Optimal model of radiocarbon residence time in exchange reservoir

International Nuclear Information System (INIS)

Dergachev, V.A.

1977-01-01

Radiocarbon content variations in the earth atmosphere were studied using a mathematical model. The so-called exchange reservoir was considered consisting of layers, and the radiocarbon exchange rate at the interfaces between these layers was supposed to be constant. The process of 14 C mixing and exchange in a dynamic system is described by a system of nonhomogeneous 1st order differential equations. The model also accounts for the change in rate of radiocarbon formation in the earth atmosphere due to cosmic and geophysical effects (solar activity, solar cycle, etc.). (J.P.)

Reservoir souring: Problems, uncertainties and modelling. Part I: Problems and uncertainty involved in prediction. Part II: Preliminary investigations of a computational model

International Nuclear Information System (INIS)

Paulsen, J.E.; Read, P.A.; Thompson, C.P.; Jelley, C.; Lezeau, P.

1996-01-01

The paper relates to improved oil recovery (IOR) techniques by mathematical modelling. The uncertainty involved in modelling of reservoir souring is discussed. IOR processes are speculated to influence a souring process in a positive direction. Most models do not take into account pH in reservoir fluids, and thus do not account for partitioning behaviour of sulfide. Also, sulfide is antagonistic to bacterial metabolism and impedes to bacterial metabolism and impedes the sulfate reduction rate, this may be an important factor in modelling. Biofilms are thought to play a crucial role in a reservoir souring process. Biofilm in a reservoir matrix is different from biofilm in open systems. This has major impact on microbial impact on microbial transport and behaviour. Studies on microbial activity in reservoir matrices must be carried out with model cores, in order to mimic a realistic situation. Sufficient data do not exist today. The main conclusion is that a model does not reflect a true situation before the nature of these elements is understood. A simplified version of an Norwegian developed biofilm model is discussed. The model incorporates all the important physical phenomena studied in the above references such as bacteria growth limited by nutrients and/or energy sources and hydrogen sulfide adsorption. 18 refs., 8 figs., 1 tab

Reservoir souring: Problems, uncertainties and modelling. Part I: Problems and uncertainty involved in prediction. Part II: Preliminary investigations of a computational model

Energy Technology Data Exchange (ETDEWEB)

Paulsen, J.E. [Rogalandsforskning, Stavanger (Norway); Read, P.A.; Thompson, C.P.; Jelley, C.; Lezeau, P.

1996-12-31

The paper relates to improved oil recovery (IOR) techniques by mathematical modelling. The uncertainty involved in modelling of reservoir souring is discussed. IOR processes are speculated to influence a souring process in a positive direction. Most models do not take into account pH in reservoir fluids, and thus do not account for partitioning behaviour of sulfide. Also, sulfide is antagonistic to bacterial metabolism and impedes to bacterial metabolism and impedes the sulfate reduction rate, this may be an important factor in modelling. Biofilms are thought to play a crucial role in a reservoir souring process. Biofilm in a reservoir matrix is different from biofilm in open systems. This has major impact on microbial impact on microbial transport and behaviour. Studies on microbial activity in reservoir matrices must be carried out with model cores, in order to mimic a realistic situation. Sufficient data do not exist today. The main conclusion is that a model does not reflect a true situation before the nature of these elements is understood. A simplified version of an Norwegian developed biofilm model is discussed. The model incorporates all the important physical phenomena studied in the above references such as bacteria growth limited by nutrients and/or energy sources and hydrogen sulfide adsorption. 18 refs., 8 figs., 1 tab.

Modeling reservoir geomechanics using discrete element method : Application to reservoir monitoring

Energy Technology Data Exchange (ETDEWEB)

Alassi, Haitham Tayseer

2008-09-15

Understanding reservoir geomechanical behavior is becoming more and more important for the petroleum industry. Reservoir compaction, which may result in surface subsidence and fault reactivation, occurs during reservoir depletion. Stress changes and possible fracture development inside and outside a depleting reservoir can be monitored using time-lapse (so-called '4D') seismic and/or passive seismic, and this can give valuable information about the conditions of a given reservoir during production. In this study we will focus on using the (particle-based) Discrete Element Method (DEM) to model reservoir geomechanical behavior during depletion and fluid injection. We show in this study that DEM can be used in modeling reservoir geomechanical behavior by comparing results obtained from DEM to those obtained from analytical solutions. The match of the displacement field between DEM and the analytical solution is good, however there is mismatch of the stress field which is related to the way stress is measured in DEM. A good match is however obtained by measuring the stress field carefully. We also use DEM to model reservoir geomechanical behavior beyond the elasticity limit where fractures can develop and faults can reactivate. A general technique has been developed to relate DEM parameters to rock properties. This is necessary in order to use correct reservoir geomechanical properties during modeling. For any type of particle packing there is a limitation that the maximum ratio between P- and S-wave velocity Vp/Vs that can be modeled is 3 . The static behavior for a loose packing is different from the dynamic behavior. Empirical relations are needed for the static behavior based on numerical test observations. The dynamic behavior for both dense and loose packing can be given by analytical relations. Cosserat continuum theory is needed to derive relations for Vp and Vs. It is shown that by constraining the particle rotation, the S-wave velocity can be

Modeling of carbonate reservoir variable secondary pore space based on CT images

Science.gov (United States)

Nie, X.; Nie, S.; Zhang, J.; Zhang, C.; Zhang, Z.

2017-12-01

Digital core technology has brought convenience to us, and X-ray CT scanning is one of the most common way to obtain 3D digital cores. However, it can only provide the original information of the only samples being scanned, and we can't modify the porosity of the scanned cores. For numerical rock physical simulations, a series of cores with variable porosities are needed to determine the relationship between the physical properties and porosity. In carbonate rocks, the secondary pore space including dissolution pores, caves and natural fractures is the key reservoir space, which makes the study of carbonate secondary porosity very important. To achieve the variation of porosities in one rock sample, based on CT scanned digital cores, according to the physical and chemical properties of carbonate rocks, several mathematical methods are chosen to simulate the variation of secondary pore space. We use the erosion and dilation operations of mathematical morphology method to simulate the pore space changes of dissolution pores and caves. We also use the Fractional Brownian Motion model to generate natural fractures with different widths and angles in digital cores to simulate fractured carbonate rocks. The morphological opening-and-closing operations in mathematical morphology method are used to simulate distribution of fluid in the pore space. The established 3D digital core models with different secondary porosities and water saturation status can be used in the study of the physical property numerical simulations of carbonate reservoir rocks.

Simulation of Reservoir Sediment Flushing of the Three Gorges Reservoir Using an Artificial Neural Network

Directory of Open Access Journals (Sweden)

Xueying Li

2016-05-01

Full Text Available Reservoir sedimentation and its effect on the environment are the most serious world-wide problems in water resources development and utilization today. As one of the largest water conservancy projects, the Three Gorges Reservoir (TGR has been controversial since its demonstration period, and sedimentation is the major concern. Due to the complex physical mechanisms of water and sediment transport, this study adopts the Error Back Propagation Training Artificial Neural Network (BP-ANN to analyze the relationship between the sediment flushing efficiency of the TGR and its influencing factors. The factors are determined by the analysis on 1D unsteady flow and sediment mathematical model, mainly including reservoir inflow, incoming sediment concentration, reservoir water level, and reservoir release. Considering the distinguishing features of reservoir sediment delivery in different seasons, the monthly average data from 2003, when the TGR was put into operation, to 2011 are used to train, validate, and test the BP-ANN model. The results indicate that, although the sample space is quite limited, the whole sediment delivery process can be schematized by the established BP-ANN model, which can be used to help sediment flushing and thus decrease the reservoir sedimentation.

Mathematical modelling

DEFF Research Database (Denmark)

Blomhøj, Morten

2004-01-01

Developing competences for setting up, analysing and criticising mathematical models are normally seen as relevant only from and above upper secondary level. The general belief among teachers is that modelling activities presuppose conceptual understanding of the mathematics involved. Mathematical...... roots for the construction of important mathematical concepts. In addition competences for setting up, analysing and criticising modelling processes and the possible use of models is a formative aim in this own right for mathematics teaching in general education. The paper presents a theoretical...... modelling, however, can be seen as a practice of teaching that place the relation between real life and mathematics into the centre of teaching and learning mathematics, and this is relevant at all levels. Modelling activities may motivate the learning process and help the learner to establish cognitive...

Prediction of radionuclide migration in the Pripyat river and Dnieper reservoirs and decision support of water protection measures on the basis of mathematical modelling

International Nuclear Information System (INIS)

Morozov, A.A.; Zheleznyak, M.J.; Voitsekhovich, O.; Aliev, K.A.; Bilotkach, U.V.

1997-01-01

Since May 1986 in Kiev in the Institute of Mathematical Machines and System Problems, Cybernetics Center of the National Academy of Sciences of Ukraine has been started the development of the computerised system for processing of Dniper basin radiological monitoring data and modelling of radionuclide dispersion in rivers and reservoirs. For this work it was established the Interdisciplinary Working Group that joints the specialists from the State Committee of Water Resources, State Committee of Hydrometeorology, National Academy of Sciences and other Ukrainian institutions. The objectives of the computerized system development were formulated by the State Emergency Commission and later by the Ukrainian Minchernobyl as follows: reliable evaluation of the surface water contamination at Pripyat River and Dnieper River on the basis of monitoring data from the different institutions; seasonal and long-term prediction of the surface water radioactive contamination; decision support for the aquatic post-accidental countermeasures, directed to diminish the radionuclides fluxes from the Chernobyl area through the Pripyat River and Dnieper Reservoirs; decision support for the countermeasures directed on changes in the water assumption

Viral persistence, latent reservoir, and blips: a review on HIV-1 dynamics and modeling during HAART and related treatment implications

Energy Technology Data Exchange (ETDEWEB)

Rong, Libin [Los Alamos National Laboratory; Perelson, Alan [Los Alamos National Laboratory

2008-01-01

HIV-1 eradication from infected individuals has not been achieved with the use of highly active antiretroviral therapy (HAART) for a prolonged period of time. The cellular reservoir for HIV-1 in resting memory CD4{sup +} T cells remains a major obstacle to viral elimination. The reservoir does not decay significantly over long periods of time as is able to release replication competent HIV-1 upon cell activation. Residual ongoing viral replication may likely occur in many patients because low levels of virus can be detected in plasma by sensitive assays and transient episodes of viremia, or HIV-1 blips, are often observed in patients even with successful viral suppression for many years. Here we review our current knowledge of the factors contributing to viral persistence, the latent reservoir, and blips, and mathematical models developed to explore them and their relationships. We show how mathematical modeling can help improve our understanding of HIV-1 dynamics in patients on HAART and the quantitative events underlying HIV-1 latency, reservoir stability, low-level viremic persistence, and emergence of intermittent viral blips. We also discuss treatment implications related to these studies.

Mathematical analysis of a model for zoonotic visceral leishmaniasis

Directory of Open Access Journals (Sweden)

Nafiu Hussaini

2017-11-01

Full Text Available Zoonotic visceral leishmaniasis (ZVL, caused by the protozoan parasite Leishmania infantum and transmitted to humans and reservoir hosts by female sandflies, is endemic in many parts of the world (notably in Africa, Asia and the Mediterranean. This study presents a new mathematical model for assessing the transmission dynamics of ZVL in human and non-human animal reservoir populations. The model undergoes the usual phenomenon of backward bifurcation exhibited by similar vector-borne disease transmission models. In the absence of such phenomenon (which is shown to arise due to the disease-induced mortality in the host populations, the nontrivial disease-free equilibrium of the model is shown to be globally-asymptotically stable when the associated reproduction number of the model is less than unity. Using case and demographic data relevant to ZVL dynamics in Arac̣atuba municipality of Brazil, it is shown, for the default case when systemic insecticide-based drugs are not used to treat infected reservoir hosts, that the associated reproduction number of the model (ℛ0 ranges from 0.3 to 1.4, with a mean of ℛ0=0.85. Furthermore, when the effect of such drug treatment is explicitly incorporated in the model (i.e., accounting for the additional larval and sandfly mortality, following feeding on the treated reservoirs, the range of ℛ0 decreases to ℛ0∈[0.1,0.6], with a mean of ℛ0=0.35 (this significantly increases the prospect of the effective control or elimination of the disease. Thus, ZVL transmission models (in communities where such treatment strategy is implemented that do not explicitly incorporate the effect of such treatment may be over-estimating the disease burden (as measured in terms of ℛ0 in the community. It is shown that ℛ0 is more sensitive to increases in sandfly lifespan than that of the animal reservoir (so, a strategy that focuses on reducing sandflies, rather than the animal reservoir (e.g., via culling, may be

System Identification Based Proxy Model of a Reservoir under Water Injection

Directory of Open Access Journals (Sweden)

Berihun M. Negash

2017-01-01

Full Text Available Simulation of numerical reservoir models with thousands and millions of grid blocks may consume a significant amount of time and effort, even when high performance processors are used. In cases where the simulation runs are required for sensitivity analysis, dynamic control, and optimization, the act needs to be repeated several times by continuously changing parameters. This makes it even more time-consuming. Currently, proxy models that are based on response surface are being used to lessen the time required for running simulations during sensitivity analysis and optimization. Proxy models are lighter mathematical models that run faster and perform in place of heavier models that require large computations. Nevertheless, to acquire data for modeling and validation and develop the proxy model itself, hundreds of simulation runs are required. In this paper, a system identification based proxy model that requires only a single simulation run and a properly designed excitation signal was proposed and evaluated using a benchmark case study. The results show that, with proper design of excitation signal and proper selection of model structure, system identification based proxy models are found to be practical and efficient alternatives for mimicking the performance of numerical reservoir models. The resulting proxy models have potential applications for dynamic well control and optimization.

Numerical Simulation of Two Dimensional Flows in Yazidang Reservoir

Science.gov (United States)

Huang, Lingxiao; Liu, Libo; Sun, Xuehong; Zheng, Lanxiang; Jing, Hefang; Zhang, Xuande; Li, Chunguang

2018-01-01

This paper studied the problem of water flow in the Yazid Ang reservoir. It built 2-D RNG turbulent model, rated the boundary conditions, used the finite volume method to discrete equations and divided the grid by the advancing-front method. It simulated the two conditions of reservoir flow field, compared the average vertical velocity of the simulated value and the measured value nearby the water inlet and the water intake. The results showed that the mathematical model could be applied to the similar industrial water reservoir.

Modeling Reservoir-River Networks in Support of Optimizing Seasonal-Scale Reservoir Operations

Science.gov (United States)

Villa, D. L.; Lowry, T. S.; Bier, A.; Barco, J.; Sun, A.

2011-12-01

HydroSCOPE (Hydropower Seasonal Concurrent Optimization of Power and the Environment) is a seasonal time-scale tool for scenario analysis and optimization of reservoir-river networks. Developed in MATLAB, HydroSCOPE is an object-oriented model that simulates basin-scale dynamics with an objective of optimizing reservoir operations to maximize revenue from power generation, reliability in the water supply, environmental performance, and flood control. HydroSCOPE is part of a larger toolset that is being developed through a Department of Energy multi-laboratory project. This project's goal is to provide conventional hydropower decision makers with better information to execute their day-ahead and seasonal operations and planning activities by integrating water balance and operational dynamics across a wide range of spatial and temporal scales. This presentation details the modeling approach and functionality of HydroSCOPE. HydroSCOPE consists of a river-reservoir network model and an optimization routine. The river-reservoir network model simulates the heat and water balance of river-reservoir networks for time-scales up to one year. The optimization routine software, DAKOTA (Design Analysis Kit for Optimization and Terascale Applications - dakota.sandia.gov), is seamlessly linked to the network model and is used to optimize daily volumetric releases from the reservoirs to best meet a set of user-defined constraints, such as maximizing revenue while minimizing environmental violations. The network model uses 1-D approximations for both the reservoirs and river reaches and is able to account for surface and sediment heat exchange as well as ice dynamics for both models. The reservoir model also accounts for inflow, density, and withdrawal zone mixing, and diffusive heat exchange. Routing for the river reaches is accomplished using a modified Muskingum-Cunge approach that automatically calculates the internal timestep and sub-reach lengths to match the conditions of

Mathematical Modeling and Pure Mathematics

Science.gov (United States)

Usiskin, Zalman

2015-01-01

Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…

A Mathematical Pressure Transient Analysis Model for Multiple Fractured Horizontal Wells in Shale Gas Reservoirs

Directory of Open Access Journals (Sweden)

Yan Zeng

2018-01-01

Full Text Available Multistage fractured horizontal wells (MFHWs have become the main technology for shale gas exploration. However, the existing models have neglected the percolation mechanism in nanopores of organic matter and failed to consider the differences among the reservoir properties in different areas. On that account, in this study, a modified apparent permeability model was proposed describing gas flow in shale gas reservoirs by integrating bulk gas flow in nanopores and gas desorption from nanopores. The apparent permeability was introduced into the macroseepage model to establish a dynamic pressure analysis model for MFHWs dual-porosity formations. The Laplace transformation and the regular perturbation method were used to obtain an analytical solution. The influences of fracture half-length, fracture permeability, Langmuir volume, matrix radius, matrix permeability, and induced fracture permeability on pressure and production were discussed. Results show that fracture half-length, fracture permeability, and induced fracture permeability exert a significant influence on production. A larger Langmuir volume results in a smaller pressure and pressure derivative. An increase in matrix permeability increases the production rate. Besides, this model fits the actual field data relatively well. It has a reliable theoretical foundation and can preferably describe the dynamic changes of pressure in the exploration process.

The reservoir model: a differential equation model of psychological regulation.

Science.gov (United States)

Deboeck, Pascal R; Bergeman, C S

2013-06-01

Differential equation models can be used to describe the relationships between the current state of a system of constructs (e.g., stress) and how those constructs are changing (e.g., based on variable-like experiences). The following article describes a differential equation model based on the concept of a reservoir. With a physical reservoir, such as one for water, the level of the liquid in the reservoir at any time depends on the contributions to the reservoir (inputs) and the amount of liquid removed from the reservoir (outputs). This reservoir model might be useful for constructs such as stress, where events might "add up" over time (e.g., life stressors, inputs), but individuals simultaneously take action to "blow off steam" (e.g., engage coping resources, outputs). The reservoir model can provide descriptive statistics of the inputs that contribute to the "height" (level) of a construct and a parameter that describes a person's ability to dissipate the construct. After discussing the model, we describe a method of fitting the model as a structural equation model using latent differential equation modeling and latent distribution modeling. A simulation study is presented to examine recovery of the input distribution and output parameter. The model is then applied to the daily self-reports of negative affect and stress from a sample of older adults from the Notre Dame Longitudinal Study on Aging. (PsycINFO Database Record (c) 2013 APA, all rights reserved).

Mathematical Modelling Approach in Mathematics Education

Science.gov (United States)

Arseven, Ayla

2015-01-01

The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…

Integration of dynamical data in a geostatistical model of reservoir; Integration des donnees dynamiques dans un modele geostatistique de reservoir

Energy Technology Data Exchange (ETDEWEB)

Costa Reis, L.

2001-01-01

We have developed in this thesis a methodology of integrated characterization of heterogeneous reservoirs, from geologic modeling to history matching. This methodology is applied to the reservoir PBR, situated in Campos Basin, offshore Brazil, which has been producing since June 1979. This work is an extension of two other thesis concerning geologic and geostatistical modeling of the reservoir PBR from well data and seismic information. We extended the geostatistical litho-type model to the whole reservoir by using a particular approach of the non-stationary truncated Gaussian simulation method. This approach facilitated the application of the gradual deformation method to history matching. The main stages of the methodology for dynamic data integration in a geostatistical reservoir model are presented. We constructed a reservoir model and the initial difficulties in the history matching led us to modify some choices in the geological, geostatistical and flow models. These difficulties show the importance of dynamic data integration in reservoir modeling. The petrophysical property assignment within the litho-types was done by using well test data. We used an inversion procedure to evaluate the petrophysical parameters of the litho-types. The up-scaling is a necessary stage to reduce the flow simulation time. We compared several up-scaling methods and we show that the passage from the fine geostatistical model to the coarse flow model should be done very carefully. The choice of the fitting parameter depends on the objective of the study. In the case of the reservoir PBR, where water is injected in order to improve the oil recovery, the water rate of the producing wells is directly related to the reservoir heterogeneity. Thus, the water rate was chosen as the fitting parameter. We obtained significant improvements in the history matching of the reservoir PBR. First, by using a method we have proposed, called patchwork. This method allows us to built a coherent

Mathematical modelling

CERN Document Server

2016-01-01

This book provides a thorough introduction to the challenge of applying mathematics in real-world scenarios. Modelling tasks rarely involve well-defined categories, and they often require multidisciplinary input from mathematics, physics, computer sciences, or engineering. In keeping with this spirit of modelling, the book includes a wealth of cross-references between the chapters and frequently points to the real-world context. The book combines classical approaches to modelling with novel areas such as soft computing methods, inverse problems, and model uncertainty. Attention is also paid to the interaction between models, data and the use of mathematical software. The reader will find a broad selection of theoretical tools for practicing industrial mathematics, including the analysis of continuum models, probabilistic and discrete phenomena, and asymptotic and sensitivity analysis.

High resolution reservoir geological modelling using outcrop information

Energy Technology Data Exchange (ETDEWEB)

Zhang Changmin; Lin Kexiang; Liu Huaibo [Jianghan Petroleum Institute, Hubei (China)] [and others

1997-08-01

This is China`s first case study of high resolution reservoir geological modelling using outcrop information. The key of the modelling process is to build a prototype model and using the model as a geological knowledge bank. Outcrop information used in geological modelling including seven aspects: (1) Determining the reservoir framework pattern by sedimentary depositional system and facies analysis; (2) Horizontal correlation based on the lower and higher stand duration of the paleo-lake level; (3) Determining the model`s direction based on the paleocurrent statistics; (4) Estimating the sandbody communication by photomosaic and profiles; (6) Estimating reservoir properties distribution within sandbody by lithofacies analysis; and (7) Building the reservoir model in sandbody scale by architectural element analysis and 3-D sampling. A high resolution reservoir geological model of Youshashan oil field has been built by using this method.

Mathematical Simulation of Contaminant Flow in Closed Reservoir

Science.gov (United States)

Agranat, V. M.; Goudov, A. M.; Perminov, V. A.

2016-01-01

A mathematical model of the propagation in flooded mine lightweight contaminant due to allocation of groundwater is considered. Mathematical model was based on an analysis of experimental data and using concept and methods from reactive media mechanics. The boundary-value problem is solved numerically using the finite volume method. The distribution of fields of velocities and concentration of impurity particles in a flooded mine have been obtained at different times. These results can be used to analyze mining water treatment process due to environment and evaluate its further possible improvements.

DEVELOPMENT OF RESERVOIR CHARACTERIZATION TECHNIQUES AND PRODUCTION MODELS FOR EXPLOITING NATURALLY FRACTURED RESERVOIRS

Energy Technology Data Exchange (ETDEWEB)

Michael L. Wiggins; Raymon L. Brown; Faruk Civan; Richard G. Hughes

2002-12-31

For many years, geoscientists and engineers have undertaken research to characterize naturally fractured reservoirs. Geoscientists have focused on understanding the process of fracturing and the subsequent measurement and description of fracture characteristics. Engineers have concentrated on the fluid flow behavior in the fracture-porous media system and the development of models to predict the hydrocarbon production from these complex systems. This research attempts to integrate these two complementary views to develop a quantitative reservoir characterization methodology and flow performance model for naturally fractured reservoirs. The research has focused on estimating naturally fractured reservoir properties from seismic data, predicting fracture characteristics from well logs, and developing a naturally fractured reservoir simulator. It is important to develop techniques that can be applied to estimate the important parameters in predicting the performance of naturally fractured reservoirs. This project proposes a method to relate seismic properties to the elastic compliance and permeability of the reservoir based upon a sugar cube model. In addition, methods are presented to use conventional well logs to estimate localized fracture information for reservoir characterization purposes. The ability to estimate fracture information from conventional well logs is very important in older wells where data are often limited. Finally, a desktop naturally fractured reservoir simulator has been developed for the purpose of predicting the performance of these complex reservoirs. The simulator incorporates vertical and horizontal wellbore models, methods to handle matrix to fracture fluid transfer, and fracture permeability tensors. This research project has developed methods to characterize and study the performance of naturally fractured reservoirs that integrate geoscience and engineering data. This is an important step in developing exploitation strategies for

Surrogate reservoir models for CSI well probabilistic production forecast

Directory of Open Access Journals (Sweden)

Saúl Buitrago

2017-09-01

Full Text Available The aim of this work is to present the construction and use of Surrogate Reservoir Models capable of accurately predicting cumulative oil production for every well stimulated with cyclic steam injection at any given time in a heavy oil reservoir in Mexico considering uncertain variables. The central composite experimental design technique was selected to capture the maximum amount of information from the model response with a minimum number of reservoir models simulations. Four input uncertain variables (the dead oil viscosity with temperature, the reservoir pressure, the reservoir permeability and oil sand thickness hydraulically connected to the well were selected as the ones with more impact on the initial hot oil production rate according to an analytical production prediction model. Twenty five runs were designed and performed with the STARS simulator for each well type on the reservoir model. The results show that the use of Surrogate Reservoir Models is a fast viable alternative to perform probabilistic production forecasting of the reservoir.

Annual Perspectives in Mathematics Education 2016: Mathematical Modeling and Modeling Mathematics

Science.gov (United States)

Hirsch, Christian R., Ed.; McDuffie, Amy Roth, Ed.

2016-01-01

Mathematical modeling plays an increasingly important role both in real-life applications--in engineering, business, the social sciences, climate study, advanced design, and more--and within mathematics education itself. This 2016 volume of "Annual Perspectives in Mathematics Education" ("APME") focuses on this key topic from a…

The impact of hydraulic flow unit & reservoir quality index on pressure profile and productivity index in multi-segments reservoirs

Directory of Open Access Journals (Sweden)

Salam Al-Rbeawi

2017-12-01

Full Text Available The objective of this paper is studying the impact of the hydraulic flow unit and reservoir quality index (RQI on pressure profile and productivity index of horizontal wells acting in finite reservoirs. Several mathematical models have been developed to investigate this impact. These models have been built based on the pressure distribution in porous media, depleted by a horizontal well, consist of multi hydraulic flow units and different reservoir quality index. The porous media are assumed to be finite rectangular reservoirs having different configurations and the wellbores may have different lengths. Several analytical models describing flow regimes have been derived wherein hydraulic flow units and reservoir quality index have been included in addition to rock and fluid properties. The impact of these two parameters on reservoir performance has also been studied using steady state productivity index.It has been found that both pressure responses and flow regimes are highly affected by the existence of multiple hydraulic flow units in the porous media and the change in reservoir quality index for these units. Positive change in the RQI could lead to positive change in both pressure drop required for reservoir fluids to move towards the wellbore and hence the productivity index.

Development of Reservoir Characterization Techniques and Production Models for Exploiting Naturally Fractured Reservoirs

Energy Technology Data Exchange (ETDEWEB)

Wiggins, Michael L.; Brown, Raymon L.; Civan, Frauk; Hughes, Richard G.

2001-08-15

Research continues on characterizing and modeling the behavior of naturally fractured reservoir systems. Work has progressed on developing techniques for estimating fracture properties from seismic and well log data, developing naturally fractured wellbore models, and developing a model to characterize the transfer of fluid from the matrix to the fracture system for use in the naturally fractured reservoir simulator.

Modeling of reservoir operation in UNH global hydrological model

Science.gov (United States)

Shiklomanov, Alexander; Prusevich, Alexander; Frolking, Steve; Glidden, Stanley; Lammers, Richard; Wisser, Dominik

2015-04-01

Climate is changing and river flow is an integrated characteristic reflecting numerous environmental processes and their changes aggregated over large areas. Anthropogenic impacts on the river flow, however, can significantly exceed the changes associated with climate variability. Besides of irrigation, reservoirs and dams are one of major anthropogenic factor affecting streamflow. They distort hydrological regime of many rivers by trapping of freshwater runoff, modifying timing of river discharge and increasing the evaporation rate. Thus, reservoirs is an integral part of the global hydrological system and their impacts on rivers have to be taken into account for better quantification and understanding of hydrological changes. We developed a new technique, which was incorporated into WBM-TrANS model (Water Balance Model-Transport from Anthropogenic and Natural Systems) to simulate river routing through large reservoirs and natural lakes based on information available from freely accessible databases such as GRanD (the Global Reservoir and Dam database) or NID (National Inventory of Dams for US). Different formulations were applied for unregulated spillway dams and lakes, and for 4 types of regulated reservoirs, which were subdivided based on main purpose including generic (multipurpose), hydropower generation, irrigation and water supply, and flood control. We also incorporated rules for reservoir fill up and draining at the times of construction and decommission based on available data. The model were tested for many reservoirs of different size and types located in various climatic conditions using several gridded meteorological data sets as model input and observed daily and monthly discharge data from GRDC (Global Runoff Data Center), USGS Water Data (US Geological Survey), and UNH archives. The best results with Nash-Sutcliffe model efficiency coefficient in the range of 0.5-0.9 were obtained for temperate zone of Northern Hemisphere where most of large

Mathematical modeling

CERN Document Server

Eck, Christof; Knabner, Peter

2017-01-01

Mathematical models are the decisive tool to explain and predict phenomena in the natural and engineering sciences. With this book readers will learn to derive mathematical models which help to understand real world phenomena. At the same time a wealth of important examples for the abstract concepts treated in the curriculum of mathematics degrees are given. An essential feature of this book is that mathematical structures are used as an ordering principle and not the fields of application. Methods from linear algebra, analysis and the theory of ordinary and partial differential equations are thoroughly introduced and applied in the modeling process. Examples of applications in the fields electrical networks, chemical reaction dynamics, population dynamics, fluid dynamics, elasticity theory and crystal growth are treated comprehensively.

