neighboring points as opposed to the mere two points that are usually used in traditional finite volume methods. We also use the experimenting pressure field approach which automatically constructs the global system of equations by solving multitude of local problems. This approach facilitates to a large extent the construction of the global system. A set of numerical examples is considered involving two-dimensional rectangular domain. A source of nanoparticles is inserted in the middle of the anisotropic layer. We investigate the effects of both anisotropy angle and anisotropy ratio on the transport of nanoparticles in saturated porous media. It is found that the concentration plume and porosity contours follow closely the principal direction of anisotropy of permeability of the central domain.
Fabric dependence of quasi-waves in anisotropic porous media.
Cardoso, Luis; Cowin, Stephen C
2011-05-01
Assessment of bone loss and osteoporosis by ultrasound systems is based on the speed of sound and broadband ultrasound attenuation of a single wave. However, the existence of a second wave in cancellous bone has been reported and its existence is an unequivocal signature of poroelastic media. To account for the fact that ultrasound is sensitive to microarchitecture as well as bone mineral density (BMD), a fabric-dependent anisotropic poroelastic wave propagation theory was recently developed for pure wave modes propagating along a plane of symmetry in an anisotropic medium. Key to this development was the inclusion of the fabric tensor--a quantitative stereological measure of the degree of structural anisotropy of bone--into the linear poroelasticity theory. In the present study, this framework is extended to the propagation of mixed wave modes along an arbitrary direction in anisotropic porous media called quasi-waves. It was found that differences between phase and group velocities are due to the anisotropy of the bone microarchitecture, and that the experimental wave velocities are more accurately predicted by the poroelastic model when the fabric tensor variable is taken into account. This poroelastic wave propagation theory represents an alternative for bone quality assessment beyond BMD. PMID:21568431
Fabric dependence of quasi-waves in anisotropic porous media
Cardoso, Luis; Cowin, Stephen C.
2011-01-01
Assessment of bone loss and osteoporosis by ultrasound systems is based on the speed of sound and broadband ultrasound attenuation of a single wave. However, the existence of a second wave in cancellous bone has been reported and its existence is an unequivocal signature of poroelastic media. To account for the fact that ultrasound is sensitive to microarchitecture as well as bone mineral density (BMD), a fabric-dependent anisotropic poroelastic wave propagation theory was recently developed ...
CAI; Ruixian; GOU; Chenhua; ZHANG; Na
2005-01-01
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, in analyzing the non-Darcy and anisotropic effects on the convection), such analytical solutions can be the benchmark solutions that can promote the development of computational heat and mass transfer. Some solutions considering the anisotropic effect of permeability have been given previously by the authors, and this paper gives solutions including the anisotropic effect of thermal conductivity and the effect of heat sources.
Coupling two-phase fluid flow with two-phase darcy flow in anisotropic porous media
Chen, J.
2014-06-03
This paper reports a numerical study of coupling two-phase fluid flow in a free fluid region with two-phase Darcy flow in a homogeneous and anisotropic porous medium region. The model consists of coupled Cahn-Hilliard and Navier-Stokes equations in the free fluid region and the two-phase Darcy law in the anisotropic porous medium region. A Robin-Robin domain decomposition method is used 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. Obtained results have shown the anisotropic properties effect on the velocity and pressure of the two-phase flow. 2014 Jie Chen et al.
Generalization of the van der Waals equation for anisotropic fluids in porous media
Holovko, Myroslav; Shmotolokha, Volodymyr
2015-01-01
The generalized van der Waals equation of state for anisotropic liquids in porous media consists of two terms.One of them is based on the equation of state for hard spherocylinders in random porous media obtained from the scaled particle theory.The second term is expressed in terms of the mean value of attractive intermolecular interactions.The obtained equation is used for the investigation of the gas-liquid-nematic phase behavior of a molecular system depending on the anisotropy of molecule...
Computation of the transient flow in zoned anisotropic porous media by the boundary element method
Bruch, E.; Grilli, S.
Results on the application of the BEM to transient two-dimensional flows in zoned anisotropic porous media are presented, including the iterative calculation of the free surface seepage position. The classical BEM equations are discretized by linear, quadratic, or cubic elements, employing special singular numerical quadrature rules. The method is improved by the incorporation of a subregion division. The present technique is shown to be very accurate and to avoid previously encountered oscillation problems.
Mechanical transport and porous media equivalence in anisotropic fracture networks
The objective of this work is to investigate the directional characteristics of hydraulic effective porosity in an effort to understand porous medium equivalence for continuous and discontinuous fracture systems. Continuous systems contain infinitely long fractures. Discontinuous systems consist of fractures with finite lengths. The distribution of apertures (heterogeneity) has a major influence on the degree of porous medium equivalence for distributed continuous and discontinuous systems. When the aperture distribution is narrow, the hydraulic effective porosity is slightly less than the total porosity for continuous systems, and greater than the rock effective porosity for discontinuous systems. However, when heterogeneity is significant, the hydraulic effective porosity is directionally dependent and greater than total porosity for both systems. Non-porous medium behavior ws found to differ for distributed continuous systems and for continuous systems with parallel sets. For the latter systems, hydraulic effective porosity abruptly decreases below total porosity in those particular directions where the hydraulic gradient and the orientation of a fracture set are orthogonal. The results for the continuous systems with parallel sets also demonstrate that a system that behaves like a continuum for fluid flux may not behave like a continuum for mechanical transport. 3 references, 13 figures
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 computat...
De Paoli, Marco; Zonta, Francesco; Soldati, Alfredo
2016-05-01
Solute convection in porous media at high Rayleigh-Darcy numbers has important fundamental features and may also bear implications for geological CO2 sequestration processes. With the aid of direct numerical simulations, we examine the role of anisotropic permeability on the distribution of solutal concentration in fluid saturated porous medium. Our computational analyses span over few decades of Rayleigh-Darcy number and confirm the linear scaling of Nusselt number that was previously found in the literature. In addition, we find that anisotropic permeability γ < 1, i.e., with vertical permeability smaller than horizontal permeability, effectively increases the Nusselt number compared with isotropic conditions. We link this seemingly counterintuitive effect with the occurring modifications to the flow topology in the anisotropic conditions. Finally, we use our data computed for the two-sided configuration (i.e., Dirichlet conditions on upper and lower boundaries) to examine the time evolution of solutal dynamics in the one-sided configuration, and we demonstrate that the finite-time (short-term) amount of CO2 that can be dissolved in anisotropic sedimentary rocks is much larger than in isotropic rocks.
Berryman, J.G.
2009-11-20
Poroelastic analysis usually progresses from assumed knowledge of dry or drained porous media to the predicted behavior of fluid-saturated and undrained porous media. Unfortunately, the experimental situation is often incompatible with these assumptions, especially when field data (from hydrological or oil/gas reservoirs) are involved. The present work considers several different experimental scenarios typified by one in which a set of undrained poroelastic (stiffness) constants has been measured using either ultrasound or seismic wave analysis, while some or all of the dry or drained constants are normally unknown. Drained constants for such a poroelastic system can be deduced for isotropic systems from available data if a complete set of undrained compliance data for the principal stresses are available - together with a few other commonly measured quantities such as porosity, fluid bulk modulus, and grain bulk modulus. Similar results are also developed here for anisotropic systems having up to orthotropic symmetry if the system is granular (i.e., composed of solid grains assembled into a solid matrix, either by a cementation process or by applied stress) and the grains are known to be elastically homogeneous. Finally, the analysis is also fully developed for anisotropic systems with nonhomogeneous (more than one mineral type), but still isotropic, grains - as well as for uniform collections of anisotropic grains as long as their axes of symmetry are either perfectly aligned or perfectly random.
Transverse mixing in three-dimensional nonstationary anisotropic heterogeneous porous media
Cirpka, Olaf; Chiogna, Gabriele; Rolle, Massimo;
2015-01-01
Groundwater plumes originating from continuously emitting sources are typically controlled by transverse mixing between the plume and reactants in the ambient solution. In two-dimensional domains, heterogeneity causes only weak enhancement of transverse mixing in steady-state flows. In three......-dimensional domains, more complex flow patterns are possible because streamlines can twist. In particular, spatially varying orientation of anisotropy can cause steady-state groundwater whirls. We analyze steady-state solute transport in three-dimensional locally isotropic heterogeneous porous media with blockwise...... anisotropic correlation structure, in which the principal directions of anisotropy differ from block to block. For this purpose, we propose a transport scheme that relies on advective transport along streamlines and transverse-dispersive mass exchange between them based on Voronoi tessellation. We compare...
Negara, Ardiansyah
2015-03-04
Numerical investigations of two-phase flows in anisotropic porous media have been conducted. In the flow model, the permeability has been considered as a full tensor and is implemented in the numerical scheme using the multipoint flux approximation within the framework of finite difference method. In addition, the experimenting pressure field approach is used to obtain the solution of the pressure field, which makes the matrix of coefficient of the global system easily constructed. A number of numerical experiments on the flow of two-phase system in two-dimensional porous medium domain are presented. In this work, the gravity is included in the model to capture the possible buoyancy-driven effects due to density differences between the two phases. Different anisotropy scenarios have been considered. From the numerical results, interesting patterns of the flow, pressure, and saturation fields emerge, which are significantly influenced by the anisotropy of the absolute permeability field. It is found that the two-phase system moves along the principal direction of anisotropy. Furthermore, the effects of anisotropy orientation on the flow rates and the cross flow index are also discussed in the paper.
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. PMID:23237543
Yong Wang; Wenzheng Yue; Mo Zhang
2016-01-01
The anisotropic transport of thermal neutron in heterogeneous porous media is of great research interests in many fields. In this paper, it is the first time that a new model based on micron X-ray computed tomography (CT) has been proposed to simultaneously consider both the separation of matrix and pore and the distribution of mineral components. We apply the Monte Carlo method to simulate thermal neutrons transporting through the model along different directions, and meanwhile detect those ...
Negara, Ardiansyah
2014-04-21
Carbon dioxide (CO2) sequestration in saline aquifers is considered as one of the most viable and promising ways to reduce CO2 concentration in the atmosphere. CO2 is injected into deep saline formations at supercritical state where its density is smaller than the hosting brine. This motivates an upward motion and eventually CO2 is trapped beneath the cap rock. The trapped CO2 slowly dissolves into the brine causing the density of the mixture to become larger than the host brine. This causes gravitational instabilities that is propagated and magnified with time. In this kind of density-driven flows, the CO2-rich brines migrate downward while the brines with low CO2 concentration move upward. With respect to the properties of the subsurface aquifers, there are instances where saline formations can possess anisotropy with respect to their hydraulic properties. Such anisotropy can have significant effect on the onset and propagation of flow instabilities. Anisotropy is predicted to be more influential in dictating the direction of the convective flow. To account for permeability anisotropy, the method of multipoint flux approximation (MPFA) in the framework of finite differences schemes is used. The MPFA method requires more point stencil than the traditional two-point flux approximation (TPFA). For example, calculation of one flux component requires 6-point stencil and 18-point stencil in 2-D and 3-D cases, respectively. As consequence, the matrix of coefficient for obtaining the pressure fields will be quite complex. Therefore, we combine the MPFA method with the experimenting pressure field technique in which the problem is reduced to solving multitude of local problems and the global matrix of coefficients is constructed automatically, which significantly reduces the complexity. We present several numerical scenarios of density-driven flow simulation in homogeneous, layered, and heterogeneous anisotropic porous media. The numerical results emphasize the
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
Streamline Simulation of a Two-Phase Flow in Heterogeneous and Anisotropic Porous Media
Cervantes, D.; Salazar, A.; de la Cruz, L.
2013-05-01
numerical errors on the solution. The domain of study is a heterogeneous and anisotropic porous media, with several distributions of injector and producer wells. [1] Muskat, M. and Wyckoff, R.: "Theoretical Analysis of Waterfooding Networks," Trans. AIME (1934) 107, 62-77.
Plouraboué, Franck; Bergeon, Alain; Azaïez, Mejdi
2001-01-01
We show how Lagrangian coordinates provide an effective representation of how difﬁcult non-linear, hyperbolic transport problems in porous media can be dealt with. Recalling Lagrangian description ﬁrst, we then derive some basic but remarkable properties useful for the numerical com- putation of projected transport operators. We furthermore introduce new generalized Lagrangian coordinates with their application to the Darcy–Muskat two-phase ﬂow models. We show how these general...
Wang, Yong; Yue, Wenzheng; Zhang, Mo
2016-06-01
The anisotropic transport of thermal neutron in heterogeneous porous media is of great research interests in many fields. In this paper, it is the first time that a new model based on micron X-ray computed tomography (CT) has been proposed to simultaneously consider both the separation of matrix and pore and the distribution of mineral components. We apply the Monte Carlo method to simulate thermal neutrons transporting through the model along different directions, and meanwhile detect those unreacted thermal neutrons by an array detector on the other side of the model. Therefore, the anisotropy of pore structure can be imaged by the amount of received thermal neutrons, due to the difference of rock matrix and pore-filling fluids in the macroscopic reaction cross section (MRCS). The new model has been verified by the consistent between the simulated data and the pore distribution from X-ray CT. The results show that the evaluation of porosity can be affected by the anisotropy of media. Based on the research, a new formula is developed to describe the correlation between the resolution of array detectors and the quality of imaging. The formula can be further used to analyze the critical resolution and the suitable number of thermal neutrons emitted in each simulation. Unconventionally, we find that a higher resolution cannot always lead to a better image.
Salama, Amgad
2014-09-01
In this work we apply the experimenting pressure field approach to the numerical solution of the single phase flow problem in anisotropic porous media using the multipoint flux approximation. We apply this method to the problem of flow in saturated anisotropic porous media. In anisotropic media the component flux representation requires, generally multiple pressure values in neighboring cells (e.g., six pressure values of the neighboring cells is required in two-dimensional rectangular meshes). This apparently results in the need for a nine points stencil for the discretized pressure equation (27 points stencil in three-dimensional rectangular mesh). The coefficients associated with the discretized pressure equation are complex and require longer expressions which make their implementation prone to errors. In the experimenting pressure field technique, the matrix of coefficients is generated automatically within the solver. A set of predefined pressure fields is operated on the domain through which the velocity field is obtained. Apparently such velocity fields do not satisfy the mass conservation equations entailed by the source/sink term and boundary conditions from which the residual is calculated. In this method the experimenting pressure fields are designed such that the residual reduces to the coefficients of the pressure equation matrix. © 2014 Elsevier B.V. All rights reserved.
Although transport calculations are often formulated in terms of mass-based isotropic distribution coefficients, it is the abundance of reactive surface areas of subsurface materials that controls contaminant adsorption. In water-saturated homogeneous systems devoid of advective fluxes (e.g., batch experiments), the available reactive surface area is similar to the total surface area (as measured by conventional methods such as BET gas adsorption). However, in physically and chemically heterogeneous systems with advective fluxes, the effective reactive surface area (i.e., the surface area that a packet of advecting water interacts with) is smaller than the laboratory measured surface area and is a complex function of advective velocity and the correlation structures of the physical and chemical heterogeneities. Theoretical derivations for an important but simple type of heterogeneity (fine-scale horizontal layering) suggest that the effective reactive surface area is an anisotropic property of the medium and is inversely correlated with the anisotropy in hydraulic conductivity. The implications of reactive transport anisotropy include the concept that the retardation factor should be treated as a directional property rather than being treated as a constant. Furthermore, because of the inverse relationship between effective reactive surface area and hydraulic conductivity, batch adsorption experiments tend to overestimate the retention of contaminants relative to intact natural materials
A review of a selection of papers describing the theory of transport in anisotropic porous media
It is now generally accepted that the dispersion length, as defined in the classical advection-dispersion equation, is scale dependent. This report collects together and reviews some of the seminal papers in which have appeared the models and techniques that have led to our present understanding of solute transport in spatially stochastic media. Thus we examine the early work of Taylor on diffusion, the work of Saffman on capillaries, through to the more recent contributions of Dagan and Gelhar which regard the advective-dispersion equation as having stochastic parameters. The reports discuss these papers highlighting the physical arguments and in places deriving some of the more obscure results. This work is carried out by a cost-sharing contract with the European Atomic Energy Community for a research programme on Management, Storage and Radioactive waste disposal. 34 refs
Fractures in anisotropic media
Shao, Siyi
Rocks may be composed of layers and contain fracture sets that cause the hydraulic, mechanical and seismic properties of a rock to be anisotropic. Coexisting fractures and layers in rock give rise to competing mechanisms of anisotropy. For example: (1) at low fracture stiffness, apparent shear-wave anisotropy induced by matrix layering can be masked or enhanced by the presence of a fracture, depending on the fracture orientation with respect to layering, and (2) compressional-wave guided modes generated by parallel fractures can also mask the presence of matrix layerings for particular fracture orientations and fracture specific stiffness. This report focuses on two anisotropic sources that are widely encountered in rock engineering: fractures (mechanical discontinuity) and matrix layering (impedance discontinuity), by investigating: (1) matrix property characterization, i.e., to determine elastic constants in anisotropic solids, (2) interface wave behavior in single-fractured anisotropic media, (3) compressional wave guided modes in parallel-fractured anisotropic media (single fracture orientation) and (4) the elastic response of orthogonal fracture networks. Elastic constants of a medium are required to understand and quantify wave propagation in anisotropic media but are affected by fractures and matrix properties. Experimental observations and analytical analysis demonstrate that behaviors of both fracture interface waves and compressional-wave guided modes for fractures in anisotropic media, are affected by fracture specific stiffness (controlled by external stresses), signal frequency and relative orientation between layerings in the matrix and fractures. A fractured layered medium exhibits: (1) fracture-dominated anisotropy when the fractures are weakly coupled; (2) isotropic behavior when fractures delay waves that are usually fast in a layered medium; and (3) matrix-dominated anisotropy when the fractures are closed and no longer delay the signal. The
Bejan, A
2006-01-01
Provides an introduction to convection in porous media, such as fibrous insulation, geological strata, and catalytic reactors. This third edition covers ""designed"" porous media, the theory of deformable media, modeling viscous dissipation in hyperporous media, and more. It is useful for researchers, practicing engineers and students.
Photon states in anisotropic media
Deepak Kumar
2002-08-01
Quantum aspects of optical polarization are discussed for waves traveling in anisotropic dielectric media with a view to relate the dynamics of polarization with that of photon spin and its manipulation by classical polarizers.
Saad, Bilal Mohammed
2014-01-01
We study the convergence of a combined finite volume nonconforming finite element scheme on general meshes for a partially miscible two-phase flow model in anisotropic porous media. This model includes capillary effects and exchange between the phase. The diffusion term,which can be anisotropic and heterogeneous, is discretized by piecewise linear nonconforming triangular finite elements. The other terms are discretized by means of a cell-centered finite volume scheme on a dual mesh. The relative permeability of each phase is decentred according the sign of the velocity at the dual interface. The convergence of the scheme is proved thanks to an estimate on the two pressures which allows to show estimates on the discrete time and compactness results in the case of degenerate relative permeabilities. A key point in the scheme is to use particular averaging formula for the dissolution function arising in the diffusion term. We show also a simulation of CO
Marsden, S.S.
1986-07-01
In 1978 a literature search on selective blocking of fluid flow in porous media was done by Professor S.S. Marsden and two of his graduate students, Tom Elson and Kern Huppy. This was presented as SUPRI Report No. TR-3 entitled ''Literature Preview of the Selected Blockage of Fluids in Thermal Recovery Projects.'' Since then a lot of research on foam in porous media has been done on the SUPRI project and a great deal of new information has appeared in the literature. Therefore we believed that a new, up-to-date search should be done on foam alone, one which would be helpful to our students and perhaps of interest to others. This is a chronological survey showing the development of foam flow, blockage and use in porous media, starting with laboratory studies and eventually getting into field tests and demonstrations. It is arbitrarily divided into five-year time periods. 81 refs.
Dickenson, Eric [Univ. of California, Davis, CA (United States)
1996-05-01
A novel non-intrusive fluorescence imaging technique is used to study microscopic transport within porous media. The system consists of a column packed with heterogeneous-transparent particles and a refractive index-matched aqueous fluid seeded with fluorescent tracer particles or an organic dye. The flow through the column is illuminated by a planar sheet of laser beam and details of flow and transport through the porous regions can be observed microscopically and qualitative and quantitative transport information can be obtained. Various geometric, flow, and concentration quantities can be determined over a three dimensional volume within the column. The quantities include local and volumetrically averaged porosities, velocity and concentration fields, microscopic and volumetrically averaged dispersive fluxes and the dispersion coefficient. The qualitative and quantitative results will provide a better understanding for modeling of transport in porous media.
Electromagnetism on anisotropic fractal media
Ostoja-Starzewski, Martin
2013-04-01
Basic equations of electromagnetic fields in anisotropic fractal media are obtained using a dimensional regularization approach. First, a formulation based on product measures is shown to satisfy the four basic identities of the vector calculus. This allows a generalization of the Green-Gauss and Stokes theorems as well as the charge conservation equation on anisotropic fractals. Then, pursuing the conceptual approach, we derive the Faraday and Ampère laws for such fractal media, which, along with two auxiliary null-divergence conditions, effectively give the modified Maxwell equations. Proceeding on a separate track, we employ a variational principle for electromagnetic fields, appropriately adapted to fractal media, so as to independently derive the same forms of these two laws. It is next found that the parabolic (for a conducting medium) and the hyperbolic (for a dielectric medium) equations involve modified gradient operators, while the Poynting vector has the same form as in the non-fractal case. Finally, Maxwell's electromagnetic stress tensor is reformulated for fractal systems. In all the cases, the derived equations for fractal media depend explicitly on fractal dimensions in three different directions and reduce to conventional forms for continuous media with Euclidean geometries upon setting these each of dimensions equal to unity.
Naff, R.L.
1998-01-01
The late-time macrodispersion coefficients are obtained for the case of flow in the presence of a small-scale deterministic transient in a three-dimensional anisotropic, heterogeneous medium. The transient is assumed to affect only the velocity component transverse to the mean flow direction and to take the form of a periodic function. For the case of a highly stratified medium, these late-time macrodispersion coefficients behave largely as the standard coefficients used in the transport equation. Only in the event that the medium is isotropic is it probable that significant deviations from the standard coefficients would occur.
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...
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....
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
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
Transport theory in anisotropic media
A theory of particle scattering in anisotropic media is developed. That is, a medium in which the microstructure causes the mean free paths of the particles to become dependent on their direction of motion with respect to some fixed axis. The equation which results is similar to the normal, one-speed Boltzmann transport equation but has cross-sections which are functions of direction. This equation is solved for arbitrary cross-sectional dependence on direction in plane geometry. Four distinct problems are considered: (1) the particle distribution arising from a plane source in an infinite medium, (2) the albedo problem and Milne problem for a half-space and the corresponding 'thick slab' transmission problem, (3) solution of the integral form of the Boltzmann equation for a special case of cross-sectional dependence which leads to results similar to the well-known rod model and (4) the energy spectrum of particles slowing down from a high energy source by elastic collisions. In each of these four problems the influence of the cross-section is seen to be significant in comparison with the conventional constant cross-section results, to which they revert in this limit. Some suggestions about physical applications of the results are made. (author)
Efficient Wavefield Extrapolation In Anisotropic Media
Alkhalifah, Tariq
2014-07-03
Various examples are provided for wavefield extrapolation in anisotropic media. In one example, among others, a method includes determining an effective isotropic velocity model and extrapolating an equivalent propagation of an anisotropic, poroelastic or viscoelastic wavefield. The effective isotropic velocity model can be based upon a kinematic geometrical representation of an anisotropic, poroelastic or viscoelastic wavefield. Extrapolating the equivalent propagation can use isotopic, acoustic or elastic operators based upon the determined effective isotropic velocity model. In another example, non-transitory computer readable medium stores an application that, when executed by processing circuitry, causes the processing circuitry to determine the effective isotropic velocity model and extrapolate the equivalent propagation of an anisotropic, poroelastic or viscoelastic wavefield. In another example, a system includes processing circuitry and an application configured to cause the system to determine the effective isotropic velocity model and extrapolate the equivalent propagation of an anisotropic, poroelastic or viscoelastic wavefield.
Anisotropic damage coupled modeling of saturated porous rock
无
2010-01-01
It is widely acknowledged that the natural rock mass is anisotropic and its failing type is also non-isotropic. An orthotropic elastic damaged model has been proposed in which the elastic deformation,the damaged deformation and irreversible deformation can be identified respectively. A second rank damage tensor is employed to characterize the induced damage and damage evolution related to the propagation conditions of microcracks. A specific form of the Gibbs free energy function is used to obtain the effective elastic stiffness and the limited scopes of damage parameters are suggested. The model’s parameter determination is proposed by virtue of conventional tri-axial test. Then,the proposed model is developed to simulate the coupled hydraulic mechanical responses and traction behaviors in different loading paths of porous media.
Transport Upscaling in Porous Media
Nedreli, Anette Cathrine
2014-01-01
Numerical models are important for modeling what happens in porous media. In this thesis we will simulate the heat transport in geothermal reservoirs. Because these reservoirs are usually quite large, we will make a model that upgrids the fine scale reservoir into a coarser scale reservoir that has a smaller amount of grid cells. We will look at upgridding based on different indicators; Cartesian, permeability, velocity and time of flight. We need to upscale the energy equation so we can solv...
Simulation of uncompressible fluid flow through a porous media
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.
Simulation of uncompressible fluid flow through a porous media
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.
Translation correlations in anisotropically scattering media
Judkewitz, Benjamin; Horstmeyer, Roarke; Vellekoop, Ivo M.; Papadopoulos, Ioannis N.; Yang, Changhuei
2015-08-01
Controlling light propagation across scattering media by wavefront shaping holds great promise for a wide range of communications and imaging applications. But, finding the right shape for the wavefront is a challenge when the mapping between input and output scattered wavefronts (that is, the transmission matrix) is not known. Correlations in transmission matrices, especially the so-called memory effect, have been exploited to address this limitation. However, the traditional memory effect applies to thin scattering layers at a distance from the target, which precludes its use within thick scattering media, such as fog and biological tissue. Here, we theoretically predict and experimentally verify new transmission matrix correlations within thick anisotropically scattering media, with important implications for biomedical imaging and adaptive optics.
A finite difference, multipoint flux numerical approach to flow in porous media: Numerical examples
Osman, Hossam
2012-06-17
It is clear that none of the current available numerical schemes which may be adopted to solve transport phenomena in porous media fulfill all the required robustness conditions. That is while the finite difference methods are the simplest of all, they face several difficulties in complex geometries and anisotropic media. On the other hand, while finite element methods are well suited to complex geometries and can deal with anisotropic media, they are more involved in coding and usually require more execution time. Therefore, in this work we try to combine some features of the finite element technique, namely its ability to work with anisotropic media with the finite difference approach. We reduce the multipoint flux, mixed finite element technique through some quadrature rules to an equivalent cell-centered finite difference approximation. We show examples on using this technique to single-phase flow in anisotropic porous media.
Gauge Field Optics with Anisotropic Media
Liu, Fu
2014-01-01
By considering gauge transformations on the macroscopic Maxwell's equations, a two dimensional gauge field, with its pseudo magnetic field in the real space, is identified as tilted anisotropy in the constitutive parameters. We show that optical spin Hall effect and one-way edge states become possible simply by using anisotropic media with broadband response. The proposed gauge field also allows us to design an optical isolator based on the Aharonov-Bohm effect. Our approach will be useful in spoof magneto-optics with arbitrary magnetic fields mimicked by metamaterials with subwavelength unit cells. It also serves as a generic way to design polarization-dependent devices.
Colloid migration in porous media
Retention of radionuclides for long periods near waste repositories depends upon multiple barriers, one of which is adsorption to immobile solid surfaces. Since small particles and colloidal matter have high adsorption capacities per unit mass and can be mobile in subsurface flows, colloidal transport of waste components requires analysis. Theories for predicting colloid migration through porous media have been developed in the filtration literature. The applicability of filtration theories for predicting particle and colloid transport. Emphasis is on suspended matter much smaller than pore sizes, where physical and chemical forces control migration rather than size dependent physical straining. In general, experimentally verifiable theories exist for particle filtration by clean media, and a sensitivity analysis is possible on particle and media properties and fluid flow rate. When particle aggregates accumulate within pores, media permeability decreases, resulting in flow field alteration and possible radionuclide isolation. An analysis of the limited experimental data available indicates that present theories cannot predict long-term colloid transport when permeability reduction occurs. The coupling of colloid attachment processes and the hydrologic flow processes requires more extensive laboratory field research than has currently been carried out. An emphasis on the fundamental mechanisms is necessary to enhance long-term predictability
Propagation of waves in porous media
Çorapçıoplu, M. Yavuz; Tuncay, Kağan
1996-01-01
Wave propagation in porous media is of interest in various diversified areas of science and engineering. The theory of the phenomenon has been studied extensively in soil mechanics, seismology, acoustics, earthquake engineering, ocean engineering, geophysics, and many other disciplines. This review presents a general survey of the literature within the context of porous media mechanics. Following a review of the Biot's theory of wave propagation in linear, elastic, fluid saturated porous medi...
Fundamental Solution of the Anisotropic Porous Medium Equation
Bin Heng SONG; Huai Yu JIAN
2005-01-01
We establish the existence of fundamental solutions for the anisotropic porous medium equation, ut = ∑n i=1(umi)xixi in sRn × (0,∞), where m1,m2,..., and mn are positive constants satisfying min1≤i≤n{mi} ≤ 1, Σni=i mi ＞ n -- 2, and max1≤i≤n{mi} ≤1/n+ Σi=1 mi).
Modeling biologically reactive transport in porous media
A one-dimensional biofilm-based reactive transport model is developed to simulate biologically mediated substrate metabolism and contaminant destruction in saturated porous media. The resulting equations are solved by a finite-difference based, three-level, operator-split approach. The numerical solution procedure is stable, easy-to-code, and computationally efficient. As an example problem, biological denitrification and fortuitous CT destruction processes in one-dimensional porous media is studied. The simulation results of the example problem show that the present model can be successfully used to predict biological processes and nutrient/contaminant transport in saturated porous media
Spin and Orbital angular momentum propagation in anisotropic media: theory
Picón, Antonio; Benseny, Albert; Mompart, Jordi; Calvo, Gabriel F.
2011-01-01
This paper is devoted to study the propagation of light beams carrying orbital angular momentum in optically anisotropic media. We first review some properties of homogeneous anisotropic media, and describe how the paraxial formalism is modified in order to proceed with a new approach dealing with a general setting of paraxial propagation along uniaxial inhomogeneous media. This approach is suitable for describing the space-variant-optical-axis phase plates.
Spin and orbital angular momentum propagation in anisotropic media: theory
This paper is devoted to a study of the propagation of light beams carrying orbital angular momentum in optically anisotropic media. We first review some properties of homogeneous anisotropic media, and describe how the paraxial formalism is modified in order to proceed with a new approach dealing with the general setting of paraxial propagation along uniaxial inhomogeneous media. This approach is suitable for describing space-variant optical-axis phase plates
Multiphase flow in fractured porous media
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.
On full-tensor permeabilities of porous media from numerical solutions of the Navier-Stokes equation
Wang, Y.
2013-01-01
A numerical method is proposed to compute full-tensor permeability of porous media without artificial simplification. Navier-Stokes (N-S) equation and Darcy\\'s law are combined to design these numerical experiments. This method can successfully detect the permeability values in principle directions of the porous media and the anisotropic degrees. It is found that the same configuration of porous media may possess isotropic features at lower Reynolds numbers while manifesting anisotropic features at higher Reynolds numbers due to the nonlinearity from convection. Anisotropy becomes pronounced especially when convection is dominant. 2013 Yi Wang et al.
Fronts of Stress Wave in Anisotropic Piezoelectric Media
刘颖; 刘凯欣; 高凌天
2004-01-01
The characteristic of wave fronts in anisotropic piezoelectric media is analysed by adopting the generalized characteristic theory. Analytical expressions for wave velocities and wave fronts are formulated. Apart from the ordinary characteristics, a new phenomenon, energy velocity funnel, is formed on the wave fronts of quasitransverse waves in anisotropic piezoelectric materials. A three-dimensional representation of wave fronts in anisotropic piezoelectric materials is given for a better understanding of the new phenomena.
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.
New permeameter for geologic porous-media
The use of a modified microbore HPLC/SFC system is described as an automated rapid-analysis permeameter for studying the interactions of liquid hazardous-waste leachates with low permeability geologic porous-media(1). Numerous advantages over currently described equipment for permeability and leachate/soil compatibility testing are shown. The system can operate in a constant pressure mode for generating precise and constant hydraulic-gradients on porous media samples, or in a constant flow-rate and mode. Both techniques allow continuous real-time monitoring of permeability changes. The system can also determine when steady-state baseline hydraulic conductivity of the porous media has been achieved and then automatically switch permeants for chemical interaction studies. The instrument continuously monitors and displays permeant flow-rate, permeameter cell pressure-drop and UV-VIS absorbance of contaminant species in solution
Trends in modeling of porous media combustion
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)
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.
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. PMID:22213663
Renormalized anisotropic exchange for representing heat assisted magnetic recording media
Jiao, Yipeng; Liu, Zengyuan; Victora, R. H., E-mail: victora@umn.edu [MINT Center, Electrical and Computer Engineering, University of Minnesota, Minneapolis, Minnesota 55455 (United States)
2015-05-07
Anisotropic exchange has been incorporated in a description of magnetic recording media near the Curie temperature, as would be found during heat assisted magnetic recording. The new parameters were found using a cost function that minimized the difference between atomistic properties and those of renormalized spin blocks. Interestingly, the anisotropic exchange description at 1.5 nm discretization yields very similar switching and magnetization behavior to that found at 1.2 nm (and below) discretization for the previous isotropic exchange. This suggests that the increased accuracy of anisotropic exchange may also reduce the computational cost during simulation.
Renormalized anisotropic exchange for representing heat assisted magnetic recording media
Anisotropic exchange has been incorporated in a description of magnetic recording media near the Curie temperature, as would be found during heat assisted magnetic recording. The new parameters were found using a cost function that minimized the difference between atomistic properties and those of renormalized spin blocks. Interestingly, the anisotropic exchange description at 1.5 nm discretization yields very similar switching and magnetization behavior to that found at 1.2 nm (and below) discretization for the previous isotropic exchange. This suggests that the increased accuracy of anisotropic exchange may also reduce the computational cost during simulation
Porous media: Analysis, reconstruction and percolation
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...
Casimir force between parallel plates separated by anisotropic media
Deng, Gang; Tan, Bao-Hua; Pei, Ling; Hu, Ni; Zhu, Jin-Rong
2015-06-01
The Casimir force between two parallel plates separated by anisotropic media is investigated. We theoretically calculate the Casimir force between two parallel plates when the interspace between the plates is filled with anisotropic media. Our result shows that the anisotropy of the material between the plates can significantly affect the Casimir force, especially the direction of the force. If ignoring the anisotropy of the in-between material makes the force repulsive (attractive), by contrast taking the anisotropy into account may produce an extra attractive (repulsive) force. The physical explanation for this phenomenon is also discussed.
Propagation of shock wave fronts in anisotrope layered media
Propagation of shock waves in layered anisotropic tectonic media is associated with their fronts transformation, scattering, bifurcation and focussing. To investigate these phenomena, a technique based on joint usage of ray theory and theory of stereomechanical impact is elaborated. It is used for computer simulation of dynamical interaction of shock waves with curvilinear interfaces between anisotropic elastic media. Issues are considered which are related to the shock waves fronts surfaces bifurcations and generation of caustics connected with stress concentration and formation of zones where the stresses tend to infinity
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...
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. This process controls the fate and transport of scalars in groundwater and in chemical reactors and it is fundamental for the understanding of many reactive processes. Three-dimensional flow fields can be characterized by a complex topological structure, which may greatly influence dilution and dilution enhancement of dissolved plumes, which is quantified by the exponential of the Shannon entropy [1]. In previous works, we identified the necessary conditions to obtain helical flow fields in non-stationary anisotropic heterogeneous porous media [2, 3]. To prove our theoretical findings, we perform steady-state bench-scale experiments with a conservative tracer and we provide a model-based investigation of the results [4]. The relevance of transverse mixing enhancement for the case of reactive solute transport is computed numerically using, as metrics of mixing, the length of a reactive plume undergoing an instantaneous complete bimolecular reaction and its critical dilution index. [1] Cirpka O.A., Chiogna G., Rolle M. and A. Bellin (2015). Transverse mixing in three-dimensional non-stationary anisotropic heterogeneous porous media. Water Resources Research, 51, DOI: 10.1002/2014WR015331. [2] Chiogna G., Cirpka O.A., Rolle M. and A. Bellin (2015). Helical flow streamlines in three-dimensional nonstationary anisotropic heterogeneous porous media. Water Resources Research, 51, DOI:10.1002/2014WR015330. [3] Chiogna G., Rolle M., Bellin A. and O.A. Cirpka (2014). Helicity and flow topology in three dimensional porous media. Advances in Water Resources, 73, 134-143, DOI: 10.1016/j.advwatres.2014.06.017. [4] Ye Y., Chiogna G., Cirpka O.A., Grathwohl P., and M. Rolle (2015). Experimental evidence of helical flow in porous media. Phys. Rev. Lett., 115, 194502, DOI: 10.1103/PhysRevLett.115.194502
Heat transfers in porous media. Phase changes
Phase change phenomena in porous media, like all poly-phase processes, are complex and still only partially understood. This article deals only with the liquid-vapor phase change (vaporization-condensation) because of its particular practical importance in numerous domains. Content: 1 - Fixing of a fluid constituent inside a porous matrix; 2 - mathematical modeling; 3 - example of reference situations: phase changes at temperatures below the saturation temperature (vaporization, condensation), phase changes at temperatures above the saturation temperature (condensation, vaporization-boiling); 4 - conclusion. (J.S.)
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
Experimental compaction of anisotropic granular media
Ribière, Philippe; RICHARD, Patrick; Bideau, Daniel; Delannay, Renaud
2005-01-01
We report on experiments to measure the temporal and spatial evolution of packin g arrangements of anisotropic and weakly confined granular material, using high-resolution $\\gamma$-ray adsorption. In these experiments, the particle configurations start from an initially disordered, low-packing-fraction state and under vertical solicitation s evolve to a dense state. We find that the packing fraction evolution is slowed by the grain anisotropy but, as for spherically shaped grains, can be well...
Simulation of Tracer Transport in Porous Media: Application to Bentonites
We present a formal framework to describe tracer transport in heterogeneous media, such as porous media like bentonites. In these media, mean field approximation is not valid because there exist some geometrical constraints and the transport is anomalous. (Author)
Inversions for MT data in 2D symmetrical anisotropic media
YANG Chang-fu; LIN Chang-you; SUN Chong-chi; LI Qing-he
2005-01-01
In the paper, a 2D symmetrical anisotropic medium whose strike agrees with one of the horizontal principal axes is considered to develop a corresponding inversion technique. In the specified conditions, if we assume an equivalent conductivity anisotropy in both the vertical and dipping directions, i.e., σzz=σyy, the differential equations obtained are formally the same as that for TE and TM modes in the 2D isotropic geoelectrical media. The same inversion technique as that in the 2D isotropic media can be employed to obtain the anisotropic conductivities. It means that the TE and TM inversion results in the isotropic media can be respectively thought as the resistivities in the two principal directions of the symmetrically anisotropic media, which has offered a new approach and a theoretical guidance for interpreting magnetotelluric data. And the inversion technique developed here is used to test the magnetotelluric data in the area of Tianzhu and Yongdeng in Gansu Province, so that the crust anisotropic geoelectrical structures in this region can be obtained.