Fuzzy rule-based model for hydropower reservoirs operation

Energy Technology Data Exchange (ETDEWEB)

Moeini, R.; Afshar, A.; Afshar, M.H. [School of Civil Engineering, Iran University of Science and Technology, Tehran (Iran, Islamic Republic of)

2011-02-15

Real-time hydropower reservoir operation is a continuous decision-making process of determining the water level of a reservoir or the volume of water released from it. The hydropower operation is usually based on operating policies and rules defined and decided upon in strategic planning. This paper presents a fuzzy rule-based model for the operation of hydropower reservoirs. The proposed fuzzy rule-based model presents a set of suitable operating rules for release from the reservoir based on ideal or target storage levels. The model operates on an 'if-then' principle, in which the 'if' is a vector of fuzzy premises and the 'then' is a vector of fuzzy consequences. In this paper, reservoir storage, inflow, and period are used as premises and the release as the consequence. The steps involved in the development of the model include, construction of membership functions for the inflow, storage and the release, formulation of fuzzy rules, implication, aggregation and defuzzification. The required knowledge bases for the formulation of the fuzzy rules is obtained form a stochastic dynamic programming (SDP) model with a steady state policy. The proposed model is applied to the hydropower operation of ''Dez'' reservoir in Iran and the results are presented and compared with those of the SDP model. The results indicate the ability of the method to solve hydropower reservoir operation problems. (author)

ECMOR III: Third European Conference on the Mathematics of Oil Recovery

Energy Technology Data Exchange (ETDEWEB)

Christie, M.A.; Da Silva, F.V.; Farmer, C.L.; Guillon, O.; Heinemann, Z.E.; Lemonnier, P.; Regtien, J.M.M.; Van Spronsen, E. [eds.

1992-12-31

35 papers are presented in four groups: reservoir characterization (11), analytical methods (6), numerical methods (11), and reservoir simulation (7). With 11 papers the mathematical aspects of reservoir characterization are getting the attention they deserve. The geological and reservoir engineering concepts must be supplied by other disciplines, but no progress would be possible without mathematical modelling of these concepts. Analytical methods can be very helpful in deepening our insight. However, in this computer age they have a hard time competing with numerical methods. Fortunately this section is well presented with some very interesting papers. The numerical section covers a number of techniques aimed at improved reservoir simulation. Some are dealing with special applications: permeability prediction, steam injection, fractured reservoirs, hydrocarbons migration. In the reservoir simulation section the emphasis is on simulation of relatively small-scale features: fractures, fingering and wells

A mathematical model of Chagas disease transmission

Science.gov (United States)

Hidayat, Dayat; Nugraha, Edwin Setiawan; Nuraini, Nuning

2018-03-01

Chagas disease is a parasitic infection caused by protozoan Trypanosoma cruzi which is transmitted to human by insects of the subfamily Triatominae, including Rhodnius prolixus. This disease is a major problem in several countries of Latin America. A mathematical model of Chagas disease with separate vector reservoir and a neighboring human resident is constructed. The basic reproductive ratio is obtained and stability analysis of the equilibria is shown. We also performed sensitivity populations dynamics of infected humans and infected insects based on migration rate, carrying capacity, and infection rate parameters. Our findings showed that the dynamics of the infected human and insect is mostly affected by carrying capacity insect in the settlement.

Static reservoir modeling of the Bahariya reservoirs for the oilfields development in South Umbarka area, Western Desert, Egypt

Science.gov (United States)

Abdel-Fattah, Mohamed I.; Metwalli, Farouk I.; Mesilhi, El Sayed I.

2018-02-01

3D static reservoir modeling of the Bahariya reservoirs using seismic and wells data can be a relevant part of an overall strategy for the oilfields development in South Umbarka area (Western Desert, Egypt). The seismic data is used to build the 3D grid, including fault sticks for the fault modeling, and horizon interpretations and surfaces for horizon modeling. The 3D grid is the digital representation of the structural geology of Bahariya Formation. When we got a reasonably accurate representation, we fill the 3D grid with facies and petrophysical properties to simulate it, to gain a more precise understanding of the reservoir properties behavior. Sequential Indicator Simulation (SIS) and Sequential Gaussian Simulation (SGS) techniques are the stochastic algorithms used to spatially distribute discrete reservoir properties (facies) and continuous reservoir properties (shale volume, porosity, and water saturation) respectively within the created 3D grid throughout property modeling. The structural model of Bahariya Formation exhibits the trapping mechanism which is a fault assisted anticlinal closure trending NW-SE. This major fault breaks the reservoirs into two major fault blocks (North Block and South Block). Petrophysical models classified Lower Bahariya reservoir as a moderate to good reservoir rather than Upper Bahariya reservoir in terms of facies, with good porosity and permeability, low water saturation, and moderate net to gross. The Original Oil In Place (OOIP) values of modeled Bahariya reservoirs show hydrocarbon accumulation in economic quantity, considering the high structural dips at the central part of South Umbarka area. The powerful of 3D static modeling technique has provided a considerable insight into the future prediction of Bahariya reservoirs performance and production behavior.

RECENT ADVANCES IN NATURALLY FRACTURED RESERVOIR MODELING

OpenAIRE

ORDOÑEZ, A; PEÑUELA, G; IDROBO, E. A; MEDINA, C. E

2001-01-01

Large amounts of oil reserves are contained in naturally fractured reservoirs. Most of these hydrocarbon volumes have been left behind because of the poor knowledge and/or description methodology of those reservoirs. This lack of knowledge has lead to the nonexistence of good quantitative models for this complicated type of reservoirs. The complexity of naturally fractured reservoirs causes the need for integration of all existing information at all scales (drilling, well logging, seismic, we...

Teaching Mathematical Modeling in Mathematics Education

Science.gov (United States)

Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant

2016-01-01

Mathematics is not only a subject but it is also a language consisting of many different symbols and relations. Taught as a compulsory subject up the 10th class, students are then able to choose whether or not to study mathematics as a main subject. The present paper discusses mathematical modeling in mathematics education. The article provides…

Reservoir management under geological uncertainty using fast model update

NARCIS (Netherlands)

Hanea, R.; Evensen, G.; Hustoft, L.; Ek, T.; Chitu, A.; Wilschut, F.

2015-01-01

Statoil is implementing "Fast Model Update (FMU)," an integrated and automated workflow for reservoir modeling and characterization. FMU connects all steps and disciplines from seismic depth conversion to prediction and reservoir management taking into account relevant reservoir uncertainty. FMU

Mathematical modelling techniques

CERN Document Server

Aris, Rutherford

1995-01-01

""Engaging, elegantly written."" - Applied Mathematical ModellingMathematical modelling is a highly useful methodology designed to enable mathematicians, physicists and other scientists to formulate equations from a given nonmathematical situation. In this elegantly written volume, a distinguished theoretical chemist and engineer sets down helpful rules not only for setting up models but also for solving the mathematical problems they pose and for evaluating models.The author begins with a discussion of the term ""model,"" followed by clearly presented examples of the different types of mode

A Statistical Graphical Model of the California Reservoir System

Science.gov (United States)

Taeb, A.; Reager, J. T.; Turmon, M.; Chandrasekaran, V.

2017-11-01

The recent California drought has highlighted the potential vulnerability of the state's water management infrastructure to multiyear dry intervals. Due to the high complexity of the network, dynamic storage changes in California reservoirs on a state-wide scale have previously been difficult to model using either traditional statistical or physical approaches. Indeed, although there is a significant line of research on exploring models for single (or a small number of) reservoirs, these approaches are not amenable to a system-wide modeling of the California reservoir network due to the spatial and hydrological heterogeneities of the system. In this work, we develop a state-wide statistical graphical model to characterize the dependencies among a collection of 55 major California reservoirs across the state; this model is defined with respect to a graph in which the nodes index reservoirs and the edges specify the relationships or dependencies between reservoirs. We obtain and validate this model in a data-driven manner based on reservoir volumes over the period 2003-2016. A key feature of our framework is a quantification of the effects of external phenomena that influence the entire reservoir network. We further characterize the degree to which physical factors (e.g., state-wide Palmer Drought Severity Index (PDSI), average temperature, snow pack) and economic factors (e.g., consumer price index, number of agricultural workers) explain these external influences. As a consequence of this analysis, we obtain a system-wide health diagnosis of the reservoir network as a function of PDSI.

Using Mathematics, Mathematical Applications, Mathematical Modelling, and Mathematical Literacy: A Theoretical Study

Science.gov (United States)

Mumcu, Hayal Yavuz

2016-01-01

The purpose of this theoretical study is to explore the relationships between the concepts of using mathematics in the daily life, mathematical applications, mathematical modelling, and mathematical literacy. As these concepts are generally taken as independent concepts in the related literature, they are confused with each other and it becomes…

Representing Reservoir Stratification in Land Surface and Earth System Models

Science.gov (United States)

Yigzaw, W.; Li, H. Y.; Leung, L. R.; Hejazi, M. I.; Voisin, N.; Payn, R. A.; Demissie, Y.

2017-12-01

A one-dimensional reservoir stratification modeling has been developed as part of Model for Scale Adaptive River Transport (MOSART), which is the river transport model used in the Accelerated Climate Modeling for Energy (ACME) and Community Earth System Model (CESM). Reservoirs play an important role in modulating the dynamic water, energy and biogeochemical cycles in the riverine system through nutrient sequestration and stratification. However, most earth system models include lake models that assume a simplified geometry featuring a constant depth and a constant surface area. As reservoir geometry has important effects on thermal stratification, we developed a new algorithm for deriving generic, stratified area-elevation-storage relationships that are applicable at regional and global scales using data from Global Reservoir and Dam database (GRanD). This new reservoir geometry dataset is then used to support the development of a reservoir stratification module within MOSART. The mixing of layers (energy and mass) in the reservoir is driven by eddy diffusion, vertical advection, and reservoir inflow and outflow. Upstream inflow into a reservoir is treated as an additional source/sink of energy, while downstream outflow represented a sink. Hourly atmospheric forcing from North American Land Assimilation System (NLDAS) Phase II and simulated daily runoff by ACME land component are used as inputs for the model over the contiguous United States for simulations between 2001-2010. The model is validated using selected observed temperature profile data in a number of reservoirs that are subject to various levels of regulation. The reservoir stratification module completes the representation of riverine mass and heat transfer in earth system models, which is a major step towards quantitative understanding of human influences on the terrestrial hydrological, ecological and biogeochemical cycles.

Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches

Science.gov (United States)

Erbas, Ayhan Kürsat; Kertil, Mahmut; Çetinkaya, Bülent; Çakiroglu, Erdinç; Alacaci, Cengiz; Bas, Sinem

2014-01-01

Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and…

Derivation and application of mathematical model for well test analysis with variable skin factor in hydrocarbon reservoirs

Directory of Open Access Journals (Sweden)

Pengcheng Liu

2016-06-01

Full Text Available Skin factor is often regarded as a constant in most of the mathematical model for well test analysis in oilfields, but this is only a kind of simplified treatment with the actual skin factor changeable. This paper defined the average permeability of a damaged area as a function of time by using the definition of skin factor. Therefore a relationship between a variable skin factor and time was established. The variable skin factor derived was introduced into existing traditional models rather than using a constant skin factor, then, this newly derived mathematical model for well test analysis considering variable skin factor was solved by Laplace transform. The dimensionless wellbore pressure and its derivative changed with dimensionless time were plotted with double logarithm and these plots can be used for type curve fitting. The effects of all the parameters in the expression of variable skin factor were analyzed based on the dimensionless wellbore pressure and its derivative. Finally, actual well testing data were used to fit the type curves developed which validates the applicability of the mathematical model from Sheng-2 Block, Shengli Oilfield, China.

Advancing reservoir operation description in physically based hydrological models

Science.gov (United States)

Anghileri, Daniela; Giudici, Federico; Castelletti, Andrea; Burlando, Paolo

2016-04-01

Last decades have seen significant advances in our capacity of characterizing and reproducing hydrological processes within physically based models. Yet, when the human component is considered (e.g. reservoirs, water distribution systems), the associated decisions are generally modeled with very simplistic rules, which might underperform in reproducing the actual operators' behaviour on a daily or sub-daily basis. For example, reservoir operations are usually described by a target-level rule curve, which represents the level that the reservoir should track during normal operating conditions. The associated release decision is determined by the current state of the reservoir relative to the rule curve. This modeling approach can reasonably reproduce the seasonal water volume shift due to reservoir operation. Still, it cannot capture more complex decision making processes in response, e.g., to the fluctuations of energy prices and demands, the temporal unavailability of power plants or varying amount of snow accumulated in the basin. In this work, we link a physically explicit hydrological model with detailed hydropower behavioural models describing the decision making process by the dam operator. In particular, we consider two categories of behavioural models: explicit or rule-based behavioural models, where reservoir operating rules are empirically inferred from observational data, and implicit or optimization based behavioural models, where, following a normative economic approach, the decision maker is represented as a rational agent maximising a utility function. We compare these two alternate modelling approaches on the real-world water system of Lake Como catchment in the Italian Alps. The water system is characterized by the presence of 18 artificial hydropower reservoirs generating almost 13% of the Italian hydropower production. Results show to which extent the hydrological regime in the catchment is affected by different behavioural models and reservoir

MATHEMATICAL MODEL MANIPULATOR ROBOTS

Directory of Open Access Journals (Sweden)

O. N. Krakhmalev

2015-12-01

Full Text Available A mathematical model to describe the dynamics of manipulator robots. Mathematical model are the implementation of the method based on the Lagrange equation and using the transformation matrices of elastic coordinates. Mathematical model make it possible to determine the elastic deviations of manipulator robots from programmed motion trajectories caused by elastic deformations in hinges, which are taken into account in directions of change of the corresponding generalized coordinates. Mathematical model is approximated and makes it possible to determine small elastic quasi-static deviations and elastic vibrations. The results of modeling the dynamics by model are compared to the example of a two-link manipulator system. The considered model can be used when performing investigations of the mathematical accuracy of the manipulator robots.

Integration of 3D photogrammetric outcrop models in the reservoir modelling workflow

Science.gov (United States)

Deschamps, Remy; Joseph, Philippe; Lerat, Olivier; Schmitz, Julien; Doligez, Brigitte; Jardin, Anne

2014-05-01

3D technologies are now widely used in geosciences to reconstruct outcrops in 3D. The technology used for the 3D reconstruction is usually based on Lidar, which provides very precise models. Such datasets offer the possibility to build well-constrained outcrop analogue models for reservoir study purposes. The photogrammetry is an alternate methodology which principles are based in determining the geometric properties of an object from photographic pictures taken from different angles. Outcrop data acquisition is easy, and this methodology allows constructing 3D outcrop models with many advantages such as: - light and fast acquisition, - moderate processing time (depending on the size of the area of interest), - integration of field data and 3D outcrops into the reservoir modelling tools. Whatever the method, the advantages of digital outcrop model are numerous as already highlighted by Hodgetts (2013), McCaffrey et al. (2005) and Pringle et al. (2006): collection of data from otherwise inaccessible areas, access to different angles of view, increase of the possible measurements, attributes analysis, fast rate of data collection, and of course training and communication. This paper proposes a workflow where 3D geocellular models are built by integrating all sources of information from outcrops (surface picking, sedimentological sections, structural and sedimentary dips…). The 3D geomodels that are reconstructed can be used at the reservoir scale, in order to compare the outcrop information with subsurface models: the detailed facies models of the outcrops are transferred into petrophysical and acoustic models, which are used to test different scenarios of seismic and fluid flow modelling. The detailed 3D models are also used to test new techniques of static reservoir modelling, based either on geostatistical approaches or on deterministic (process-based) simulation techniques. A modelling workflow has been designed to model reservoir geometries and properties from

Physical Model-Based Investigation of Reservoir Sedimentation Processes

Directory of Open Access Journals (Sweden)

Cheng-Chia Huang

2018-03-01

Full Text Available Sedimentation is a serious problem in the operations of reservoirs. In Taiwan, the situation became worse after the Chi-Chi Earthquake recorded on 21 September 1999. The sediment trap efficiency in several regional reservoirs has been sharply increased, adversely affecting the operations on water supplies. According to the field record, the average annual sediment deposition observed in several regional reservoirs in Taiwan has been increased. For instance, the typhoon event recorded in 2008 at the Wushe Reservoir, Taiwan, produced a 3 m sediment deposit upstream of the dam. The remaining storage capacity in the Wushe Reservoir was reduced to 35.9% or a volume of 53.79 million m3 for flood water detention in 2010. It is urgent that research should be conducted to understand the sediment movement in the Wushe Reservoir. In this study, a scale physical model was built to reproduce the flood flow through the reservoir, investigate the long-term depositional pattern, and evaluate sediment trap efficiency. This allows us to estimate the residual life of the reservoir by proposing a modification of Brune’s method. It can be presented to predict the lifespan of Taiwan reservoirs due to higher applicability in both the physical model and the observed data.

Improving reservoir conformance using gelled polymer systems. Eleventh quarterly report, April 1, 1995--June 30, 1995

Energy Technology Data Exchange (ETDEWEB)

Green, D.W.; Willhite, G.P.; Buller, C.; McCool, S.; Vossoughi, S.; Michnick, M.

1995-07-24

The general objectives are to (1) to identify and develop gelled polymer systems which have potential to improve reservoir conformance of fluid displacement processes, (2) to determine the performance of these systems in bulk and in porous media, and (3) to develop methods to predict the capability of these systems to recover oil from petroleum reservoirs. This work focuses on three types of gel systems -- an aqueous polysaccharide (KUSP1) system that gels as a function of pH, the chromium(III)-polyacrylamide system and the aluminum citrate-polyacrylamide system. Laboratory research is directed at the fundamental understanding of the physics and chemistry of the gelation process in bulk form and in porous media. This knowledge will be used to develop conceptual and mathematical models of the gelation process. Mathematical models will then be extended to predict the performance of gelled polymer treatments in oil reservoirs. Technical progress is described for the following tasks: physical and chemical characterization of gel systems; mechanisms of in situ gelation; and mathematical modelling of the gel systems.

Computer Modeling of the Displacement Behavior of Carbon Dioxide in Undersaturated Oil Reservoirs

Directory of Open Access Journals (Sweden)

Ju Binshan

2015-11-01

Full Text Available The injection of CO2 into oil reservoirs is performed not only to improve oil recovery but also to store CO2 captured from fuel combustion. The objective of this work is to develop a numerical simulator to predict quantitatively supercritical CO2 flooding behaviors for Enhanced Oil Recovery (EOR. A non-isothermal compositional flow mathematical model is developed. The phase transition diagram is designed according to the Minimum Miscibility Pressure (MMP and CO2 maximum solubility in oil phase. The convection and diffusion of CO2 mixtures in multiphase fluids in reservoirs, mass transfer between CO2 and crude and phase partitioning are considered. The governing equations are discretized by applying a fully implicit finite difference technique. Newton-Raphson iterative technique was used to solve the nonlinear equation systems and a simulator was developed. The performances of CO2 immiscible and miscible flooding in oil reservoirs are predicted by the new simulator. The distribution of pressure and temperature, phase saturations, mole fraction of each component in each phase, formation damage caused by asphaltene precipitation and the improved oil recovery are predicted by the simulator. Experimental data validate the developed simulator by comparison with simulation results. The applications of the simulator in prediction of CO2 flooding in oil reservoirs indicate that the simulator is robust for predicting CO2 flooding performance.

Hydrodynamic modeling of petroleum reservoirs using simulator MUFITS

Science.gov (United States)

Afanasyev, Andrey

2015-04-01

MUFITS is new noncommercial software for numerical modeling of subsurface processes in various applications (www.mufits.imec.msu.ru). To this point, the simulator was used for modeling nonisothermal flows in geothermal reservoirs and for modeling underground carbon dioxide storage. In this work, we present recent extension of the code to petroleum reservoirs. The simulator can be applied in conventional black oil modeling, but it also utilizes a more complicated models for volatile oil and gas condensate reservoirs as well as for oil rim fields. We give a brief overview of the code by providing the description of internal representation of reservoir models, which are constructed of grid blocks, interfaces, stock tanks as well as of pipe segments and pipe junctions for modeling wells and surface networks. For conventional black oil approach, we present the simulation results for SPE comparative tests. We propose an accelerated compositional modeling method for sub- and supercritical flows subjected to various phase equilibria, particularly to three-phase equilibria of vapour-liquid-liquid type. The method is based on the calculation of the thermodynamic potential of reservoir fluid as a function of pressure, total enthalpy and total composition and storing its values as a spline table, which is used in hydrodynamic simulation for accelerated PVT properties prediction. We provide the description of both the spline calculation procedure and the flashing algorithm. We evaluate the thermodynamic potential for a mixture of two pseudo-components modeling the heavy and light hydrocarbon fractions. We develop a technique for converting black oil PVT tables to the potential, which can be used for in-situ hydrocarbons multiphase equilibria prediction under sub- and supercritical conditions, particularly, in gas condensate and volatile oil reservoirs. We simulate recovery from a reservoir subject to near-critical initial conditions for hydrocarbon mixture. We acknowledge

Modeling and optimizing the design of matrix treatments in carbonate reservoirs with self-diverting acid systems

International Nuclear Information System (INIS)

Bulgakova, G T; Kharisov, R Ya; Sharifullin, A R; Pestrikov, A V

2015-01-01

Application of a self-diverting-acid based on viscoelastic surfactant (SDVA) is a promising technology for improving the efficacy of acid treatment in oil and gas-bearing carbonate reservoirs. In this study, we present a mathematical model for assessing SDVA flow and reaction with carbonate rock using the SDVA rheological characteristics. The model calculates the technological parameters for acidizing operations and the prediction of well productivity after acid treatment, in addition to technical and economic optimization of the acidizing process by modeling different acid treatment options with varying volumes, injection rates, process fluids stages and initial economic scenarios

Sampling from stochastic reservoir models constrained by production data

Energy Technology Data Exchange (ETDEWEB)

Hegstad, Bjoern Kaare

1997-12-31

When a petroleum reservoir is evaluated, it is important to forecast future production of oil and gas and to assess forecast uncertainty. This is done by defining a stochastic model for the reservoir characteristics, generating realizations from this model and applying a fluid flow simulator to the realizations. The reservoir characteristics define the geometry of the reservoir, initial saturation, petrophysical properties etc. This thesis discusses how to generate realizations constrained by production data, that is to say, the realizations should reproduce the observed production history of the petroleum reservoir within the uncertainty of these data. The topics discussed are: (1) Theoretical framework, (2) History matching, forecasting and forecasting uncertainty, (3) A three-dimensional test case, (4) Modelling transmissibility multipliers by Markov random fields, (5) Up scaling, (6) The link between model parameters, well observations and production history in a simple test case, (7) Sampling the posterior using optimization in a hierarchical model, (8) A comparison of Rejection Sampling and Metropolis-Hastings algorithm, (9) Stochastic simulation and conditioning by annealing in reservoir description, and (10) Uncertainty assessment in history matching and forecasting. 139 refs., 85 figs., 1 tab.

Developing mathematical modelling competence

DEFF Research Database (Denmark)

Blomhøj, Morten; Jensen, Tomas Højgaard

2003-01-01

In this paper we introduce the concept of mathematical modelling competence, by which we mean being able to carry through a whole mathematical modelling process in a certain context. Analysing the structure of this process, six sub-competences are identified. Mathematical modelling competence...... cannot be reduced to these six sub-competences, but they are necessary elements in the development of mathematical modelling competence. Experience from the development of a modelling course is used to illustrate how the different nature of the sub-competences can be used as a tool for finding...... the balance between different kinds of activities in a particular educational setting. Obstacles of social, cognitive and affective nature for the students' development of mathematical modelling competence are reported and discussed in relation to the sub-competences....

Modeling of Gas Production from Shale Reservoirs Considering Multiple Transport Mechanisms.

Directory of Open Access Journals (Sweden)

Chaohua Guo

Full Text Available Gas transport in unconventional shale strata is a multi-mechanism-coupling process that is different from the process observed in conventional reservoirs. In micro fractures which are inborn or induced by hydraulic stimulation, viscous flow dominates. And gas surface diffusion and gas desorption should be further considered in organic nano pores. Also, the Klinkenberg effect should be considered when dealing with the gas transport problem. In addition, following two factors can play significant roles under certain circumstances but have not received enough attention in previous models. During pressure depletion, gas viscosity will change with Knudsen number; and pore radius will increase when the adsorption gas desorbs from the pore wall. In this paper, a comprehensive mathematical model that incorporates all known mechanisms for simulating gas flow in shale strata is presented. The objective of this study was to provide a more accurate reservoir model for simulation based on the flow mechanisms in the pore scale and formation geometry. Complex mechanisms, including viscous flow, Knudsen diffusion, slip flow, and desorption, are optionally integrated into different continua in the model. Sensitivity analysis was conducted to evaluate the effect of different mechanisms on the gas production. The results showed that adsorption and gas viscosity change will have a great impact on gas production. Ignoring one of following scenarios, such as adsorption, gas permeability change, gas viscosity change, or pore radius change, will underestimate gas production.

Improving reservoir conformance using gelled polymer systems. Quarterly report, September 25--December 24, 1993

Energy Technology Data Exchange (ETDEWEB)

Green, D.W.; Willhite, G.P.; Buller, C.; McCool, S.; Vossoughi, S.; Michnick, M.

1994-01-19

The general objectives are to (1) to identify and develop gelled polymer systems which have potential to improve reservoir conformance of fluid displacement processes, (2) to determine the performance of these systems in bulk and in porous media, and (3) to develop methods to predict the capability of these systems to recover oil from petroleum reservoirs. This work focuses on three types of gel systems -- an aqueous polysaccharide (KUSP1) system that gels as a function of pH, the chromium(III)-polyacrylamide system and the aluminum citrate-polyacrylamide system. Laboratory research is directed at the fundamental understanding of the physics and chemistry of the gelation process in bulk form and in porous media. This knowledge will be used to develop conceptual and mathematical models of the gelation process. Mathematical models will then be extended to predict the performance of gelled polymer treatments in oil reservoirs. Results to date are summarized.

A Study of the Optimal Planning Model for Reservoir Sustainable Management- A Case Study of Shihmen Reservoir

Science.gov (United States)

Chen, Y. Y.; Ho, C. C.; Chang, L. C.

2017-12-01

The reservoir management in Taiwan faces lots of challenge. Massive sediment caused by landslide were flushed into reservoir, which will decrease capacity, rise the turbidity, and increase supply risk. Sediment usually accompanies nutrition that will cause eutrophication problem. Moreover, the unevenly distribution of rainfall cause water supply instability. Hence, how to ensure sustainable use of reservoirs has become an important task in reservoir management. The purpose of the study is developing an optimal planning model for reservoir sustainable management to find out an optimal operation rules of reservoir flood control and sediment sluicing. The model applies Genetic Algorithms to combine with the artificial neural network of hydraulic analysis and reservoir sediment movement. The main objective of operation rules in this study is to prevent reservoir outflow caused downstream overflow, minimum the gap between initial and last water level of reservoir, and maximum sluicing sediment efficiency. A case of Shihmen reservoir was used to explore the different between optimal operating rule and the current operation of the reservoir. The results indicate optimal operating rules tended to open desilting tunnel early and extend open duration during flood discharge period. The results also show the sluicing sediment efficiency of optimal operating rule is 36%, 44%, 54% during Typhoon Jangmi, Typhoon Fung-Wong, and Typhoon Sinlaku respectively. The results demonstrate the optimal operation rules do play a role in extending the service life of Shihmen reservoir and protecting the safety of downstream. The study introduces a low cost strategy, alteration of operation reservoir rules, into reservoir sustainable management instead of pump dredger in order to improve the problem of elimination of reservoir sediment and high cost.

Reservoir Models for Gas Hydrate Numerical Simulation

Science.gov (United States)

Boswell, R.

2016-12-01

Scientific and industrial drilling programs have now providing detailed information on gas hydrate systems that will increasingly be the subject of field experiments. The need to carefully plan these programs requires reliable prediction of reservoir response to hydrate dissociation. Currently, a major emphasis in gas hydrate modeling is the integration of thermodynamic/hydrologic phenomena with geomechanical response for both reservoir and bounding strata. However, also critical to the ultimate success of these efforts is the appropriate development of input geologic models, including several emerging issues, including (1) reservoir heterogeneity, (2) understanding of the initial petrophysical characteristics of the system (reservoirs and seals), the dynamic evolution of those characteristics during active dissociation, and the interdependency of petrophysical parameters and (3) the nature of reservoir boundaries. Heterogeneity is ubiquitous aspect of every natural reservoir, and appropriate characterization is vital. However, heterogeneity is not random. Vertical variation can be evaluated with core and well log data; however, core data often are challenged by incomplete recovery. Well logs also provide interpretation challenges, particularly where reservoirs are thinly-bedded due to limitation in vertical resolution. This imprecision will extend to any petrophysical measurements that are derived from evaluation of log data. Extrapolation of log data laterally is also complex, and should be supported by geologic mapping. Key petrophysical parameters include porosity, permeability and it many aspects, and water saturation. Field data collected to date suggest that the degree of hydrate saturation is strongly controlled by/dependant upon reservoir quality and that the ratio of free to bound water in the remaining pore space is likely also controlled by reservoir quality. Further, those parameters will also evolve during dissociation, and not necessary in a simple

Integrated workflow for characterizing and modeling fracture network in unconventional reservoirs using microseismic data

Science.gov (United States)

Ayatollahy Tafti, Tayeb

We develop a new method for integrating information and data from different sources. We also construct a comprehensive workflow for characterizing and modeling a fracture network in unconventional reservoirs, using microseismic data. The methodology is based on combination of several mathematical and artificial intelligent techniques, including geostatistics, fractal analysis, fuzzy logic, and neural networks. The study contributes to scholarly knowledge base on the characterization and modeling fractured reservoirs in several ways; including a versatile workflow with a novel objective functions. Some the characteristics of the methods are listed below: 1. The new method is an effective fracture characterization procedure estimates different fracture properties. Unlike the existing methods, the new approach is not dependent on the location of events. It is able to integrate all multi-scaled and diverse fracture information from different methodologies. 2. It offers an improved procedure to create compressional and shear velocity models as a preamble for delineating anomalies and map structures of interest and to correlate velocity anomalies with fracture swarms and other reservoir properties of interest. 3. It offers an effective way to obtain the fractal dimension of microseismic events and identify the pattern complexity, connectivity, and mechanism of the created fracture network. 4. It offers an innovative method for monitoring the fracture movement in different stages of stimulation that can be used to optimize the process. 5. Our newly developed MDFN approach allows to create a discrete fracture network model using only microseismic data with potential cost reduction. It also imposes fractal dimension as a constraint on other fracture modeling approaches, which increases the visual similarity between the modeled networks and the real network over the simulated volume.

Modelling of Reservoir Operations using Fuzzy Logic and ANNs

Science.gov (United States)

Van De Giesen, N.; Coerver, B.; Rutten, M.

2015-12-01

Today, almost 40.000 large reservoirs, containing approximately 6.000 km3 of water and inundating an area of almost 400.000 km2, can be found on earth. Since these reservoirs have a storage capacity of almost one-sixth of the global annual river discharge they have a large impact on the timing, volume and peaks of river discharges. Global Hydrological Models (GHM) are thus significantly influenced by these anthropogenic changes in river flows. We developed a parametrically parsimonious method to extract operational rules based on historical reservoir storage and inflow time-series. Managing a reservoir is an imprecise and vague undertaking. Operators always face uncertainties about inflows, evaporation, seepage losses and various water demands to be met. They often base their decisions on experience and on available information, like reservoir storage and the previous periods inflow. We modeled this decision-making process through a combination of fuzzy logic and artificial neural networks in an Adaptive-Network-based Fuzzy Inference System (ANFIS). In a sensitivity analysis, we compared results for reservoirs in Vietnam, Central Asia and the USA. ANFIS can indeed capture reservoirs operations adequately when fed with a historical monthly time-series of inflows and storage. It was shown that using ANFIS, operational rules of existing reservoirs can be derived without much prior knowledge about the reservoirs. Their validity was tested by comparing actual and simulated releases with each other. For the eleven reservoirs modelled, the normalised outflow, , was predicted with a MSE of 0.002 to 0.044. The rules can be incorporated into GHMs. After a network for a specific reservoir has been trained, the inflow calculated by the hydrological model can be combined with the release and initial storage to calculate the storage for the next time-step using a mass balance. Subsequently, the release can be predicted one time-step ahead using the inflow and storage.

Mathematical Modeling Using MATLAB

National Research Council Canada - National Science Library

Phillips, Donovan

1998-01-01

.... Mathematical Modeling Using MA MATLAB acts as a companion resource to A First Course in Mathematical Modeling with the goal of guiding the reader to a fuller understanding of the modeling process...

Use of natural geochemical tracers to improve reservoir simulation models

Energy Technology Data Exchange (ETDEWEB)

Huseby, O.; Chatzichristos, C.; Sagen, J.; Muller, J.; Kleven, R.; Bennett, B.; Larter, S.; Stubos, A.K.; Adler, P.M.

2005-01-01

This article introduces a methodology for integrating geochemical data in reservoir simulations to improve hydrocarbon reservoir models. The method exploits routine measurements of naturally existing inorganic ion concentration in hydrocarbon reservoir production wells, and uses the ions as non-partitioning water tracers. The methodology is demonstrated on a North Sea field case, using the field's reservoir model, together with geochemical information (SO{sub 4}{sup 2}, Mg{sup 2+} K{sup +}, Ba{sup 2+}, Sr{sup 2+}, Ca{sup 2+}, Cl{sup -} concentrations) from the field's producers. From the data-set we show that some of the ions behave almost as ideal sea-water tracers, i.e. without sorption to the matrix, ion-exchange with the matrix or scale-formation with other ions in the formation water. Moreover, the dataset shows that ion concentrations in pure formation-water vary according to formation. This information can be used to allocate produced water to specific water-producing zones in commingled production. Based on an evaluation of the applicability of the available data, one inorganic component, SO{sub 4}{sup 2}, is used as a natural seawater tracer. Introducing SO{sub 4}{sup 2} as a natural tracer in a tracer simulation has revealed a potential for improvements of the reservoir model. By tracking the injected seawater it was possible to identify underestimated fault lengths in the reservoir model. The demonstration confirms that geochemical data are valuable additional information for reservoir characterization, and shows that integration of geochemical data into reservoir simulation procedures can improve reservoir simulation models. (author)

Multi-time scale Climate Informed Stochastic Hybrid Simulation-Optimization Model (McISH model) for Multi-Purpose Reservoir System

Science.gov (United States)

Lu, M.; Lall, U.

2013-12-01

In order to mitigate the impacts of climate change, proactive management strategies to operate reservoirs and dams are needed. A multi-time scale climate informed stochastic model is developed to optimize the operations for a multi-purpose single reservoir by simulating decadal, interannual, seasonal and sub-seasonal variability. We apply the model to a setting motivated by the largest multi-purpose dam in N. India, the Bhakhra reservoir on the Sutlej River, a tributary of the Indus. This leads to a focus on timing and amplitude of the flows for the monsoon and snowmelt periods. The flow simulations are constrained by multiple sources of historical data and GCM future projections, that are being developed through a NSF funded project titled 'Decadal Prediction and Stochastic Simulation of Hydroclimate Over Monsoon Asia'. The model presented is a multilevel, nonlinear programming model that aims to optimize the reservoir operating policy on a decadal horizon and the operation strategy on an updated annual basis. The model is hierarchical, in terms of having a structure that two optimization models designated for different time scales are nested as a matryoshka doll. The two optimization models have similar mathematical formulations with some modifications to meet the constraints within that time frame. The first level of the model is designated to provide optimization solution for policy makers to determine contracted annual releases to different uses with a prescribed reliability; the second level is a within-the-period (e.g., year) operation optimization scheme that allocates the contracted annual releases on a subperiod (e.g. monthly) basis, with additional benefit for extra release and penalty for failure. The model maximizes the net benefit of irrigation, hydropower generation and flood control in each of the periods. The model design thus facilitates the consistent application of weather and climate forecasts to improve operations of reservoir systems. The

Digital Core Modelling for Clastic Oil and Gas Reservoir

Science.gov (United States)

Belozerov, I.; Berezovsky, V.; Gubaydullin, M.; Yur’ev, A.

2018-05-01

"Digital core" is a multi-purpose tool for solving a variety of tasks in the field of geological exploration and production of hydrocarbons at various stages, designed to improve the accuracy of geological study of subsurface resources, the efficiency of reproduction and use of mineral resources, as well as applying the results obtained in production practice. The actuality of the development of the "Digital core" software is that even a partial replacement of natural laboratory experiments with mathematical modelling can be used in the operative calculation of reserves in exploratory drilling, as well as in the absence of core material from wells. Or impossibility of its research by existing laboratory methods (weakly cemented, loose, etc. rocks). 3D-reconstruction of the core microstructure can be considered as a cheap and least time-consuming method for obtaining petrophysical information about the main filtration-capacitive properties and fluid motion in reservoir rocks.

Modeling of Reservoir Inflow for Hydropower Dams Using Artificial ...

African Journals Online (AJOL)

The stream flow at the three hydropower reservoirs in Nigeria were modeled using hydro-meteorological parameters and Artificial Neural Network (ANN). The model revealed positive relationship between the observed and the modeled reservoir inflow with values of correlation coefficient of 0.57, 0.84 and 0.92 for Kainji, ...

Mathematical Modeling: A Structured Process

Science.gov (United States)

Anhalt, Cynthia Oropesa; Cortez, Ricardo

2015-01-01

Mathematical modeling, in which students use mathematics to explain or interpret physical, social, or scientific phenomena, is an essential component of the high school curriculum. The Common Core State Standards for Mathematics (CCSSM) classify modeling as a K-12 standard for mathematical practice and as a conceptual category for high school…

Primary School Pre-Service Mathematics Teachers' Views on Mathematical Modeling

Science.gov (United States)

Karali, Diren; Durmus, Soner

2015-01-01

The current study aimed to identify the views of pre-service teachers, who attended a primary school mathematics teaching department but did not take mathematical modeling courses. The mathematical modeling activity used by the pre-service teachers was developed with regards to the modeling activities utilized by Lesh and Doerr (2003) in their…

Finite mathematics models and applications

CERN Document Server

Morris, Carla C

2015-01-01

Features step-by-step examples based on actual data and connects fundamental mathematical modeling skills and decision making concepts to everyday applicability Featuring key linear programming, matrix, and probability concepts, Finite Mathematics: Models and Applications emphasizes cross-disciplinary applications that relate mathematics to everyday life. The book provides a unique combination of practical mathematical applications to illustrate the wide use of mathematics in fields ranging from business, economics, finance, management, operations research, and the life and social sciences.

Modelling and simulation of compressible fluid flow in oil reservoir: a case study of the Jubilee Field, Tano Basin (Ghana)

International Nuclear Information System (INIS)

Gawusu, S.

2015-07-01

Oil extraction represents an important investment and the control of a rational exploitation of a field means mastering various scientific techniques including the understanding of the dynamics of fluids in place. This thesis presents a theoretical investigation of the dynamic behaviour of an oil reservoir during its exploitation. The study investigated the dynamics of fluid flow patterns in a homogeneous oil reservoir using the Radial Diffusivity Equation (RDE) as well as two phase oil-water flow equations. The RDE model was solved analytically and numerically for pressure using the Constant Terminal Rate Solution (CTRS) and the fully implicit Finite Difference Method (FDM) respectively. The mathematical derivations of the models and their solution procedures were presented to allow for easy utilization of the techniques for reservoir and engineering applications. The study predicted that the initial oil reservoir pressure will be able to do the extraction for a very long time before any other recovery method will be used to aid in the extraction process depending on the rate of production. Reservoir simulation describing a one dimensional radial flow of a compressible fluid in porous media may be adequately performed using ordinary laptop computers as revealed by the study. For the simulation of MATLAB, the case of the Jubilee Fields, Tano Basin was studied, an algorithm was developed for the simulation of pressure in the reservoir. It ensues from the analysis of the plots of pressure vrs time and space that the Pressure Transient Analysis (PTA) was duly followed. The approximate solutions of the analytical and numerical solutions to the Radial Diffusivity Equation (RDE) were in excellent agreement, thus the reservoir simulation model developed can be used to describe typical pressure-time relationships that are used in conventional Pressure Transient Analysis (PTA). The study was extended to two phase oil-water flow in reservoirs. The flow of fluids in multi

The 24-Hour Mathematical Modeling Challenge

Science.gov (United States)

Galluzzo, Benjamin J.; Wendt, Theodore J.

2015-01-01

Across the mathematics curriculum there is a renewed emphasis on applications of mathematics and on mathematical modeling. Providing students with modeling experiences beyond the ordinary classroom setting remains a challenge, however. In this article, we describe the 24-hour Mathematical Modeling Challenge, an extracurricular event that exposes…

Mathematical Models of Elementary Mathematics Learning and Performance. Final Report.

Science.gov (United States)

Suppes, Patrick

This project was concerned with the development of mathematical models of elementary mathematics learning and performance. Probabilistic finite automata and register machines with a finite number of registers were developed as models and extensively tested with data arising from the elementary-mathematics strand curriculum developed by the…

Mathematical problems in meteorological modelling

CERN Document Server

Csomós, Petra; Faragó, István; Horányi, András; Szépszó, Gabriella

2016-01-01

This book deals with mathematical problems arising in the context of meteorological modelling. It gathers and presents some of the most interesting and important issues from the interaction of mathematics and meteorology. It is unique in that it features contributions on topics like data assimilation, ensemble prediction, numerical methods, and transport modelling, from both mathematical and meteorological perspectives. The derivation and solution of all kinds of numerical prediction models require the application of results from various mathematical fields. The present volume is divided into three parts, moving from mathematical and numerical problems through air quality modelling, to advanced applications in data assimilation and probabilistic forecasting. The book arose from the workshop “Mathematical Problems in Meteorological Modelling” held in Budapest in May 2014 and organized by the ECMI Special Interest Group on Numerical Weather Prediction. Its main objective is to highlight the beauty of the de...

MATHEMATICAL MODELING OF UNSTEADY FILTRATION OF ELASTIC LIQUID IN AN INHOMOGENEOUS RESERVOIR

Directory of Open Access Journals (Sweden)

A. G. Balamirzoev

2013-01-01

Full Text Available The article considers the possibility of numerical solution of two-dimensional problem of unsteady filtration in an inhomogeneous elastic liquid reservoir. The problem of finding the distribution of the pressure p(x,y,t in the process of exploitation of deposits is reduced to the solution of a differential equation of parabolic type with variable coefficients. The problem is solved approximately by using the method of finite differences.

An Investigation of Mathematical Modeling with Pre-Service Secondary Mathematics Teachers

Science.gov (United States)

Thrasher, Emily Plunkett

2016-01-01

The goal of this thesis was to investigate and enhance our understanding of what occurs while pre-service mathematics teachers engage in a mathematical modeling unit that is broadly based upon mathematical modeling as defined by the Common Core State Standards for Mathematics (National Governors Association Center for Best Practices & Council…

Understanding Prospective Teachers' Mathematical Modeling Processes in the Context of a Mathematical Modeling Course

Science.gov (United States)

Zeytun, Aysel Sen; Cetinkaya, Bulent; Erbas, Ayhan Kursat

2017-01-01

This paper investigates how prospective teachers develop mathematical models while they engage in modeling tasks. The study was conducted in an undergraduate elective course aiming to improve prospective teachers' mathematical modeling abilities, while enhancing their pedagogical knowledge for the integrating of modeling tasks into their future…

Mathematical modeling with multidisciplinary applications

CERN Document Server

Yang, Xin-She

2013-01-01

Features mathematical modeling techniques and real-world processes with applications in diverse fields Mathematical Modeling with Multidisciplinary Applications details the interdisciplinary nature of mathematical modeling and numerical algorithms. The book combines a variety of applications from diverse fields to illustrate how the methods can be used to model physical processes, design new products, find solutions to challenging problems, and increase competitiveness in international markets. Written by leading scholars and international experts in the field, the

Reservoirs operation and water resources utilization coordination in Hongshuihe basin

Science.gov (United States)

Li, Chonghao; Chi, Kaige; Pang, Bo; Tang, Hongbin

2018-06-01

In the recent decade, the demand for water resources has been increasing with the economic development. The reservoirs of cascade hydropower stations in Hongshuihe basin, which are constructed with a main purpose of power generation, are facing more integrated water resources utilization problem. The conflict between power generation of cascade reservoirs and flood control, shipping, environmental protection and water supply has become increasingly prominent. This paper introduces the general situation and integrated water demand of cascade reservoirs in Hongshuihe basin, and it analyses the impact of various types of integrated water demand on power generation and supply. It establishes mathematic models, constrained by various types of integrated water demand, to guide the operation and water resources utilization management of cascade reservoirs in Hongshuihe basin. Integrated water coordination mechanism of Hongshuihe basin is also introduced. It provides a technical and management guide and demonstration for cascade reservoirs operation and integrated water management at home and abroad.

Prediction of tectonic stresses and fracture networks with geomechanical reservoir models

International Nuclear Information System (INIS)

Henk, A.; Fischer, K.

2014-09-01

This project evaluates the potential of geomechanical Finite Element (FE) models for the prediction of in situ stresses and fracture networks in faulted reservoirs. Modeling focuses on spatial variations of the in situ stress distribution resulting from faults and contrasts in mechanical rock properties. In a first methodological part, a workflow is developed for building such geomechanical reservoir models and calibrating them to field data. In the second part, this workflow was applied successfully to an intensively faulted gas reservoir in the North German Basin. A truly field-scale geomechanical model covering more than 400km 2 was built and calibrated. It includes a mechanical stratigraphy as well as a network of 86 faults. The latter are implemented as distinct planes of weakness and allow the fault-specific evaluation of shear and normal stresses. A so-called static model describes the recent state of the reservoir and, thus, after calibration its results reveal the present-day in situ stress distribution. Further geodynamic modeling work considers the major stages in the tectonic history of the reservoir and provides insights in the paleo stress distribution. These results are compared to fracture data and hydraulic fault behavior observed today. The outcome of this project confirms the potential of geomechanical FE models for robust stress and fracture predictions. The workflow is generally applicable and can be used for modeling of any stress-sensitive reservoir.

Prediction of tectonic stresses and fracture networks with geomechanical reservoir models

Energy Technology Data Exchange (ETDEWEB)

Henk, A.; Fischer, K. [TU Darmstadt (Germany). Inst. fuer Angewandte Geowissenschaften

2014-09-15

This project evaluates the potential of geomechanical Finite Element (FE) models for the prediction of in situ stresses and fracture networks in faulted reservoirs. Modeling focuses on spatial variations of the in situ stress distribution resulting from faults and contrasts in mechanical rock properties. In a first methodological part, a workflow is developed for building such geomechanical reservoir models and calibrating them to field data. In the second part, this workflow was applied successfully to an intensively faulted gas reservoir in the North German Basin. A truly field-scale geomechanical model covering more than 400km{sup 2} was built and calibrated. It includes a mechanical stratigraphy as well as a network of 86 faults. The latter are implemented as distinct planes of weakness and allow the fault-specific evaluation of shear and normal stresses. A so-called static model describes the recent state of the reservoir and, thus, after calibration its results reveal the present-day in situ stress distribution. Further geodynamic modeling work considers the major stages in the tectonic history of the reservoir and provides insights in the paleo stress distribution. These results are compared to fracture data and hydraulic fault behavior observed today. The outcome of this project confirms the potential of geomechanical FE models for robust stress and fracture predictions. The workflow is generally applicable and can be used for modeling of any stress-sensitive reservoir.

Mathematical Modelling in the Junior Secondary Years: An Approach Incorporating Mathematical Technology

Science.gov (United States)

Lowe, James; Carter, Merilyn; Cooper, Tom

2018-01-01

Mathematical models are conceptual processes that use mathematics to describe, explain, and/or predict the behaviour of complex systems. This article is written for teachers of mathematics in the junior secondary years (including out-of-field teachers of mathematics) who may be unfamiliar with mathematical modelling, to explain the steps involved…

Mathematical Modeling of Rotary Blood Pumps in a Pulsatile In Vitro Flow Environment.

Science.gov (United States)

Pirbodaghi, Tohid

2017-08-01

Nowadays, sacrificing animals to develop medical devices and receive regulatory approval has become more common, which increases ethical concerns. Although in vivo tests are necessary for development and evaluation of new devices, nonetheless, with appropriate in vitro setups and mathematical models, a part of the validation process can be performed using these models to reduce the number of sacrificed animals. The main aim of this study is to present a mathematical model simulating the hydrodynamic function of a rotary blood pump (RBP) in a pulsatile in vitro flow environment. This model relates the pressure head of the RBP to the flow rate, rotational speed, and time derivatives of flow rate and rotational speed. To identify the model parameters, an in vitro setup was constructed consisting of a piston pump, a compliance chamber, a throttle, a buffer reservoir, and the CentriMag RBP. A 40% glycerin-water mixture as a blood analog fluid and deionized water were used in the hydraulic circuit to investigate the effect of viscosity and density of the working fluid on the model parameters. First, model variables were physically measured and digitally acquired. Second, an identification algorithm based on regression analysis was used to derive the model parameters. Third, the completed model was validated with a totally different set of in vitro data. The model is usable for both mathematical simulations of the interaction between the pump and heart and indirect pressure measurement in a clinical context. © 2017 International Center for Artificial Organs and Transplantation and Wiley Periodicals, Inc.

Applied impulsive mathematical models

CERN Document Server

Stamova, Ivanka

2016-01-01

Using the theory of impulsive differential equations, this book focuses on mathematical models which reflect current research in biology, population dynamics, neural networks and economics. The authors provide the basic background from the fundamental theory and give a systematic exposition of recent results related to the qualitative analysis of impulsive mathematical models. Consisting of six chapters, the book presents many applicable techniques, making them available in a single source easily accessible to researchers interested in mathematical models and their applications. Serving as a valuable reference, this text is addressed to a wide audience of professionals, including mathematicians, applied researchers and practitioners.

A Primer for Mathematical Modeling

Science.gov (United States)

Sole, Marla

2013-01-01

With the implementation of the National Council of Teachers of Mathematics recommendations and the adoption of the Common Core State Standards for Mathematics, modeling has moved to the forefront of K-12 education. Modeling activities not only reinforce purposeful problem-solving skills, they also connect the mathematics students learn in school…

Introducing Modeling Transition Diagrams as a Tool to Connect Mathematical Modeling to Mathematical Thinking

Science.gov (United States)

Czocher, Jennifer A.

2016-01-01

This study contributes a methodological tool to reconstruct the cognitive processes and mathematical activities carried out by mathematical modelers. Represented as Modeling Transition Diagrams (MTDs), individual modeling routes were constructed for four engineering undergraduate students. Findings stress the importance and limitations of using…

Mathematical modelling of membrane separation

DEFF Research Database (Denmark)

Vinther, Frank

This thesis concerns mathematical modelling of membrane separation. The thesis consists of introductory theory on membrane separation, equations of motion, and properties of dextran, which will be the solute species throughout the thesis. Furthermore, the thesis consist of three separate mathemat......This thesis concerns mathematical modelling of membrane separation. The thesis consists of introductory theory on membrane separation, equations of motion, and properties of dextran, which will be the solute species throughout the thesis. Furthermore, the thesis consist of three separate...... mathematical models, each with a different approach to membrane separation. The first model is a statistical model investigating the interplay between solute shape and the probability of entering the membrane. More specific the transition of solute particles from being spherical to becoming more elongated...

Three dimensional heat transport modeling in Vossoroca reservoir

Science.gov (United States)

Arcie Polli, Bruna; Yoshioka Bernardo, Julio Werner; Hilgert, Stephan; Bleninger, Tobias

2017-04-01

Freshwater reservoirs are used for many purposes as hydropower generation, water supply and irrigation. In Brazil, according to the National Energy Balance of 2013, hydropower energy corresponds to 70.1% of the Brazilian demand. Superficial waters (which include rivers, lakes and reservoirs) are the most used source for drinking water supply - 56% of the municipalities use superficial waters as a source of water. The last two years have shown that the Brazilian water and electricity supply is highly vulnerable and that improved management is urgently needed. The construction of reservoirs affects physical, chemical and biological characteristics of the water body, e.g. stratification, temperature, residence time and turbulence reduction. Some water quality issues related to reservoirs are eutrophication, greenhouse gas emission to the atmosphere and dissolved oxygen depletion in the hypolimnion. The understanding of the physical processes in the water body is fundamental to reservoir management. Lakes and reservoirs may present a seasonal behavior and stratify due to hydrological and meteorological conditions, and especially its vertical distribution may be related to water quality. Stratification can control heat and dissolved substances transport. It has been also reported the importance of horizontal temperature gradients, e.g. inflows and its density and processes of mass transfer from shallow to deeper regions of the reservoir, that also may impact water quality. Three dimensional modeling of the heat transport in lakes and reservoirs is an important tool to the understanding and management of these systems. It is possible to estimate periods of large vertical temperature gradients, inhibiting vertical transport and horizontal gradients, which could be responsible for horizontal transport of heat and substances (e.g. differential cooling or inflows). Vossoroca reservoir was constructed in 1949 by the impoundment of São João River and is located near to

Mechanical and mathematical models of multi-stage horizontal fracturing strings and their application

Directory of Open Access Journals (Sweden)

Zhanghua Lian

2015-03-01

Full Text Available Multi-stage SRV fracturing in horizontal wells is a new technology developed at home and abroad in recent years to effectively develop shale gas or low-permeability reservoirs, but on the other hand makes the mechanical environment of fracturing strings more complicated at the same time. In view of this, based on the loading features of tubing strings during the multi-stage fracturing of a horizontal well, mechanical models were established for three working cases of multiple packer setting, open differential-pressure sliding sleeve, and open ball-injection sliding sleeve under a hold-down packer. Moreover, mathematical models were respectively built for the above three cases. According to the Lame formula and Von Mises stress calculation formula for the thick-walled cylinder in the theory of elastic mechanics, a mathematical model was also established to calculate the equivalent stress for tubing string safety evaluation when the fracturing string was under the combined action of inner pressure, external squeezing force and axial stress, and another mathematical model was built for the mechanical strength and safety evaluation of multi-stage fracturing strings. In addition, a practical software was developed for the mechanical safety evaluation of horizontal well multi-stage fracturing strings according to the mathematical model developed for the mechanical calculation of the multi-packer string in horizontal wells. The research results were applied and verified in a gas well of Tahe Oilfield in the Tarim Basin with excellent effects, providing a theoretical basis and a simple and reliable technical means for optimal design and safety evaluation of safe operational parameters of multi-stage fracturing strings in horizontal wells.

Mathematical Modeling: Challenging the Figured Worlds of Elementary Mathematics

Science.gov (United States)

Wickstrom, Megan H.

2017-01-01

This article is a report on a teacher study group that focused on three elementary teachers' perceptions of mathematical modeling in contrast to typical mathematics instruction. Through the theoretical lens of figured worlds, I discuss how mathematics instruction was conceptualized across the classrooms in terms of artifacts, discourse, and…

Mathematics Teachers' Ideas about Mathematical Models: A Diverse Landscape

Science.gov (United States)

Bautista, Alfredo; Wilkerson-Jerde, Michelle H.; Tobin, Roger G.; Brizuela, Bárbara M.

2014-01-01

This paper describes the ideas that mathematics teachers (grades 5-9) have regarding mathematical models of real-world phenomena, and explores how teachers' ideas differ depending on their educational background. Participants were 56 United States in-service mathematics teachers. We analyzed teachers' written responses to three open-ended…

A poroelastic reservoir model for predicting subsidence and mapping subsurface pressure fronts

International Nuclear Information System (INIS)

Du, J.; Olson, J.E.

2001-01-01

A forward model was constructed to numerically predict surface subsidence and reservoir compaction following the approach of Segall [Pure Appl. Phys. 139 (1992) 536]. A nucleus of poroelastic strain is numerically integrated over a rectangular prism assuming constant pressure change. This fundamental geometry allows a reservoir to be divided into many small cubic blocks in a manner similar to reservoir simulation. The subsidence and compaction effects of the pressure change throughout the reservoir are calculated by the superposition of results from each individual block. Using forward modeling, pressure boundary conditions can be acquired from pressure test data or reservoir simulation predictions. An inversion model also was developed that can track pressure fronts in a subsurface reservoir using surface displacements. The capability of the inversion model was demonstrated using synthetic examples of one-well and four-well cases with different layouts of surface observation locations. The impact of noise on the inversion result is also included

An introduction to mathematical modeling

CERN Document Server

Bender, Edward A

2000-01-01

Employing a practical, ""learn by doing"" approach, this first-rate text fosters the development of the skills beyond the pure mathematics needed to set up and manipulate mathematical models. The author draws on a diversity of fields - including science, engineering, and operations research - to provide over 100 reality-based examples. Students learn from the examples by applying mathematical methods to formulate, analyze, and criticize models. Extensive documentation, consisting of over 150 references, supplements the models, encouraging further research on models of particular interest. The

Mathematical Modeling in the Undergraduate Curriculum

Science.gov (United States)

Toews, Carl

2012-01-01

Mathematical modeling occupies an unusual space in the undergraduate mathematics curriculum: typically an "advanced" course, it nonetheless has little to do with formal proof, the usual hallmark of advanced mathematics. Mathematics departments are thus forced to decide what role they want the modeling course to play, both as a component of the…

Teachers' Conceptions of Mathematical Modeling

Science.gov (United States)

Gould, Heather

2013-01-01

The release of the "Common Core State Standards for Mathematics" in 2010 resulted in a new focus on mathematical modeling in United States curricula. Mathematical modeling represents a way of doing and understanding mathematics new to most teachers. The purpose of this study was to determine the conceptions and misconceptions held by…

Data Integration for the Generation of High Resolution Reservoir Models

Energy Technology Data Exchange (ETDEWEB)

Albert Reynolds; Dean Oliver; Gaoming Li; Yong Zhao; Chaohui Che; Kai Zhang; Yannong Dong; Chinedu Abgalaka; Mei Han

2009-01-07

The goal of this three-year project was to develop a theoretical basis and practical technology for the integration of geologic, production and time-lapse seismic data in a way that makes best use of the information for reservoir description and reservoir performance predictions. The methodology and practical tools for data integration that were developed in this research project have been incorporated into computational algorithms that are feasible for large scale reservoir simulation models. As the integration of production and seismic data require calibrating geological/geostatistical models to these data sets, the main computational tool is an automatic history matching algorithm. The following specific goals were accomplished during this research. (1) We developed algorithms for calibrating the location of the boundaries of geologic facies and the distribution of rock properties so that production and time-lapse seismic data are honored. (2) We developed and implemented specific procedures for conditioning reservoir models to time-lapse seismic data. (3) We developed and implemented algorithms for the characterization of measurement errors which are needed to determine the relative weights of data when conditioning reservoir models to production and time-lapse seismic data by automatic history matching. (4) We developed and implemented algorithms for the adjustment of relative permeability curves during the history matching process. (5) We developed algorithms for production optimization which accounts for geological uncertainty within the context of closed-loop reservoir management. (6) To ensure the research results will lead to practical public tools for independent oil companies, as part of the project we built a graphical user interface for the reservoir simulator and history matching software using Visual Basic.