Effective Elliptic Models for Efficient Wavefield Extrapolation in Anisotropic Media
Waheed, Umair bin
2014-05-01
Wavefield extrapolation operator for elliptically anisotropic media offers significant cost reduction compared to that of transversely isotropic media (TI), especially when the medium exhibits tilt in the symmetry axis (TTI). However, elliptical anisotropy does not provide accurate focusing for TI media. Therefore, we develop effective elliptically anisotropic models that correctly capture the kinematic behavior of the TTI wavefield. Specifically, we use an iterative elliptically anisotropic eikonal solver that provides the accurate traveltimes for a TI model. The resultant coefficients of the elliptical eikonal provide the effective models. These effective models allow us to use the cheaper wavefield extrapolation operator for elliptic media to obtain approximate wavefield solutions for TTI media. Despite the fact that the effective elliptic models are obtained by kinematic matching using high-frequency asymptotic, the resulting wavefield contains most of the critical wavefield components, including the frequency dependency and caustics, if present, with reasonable accuracy. The methodology developed here offers a much better cost versus accuracy tradeoff for wavefield computations in TTI media, considering the cost prohibitive nature of the problem. We demonstrate the applicability of the proposed approach on the BP TTI model.
Simulation of penetration into porous geologic media
Vorobiev, O Y; Liu, B T; Lomov, I N; Antoun, T
2005-05-31
We present a computational study on the penetration of steel projectiles into porous geologic materials. The purpose of the study is to extend the range of applicability of a recently developed constitutive model to simulations involving projectile penetration into geologic media. The constitutive model is non-linear, thermodynamically consistent, and properly invariant under superposed rigid body motions. The equations are valid for large deformations and they are hyperelastic in the sense that the stress tensor is related to a derivative of the Helmholtz free energy. The model uses the mathematical structure of plasticity theory to capture the basic features of the mechanical response of geological materials including the effects of bulking, yielding, damage, porous compaction and loading rate on the material response. The new constitutive model has been successfully used to simulate static laboratory tests under a wide range of triaxial loading conditions, and dynamic spherical wave propagation tests in both dry and saturated geologic media.
Theory of porous media - past and present
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.)
Magnetic Fluid Flows in Porous Media
LI Ming-Jun; CHEN Liang
2011-01-01
@@ The seepage law under a magnetic field is obtained by up-scaling the flow at the pore scale of rigid porous media,and the macroscopic equivalent model is also obtained.It is proved that the macroscopic mass flow depends on the macroscopic magnetic force and the gradients of pressure and of magnetic pressure, as Zahn and Rosensweig have described in their experiments.The permeability tensor is symmetric and positive.
Unsaturated porous media flow with thermomechanical interaction
Albers, B.; Krejčí, Pavel
2016-01-01
Roč. 39, č. 9 (2016), s. 2220-2238. ISSN 0170-4214 R&D Projects: GA ČR(CZ) GA15-12227S Institutional support: RVO:67985840 Keywords : flows in porous media * problems involving hysteresis Subject RIV: BA - General Mathematics Impact factor: 0.918, year: 2014 http://onlinelibrary.wiley.com/ doi /10.1002/mma.3635/abstract
Morphology of diblock copolymers in porous media
Maniadis, Panagiotis; Tsimpanogiannis, I. N.; Kober, E.M.; Lookman, T.
2014-01-01
Roč. 112, č. 17 (2014), s. 2297-2309. ISSN 0026-8976 R&D Projects: GA MŠk(CZ) ED1.1.00/02.0068; GA MŠk(CZ) EE2.3.20.0214 Institutional support: RVO:68081723 Keywords : confinement * diblock copolymer s * porous media * self-assembly * self-consistent field theory Subject RIV: BE - Theoretical Physics Impact factor: 1.720, year: 2014
Wave propagation in fractured porous media
Tuncay, Kağan; Çorapçıoplu, M. Yavuz
1996-01-01
A theory of wave propagation in fractured porous media is presented based on the double-porosity concept. The macroscopic constitutive relations and mass and momentum balance equations are obtained by volume averaging the microscale balance and constitutive equations and assuming small deformations. In microscale, the grains are assumed to be linearly elastic and the fluids are Newtonian. Momentum transfer terms are expressed in terms of intrinsic and relative permeabilities assuming the vali...
Finite volume hydromechanical simulation in porous media
Nordbotten, Jan Martin
2014-01-01
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 equ...
The effect of rotation on the onset of convection in a horizontal anisotropic porous layer
Malashetty, M.S.; Swamy, Mahantesh [Department of Mathematics, Gulbarga University, Jnana Ganga, Gulbarga 585 106 (India)
2007-10-15
The effect of rotation and anisotropy on the onset of convection in a horizontal porous layer is investigated using a linear theory and a weak nonlinear theory. The linear theory is based on the usual normal mode technique and the nonlinear theory on the truncated Fourier series analysis. Darcy model extended to include time derivative and Coriolis terms with anisotropic permeability is used to describe the flow through porous media. A modified energy equation including the thermal anisotropy is used. The effect of rotation, mechanical and thermal anisotropy parameters and the Prandtl number on the stationary and overstable convection is discussed. It is found that the effect of mechanical anisotropy is to allow the onset of oscillatory convection instead of stationary. It is also found that the existence of overstable motions in case of rotating porous medium is not restricted to a particular range of Prandtl number as compared to the pure viscous fluid case. The steady finite amplitude analysis is performed using truncated Fourier series to find the Nusselt number. The effect of various parameters on heat transfer is investigated. (author)
OPM: The Open Porous Media Initiative
Flemisch, B.; Flornes, K. M.; Lie, K.; Rasmussen, A.
2011-12-01
The principal objective of the Open Porous Media (OPM) initiative is to develop a simulation suite that is capable of modeling industrially and scientifically relevant flow and transport processes in porous media and bridge the gap between the different application areas of porous media modeling, including reservoir mechanics, CO2 sequestration, biological systems, and product development of engineered media. The OPM initiative will provide a long-lasting, efficient, and well-maintained open-source software for flow and transport in porous media built on modern software principles. The suite is released under the GNU General Public License (GPL). Our motivation is to provide a means to unite industry and public research on simulation of flow and transport in porous media. For academic users, we seek to provide a software infrastructure that facilitates testing of new ideas on models with industry-standard complexity, while at the same time giving the researcher control over discretization and solvers. Similarly, we aim to accelerate the technology transfer from academic institutions to professional companies by making new research results available as free software of professional standard. The OPM initiative is currently supported by six research groups in Norway and Germany and funded by existing grants from public research agencies as well as from Statoil Petroleum and Total E&P Norge. However, a full-scale development of the OPM initiative requires substantially more funding and involvement of more research groups and potential end users. In this talk, we will provide an overview of the current activities in the OPM initiative. Special emphasis will be given to the demonstration of the synergies achieved by combining the strengths of individual open-source software components. In particular, a new fully implicit solver developed within the DUNE-based simulator DuMux could be enhanced by the ability to read industry-standard Eclipse input files and to run on
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
Quantum electrodynamics of inhomogeneous anisotropic media
Lopez, Adrian E.R.; Lombardo, Fernando C. [Ciudad Universitaria, Departamento de Fisica Juan Jose Giambiagi, Buenos Aires (Argentina); IFIBA CONICET-UBA, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina)
2015-02-01
In this work we calculate the closed time path generating functional for the electromagnetic (EM) field interacting with inhomogeneous anisotropic matter. For this purpose, we first find a general expression for the electromagnetic field's influence action from the interaction of the field with a composite environment consisting in the quantum polarization degrees of freedom in each point of space, at arbitrary temperatures, connected to thermal baths. Then we evaluate the generating functional for the gauge field, in the temporal gauge, by implementing the Faddeev-Popov procedure. Finally, through the point-splitting technique, we calculate closed expressions for the energy, the Poynting vector, and the Maxwell tensor in terms of the Hadamard propagator. We show that all the quantities have contributions from the field's initial conditions and also from the matter degrees of freedom. Throughout the whole work we discuss how the gauge invariance must be treated in the formalism when the EM-field is interacting with inhomogeneous anisotropic matter. We study the electrodynamics in the temporal gauge, obtaining the EM-field's equation and a residual condition. Finally we analyze the case of the EM-field in bulk material and also discuss several general implications of our results in relation with the Casimir physics in a non-equilibrium scenario. (orig.)
Finite-size anisotropy in statistically uniform porous media
Koza, Zbigniew; Khalili, Arzhang
2009-01-01
Anisotropy of the permeability tensor in statistically uniform porous media of sizes used in typical computer simulations is studied. Although such systems are assumed to be isotropic by default, we show that de facto their anisotropic permeability can give rise to significant changes of transport parameters such as permeability and tortuosity. The main parameter controlling the anisotropy is $a/L$, being the ratio of the obstacle to system size. Distribution of the angle $\\alpha$ between the external force and the volumetric fluid stream is found to be approximately normal, and the standard deviation of $\\alpha$ is found to decay with the system size as $(a/L)^{d/2}$, where $d$ is the space dimensionality. These properties can be used to estimate both anisotropy-related statistical errors in large-scale simulations and the size of the representative elementary volume.
Surface waves in ﬁbre-reinforced anisotropic elastic media
P R Sengupta; Sisir Nath
2001-08-01
The aim of this paper is to investigate surface waves in anisotropic ﬁbre-reinforced solid elastic media. First, the theory of general surface waves has been derived and applied to study the particular cases of surface waves – Rayleigh, Love and Stoneley types. The wave velocity equations are found to be in agreement with the corresponding classical result when the anisotropic elastic parameters tends to zero. It is important to note that the Rayleigh type of wave velocity in the ﬁbre-reinforced elastic medium increases to a considerable amount in comparison with the Rayleigh wave velocity in isotropic materials.
Anisotropic multiple scattering in diffuse media
Amic, E.; Luck, J. M.; Nieuwenhuizen, T.M.
1996-01-01
The multiple scattering of scalar waves in diffusive media is investigated by means of the radiative transfer equation. This approach amounts to a resummation of the ladder diagrams of the Born series; it does not rely on the diffusion approximation. Quantitative predictions are obtained, concerning various observables pertaining to optically thick slabs, such as the mean angle-resolved reflected and transmitted intensities, and the shape of the enhanced backscattering cone. Special emphasis ...
Analytical solutions of transport problems in anisotropic media
Recently, the problem of neutron transport in anisotropic media has received new attention in connection with safety studies of water reactors and design of gas-cooled systems. In situations presenting large voided regions, as the axial streaming is dominating with respect to the transverse one, the average properties of the homogenized material should physically account for such macroscopic anisotropy. Hence, it is suggested that cell calculations produce anisotropic average cross sections, e.g., axial (σA) and transverse (σT) values. Since material anisotropy is due to leakage, as a first-step approximation, the medium can be considered isotropic with respect to scattering phenomena. Transport codes are currently being adapted to include anisotropic cross sections. An important aspect of code development is the validation of algorithms by analytical benchmarks. For that purpose, the present work is devoted to the fully analytical solution of transport problems in slab geometry
Fluid flow and heat transfer in rotating porous media
Vadasz, Peter
2016-01-01
This Book concentrates the available knowledge on rotating fluid flow and heat transfer in porous media in one single reference. Dr. Vadasz develops the fundamental theory of rotating flow and heat transfer in porous media and introduces systematic classification and identification of the relevant problems. An initial distinction between rotating flows in isothermal heterogeneous porous systems and natural convection in homogeneous non-‐isothermal porous systems provides the two major classes of problems to be considered. A few examples of solutions to selected problems are presented, highlighting the significant impact of rotation on the flow in porous media.
Effective wavefield extrapolation in anisotropic media: Accounting for resolvable anisotropy
Alkhalifah, Tariq Ali
2014-04-30
Spectral methods provide artefact-free and generally dispersion-free wavefield extrapolation in anisotropic media. Their apparent weakness is in accessing the medium-inhomogeneity information in an efficient manner. This is usually handled through a velocity-weighted summation (interpolation) of representative constant-velocity extrapolated wavefields, with the number of these extrapolations controlled by the effective rank of the original mixed-domain operator or, more specifically, by the complexity of the velocity model. Conversely, with pseudo-spectral methods, because only the space derivatives are handled in the wavenumber domain, we obtain relatively efficient access to the inhomogeneity in isotropic media, but we often resort to weak approximations to handle the anisotropy efficiently. Utilizing perturbation theory, I isolate the contribution of anisotropy to the wavefield extrapolation process. This allows us to factorize as much of the inhomogeneity in the anisotropic parameters as possible out of the spectral implementation, yielding effectively a pseudo-spectral formulation. This is particularly true if the inhomogeneity of the dimensionless anisotropic parameters are mild compared with the velocity (i.e., factorized anisotropic media). I improve on the accuracy by using the Shanks transformation to incorporate a denominator in the expansion that predicts the higher-order omitted terms; thus, we deal with fewer terms for a high level of accuracy. In fact, when we use this new separation-based implementation, the anisotropy correction to the extrapolation can be applied separately as a residual operation, which provides a tool for anisotropic parameter sensitivity analysis. The accuracy of the approximation is high, as demonstrated in a complex tilted transversely isotropic model. © 2014 European Association of Geoscientists & Engineers.
Wave propagation in layered anisotropic media with application to composites
Nayfeh, AH
1995-01-01
Recent advances in the study of the dynamic behavior of layered materials in general, and laminated fibrous composites in particular, are presented in this book. The need to understand the microstructural behavior of such classes of materials has brought a new challenge to existing analytical tools. This book explores the fundamental question of how mechanical waves propagate and interact with layered anisotropic media. The chapters are organized in a logical sequence depending upon the complexity of the physical model and its mathematical treatment.
Diffusion of oriented particles in porous media
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.
Diffusion of oriented particles in porous media
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.
Anisotropic parameter inversion in VTI media using diffraction data
Waheed, Umair bin
2013-09-22
Diffracted waves contain useful information regarding the subsurface geometry and velocity. They are particularly valuable for anisotropic media as they inherently possess a wide range of dips necessary to resolve angular dependence of velocity. Using this property of diffraction data to our vantage, we develop an algorithm to invert for effective η model, assuming no prior knowledge of it. The obtained effective η model is then converted to interval η model using Dix-type inversion formula. The effectiveness of this approach is tested on the VTI Marmousi model, which yields good structural match even for a highly complex media such as the Marmousi model.
An efficient wave extrapolation method for anisotropic media with tilt
Waheed, Umair bin
2015-03-23
Wavefield extrapolation operators for elliptically anisotropic media offer significant cost reduction compared with that for the transversely isotropic case, particularly when the axis of symmetry exhibits tilt (from the vertical). However, elliptical anisotropy does not provide accurate wavefield representation or imaging for transversely isotropic media. Therefore, we propose effective elliptically anisotropic models that correctly capture the kinematic behaviour of wavefields for transversely isotropic media. Specifically, we compute source-dependent effective velocities for the elliptic medium using kinematic high-frequency representation of the transversely isotropic wavefield. The effective model allows us to use cheaper elliptic wave extrapolation operators. Despite the fact that the effective models are obtained by matching kinematics using high-frequency asymptotic, the resulting wavefield contains most of the critical wavefield components, including frequency dependency and caustics, if present, with reasonable accuracy. The methodology developed here offers a much better cost versus accuracy trade-off for wavefield computations in transversely isotropic media, particularly for media of low to moderate complexity. In addition, the wavefield solution is free from shear-wave artefacts as opposed to the conventional finite-difference-based transversely isotropic wave extrapolation scheme. We demonstrate these assertions through numerical tests on synthetic tilted transversely isotropic models.
Fluid flow in porous media with rough pore-solid interface
Ghanbarian, Behzad; Hunt, Allen G.; Daigle, Hugh
2016-03-01
Quantifying fluid flow through porous media hinges on the description of permeability, a property of considerable importance in many fields ranging from oil and gas exploration to hydrology. A common building block for modeling porous media permeability is consideration of fluid flow through tubes with circular cross section described by Poiseuille's law in which flow discharge is proportional to the fourth power of the tube's radius. In most natural porous media, pores are neither cylindrical nor smooth; they often have an irregular cross section and rough surfaces. This study presents a theoretical scaling of Poiseuille's approximation for flow in pores with irregular rough cross section quantified by a surface fractal dimension Ds2. The flow rate is a function of the average pore radius to the power 2(3-Ds2) instead of 4 in the original Poiseuille's law. Values of Ds2 range from 1 to 2, hence, the power in the modified Poiseuille's approximation varies between 4 and 2, indicating that flow rate decreases as pore surface roughness (and surface fractal dimension Ds2) increases. We also proposed pore length-radius relations for isotropic and anisotropic fractal porous media. The new theoretical derivations are compared with standard approximations and with experimental values of relative permeability. The new approach results in substantially improved prediction of relative permeability of natural porous media relative to the original Poiseuille equation.
Dynamics of clogging in drying porous media
Kaplan, C. Nadir; Mahadevan, L.
2014-11-01
Drying in porous media pervades a range of phenomena from brine evaporation arrested in porous bricks, causing efflorescence, i.e. salt aggregation on the surface where vapor leaves the medium, to clogging of reservoir rocks via salt precipitation when carbon dioxide is injected for geological storage. During the process of drying, the permeability and porosity of the medium may change due to the solute accumulation as a function of the particle concentration, in turn affecting the evaporation rate and the dynamics of the fluid flow imposed by it. To examine the dynamics of these coupled quantities, we develop a multiphase model of the particulate flow of a saline suspension in a porous medium, induced by evaporation. We further provide dimensional arguments as to how the salt concentration and the resulting change in permeability determine the transition between efflorescence and salt precipitation in the bulk. This research was supported by the Air Force Office of Scientific Research (AFOSR) under Award FA9550-09-1-0669-DOD35CAP and the Kavli Institute for Bionano Science and Technology at Harvard University.
Resonant electromagnetic scattering in anisotropic layered media
The resonant excitation of an electromagnetic guided mode of a slab structure by exterior radiation results in anomalous scattering behavior, including sharp energy-transmission anomalies and field amplification around the frequency of the slab mode. In the case of a periodically layered ambient medium, anisotropy serves to couple the slab mode to radiation. Exact expressions for scattering phenomena are proved by analyzing a pole of the full scattering matrix as it moves off the real frequency axis into the lower half complex plane under a detuning of the wavevector parallel to the slab. The real pole is the frequency of a perfect (infinite Q) guided mode, which becomes lossy as the frequency gains an imaginary part. This work extends results of Shipman and Venakides to evanescent source fields and two-dimensional parallel wavevector and demonstrates by example how the latter allows one to control independently the width and central frequency of a resonance by varying the angle of incidence of the source field. The analysis relies on two nondegeneracy conditions of the complex dispersion relation for slab modes (relating poles of the scattering matrix to wavevector), which were assumed in previous works and are proved in this work for layered media. One of them asserts that the dispersion relation near the wavevector κ and frequency ω of a perfect guided mode is the zero set of a simple eigenvalue ℓ(κ, ω), and the other relates ∂ℓ/∂ω to the total energy of the mode, thereby implying that this derivative is nonzero
Review of enhanced vapor diffusion in porous media
Vapor diffusion in porous media in the presence of its own liquid has often been treated similar to gas diffusion. The gas diffusion rate in porous media is much lower than in free space due to the presence of the porous medium and any liquid present. However, enhanced vapor diffusion has also been postulated such that the diffusion rate may approach free-space values. Existing data and models for enhanced vapor diffusion, including those in TOUGH2, are reviewed in this paper
Upscaling diffusion waves in porous media
Valdés-Parada, Francisco J.; Álvarez Ramírez, José; Ochoa-Tapia, J. Alberto
2016-04-01
The aim of this work is to derive the effective-medium equations and to estimate the related effective diffusivities for diffusion waves in porous media. Effective diffusivities are estimated within the framework of the volume averaging method, where they are obtained from the solution of the associated closure problems in 2D and 3D periodic unit cells. The results showed that the transport of diffusion waves are governed by the diffusion and co-diffusion mechanisms of harmonic waves. In addition, numerical results showed that the effective diffusivities increase with frequency, while the effective co-diffusivities display a resonance-like behavior. Our results also indicate that geometry plays a more significant effect over the predictions of the co-diffusion coefficient at moderate frequencies and it mainly influences the predictions of the direct diffusivity at low frequencies (i . e .,ω∗ ≪ 1).