Mathematical Modelling of Predatory Prokaryotes

NARCIS (Netherlands)

Wilkinson, Michael H.F.

2006-01-01

Predator–prey models have a long history in mathematical modelling of ecosystem dynamics and evolution. In this chapter an introduction to the methodology of mathematical modelling is given, with emphasis on microbial predator–prey systems, followed by a description of variants of the basic

The egg model - a geological ensemble for reservoir simulation

NARCIS (Netherlands)

Jansen, J.D.; Fonseca, R.M.; Kahrobaei, S.; Siraj, M.M.; Essen, van G.M.; Hof, Van den P.M.J.

2014-01-01

The ‘Egg Model’ is a synthetic reservoir model consisting of an ensemble of 101 relatively small three-dimensional realizations of a channelized oil reservoir produced under water flooding conditions with eight water injectors and four oil producers. It has been used in numerous publications to

Local Refinement of the Super Element Model of Oil Reservoir

Directory of Open Access Journals (Sweden)

A.B. Mazo

2017-12-01

Full Text Available In this paper, we propose a two-stage method for petroleum reservoir simulation. The method uses two models with different degrees of detailing to describe hydrodynamic processes of different space-time scales. At the first stage, the global dynamics of the energy state of the deposit and reserves is modeled (characteristic scale of such changes is km / year. The two-phase flow equations in the model of global dynamics operate with smooth averaged pressure and saturation fields, and they are solved numerically on a large computational grid of super-elements with a characteristic cell size of 200-500 m. The tensor coefficients of the super-element model are calculated using special procedures of upscaling of absolute and relative phase permeabilities. At the second stage, a local refinement of the super-element model is constructed for calculating small-scale processes (with a scale of m / day, which take place, for example, during various geological and technical measures aimed at increasing the oil recovery of a reservoir. Then we solve the two-phase flow problem in the selected area of the measure exposure on a detailed three-dimensional grid, which resolves the geological structure of the reservoir, and with a time step sufficient for describing fast-flowing processes. The initial and boundary conditions of the local problem are formulated on the basis of the super-element solution. This approach allows us to reduce the computational costs in order to solve the problems of designing and monitoring the oil reservoir. To demonstrate the proposed approach, we give an example of the two-stage modeling of the development of a layered reservoir with a local refinement of the model during the isolation of a water-saturated high-permeability interlayer. We show a good compliance between the locally refined solution of the super-element model in the area of measure exposure and the results of numerical modeling of the whole history of reservoir

Modelling CO2 emissions from water surface of a boreal hydroelectric reservoir.

Science.gov (United States)

Wang, Weifeng; Roulet, Nigel T; Kim, Youngil; Strachan, Ian B; Del Giorgio, Paul; Prairie, Yves T; Tremblay, Alain

2018-01-15

To quantify CO 2 emissions from water surface of a reservoir that was shaped by flooding the boreal landscape, we developed a daily time-step reservoir biogeochemistry model. We calibrated the model using the measured concentrations of dissolved organic and inorganic carbon (C) in a young boreal hydroelectric reservoir, Eastmain-1 (EM-1), in northern Quebec, Canada. We validated the model against observed CO 2 fluxes from an eddy covariance tower in the middle of EM-1. The model predicted the variability of CO 2 emissions reasonably well compared to the observations (root mean square error: 0.4-1.3gCm -2 day -1 , revised Willmott index: 0.16-0.55). In particular, we demonstrated that the annual reservoir surface effluxes were initially high, steeply declined in the first three years, and then steadily decreased to ~115gCm -2 yr -1 with increasing reservoir age over the estimated "engineering" reservoir lifetime (i.e., 100years). Sensitivity analyses revealed that increasing air temperature stimulated CO 2 emissions by enhancing CO 2 production in the water column and sediment, and extending the duration of open water period over which emissions occur. Increasing the amount of terrestrial organic C flooded can enhance benthic CO 2 fluxes and CO 2 emissions from the reservoir water surface, but the effects were not significant over the simulation period. The model is useful for the understanding of the mechanism of C dynamics in reservoirs and could be used to assist the hydro-power industry and others interested in the role of boreal hydroelectric reservoirs as sources of greenhouse gas emissions. Copyright © 2017 Elsevier B.V. All rights reserved.

Mathematical Modeling: A Bridge to STEM Education

Science.gov (United States)

Kertil, Mahmut; Gurel, Cem

2016-01-01

The purpose of this study is making a theoretical discussion on the relationship between mathematical modeling and integrated STEM education. First of all, STEM education perspective and the construct of mathematical modeling in mathematics education is introduced. A review of literature is provided on how mathematical modeling literature may…

Wind tunnel modeling of roadways: Comparison with mathematical models

International Nuclear Information System (INIS)

Heidorn, K.; Davies, A.E.; Murphy, M.C.

1991-01-01

The assessment of air quality impacts from roadways is a major concern to urban planners. In order to assess future road and building configurations, a number of techniques have been developed including mathematical models, which simulate traffic emissions and atmospheric dispersion through a series of mathematical relationships and physical models. The latter models simulate emissions and dispersion through scaling of these processes in a wind tunnel. Two roadway mathematical models, HIWAY-2 and CALINE-4, were applied to a proposed development in a large urban area. Physical modeling procedures developed by Rowan Williams Davies and Irwin Inc. (RWDI) in the form of line source simulators were also applied, and the resulting carbon monoxide concentrations were compared. The results indicated a factor of two agreement between the mathematical and physical models. The physical model, however, reacted to change in building massing and configuration. The mathematical models did not, since no provision for such changes was included in the mathematical models. In general, the RWDI model resulted in higher concentrations than either HIWAY-2 or CALINE-4. Where there was underprediction, it was often due to shielding of the receptor by surrounding buildings. Comparison of these three models with the CALTRANS Tracer Dispersion Experiment showed good results although concentrations were consistently underpredicted

Evaluation of Gaussian approximations for data assimilation in reservoir models

KAUST Repository

Iglesias, Marco A.; Law, Kody J H; Stuart, Andrew M.

2013-01-01

is fundamental for the optimal management of reservoirs. Unfortunately, due to the large-scale highly nonlinear properties of standard reservoir models, characterizing the posterior is computationally prohibitive. Instead, more affordable ad hoc techniques, based

Mathematical models for plant-herbivore interactions

Science.gov (United States)

Feng, Zhilan; DeAngelis, Donald L.

2017-01-01

Mathematical Models of Plant-Herbivore Interactions addresses mathematical models in the study of practical questions in ecology, particularly factors that affect herbivory, including plant defense, herbivore natural enemies, and adaptive herbivory, as well as the effects of these on plant community dynamics. The result of extensive research on the use of mathematical modeling to investigate the effects of plant defenses on plant-herbivore dynamics, this book describes a toxin-determined functional response model (TDFRM) that helps explains field observations of these interactions. This book is intended for graduate students and researchers interested in mathematical biology and ecology.

Monte Carlo Analysis of Reservoir Models Using Seismic Data and Geostatistical Models

Science.gov (United States)

Zunino, A.; Mosegaard, K.; Lange, K.; Melnikova, Y.; Hansen, T. M.

2013-12-01

We present a study on the analysis of petroleum reservoir models consistent with seismic data and geostatistical constraints performed on a synthetic reservoir model. Our aim is to invert directly for structure and rock bulk properties of the target reservoir zone. To infer the rock facies, porosity and oil saturation seismology alone is not sufficient but a rock physics model must be taken into account, which links the unknown properties to the elastic parameters. We then combine a rock physics model with a simple convolutional approach for seismic waves to invert the "measured" seismograms. To solve this inverse problem, we employ a Markov chain Monte Carlo (MCMC) method, because it offers the possibility to handle non-linearity, complex and multi-step forward models and provides realistic estimates of uncertainties. However, for large data sets the MCMC method may be impractical because of a very high computational demand. To face this challenge one strategy is to feed the algorithm with realistic models, hence relying on proper prior information. To address this problem, we utilize an algorithm drawn from geostatistics to generate geologically plausible models which represent samples of the prior distribution. The geostatistical algorithm learns the multiple-point statistics from prototype models (in the form of training images), then generates thousands of different models which are accepted or rejected by a Metropolis sampler. To further reduce the computation time we parallelize the software and run it on multi-core machines. The solution of the inverse problem is then represented by a collection of reservoir models in terms of facies, porosity and oil saturation, which constitute samples of the posterior distribution. We are finally able to produce probability maps of the properties we are interested in by performing statistical analysis on the collection of solutions.

Mathematical Modelling of Thermal Process to Aquatic Environment with Different Hydrometeorological Conditions

Directory of Open Access Journals (Sweden)

Alibek Issakhov

2014-01-01

Full Text Available This paper presents the mathematical model of the thermal process from thermal power plant to aquatic environment of the reservoir-cooler, which is located in the Pavlodar region, 17 Km to the north-east of Ekibastuz town. The thermal process in reservoir-cooler with different hydrometeorological conditions is considered, which is solved by three-dimensional Navier-Stokes equations and temperature equation for an incompressible flow in a stratified medium. A numerical method based on the projection method, divides the problem into three stages. At the first stage, it is assumed that the transfer of momentum occurs only by convection and diffusion. Intermediate velocity field is solved by fractional steps method. At the second stage, three-dimensional Poisson equation is solved by the Fourier method in combination with tridiagonal matrix method (Thomas algorithm. Finally, at the third stage, it is expected that the transfer is only due to the pressure gradient. Numerical method determines the basic laws of the hydrothermal processes that qualitatively and quantitatively are approximated depending on different hydrometeorological conditions.

Spatial Stochastic Point Models for Reservoir Characterization

Energy Technology Data Exchange (ETDEWEB)

Syversveen, Anne Randi

1997-12-31

The main part of this thesis discusses stochastic modelling of geology in petroleum reservoirs. A marked point model is defined for objects against a background in a two-dimensional vertical cross section of the reservoir. The model handles conditioning on observations from more than one well for each object and contains interaction between objects, and the objects have the correct length distribution when penetrated by wells. The model is developed in a Bayesian setting. The model and the simulation algorithm are demonstrated by means of an example with simulated data. The thesis also deals with object recognition in image analysis, in a Bayesian framework, and with a special type of spatial Cox processes called log-Gaussian Cox processes. In these processes, the logarithm of the intensity function is a Gaussian process. The class of log-Gaussian Cox processes provides flexible models for clustering. The distribution of such a process is completely characterized by the intensity and the pair correlation function of the Cox process. 170 refs., 37 figs., 5 tabs.

Guiding rational reservoir flood operation using penalty-type genetic algorithm

Science.gov (United States)

Chang, Li-Chiu

2008-06-01

SummaryReal-time flood control of a multi-purpose reservoir should consider decreasing the flood peak stage downstream and storing floodwaters for future usage during typhoon seasons. This study proposes a reservoir flood control optimization model with linguistic description of requirements and existing regulations for rational operating decisions. The approach involves formulating reservoir flood operation as an optimization problem and using the genetic algorithm (GA) as a search engine. The optimizing formulation is expressed not only by mathematical forms of objective function and constraints, but also by no analytic expression in terms of parameters. GA is used to search a global optimum of a mixture of mathematical and nonmathematical formulations. Due to the great number of constraints and flood control requirements, it is difficult to reach a solution without violating constraints. To tackle this bottleneck, the proper penalty strategy for each parameter is proposed to guide the GA searching process. The proposed approach is applied to the Shihmen reservoir in North Taiwan for finding the rational release and desired storage as a case study. The hourly historical data sets of 29 typhoon events that have hit the area in last thirty years are investigated bye the proposed method. To demonstrate the effectiveness of the proposed approach, the simplex method was performed. The results demonstrated that a penalty-type genetic algorithm could effectively provide rational hydrographs to reduce flood damage during the flood operation and to increase final storage for future usages.

The Potosi Reservoir Model 2013c, Property Modeling Update

Energy Technology Data Exchange (ETDEWEB)

Adushita, Yasmin; Smith, Valerie; Leetaru, Hannes

2014-09-30

As part of a larger project co-funded by the United States Department of Energy (US DOE) to evaluate the potential of formations within the Cambro-Ordovician strata above the Mt. Simon as potential targets for carbon sequestration in the Illinois and Michigan Basins, the Illinois Clean Coal Institute (ICCI) requested Schlumberger to evaluate the potential injectivity and carbon dioxide (CO2) plume size of the Cambrian Potosi Formation. The evaluation of this formation was accomplished using wireline data, core data, pressure data, and seismic data from this project as well as two other separately funded projects: the US DOE-funded Illinois Basin–Decatur Project (IBDP) being conducted by the Midwest Geological Sequestration Consortium (MGSC) in Macon County, Illinois, and the Illinois Industrial Carbon Capture and Sequestration (ICCS) project funded through the American Recovery and Reinvestment Act. In 2010, technical performance evaluations on the Cambrian Potosi Formation were performed through reservoir modeling. The data included formation tops from mud logs, well logs from the Verification Well #1 (VW1) and the Injection Well (CCS1), structural and stratigraphic formation from three dimensional (3D) seismic data, and field data from several waste water injection wells for Potosi Formation. The intention was for 2.2 million tons per annum (2 million tonnes per annum [MTPA]) of CO2 to be injected for 20 years. In the Task Error! Reference source not found., the 2010 Potosi heterogeneous model (referred to as the "Potosi Dynamic Model 2010") was re-run using a new injection scenario of 3.5 million tons per annum (3.2 MTPA) for 30 years. The extent of the Potosi Dynamic Model 2010, however, appeared too small for the new injection target. The models size was insufficient to accommodate the evolution of the plume. The new model, Potosi Dynamic Model 2013a, was built by extending the Potosi Dynamic Model 2010 grid to 30 by 30 mi (48 by 48 km), while preserving all

Causal Bayes Model of Mathematical Competence in Kindergarten

Directory of Open Access Journals (Sweden)

Božidar Tepeš

2016-06-01

Full Text Available In this paper authors define mathematical competences in the kindergarten. The basic objective was to measure the mathematical competences or mathematical knowledge, skills and abilities in mathematical education. Mathematical competences were grouped in the following areas: Arithmetic and Geometry. Statistical set consisted of 59 children, 65 to 85 months of age, from the Kindergarten Milan Sachs from Zagreb. The authors describe 13 variables for measuring mathematical competences. Five measuring variables were described for the geometry, and eight measuring variables for the arithmetic. Measuring variables are tasks which children solved with the evaluated results. By measuring mathematical competences the authors make causal Bayes model using free software Tetrad 5.2.1-3. Software makes many causal Bayes models and authors as experts chose the model of the mathematical competences in the kindergarten. Causal Bayes model describes five levels for mathematical competences. At the end of the modeling authors use Bayes estimator. In the results, authors describe by causal Bayes model of mathematical competences, causal effect mathematical competences or how intervention on some competences cause other competences. Authors measure mathematical competences with their expectation as random variables. When expectation of competences was greater, competences improved. Mathematical competences can be improved with intervention on causal competences. Levels of mathematical competences and the result of intervention on mathematical competences can help mathematical teachers.

Quantifying the clay content with borehole depth and impact on reservoir flow

Science.gov (United States)

Sarath Kumar, Aaraellu D.; Chattopadhyay, Pallavi B.

2017-04-01

This study focuses on the application of reservoir well log data and 3D transient numerical model for proper optimization of flow dynamics and hydrocarbon potential. Fluid flow through porous media depends on clay content that controls porosity, permeability and pore pressure. The pressure dependence of permeability is more pronounced in tight formations. Therefore, preliminary clay concentration analysis and geo-mechanical characterizations have been done by using wells logs. The assumption of a constant permeability for a reservoir is inappropriate and therefore the study deals with impact of permeability variation for pressure-sensitive formation. The study started with obtaining field data from available well logs. Then, the mathematical models are developed to understand the efficient extraction of oil in terms of reservoir architecture, porosity and permeability. The fluid flow simulations have been done using COMSOL Multiphysics Software by choosing time dependent subsurface flow module that is governed by Darcy's law. This study suggests that the reservoir should not be treated as a single homogeneous structure with unique porosity and permeability. The reservoir parameters change with varying clay content and it should be considered for effective planning and extraction of oil. There is an optimum drawdown for maximum production with varying permeability in a reservoir.

Reservoir characterization using production data and time-lapse seismic data

Energy Technology Data Exchange (ETDEWEB)

Dadashpour, Mohsen

2009-12-15

horizontal direction, and give a significant image of fluid and pressure changes from the entire reservoir. However, the results are associated with errors and uncertainties that are related to the repeatability of data acquisition, data processing sequences, low resolution in vertical direction, lack of rock physics understanding, and an error in up-scaling and cross-scaling seismic and simulation data. This project uses exact amplitudes related to the seismic images after processing them in two different forms: Zero offset amplitudes and Amplitude versus offset (AVO) gradients. The effect of adding AVO gradients in the objective function (the misfit between responses of model and real reservoir) is discussed. One of the key issues in parameter estimation is to develop an efficient and reliable non-linear regression procedure. This procedure is based on three concepts: mathematical model, objective function and optimization algorithm. The mathematical model (Forward model) in this project consists of two parts: a Reservoir simulator and a Forward seismic model. A three phase black oil commercial simulator (ECLIPSE 100) is used to simulate fluid and pressure changes within the reservoir due to depletion and water injection. Forward seismic modeling software, based on rock physic formulations (Gassmann equation and Hertz-Mindlin model) and matrix propagating techniques developed at NTNU, is used to provide 4D seismic amplitudes from saturation and pressure changes. A new objective function which is defined as the difference between observation data and simulated data contains 4D seismic and production parts. Because these data are from different natures, integrating them still present a challenge. A key issue is the type of 4D seismic data and the weighting factor between these terms. Different scenarios and weighting factors are tested and discussed. Different optimization techniques are tested to choose the easiest, fastest and most efficient and robust optimization

Depositional sequence analysis and sedimentologic modeling for improved prediction of Pennsylvanian reservoirs

Energy Technology Data Exchange (ETDEWEB)

Watney, W.L.

1994-12-01

Reservoirs in the Lansing-Kansas City limestone result from complex interactions among paleotopography (deposition, concurrent structural deformation), sea level, and diagenesis. Analysis of reservoirs and surface and near-surface analogs has led to developing a {open_quotes}strandline grainstone model{close_quotes} in which relative sea-level stabilized during regressions, resulting in accumulation of multiple grainstone buildups along depositional strike. Resulting stratigraphy in these carbonate units are generally predictable correlating to inferred topographic elevation along the shelf. This model is a valuable predictive tool for (1) locating favorable reservoirs for exploration, and (2) anticipating internal properties of the reservoir for field development. Reservoirs in the Lansing-Kansas City limestones are developed in both oolitic and bioclastic grainstones, however, re-analysis of oomoldic reservoirs provides the greatest opportunity for developing bypassed oil. A new technique, the {open_quotes}Super{close_quotes} Pickett crossplot (formation resistivity vs. porosity) and its use in an integrated petrophysical characterization, has been developed to evaluate extractable oil remaining in these reservoirs. The manual method in combination with 3-D visualization and modeling can help to target production limiting heterogeneities in these complex reservoirs and moreover compute critical parameters for the field such as bulk volume water. Application of this technique indicates that from 6-9 million barrels of Lansing-Kansas City oil remain behind pipe in the Victory-Northeast Lemon Fields. Petroleum geologists are challenged to quantify inferred processes to aid in developing rationale geologically consistent models of sedimentation so that acceptable levels of prediction can be obtained.

Coupling of a reservoir model and of a poro-mechanical model. Application to the study of the compaction of petroleum reservoirs and of the associated subsidence; Couplage d'un modele de gisement et d'un modele mecanique. Application a l'etude de la compaction des reservoirs petroliers et de la subsidence associee

Energy Technology Data Exchange (ETDEWEB)

Bevillon, D.

2000-11-30

The aim of this study is to provide a better description of the rock contribution to fluid flows in petroleum reservoirs. The production of oil/gas in soft highly compacting reservoirs induces important reduction of the pore volume, which increases oil productivity. This compaction leads to undesirable effects such as surface subsidence or damage of well equipment. Analysis of compaction and subsidence can be performed using either engineering reservoir models or coupled poro-mechanical models. Poro-mechanical model offers a rigorous mechanical framework, but does not permit a complete description of the fluids. The reservoir model gives a good description of the fluid phases, but the description of the mechanic phenomenon is then simplified. To satisfy the set of equations (mechanical equilibrium and diffusivity equations), two simulators can be used together sequentially. Each of the two simulators solves its own system independently, and information passed both directions between simulators. This technique is usually referred to the partially coupled scheme. In this study, reservoir and hydro-mechanical simulations show that reservoir theory is not a rigorous framework to represent the evolution of the high porous rocks strains. Then, we introduce a partially coupled scheme that is shown to be consistent and unconditionally stable, which permits to describe correctly poro-mechanical theory in reservoir models. (author)

Fractured reservoir discrete feature network technologies. Annual report, March 7, 1996--February 28, 1997

Energy Technology Data Exchange (ETDEWEB)

Dershowitz, W.S.; La Pointe, P.R.; Einstein, H.H.; Ivanova, V.

1998-01-01

This report describes progress on the project, {open_quotes}Fractured Reservoir Discrete Feature Network Technologies{close_quotes} during the period March 7, 1996 to February 28, 1997. The report presents summaries of technology development for the following research areas: (1) development of hierarchical fracture models, (2) fractured reservoir compartmentalization and tributary volume, (3) fractured reservoir data analysis, and (4) integration of fractured reservoir data and production technologies. In addition, the report provides information on project status, publications submitted, data collection activities, and technology transfer through the world wide web (WWW). Research on hierarchical fracture models included geological, mathematical, and computer code development. The project built a foundation of quantitative, geological and geometrical information about the regional geology of the Permian Basin, including detailed information on the lithology, stratigraphy, and fracturing of Permian rocks in the project study area (Tracts 17 and 49 in the Yates field). Based on the accumulated knowledge of regional and local geology, project team members started the interpretation of fracture genesis mechanisms and the conceptual modeling of the fracture system in the study area. Research on fractured reservoir compartmentalization included basic research, technology development, and application of compartmentalized reservoir analyses for the project study site. Procedures were developed to analyze compartmentalization, tributary drainage volume, and reservoir matrix block size. These algorithms were implemented as a Windows 95 compartmentalization code, FraCluster.

Mathematical models in medicine: Diseases and epidemics

International Nuclear Information System (INIS)

Witten, M.

1987-01-01

This volume presents the numerous applications of mathematics in the life sciences and medicine, and demonstrates how mathematics and computers have taken root in these fields. The work covers a variety of techniques and applications including mathematical and modelling methodology, modelling/simulation technology, and philosophical issues in model formulation, leading to speciality medical modelling, artificial intelligence, psychiatric models, medical decision making, and molecular modelling

Constructing reservoir-scale 3D geomechanical FE-models. A refined workflow for model generation and calculation

Energy Technology Data Exchange (ETDEWEB)

Fischer, K.; Henk, A. [Technische Univ. Darmstadt (Germany). Inst. fuer Angewandte Geowissenschaften

2013-08-01

The tectonic stress field strongly affects the optimal exploitation of conventional and unconventional hydrocarbon reservoirs. Amongst others, wellbore stability, orientation of hydraulically induced fractures and - particularly in fractured reservoirs - permeability anisotropies depend on the magnitudes and orientations of the recent stresses. Geomechanical reservoir models can provide unique insights into the tectonic stress field revealing the local perturbations resulting from faults and lithological changes. In order to provide robust predictions, such numerical models are based on the finite element (FE) method and account for the complexities of real reservoirs with respect to subsurface geometry, inhomogeneous material distribution and nonlinear rock mechanical behavior. We present a refined workflow for geomechanical reservoir modeling which allows for an easier set-up of the model geometry, high resolution submodels and faster calculation times due to element savings in the load frame. Transferring the reservoir geometry from the geological subsurface model, e.g., a Petrel {sup registered} project, to the FE model represents a special challenge as the faults are discontinuities in the numerical model and no direct interface exists between the two software packages used. Point clouds displaying faults and lithostratigraphic horizons can be used for geometry transfer but this labor-intensive approach is not feasible for complex field-scale models with numerous faults. Instead, so-called Coon's patches based on horizon lines, i.e. the intersection lines between horizons and faults, are well suited to re-generate the various surfaces in the FE software while maintaining their topology. High-resolution submodels of individual fault blocks can be incorporated into the field-scale model. This allows to consider both a locally refined mechanical stratigraphy and the impact of the large-scale fault pattern. A pressure load on top of the model represents the

Forecasting monthly inflow discharge of the Iffezheim reservoir using data-driven models

Science.gov (United States)

Zhang, Qing; Aljoumani, Basem; Hillebrand, Gudrun; Hoffmann, Thomas; Hinkelmann, Reinhard

2017-04-01

River stream flow is an essential element in hydrology study fields, especially for reservoir management, since it defines input into reservoirs. Forecasting this stream flow plays an important role in short or long-term planning and management in the reservoir, e.g. optimized reservoir and hydroelectric operation or agricultural irrigation. Highly accurate flow forecasting can significantly reduce economic losses and is always pursued by reservoir operators. Therefore, hydrologic time series forecasting has received tremendous attention of researchers. Many models have been proposed to improve the hydrological forecasting. Due to the fact that most natural phenomena occurring in environmental systems appear to behave in random or probabilistic ways, different cases may need a different methods to forecast the inflow and even a unique treatment to improve the forecast accuracy. The purpose of this study is to determine an appropriate model for forecasting monthly inflow to the Iffezheim reservoir in Germany, which is the last of the barrages in the Upper Rhine. Monthly time series of discharges, measured from 1946 to 2001 at the Plittersdorf station, which is located 6 km downstream of the Iffezheim reservoir, were applied. The accuracies of the used stochastic models - Fiering model and Auto-Regressive Integrated Moving Average models (ARIMA) are compared with Artificial Intelligence (AI) models - single Artificial Neural Network (ANN) and Wavelet ANN models (WANN). The Fiering model is a linear stochastic model and used for generating synthetic monthly data. The basic idea in modeling time series using ARIMA is to identify a simple model with as few model parameters as possible in order to provide a good statistical fit to the data. To identify and fit the ARIMA models, four phase approaches were used: identification, parameter estimation, diagnostic checking, and forecasting. An automatic selection criterion, such as the Akaike information criterion, is utilized

Mathematical Modeling and Computational Thinking

Science.gov (United States)

Sanford, John F.; Naidu, Jaideep T.

2017-01-01

The paper argues that mathematical modeling is the essence of computational thinking. Learning a computer language is a valuable assistance in learning logical thinking but of less assistance when learning problem-solving skills. The paper is third in a series and presents some examples of mathematical modeling using spreadsheets at an advanced…

ADVANCED TECHNIQUES FOR RESERVOIR SIMULATION AND MODELING OF NONCONVENTIONAL WELLS

Energy Technology Data Exchange (ETDEWEB)

Louis J. Durlofsky; Khalid Aziz

2004-08-20

Nonconventional wells, which include horizontal, deviated, multilateral and ''smart'' wells, offer great potential for the efficient management of oil and gas reservoirs. These wells are able to contact larger regions of the reservoir than conventional wells and can also be used to target isolated hydrocarbon accumulations. The use of nonconventional wells instrumented with downhole inflow control devices allows for even greater flexibility in production. Because nonconventional wells can be very expensive to drill, complete and instrument, it is important to be able to optimize their deployment, which requires the accurate prediction of their performance. However, predictions of nonconventional well performance are often inaccurate. This is likely due to inadequacies in some of the reservoir engineering and reservoir simulation tools used to model and optimize nonconventional well performance. A number of new issues arise in the modeling and optimization of nonconventional wells. For example, the optimal use of downhole inflow control devices has not been addressed for practical problems. In addition, the impact of geological and engineering uncertainty (e.g., valve reliability) has not been previously considered. In order to model and optimize nonconventional wells in different settings, it is essential that the tools be implemented into a general reservoir simulator. This simulator must be sufficiently general and robust and must in addition be linked to a sophisticated well model. Our research under this five year project addressed all of the key areas indicated above. The overall project was divided into three main categories: (1) advanced reservoir simulation techniques for modeling nonconventional wells; (2) improved techniques for computing well productivity (for use in reservoir engineering calculations) and for coupling the well to the simulator (which includes the accurate calculation of well index and the modeling of multiphase flow

Summer Camp of Mathematical Modeling in China

Science.gov (United States)

Tian, Xiaoxi; Xie, Jinxing

2013-01-01

The Summer Camp of Mathematical Modeling in China is a recently created experience designed to further Chinese students' academic pursuits in mathematical modeling. Students are given more than three months to research on a mathematical modeling project. Researchers and teams with outstanding projects are invited to the Summer Camp to present…

Strategies to Support Students' Mathematical Modeling

Science.gov (United States)

Jung, Hyunyi

2015-01-01

An important question for mathematics teachers is this: "How can we help students learn mathematics to solve everyday problems, rather than teaching them only to memorize rules and practice mathematical procedures?" Teaching students using modeling activities can help them learn mathematics in real-world problem-solving situations that…

Explorations in Elementary Mathematical Modeling

Science.gov (United States)

Shahin, Mazen

2010-01-01

In this paper we will present the methodology and pedagogy of Elementary Mathematical Modeling as a one-semester course in the liberal arts core. We will focus on the elementary models in finance and business. The main mathematical tools in this course are the difference equations and matrix algebra. We also integrate computer technology and…

Advanced Techniques for Reservoir Simulation and Modeling of Non-Conventional Wells

Energy Technology Data Exchange (ETDEWEB)

Durlofsky, Louis J.

2000-08-28

This project targets the development of (1) advanced reservoir simulation techniques for modeling non-conventional wells; (2) improved techniques for computing well productivity (for use in reservoir engineering calculations) and well index (for use in simulation models), including the effects of wellbore flow; and (3) accurate approaches to account for heterogeneity in the near-well region.

Mathematical Modeling of Diverse Phenomena

Science.gov (United States)

Howard, J. C.

1979-01-01

Tensor calculus is applied to the formulation of mathematical models of diverse phenomena. Aeronautics, fluid dynamics, and cosmology are among the areas of application. The feasibility of combining tensor methods and computer capability to formulate problems is demonstrated. The techniques described are an attempt to simplify the formulation of mathematical models by reducing the modeling process to a series of routine operations, which can be performed either manually or by computer.

An introduction to mathematical modeling of infectious diseases

CERN Document Server

Li, Michael Y

2018-01-01

This text provides essential modeling skills and methodology for the study of infectious diseases through a one-semester modeling course or directed individual studies.  The book includes mathematical descriptions of epidemiological concepts, and uses classic epidemic models to introduce different mathematical methods in model analysis.  Matlab codes are also included for numerical implementations. It is primarily written for upper undergraduate and beginning graduate students in mathematical sciences who have an interest in mathematical modeling of infectious diseases.  Although written in a rigorous mathematical manner, the style is not unfriendly to non-mathematicians.

Integrated Reflection Seismic Monitoring and Reservoir Modeling for Geologic CO2 Sequestration

Energy Technology Data Exchange (ETDEWEB)

John Rogers

2011-12-31

The US DOE/NETL CCS MVA program funded a project with Fusion Petroleum Technologies Inc. (now SIGMA) to model the proof of concept of using sparse seismic data in the monitoring of CO{sub 2} injected into saline aquifers. The goal of the project was to develop and demonstrate an active source reflection seismic imaging strategy based on deployment of spatially sparse surface seismic arrays. The primary objective was to test the feasibility of sparse seismic array systems to monitor the CO{sub 2} plume migration injected into deep saline aquifers. The USDOE/RMOTC Teapot Dome (Wyoming) 3D seismic and reservoir data targeting the Crow Mountain formation was used as a realistic proxy to evaluate the feasibility of the proposed methodology. Though the RMOTC field has been well studied, the Crow Mountain as a saline aquifer has not been studied previously as a CO{sub 2} sequestration (storage) candidate reservoir. A full reprocessing of the seismic data from field tapes that included prestack time migration (PSTM) followed by prestack depth migration (PSDM) was performed. A baseline reservoir model was generated from the new imaging results that characterized the faults and horizon surfaces of the Crow Mountain reservoir. The 3D interpretation was integrated with the petrophysical data from available wells and incorporated into a geocellular model. The reservoir structure used in the geocellular model was developed using advanced inversion technologies including Fusion's ThinMAN{trademark} broadband spectral inversion. Seal failure risk was assessed using Fusion's proprietary GEOPRESS{trademark} pore pressure and fracture pressure prediction technology. CO{sub 2} injection was simulated into the Crow Mountain with a commercial reservoir simulator. Approximately 1.2MM tons of CO{sub 2} was simulated to be injected into the Crow Mountain reservoir over 30 years and subsequently let 'soak' in the reservoir for 970 years. The relatively small plume

Kondo dynamics of quasiparticle tunneling in a two-reservoir Anderson model.

Science.gov (United States)

Hong, Jongbae

2011-07-13

We study the Kondo dynamics in a two-reservoir Anderson impurity model in which quasiparticle tunneling occurs between two reservoirs. We show that singlet hopping is an essential component of Kondo dynamics in the quasiparticle tunneling. We prove that two resonant tunneling levels exist in the two-reservoir Anderson impurity model and the quasiparticle tunnels through one of these levels when a bias is applied. The Kondo dynamics is explained by obtaining the retarded Green's function. We obtain the analytic expressions of the spectral weights of coherent peaks by analyzing the Green's function at the atomic limit.

Kondo dynamics of quasiparticle tunneling in a two-reservoir Anderson model

International Nuclear Information System (INIS)

Hong, Jongbae

2011-01-01

We study the Kondo dynamics in a two-reservoir Anderson impurity model in which quasiparticle tunneling occurs between two reservoirs. We show that singlet hopping is an essential component of Kondo dynamics in the quasiparticle tunneling. We prove that two resonant tunneling levels exist in the two-reservoir Anderson impurity model and the quasiparticle tunnels through one of these levels when a bias is applied. The Kondo dynamics is explained by obtaining the retarded Green's function. We obtain the analytic expressions of the spectral weights of coherent peaks by analyzing the Green's function at the atomic limit.

Study on fine geological modelling of the fluvial sandstone reservoir in Daqing oilfield

Energy Technology Data Exchange (ETDEWEB)

Zhoa Han-Qing [Daqing Research Institute, Helongjiang (China)

1997-08-01

These paper aims at developing a method for fine reservoir description in maturing oilfields by using close spaced well logging data. The main productive reservoirs in Daqing oilfield is a set of large fluvial-deltaic deposits in the Songliao Lake Basin, characterized by multi-layers and serious heterogeneities. Various fluvial channel sandstone reservoirs cover a fairly important proportion of reserves. After a long period of water flooding, most of them have turned into high water cut layers, but there are considerable residual reserves within them, which are difficult to find and tap. Making fine reservoir description and developing sound a geological model is essential for tapping residual oil and enhancing oil recovery. The principal reason for relative lower precision of predicting model developed by using geostatistics is incomplete recognition of complex distribution of fluvial reservoirs and their internal architecture`s. Tasking advantage of limited outcrop data from other regions (suppose no outcrop data available in oilfield) can only provide the knowledge of subtle changing of reservoir parameters and internal architecture. For the specific geometry distribution and internal architecture of subsurface reservoirs (such as in produced regions) can be gained only from continuous infilling logging well data available from studied areas. For developing a geological model, we think the first important thing is to characterize sandbodies geometries and their general architecture`s, which are the framework of models, and then the slight changing of interwell parameters and internal architecture`s, which are the contents and cells of the model. An excellent model should possess both of them, but the geometry is the key to model, because it controls the contents and cells distribution within a model.

APPLICATION OF INTEGRATED RESERVOIR MANAGEMENT AND RESERVOIR CHARACTERIZATION

Energy Technology Data Exchange (ETDEWEB)

Jack Bergeron; Tom Blasingame; Louis Doublet; Mohan Kelkar; George Freeman; Jeff Callard; David Moore; David Davies; Richard Vessell; Brian Pregger; Bill Dixon; Bryce Bezant

2000-03-01

Reservoir performance and characterization are vital parameters during the development phase of a project. Infill drilling of wells on a uniform spacing, without regard to characterization does not optimize development because it fails to account for the complex nature of reservoir heterogeneities present in many low permeability reservoirs, especially carbonate reservoirs. These reservoirs are typically characterized by: (1) large, discontinuous pay intervals; (2) vertical and lateral changes in reservoir properties; (3) low reservoir energy; (4) high residual oil saturation; and (5) low recovery efficiency. The operational problems they encounter in these types of reservoirs include: (1) poor or inadequate completions and stimulations; (2) early water breakthrough; (3) poor reservoir sweep efficiency in contacting oil throughout the reservoir as well as in the nearby well regions; (4) channeling of injected fluids due to preferential fracturing caused by excessive injection rates; and (5) limited data availability and poor data quality. Infill drilling operations only need target areas of the reservoir which will be economically successful. If the most productive areas of a reservoir can be accurately identified by combining the results of geological, petrophysical, reservoir performance, and pressure transient analyses, then this ''integrated'' approach can be used to optimize reservoir performance during secondary and tertiary recovery operations without resorting to ''blanket'' infill drilling methods. New and emerging technologies such as geostatistical modeling, rock typing, and rigorous decline type curve analysis can be used to quantify reservoir quality and the degree of interwell communication. These results can then be used to develop a 3-D simulation model for prediction of infill locations. The application of reservoir surveillance techniques to identify additional reservoir ''pay'' zones

Principles of mathematical modeling

CERN Document Server

Dym, Clive

2004-01-01

Science and engineering students depend heavily on concepts of mathematical modeling. In an age where almost everything is done on a computer, author Clive Dym believes that students need to understand and "own" the underlying mathematics that computers are doing on their behalf. His goal for Principles of Mathematical Modeling, Second Edition, is to engage the student reader in developing a foundational understanding of the subject that will serve them well into their careers. The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools including dimensional analysis, scaling techniques, and approximation and validation techniques. The second half demonstrates the latest applications for these tools to a broad variety of subjects, including exponential growth and decay in fields ranging from biology to economics, traffic flow, free and forced vibration of mechanical and other systems, and optimization problems in biology, structures, an...

Reservoir Modeling Combining Geostatistics with Markov Chain Monte Carlo Inversion

DEFF Research Database (Denmark)

Zunino, Andrea; Lange, Katrine; Melnikova, Yulia

2014-01-01

We present a study on the inversion of seismic reflection data generated from a synthetic reservoir model. Our aim is to invert directly for rock facies and porosity of the target reservoir zone. We solve this inverse problem using a Markov chain Monte Carlo (McMC) method to handle the nonlinear...

Concepts of mathematical modeling

CERN Document Server

Meyer, Walter J

2004-01-01

Appropriate for undergraduate and graduate students, this text features independent sections that illustrate the most important principles of mathematical modeling, a variety of applications, and classic models. Students with a solid background in calculus and some knowledge of probability and matrix theory will find the material entirely accessible. The range of subjects includes topics from the physical, biological, and social sciences, as well as those of operations research. Discussions cover related mathematical tools and the historical eras from which the applications are drawn. Each sec

Daily reservoir inflow forecasting combining QPF into ANNs model

Science.gov (United States)

Zhang, Jun; Cheng, Chun-Tian; Liao, Sheng-Li; Wu, Xin-Yu; Shen, Jian-Jian

2009-01-01

Daily reservoir inflow predictions with lead-times of several days are essential to the operational planning and scheduling of hydroelectric power system. The demand for quantitative precipitation forecasting (QPF) is increasing in hydropower operation with the dramatic advances in the numerical weather prediction (NWP) models. This paper presents a simple and an effective algorithm for daily reservoir inflow predictions which solicits the observed precipitation, forecasted precipitation from QPF as predictors and discharges in following 1 to 6 days as predicted targets for multilayer perceptron artificial neural networks (MLP-ANNs) modeling. An improved error back-propagation algorithm with self-adaptive learning rate and self-adaptive momentum coefficient is used to make the supervised training procedure more efficient in both time saving and search optimization. Several commonly used error measures are employed to evaluate the performance of the proposed model and the results, compared with that of ARIMA model, show that the proposed model is capable of obtaining satisfactory forecasting not only in goodness of fit but also in generalization. Furthermore, the presented algorithm is integrated into a practical software system which has been severed for daily inflow predictions with lead-times varying from 1 to 6 days of more than twenty reservoirs operated by the Fujian Province Grid Company, China.

Modelling Formation of a Drug Reservoir in the Stratum Corneum and Its Impact on Drug Monitoring Using Reverse Iontophoresis

Directory of Open Access Journals (Sweden)

Yvonne Paulley

2010-01-01

Full Text Available Reverse iontophoresis is a relatively new technique for non-invasive drug monitoring in the body. It involves a small electrical current being passed through the skin to facilitate the movement of small charged ions and polar molecules on the skin's surface where the amount of drug can then be measured and hence an accurate estimate of the blood concentration can be made. In vivo studies for several molecules show that initially large amounts of drug are extracted from the body, which are unrelated to the magnitude of the blood concentration; over time the fluxes of extraction decrease to a level proportional to the steady state blood concentration. This suggests that, at first, the drug is being extracted from some source other than the blood; one such candidate for this source is the dead cells which form the stratum corneum. In this paper, we construct two related mathematical models; the first describes the formation of the drug reservoir in the stratum corneum as a consequence of repeated drug intake and natural death of skin cells in the body. The output from this model provides initial conditions for the model of reverse iontophoresis in which charged ions from both the blood and the stratum corneum reservoir compete for the electric current. Model parameters are estimated from data collected for lithium monitoring. Our models will improve interpretation of reverse iontophoretic data by discriminating the subdermal from the skin contribution to the fluxes of extraction. They also suggest that analysis of the skin reservoir might be a valuable tool to investigate patients' exposure to chemicals including therapeutic drugs.

Geological model of supercritical geothermal reservoir related to subduction system

Science.gov (United States)

Tsuchiya, Noriyoshi

2017-04-01

Following the Great East Japan Earthquake and the accident at the Fukushima Daiichi Nuclear power station on 3.11 (11th March) 2011, geothermal energy came to be considered one of the most promising sources of renewable energy for the future in Japan. The temperatures of geothermal fields operating in Japan range from 200 to 300 °C (average 250 °C), and the depths range from 1000 to 2000 m (average 1500 m). In conventional geothermal reservoirs, the mechanical behavior of the rocks is presumed to be brittle, and convection of the hydrothermal fluid through existing network is the main method of circulation in the reservoir. In order to minimize induced seismicity, a rock mass that is "beyond brittle" is one possible candidate, because the rock mechanics of "beyond brittle" material is one of plastic deformation rather than brittle failure. Supercritical geothermal resources could be evaluated in terms of present volcanic activities, thermal structure, dimension of hydrothermal circulation, properties of fracture system, depth of heat source, depth of brittle factures zone, dimension of geothermal reservoir. On the basis of the GIS, potential of supercritical geothermal resources could be characterized into the following four categories. 1. Promising: surface manifestation d shallow high temperature, 2 Probability: high geothermal gradient, 3 Possibility: Aseismic zone which indicates an existence of melt, 4 Potential : low velocity zone which indicates magma input. Base on geophysical data for geothermal reservoirs, we have propose adequate tectonic model of development of the supercritical geothermal reservoirs. To understand the geological model of a supercritical geothermal reservoir, granite-porphyry system, which had been formed in subduction zone, was investigated as a natural analog of the supercritical geothermal energy system. Quartz veins, hydrothermal breccia veins, and glassy veins are observed in a granitic body. The glassy veins formed at 500-550 �

PEMODELAN DAERAH TANGKAPAN AIR WADUK KELILING DENGAN MODEL SWAT (Keliling Reservoir Catchment Area Modeling Using SWAT Model

Directory of Open Access Journals (Sweden)

Teuku Ferijal

2015-05-01

Full Text Available This study aimed to model watershed area of Keliling Reservoir using SWAT model. The reservoir is located in Aceh Besar District, Province of Aceh. The model was setup using 90m x 90m digital elevation model, land use data extracted from remote sensing data and soil characteristic obtained from laboratory analysis on soil samples. Model was calibrated using observed daily reservoir volume and the model performance was analyzed using RMSE-observations standard deviation ratio (RSR, Nash-Sutcliffe efficiency (NSE and percent bias (PBIAS. The model delineated the study area into 3,448 Ha having 13 subwatersheds and 76 land units (HRUs. The watershed is mostly covered by forest (53% and grassland (31%. The analysis revealed the 10 most sensitive parameters i.e. GW_DELAY, CN2, REVAPMN, ALPHA_BF, SOL_AWC, GW_REVAP, GWQMN, CH_K2 and ESCO. Model performances were categorized into very good for monthly reservoir volume with ENS 0.95, RSR 0.23, and PBIAS 2.97. The model performance decreased when it used to analyze daily reservoir inflow with ENS 0.55, RSR 0.67, and PBIAS 3.46. Keywords: Keliling Reservoir, SWAT, Watershed   ABSTRAK Penelitian ini bertujuan untuk untuk memodelkan daerah tangkapan air Waduk Keliling dengan menggunakan Model SWAT. Waduk Keliling terletak di Kabupaten Aceh Besar, Propinsi Aceh. Dalam penelitian ini Model SWAT dikembangkan berdasarkan data digital elevasi model resolusi 90 m x90 m, tata guna lahan yang diperoleh dari intepretasi citra satelit dan data soil dari hasil analisa sampel tanah yang diperoleh di daerah penelitian. Model dikalibrasi dengan data volume waduk dan kinerja model dianalisa menggunakan parameter rasio akar rata-rata kuadrat error dan standard deviasi observasi (RSR, efesiensi Nash-Sutcliffe (NSE dan persentase bias (PBIAS. Hasil deleniasi untuk daerah penelitian menghasilkan suatu DAS dengan luas 3,448 Ha dan memiliki 13 Sub DAS yang dikelompokkan menjadi 76 unit lahan. Sebagian besar wilayah study

Teaching mathematical modelling through project work

DEFF Research Database (Denmark)

Blomhøj, Morten; Kjeldsen, Tinne Hoff

2006-01-01

are reported in manners suitable for internet publication for colleagues. The reports and the related discussions reveal interesting dilemmas concerning the teaching of mathematical modelling and how to cope with these through “setting the scene” for the students modelling projects and through dialogues......The paper presents and analyses experiences from developing and running an in-service course in project work and mathematical modelling for mathematics teachers in the Danish gymnasium, e.g. upper secondary level, grade 10-12. The course objective is to support the teachers to develop, try out...... in their own classes, evaluate and report a project based problem oriented course in mathematical modelling. The in-service course runs over one semester and includes three seminars of 3, 1 and 2 days. Experiences show that the course objectives in general are fulfilled and that the course projects...

Mathematical modelling of scour: A review

DEFF Research Database (Denmark)

Sumer, B. Mutlu

2007-01-01

A review is presented of mathematical modelling of scour around hydraulic and marine structures. Principal ideas, general features and procedures are given. The paper is organized in three sections: the first two sections deal with the mathematical modelling of scour around piers....../piles and pipelines, respectively, the two benchmark cases, while the third section deals with the mathematical modelling of scour around other structures such as groins, breakwaters and sea walls. A section is also added to discuss potential future research areas. Over one hundred references are included...

Mathematical modeling a chemical engineer's perspective

CERN Document Server

Rutherford, Aris

1999-01-01

Mathematical modeling is the art and craft of building a system of equations that is both sufficiently complex to do justice to physical reality and sufficiently simple to give real insight into the situation. Mathematical Modeling: A Chemical Engineer's Perspective provides an elementary introduction to the craft by one of the century's most distinguished practitioners.Though the book is written from a chemical engineering viewpoint, the principles and pitfalls are common to all mathematical modeling of physical systems. Seventeen of the author's frequently cited papers are reprinted to illus

Modelling of fractured reservoirs. Case of multi-scale media; Modelisation des reservoirs fractures. Cas des milieux multi-echelles

Energy Technology Data Exchange (ETDEWEB)

Henn, N.

2000-12-13

Some of the most productive oil and gas reservoirs are found in formations crossed by multi-scale fractures/faults. Among them, conductive faults may closely control reservoir performance. However, their modelling encounters numerical and physical difficulties linked with (a) the necessity to keep an explicit representation of faults through small-size grid blocks, (b) the modelling of multiphase flow exchanges between the fault and the neighbouring medium. In this thesis, we propose a physically-representative and numerically efficient modelling approach in order to incorporate sub-vertical conductive faults in single and dual-porosity simulators. To validate our approach and demonstrate its efficiency, simulation results of multiphase displacements in representative field sector models are presented. (author)

A simple multistage closed-(box+reservoir model of chemical evolution

Directory of Open Access Journals (Sweden)

Caimmi R.

2011-01-01

Full Text Available Simple closed-box (CB models of chemical evolution are extended on two respects, namely (i simple closed-(box+reservoir (CBR models allowing gas outflow from the box into the reservoir (Hartwick 1976 or gas inflow into the box from the reservoir (Caimmi 2007 with rate proportional to the star formation rate, and (ii simple multistage closed-(box+reservoir (MCBR models allowing different stages of evolution characterized by different inflow or outflow rates. The theoretical differential oxygen abundance distribution (TDOD predicted by the model maintains close to a continuous broken straight line. An application is made where a fictitious sample is built up from two distinct samples of halo stars and taken as representative of the inner Galactic halo. The related empirical differential oxygen abundance distribution (EDOD is represented, to an acceptable extent, as a continuous broken line for two viable [O/H]-[Fe/H] empirical relations. The slopes and the intercepts of the regression lines are determined, and then used as input parameters to MCBR models. Within the errors (-+σ, regression line slopes correspond to a large inflow during the earlier stage of evolution and to low or moderate outflow during the subsequent stages. A possible inner halo - outer (metal-poor bulge connection is also briefly discussed. Quantitative results cannot be considered for applications to the inner Galactic halo, unless selection effects and disk contamination are removed from halo samples, and discrepancies between different oxygen abundance determination methods are explained.

Opinions of Secondary School Mathematics Teachers on Mathematical Modelling

Science.gov (United States)

Tutak, Tayfun; Güder, Yunus

2013-01-01

The aim of this study is to identify the opinions of secondary school mathematics teachers about mathematical modelling. Qualitative research was used. The participants of the study were 40 secondary school teachers working in the Bingöl Province in Turkey during 2012-2013 education year. Semi-structured interview form prepared by the researcher…

Level-set techniques for facies identification in reservoir modeling

Science.gov (United States)

Iglesias, Marco A.; McLaughlin, Dennis

2011-03-01

In this paper we investigate the application of level-set techniques for facies identification in reservoir models. The identification of facies is a geometrical inverse ill-posed problem that we formulate in terms of shape optimization. The goal is to find a region (a geologic facies) that minimizes the misfit between predicted and measured data from an oil-water reservoir. In order to address the shape optimization problem, we present a novel application of the level-set iterative framework developed by Burger in (2002 Interfaces Free Bound. 5 301-29 2004 Inverse Problems 20 259-82) for inverse obstacle problems. The optimization is constrained by (the reservoir model) a nonlinear large-scale system of PDEs that describes the reservoir dynamics. We reformulate this reservoir model in a weak (integral) form whose shape derivative can be formally computed from standard results of shape calculus. At each iteration of the scheme, the current estimate of the shape derivative is utilized to define a velocity in the level-set equation. The proper selection of this velocity ensures that the new shape decreases the cost functional. We present results of facies identification where the velocity is computed with the gradient-based (GB) approach of Burger (2002) and the Levenberg-Marquardt (LM) technique of Burger (2004). While an adjoint formulation allows the straightforward application of the GB approach, the LM technique requires the computation of the large-scale Karush-Kuhn-Tucker system that arises at each iteration of the scheme. We efficiently solve this system by means of the representer method. We present some synthetic experiments to show and compare the capabilities and limitations of the proposed implementations of level-set techniques for the identification of geologic facies.

Level-set techniques for facies identification in reservoir modeling

International Nuclear Information System (INIS)

Iglesias, Marco A; McLaughlin, Dennis

2011-01-01

In this paper we investigate the application of level-set techniques for facies identification in reservoir models. The identification of facies is a geometrical inverse ill-posed problem that we formulate in terms of shape optimization. The goal is to find a region (a geologic facies) that minimizes the misfit between predicted and measured data from an oil–water reservoir. In order to address the shape optimization problem, we present a novel application of the level-set iterative framework developed by Burger in (2002 Interfaces Free Bound. 5 301–29; 2004 Inverse Problems 20 259–82) for inverse obstacle problems. The optimization is constrained by (the reservoir model) a nonlinear large-scale system of PDEs that describes the reservoir dynamics. We reformulate this reservoir model in a weak (integral) form whose shape derivative can be formally computed from standard results of shape calculus. At each iteration of the scheme, the current estimate of the shape derivative is utilized to define a velocity in the level-set equation. The proper selection of this velocity ensures that the new shape decreases the cost functional. We present results of facies identification where the velocity is computed with the gradient-based (GB) approach of Burger (2002) and the Levenberg–Marquardt (LM) technique of Burger (2004). While an adjoint formulation allows the straightforward application of the GB approach, the LM technique requires the computation of the large-scale Karush–Kuhn–Tucker system that arises at each iteration of the scheme. We efficiently solve this system by means of the representer method. We present some synthetic experiments to show and compare the capabilities and limitations of the proposed implementations of level-set techniques for the identification of geologic facies

Modeling the impact of Plasmodium falciparum sexual stage immunity on the composition and dynamics of the human infectious reservoir for malaria in natural settings.

Directory of Open Access Journals (Sweden)

André Lin Ouédraogo

2018-05-01

Full Text Available Malaria transmission remains high in Sub-Saharan Africa despite large-scale implementation of malaria control interventions. A comprehensive understanding of the transmissibility of infections to mosquitoes may guide the design of more effective transmission reducing strategies. The impact of P. falciparum sexual stage immunity on the infectious reservoir for malaria has never been studied in natural settings. Repeated measurements were carried out at start-wet, peak-wet and dry season, and provided data on antibody responses against gametocyte/gamete antigens Pfs48/45 and Pfs230 as anti-gametocyte immunity. Data on high and low-density infections and their infectiousness to anopheline mosquitoes were obtained using quantitative molecular methods and mosquito feeding assays, respectively. An event-driven model for P. falciparum sexual stage immunity was developed and fit to data using an agent based malaria model infrastructure. We found that Pfs48/45 and Pfs230 antibody densities increased with increasing concurrent gametocyte densities; associated with 55-70% reduction in oocyst intensity and achieved up to 44% reduction in proportions of infected mosquitoes. We showed that P. falciparum sexual stage immunity significantly reduces transmission of microscopic (p < 0.001 but not submicroscopic (p = 0.937 gametocyte infections to mosquitoes and that incorporating sexual stage immunity into mathematical models had a considerable impact on the contribution of different age groups to the infectious reservoir of malaria. Human antibody responses to gametocyte antigens are likely to be dependent on recent and concurrent high-density gametocyte exposure and have a pronounced impact on the likelihood of onward transmission of microscopic gametocyte densities compared to low density infections. Our mathematical simulations indicate that anti-gametocyte immunity is an important factor for predicting and understanding the composition and dynamics of the

Specific Type of Knowledge Map: Mathematical Model

OpenAIRE

Milan, Houška; Martina, Beránková

2005-01-01

The article deals with relationships between mathematical models and knowledge maps. The goal of the article is to suggest how to use the mathematical model as a knowledge map and/or as a part (esp. the inference mechanism) of the knowledge system. The results are demonstrated on the case study, when the knowledge from a story is expressed by mathematical model. The model is used for both knowledge warehousing and inferencing new artificially derived knowledge.

The Relationship between Students' Performance on Conventional Standardized Mathematics Assessments and Complex Mathematical Modeling Problems

Science.gov (United States)

Kartal, Ozgul; Dunya, Beyza Aksu; Diefes-Dux, Heidi A.; Zawojewski, Judith S.