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.
On a singular incompressible porous media equation
Friedlander, Susan; Sun, Weiran; Vicol, Vlad
2012-01-01
In this paper we study a singularly modified version of the incompressible porous media equation. We investigate the implications for the local well-posedness of the equations by modifying, with a fractional derivative, the constitutive relation between the scalar density and the convecting divergence free velocity vector. Our analysis is motivated by recent work \\cite{CCCGW} where it is shown that for the surface quasi-geostrophic equation such a singular modification of the constitutive law for the velocity, quite surprisingly still yields a locally well-posed problem. In contrast, for the singular active scalar equation discussed in this paper, local well-posedness does not hold for smooth solutions, but it does hold for certain weak solutions.
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...
Mechanics of fluids in porous media
Bear, Jacob; Corapcioglu, M. Yavuz
Transport of quantities such as mass component of a phase and/or heat occurs in fields as diversified as petroleum reservoir engineering, groundwater hydraulics, soil mechanics, industrial filtration, water purification, wastewater treatment, soil drainage and irrigation, and geothermal energy production. In all these areas, scientists, engineers, and planners make use of mathematical models; these models describe the relevant transport processes that occur within controlled porous medium domains and enable forecasting of the future behavior of these domains in response to planned activities. The mathematical models, in turn, are based on the understanding of phenomena, often within the void space, and on theories that relate these phenomena to measurable quantities.Because of the pressing needs in areas of practical interest such as the development of groundwater energy storage and geothermal energy production, a vast amount of research in all these fields has contributed, especially in the last two decades, to our understanding and ability to describe transport phenomena in porous media. In recent years these research efforts have been significantly accelerated, attracting scientists from many disciplines. The practical needs of solving boundary value problems in heterogeneous domains, irregular boundaries, coupled phenomena and multiple dependent variables led to the development of a variety of powerful numerical techniques. The realization that fields are highly heterogeneous and that the degree of heterogeneity depends on the scale of the problem led to the introduction of stochastic concepts as an additional tool for the description of phenomena.
Sophia Haussener; Aldo Steinfeld
2012-01-01
High-resolution X-ray computed tomography is employed to obtain the exact 3D geometrical configuration of porous anisotropic ceria applied in solar-driven thermochemical cycles for splitting H2O and CO2. The tomography data are, in turn, used in direct pore-level numerical simulations for determining the morphological and effective heat/mass transport properties of porous ceria, namely: porosity, specific surface area, pore size distribution, extinction coefficient, thermal conductivity, conv...
Gaussian beam diffraction in weakly anisotropic inhomogeneous media
Combination of quasi-isotropic approximation (QIA) of geometric optics with paraxial complex geometric optics (PCGO) is suggested, which allows describing both diffraction and polarization evolution of Gaussian electromagnetic beams in weakly anisotropic inhomogeneous media. Combination QIA/PCGO reduces Maxwell equations to the system of the ordinary differential equations of the first order and radically simplifies solution of various problems, related to microwave plasma diagnostics, including plasma polarimetry, interferometry and refractometry in thermonuclear reactors. Efficiency of the method is demonstrated by the example of electromagnetic beam diffraction in a linear layer of magnetized plasma with parameters, modeling tokamak plasma in the project ITER.
Gaussian beam diffraction in weakly anisotropic inhomogeneous media
Kravtsov, Yu. A.; Berczynski, P.; Bieg, B.
2009-08-01
Combination of quasi-isotropic approximation (QIA) of geometric optics with paraxial complex geometric optics (PCGO) is suggested, which allows describing both diffraction and polarization evolution of Gaussian electromagnetic beams in weakly anisotropic inhomogeneous media. Combination QIA/PCGO reduces Maxwell equations to the system of the ordinary differential equations of the first order and radically simplifies solution of various problems, related to microwave plasma diagnostics, including plasma polarimetry, interferometry and refractometry in thermonuclear reactors. Efficiency of the method is demonstrated by the example of electromagnetic beam diffraction in a linear layer of magnetized plasma with parameters, modeling tokamak plasma in the project ITER.
Gaussian beam diffraction in weakly anisotropic inhomogeneous media
Kravtsov, Yu.A., E-mail: kravtsov@am.szczecin.p [Institute of Physics, Maritime University of Szczecin, Szczecin 70-500 (Poland); Space Research Institute, Russian Academy of Science, Moscow 117 997 (Russian Federation); Berczynski, P., E-mail: pawel.berczynski@ps.p [Institute of Physics, West Pomeranian University of Technology, Szczecin 70-310 (Poland); Bieg, B., E-mail: b.bieg@am.szczecin.p [Institute of Physics, Maritime University of Szczecin, Szczecin 70-500 (Poland)
2009-08-10
Combination of quasi-isotropic approximation (QIA) of geometric optics with paraxial complex geometric optics (PCGO) is suggested, which allows describing both diffraction and polarization evolution of Gaussian electromagnetic beams in weakly anisotropic inhomogeneous media. Combination QIA/PCGO reduces Maxwell equations to the system of the ordinary differential equations of the first order and radically simplifies solution of various problems, related to microwave plasma diagnostics, including plasma polarimetry, interferometry and refractometry in thermonuclear reactors. Efficiency of the method is demonstrated by the example of electromagnetic beam diffraction in a linear layer of magnetized plasma with parameters, modeling tokamak plasma in the project ITER.
Polarization ray tracing in anisotropic optically active media. I. Algorithms
Procedures for performing polarization ray tracing through birefringent media are presented in a form compatible with the standard methods of geometrical ray tracing. The birefringent materials treated include the following: anisotropic optically active materials such as quartz, non-optically active uniaxial materials such as calcite, and isotropic optically active materials such as mercury sulfide and organic liquids. Refraction and reflection algorithms are presented that compute both ray directions and wave directions. Methods for computing polarization modes, refractive indices, optical path lengths, and Fresnel transmission and reflection coefficients are also specified. A numerical example of these algorithms is given for analyzing the field of view of a quartz rotator. 37 refs., 3 figs
Minor Losses During Air Flow into Granular Porous Media
Poulsen, Tjalfe; Minelgaite, Greta; Bentzen, Thomas Ruby;
2013-01-01
Pressure gradients during uniform fluid flow in porous media are traditionally assumed to be linear. Thus pressure loss across a sample of porous medium is assumed directly proportional to the thickness of the sample. In this study, measurements of pressure gradients inside coarse granular (2 – 18...... mm particle size) porous media during steady gas flow were carried out. The results showed that pressure variation with distance in the porous media were nonlinear near the inlet (where pressure gradients were higher) but became linear at greater distances (with a lower gradient). This indicates that...... pressure loss in porous media consists of two components: (1) a linear pressure gradient and (2) an initial pressure loss near the inlet. This initial pressure loss is also known from hydraulics in tubes as a minor loss and is associated with abrupt changes in the flow field such as narrowings and bends...
A Fractal Model for Capillary Pressure of Porous Media
Boqi Xiao
2013-06-01
Full Text Available Capillary pressure is a basic parameter in the study of the behavior of porous media containing two or more immiscible fluid phases. In this study, the capillary pressure of porous media is predicted based on based on fractal property of pore in porous media. The formula of calculating the capillary pressure of porous media is given. The capillary pressure of porous media is expressed as a function of porosity, fractal dimension of pore and saturation. Based on the parametric effect analysis, we conclude that the capillary pressure of porous media is negatively correlated with the porosity and saturation. Besides, it is shown that the capillary pressure of unsaturated porous media decreases with the increase of saturation. No additional empirical constant is introduced. This model contains less empirical constants than the conventional correlations. The model predictions are compared with the existing experimental data and good agreement between the model predictions and experimental data is found. The validity of the present fractal model is thus verified.
Nanoparticle tracers in calcium carbonate porous media
Li, Yan Vivian
2014-07-15
Tracers are perhaps the most direct way of diagnosing subsurface fluid flow pathways for ground water decontamination and for natural gas and oil production. Nanoparticle tracers could be particularly effective because they do not diffuse away from the fractures or channels where flow occurs and thus take much less time to travel between two points. In combination with a chemical tracer they can measure the degree of flow concentration. A prerequisite for tracer applications is that the particles are not retained in the porous media as the result of aggregation or sticking to mineral surfaces. By screening eight nanoparticles (3-100 nm in diameter) for retention when passed through calcium carbonate packed laboratory columns in artificial oil field brine solutions of variable ionic strength we show that the nanoparticles with the least retention are 3 nm in diameter, nearly uncharged, and decorated with highly hydrophilic polymeric ligands. The details of these column experiments and the tri-modal distribution of zeta potential of the calcite sand particles in the brine used in our tests suggests that parts of the calcite surface have positive zeta potential and the retention of negatively charged nanoparticles occurs at these sites. Only neutral nanoparticles are immune to at least some retention. © 2014 Springer Science+Business Media.
Experimental investigation of transverse mixing in porous media under helical flow conditions
Ye, Yu; Chiogna, Gabriele; Cirpka, Olaf A.; Grathwohl, Peter; Rolle, Massimo
2016-07-01
Plume dilution and transverse mixing can be considerably enhanced by helical flow occurring in three-dimensional heterogeneous anisotropic porous media. In this study, we perform tracer experiments in a fully three-dimensional flow-through chamber to investigate the effects of helical flow on plume spiraling and deformation, as well as on its dilution. Porous media were packed in angled stripes of materials with different grain sizes to create blocks with macroscopically anisotropic hydraulic conductivity, which caused helical flows. Steady-state transport experiments were carried out by continuously injecting dye tracers at different inlet ports. High-resolution measurements of concentration and flow rates were performed at 49 outlet ports. These measurements allowed quantifying the spreading and dilution of the solute plumes at the outlet cross section. Direct evidence of plume spiraling and visual proof of helical flow was obtained by freezing and slicing the porous media at different cross sections and observing the dye-tracer distribution. We simulated flow and transport to interpret our experimental observations and investigate the effects of helical flow on mixing-controlled reactive transport. The simulation results were evaluated using metrics of reactive mixing such as the critical dilution index and the length of continuously injected steady-state plumes. The results show considerable reaction enhancement, quantified by the remarkable decrease of reactive plume lengths (up to four times) in helical flows compared to analogous scenarios in uniform flows.
Chiogna, Gabriele; Herrera, Paulo
2015-04-01
Several studies have demonstrated how plume deformation induced by flow heterogeneity in porous media can enhance mixing of reactants. This enhancement can have important impact on mixing controlled reactions such a biodegradation of plumes of organic compounds. On the other hand, recent studies have indicated the possibility of observing complex flow topology on groundwater flow that occurs in anisotropic yet homogenous porous media. Moreover, it has been demonstrated that those complex flow topologies can also enhance solute mixing. We study the effect of medium anisotropy on reactive solute transport for the case of a chemical reactor composed of two homogeneous anisotropic layers. We simulate different injection strategies for different chemical reactions that involve two reactants. We demonstrate the effect of the medium anisotropy by analyzing the results of the simulations and identify best strategies for the operation and design of the system to maximize reaction rates. These findings could have potential application in the design of new remediation systems for contaminated groundwater, chemical reactors and other engineering problems that involve flow through porous media.
Propagation of plane waves in poroviscoelastic anisotropic media
A.K.Vashishth,M.D.Sharma
2008-01-01
This study discusses wave propagation in perhaps the most general model of a poroelastic medium.The medium is considered as a viscoelastic,anisotropic and porous solid frame such that its pores of anisotropic permeability are filled with a viscous fluid.The anisotropy considered is of general type,and the attenuating waves in the medium are treated as the inhomogeneous waves.The complex slowness vector is resolved to define the phase velocity,homogeneous attenuation,inhomogeneous attenuation,and angle of attenuation for each of the four attenuating waves in the medium.A non-dimensional parameter measures the deviation of an inhomogeneous wave from its homogeneous version.An numerical model of a North-Sea sandstone is used to analyze the effects of the propagation direction,inhomogeneity parameter,frequency regime,anisotropy symmetry,anelasticity of the frame,and viscosity of the pore-fluid on the propagation characteristics of waves in such a medium.
Foam Transport in Porous Media - A Review
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
Elastodynamic analysis of anisotropic liquid-saturated porous medium due to mechanical sources
无
2007-01-01
Elastodynamlc analysis of an anisotropic liquid-saturated porous medium is made to study a deformation problem of a transversely isotropic liquid-saturated porous medium due to mechanical sources. Certain physical problems are of the nature, in which the deformation takes place only in one direction, e.g., the problem relating to deformed structures and columns. In soil mechanics, an assumption of only vertical subsidence is often invoked and this leads to the one dimensional model of poroelasticity. By considering a model of one-dimensional deformation of the anisotropic liquid-saturated porous medium, variations in disturbances are observed with reference to time and distance.The distributions of displacements and stresses are affected due to the anisotropy of the medium, and also due to the type of sources causing the disturbances.
Particle tracing techniques for flows in porous media
Fox, R.L.; Eaton, R.R.; Krueger, D.A.
1978-01-01
The prediction of flow in porous media has been of both current and historical interest. Recent developments, for example, in the in-situ gasification of coal, the removal of hydrocarbons from oil shale, and the extraction of oil and gas require an in-depth understanding of flow in porous geologic media. Existing procedures for investigating these problems require more empirical input than should be necessary if the porous media were adequately described by the computational scheme. The purpose of this paper is to develop a particle tracing scheme for calculating flows in porous media which will reduce the number of required empirical properties, such as permeability, and have application to more general flow regimes such as non-Darcy flows.
刘洋; 魏修成
2003-01-01
Based on Biot theory of two-phase anisotropic media and Hamilton theory about dynamic problem, finite elementequations of elastic wave propagation in two-phase anisotropic media are derived in this paper. Numerical solutionof finite element equations is given. Finally, properties of elastic wave propagation are observed and analyzedthrough FEM modeling.
Numerical methods for flow and transport in porous media
Vu Do, Huy Cuong
2014-01-01
This thesis bears on the modelling of groundwater flow and transport in porous media; we perform numerical simulations by means of finite volume methods and prove convergence results. In Chapter 1, we first apply a semi-implicit standard finite volume method and then the generalized finite volume method SUSHI for the numerical simulation of density driven flows in porous media; we solve a nonlinear convection-diffusion parabolic equation for the concentration coupled with an elliptic equation...
A Particle Resistance Model for Flow through Porous Media
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. (fundamental areas of phenomenology (including applications))
A Particle Resistance Model for Flow through Porous Media
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.
Filtration gases burning at profiles symmetry of porous media temperature
The mathematical model of filtration gases burning at profiles symmetry in temperature of inert porous media is defined. This mathematic model allows to find the conditions of symmetric profiles of concentration of components of the gas mixture and the temperature of porous media and, in particular, calculations of characteristics of burning wave depending on Lewis number and other parameters. The diagrams of these dependences are analyzed. (author)
Characterization of an impinging jet into porous media
Wang, Cong; Alhani, Salwan; Gharib, Morteza
2015-11-01
In this work, characteristic behavior of a liquid jet into porous hydrophobic / hydrophilic particle media is investigated. In porous media, the capillary effect becomes significant, especially when the jet Reynolds Number is low. To analyze the cavity creation phenomena, the effect of jet's diameter, speed and acceleration as well as particles' size are carefully studied. Such knowledge of fluid behavior will provide guidance for medicine injection process. This work is supported by Caltech GALCIT STEM program.
Discrete Morse flow for Ricci flow and Porous Media equation
Ma, Li
2012-01-01
In this paper, we study the discrete Morse flow for the Ricci flow on football, which is the 2-sphere with removed north and south poles and with the metric $g_0$ of constant scalar curvature, and and for Porous media equation on a bounded regular domain in the plane. We show that with a suitable assumption about $g(0)$ we have a weak approximated discrete Morse flow for the approximated Ricci flow and Porous media equation on any time intervals.
Mass Transfer and Porous Media (MTPM)
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
Mass Transfer and Porous Media (MTPM)
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
Impact of space-time mesh adaptation on solute transport modeling in porous media
Esfandiar, Bahman; Porta, Giovanni; Perotto, Simona; Guadagnini, Alberto
2015-02-01
We implement a space-time grid adaptation procedure to efficiently improve the accuracy of numerical simulations of solute transport in porous media in the context of model parameter estimation. We focus on the Advection Dispersion Equation (ADE) for the interpretation of nonreactive transport experiments in laboratory-scale heterogeneous porous media. When compared to a numerical approximation based on a fixed space-time discretization, our approach is grounded on a joint automatic selection of the spatial grid and the time step to capture the main (space-time) system dynamics. Spatial mesh adaptation is driven by an anisotropic recovery-based error estimator which enables us to properly select the size, shape, and orientation of the mesh elements. Adaptation of the time step is performed through an ad hoc local reconstruction of the temporal derivative of the solution via a recovery-based approach. The impact of the proposed adaptation strategy on the ability to provide reliable estimates of the key parameters of an ADE model is assessed on the basis of experimental solute breakthrough data measured following tracer injection in a nonuniform porous system. Model calibration is performed in a Maximum Likelihood (ML) framework upon relying on the representation of the ADE solution through a generalized Polynomial Chaos Expansion (gPCE). Our results show that the proposed anisotropic space-time grid adaptation leads to ML parameter estimates and to model results of markedly improved quality when compared to classical inversion approaches based on a uniform space-time discretization.
Capillary thermomechanics in serially porous media, with implications for randomly porous media
Miller, Robert D.
Visions of a single mobile substance present as two rival phases more or less cleanly segregated by capillarity between rival strata of a serially porous medium (a ``discontinuum'') imply explicit testable equations for externally measured capillary thermo-osmotic pressures and capillary thermo-osmosis, with implications for thermomechanical consolidation, dilation, and cracking. Underlying equations assume fluid phases governed by the laws of surface tension and viscous flow, moderated by an appropriate form of the Clapeyron equation. Derived phenomenological coefficients in macroscopic equations for steady coupled transports of mass and heat include only path-length-weighted fluid and heat conductances for rival domains and the heat of phase transformation. Expressions emphasize the phase-specific nature of Onsager's reciprocity principle and apply to serial media held within permeameters set up for measuring either ``isothermal'' or ``adiabatic'' mass transport or held within sealed containers intended for measurements of ``thermal conductivities.'' Results clarify unmet challenges facing modelers of similar processes and attributes in randomly porous media.
The Kinematics and Field Equations for Porous Media
无
1999-01-01
With a porous medium regarded as an immiscible mixture of multiphase and each phase as a miscible mixture of multi-constituent, a systematical research on the kinematics and field equations for porous media is carried out from the point of view of mixture theory. It is shown that the motion of each phase is the mathematical average of the motions of all constituents in the phase, and that the motion of porous media may be described as the motion of the skeleton and the relative motion of each phase with respect to the skeleton. The influence of mass exchange between different constituents in each phase and the influence of mass exchange of same constituent between different phases in porous media are considered in field equations which are self-consistent in theory. All the field equations in the references are special cases of the equations proposed in this paper.
Experimental investigation of transverse mixing in porous media under helical flow conditions
Ye, Yu; Chiogna, Gabriele; Cirpka, Olaf A.;
2016-01-01
transport. The simulation results were evaluated using metrics of reactive mixing such as the critical dilution index and the length of continuously injected steady-state plumes. The results show considerable reaction enhancement, quantified by the remarkable decrease of reactive plume lengths (up to four...... spiraling and deformation, as well as on its dilution. Porous media were packed in angled stripes of materials with different grain sizes to create blocks with macroscopically anisotropic hydraulic conductivity, which caused helical flows. Steady-state transport experiments were carried out by continuously...... times) in helical flows compared to analogous scenarios in uniform flows....
Porous media heat transfer for injection molding
Beer, Neil Reginald
2016-05-31
The cooling of injection molded plastic is targeted. Coolant flows into a porous medium disposed within an injection molding component via a porous medium inlet. The porous medium is thermally coupled to a mold cavity configured to receive injected liquid plastic. The porous medium beneficially allows for an increased rate of heat transfer from the injected liquid plastic to the coolant and provides additional structural support over a hollow cooling well. When the temperature of the injected liquid plastic falls below a solidifying temperature threshold, the molded component is ejected and collected.
Wang, Ding; Wang, Liji; Ding, Pinbo
2016-08-01
An illustrative theory is developed to analyze the acoustic wave propagation characteristics in the porous media with anisotropic permeability. We focus here on the role of fracture permeability in the unconsolidated porous media, looking in particular at the compressional P-wave phase velocity and attenuation. Two fluid pressure equilibration characteristic time factors are defined, which are corresponding to crack-pore system and crack-crack system, respectively. The theoretical results show that the dispersion and attenuation characteristics of acoustic wave are affected by porous matrix and fracture permeability simultaneously. Due to the fluid exchange that takes place between fractures and pores dominantly, the influence of the fracture connectivity on the wave propagation is very weak when the permeability of background medium is relatively high. However, correlation between wave propagation and fracture permeability is significant when the matrix permeability at a low level. A second attenuation peak occurs for the fluid flow within fractures in high-frequency region for more and more higher fracture permeability. The exact analytical solutions that are compared to numerical forward modeling of wave propagation in fractured media allow us to verify the correctness of the new model. If there exists another approach for obtaining the connectivity information of background media, we can use this model to analyze qualitatively the permeability of fractures or afford an indicator of in-situ permeability changes in a oil reservoir, for example, fracturing operations. PMID:27259119
Nuclear magnetic relaxation of liquids in porous media
Nuclear magnetic relaxation is useful for probing physical and chemical properties of liquids in porous media. Examples are given on high surface area porous materials including calibrated porous silica glasses, granular packings, plaster pastes, cement-based materials and natural porous materials, such as sandstone and carbonate rocks. Here, we outline our recent NMR relaxation work for these very different porous materials. For instance, low field NMR relaxation of water in calibrated granular packings leads to striking different pore-size dependencies of the relaxation times T1 and T2 when changing the amount of surface paramagnetic impurities. This allows separation of the diffusion and surface limited regimes of relaxation in these macroporous media. The magnetic field dependence of the nuclear spin-lattice relaxation rate 1/T1(ω0) is also a rich source of dynamical information for characterizing the molecular dynamics of liquids in porous media. This allows a continuous characterization of the evolving microstructure of various cementitious materials. Our recent applications of two-dimensional (2D) T1-T2 and T2-z-store-T2 correlation experiments have evidenced the water exchange in connected micropores of cement pastes. The direct probing of water adsorption time on a solid surface gives access to an original characterization of the surface nano-wettability of porous plaster pastes. We show that such a parameter depends directly on the physical chemistry of the pore surfaces. Lastly, we outline our recent measurements of wettability in oil/brine/reservoir carbonate rocks.
Asymptotics of the filtration problem for suspension in porous media
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.
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.
Tritium transport in lithium ceramics porous media
Tam, S.W.; Ambrose, V.
1991-12-31
A random network model has been utilized to analyze the problem of tritium percolation through porous Li ceramic breeders. Local transport in each pore channel is described by a set of convection-diffusion-reaction equations. Long range transport is described by a matrix technique. The heterogeneous structure of the porous medium is accounted for via Monte Carlo methods. The model was then applied to an analysis of the relative contribution of diffusion and convective flow to tritium transport in porous lithium ceramics. 15 refs., 4 figs.
Tritium transport in lithium ceramics porous media
Tam, S.W.; Ambrose, V.
1991-01-01
A random network model has been utilized to analyze the problem of tritium percolation through porous Li ceramic breeders. Local transport in each pore channel is described by a set of convection-diffusion-reaction equations. Long range transport is described by a matrix technique. The heterogeneous structure of the porous medium is accounted for via Monte Carlo methods. The model was then applied to an analysis of the relative contribution of diffusion and convective flow to tritium transport in porous lithium ceramics. 15 refs., 4 figs.
Tritium transport in lithium ceramics porous media
A random network model has been utilized to analyze the problem of tritium percolation through porous Li ceramic breeders. Local transport in each pore channel is described by a set of convection-diffusion-reaction equations. Long range transport is described by a matrix technique. The heterogeneous structure of the porous medium is accounted for via Monte Carlo methods. The model was then applied to an analysis of the relative contribution of diffusion and convective flow to tritium transport in porous lithium ceramics. 15 refs., 4 figs
Reptation of a semiflexible polymer through porous media
Nam, Gimoon; Johner, Albert; Lee, Nam-Kyung
2010-07-01
We study the motion of a single stiff semiflexible filament of length S through an array of topological obstacles. By means of scaling arguments and two-dimensional computer simulations, we show that the stiff chain kinetics follows the reptation picture, albeit with kinetic exponents (for the central monomer) different from those for flexible chain reptation. At early times when topological constraints are irrelevant, the chain kinetics is the anisotropic dynamics of a free filament. After the entanglement time τe transverse modes are equilibrated under the topological constraints, but the chain is not yet correlated over its whole length. During the relaxation of longitudinal modes, both the longitudinal fluctuation of the central monomer and the longitudinal correlation length grow as ˜√t . After time τr˜S2 chain ends are correlated, the chain then diffuses globally along the tube and tube renewal takes place. In the reptation regime, the longitudinal fluctuation of the central monomer grows like ˜t1. The opening of the intermediate ˜√t regime, absent for a free filament, is a signature of the reptation process. Although the underlying physics is quite different, the intermediate regime is reminiscent of the internal Rouse mode relaxation found for reptating flexible chains. In most cases asymptotic power laws from scaling could be complemented by prefactors calculated analytically. Our results are supported by two-dimensional Langevin simulations with fixed obstacles via evaluation of the mean squared displacement of the central monomer. The scaling theory can be extended to long semiflexible polymers adopting random-walk equilibrium configurations and should also apply in three dimensions for porous media with pore diameter smaller than the persistence length of the filament.
Acoustically driven filtration of particulate suspensions in porous media
Gupta, Sanjay
1997-12-01
A novel method of filtration of liquid suspensions containing micron to millimeter size particles has been developed. A resonant ultrasonic field, applied across a highly porous medium, has been used to trap fine particles inside the large pores (relative to the particle size) of the medium. Three types of porous media, unconsolidated bed of 3 mm glass beads, consolidated open pore aluminum mesh, and reticulated polyester polyurethane foam were investigated as the test media. Reasonable filtration efficiencies were achieved for model aqueous suspensions of 325 mesh polystyrene particles in all three porous media. The expected trends of filtration performance with respect to suspension flow rate, its concentration, and the acoustic field intensity were confirmed. The Filtration phenomena was found to be limited by non-physical saturation of porous media. At saturation, the particles collected inside the media were found to exhibit macroscopic vibrations which allows them to escape with the carrier fluid. The highly porous POLY foam (95% porosity) was found to be the best media for suspension studied in terms of the duration of particle retention and percentage filtration efficiencies. The aluminum mesh performed slightly poorer. The unconsolidated porous media collected the least amount of solids. A simple theoretical development based on particle trajectory around an infinitely long cylindrical fiber, in the presence of acoustic field, has been initiated. In principle, the new filtration method is similar to high gravity magnetic separation but the acoustic method has a wider scope due to inherent acoustic contrast present in most suspensions. The low pressure drop, ease of operation, amenability to large scale operation and reasonable filtration efficiency make the new method highly attractive and suitable for practical applications.
Preliminary study on ECT imaging of flames in porous media
This preliminary study for the first time investigated the feasibility of tomographic monitoring of flames in porous media, in which the cross-sectional profiles of flames inside a porous medium were imaged by electrical capacitance tomography (ECT). The relationship between the flame ionization and relative permittivity was established as the basis for ECT imaging of flames. Image reconstruction algorithms were discussed and an online iterative method OIOR was selected for image reconstruction. Experimental measurements were carried out and images of the flames were reconstructed. The shape, size and motion of the flames in a porous block were clearly monitored. Also the images correspond clearly to the variations of the combustion intensity. The feasibility of ECT monitoring of flames in porous media is proven by this study
Laha, P.; Nazarkin, M. Y.; Volkova, A. V.; Simunin, M. M.; Terryn, H.; Gavrilov, S. A.; Ustarroz, J.
2015-03-01
ZnO films have increasingly been in the spotlight due to their largely varied electro-physical and optical properties. For several applications, porous anisotropic nanocrystalline layers are especially interesting. To study the growth kinetics of such films during different fabrication processes, a powerful non-destructive in-situ technique is required. In this work, both ex-situ and in-situ spectroscopic ellipsometry are used along with advanced modelling techniques that are able to take both the anisotropy and the porosity of the films into account. Scanning electron microscopy, along with nitrogen absorption methods for measuring porosity, validated the ellipsometric data and proposed model. The film, grown by chemical bath deposition, was monitored from around 700 to 1800 nm in thickness. This same principle can now be used to monitor any other porous and/or anisotropic structure in an effective in-situ manner, e.g., growth of porous anodic aluminium oxides, nano-porous silica films, etc.
ZnO films have increasingly been in the spotlight due to their largely varied electro-physical and optical properties. For several applications, porous anisotropic nanocrystalline layers are especially interesting. To study the growth kinetics of such films during different fabrication processes, a powerful non-destructive in-situ technique is required. In this work, both ex-situ and in-situ spectroscopic ellipsometry are used along with advanced modelling techniques that are able to take both the anisotropy and the porosity of the films into account. Scanning electron microscopy, along with nitrogen absorption methods for measuring porosity, validated the ellipsometric data and proposed model. The film, grown by chemical bath deposition, was monitored from around 700 to 1800 nm in thickness. This same principle can now be used to monitor any other porous and/or anisotropic structure in an effective in-situ manner, e.g., growth of porous anodic aluminium oxides, nano-porous silica films, etc
Laha, P., E-mail: plaha@vub.ac.be; Terryn, H.; Ustarroz, J., E-mail: justarro@vub.ac.be [Research Group Electrochemical and Surface Engineering (SURF), Vrije Universiteit Brussel, Pleinlaan 2, 1050 Elsene, Brussels (Belgium); Nazarkin, M. Y., E-mail: mikleo@mail.ru; Gavrilov, S. A. [Department of Materials of Functional Electronics (MFE), National Research University of Electronic Technology, Bld. 5, Pas. 4806, Zelenograd, Moscow 124498 (Russian Federation); Volkova, A. V.; Simunin, M. M. [Department of Quantum Physics and Nanoelectronics (QPN), National Research University of Electronic Technology, Bld. 5, Pas. 4806, Zelenograd, Moscow 124498 (Russian Federation)
2015-03-09
ZnO films have increasingly been in the spotlight due to their largely varied electro-physical and optical properties. For several applications, porous anisotropic nanocrystalline layers are especially interesting. To study the growth kinetics of such films during different fabrication processes, a powerful non-destructive in-situ technique is required. In this work, both ex-situ and in-situ spectroscopic ellipsometry are used along with advanced modelling techniques that are able to take both the anisotropy and the porosity of the films into account. Scanning electron microscopy, along with nitrogen absorption methods for measuring porosity, validated the ellipsometric data and proposed model. The film, grown by chemical bath deposition, was monitored from around 700 to 1800 nm in thickness. This same principle can now be used to monitor any other porous and/or anisotropic structure in an effective in-situ manner, e.g., growth of porous anodic aluminium oxides, nano-porous silica films, etc.
Van der Waals interaction torque and force between dielectrically anisotropic layered media
Lu, Bing-Sui
2016-01-01
We analyse the van der Waals interaction for a pair of dielectrically anisotropic plane-layered media interacting across a dielectrically isotropic medium. We investigate the van der Waals torque and force for the following cases: (i) a pair of single anisotropic layers, (ii) a single anisotropic layer interacting with a multilayered slab consisting of alternating anisotropic and isotropic layers, and (iii) a pair of multilayered slabs each consisting of alternating anisotropic and isotropic layers, looking at the cases where the optical axes lie parallel and/or perpendicular to the plane of the layers. For the first case, the optical axes of the oppositely facing anisotropic layers of the two interacting slabs generally have an angular mismatch, and within each multilayered slab the optical axes may either be the same, or undergo constant angular increments across the anisotropic layers. In particular, we examine how the behaviors of the van der Waals torque and force can be "tuned" by adjusting the layer th...
Advanced modeling in porous media: Use of DNS
Two-phase flows in porous media appear in a large number of engineering applications including heat-exchangers, drying process and nuclear reactors. More particularly, in the framework of its research programme on severe nuclear reactor accidents, IPSN investigates the water flooding of an overheated porous bed, where such complex flows are likely to exist. The goal is to describe the flow with a general model, covering rods and debris beds regions in the vessel. (authors)
Impact of wettability correlations on multiphase flow through porous media
de la Lama, Marta S.; Brinkmann, Martin
2012-01-01
In the last decades, significant progress has been made in understanding the multiphase displacement through porous media with homogeneous wettability and its relation to the pore geometry. However, the role of wettability at the scale of the pore remains still little understood. In the present study the displacement of immiscible fluids through a two-dimensional porous medium is simulated by means of a mesoscopic particle approach. The substrate is described as an assembly of non-overlapping...
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
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).
Relationship between fluid resistance and heat transfer in porous media
A relationship is established between the drag coefficient and heat-transfer coefficient in a turbulent flow in a porous medium. The relationship is described in the form of criterional equations which contain a unique empirical (evidently universal) constant, and it is based on the determining effect of the scale of the fluctuation velocity of the heat carrier on the heat-transfer coefficient. It is found that satisfactory results are obtained for porous media by using the Kolmogorov scale of fluctuation velocity. A comparison is made between the results of present calculations and experimental data on heat transfer in spherical packings and reticular and fibrous media and for transverse flow in rod bundles cooled by liquid metals, gases, water, and oils. The formulas obtained are convenient to use to estimate heat transfer in porous media from measurements of drag
Channelization in Porous Media driven by Erosion and Deposition
Jäger, Robin; Herrmann, Hans Jürgen
2016-01-01
We develop and validate a new model to study simultaneous erosion and deposition in three-dimensional porous media. We study the changes of the porous structure induced by the deposition and erosion of matter on the solid surface and find that when both processes are active, channelization in the porous structure always occurs. The channels can be stable or only temporary depending mainly on the driving mechanism. Whereas a fluid driven by a constant pressure drop in general does not form steady channels, imposing a constant flux always produces stable channels within the porous structure. Furthermore we investigate how changes of the local deposition and erosion properties affect the final state of the porous structure, finding that the larger the range of wall shear stress for which there is neither erosion nor deposition, the more steady channels are formed in the structure.
Linking Colloid Deposit Morphology and Clogging in Porous Media
Roth, E. J.; Mont-eton, M. E.; Mays, D. C.
2012-12-01
Innovations in the field of groundwater remediation have been hampered by delivery limitations in the porous media. For example, colloid deposits (comprising clays or silts) can cause a detrimental reduction in permeability, or clogging, which is problematic for groundwater remediation as well as granular media filtration and aquifer storage and recovery. During remediation, clogging creates preferential pathways in the media, leading to localized rather than spatially extensive contaminant treatment. Consequentially, remediation efforts become more expensive, less effective, and take a very long time. This presentation describes ongoing research investigating the link between colloid deposit morphology and clogging in porous media. As described by Darcy's Law, the velocity of fluid flow through porous media is proportional to permeability, which depends, in part, on porosity. However, changes in permeability are not in accord with changes in porosity as predicted by the Kozeny-Carman equation. It is hypothesized that unmeasured aspects of colloid deposit morphology could be the cause of this anomaly. Colloidal phenomena have important and dynamic effects on the permeability of natural porous media, and several lines of evidence suggest a correlation between clogging in porous media and the fractal dimension of colloid deposits. Here, a custom-built static light scattering apparatus is used to measure the fractal dimension of colloid deposits in refractive index matched porous media within a flow column. The media in our flow column is Nafion, which becomes essentially invisible when saturated by a solution of isopropanol and water. Polystyrene microspheres are then added to the influent through the column as a surrogate for natural colloids. Light from a laser is passed through the column, scattering from the deposited colloids, but not from the index matched Nafion. The resulting intensity of scattered light is measured as a function of scattering angle, and then
Combustion and heat transfer in porous media
Sathe, S.B.; Peck, R.E.; Tong, T.W.
1990-06-01
The objective of the present study is to generate fundamental knowledge about heat transfer and combustion in porous radiant burners (PRBs) in order to improve their performance. A theoretical heat transfer and combustion model is developed to study the characteristics of PRBs. The model accounts for non-local thermal equilibrium between the solid and gas phases. The solid is assumed to absorb, emit and scatter radiant energy. Combustion is modeled as a one-step global reaction. It is revealed that the flame speed inside the porous medium is enhanced compared to the adiabatic flame speeds due to the higher conductivity of the solid compared to the gas as well as due to radiative preheating of the reactants. The effects of the properties of the porous material on the flame speeds, radiative outputs and efficiencies were investigated. To improve the radiative output from the burner, it is desirable that the porous layer has an optical thickness of about ten. The radiative output and the efficiency is higher for lower scattering albedo. The heat transfer coupling between the solid and gas phases should be high enough to ensure local thermal equilibrium, by choosing a fine porous matrix. Higher solid phase conduction enhances the flame speed and the radiative output. Experiments are performed on a ceramic foam to verify the theoretical findings. The existence of the two stability regions was verified experimentally.
Density-Driven Compactional Flow in Porous Media
Yang, Xin-She
2010-01-01
In the mathematical modelling of compactional flow in porous media, the constitutive relation is typically modelled in terms of a nonlinear relationship between effective pressure and porosity, and compaction is essentially poroelastic. However, at depths deeper than 1 km where pressure is high, compaction becomes more akin to a viscous one. Two mathematical models of compaction in porous media are formulated and the noninear equations are then solved numerically. The essential features of numerical profiles of poroelastic and viscous compaction are thus compared with asymptotic solutions. Two distinguished styles of density-driven compaction in fast and slow compacting sediments are analysed and shown in this paper.
Traveling time and traveling length for flow in porous media
Lee, Youngki; Andrade Jr., Jose S.; Buldyrev, Sergey V.; Dokholyan, Nikolay V.; Havlin, Shlomo; King, Peter R.; Paul, Gerald; Stanley, H. Eugene
1999-01-01
We study traveling time and traveling length for tracer dispersion in porous media. We model porous media by two-dimensional bond percolation, and we model flow by tracer particles driven by a pressure difference between two points separated by Euclidean distance $r$. We find that the minimal traveling time $t_{min}$ scales as $t_{min} \\sim r^{1.40}$, which is different from the scaling of the most probable traveling time, ${\\tilde t} \\sim r^{1.64}$. We also calculate the length of the path c...
Study of water radiolysis in porous media
The understanding of the production of H2 in the radiolysis of water confined into pores of concrete is important for the disposal of radioactive waste. In order to describe the mechanisms of water radiolysis in such heterogeneous porous systems we have studied the behaviour under gamma radiation of water confined in porous silica glasses with pores going from 8 to 300 nm of diameter and meso-porous molecular sieves (MCM-41). The radiolytic yields of hydroxyl radicals, hydrated electron and dihydrogen, have been determined with respect to the pore size of materials. The increase of these radiolytic yields compared to those of free water allowed us to show a charge transfer from silica to confined water. On the other hand the kinetics of hydrated electron reactions measured by pulse radiolysis are not modified. (author)
SHU Wei-Xing; LUO Hai-Lu; LI Fei; REN Zhong-Zhou
2006-01-01
@@ We investigate the propagation of electromagnetic waves at the interface between an isotropic material and the anisotropic medium with a unique dispersion relation. We show that the refraction behaviour of E-polarized waves is opposite to that of H-polarized waves, though the dispersion relations for E- and H-polarized waves are the same. It is found that waves exhibit different propagation properties in anisotropic media with different sign combinations of the permittivity and permeability tensors. Some interesting properties of propagation are also found in the special anisotropic media, leading to potential applications.