2016-01-01

Critical to many science, technology, engineering, and mathematics (STEM) career paths is mathematical modeling--specifically, the creation and adaptation of mathematical models to solve problems in complex settings. Conventional standardized measures of mathematics achievement are not structured to directly assess this type of mathematical…

A global water supply reservoir yield model with uncertainty analysis

International Nuclear Information System (INIS)

Kuria, Faith W; Vogel, Richard M

2014-01-01

Understanding the reliability and uncertainty associated with water supply yields derived from surface water reservoirs is central for planning purposes. Using a global dataset of monthly river discharge, we introduce a generalized model for estimating the mean and variance of water supply yield, Y, expected from a reservoir for a prespecified reliability, R, and storage capacity, S assuming a flow record of length n. The generalized storage–reliability–yield (SRY) relationships reported here have numerous water resource applications ranging from preliminary water supply investigations, to economic and climate change impact assessments. An example indicates how our generalized SRY relationship can be combined with a hydroclimatic model to determine the impact of climate change on surface reservoir water supply yields. We also document that the variability of estimates of water supply yield are invariant to characteristics of the reservoir system, including its storage capacity and reliability. Standardized metrics of the variability of water supply yields are shown to depend only on the sample size of the inflows and the statistical characteristics of the inflow series. (paper)

The HYDROMED model and its application to semi-arid Mediterranean catchments with hill reservoirs 3: Reservoir storage capacity and probability of failure model

Directory of Open Access Journals (Sweden)

R. Ragab

2001-01-01

Full Text Available This paper addresses the issue of "what reservoir storage capacity is required to maintain a yield with a given probability of failure?". It is an important issue in terms of construction and cost. HYDROMED offers a solution based on the modified Gould probability matrix method. This method has the advantage of sampling all years data without reference to the sequence and is therefore particularly suitable for catchments with patchy data. In the HYDROMED model, the probability of failure is calculated on a monthly basis. The model has been applied to the El-Gouazine catchment in Tunisia using a long rainfall record from Kairouan together with the estimated Hortonian runoff, class A pan evaporation data and estimated abstraction data. Generally, the probability of failure differed from winter to summer. Generally, the probability of failure approaches zero when the reservoir capacity is 500,000 m3. The 25% probability of failure (75% success is achieved with a reservoir capacity of 58,000 m3 in June and 95,000 m3 in January. The probability of failure for a 240,000 m3 capacity reservoir (closer to storage capacity of El-Gouazine 233,000 m3, is approximately 5% in November, December and January, 3% in March, and 1.1% in May and June. Consequently there is no high risk of El-Gouazine being unable to meet its requirements at a capacity of 233,000 m3. Subsequently the benefit, in terms of probability of failure, by increasing the reservoir volume of El-Gouazine to greater than the 250,000 m3 is not high. This is important for the design engineers and the funding organizations. However, the analysis is based on the existing water abstraction policy, absence of siltation rate data and on the assumption that the present climate will prevail during the lifetime of the reservoir. Should these conditions change, a new analysis should be carried out. Keywords: HYDROMED, reservoir, storage capacity, probability of failure, Mediterranean

Experiments with Interaction between the National Water Model and the Reservoir System Simulation Model: A Case Study of Russian River Basin

Science.gov (United States)

Kim, J.; Johnson, L.; Cifelli, R.; Chandra, C. V.; Gochis, D.; McCreight, J. L.; Yates, D. N.; Read, L.; Flowers, T.; Cosgrove, B.

2017-12-01

NOAA National Water Center (NWC) in partnership with the National Centers for Environmental Prediction (NCEP), the National Center for Atmospheric Research (NCAR) and other academic partners have produced operational hydrologic predictions for the nation using a new National Water Model (NWM) that is based on the community WRF-Hydro modeling system since the summer of 2016 (Gochis et al., 2015). The NWM produces a variety of hydrologic analysis and prediction products, including gridded fields of soil moisture, snowpack, shallow groundwater levels, inundated area depths, evapotranspiration as well as estimates of river flow and velocity for approximately 2.7 million river reaches. Also included in the NWM are representations for more than 1,200 reservoirs which are linked into the national channel network defined by the USGS NHDPlusv2.0 hydrography dataset. Despite the unprecedented spatial and temporal coverage of the NWM, many known deficiencies exist, including the representation of lakes and reservoirs. This study addresses the implementation of a reservoir assimilation scheme through coupling of a reservoir simulation model to represent the influence of managed flows. We examine the use of the reservoir operations to dynamically update lake/reservoir storage volume states, characterize flow characteristics of river reaches flowing into and out of lakes and reservoirs, and incorporate enhanced reservoir operating rules for the reservoir model options within the NWM. Model experiments focus on a pilot reservoir domain-Lake Mendocino, CA, and its contributing watershed, the East Fork Russian River. This reservoir is modeled using United States Army Corps of Engineers (USACE) HEC-ResSim developed for application to examine forecast informed reservoir operations (FIRO) in the Russian River basin.

Beyond Motivation: Exploring Mathematical Modeling as a Context for Deepening Students' Understandings of Curricular Mathematics

Science.gov (United States)

Zbiek, Rose Mary; Conner, Annamarie

2006-01-01

Views of mathematical modeling in empirical, expository, and curricular references typically capture a relationship between real-world phenomena and mathematical ideas from the perspective that competence in mathematical modeling is a clear goal of the mathematics curriculum. However, we work within a curricular context in which mathematical…

Petroacoustic Modelling of Heterolithic Sandstone Reservoirs: A Novel Approach to Gassmann Modelling Incorporating Sedimentological Constraints and NMR Porosity data

Science.gov (United States)

Matthews, S.; Lovell, M.; Davies, S. J.; Pritchard, T.; Sirju, C.; Abdelkarim, A.

2012-12-01

Heterolithic or 'shaly' sandstone reservoirs constitute a significant proportion of hydrocarbon resources. Petroacoustic models (a combination of petrophysics and rock physics) enhance the ability to extract reservoir properties from seismic data, providing a connection between seismic and fine-scale rock properties. By incorporating sedimentological observations these models can be better constrained and improved. Petroacoustic modelling is complicated by the unpredictable effects of clay minerals and clay-sized particles on geophysical properties. Such effects are responsible for erroneous results when models developed for "clean" reservoirs - such as Gassmann's equation (Gassmann, 1951) - are applied to heterolithic sandstone reservoirs. Gassmann's equation is arguably the most popular petroacoustic modelling technique in the hydrocarbon industry and is used to model elastic effects of changing reservoir fluid saturations. Successful implementation of Gassmann's equation requires well-constrained drained rock frame properties, which in heterolithic sandstones are heavily influenced by reservoir sedimentology, particularly clay distribution. The prevalent approach to categorising clay distribution is based on the Thomas - Stieber model (Thomas & Stieber, 1975), this approach is inconsistent with current understanding of 'shaly sand' sedimentology and omits properties such as sorting and grain size. The novel approach presented here demonstrates that characterising reservoir sedimentology constitutes an important modelling phase. As well as incorporating sedimentological constraints, this novel approach also aims to improve drained frame moduli estimates through more careful consideration of Gassmann's model assumptions and limitations. A key assumption of Gassmann's equation is a pore space in total communication with movable fluids. This assumption is often violated by conventional applications in heterolithic sandstone reservoirs where effective porosity, which

An Analysis Model for Water Cone Subsidence in Bottom Water Drive Reservoirs

Science.gov (United States)

Wang, Jianjun; Xu, Hui; Wu, Shucheng; Yang, Chao; Kong, lingxiao; Zeng, Baoquan; Xu, Haixia; Qu, Tailai

2017-12-01

Water coning in bottom water drive reservoirs, which will result in earlier water breakthrough, rapid increase in water cut and low recovery level, has drawn tremendous attention in petroleum engineering field. As one simple and effective method to inhibit bottom water coning, shut-in coning control is usually preferred in oilfield to control the water cone and furthermore to enhance economic performance. However, most of the water coning researchers just have been done on investigation of the coning behavior as it grows up, the reported studies for water cone subsidence are very scarce. The goal of this work is to present an analytical model for water cone subsidence to analyze the subsidence of water cone when the well shut in. Based on Dupuit critical oil production rate formula, an analytical model is developed to estimate the initial water cone shape at the point of critical drawdown. Then, with the initial water cone shape equation, we propose an analysis model for water cone subsidence in bottom water reservoir reservoirs. Model analysis and several sensitivity studies are conducted. This work presents accurate and fast analytical model to perform the water cone subsidence in bottom water drive reservoirs. To consider the recent interests in development of bottom drive reservoirs, our approach provides a promising technique for better understanding the subsidence of water cone.

Reservoir pressure evolution model during exploration drilling

Directory of Open Access Journals (Sweden)

Korotaev B. A.

2017-03-01

Full Text Available Based on the analysis of laboratory studies and literature data the method for estimating reservoir pressure in exploratory drilling has been proposed, it allows identify zones of abnormal reservoir pressure in the presence of seismic data on reservoir location depths. This method of assessment is based on developed at the end of the XX century methods using d- and σ-exponentials taking into account the mechanical drilling speed, rotor speed, bit load and its diameter, lithological constant and degree of rocks' compaction, mud density and "regional density". It is known that in exploratory drilling pulsation of pressure at the wellhead is observed. Such pulsation is a consequence of transferring reservoir pressure through clay. In the paper the mechanism for transferring pressure to the bottomhole as well as the behaviour of the clay layer during transmission of excess pressure has been described. A laboratory installation has been built, it has been used for modelling pressure propagation to the bottomhole of the well through a layer of clay. The bulge of the clay layer is established for 215.9 mm bottomhole diameter. Functional correlation of pressure propagation through the layer of clay has been determined and a reaction of the top clay layer has been shown to have bulge with a height of 25 mm. A pressure distribution scheme (balance has been developed, which takes into account the distance from layers with abnormal pressure to the bottomhole. A balance equation for reservoir pressure evaluation has been derived including well depth, distance from bottomhole to the top of the formation with abnormal pressure and density of clay.

HIV Model Parameter Estimates from Interruption Trial Data including Drug Efficacy and Reservoir Dynamics

Science.gov (United States)

Luo, Rutao; Piovoso, Michael J.; Martinez-Picado, Javier; Zurakowski, Ryan

2012-01-01

Mathematical models based on ordinary differential equations (ODE) have had significant impact on understanding HIV disease dynamics and optimizing patient treatment. A model that characterizes the essential disease dynamics can be used for prediction only if the model parameters are identifiable from clinical data. Most previous parameter identification studies for HIV have used sparsely sampled data from the decay phase following the introduction of therapy. In this paper, model parameters are identified from frequently sampled viral-load data taken from ten patients enrolled in the previously published AutoVac HAART interruption study, providing between 69 and 114 viral load measurements from 3–5 phases of viral decay and rebound for each patient. This dataset is considerably larger than those used in previously published parameter estimation studies. Furthermore, the measurements come from two separate experimental conditions, which allows for the direct estimation of drug efficacy and reservoir contribution rates, two parameters that cannot be identified from decay-phase data alone. A Markov-Chain Monte-Carlo method is used to estimate the model parameter values, with initial estimates obtained using nonlinear least-squares methods. The posterior distributions of the parameter estimates are reported and compared for all patients. PMID:22815727

The influence of mathematics learning using SAVI approach on junior high school students’ mathematical modelling ability

Science.gov (United States)

Khusna, H.; Heryaningsih, N. Y.

2018-01-01

The aim of this research was to examine mathematical modeling ability who learn mathematics by using SAVI approach. This research was a quasi-experimental research with non-equivalent control group designed by using purposive sampling technique. The population of this research was the state junior high school students in Lembang while the sample consisted of two class at 8th grade. The instrument used in this research was mathematical modeling ability. Data analysis of this research was conducted by using SPSS 20 by Windows. The result showed that students’ ability of mathematical modeling who learn mathematics by using SAVI approach was better than students’ ability of mathematical modeling who learn mathematics using conventional learning.

Mathematical Modelling as a Professional Task

Science.gov (United States)

Frejd, Peter; Bergsten, Christer

2016-01-01

Educational research literature on mathematical modelling is extensive. However, not much attention has been paid to empirical investigations of its scholarly knowledge from the perspective of didactic transposition processes. This paper reports from an interview study of mathematical modelling activities involving nine professional model…

Time-lapse seismic waveform modelling and attribute analysis using hydromechanical models for a deep reservoir undergoing depletion

Science.gov (United States)

He, Y.-X.; Angus, D. A.; Blanchard, T. D.; Wang, G.-L.; Yuan, S.-Y.; Garcia, A.

2016-04-01

Extraction of fluids from subsurface reservoirs induces changes in pore pressure, leading not only to geomechanical changes, but also perturbations in seismic velocities and hence observable seismic attributes. Time-lapse seismic analysis can be used to estimate changes in subsurface hydromechanical properties and thus act as a monitoring tool for geological reservoirs. The ability to observe and quantify changes in fluid, stress and strain using seismic techniques has important implications for monitoring risk not only for petroleum applications but also for geological storage of CO2 and nuclear waste scenarios. In this paper, we integrate hydromechanical simulation results with rock physics models and full-waveform seismic modelling to assess time-lapse seismic attribute resolution for dynamic reservoir characterization and hydromechanical model calibration. The time-lapse seismic simulations use a dynamic elastic reservoir model based on a North Sea deep reservoir undergoing large pressure changes. The time-lapse seismic traveltime shifts and time strains calculated from the modelled and processed synthetic data sets (i.e. pre-stack and post-stack data) are in a reasonable agreement with the true earth models, indicating the feasibility of using 1-D strain rock physics transform and time-lapse seismic processing methodology. Estimated vertical traveltime shifts for the overburden and the majority of the reservoir are within ±1 ms of the true earth model values, indicating that the time-lapse technique is sufficiently accurate for predicting overburden velocity changes and hence geomechanical effects. Characterization of deeper structure below the overburden becomes less accurate, where more advanced time-lapse seismic processing and migration is needed to handle the complex geometry and strong lateral induced velocity changes. Nevertheless, both migrated full-offset pre-stack and near-offset post-stack data image the general features of both the overburden and

Mathematical models of hysteresis

International Nuclear Information System (INIS)

1998-01-01

The ongoing research has largely been focused on the development of mathematical models of hysteretic nonlinearities with nonlocal memories. The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experiments show that only some past input extrema (not the entire input variations) leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are needed in order to describe nonlocal selective memories of hysteretic nonlinearities. The origin of such tools can be traced back to the landmark paper of Preisach. Their research has been primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic nonlinearities-rectangular loops. During the past four years, the study has been by and large centered around the following topics: (1) further development of Scalar and vector Preisach-type models of hysteresis; (2) experimental testing of Preisach-type models of hysteresis; (3) development of new models for viscosity (aftereffect) in hysteretic systems; (4) development of mathematical models for superconducting hysteresis in the case of gradual resistive transitions; (5) software implementation of Preisach-type models of hysteresis; and (6) development of new ideas which have emerged in the course of the research work. The author briefly describes the main scientific results obtained in the areas outlined above

Mathematical models of hysteresis

Energy Technology Data Exchange (ETDEWEB)

NONE

1998-08-01

The ongoing research has largely been focused on the development of mathematical models of hysteretic nonlinearities with nonlocal memories. The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experiments show that only some past input extrema (not the entire input variations) leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are needed in order to describe nonlocal selective memories of hysteretic nonlinearities. The origin of such tools can be traced back to the landmark paper of Preisach. Their research has been primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic nonlinearities-rectangular loops. During the past four years, the study has been by and large centered around the following topics: (1) further development of Scalar and vector Preisach-type models of hysteresis; (2) experimental testing of Preisach-type models of hysteresis; (3) development of new models for viscosity (aftereffect) in hysteretic systems; (4) development of mathematical models for superconducting hysteresis in the case of gradual resistive transitions; (5) software implementation of Preisach-type models of hysteresis; and (6) development of new ideas which have emerged in the course of the research work. The author briefly describes the main scientific results obtained in the areas outlined above.

Mathematical modelling of metabolism

DEFF Research Database (Denmark)

Gombert, Andreas Karoly; Nielsen, Jens

2000-01-01

Mathematical models of the cellular metabolism have a special interest within biotechnology. Many different kinds of commercially important products are derived from the cell factory, and metabolic engineering can be applied to improve existing production processes, as well as to make new processes...... availability of genomic information and powerful analytical techniques, mathematical models also serve as a tool for understanding the cellular metabolism and physiology....... available. Both stoichiometric and kinetic models have been used to investigate the metabolism, which has resulted in defining the optimal fermentation conditions, as well as in directing the genetic changes to be introduced in order to obtain a good producer strain or cell line. With the increasing...

Using Covariation Reasoning to Support Mathematical Modeling

Science.gov (United States)

Jacobson, Erik

2014-01-01

For many students, making connections between mathematical ideas and the real world is one of the most intriguing and rewarding aspects of the study of mathematics. In the Common Core State Standards for Mathematics (CCSSI 2010), mathematical modeling is highlighted as a mathematical practice standard for all grades. To engage in mathematical…

The many faces of the mathematical modeling cycle

NARCIS (Netherlands)

Perrenet, J.C.; Zwaneveld, B.

2012-01-01

In literature about mathematical modeling a diversity can be seen in ways of presenting the modeling cycle. Every year, students in the Bachelor’s program Applied Mathematics of the Eindhoven University of Technology, after having completed a series of mathematical modeling projects, have been

Three-Dimensional Modeling of Fracture Clusters in Geothermal Reservoirs

Energy Technology Data Exchange (ETDEWEB)

Ghassemi, Ahmad [Univ. of Oklahoma, Norman, OK (United States)

2017-08-11

The objective of this is to develop a 3-D numerical model for simulating mode I, II, and III (tensile, shear, and out-of-plane) propagation of multiple fractures and fracture clusters to accurately predict geothermal reservoir stimulation using the virtual multi-dimensional internal bond (VMIB). Effective development of enhanced geothermal systems can significantly benefit from improved modeling of hydraulic fracturing. In geothermal reservoirs, where the temperature can reach or exceed 350oC, thermal and poro-mechanical processes play an important role in fracture initiation and propagation. In this project hydraulic fracturing of hot subsurface rock mass will be numerically modeled by extending the virtual multiple internal bond theory and implementing it in a finite element code, WARP3D, a three-dimensional finite element code for solid mechanics. The new constitutive model along with the poro-thermoelastic computational algorithms will allow modeling the initiation and propagation of clusters of fractures, and extension of pre-existing fractures. The work will enable the industry to realistically model stimulation of geothermal reservoirs. The project addresses the Geothermal Technologies Office objective of accurately predicting geothermal reservoir stimulation (GTO technology priority item). The project goal will be attained by: (i) development of the VMIB method for application to 3D analysis of fracture clusters; (ii) development of poro- and thermoelastic material sub-routines for use in 3D finite element code WARP3D; (iii) implementation of VMIB and the new material routines in WARP3D to enable simulation of clusters of fractures while accounting for the effects of the pore pressure, thermal stress and inelastic deformation; (iv) simulation of 3D fracture propagation and coalescence and formation of clusters, and comparison with laboratory compression tests; and (v) application of the model to interpretation of injection experiments (planned by our

Modeling the Transport and Fate of Fecal Pollution and Nutrients of Miyun Reservoir

Science.gov (United States)

Liu, L.; Fu, X.; Wang, G.

2009-12-01

Miyun Reservoir, a mountain valley reservoir, is located 100 km northeast of Beijing City. Besides the functions of flood control, irrigation and fishery for Beijing area, Miyun Reservoir is the main drinking water storage for Beijing city. The water quality is therefore of great importance. Recently, the concentration of fecal pollution and nutrients in the reservoir are constantly rising to arrest the attention of Beijing municipality. Fecal pollution from sewage is a significant public health concern due to the known presence of human viruses and parasites in these discharges. To investigate the transport and fate of the fecal pollution and nutrients at Miyun reservoir and the health risks associated with drinking and fishery, the reservoir and two tributaries, Chaohe river and Baihe river discharging into it are being examined for bacterial, nutrients and other routine pollution. To understand the relative importance of different processes influencing pollution transport and inactivation, a finite-element model of surf-zone hydrodynamics (coupled with models for temperature, fecal pollution, nutrients and other routine contaminants) is used. The developed models are being verified by the observed water quality data including water temperature, conductivities and dissolved oxygen from the reservoir and its tributaries. Different factors impacting the inactivation of fecal pollution and the transport of nutrients such as water temperature, sedimentation, sunlight insolation are evaluated for Miyun reservoir by a sensitivity analysis analogized from the previous research of Lake Michigan (figure 1, indicating that solar insolation dominates the inactivation of E. Coli, an indicator of fecal pollution, Liu et al. 2006). The calibrated modeling system can be used to temporally and spatially simulate and predict the variation of the concentration of fecal pollution and nutrients of Miyun reservoir. Therefore this research can provide a forecasting tool for the

Combined reservoir simulation and seismic technology, a new approach for modeling CHOPS

Energy Technology Data Exchange (ETDEWEB)

Aghabarati, H.; Lines, L.; Settari, A. [Calgary Univ., AB (Canada); Dumitrescu, C. [Sensor Geophysical Ltd., Calgary, AB (Canada)

2008-10-15

One of the primary recovery schemes for developing heavy oil reservoirs in Canada is cold heavy oil production with sand (CHOPS). With the introduction of progressive cavity pumps, CHOPS can be applied in unconsolidated or weakly consolidated formations. In order to better understand reservoir properties and recovery mechanism, this paper discussed the use of a combined reservoir simulation and seismic technology that were applied for a heavy oil reservoir situated in Saskatchewan, Canada. Using a seismic survey acquired in 1989, the study used geostatistical methods to estimate the initial reservoir porosity. Sand production was then modeled using an erosional velocity approach and the model was run based on oil production. The paper also compared the results of true porosity derived from simulation against the porosity estimated from a second seismic survey acquired in 2001. Last, the extent and the shape of the enhanced permeability region was modelled in order to estimate porosity distribution. It was concluded that the performance of the CHOPS wells depended greatly on the rate of creation of the high permeability zone around the wells. 9 refs., 2 tabs., 18 figs., 1 appendix.

Reservoir management

International Nuclear Information System (INIS)

Satter, A.; Varnon, J.E.; Hoang, M.T.

1992-01-01

A reservoir's life begins with exploration leading to discovery followed by delineation of the reservoir, development of the field, production by primary, secondary and tertiary means, and finally to abandonment. Sound reservoir management is the key to maximizing economic operation of the reservoir throughout its entire life. Technological advances and rapidly increasing computer power are providing tools to better manage reservoirs and are increasing the gap between good and neural reservoir management. The modern reservoir management process involves goal setting, planning, implementing, monitoring, evaluating, and revising plans. Setting a reservoir management strategy requires knowledge of the reservoir, availability of technology, and knowledge of the business, political, and environmental climate. Formulating a comprehensive management plan involves depletion and development strategies, data acquisition and analyses, geological and numerical model studies, production and reserves forecasts, facilities requirements, economic optimization, and management approval. This paper provides management, engineers, geologists, geophysicists, and field operations staff with a better understanding of the practical approach to reservoir management using a multidisciplinary, integrated team approach

Reservoir management

International Nuclear Information System (INIS)

Satter, A.; Varnon, J.E.; Hoang, M.T.

1992-01-01

A reservoir's life begins with exploration leading to discovery followed by delineation of the reservoir, development of the field, production by primary, secondary and tertiary means, and finally to abandonment. Sound reservoir management is the key to maximizing economic operation of the reservoir throughout its entire life. Technological advances and rapidly increasing computer power are providing tools to better manage reservoirs and are increasing the gap between good and neutral reservoir management. The modern reservoir management process involves goal setting, planning, implementing, monitoring, evaluating, and revising plans. Setting a reservoir management strategy requires knowledge of the reservoir, availability of technology, and knowledge of the business, political, and environmental climate. Formulating a comprehensive management plan involves depletion and development strategies, data acquisition and analyses, geological and numerical model studies, production and reserves forecasts, facilities requirements, economic optimization, and management approval. This paper provides management, engineers geologists, geophysicists, and field operations staff with a better understanding of the practical approach to reservoir management using a multidisciplinary, integrated team approach

Mathematical Modeling of Multiphase Filtration in Porous Media with a Chemically Active Skeleton

Science.gov (United States)

Khramchenkov, M. G.; Khramchenkov, É. M.

2018-01-01

The authors propose a mathematical model of two-phase filtration that occurs under the conditions of dissolution of a porous medium. The model can be used for joint description of complex chemical-hydrogeomechanical processes that are of frequent occurrence in the oil-and-gas producing and nature conservation practice. As an example, consideration is given to the acidizing of the bottom zone of the injection well of an oil reservoir. Enclosing rocks are represented by carbonates. The phases of the process are an aqueous solution of hydrochloric acid and oil. A software product for computational experiments is developed. For the numerical experiments, use is made of the data on the wells of an actual oil field. Good agreement is obtained between the field data and the calculated data. Numerical experiments with different configurations of the permeability of an oil stratum are conducted.

Seismic Modeling Of Reservoir Heterogeneity Scales: An Application To Gas Hydrate Reservoirs

Science.gov (United States)

Huang, J.; Bellefleur, G.; Milkereit, B.

2008-12-01

Natural gas hydrates, a type of inclusion compound or clathrate, are composed of gas molecules trapped within a cage of water molecules. The occurrence of gas hydrates in permafrost regions has been confirmed by core samples recovered from the Mallik gas hydrate research wells located within Mackenzie Delta in Northwest Territories of Canada. Strong vertical variations of compressional and shear sonic velocities and weak surface seismic expressions of gas hydrates indicate that lithological heterogeneities control the distribution of hydrates. Seismic scattering studies predict that typical scales and strong physical contrasts due to gas hydrate concentration will generate strong forward scattering, leaving only weak energy captured by surface receivers. In order to understand the distribution of hydrates and the seismic scattering effects, an algorithm was developed to construct heterogeneous petrophysical reservoir models. The algorithm was based on well logs showing power law features and Gaussian or Non-Gaussian probability density distribution, and was designed to honor the whole statistical features of well logs such as the characteristic scales and the correlation among rock parameters. Multi-dimensional and multi-variable heterogeneous models representing the same statistical properties were constructed and applied to the heterogeneity analysis of gas hydrate reservoirs. The petrophysical models provide the platform to estimate rock physics properties as well as to study the impact of seismic scattering, wave mode conversion, and their integration on wave behavior in heterogeneous reservoirs. Using the Biot-Gassmann theory, the statistical parameters obtained from Mallik 5L-38, and the correlation length estimated from acoustic impedance inversion, gas hydrate volume fraction in Mallik area was estimated to be 1.8%, approximately 2x108 m3 natural gas stored in a hydrate bearing interval within 0.25 km2 lateral extension and between 889 m and 1115 m depth

Mathematical models in radiogeochronology

International Nuclear Information System (INIS)

Abril, J.M.; Garcia Leon, M.

1991-01-01

The study of activity vs. depth profiles in sediment cores of some man-made and natural ocurring radionuclides have shown to be a poweful tool for dating purposes. Nevertheless, in most cases, an adecuate interpretation of such profiles requires mathematical models. In this paper, by considering the sediment as a continuum, a general equation for diffusion of radionuclides through it is obtained. Consequentely, some previously published dating models are found to be particular solutions of such general advenction-diffusion problem. Special emphasis is given to the mathematical treatment of compactation effect and time dependent problems. (author)

Mathematical modelling a case studies approach

CERN Document Server

Illner, Reinhard; McCollum, Samantha; Roode, Thea van

2004-01-01

Mathematical modelling is a subject without boundaries. It is the means by which mathematics becomes useful to virtually any subject. Moreover, modelling has been and continues to be a driving force for the development of mathematics itself. This book explains the process of modelling real situations to obtain mathematical problems that can be analyzed, thus solving the original problem. The presentation is in the form of case studies, which are developed much as they would be in true applications. In many cases, an initial model is created, then modified along the way. Some cases are familiar, such as the evaluation of an annuity. Others are unique, such as the fascinating situation in which an engineer, armed only with a slide rule, had 24 hours to compute whether a valve would hold when a temporary rock plug was removed from a water tunnel. Each chapter ends with a set of exercises and some suggestions for class projects. Some projects are extensive, as with the explorations of the predator-prey model; oth...

Seismic modeling of acid-gas injection in a deep saline reservoir

Energy Technology Data Exchange (ETDEWEB)

Ursenbach, C.P.; Lawton, D.C. [Calgary Univ., AB (Canada). Dept. of Geoscience, Consortium for Research in Elastic Wave Exploration Seismology

2008-07-01

Carbon dioxide (CO{sub 2}) and hydrogen sulfide (H{sub 2}S) are common byproducts of the energy industry. As such, remediation studies are underway to determine the feasibility of sequestering these byproducts in subsurface reservoirs, including deep saline reservoirs. Acid gas injection at smaller gas wells holds promise. However, in order for such injection programs to work, the progress of the injection plume must be tracked. A modeling study of fluid substitution was carried out to gain insight into the ability of seismic monitoring to distinguish pre- and post-injection states of the reservoir medium. The purpose of this study was to carry out fluid substitution calculations for the modeling of an injection process. A methodology that may be applied or adapted to a variety of acid-gas injection scenarios was also developed. The general approach involved determining acoustic properties at reservoir temperature and pressure of relevant fluids; obtaining elastic properties of the reservoir rock for some reference saturated state, and the elastic properties of the mineral comprising it; and, determining the change in reservoir elastic properties due to fluid substitution via Gassmann's equation. Water, brine and non-aqueous acid gas were the 3 fluids of interest in this case. The feasibility of monitoring was judged by the sensitivity of travel times and reflection coefficients to fluid substitution. 4 refs., 2 figs.

Engaging Elementary Students in the Creative Process of Mathematizing Their World through Mathematical Modeling

Directory of Open Access Journals (Sweden)

Jennifer M. Suh

2017-06-01

Full Text Available This paper examines the experiences of two elementary teachers’ implementation of mathematical modeling in their classrooms and how the enactment by the teachers and the engagement by students exhibited their creativity, critical thinking, collaboration and communication skills. In particular, we explore the questions: (1 How can phases of mathematical modeling as a process serve as a venue for exhibiting students’ critical 21st century skills? (2 What were some effective pedagogical practices teachers used as they implemented mathematical modeling with elementary students and how did these promote students’ 21st century skills? We propose that mathematical modeling provides space for teachers and students to have a collective experience through the iterative process of making sense of and building knowledge of important mathematical ideas while engaging in the critical 21st century skills necessary in our complex modern world.

More Novel Hantaviruses and Diversifying Reservoir Hosts — Time for Development of Reservoir-Derived Cell Culture Models?

Directory of Open Access Journals (Sweden)

Isabella Eckerle

2014-02-01

Full Text Available Due to novel, improved and high-throughput detection methods, there is a plethora of newly identified viruses within the genus Hantavirus. Furthermore, reservoir host species are increasingly recognized besides representatives of the order Rodentia, now including members of the mammalian orders Soricomorpha/Eulipotyphla and Chiroptera. Despite the great interest created by emerging zoonotic viruses, there is still a gross lack of in vitro models, which reflect the exclusive host adaptation of most zoonotic viruses. The usually narrow host range and genetic diversity of hantaviruses make them an exciting candidate for studying virus-host interactions on a cellular level. To do so, well-characterized reservoir cell lines covering a wide range of bat, insectivore and rodent species are essential. Most currently available cell culture models display a heterologous virus-host relationship and are therefore only of limited value. Here, we review the recently established approaches to generate reservoir-derived cell culture models for the in vitro study of virus-host interactions. These successfully used model systems almost exclusively originate from bats and bat-borne viruses other than hantaviruses. Therefore we propose a parallel approach for research on rodent- and insectivore-borne hantaviruses, taking the generation of novel rodent and insectivore cell lines from wildlife species into account. These cell lines would be also valuable for studies on further rodent-borne viruses, such as orthopox- and arenaviruses.

Simulation and optimisation modelling approach for operation of the Hoa Binh Reservoir, Vietnam

DEFF Research Database (Denmark)

Ngo, Long le; Madsen, Henrik; Rosbjerg, Dan

2007-01-01

Hoa Binh, the largest reservoir in Vietnam, plays an important role in flood control for the Red River delta and hydropower generation. Due to its multi-purpose character, conflicts and disputes in operating the reservoir have been ongoing since its construction, particularly in the flood season....... This paper proposes to optimise the control strategies for the Hoa Binh reservoir operation by applying a combination of simulation and optimisation models. The control strategies are set up in the MIKE 11 simulation model to guide the releases of the reservoir system according to the current storage level......, the hydro-meteorological conditions, and the time of the year. A heuristic global optimisation tool, the shuffled complex evolution (SCE) algorithm, is adopted for optimising the reservoir operation. The optimisation puts focus on the trade-off between flood control and hydropower generation for the Hoa...

Mathematical Modeling in the High School Curriculum

Science.gov (United States)

Hernández, Maria L.; Levy, Rachel; Felton-Koestler, Mathew D.; Zbiek, Rose Mary

2016-01-01

In 2015, mathematics leaders and instructors from the Society for Industrial and Applied Mathematics (SIAM) and the Consortium for Mathematics and Its Applications (COMAP), with input from NCTM, came together to write the "Guidelines for Assessment and Instruction in Mathematical Modeling Education" (GAIMME) report as a resource for…

Mathematical Modeling Approaches in Plant Metabolomics.

Science.gov (United States)

Fürtauer, Lisa; Weiszmann, Jakob; Weckwerth, Wolfram; Nägele, Thomas

2018-01-01

The experimental analysis of a plant metabolome typically results in a comprehensive and multidimensional data set. To interpret metabolomics data in the context of biochemical regulation and environmental fluctuation, various approaches of mathematical modeling have been developed and have proven useful. In this chapter, a general introduction to mathematical modeling is presented and discussed in context of plant metabolism. A particular focus is laid on the suitability of mathematical approaches to functionally integrate plant metabolomics data in a metabolic network and combine it with other biochemical or physiological parameters.

Students’ mathematical learning in modelling activities

DEFF Research Database (Denmark)

Kjeldsen, Tinne Hoff; Blomhøj, Morten

2013-01-01

Ten years of experience with analyses of students’ learning in a modelling course for first year university students, led us to see modelling as a didactical activity with the dual goal of developing students’ modelling competency and enhancing their conceptual learning of mathematical concepts i...... create and help overcome hidden cognitive conflicts in students’ understanding; that reflections within modelling can play an important role for the students’ learning of mathematics. These findings are illustrated with a modelling project concerning the world population....

Towards an Improved Represenation of Reservoirs and Water Management in a Land Surface-Hydrology Model

Science.gov (United States)

Yassin, F.; Anis, M. R.; Razavi, S.; Wheater, H. S.

2017-12-01

Water management through reservoirs, diversions, and irrigation have significantly changed river flow regimes and basin-wide energy and water balance cycles. Failure to represent these effects limits the performance of land surface-hydrology models not only for streamflow prediction but also for the estimation of soil moisture, evapotranspiration, and feedbacks to the atmosphere. Despite recent research to improve the representation of water management in land surface models, there remains a need to develop improved modeling approaches that work in complex and highly regulated basins such as the 406,000 km2 Saskatchewan River Basin (SaskRB). A particular challenge for regional and global application is a lack of local information on reservoir operational management. To this end, we implemented a reservoir operation, water abstraction, and irrigation algorithm in the MESH land surface-hydrology model and tested it over the SaskRB. MESH is Environment Canada's Land Surface-hydrology modeling system that couples Canadian Land Surface Scheme (CLASS) with hydrological routing model. The implemented reservoir algorithm uses an inflow-outflow relationship that accounts for the physical characteristics of reservoirs (e.g., storage-area-elevation relationships) and includes simplified operational characteristics based on local information (e.g., monthly target volume and release under limited, normal, and flood storage zone). The irrigation algorithm uses the difference between actual and potential evapotranspiration to estimate irrigation water demand. This irrigation demand is supplied from the neighboring reservoirs/diversion in the river system. We calibrated the model enabled with the new reservoir and irrigation modules in a multi-objective optimization setting. Results showed that the reservoir and irrigation modules significantly improved the MESH model performance in generating streamflow and evapotranspiration across the SaskRB and that this our approach provides

Mathematical Modeling with Middle School Students: The Robot Art Model-Eliciting Activity

Science.gov (United States)

Stohlmann, Micah S.

2017-01-01

Internationally mathematical modeling is garnering more attention for the benefits associated with it. Mathematical modeling can develop students' communication skills and the ability to demonstrate understanding through different representations. With the increased attention on mathematical modeling, there is a need for more curricula to be…

Effect of reservoir heterogeneity on air injection performance in a light oil reservoir

Directory of Open Access Journals (Sweden)

Hu Jia

2018-03-01

Full Text Available Air injection is a good option to development light oil reservoir. As well-known that, reservoir heterogeneity has great effect for various EOR processes. This also applies to air injection. However, oil recovery mechanisms and physical processes for air injection in heterogeneous reservoir with dip angle are still not well understood. The reported setting of reservoir heterogeneous for physical model or simulation model of air injection only simply uses different-layer permeability of porous media. In practice, reservoir heterogeneity follows the principle of geostatistics. How much of contrast in permeability actually challenges the air injection in light oil reservoir? This should be investigated by using layered porous medial settings of the classical Dykstra-Parsons style. Unfortunately, there has been no work addressing this issue for air injection in light oil reservoir. In this paper, Reservoir heterogeneity is quantified based on the use of different reservoir permeability distribution according to classical Dykstra-Parsons coefficients method. The aim of this work is to investigate the effect of reservoir heterogeneity on physical process and production performance of air injection in light oil reservoir through numerical reservoir simulation approach. The basic model is calibrated based on previous study. Total eleven pseudo compounders are included in this model and ten complexity of reactions are proposed to achieve the reaction scheme. Results show that oil recovery factor is decreased with the increasing of reservoir heterogeneity both for air and N2 injection from updip location, which is against the working behavior of air injection from updip location. Reservoir heterogeneity sometimes can act as positive effect to improve sweep efficiency as well as enhance production performance for air injection. High O2 content air injection can benefit oil recovery factor, also lead to early O2 breakthrough in heterogeneous reservoir. Well

New modelling of transient well test and rate decline analysis for a horizontal well in a multiple-zone reservoir

International Nuclear Information System (INIS)

Nie, Ren-Shi; Guo, Jian-Chun; Jia, Yong-Lu; Zhu, Shui-Qiao; Rao, Zheng; Zhang, Chun-Guang

2011-01-01

The no-type curve with negative skin of a horizontal well has been found in the current research. Negative skin is very significant to transient well test and rate decline analysis. This paper first presents the negative skin problem where the type curves with negative skin of a horizontal well are oscillatory. In order to solve the problem, we propose a new model of transient well test and rate decline analysis for a horizontal well in a multiple-zone composite reservoir. A new dimensionless definition of r D is introduced in the dimensionless mathematical modelling under different boundaries. The model is solved using the Laplace transform and separation of variables techniques. In Laplace space, the solutions for both constant rate production and constant wellbore pressure production are expressed in a unified formula. We provide graphs and thorough analysis of the new standard type curves for both well test and rate decline analysis; the characteristics of type curves are the reflections of horizontal well production in a multiple-zone reservoir. An important contribution of our paper is that our model removed the oscillation in type curves and thus solved the negative skin problem. We also show that the characteristics of type curves depend heavily on the properties of different zones, skin factor, well length, formation thickness, etc. Our research can be applied to a real case study

Spillways Scheduling for Flood Control of Three Gorges Reservoir Using Mixed Integer Linear Programming Model

Directory of Open Access Journals (Sweden)

Maoyuan Feng

2014-01-01

Full Text Available This study proposes a mixed integer linear programming (MILP model to optimize the spillways scheduling for reservoir flood control. Unlike the conventional reservoir operation model, the proposed MILP model specifies the spillways status (including the number of spillways to be open and the degree of the spillway opened instead of reservoir release, since the release is actually controlled by using the spillway. The piecewise linear approximation is used to formulate the relationship between the reservoir storage and water release for a spillway, which should be open/closed with a status depicted by a binary variable. The control order and symmetry rules of spillways are described and incorporated into the constraints for meeting the practical demand. Thus, a MILP model is set up to minimize the maximum reservoir storage. The General Algebraic Modeling System (GAMS and IBM ILOG CPLEX Optimization Studio (CPLEX software are used to find the optimal solution for the proposed MILP model. The China’s Three Gorges Reservoir, whose spillways are of five types with the total number of 80, is selected as the case study. It is shown that the proposed model decreases the flood risk compared with the conventional operation and makes the operation more practical by specifying the spillways status directly.

River and Reservoir Operations Model, Truckee River basin, California and Nevada, 1998

Science.gov (United States)

Berris, Steven N.; Hess, Glen W.; Bohman, Larry R.

2001-01-01

The demand for all uses of water in the Truckee River Basin, California and Nevada, commonly is greater than can be supplied. Storage reservoirs in the system have a maximum effective total capacity equivalent to less than two years of average river flows, so longer-term droughts can result in substantial water-supply shortages for irrigation and municipal users and may stress fish and wildlife ecosystems. Title II of Public Law (P.L.) 101-618, the Truckee?Carson?Pyramid Lake Water Rights Settlement Act of 1990, provides a foundation for negotiating and developing operating criteria, known as the Truckee River Operating Agreement (TROA), to balance interstate and interbasin allocation of water rights among the many interests competing for water from the Truckee River. In addition to TROA, the Truckee River Water Quality Settlement Agreement (WQSA), signed in 1996, provides for acquisition of water rights to resolve water-quality problems during low flows along the Truckee River in Nevada. Efficient execution of many of the planning, management, or environmental assessment requirements of TROA and WQSA will require detailed water-resources data coupled with sound analytical tools. Analytical modeling tools constructed and evaluated with such data could help assess effects of alternative operational scenarios related to reservoir and river operations, water-rights transfers, and changes in irrigation practices. The Truckee?Carson Program of the U.S. Geological Survey, to support U.S. Department of the Interior implementation of P.L. 101-618, is developing a modeling system to support efficient water-resources planning, management, and allocation. The daily operations model documented herein is a part of the modeling system that includes a database management program, a graphical user interface program, and a program with modules that simulate river/reservoir operations and a variety of hydrologic processes. The operations module is capable of simulating lake

Mathematical modelling of fracture hydrology

International Nuclear Information System (INIS)

Herbert, A.W.; Hodgkindon, D.P.; Lever, D.A.; Robinson, P.C.; Rae, J.

1985-01-01

This report reviews work carried out between January 1983 and December 1984 for the CEC/DOE contract 'Mathematical Modelling of Fracture Hydrology' which forms part of the CEC Mirage project (CEC 1984. Come 1985. Bourke et. al. 1983). It describes the development and use of a variety of mathematical models for the flow of water and transport of radionuclides in flowing groundwater. These models have an important role to play in assessing the long-term safety of radioactive waste burial, and in the planning and interpretation of associated experiments. The work is reported under five headings, namely 1) Statistical fracture network modelling, 2) Continuum models of flow and transport, 3) Simplified models, 4) Analysis of laboratory experiments, 5) Analysis of field experiments

Mathematical modeling of laser lipolysis

Directory of Open Access Journals (Sweden)

Reynaud Jean

2008-02-01

Full Text Available Abstract Background and Objectives Liposuction continues to be one of the most popular procedures performed in cosmetic surgery. As the public's demand for body contouring continues, laser lipolysis has been proposed to improve results, minimize risk, optimize patient comfort, and reduce the recovery period. Mathematical modeling of laser lipolysis could provide a better understanding of the laser lipolysis process and could determine the optimal dosage as a function of fat volume to be removed. Study design/Materials and Methods An Optical-Thermal-Damage Model was formulated using finite-element modeling software (Femlab 3.1, Comsol Inc. The general model simulated light distribution using the diffusion approximation of the transport theory, temperature rise using the bioheat equation and laser-induced injury using the Arrhenius damage model. Biological tissue was represented by two homogenous regions (dermis and fat layer with a nonlinear air-tissue boundary condition including free convection. Video recordings were used to gain a better understanding of the back and forth movement of the cannula during laser lipolysis in order to consider them in our mathematical model. Infrared video recordings were also performed in order to compare the actual surface temperatures to our calculations. The reduction in fat volume was determined as a function of the total applied energy and subsequently compared to clinical data reported in the literature. Results In patients, when using cooled tumescent anesthesia, 1064 nm Nd:YAG laser or 980 nm diode laser: (6 W, back and forth motion: 100 mm/s give similar skin surface temperature (max: 41°C. These measurements are in accordance with those obtained by mathematical modeling performed with a 1 mm cannula inserted inside the hypodermis layer at 0.8 cm below the surface. Similarly, the fat volume reduction observed in patients at 6-month follow up can be determined by mathematical modeling. This fat reduction

Integrated reservoir characterization: Improvement in heterogeneities stochastic modelling by integration of additional external constraints

Energy Technology Data Exchange (ETDEWEB)

Doligez, B.; Eschard, R. [Institut Francais du Petrole, Rueil Malmaison (France); Geffroy, F. [Centre de Geostatistique, Fontainebleau (France)] [and others

1997-08-01

The classical approach to construct reservoir models is to start with a fine scale geological model which is informed with petrophysical properties. Then scaling-up techniques allow to obtain a reservoir model which is compatible with the fluid flow simulators. Geostatistical modelling techniques are widely used to build the geological models before scaling-up. These methods provide equiprobable images of the area under investigation, which honor the well data, and which variability is the same than the variability computed from the data. At an appraisal phase, when few data are available, or when the wells are insufficient to describe all the heterogeneities and the behavior of the field, additional constraints are needed to obtain a more realistic geological model. For example, seismic data or stratigraphic models can provide average reservoir information with an excellent areal coverage, but with a poor vertical resolution. New advances in modelisation techniques allow now to integrate this type of additional external information in order to constrain the simulations. In particular, 2D or 3D seismic derived information grids, or sand-shale ratios maps coming from stratigraphic models can be used as external drifts to compute the geological image of the reservoir at the fine scale. Examples are presented to illustrate the use of these new tools, their impact on the final reservoir model, and their sensitivity to some key parameters.

Detailed geologic modeling of a turbidity reservoir interval at the Mars discovery

Energy Technology Data Exchange (ETDEWEB)

Mahaffie, M.J.; Chapin, M.A. [Shell Exploration and Production Technology Co. (United States); Henry, W.A. [Shell Offshore, Inc. (United States)

1995-12-31

Detailed reservoir architecture studies using high resolution seismic data coupled with geologic and seismic inversion modeling have been used to evaluate a major hydrocarbon bearing turbidite reservoir found within Prospect Mars. Early interpretations of this interval, based on lower frequency (40 Hz) seismic data, indicated the presence of a single, laterally continuous event covering an area nearly 3 miles square ({approx} 5200 acres). Correlations from well control supported the notion that this seismic event comprised a series of continuous sheet sands exhibiting a high degree of lateral continuity and connectivity. However pressure data taken during fluid sampling of the reservoir suggested the possibility of discontinuities not observed within the resolution of the seismic data. Seismic reprocessing enhancements to increase frequency content revealed the presence of multiple stratigraphic features not previously recognized. Detailed seismic mapping using loop-level seismic attributes and seismic inversion studies constrained by geologic models provide a more realistic depiction of the environment of deposition and improve reservoir simulation modeling for this stratigraphic interval. (author). 3 figs

Modeling surface energy fluxes and thermal dynamics of a seasonally ice-covered hydroelectric reservoir.

Science.gov (United States)

Wang, Weifeng; Roulet, Nigel T; Strachan, Ian B; Tremblay, Alain

2016-04-15

The thermal dynamics of human created northern reservoirs (e.g., water temperatures and ice cover dynamics) influence carbon processing and air-water gas exchange. Here, we developed a process-based one-dimensional model (Snow, Ice, WAater, and Sediment: SIWAS) to simulate a full year's surface energy fluxes and thermal dynamics for a moderately large (>500km(2)) boreal hydroelectric reservoir in northern Quebec, Canada. There is a lack of climate and weather data for most of the Canadian boreal so we designed SIWAS with a minimum of inputs and with a daily time step. The modeled surface energy fluxes were consistent with six years of observations from eddy covariance measurements taken in the middle of the reservoir. The simulated water temperature profiles agreed well with observations from over 100 sites across the reservoir. The model successfully captured the observed annual trend of ice cover timing, although the model overestimated the length of ice cover period (15days). Sensitivity analysis revealed that air temperature significantly affects the ice cover duration, water and sediment temperatures, but that dissolved organic carbon concentrations have little effect on the heat fluxes, and water and sediment temperatures. We conclude that the SIWAS model is capable of simulating surface energy fluxes and thermal dynamics for boreal reservoirs in regions where high temporal resolution climate data are not available. SIWAS is suitable for integration into biogeochemical models for simulating a reservoir's carbon cycle. Copyright © 2016 Elsevier B.V. All rights reserved.

Evaluation of Gaussian approximations for data assimilation in reservoir models

KAUST Repository

Iglesias, Marco A.

2013-07-14

The Bayesian framework is the standard approach for data assimilation in reservoir modeling. This framework involves characterizing the posterior distribution of geological parameters in terms of a given prior distribution and data from the reservoir dynamics, together with a forward model connecting the space of geological parameters to the data space. Since the posterior distribution quantifies the uncertainty in the geologic parameters of the reservoir, the characterization of the posterior is fundamental for the optimal management of reservoirs. Unfortunately, due to the large-scale highly nonlinear properties of standard reservoir models, characterizing the posterior is computationally prohibitive. Instead, more affordable ad hoc techniques, based on Gaussian approximations, are often used for characterizing the posterior distribution. Evaluating the performance of those Gaussian approximations is typically conducted by assessing their ability at reproducing the truth within the confidence interval provided by the ad hoc technique under consideration. This has the disadvantage of mixing up the approximation properties of the history matching algorithm employed with the information content of the particular observations used, making it hard to evaluate the effect of the ad hoc approximations alone. In this paper, we avoid this disadvantage by comparing the ad hoc techniques with a fully resolved state-of-the-art probing of the Bayesian posterior distribution. The ad hoc techniques whose performance we assess are based on (1) linearization around the maximum a posteriori estimate, (2) randomized maximum likelihood, and (3) ensemble Kalman filter-type methods. In order to fully resolve the posterior distribution, we implement a state-of-the art Markov chain Monte Carlo (MCMC) method that scales well with respect to the dimension of the parameter space, enabling us to study realistic forward models, in two space dimensions, at a high level of grid refinement. Our

A Step Forward to Closing the Loop between Static and Dynamic Reservoir Modeling

Directory of Open Access Journals (Sweden)

Cancelliere M.

2014-12-01

Full Text Available The current trend for history matching is to find multiple calibrated models instead of a single set of model parameters that match the historical data. The advantage of several current workflows involving assisted history matching techniques, particularly those based on heuristic optimizers or direct search, is that they lead to a number of calibrated models that partially address the problem of the non-uniqueness of the solutions. The importance of achieving multiple solutions is that calibrated models can be used for a true quantification of the uncertainty affecting the production forecasts, which represent the basis for technical and economic risk analysis. In this paper, the importance of incorporating the geological uncertainties in a reservoir study is demonstrated. A workflow, which includes the analysis of the uncertainty associated with the facies distribution for a fluvial depositional environment in the calibration of the numerical dynamic models and, consequently, in the production forecast, is presented. The first step in the workflow was to generate a set of facies realizations starting from different conceptual models. After facies modeling, the petrophysical properties were assigned to the simulation domains. Then, each facies realization was calibrated separately by varying permeability and porosity fields. Data assimilation techniques were used to calibrate the models in a reasonable span of time. Results showed that even the adoption of a conceptual model for facies distribution clearly representative of the reservoir internal geometry might not guarantee reliable results in terms of production forecast. Furthermore, results also showed that realizations which seem fully acceptable after calibration were not representative of the true reservoir internal configuration and provided wrong production forecasts; conversely, realizations which did not show a good fit of the production data could reliably predict the reservoir

Fortescue reservoir development and reservoir studies

Energy Technology Data Exchange (ETDEWEB)

Henzell, S.T.; Hicks, G.J.; Horden, M.J.; Irrgang, H.R.; Janssen, E.J.; Kable, C.W.; Mitchell, R.A.H.; Morrell, N.W.; Palmer, I.D.; Seage, N.W.

1985-03-01

The Fortescue field in the Gippsland Basin, offshore southeastern Australia is being developed from two platforms (Fortescue A and Cobia A) by Esso Australia Ltd. (operator) and BHP Petroleum. The Fortescue reservoir is a stratigraphic trap at the top of the Latrobe Group of sediments. It overlies the western flank of the Halibut and Cobia fields and is separated from them by a non-net sequence of shales and coals which form a hydraulic barrier between the two systems. Development drilling into the Fortescue reservoir commenced in April 1983 with production coming onstream in May 1983. Fortescue, with booked reserves of 44 stock tank gigalitres (280 million stock tank barrels) of 43/sup 0/ API oil, is the seventh major oil reservoir to be developed in the offshore Gippsland Basin by Esso/BHP. In mid-1984, after drilling a total of 20 exploration and development wells, and after approximately one year of production, a detailed three-dimensional, two-phase reservoir simulation study was performed to examine the recovery efficiency, drainage patterns, pressure performance and production rate potential of the reservoir. The model was validated by history matching an extensive suite of Repeat Formation Test (RFT) pressure data. The results confirmed the reserves basis, and demonstrated that the ultimate oil recovery from the reservoir is not sensitive to production rate. This result is consistent with studies on other high quality Latrobe Group reservoirs in the Gippsland Basin which contain undersaturated crudes and receive very strong water drive from the Basin-wide aquifer system. With the development of the simulation model during the development phase, it has been possible to more accurately define the optimal well pattern for the remainder of the development.

Fluid-line math model

Science.gov (United States)

Kandelman, A.; Nelson, D. J.

1977-01-01

Simplified mathematical model simulates large hydraulic systems on either analog or digital computers. Models of pumps, servoactuators, reservoirs, accumulators, and valves are connected generating systems containing six hundred elements.

Exploring Yellowstone National Park with Mathematical Modeling

Science.gov (United States)

Wickstrom, Megan H.; Carr, Ruth; Lackey, Dacia

2017-01-01

Mathematical modeling, a practice standard in the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010), is a process by which students develop and use mathematics as a tool to make sense of the world around them. Students investigate a real-world situation by asking mathematical questions; along the way, they need to decide how to use…

PENGEMBANGAN MODEL COMPREHENSIVE MATHEMATICS INSTRUCTION (CMI DALAM MEMBANGUN KEMAMPUAN MATHEMATICAL THINKING SISWA

Directory of Open Access Journals (Sweden)

Nita Delima

2017-03-01

Full Text Available Kesetaraan dalam pendidikan merupakan elemen penting dari beberapa standar visi NCTM dalam pendidikan matematika. Kesetaraan yang dimaksud, tidak berarti bahwa setiap siswa harus menerima pembelajaran yang identik dari guru; sebaliknya, menuntut sebuah pembelajaran yang mengakomodasi sebuah akses dalam mencapai kemampuan setiap siswa. Selain itu, NCTM juga mengemukakan bahwa dalam pembelajaran matematika terdapat lima standar proses yang harus terpenuhi, yakni problem solving, reasoning and proof, connections, communication, dan representation. Sementara itu, kemampuan problem solving yang dimiliki oleh seseorang akan mempengaruhi pada fleksibilitas proses berpikir mereka. Proses berpikir yang dimaksud dapat berupa proses dinamik yang memuat kompleksitas ide–ide matematik yang dimiliki serta dapat mengekspansi pemahaman tentang matematika yang disebut sebagai mathematical thinking. Dengan demikian, diperlukan sebuah model pembelajaran yang dapat berfungsi sebagai alat pedagogis guru, baik sebelum, selama dan setelah pembelajaran, terutama dalam membangun mathematical thinking siswa. Kerangka Comprehensive Mathematics Instruction (CMI merupakan sebuah kerangka prinsip – prinsip praktek pembelajaran yang bertujuan untuk menciptakan pengalaman matematika yang seimbang, sehingga siswa dapat memiliki pemikiran dan pemahaman matematika secara mendalam, kerangka CMI memiliki semua kriteria sebuah model pembelajaran. Adapun syntax untuk model CMI terdiri dari develop, solidify dan practice. Dalam penerapannya, setiap syntax tersebut meliputi tiga tahapan, yakni tujuan (purpose, peran guru (teacher role dan peran siswa (student role. Berdasarkan hasil analisis eksploratif yang telah dilakukan, dapat disimpulkan bahwa model pembelajaran CMI ini dapat menjadi sebuah alat pedagogis yang baru bagi guru yang dapat digunakan, baik sebelum, selama dan setelah pembelajaran dalam membangun kemampuan mathematical thinking siswa.    Kata Kunci: Comprehensive

Pre-Service Teachers' Developing Conceptions about the Nature and Pedagogy of Mathematical Modeling in the Context of a Mathematical Modeling Course

Science.gov (United States)

Cetinkaya, Bulent; Kertil, Mahmut; Erbas, Ayhan Kursat; Korkmaz, Himmet; Alacaci, Cengiz; Cakiroglu, Erdinc

2016-01-01

Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers' developing conceptions about (a) the nature of mathematical modeling in simulations of "real life" problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike…

Mathematical modeling courses for Media technology students

DEFF Research Database (Denmark)

Timcenko, Olga

2009-01-01

This paper addresses curriculum development for Mathematical Modeling course at Medialogy education. Medialogy as a study line was established in 2002 at Faculty for Engineering and Natural Sciences at Aalborg University, and mathematics curriculum has already been revised three times, Mathematic...

Evaluation of field development plans using 3-D reservoir modelling

Energy Technology Data Exchange (ETDEWEB)

Seifert, D.; Lewis, J.J.M. [Heriot-Watt Univ., Edinburgh (United Kingdom); Newbery, J.D.H. [Conoco, UK Ltd., Aberdeen (United Kingdom)] [and others

1997-08-01

Three-dimensional reservoir modelling has become an accepted tool in reservoir description and is used for various purposes, such as reservoir performance prediction or integration and visualisation of data. In this case study, a small Northern North Sea turbiditic reservoir was to be developed with a line drive strategy utilising a series of horizontal producer and injector pairs, oriented north-south. This development plan was to be evaluated and the expected outcome of the wells was to be assessed and risked. Detailed analyses of core, well log and analogue data has led to the development of two geological {open_quotes}end member{close_quotes} scenarios. Both scenarios have been stochastically modelled using the Sequential Indicator Simulation method. The resulting equiprobable realisations have been subjected to detailed statistical well placement optimisation techniques. Based upon bivariate statistical evaluation of more than 1000 numerical well trajectories for each of the two scenarios, it was found that the wells inclinations and lengths had a great impact on the wells success, whereas the azimuth was found to have only a minor impact. After integration of the above results, the actual well paths were redesigned to meet external drilling constraints, resulting in substantial reductions in drilling time and costs.

Use of black oil simulator for coal bed methane reservoir model

Energy Technology Data Exchange (ETDEWEB)

Sonwa, R.; Enachescu, C.; Rohs, S. [Golder Associates GmbH, Celle (Germany)

2013-08-01

This paper starts from the work done by Seidle et al. (1990) and other authors on the topic of coal degasification and develops a more accurate representative naturally fractured CBM-reservoir by using a Discrete Fracture Network modeling approach. For this issue we firstly calibrate the reservoir simulator tNAVIGATOR by showing his ability to reproduce the work done by Seidle et al. and secondly generate a DFN model using FracMan in accordance with the distribution and orientation of the cleats. tNavigator was then used to simulate multiphase flow through the DFN- Model. (orig.)