Mathematical models of a diffusion-convection in porous media
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.
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
Simulation of impaction filtration of aerosol droplets in porous media
Ghazaryan, Lilya; Lopez Penha, David J.; Geurts, Bernard J.; Stolz, Steffen; Winkelmann, Christoph; Pereira, J.C.F.; Sequeira, A.; Pereira, J.M.C.
2010-01-01
We report on the development of a method to simulate from first principles the particle filtration efficiency of filters that are composed of structured porous media. We assume that the ratio of particle density to the fluid density is high. We concentrate on the motion of the particles in a laminar
magnetic resonance of 3He nuclei in porous media
The data on 3He spin kinetics in porous media above the Fermi temperature of 3He are summarized. Presented results are obtained in Kazan Federal University in last ten years and are the base of developing method of helium porometry. Guidelines for investigation of samples with unknown pore sizes and superficial their properties are proposed
A non-Darcian approach to flows through porous media
Darcy's law is inadequate to describe viscous flows through porous media near solid boundaries-interfaces, permeable or not, and also at high speeds. The convective accelerations and viscous stresses play a dominating role in determining the flow pattern in a layer close to such surfaces. Of course, the flow at large distances is very much closer to the Darcian flow
Determination of permeability using fractal method for porous media
施明恒; 陈永平
2001-01-01
A theoretical formulation was developed to express permeability as a function of different fractal dimensions and other scales for porous media . The effective fractal void ratio, the spectral dimension and the fractal dimension of particle mass distribution were introduced. The permeabilities for different soils in China are calculated. The predicted permeability for rice soil was compared with the measured data available in literature.
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 ...
Diffusive–Dispersive and Reactive Fronts in Porous Media
Haberer, Christina M.; Muniruzzaman, Muhammad; Grathwohl, Peter;
2015-01-01
Diffusive–dispersive mass transfer is important for many groundwater quality problems as it drives the interaction between different reactants, thus influencing a wide variety of biogeochemical processes. In this study, we performed laboratory experiments to quantify O2 transport in porous media...
Microscopic interfacial phenomena during flow in porous media
Miksis, M.J.; Ida, M.P. [Northwestern Univ., Evanston, IL (United States)
1996-12-31
A fundamental process during any multiphase flow in porous media is the breaking apart of one of the phases into smaller components. Here the authors investigate this breaking process as applied to a thin liquid film. They study the breaking of both a two dimensional planar film and a cylindrical thread of liquid using both analytical and numerical methods.
Acoustic Wave Monitoring of Biofilm Development in Porous Media
Biofilm development in porous media can result in significant changes to the hydrogeological properties of subsurface systems with implications for fluid flow and contaminant transport. As such, a number of numerical models and simulations have been developed in an attempt to qua...
Coupled Flow and Reactivity in the Variably Saturated Porous Media
Palmer, Carl; Smith Bob W.
2003-06-01
This Environmental Management Science Program project (86598) is a collaborative effort between the University of Idaho (UI) and the Idaho National Engineering and Environmental Laboratory (INEEL) with the goal of developing a better understanding of the relationships between chemical reactivity, moisture content, and reactive transport for vadose zone porous media.
Chaotic advection in 2D anisotropic porous media
Varghese, Stephen; Speetjens, Michel; Trieling, Ruben; Toschi, Federico
2015-11-01
Traditional methods for heat recovery from underground geothermal reservoirs employ a static system of injector-producer wells. Recent studies in literature have shown that using a well-devised pumping scheme, through actuation of multiple injector-producer wells, can dramatically enhance production rates due to the increased scalar / heat transport by means of chaotic advection. However the effect of reservoir anisotropy on kinematic mixing and heat transport is unknown and has to be incorporated and studied for practical deployment in the field. As a first step, we numerically investigate the effect of anisotropy (both magnitude and direction) on (chaotic) advection of passive tracers in a time-periodic Darcy flow within a 2D circular domain driven by periodically reoriented diametrically opposite source-sink pairs. Preliminary results indicate that anisotropy has a significant impact on the location, shape and size of coherent structures in the Poincare sections. This implies that the optimal operating parameters (well spacing, time period of well actuation) may vary strongly and must be carefully chosen so as to enhance subsurface transport. This work is part of the research program of the Foundation for Fundamental Research on Matter (FOM), which is part of Netherlands Organisation for Scientific Research (NWO). This research program is co-financed by Shell Global Solutions International B.V.
Zhiming Chen
2006-01-01
We review some of our recent efforts in developing upscaling methods for simulating the flow transport through heterogeneous porous media. In particular, the steady flow transport through highly heterogeneous porous media driven by extraction wells and the flow transport through unsaturated porous media will be considered.
Osmosis, filtration and fracture of porous media
Filtration was produced in a small scale physical model of a granular porous medium of cylindrical shape.The same volume flow was obtained either applying a difference in hydrostatic pressure or in osmotic pressure.In the first case a process of sustained erosion ending in an hydraulic short circuit was observed,while in the second case the material remained stable.This paradoxical strength behaviour is explained using some results from differential geometry,classical field theory and thermo-kinetic theory.The fracture process of a continuous matrix in a porous medium under the combined effect of filtration and external mechanical loads in then considered.The obtained results can be applied to the textural and compressive strength of wet concrete
Novel lattice models for porous media
Andrey P Jivkov, Joseph E Olele
2011-01-01
Several barriers in a nuclear waste repository, such as waste immobilisers, backfills and host rock are porous. Predicting the changes in their permeability over the repository lifetime is critical to the assessment of radionuclide transport. Pore network models used in petrology offer an advantageous way for such predictions, because they can be linked elegantly to physical mechanisms that could lead to pore structure changes, e.g. mechanical damage, gas generation, or irradiation. The ex...
Migration of radionuclides in porous media
One- and three-dimensional solutions based on the classical advection-dispersion equation have been developed and classified for the analysis of radionuclide transport in unconsolidated porous materials. The one-dimensional solutions have been applied for interpretation of experimental data obtained from radio-tracer tests with laboratory and field columns whereas both types of solutions were employed for interpretation of the field tracer test data
Superfluid Helium Flow in Porous Media
Allain, Hervé; Quintard, Michel; Soulaine, Cyprien; Prat, Marc; Baudouy, Bertrand; Van Weelderen, Rob
2013-01-01
Superfluid helium is primarily used in the field of applied superconductivity. Given the complexity of the magnet geometry and the scales involved, a real 3D simulation of heat transfer in such devices at the micro-channel scale is very difficult, even impossible. However, the repeatability or even periodicity of the structure suggests the possibility of a macro-scale description following a porous medium approach. Which macro-scale model may be used? This largely remains an open field while ...
Sophia Haussener
2012-01-01
Full Text Available High-resolution X-ray computed tomography is employed to obtain the exact 3D geometrical configuration of porous anisotropic ceria applied in solar-driven thermochemical cycles for splitting H2O and CO2. The tomography data are, in turn, used in direct pore-level numerical simulations for determining the morphological and effective heat/mass transport properties of porous ceria, namely: porosity, specific surface area, pore size distribution, extinction coefficient, thermal conductivity, convective heat transfer coefficient, permeability, Dupuit-Forchheimer coefficient, and tortuosity and residence time distributions. Tailored foam designs for enhanced transport properties are examined by means of adjusting morphologies of artificial ceria samples composed of bimodal distributed overlapping transparent spheres in an opaque medium.
Wang, Hui
2014-05-01
This thesis addresses the efficiency improvement of seismic wave modeling and migration in anisotropic media. This improvement becomes crucial in practice as the process of imaging complex geological structures of the Earth\\'s subsurface requires modeling and migration as building blocks. The challenge comes from two aspects. First, the underlying governing equations for seismic wave propagation in anisotropic media are far more complicated than that in isotropic media which demand higher computational costs to solve. Second, the usage of whole prestack seismic data still remains a burden considering its storage volume and the existing wave equation solvers. In this thesis, I develop two approaches to tackle the challenges. In the first part, I adopt the concept of prestack exploding reflector model to handle the whole prestack data and bridge the data space directly to image space in a single kernel. I formulate the extrapolation operator in a two-way fashion to remove he restriction on directions that waves propagate. I also develop a generic method for phase velocity evaluation within anisotropic media used in this extrapolation kernel. The proposed method provides a tool for generating prestack images without wavefield cross correlations. In the second part of this thesis, I approximate the anisotropic models using effective isotropic models. The wave phenomena in these effective models match that in anisotropic models both kinematically and dynamically. I obtain the effective models through equating eikonal equations and transport equations of anisotropic and isotropic models, thereby in the high frequency asymptotic approximation sense. The wavefields extrapolation costs are thus reduced using isotropic wave equation solvers while the anisotropic effects are maintained through this approach. I benchmark the two proposed methods using synthetic datasets. Tests on anisotropic Marmousi model and anisotropic BP2007 model demonstrate the applicability of my
Studies of Tracer Dispersion and Fluid Flow in Porous Media
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
Particle dispersion and deposition in porous media: a computational perspective
Boccardo, Gianluca; Crevacore, Eleonora; Sethi, Rajandrea; Marchisio, Daniele
2015-11-01
This work investigates particle dispersion in porous media, which is of central relevance in a number of applications ranging from groundwater remediation tochemical engineering. The challenge lies in studying the complex fluid dynamics behavior arising at the microscale (very difficult to observe experimentally) and obtaining transport models to be employed at the macroscopic scale of interest. While a wealth of studies have approached this problem, the case of particle transport with a concurrent heterogeneous chemical reaction (e.g.: particle deposition) still lacks a satisfactory description, especially when considering a polydisperse population of solid particles. Moreover, the oft-used simplified descriptions of the porous medium (via array of spheres or similar strategies) fail to fully take into account the effect of the packing structure. Our novel approach relies on an ``in-silico'' procedure where many 3-D realistic porous media models are constructed via rigid-body simulations and fluid flowand particle transport are then investigated through computational fluid dynamics. The results evidence the need for a deeper look, afforded by these methodology, into the influence of the features of realistic porous media on particle transport and deposition.
Statistical mechanics of unsaturated porous media
Xu, Jin; Louge, Michel Y.
2015-12-01
We explore a mean-field theory of fluid imbibition and drainage through permeable porous solids. In the limit of vanishing inertial and viscous forces, the theory predicts the hysteretic "retention curves" relating the capillary pressure applied across a connected domain to its degree of saturation in wetting fluid in terms of known surface energies and void space geometry. To avoid complicated calculations, we adopt the simplest statistical mechanics, in which a pore interacts with its neighbors through narrow openings called "necks," while being either full or empty of wetting fluid. We show how the main retention curves can be calculated from the statistical distribution of two dimensionless parameters λ and α measuring the specific areas of, respectively, neck cross section and wettable pore surface relative to pore volume. The theory attributes hysteresis of these curves to collective first-order phase transitions. We illustrate predictions with a porous domain consisting of a random packing of spheres, show that hysteresis strength grows with λ and weakens as the distribution of α broadens, and reproduce the behavior of Haines jumps observed in recent experiments on an ordered pore network.
Statistical mechanics of unsaturated porous media.
Xu, Jin; Louge, Michel Y
2015-12-01
We explore a mean-field theory of fluid imbibition and drainage through permeable porous solids. In the limit of vanishing inertial and viscous forces, the theory predicts the hysteretic "retention curves" relating the capillary pressure applied across a connected domain to its degree of saturation in wetting fluid in terms of known surface energies and void space geometry. To avoid complicated calculations, we adopt the simplest statistical mechanics, in which a pore interacts with its neighbors through narrow openings called "necks," while being either full or empty of wetting fluid. We show how the main retention curves can be calculated from the statistical distribution of two dimensionless parameters λ and α measuring the specific areas of, respectively, neck cross section and wettable pore surface relative to pore volume. The theory attributes hysteresis of these curves to collective first-order phase transitions. We illustrate predictions with a porous domain consisting of a random packing of spheres, show that hysteresis strength grows with λ and weakens as the distribution of α broadens, and reproduce the behavior of Haines jumps observed in recent experiments on an ordered pore network. PMID:26764701
MULTIPHASE FLOW AND TRANSPORT IN POROUS MEDIA
Multiphase flow and transport of compositionally complex fluids in geologic media is of importance in a number of applied problems which have major social and economic effects. n petroleum reservoir engineering efficient recovery of energy reserves is the principal goal. nfortuna...
Slip effects associated with Knudsen transport phenomena in porous media
Frederking, T. H. K.; Hepler, W. A.; Khandhar, P. K.
1988-01-01
Porous media used in phase separators and thermomechanical pumps have been the subject of characterization efforts based on the Darcy permeability of laminar continuum flow. The latter is not always observed at low speed, in particular at permeabilities below 10 to the -9th/squared cm. The present experimental and theoretical studies address questions of slip effects associated with long mean free paths of gas flow at room temperature. Data obtained are in good agreement, within data uncertainty, with a simplified asymptotic Knudsen equation proposed for porous plugs on the basis of Knudsen's classical flow equation for long mean free paths.
Overlimiting Current and Shock Electrodialysis in Porous Media
Deng, Daosheng; Dydek, E. Victoria; Han, Ji-Hyung; Schlumpberger, Sven; Mani, Ali; Zaltzman, Boris; Bazant, Martin Z.
2013-01-01
Most electrochemical processes, such as electrodialysis, are limited by diffusion, but in porous media, surface conduction and electro-osmotic flow also contribute to ionic fluxes. In this paper, we report experimental evidence for surface-driven over-limiting current (faster than diffusion) and deionization shocks (propagating salt removal) in a porous medium. The apparatus consists of a silica glass frit (1 mm thick with 500 nm mean pore size) in an aqueous electrolyte (CuSO$_4$ or AgNO$_3$...
Multiphase lattice Boltzmann simulations for porous media applications -- a review
Liu, Haihu; Leonardi, Christopher R; Jones, Bruce D; Schmieschek, Sebastian; Narváez, Ariel; Williams, John R; Valocchi, Albert J; Harting, Jens
2014-01-01
Over the last two decades, lattice Boltzmann methods have become an increasingly popular tool to compute the flow in complex geometries such as porous media. In addition to single phase simulations allowing, for example, a precise quantification of the permeability of a porous sample, a number of extensions to the lattice Boltzmann method are available which allow to study multiphase and multicomponent flows on a pore scale level. In this article we give an extensive overview on a number of these diffuse interface models and discuss their advantages and disadvantages. Furthermore, we shortly report on multiphase flows containing solid particles, as well as implementation details and optimization issues.
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.
Poroelastic Response of Orthotropic Fractured Porous Media
Berryman, James G.
2011-12-16
An algorithm is presented for inverting either laboratory or field poroelastic data for all the drained constants of an anisotropic (specifically orthotropic) fractured poroelastic system. While fractures normally weaken the system by increasing the mechanical compliance, any liquids present in these fractures are expected to increase the stiffness somewhat, thus negating to some extent the mechanical weakening influence of the fractures themselves. The analysis presented quantifies these effects and shows that the key physical variable needed to account for the pore-fluid effects is a factor of (1 - B), where B is Skempton's second coe fficient and satisfies 0 {<=} B < 1. This scalar factor uniformly reduces the increase in compliance due to the presence of communicating fractures, thereby stiffening the fractured composite medium by a predictable amount. One further goal of the discussion is to determine how many of the poroelastic constants need to be known by other means in order to determine the rest from remote measurements, such as seismic wave propagation data in the field. Quantitative examples arising in the analysis show that, if the fracture aspect ratio a{sub f} ~ 0.1 and the pore fluid is liquid water, then for several cases considered Skempton's B ~ 0:9, so the stiffening effect of the pore-liquid reduces the change in compliance due to the fractures by a factor 1-B ~ 0.1, in these examples. The results do however depend on the actual moduli of the unfractured elastic material, as well as on the pore-liquid bulk modulus, so these quantitative predictions are just examples, and should not be treated as universal results. Attention is also given to two previously unremarked poroelastic identities, both being useful variants of Gassmann's equations for homogeneous -- but anisotropic -- poroelasticity. Relationships to Skempton's analysis of saturated soils are also noted. The paper concludes with a discussion of alternative methods
An iterative, fast-sweeping-based eikonal solver for 3D tilted anisotropic media
Waheed, Umair bin
2015-03-30
Computation of first-arrival traveltimes for quasi-P waves in the presence of anisotropy is important for high-end near-surface modeling, microseismic-source localization, and fractured-reservoir characterization - and it requires solving an anisotropic eikonal equation. Anisotropy deviating from elliptical anisotropy introduces higher order nonlinearity into the eikonal equation, which makes solving the eikonal equation a challenge. We addressed this challenge by iteratively solving a sequence of simpler tilted elliptically anisotropic eikonal equations. At each iteration, the source function was updated to capture the effects of the higher order nonlinear terms. We used Aitken\\'s extrapolation to speed up convergence rate of the iterative algorithm. The result is an algorithm for computing first-arrival traveltimes in tilted anisotropic media. We evaluated the applicability and usefulness of our method on tilted transversely isotropic media and tilted orthorhombic media. Our numerical tests determined that the proposed method matches the first arrivals obtained by wavefield extrapolation, even for strongly anisotropic and highly complex subsurface structures. Thus, for the cases where two-point ray tracing fails, our method can be a potential substitute for computing traveltimes. The approach presented here can be easily extended to compute first-arrival traveltimes for anisotropic media with lower symmetries, such as monoclinic or even the triclinic media.
Hydraulic tortuosity in arbitrary porous media flow
Duda, Artur; Matyka, Maciej
2011-01-01
Tortuosity ($T$) is a parameter describing an average elongation of fluid streamlines in a porous medium as compared to free flow. In this paper several methods of calculating this quantity from lengths of individual streamlines are compared and their weak and strong features are discussed. An alternative method is proposed, which enables one to calculate $T$ directly from the fluid velocity field, without the need of determining streamlines, which greatly simplifies determination of tortuosity in complex geometries, including those found in experiments or 3D computer models. Numerical results obtained with this method suggest that (a) the hydraulic tortuosity of an isotropic fibrous medium takes on the form $T = 1 + p\\sqrt{1-\\phi}$, where $\\phi$ is the porosity and $p$ is a constant and (b) the exponent controlling the divergence of $T$ with the system size at percolation threshold is related to an exponent describing the scaling of the most probable traveling length at bond percolation.
Pore-scale simulation of laminar flow through porous media
The experimental investigation of flow through porous media is inherently difficult due to the lack of optical access. The recent developments in the fields of X-ray micro-tomography (micro-CT hereafter), digital sample reconstruction by image-processing techniques and fluid-dynamics simulation, together with the increasing power of super-computers, allow to carry out pore-scale simulations through digitally-reconstructed porous samples. The scientific relevance of pore-scale simulations lies in the possibility of upscaling the pore-level data, yielding volume-averaged quantities useful for practical purposes. One of the best-known examples of upscaling is the calculation of absolute and relative permeability of reservoir rocks. This contribution presents a complete work-flow for setting up pore-scale simulations, starting from the micro-CT of a (in general small) porous sample. Relevant applications are discussed in order to reveal the potential of the proposed methodology.
Pore-scale simulation of laminar flow through porous media
Piller, M.; Casagrande, D.; Schena, G.; Santini, M.
2014-04-01
The experimental investigation of flow through porous media is inherently difficult due to the lack of optical access. The recent developments in the fields of X-ray micro-tomography (micro-CT hereafter), digital sample reconstruction by image-processing techniques and fluid-dynamics simulation, together with the increasing power of super-computers, allow to carry out pore-scale simulations through digitally-reconstructed porous samples. The scientific relevance of pore-scale simulations lies in the possibility of upscaling the pore-level data, yielding volume-averaged quantities useful for practical purposes. One of the best-known examples of upscaling is the calculation of absolute and relative permeability of reservoir rocks. This contribution presents a complete work-flow for setting up pore-scale simulations, starting from the micro-CT of a (in general small) porous sample. Relevant applications are discussed in order to reveal the potential of the proposed methodology.
3-D waveform tomography sensitivity kernels for anisotropic media
Djebbi, R.
2014-01-01
The complications in anisotropic multi-parameter inversion lie in the trade-off between the different anisotropy parameters. We compute the tomographic waveform sensitivity kernels for a VTI acoustic medium perturbation as a tool to investigate this ambiguity between the different parameters. We use dynamic ray tracing to efficiently handle the expensive computational cost for 3-D anisotropic models. Ray tracing provides also the ray direction information necessary for conditioning the sensitivity kernels to handle anisotropy. The NMO velocity and η parameter kernels showed a maximum sensitivity for diving waves which results in a relevant choice of those parameters in wave equation tomography. The δ parameter kernel showed zero sensitivity; therefore it can serve as a secondary parameter to fit the amplitude in the acoustic anisotropic inversion. Considering the limited penetration depth of diving waves, migration velocity analysis based kernels are introduced to fix the depth ambiguity with reflections and compute sensitivity maps in the deeper parts of the model.
Polarisations of quasi-waves in a general anisotropic porous solid saturated with viscous liquid
M D Sharma
2005-08-01
Wave propagation is studied in a general anisotropic poroelastic solid saturated with a viscous fluid flowing through its pores of anisotropic permeability. The extended version of Biot's theory is used to derive a system of modified Christoffel equations for the propagation of plane harmonic waves in such media. The non-trivial solution of this system is ensured by a biquadratic equation whose roots represent the complex velocities of four attenuating quasi-waves in the medium. These complex velocities define phase velocity and attenuation of each quasi-wave propagating along a given phase direction in three-dimensional space. The solution itself defines the polarisations of the quasi-waves along with phase shift. The variations of polarisations of quasi-waves with their phase direction, are computed for a realistic numerical model.
FEMWASTE FEMWATER, Finite Elements Method Waste Transport Through Porous Media
1 - Description of program or function: FEMWASTE is a two-dimensional transient model for the transport of dissolved constituents through porous media. The transport mechanisms include: convection, hydro- dynamic dispersion, chemical sorption, and first-order decay. The waste transport model is compatible with the water flow model (FEMWATER)) for predicting convective Darcy velocities in porous media which may be partially saturated. 2 - Method of solution: Implementation of quadrilateral iso-parametric finite elements, bilinear spatial interpolation, asymmetric weighting functions, several time-marching techniques, and Gaussian elimination are employed in the numerical formulation of the transport equation. The application of the finite element method ensures that mass balance over the whole region is preserved. A mixture-dependent retardation factor is employed in the definition of solute sorption
Analytic studies of colloid transport in fractured porous media
We analyze the interactive migration of radioactive colloids and solute in fractured rock. Two possible interactions between radionuclides as colloids and as solute are considered: solute sorption on nonradioactive colloids to form pseudocolloids, and dissolution of radioactive colloids. Previous studies have discussed the formation and transport of colloids in porous media, including removal of colloids by filtration and sedimentation. Colloids can migrate faster than solute because of weaker sorption on stationary solids and because of hydrochromatography of colloid particles in flow channels. However, the migration of colloids and pseudocolloids can be retarded by the interaction of colloids with solute, and the migration of solute in local equilibrium with colloids can be more rapid than if colloids were not present. Here we present a new quantative analysis to predict the interactive migration of colloids and solute in porous and fractured media. 4 figs
Dissipative particle dynamics model for colloid transport in porous media
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.
On growth and flow: bacterial biofilms in porous media
Durham, William; Leombruni, Alberto; Tranzer, Olivier; Stocker, Roman
2011-11-01
Bacterial biofilms often occur in porous media, where they play pivotal roles in medicine, industry and the environment. Though flow is ubiquitous in porous media, its effects on biofilm growth have been largely ignored. Using patterned microfluidic devices that simulate unconsolidated soil, we find that the structure of Escherichia coli biofilms undergoes a self-organization mediated by the interaction of growth and flow. Intriguingly, we find that biofilm productivity peaks at intermediate flow rates, when the biofilm is irrigated by a minimum number of preferential flow channels. At larger and smaller flow rates, fluid flows more uniformly through the matrix, but productivity drops due to removal by shear and reduced nutrient transport, respectively. These dynamics are correctly predicted by a simple network model. The observed tradeoff between growth and flow may have important consequences on biofilm-mediated processes such as biochemical cycling, antibiotic resistance and water filtration.
Boiling heat transfer in porous media composed of particles
The boiling heat transfer in the porous media composed of spherical fuel elements exerts significant influences on the reactor's efficiency and safety. In the present study an experimental setup was designed and the boiling heat transfer in the porous media composed of spheres of regular distribution was investigated. Four spheres with diameters of 5mm, 6mm, 7mm and 8mm were used in the test sections. The greater particle diameter led to lower heat transfer coefficient, and resulted in higher wall superheat of original nucleation boiling. The variation of heat transfer coefficient was divided into three groups according to two-phase flow patterns and void fraction. A correlation of heat transfer coefficient was proposed with a mean relative deviation of ± 16%. (author)
Characteristics of heat transport in porous media with water infiltration
In this paper heat and water transports in porous media with waster infiltration are discussed experimentally and theoretically. The distributions of water content and temperature were predicted for one- and tow-dimensional porous media, based on a model that there is thermal equilibrium between the water and the matrix at any specific space. The predicted temperature distributions were compared of the experimental results obtained using various glass bead sizes. A larger bead size has a faster infiltration rate and forms a wider infiltration layer, especially to the direction of gravity. But the heated layer does not extend so wide as the infiltration layer because the temperature of water infiltrating gradually drops due to heat transport at upstream
Resistance absorption of some groundwater tracers in porous media
Jafari, Fateme
2010-05-01
Absorption of tracer to the aquifer material is among the most important factors which should be considered when a tracing program is considered. In this study, the absorption of the tracer into the porous media is analyzed experimentally for some of the most important and applied tracers as uranine, rhodamine B, eosin, potassium permanganate, sodium chloride and potassium chloride. For each tracer, effect of initial tracer concentration and percentage of fine grain sediments on tracer absorption in porous media is analyzed. According to the final results, rhodamine B and potassium permanganate have the less resistance against absorption to aquifer material, whilst eosin and uranine are the most resistant tracers among the examined ones. Key Words: Tracer, Absorption, Aquifer, Column Method
Filtration characteristics of porous silicon carbide media
The characteristics of a filter such as clean filter pressure drop, filtering performance and filter drag variation with dust loading have been studied with fabricated SiC filter specimens in the laboratory and commercial ceramic filters. Several theoretical equations have been modified and applied to investigate such characteristics. To estimate the pressure drop of clean gas flow through a cylindrical porous filter, Forchheimer equation, which contains the terms of permeability and turbulent factor at a high velocity of gas, has been modified and tested with experimental data. The filtering efficiency was found to be above 99.9% and the penetration of dust decreased exponentially with dust loading. The pressure drop during filtration was measured and showed to increase exponentially with dust loading in the beginning because particles were intercepted and a cake layer was formed by structural properties of a filter. And then it increased in proportion as the cake layer thickened. The effect of dust deposition on the pressure drop could be explained theoretically using several characteristic parameters relevant to dust size, structure of filters and cake layer formation
Soltanian, Mohamad Reza; Ritzi, Robert W; Dai, Zhenxue; Huang, Chao Cheng
2015-03-01
Physical and chemical heterogeneities have a large impact on reactive transport in porous media. Examples of heterogeneous attributes affecting reactive mass transport are the hydraulic conductivity (K), and the equilibrium sorption distribution coefficient (Kd). This paper uses the Deng et al. (2013) conceptual model for multimodal reactive mineral facies and a Lagrangian-based stochastic theory in order to analyze the reactive solute dispersion in three-dimensional anisotropic heterogeneous porous media with hierarchical organization of reactive minerals. An example based on real field data is used to illustrate the time evolution trends of reactive solute dispersion. The results show that the correlation between the hydraulic conductivity and the equilibrium sorption distribution coefficient does have a significant effect on reactive solute dispersion. The anisotropy ratio does not have a significant effect on reactive solute dispersion. Furthermore, through a sensitivity analysis we investigate the impact of changing the mean, variance, and integral scale of K and Kd on reactive solute dispersion. PMID:25532767
Soltanian, Mohamad Reza; Dai, Zhenxue; Huang, Chaocheng
2014-01-01
Physical and chemical heterogeneities have a large impact on reactive transport in porous media. Examples of heterogeneous attributes affecting reactive mass transport are the hydraulic conductivity (K), and the equilibrium sorption distribution coefficient (Kd). This paper uses the Deng et al. (2013) conceptual model for multimodal reactive mineral facies and a Lagrangian-based stochastic theory in order to analyze the reactive solute dispersion in three-dimensional anisotropic heterogeneous porous media with hierarchical organization of reactive minerals. An example based on real field data is used to illustrate the time evolution trends of reactive solute dispersion. The results show that the correlation between the hydraulic conductivity and the equilibrium sorption distribution coefficient does have a significant effect on reactive solute dispersion. The anisotropy ratio does not have a significant effect on reactive solute dispersion. Furthermore, through a sensitivity analysis we investigate the impact...
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.
Denitrification and chemotaxis of Pseudomonas stutzeri KC in porous media.
Roush, Caroline J; Lastoskie, Christian M; Worden, R Mark
2006-01-01
Chemotaxis is an important mechanism by which microorganisms are dispersed in porous media. A vigorous chemotactic response to concentration gradients formed by microbial consumption of chemoattractants can accelerate transport of bacteria to highly contaminated regions of soils and sediments, enhancing the efficiency of in situ bioremediation operations. Although chemotaxis plays a key role in establishment of biodegradation zones in the subsurface, the effects of physical heterogeneity on bacterial motility are poorly understood. To investigate the influence of porous media heterogeneity on microbial chemotaxis, swarm plate migration experiments were conducted using Pseudomonas stutzeri strain KC, a denitrifying bacterium used for in situ biodegradation of carbon tetrachloride in groundwater. Swarm plate measurements indicate that strain KC is strongly chemotactic toward both acetate and nitrate. A three-component mathematical model was developed to describe the migration of strain KC. Estimates of chemotactic sensitivity were obtained in the homogeneous (agar) phase and in a heterogeneous medium of aquifer solids extracted from the Schoolcraft bioremediation field site in western Michigan. Interestingly, the motility of strain KC is significantly larger in the porous medium than in the aqueous phase. We hypothesize that chemotactic response is enhanced within the heterogeneous medium because chemoattractant gradients formed by nitrate consumption are larger in the confined spaces of the porous medium than in unconfined agar solution. PMID:16760079
Borgne, H.
2004-12-01
modelling of waves propagation in anisotropic media. With the approximations of ray theory, 1 develop an expression of the geometrical spreading, the amplitude, and their reciprocity relations. I set up imaging formulas in order to reconstruct the reflection coefficients of the subsurface in elastic anisotropic media. In a first time, 1 salve the direct problem, by expressing the integral relation between the scattered wave field recorded by the receivers and the subsurface reflection coefficients. In a second time, 1 apply an elastic anisotropic quantitative migration method, based on the properties of the inverse Radon transforms (Beylkin's approach), in order to express the reflection coefficient in 2D, 2.5D and 3D media. 1 implemented these formulas in a new preserved amplitude migration algorithm, where the images are sorted by angle classes. At last, 1 apply these theoretical results to synthetic and real datasets. 1 show that migration is able to reconstruct the correct A V A behavior of anisotropic reflection coefficients if hath. modifications are achieved. Then, 1 degrade the process, by keeping an anisotropic ray tracing but using the classical isotropic imaging formula. F'or this commonly used configuration, 1 evaluate the error that can be expected in the A V A response of the migrated reflection coefficient. Methodological applications show the sensibility of the migration results to the velocity model smoothing and to an error on the anisotropic axis. (author)
Finite difference approach for modeling multispecies transport in porous media
N. Natarajan; G. Suresh Kumar
2010-01-01
An alternative approach to the decomposition method for solving multispecies transport in porous media, coupled with first-order reactions has been proposed. The numerical solution is based on implicit finite difference method. The task of decoupling the coupled partial differential equations has been overcome in this method. The proposed approach is very much advantageous because of its simplicity and also can be adopted in situations where non linear processes are coupled with multi-species...
Displacement of Colloidal Dispersions in Porous Media: Experimental & Numerical Approaches
AHMADI-SENICHAULT, Azita; OMARI, Aziz; BERTIN, Henri
2015-01-01
The displacement of colloidal dispersions is of particular interest in many applications ranging from environmental issues to petroleum recovery. Natural porous media such as soils, aquifers or reservoirs contain colloidal particles of different nature (bacteria, viruses, clay, metal complexes …). Colloids can act as vehicles for micro organisms’ transport in aquifers causing danger for human health. In petroleum recovery techniques, water containing colloids is sometimes injected and their r...
Multidimenstional Models for Macroscopic Virus Transport in Porous Media
Chrysikopoulos, Constantinos V; Sim, Youn
1997-01-01
Analytical models for virus transport in saturated, homogeneous porous media are developed. The models account for three-dimensional dispersion in a uniform flow field, and first-order inactivation of suspended and deposited viruses with different inactivation rate coefficients. Virus deposition onto solid particles is described by two different processes: nonequilibrium adsorption which is applicable to viruses behaving as solutes; and colloid filtration which is applicable to viruses behavi...
Finite difference approach for modeling multispecies transport in porous media
N.Natarajan
2010-08-01
Full Text Available An alternative approach to the decomposition method for solving multispecies transport in porous media, coupled with first-order reactions has been proposed. The numerical solution is based on implicit finite difference method. The task of decoupling the coupled partial differential equations has been overcome in this method. The proposed approach is very much advantageous because of its simplicity and also can be adopted in situations where non linear processes are coupled with multi-species transport problems.
Solute Transport Across a Contact Interface in Deformable Porous Media
Ateshian, Gerard A.; Maas, Steve; Weiss, Jeffrey A.
2012-01-01
A finite element formulation of neutral solute transport across a contact interface between deformable porous media is implemented and validated against analytical solutions. By reducing the integral statements of external virtual work on the two contacting surfaces into a single contact integral, the algorithm automatically enforces continuity of solute molar flux across the contact interface, whereas continuity of the effective solute concentration (a measure of the solute mechano-chemical ...
Competitive positron and positronium trapping in porous media
Positron annihilation acquired acceptance for structural investigation of solids but results in porous media-where positron lifetime spectroscopy (LT) reveals substantial Ps formation-were ambiguous. Data on zeolites lead to the conclusion that Ps trapping in competing 'extended free volume' sites, inhomogeneous regions and grain boundaries occurs. Furthermore, positron trapping must also be considered. Systematic errors due to incomplete time range selection are discussed, significance and importance of corrections for 3γ/2γ counting efficiency differences are shown in practice
Mathematical analysis of variable density flows in porous media
Feireisl, Eduard; Hilhorst, D.; Petzeltová, Hana; Takáč, P.
2016-01-01
Roč. 16, č. 1 (2016), s. 1-19. ISSN 1424-3199 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : variable density flow * flows in porous media * global-in-time solutions Subject RIV: BA - General Mathematics Impact factor: 0.783, year: 2014 http://link.springer.com/article/10.1007/s00028-015-0290-6
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.
The multiphase flow and heat transfer in porous media
Starikovicius, V.
2003-01-01
In first part of this work, summaries of traditional Multiphase Flow Model and more recent Multiphase Mixture Model are presented. Attention is being paid to attempts include various heterogeneous aspects into models. In second part, MMM based differential model for two-phase immiscible flow in porous media is considered. A numerical scheme based on the sequential solution procedure and control volume based finite difference schemes for the pressure and saturation-conservation equations is de...
RADICAL FLOW IN POROUS MEDIA WITH DISPERSION AND ADSORPTION
LIU Ci-qun; GUO Bai-qi; SONG Fu-quan; WANG Jin-ying
2004-01-01
The radical transport of chemical concentration in porous media with dispersion and adsorption was studied in this paper. Using Langmuir's adsorption model, the numerical equation of concentration transport was derived. The flows with and without adsorption were simulated and analyzed.Comparison of the obtained solution with the known analytical solution for flow without adsorption shows the presented numerical method is correct and effective, which can be used in reservoir engineering.
Pore Scale Simulation of Transport in Porous Media
Fahlke, Jorrit
2008-01-01
When performing solute transport in porous media one often observes an asymmetric break-through curve with a very slow decline of the concentration. This phenomenon even appears with non-sorbing solutes and is known as tailing. There are several hypotheses to explain this phenomenon. The modelling is often done using the mobile-immobile model (MIM), which assumes that parts of the solvent are not moving along with the general flow. The solutes can move into these stagnant zones by diffusion...
Logarithmic diffusion and porous media equations: a unified description
Pedron, I. T.; Mendes, R. S.; Buratta, T. J.; L. C. Malacarne; Lenzi, E. K.
2005-01-01
In this work we present the logarithmic diffusion equation as a limit case when the index that characterizes a nonlinear Fokker-Planck equation, in its diffusive term, goes to zero. A linear drift and a source term are considered in this equation. Its solution has a lorentzian form, consequently this equation characterizes a super diffusion like a L\\'evy kind. In addition is obtained an equation that unifies the porous media and the logarithmic diffusion equations, including a generalized dif...
Consolidation of elastic porous media saturated by two immiscible fluids
Tuncay, Kağan; Çorapçıoğlu, M. Yavuz
1996-01-01
A theory is presented to simulate the consolidation of elastic porous media saturated by two immiscible Newtonian fluids. The macroscopic equations, including mass and momentum balance equations and constitutive relations, are obtained by volume averaging the microscale equations. The theory is based on the small deformation assumption. In the microscale, the grains are assumed to be linearly elastic and the fluids are Newtonian. The bulk and shear moduli of the solid matrix are introduced to...
Cell-centered finite volume discretizations for deformable porous media
Nordbotten, Jan Martin
2014-01-01
The development of cell-centered finite volume discretizations for deformation is motivated by the desire for a compatible approach with the discretization of fluid flow in deformable porous media. We express the conservation of momentum in the finite volume sense, and introduce three approximations methods for the cell-face stresses. The discretization method is developed for general grids in one to three spatial dimensions, and leads to a global discrete system of equations for the displace...
Solute transport through porous media using asymptotic dispersivity
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.
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.
Particle retention in porous media: Applications to water injectivity decline
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.
Pore Scale View of Fluid Displacement Fronts in Porous Media
Or, D.; Moebius, F.
2014-12-01
The macroscopically smooth and regular motion of fluid fronts in porous media is composed of abrupt pore-scale interfacial jumps involving intense interfacial energy release marked by pressure bursts and acoustic emissions. The characteristics of these pore scale events affect residual phase entrapment and the resulting unsaturated transport properties behind the front. Experimental studies using acoustic emissions technique (AE), rapid imaging, and pressure measurements help characterize pore scale processes during drainage and imbibition in model porous media. Imbibition and drainage produce different AE signatures (obeying a power law). For rapid drainage, AE signals persist long after cessation of front motion indicative of redistribution and interfacial relaxation. Rapid imaging revealed that interfacial jumps exceed mean front velocity and are highly inertial (Re>1000). Imaged pore invasion volumes and pore volumes deduced from waiting times between pressure fluctuations were in remarkable agreement with geometric pores. Differences between invaded volumes and geometrical pores increase with increasing capillary numbers due to shorter pore evacuation times and onset of simultaneous invasion events. A new mechanistic model for interfacial motions through a pore-throat network enabled systematic evaluation of inertia in interfacial dynamics. Results suggest that in contrast to great sensitivity of pore scale dynamics to variations in pore geometry and boundary conditions, inertia exerts only a minor effect on average phase entrapment. Pore scale invasion events paint a complex picture of rapid and inertial motions and provide new insights on mechanisms at displacement fronts essential for improving the macroscopic description of multiphase flow in porous media.
Statistical fusion of two-scale images of porous media
Mohebi, Azadeh; Fieguth, Paul; Ioannidis, Marios A.
2009-11-01
The reconstruction of the architecture of void space in porous media is a challenging task, since porous media contain pore structures at multiple scales. Whereas past methods have been limited to producing samples with matching statistical behavior, the patterns of grey-level values in a measured sample actually say something about the unresolved details, thus we propose a statistical fusion framework for reconstructing high-resolution porous media images from low-resolution measurements. The proposed framework is based on a posterior sampling approach in which information obtained by low-resolution (MRI or X-ray) measurements is combined with prior models inferred from high-resolution microscopic data, typically 2D. In this paper, we focus on two-scale reconstruction tasks in which the measurements resolve only the large scale structures, leaving the small-scale to be inferred. The evaluation of the results generated by the proposed method shows the strong ability of the proposed method in reconstructing fine-scale structures positively correlated with the underlying ground truth. Comparing our method with the recent method of Okabe and Blunt [12], in which the measurements are also used in the reconstruction, we conclude that our method is more robust to the resolution of the measurement, and more closely matches the underlying fine-scale field.
Prestack exploding reflector modelling and migration for anisotropic media
Alkhalifah, Tariq Ali
2014-10-09
The double-square-root equation is commonly used to image data by downward continuation using one-way depth extrapolation methods. A two-way time extrapolation of the double-square-root-derived phase operator allows for up and downgoing wavefields but suffers from an essential singularity for horizontally travelling waves. This singularity is also associated with an anisotropic version of the double-square-root extrapolator. Perturbation theory allows us to separate the isotropic contribution, as well as the singularity, from the anisotropic contribution to the operator. As a result, the anisotropic residual operator is free from such singularities and can be applied as a stand alone operator to correct for anisotropy. We can apply the residual anisotropy operator even if the original prestack wavefield was obtained using, for example, reverse-time migration. The residual correction is also useful for anisotropic parameter estimation. Applications to synthetic data demonstrate the accuracy of the new prestack modelling and migration approach. It also proves useful in approximately imaging the Vertical Transverse Isotropic Marmousi model.
An analysis of seismic attenuation in random porous media
无
2010-01-01
The attenuation of seismic wave in rocks has been one of the interesting research topics, but till now no poroelasticity models can thoroughly explain the strong attenuation of wave in rocks. In this paper, a random porous medium model is designed to study the law of wave propagation in complex rocks based on the theory of Biot poroelasticity and the general theory of stochastic process. This model sets the density of grain, porosity, permeability and modulus of frame as random parameters in space, and only one fluid infiltrates in rocks for the sake of better simulation effect in line with real rocks in earth strata. Numerical simulations are implemented. Two different inverse quality factors of fast P-wave are obtained by different methods to assess attenuation through records of virtual detectors in wave field (One is amplitude decay method in time domain and the other is spectral ratio method in frequency domain). Comparing the attenuation results of random porous medium with those of homogeneous porous medium, we conclude that the attenuation of seismic wave of homogeneous porous medium is far weaker than that of random porous medium. In random porous media, the higher heterogeneous level is, the stronger the attenuation becomes, and when heterogeneity σ = 0.15 in simulation, the attenuation result is consistent with that by actual observation. Since the central frequency (50 Hz) of source in numerical simulation is in earthquake band, the numerical results prove that heterogeneous porous structure is one of the important factors causing strong attenuation in real stratum at intermediate and low frequency.
Observation of anisotropic diffusion of light in compacted granular porous materials
Alerstam, Erik
2011-01-01
Employing spatially resolved photon time-of-flight spectroscopy, we reveal anisotropic diffusion of light in compressed granular media. Findings correlate well with recent reports of pore structural anisotropy and its pressure dependence, and significantly reshape our understanding of the optics of compacted granular matter. New routes to material characterization and investigations of compression-induced anisotropy are opened, and an urgent need for better understanding of the relation between compression, microstructure and light scattering is disclosed. Important implications for quantitative spectroscopy of powder compacts in general, and pharmaceutical tablets in particular, are also discussed.
Thermal diffusion of radon in porous media
Based on the non-intersection model of cylindrical capillaries, the mean radius of the pores of some soils and building materials are estimated. In size, the above-mentioned radii are usually of the order of the free path of gas molecules at atmospheric pressure. A review of pore size distribution data also reveals that a large fraction of concrete pores belong to Knudsen's region. This fact indicates that the thermal gradient in these media must cause gas (radon) transport. The interpretation of the experimental data concerning the rate of emanation of 222Rn from a concrete-capped source subjected to a sudden increase in temperature is given, based on irreversible thermodynamics theory. The calculations given here for radon flux, caused by concentration and thermal gradients, are in satisfactory agreement with the experimental data. It is shown that thermodiffusion can significantly contribute to radon flux in concrete. The need to include the thermodiffusion radon flux in the radon entry model is discussed. (author)
Antonova, A.M.; Moiseikina, I.I. [Kiev Univ. (Ukraine)
1994-10-05
We consider nonstationary seepage in a bounded nonhomogeneously anisotropic fissured-porous layer. The layer contains by an imperfect well, which operates with a constant discharge. Formulas for the distribution of fluid pressure are obtained using the Laplace transform and the separation of variables method.
Anisotropic fractal media by vector calculus in non-integer dimensional space
Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru [Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991 (Russian Federation)
2014-08-15
A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.
Anisotropic fractal media by vector calculus in non-integer dimensional space
A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media
Anisotropic fractal media by vector calculus in non-integer dimensional space
Tarasov, Vasily E.
2014-08-01
A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.
Diffusion with condensation and evaporation in porous media
Vapor phase transport in porous media is important in a number of environmental and industrial processes: soil moisture transport, vapor phase transport in the vadose zone, transport in the vicinity of buried nuclear waste, and industrial processes such as drying. The diffusion of water vapor in a packed bed containing residual liquid is examined experimentally. The objective is to quantify the effect of enhanced vapor diffusion resulting from evaporation/condensation in porous media subjected to a temperature gradient. Isothermal diffusion experiments in free-space were conducted to qualify the experimental apparatus and techniques. For these experiments measured diffusion coefficients are within 3.6% of those reported in the literature for the temperature range from 25 C to 40 C. Isothermal experiments in packed beds of glass beads were used to determine the tortuosity coefficient resulting in τ = 0.78 ± 0.028, which is also consistent with previously reported results. Nonisothermal experiments in packed beds in which condensation occurs were conducted to examine enhanced vapor diffusion. The interpretation of the results for these experiments is complicated by a gradual, but continuous, build-up of condensate in the packed beds during the course of the experiment. Results indicate diffusion coefficients which increase as a function of saturation resulting in enhancement of the vapor-phase transport by a factor of approximately four compared to a dry porous medium
Measurement of Interfacial Area Production and Permeability within Porous Media
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.
Computational models of the hydrodynamics of fractured-porous media
The prediction of the flow pattern in fractured-porous media has great importance in the assessment of the local thermohydrological effects of the siting of a nuclear waste repository, among many other technological applications. Computational models must be used due to the complexity of the different phenomena involved which restricts the use of analytical techniques. A new numerical method, based on the boundary-fitted finite-difference technique, is presented in this thesis. The boundaries are external (the boundary of the physical domain), and internal (which correspond to the fracture network). The inclusion of the discrete fracture representation in the volume that represents the porous medium is the difference between the usual approach and the present one. The numerical model has been used in the prediction of the flow pattern in several internationally recognized verification cases and to hypothetical problems of our interest. The results obtained proved that the numerical approach considered gives accurate and reliable predictions of the hydrodynamics of fractured-porous media, allowing its use for the above mentioned studies. (Author)
Sekar, R., E-mail: rsekar@pec.edu [Department of Mathematics, Pondicherry Engineering College, Puducherry 605014 (India); Raju, K. [Department of Mathematics, Pondicherry Engineering College, Puducherry 605014 (India); Vasanthakumari, R. [Kasthurba College for Women, Villianur, Puducherry 605110 (India)
2013-04-15
The Soret-driven ferrothermoconvective instability of multi- component fluid in an anisotropic porous medium heated from below and salted from above has been analyzed using Brinkman model for various values of anisotropic parameter. The salinity effect is contained in magnetization and density of the ferrofluid and the system is assumed to have anisotropy in the vertical direction and isotropy in the horizontal direction. A small perturbation imparted on the basic state and a linear stability analysis is used for this model for which the normal mode technique is applied. The present analysis has been carried out through both stationary as well as oscillatory modes. The vertical anisotropy tends to destabilize the system. -- Highlights: ► We examine the effect of anisotropy and magnetization of convection in Soret effect. ► The system loses its stability for critical Rayleigh number for various parameters like R{sub s} and K{sub 1}. ► The larger temperature difference is needed to guarantee the occurring of convection. ► The Soret effect plays a dominant role for the stability of the system.
The Soret-driven ferrothermoconvective instability of multi- component fluid in an anisotropic porous medium heated from below and salted from above has been analyzed using Brinkman model for various values of anisotropic parameter. The salinity effect is contained in magnetization and density of the ferrofluid and the system is assumed to have anisotropy in the vertical direction and isotropy in the horizontal direction. A small perturbation imparted on the basic state and a linear stability analysis is used for this model for which the normal mode technique is applied. The present analysis has been carried out through both stationary as well as oscillatory modes. The vertical anisotropy tends to destabilize the system. -- Highlights: ► We examine the effect of anisotropy and magnetization of convection in Soret effect. ► The system loses its stability for critical Rayleigh number for various parameters like Rs and K1. ► The larger temperature difference is needed to guarantee the occurring of convection. ► The Soret effect plays a dominant role for the stability of the system
A reconstruction method of porous media integrating soft data with hard data
LU DeTang; ZHANG Ting; YANG JiaQing; LI DaoLun; KONG XiangYan
2009-01-01
The three-dimensional reconstruction of porous media is of great significance to the research of mechanisms of fluid flow. The real three-dimensional structural data of porous media are helpful to describe the irregular topologic structures in porous media. The reconstruction of porous media will be inaccurate while only hard data or no conditional data are available. Reconstructed results can be more accurate, using soft data during reconstruction. Integrating soft data with hard data, a method based on multiple-point geostatistics (MPS) is proposed to reconstruct three-dimensional structures of porous media. The variogram curves and permeability, computed by lattice Boltzmann method (LBM), of the reconstructed images and the target image obtained from real volume data were compared, showing that the structural characteristics of reconstructed porous media using both soft data and hard data as conditional data are most similar to those of real volume data.
A cellular automaton simulation of contaminant transport in porous media
A simulation tool to investigate radionuclide transport in porous groundwater flow is described. The flow systems of interest are those important in determining the fate of radionuclides emplaced in an underground repository, such as saturated matrix flow, matrix and fracture flow in the unsaturated zone, and viscous fingering in porous fractures. The work discussed here is confined to consideration of saturated flow in porous media carrying a dilute, sorptive species. The simulation technique is based on a special class of cellular automata known as lattice gas automata (LGA) which are capable of predicting hydrodynamic behavior. The original two-dimensional scheme (that of Frisch et. al. known as the FHP model) used particles of unit mass traveling on a triangular lattice with unit velocity and undergoing simple collisions which conserve mass and momentum at each node. These microscopic rules go over to the incompressible Navier-Stokes equations in the macroscopic limit. One of the strengths of this technique is the natural way that heterogeneities, such as boundaries, are accommodated. Complex geometries such as those associated with porous microstructures can be modeled effectively. Several constructions based on the FHP model have been devised, including techniques to eliminate statistical noise, extension to three dimensions, and the addition of surface tension which leads to multiphase flow
The kinetics of ice-lens growth in porous media
Style, Robert W.
2012-01-09
Abstract We analyse the growth rate of segregated ice (ice lenses) in freezing porous media. For typical colloidal materials such as soils we show that the commonly employed Clapeyron equation is not valid macroscopically at the interface between the ice lens and the surrounding porous medium owing to the viscous dynamics of flow in premelted films. The flow in these films gives rise to an \\'interfacial resistance\\' to flow towards the growing ice which causes a significant drop in predicted ice-growth (heave) rates. This explains why many previous models predict ice-growth rates that are much larger than those seen in experiments. We derive an explicit formula for the ice-growth rate in a given porous medium, and show that this only depends on temperature and on the external pressures imposed on the freezing system. This growth-rate formula contains a material-specific function which can be calculated (with knowledge of the geometry and material of the porous medium), but which is also readily experimentally measurable. We apply the formula to plate-like particles, and show that the results can be matched with previous experimental data. Finally we show how the interfacial resistance explains the observation that the maximum heave rate in soils occurs in medium-grained particles such as silts, while heave rates are smaller for fine-and coarse-grained particles. © 2012 Cambridge University Press.
Bound dipole solitary solutions in anisotropic nonlocal self-focusing media
Mamaev, A.V.; Zozulya, A.A.; Mezentsev, V.K.;
1997-01-01
We find and analyze bound dipole solitary solutions in media with anisotropic nonlocal photorefractive material response. The dipole solutions consist of two elliptically shaped Gaussian-type beams separated by several diameters, and with a pi phase shift between their fields. Spatial evolution o...
Djebbi, Ramzi
2013-08-19
Anisotropy is an inherent character of the Earth subsurface. It should be considered for modeling and inversion. The acoustic VTI wave equation approximates the wave behavior in anisotropic media, and especially it\\'s kinematic characteristics. To analyze which parts of the model would affect the traveltime for anisotropic traveltime inversion methods, especially for wave equation tomography (WET), we drive the sensitivity kernels for anisotropic media using the VTI acoustic wave equation. A Born scattering approximation is first derived using the Fourier domain acoustic wave equation as a function of perturbations in three anisotropy parameters. Using the instantaneous traveltime, which unwraps the phase, we compute the kernels. These kernels resemble those for isotropic media, with the η kernel directionally dependent. They also have a maximum sensitivity along the geometrical ray, which is more realistic compared to the cross-correlation based kernels. Focusing on diving waves, which is used more often, especially recently in waveform inversion, we show sensitivity kernels in anisotropic media for this case.
Convection heat transfer in the double pass solar collector with porous media
This paper describes about heat transfer characteristics in the double pass solar heater with porous media. Nusselt and Stanton number had been used to shown the heat transfer. Nusselt number had been measured and compared with several theories. Stanton number in the double pass solar heater with porous media and without porous media had been compared. Predicted value of Stanton number will be shown in this paper
Investigations on the porous media equations and resistance coefficients for coastal structures
Jensen, Bjarne; Jacobsen, Niels Gjøl; Christensen, Erik Damgaard
2014-01-01
This paper considers the flow in porous media that occurs in coastal and offshore engineering problems. Over the past decades numerous formulations of flow equations for porous media have been presented. The present work re-examines the porous media equations of the most recent form and corrects ...... source CFD library OpenFOAM® and has been made publicly available to the engineering community as part of the wave generation framework waves2Foam....
An electrical conductivity model for fractal porous media
Wei, Wei; Cai, Jianchao; Hu, Xiangyun; Han, Qi
2015-06-01
Archie's equation is an empirical electrical conductivity-porosity model that has been used to predict the formation factor of porous rock for more than 70 years. However, the physical interpretation of its parameters, e.g., the cementation exponent m, remains questionable. In this study, a theoretical electrical conductivity equation is derived based on the fractal characteristics of porous media. The proposed model is expressed in terms of the tortuosity fractal dimension (DT), the pore fractal dimension (Df), the electrical conductivity of the pore liquid, and the porosity. The empirical parameter m is then determined from physically based parameters, such as DT and Df. Furthermore, a distinct interrelationship between DT and Df is obtained. We find a reasonably good match between the predicted formation factor by our model and experimental data.
High-precision synthetic computed tomography of reconstructed porous media
Hilfer, R.; Zauner, Th.
2011-12-01
Multiscale simulation of transport in disordered and porous media requires microstructures covering several decades in length scale. X-ray and synchrotron computed tomography are presently unable to resolve more than one decade of geometric detail. Recent advances in pore scale modeling [Biswal, Held, Khanna, Wang, and Hilfer, Phys. Rev. E PLEEE81539-375510.1103/PhysRevE.80.041301 80, 041301 (2009)] provide strongly correlated microstructures with several decades in microstructural detail. A carefully calibrated microstructure model for Fontainebleau sandstone has been discretized into a suite of three-dimensional microstructures with resolutions from roughly 128 μm down to roughly 500 nm. At the highest resolution the three-dimensional image consists of 327683=35184372088832 discrete cubic volume elements with gray values between 0 and 216. To the best of our knowledge, this synthetic image is the largest computed tomogram of a porous medium available at present.
Ferrofluid magnetoviscous control of wall flow channeling in porous media
Fa(ic)al Larachi; Damien Desvigne
2007-01-01
We analyzed the phenomenon of ferrofluid magnetoviscosity in high-permeability wall-region non-magnetic porous media of the Müller kind.After upscaling the pore-level ferrohydrodynamic model, we obtained a simplified volume-average zero-order axisymmetric model for non-Darcy non-turbulent flow of steady-state isothermal incompressible Newtonian ferrofluids through a porous medium experiencing external constant bulk-flow oriented gradient magnetic field, ferrofluid self-consistent demagnetizing field and induced magnetic field in the solid. The model was explored in contexts plagued by wall flow maldistribution due to low column-to-particle diameter ratios. It was shown that for proper magnetic field arrangement, wall channeling can be reduced by inflating wall flow resistance through magnetovisco-thickening and Kelvin body force density which reroute a fraction of wall flow towards bed core.
Anomalous dynamics of capillary rise in porous media
Shikhmurzaev, Yulii D.
2012-07-09
The anomalous dynamics of capillary rise in a porous medium discovered experimentally more than a decade ago is described. The developed theory is based on considering the principal modes of motion of the menisci that collectively form the wetting front on the Darcy scale. These modes, which include (i) dynamic wetting mode, (ii) threshold mode, and (iii) interface depinning process, are incorporated into the boundary conditions for the bulk equations formulated in the regular framework of continuum mechanics of porous media, thus allowing one to consider a general case of three-dimensional flows. The developed theory makes it possible to describe all regimes observed in the experiment, with the time spanning more than four orders of magnitude, and highlights the dominant physical mechanisms at different stages of the process. © 2012 American Physical Society.
Solute transport in dual-permeability porous media
Leij, Feike J.; Toride, Nobuo; Field, Malcolm S.; Sciortino, Antonella
2012-04-01
A dual-advection dispersion equation (DADE) is presented and solved to describe solute transport in structured or layered porous media with different nonzero flow rates in two distinct pore domains with linear solute transfer between them. This dual-permeability model constitutes a generalized version of the advection-dispersion equation (ADE) for transport in uniform porous media and the mobile-immobile model (MIM) for transport in media with a mobile and an immobile pore domain. Analytical tools for the DADE have mostly been lacking. An analytical solution has therefore been derived using Laplace transformation with time and modal decomposition based on matrix diagonalization, assuming the same dispersivity for both domains. Temporal moments are derived for the DADE and contrasted with those for the ADE and the MIM. The effective dispersion coefficient for the DADE approaches that of the ADE for a similar velocity in both pore domains and large values for the first-order transfer parameter, and approaches that of the MIM for the opposite conditions. The solution of the DADE is used to illustrate how differences in pore water velocity between the domains and low transfer rates will lead to double peaks in the volume- or flux-averaged concentration profiles versus time or position. The DADE is applied to optimize experimental breakthrough curves for an Andisol with a distinct intra- and interaggregate porosity. The DADE improved the description of the breakthrough data compared to the ADE and the MIM.