Teaching Mathematical Modelling for Earth Sciences via Case Studies

Science.gov (United States)

Yang, Xin-She

2010-05-01

Mathematical modelling is becoming crucially important for earth sciences because the modelling of complex systems such as geological, geophysical and environmental processes requires mathematical analysis, numerical methods and computer programming. However, a substantial fraction of earth science undergraduates and graduates may not have sufficient skills in mathematical modelling, which is due to either limited mathematical training or lack of appropriate mathematical textbooks for self-study. In this paper, we described a detailed case-study-based approach for teaching mathematical modelling. We illustrate how essential mathematical skills can be developed for students with limited training in secondary mathematics so that they are confident in dealing with real-world mathematical modelling at university level. We have chosen various topics such as Airy isostasy, greenhouse effect, sedimentation and Stokes' flow,free-air and Bouguer gravity, Brownian motion, rain-drop dynamics, impact cratering, heat conduction and cooling of the lithosphere as case studies; and we use these step-by-step case studies to teach exponentials, logarithms, spherical geometry, basic calculus, complex numbers, Fourier transforms, ordinary differential equations, vectors and matrix algebra, partial differential equations, geostatistics and basic numeric methods. Implications for teaching university mathematics for earth scientists for tomorrow's classroom will also be discussed. Refereces 1) D. L. Turcotte and G. Schubert, Geodynamics, 2nd Edition, Cambridge University Press, (2002). 2) X. S. Yang, Introductory Mathematics for Earth Scientists, Dunedin Academic Press, (2009).

Rival approaches to mathematical modelling in immunology

Science.gov (United States)

Andrew, Sarah M.; Baker, Christopher T. H.; Bocharov, Gennady A.

2007-08-01

In order to formulate quantitatively correct mathematical models of the immune system, one requires an understanding of immune processes and familiarity with a range of mathematical techniques. Selection of an appropriate model requires a number of decisions to be made, including a choice of the modelling objectives, strategies and techniques and the types of model considered as candidate models. The authors adopt a multidisciplinary perspective.

Development and application of 3-D fractal reservoir model based on collage theorem

Energy Technology Data Exchange (ETDEWEB)

Kim, I.K.; Kim, K.S.; Sung, W.M. [Hanyang Univ., Seoul (Korea, Republic of)

1995-04-30

Reservoir characterization is the essential process to accurately evaluate the reservoir and has been conducted by geostatistical method, SRA algorithm, and etc. The characterized distribution of heterogeneous property by these methods shows randomly distributed phenomena, and does not present anomalous shape of property variation at discontinued space as compared with the observed shape in nature. This study proposed a new algorithm of fractal concept based on collage theorem, which can virtually present not only geometric shape of irregular and anomalous pore structures or coastlines, but also property variation for discontinuously observed data. With a basis of fractal concept, three dimensional fractal reservoir model was developed to more accurately characterize the heterogeneous reservoir. We performed analysis of pre-predictable hypothetically observed permeability data by using the fractal reservoir model. From the results, we can recognize that permeability distributions in the areal view or the cross-sectional view were consistent with the observed data. (author). 8 refs., 1 tab., 6 figs.

Mathematical manipulative models: in defense of "beanbag biology".

Science.gov (United States)

Jungck, John R; Gaff, Holly; Weisstein, Anton E

2010-01-01

Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process-1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core principles, and 4) analysis of real data sets-we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational research that has convincingly demonstrated the utility of multiple models that involve physical, kinesthetic learning to actual data and interactive simulations. Two projects that use this approach are introduced: The Biological Excel Simulations and Tools in Exploratory, Experiential Mathematics (ESTEEM) Project (http://bioquest.org/esteem) and Numerical Undergraduate Mathematical Biology Education (NUMB3R5 COUNT; http://bioquest.org/numberscount). Examples here emphasize genetics, ecology, population biology, photosynthesis, cancer, and epidemiology. Mathematical manipulative models help learners break through prior fears to develop an appreciation for how mathematical reasoning informs problem solving, inference, and precise communication in biology and enhance the diversity of quantitative biology education.

Reservoirs on the mountain rivers and their safety

Directory of Open Access Journals (Sweden)

Ts.Z. Basilashvili

2016-06-01

Full Text Available Water resource issues and problems in the world's developing countries, present special challenges, as development of these countries significantly depends on the utilization of water resources. Georgia nestled between the Black Sea, Russia, and Turkey, and surrounded by the Caucasus Mountains, occupies a unique geographic space, which gives it strategic importance far beyond its size. Though blessed by its rich hydro resources, Georgia due to its uneven distribution, experiences some problems as the demand on water frequently doesn't coincide with water provision. As a result it causes acute deficit situation. Due to the global warming of the climate, it is expected that the fresh water amount will decrease in Georgia. This is why it is necessary to approach the use of water resources in a complex way by means of water reservoirs, which will enable attaining of a large economic effect. In the mountainous conditions filling of reservoirs take place in spring time, when snow and glaciers melt. In Georgia as in mountainous country, abundant rains take place, thus causing catastrophic flooding on rivers. In summer and winter water amount decreases 10 times and irrigation, water provision and energy production is impeded. Thus, the lack of water just like the excess amount of water causes damage. This is why it is needed to forecast water amount in water reservoirs for different periods of the year. But in a complex, mountainous terrain operative data of hydrometeorology is not sufficient for application of modern mathematical methods. We have elaborated multiple-factor statistical model for a forecast, which by means of different mathematical criteria and methods can simultaneously research the increase of the timeliness of forecasts and the level of their precision. We have obtained methodologies for short and long term forecasts of inflowing water properties in Georgia's main water reservoirs to further plan optimally and regulate water resources

From axiomatics of quantum probability to modelling geological uncertainty and management of intelligent hydrocarbon reservoirs with the theory of open quantum systems

Science.gov (United States)

Lozada Aguilar, Miguel Ángel; Khrennikov, Andrei; Oleschko, Klaudia

2018-04-01

As was recently shown by the authors, quantum probability theory can be used for the modelling of the process of decision-making (e.g. probabilistic risk analysis) for macroscopic geophysical structures such as hydrocarbon reservoirs. This approach can be considered as a geophysical realization of Hilbert's programme on axiomatization of statistical models in physics (the famous sixth Hilbert problem). In this conceptual paper, we continue development of this approach to decision-making under uncertainty which is generated by complexity, variability, heterogeneity, anisotropy, as well as the restrictions to accessibility of subsurface structures. The belief state of a geological expert about the potential of exploring a hydrocarbon reservoir is continuously updated by outputs of measurements, and selection of mathematical models and scales of numerical simulation. These outputs can be treated as signals from the information environment E. The dynamics of the belief state can be modelled with the aid of the theory of open quantum systems: a quantum state (representing uncertainty in beliefs) is dynamically modified through coupling with E; stabilization to a steady state determines a decision strategy. In this paper, the process of decision-making about hydrocarbon reservoirs (e.g. `explore or not?'; `open new well or not?'; `contaminated by water or not?'; `double or triple porosity medium?') is modelled by using the Gorini-Kossakowski-Sudarshan-Lindblad equation. In our model, this equation describes the evolution of experts' predictions about a geophysical structure. We proceed with the information approach to quantum theory and the subjective interpretation of quantum probabilities (due to quantum Bayesianism). This article is part of the theme issue `Hilbert's sixth problem'.

From axiomatics of quantum probability to modelling geological uncertainty and management of intelligent hydrocarbon reservoirs with the theory of open quantum systems.

Science.gov (United States)

Lozada Aguilar, Miguel Ángel; Khrennikov, Andrei; Oleschko, Klaudia

2018-04-28

As was recently shown by the authors, quantum probability theory can be used for the modelling of the process of decision-making (e.g. probabilistic risk analysis) for macroscopic geophysical structures such as hydrocarbon reservoirs. This approach can be considered as a geophysical realization of Hilbert's programme on axiomatization of statistical models in physics (the famous sixth Hilbert problem). In this conceptual paper , we continue development of this approach to decision-making under uncertainty which is generated by complexity, variability, heterogeneity, anisotropy, as well as the restrictions to accessibility of subsurface structures. The belief state of a geological expert about the potential of exploring a hydrocarbon reservoir is continuously updated by outputs of measurements, and selection of mathematical models and scales of numerical simulation. These outputs can be treated as signals from the information environment E The dynamics of the belief state can be modelled with the aid of the theory of open quantum systems: a quantum state (representing uncertainty in beliefs) is dynamically modified through coupling with E ; stabilization to a steady state determines a decision strategy. In this paper, the process of decision-making about hydrocarbon reservoirs (e.g. 'explore or not?'; 'open new well or not?'; 'contaminated by water or not?'; 'double or triple porosity medium?') is modelled by using the Gorini-Kossakowski-Sudarshan-Lindblad equation. In our model, this equation describes the evolution of experts' predictions about a geophysical structure. We proceed with the information approach to quantum theory and the subjective interpretation of quantum probabilities (due to quantum Bayesianism).This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).

Third workshop on geothermal reservoir engineering: Proceedings

Energy Technology Data Exchange (ETDEWEB)

Ramey, H.J. Jr.; Kruger, P. (eds.)

1977-12-15

The Third Workshop on Geothermal Reservoir Engineering convened at Stanford University on December 14, 1977, with 104 attendees from six nations. In keeping with the recommendations expressed by the participants at the Second Workshop, the format of the Workshop was retained, with three days of technical sessions devoted to reservoir physics, well and reservoir testing, field development, and mathematical modeling of geothermal reservoirs. The program presented 33 technical papers, summaries of which are included in these Proceedings. Although the format of the Workshop has remained constant, it is clear from a perusal of the Table of Contents that considerable advances have occurred in all phases of geothermal reservoir engineering over the past three years. Greater understanding of reservoir physics and mathematical representations of vapor-dominated and liquid-dominated reservoirs are evident; new techniques for their analysis are being developed, and significant field data from a number of newer reservoirs are analyzed. The objectives of these workshops have been to bring together researchers active in the various physical and mathematical disciplines comprising the field of geothermal reservoir engineering, to give the participants a forum for review of progress and exchange of new ideas in this rapidly developing field, and to summarize the effective state of the art of geothermal reservoir engineering in a form readily useful to the many government and private agencies involved in the development of geothermal energy. To these objectives, the Third Workshop and these Proceedings have been successfully directed. Several important events in this field have occurred since the Second Workshop in December 1976. The first among these was the incorporation of the Energy Research and Development Administration (ERDA) into the newly formed Department of Energy (DOE) which continues as the leading Federal agency in geothermal reservoir engineering research. The Third

Coupling a fluid flow simulation with a geomechanical model of a fractured reservoir

OpenAIRE

Segura Segarra, José María; Paz, C.M.; de Bayser, M.; Zhang, J.; Bryant, P.W.; Gonzalez, Nubia Aurora; Rodrigues, E.; Vargas, P.E.; Carol, Ignacio; Lakshmikantha, Ramasesha Mookanahallipatna; Das, K. C.; Sandha, S.S.; Cerqueira, R.; Mello,, U.

2013-01-01

Improving the reliability of integrated reservoir development planning and addressing subsidence, fault reactivation and other environmental impacts, requires increasingly sophisticated geomechanical models, especially in the case of fractured reservoirs where fracture deformation is strongly coupled with its permeability change. Reservoir simulation has historically treated any geomechanical effects by means of a rock compressibility term/table, which can be improved by simulating the actual...

Assessment of Primary 5 Students' Mathematical Modelling Competencies

Science.gov (United States)

Chan, Chun Ming Eric; Ng, Kit Ee Dawn; Widjaja, Wanty; Seto, Cynthia

2012-01-01

Mathematical modelling is increasingly becoming part of an instructional approach deemed to develop students with competencies to function as 21st century learners and problem solvers. As mathematical modelling is a relatively new domain in the Singapore primary school mathematics curriculum, many teachers may not be aware of the learning outcomes…

Using microstructure observations to quantify fracture properties and improve reservoir simulations. Final report, September 1998

Energy Technology Data Exchange (ETDEWEB)

Laubach, S.E.; Marrett, R.; Rossen, W.; Olson, J.; Lake, L.; Ortega, O.; Gu, Y.; Reed, R.

1999-01-01

The research for this project provides new technology to understand and successfully characterize, predict, and simulate reservoir-scale fractures. Such fractures have worldwide importance because of their influence on successful extraction of resources. The scope of this project includes creation and testing of new methods to measure, interpret, and simulate reservoir fractures that overcome the challenge of inadequate sampling. The key to these methods is the use of microstructures as guides to the attributes of the large fractures that control reservoir behavior. One accomplishment of the project research is a demonstration that these microstructures can be reliably and inexpensively sampled. Specific goals of this project were to: create and test new methods of measuring attributes of reservoir-scale fractures, particularly as fluid conduits, and test the methods on samples from reservoirs; extrapolate structural attributes to the reservoir scale through rigorous mathematical techniques and help build accurate and useful 3-D models of the interwell region; and design new ways to incorporate geological and geophysical information into reservoir simulation and verify the accuracy by comparison with production data. New analytical methods developed in the project are leading to a more realistic characterization of fractured reservoir rocks. Testing diagnostic and predictive approaches was an integral part of the research, and several tests were successfully completed.

Mathematical modeling and computational intelligence in engineering applications

CERN Document Server

Silva Neto, Antônio José da; Silva, Geraldo Nunes

2016-01-01

This book brings together a rich selection of studies in mathematical modeling and computational intelligence, with application in several fields of engineering, like automation, biomedical, chemical, civil, electrical, electronic, geophysical and mechanical engineering, on a multidisciplinary approach. Authors from five countries and 16 different research centers contribute with their expertise in both the fundamentals and real problems applications based upon their strong background on modeling and computational intelligence. The reader will find a wide variety of applications, mathematical and computational tools and original results, all presented with rigorous mathematical procedures. This work is intended for use in graduate courses of engineering, applied mathematics and applied computation where tools as mathematical and computational modeling, numerical methods and computational intelligence are applied to the solution of real problems.

The (Mathematical) Modeling Process in Biosciences.

Science.gov (United States)

Torres, Nestor V; Santos, Guido

2015-01-01

In this communication, we introduce a general framework and discussion on the role of models and the modeling process in the field of biosciences. The objective is to sum up the common procedures during the formalization and analysis of a biological problem from the perspective of Systems Biology, which approaches the study of biological systems as a whole. We begin by presenting the definitions of (biological) system and model. Particular attention is given to the meaning of mathematical model within the context of biology. Then, we present the process of modeling and analysis of biological systems. Three stages are described in detail: conceptualization of the biological system into a model, mathematical formalization of the previous conceptual model and optimization and system management derived from the analysis of the mathematical model. All along this work the main features and shortcomings of the process are analyzed and a set of rules that could help in the task of modeling any biological system are presented. Special regard is given to the formative requirements and the interdisciplinary nature of this approach. We conclude with some general considerations on the challenges that modeling is posing to current biology.

Effect of boundary conditions on pressure behavior of finite-conductivity fractures in bounded stratified reservoirs

Energy Technology Data Exchange (ETDEWEB)

Osman, Mohammed E.; Abou-Kassem, J.H. [Chemical and Petroleum Engineering Department, UAE University, Al-Ain (United Arab Emirates)

1996-08-15

In this study, a mathematical model was developed to model the pressure behavior of a well located in a bounded multilayer reservoir and crossed by a finite-conductivity vertical fracture. It was found that the dimensionless pressure function and its derivative strongly depend on fracture conductivity and fracture extension during early times. The effect of reservoir heterogeneity on the pressure function is negligible compared to that on the pressure derivative. Both functions exhibit four flow periods: bilinear, formation linear, pseudoradial and pseudosteady-state which are separated by transition periods. One or more of these flow periods may be missing. Data obtained from a long test and which are characterized by a unit slope line indicate that the well is intercepted by deeply extended fractures. It has been found that the fractional production rates of different layers are a good measure of reservoir and fracture characteristics. Flowmeter survey data can be used to eliminate the non-uniqueness problem when using the type curves presented in this study

Continuum mechanics the birthplace of mathematical models

CERN Document Server

Allen, Myron B

2015-01-01

Continuum mechanics is a standard course in many graduate programs in engineering and applied mathematics as it provides the foundations for the various differential equations and mathematical models that are encountered in fluid mechanics, solid mechanics, and heat transfer.  This book successfully makes the topic more accessible to advanced undergraduate mathematics majors by aligning the mathematical notation and language with related courses in multivariable calculus, linear algebra, and differential equations; making connections with other areas of applied mathematics where parial differe

[Coupling SWAT and CE-QUAL-W2 models to simulate water quantity and quality in Shanmei Reservoir watershed].

Science.gov (United States)

Liu, Mei-Bing; Chen, Dong-Ping; Chen, Xing-Wei; Chen, Ying

2013-12-01

A coupled watershed-reservoir modeling approach consisting of a watershed distributed model (SWAT) and a two-dimensional laterally averaged model (CE-QUAL-W2) was adopted for simulating the impact of non-point source pollution from upland watershed on water quality of Shanmei Reservoir. Using the daily serial output from Shanmei Reservoir watershed by SWAT as the input to Shanmei Reservoir by CE-QUAL-W2, the coupled modeling was calibrated for runoff and outputs of sediment and pollutant at watershed scale and for elevation, temperature, nitrate, ammonium and total nitrogen in Shanmei Reservoir. The results indicated that the simulated values agreed fairly well with the observed data, although the calculation precision of downstream model would be affected by the accumulative errors generated from the simulation of upland model. The SWAT and CE-QUAL-W2 coupled modeling could be used to assess the hydrodynamic and water quality process in complex watershed comprised of upland watershed and downstream reservoir, and might further provide scientific basis for positioning key pollution source area and controlling the reservoir eutrophication.

Mathematical models in marketing a collection of abstracts

CERN Document Server

Funke, Ursula H

1976-01-01

Mathematical models can be classified in a number of ways, e.g., static and dynamic; deterministic and stochastic; linear and nonlinear; individual and aggregate; descriptive, predictive, and normative; according to the mathematical technique applied or according to the problem area in which they are used. In marketing, the level of sophistication of the mathe­ matical models varies considerably, so that a nurnber of models will be meaningful to a marketing specialist without an extensive mathematical background. To make it easier for the nontechnical user we have chosen to classify the models included in this collection according to the major marketing problem areas in which they are applied. Since the emphasis lies on mathematical models, we shall not as a rule present statistical models, flow chart models, computer models, or the empirical testing aspects of these theories. We have also excluded competitive bidding, inventory and transportation models since these areas do not form the core of ·the market...

A new approach to integrate seismic and production data in reservoir models

Energy Technology Data Exchange (ETDEWEB)

Ouenes, A.; Chawathe, A.; Weiss, W. [New Mexico Tech, Socorro, NM (United States)] [and others

1997-08-01

A great deal of effort is devoted to reducing the uncertainties in reservoir modeling. For example, seismic properties are used to improve the characterization of interwell properties by providing porosity maps constrained to seismic impedance. Another means to reduce uncertainties is to constrain the reservoir model to production data. This paper describes a new approach where the production and seismic data are simultaneously used to reduce the uncertainties. In this new approach, the primary geologic parameter that controls reservoir properties is identified. Next, the geophysical parameter that is sensitive to the dominant geologic parameter is determined. Then the geology and geophysics are linked using analytic correlations. Unfortunately, the initial guess resulted in a reservoir model that did not match the production history. Since the time required for trial and error matching of production history is exorbitant, an automatic history matching method based on a fast optimization method was used to find the correlating parameters. This new approach was illustrated with an actual field in the Williston Basin. Upscalling problems do not arise since the scale is imposed by the size of the seismic bin (66m, 219 ft) which is the size of the simulator gridblocks.

Modelling and Optimizing Mathematics Learning in Children

Science.gov (United States)

Käser, Tanja; Busetto, Alberto Giovanni; Solenthaler, Barbara; Baschera, Gian-Marco; Kohn, Juliane; Kucian, Karin; von Aster, Michael; Gross, Markus

2013-01-01

This study introduces a student model and control algorithm, optimizing mathematics learning in children. The adaptive system is integrated into a computer-based training system for enhancing numerical cognition aimed at children with developmental dyscalculia or difficulties in learning mathematics. The student model consists of a dynamic…

Mathematical modeling of a process the rolling delivery

Science.gov (United States)

Stepanov, Mikhail A.; Korolev, Andrey A.

2018-03-01

An adduced analysis of the scientific researches in a domain of the rolling equipments, also research of properties the working material. A one of perspective direction of scientific research this is mathematical modeling. That is broadly used in many scientific disciplines and especially at the technical, applied sciences. With the aid of mathematical modeling it can be study of physical properties of the researching objects and systems. A research of the rolling delivery and transporting devices realized with the aid of a construction of mathematical model of appropriate process. To be described the basic principles and conditions of a construction of mathematical models of the real objects. For example to be consider a construction of mathematical model the rolling delivery device. For a construction that is model used system of the equations, which consist of: Lagrange’s equation of a motion, describing of the law conservation of energy of a mechanical system, and the Navier - Stokes equations, which characterize of the flow of a continuous non-compressed fluid. A construction of mathematical model the rolling deliver to let determined of a total energy of device, and therefore to got the dependence upon the power of drive to a gap between of rolls. A corroborate the hypothesis about laminar the flow of a material into the rolling gap of deliver.

Mathematical modeling of the lithium, thionyl chloride static cell. I. Neutral electrolyte. II - Acid electrolyte

Energy Technology Data Exchange (ETDEWEB)

Tsaur, K.C.; Pollard, R.

1984-05-01

Mathematical models are presented for a Li-LiAlCl4/SOCl2-C static cell with neutral electrolyte and a Li/SOCl2-C static cell with acid electrolyte. The model for the Li-LiAlCl4/SOCl2-C cell with neutral solution predicts that high internal resistance can develop in the positive electrode as a result of low local porosities which are, in turn, caused by large-volume, solid reaction products. Consequently, the maximum usable cell capacity is dictated by the nonuniformity of the reaction distribution at the front of the positive electrode. In many respects, a cell with acid electrolyte can be regarded as a combination of an equivalent neutral electrolyte system and an acid reservoir. The model for the Li/SOCl2 cell suggests that the cell life depends primarily on the quantity of acid added to the electrolyte. 58 references.

Mathematical modeling of the lithium, thionyl chloride static cell. I - Neutral electrolyte. II - Acid electrolyte

Science.gov (United States)

Tsaur, K.-C.; Pollard, R.

1984-05-01

Mathematical models are presented for a Li-LiAlCl4/SOCl2-C static cell with neutral electrolyte and a Li/SOCl2-C static cell with acid electrolyte. The model for the Li-LiAlCl4/SOCl2-C cell with neutral solution predicts that high internal resistance can develop in the positive electrode as a result of low local porosities which are, in turn, caused by large-volume, solid reaction products. Consequently, the maximum usable cell capacity is dictated by the nonuniformity of the reaction distribution at the front of the positive electrode. In many respects, a cell with acid electrolyte can be regarded as a combination of an equivalent neutral electrolyte system and an acid reservoir. The model for the Li/SOCl2 cell suggests that the cell life depends primarily on the quantity of acid added to the electrolyte.

Mathematical Problem Solving Ability of Junior High School Students through Ang’s Framework for Mathematical Modelling Instruction

Science.gov (United States)

Fasni, N.; Turmudi, T.; Kusnandi, K.

2017-09-01

This research background of this research is the importance of student problem solving abilities. The purpose of this study is to find out whether there are differences in the ability to solve mathematical problems between students who have learned mathematics using Ang’s Framework for Mathematical Modelling Instruction (AFFMMI) and students who have learned using scientific approach (SA). The method used in this research is a quasi-experimental method with pretest-postest control group design. Data analysis of mathematical problem solving ability using Indepent Sample Test. The results showed that there was a difference in the ability to solve mathematical problems between students who received learning with Ang’s Framework for Mathematical Modelling Instruction and students who received learning with a scientific approach. AFFMMI focuses on mathematical modeling. This modeling allows students to solve problems. The use of AFFMMI is able to improve the solving ability.

Simulating reservoir lithologies by an actively conditioned Markov chain model

Science.gov (United States)

Feng, Runhai; Luthi, Stefan M.; Gisolf, Dries

2018-06-01

The coupled Markov chain model can be used to simulate reservoir lithologies between wells, by conditioning them on the observed data in the cored wells. However, with this method, only the state at the same depth as the current cell is going to be used for conditioning, which may be a problem if the geological layers are dipping. This will cause the simulated lithological layers to be broken or to become discontinuous across the reservoir. In order to address this problem, an actively conditioned process is proposed here, in which a tolerance angle is predefined. The states contained in the region constrained by the tolerance angle will be employed for conditioning in the horizontal chain first, after which a coupling concept with the vertical chain is implemented. In order to use the same horizontal transition matrix for different future states, the tolerance angle has to be small. This allows the method to work in reservoirs without complex structures caused by depositional processes or tectonic deformations. Directional artefacts in the modeling process are avoided through a careful choice of the simulation path. The tolerance angle and dipping direction of the strata can be obtained from a correlation between wells, or from seismic data, which are available in most hydrocarbon reservoirs, either by interpretation or by inversion that can also assist the construction of a horizontal probability matrix.

Mathematical modelling of two-phase flows

International Nuclear Information System (INIS)

Komen, E.M.J.; Stoop, P.M.

1992-11-01

A gradual shift from methods based on experimental correlations to methods based on mathematical models to study 2-phase flows can be observed. The latter can be used to predict dynamical behaviour of 2-phase flows. This report discusses various mathematical models for the description of 2-phase flows. An important application of these models can be found in thermal-hydraulic computer codes used for analysis of the thermal-hydraulic behaviour of water cooled nuclear power plants. (author). 17 refs., 7 figs., 6 tabs

Modelling Mathematical Reasoning in Physics Education

Science.gov (United States)

Uhden, Olaf; Karam, Ricardo; Pietrocola, Maurício; Pospiech, Gesche

2012-04-01

Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a tool for calculation which hinders a conceptual understanding of physical principles. However, the role of mathematics cannot be reduced to this technical aspect. Hence, instead of putting mathematics away we delve into the nature of physical science to reveal the strong conceptual relationship between mathematics and physics. Moreover, we suggest that, for both prospective teaching and further research, a focus on deeply exploring such interdependency can significantly improve the understanding of physics. To provide a suitable basis, we develop a new model which can be used for analysing different levels of mathematical reasoning within physics. It is also a guideline for shifting the attention from technical to structural mathematical skills while teaching physics. We demonstrate its applicability for analysing physical-mathematical reasoning processes with an example.

The geological model calibration - Learnings from integration of reservoir geology and field performance - Example from the upper carboniferous reservoirs of the Southern North Sea

NARCIS (Netherlands)

Moscariello, A.; Hoof, T.B. van; Kunakbayeva, G.; Veen, J.H. ten; Belt, F. van den; Twerda, A.; Peters, L.; Davis, P.; Williams, H.

2013-01-01

The Geological Model Calibration - Learnings from Integration of Reservoir Geology and Field Performance: example from the Upper Carboniferous Reservoirs of the Southern North Sea. Copyright © (2012) by the European Association of Geoscientists & Engineers All rights reserved.

An introduction to mathematical modeling a course in mechanics

CERN Document Server

Oden, Tinsley J

2011-01-01

A modern approach to mathematical modeling, featuring unique applications from the field of mechanics An Introduction to Mathematical Modeling: A Course in Mechanics is designed to survey the mathematical models that form the foundations of modern science and incorporates examples that illustrate how the most successful models arise from basic principles in modern and classical mathematical physics. Written by a world authority on mathematical theory and computational mechanics, the book presents an account of continuum mechanics, electromagnetic field theory, quantum mechanics, and statistical mechanics for readers with varied backgrounds in engineering, computer science, mathematics, and physics. The author streamlines a comprehensive understanding of the topic in three clearly organized sections: Nonlinear Continuum Mechanics introduces kinematics as well as force and stress in deformable bodies; mass and momentum; balance of linear and angular momentum; conservation of energy; and constitutive equation...

Assessing the operation rules of a reservoir system based on a detailed modelling-chain

Science.gov (United States)

Bruwier, M.; Erpicum, S.; Pirotton, M.; Archambeau, P.; Dewals, B.

2014-09-01

According to available climate change scenarios for Belgium, drier summers and wetter winters are expected. In this study, we focus on two muti-purpose reservoirs located in the Vesdre catchment, which is part of the Meuse basin. The current operation rules of the reservoirs are first analysed. Next, the impacts of two climate change scenarios are assessed and enhanced operation rules are proposed to mitigate these impacts. For this purpose, an integrated model of the catchment was used. It includes a hydrological model, one-dimensional and two-dimensional hydraulic models of the river and its main tributaries, a model of the reservoir system and a flood damage model. Five performance indicators of the reservoir system have been defined, reflecting its ability to provide sufficient drinking, to control floods, to produce hydropower and to reduce low-flow condition. As shown by the results, enhanced operation rules may improve the drinking water potential and the low-flow augmentation while the existing operation rules are efficient for flood control and for hydropower production.

Assessing the operation rules of a reservoir system based on a detailed modelling chain

Science.gov (United States)

Bruwier, M.; Erpicum, S.; Pirotton, M.; Archambeau, P.; Dewals, B. J.

2015-03-01

According to available climate change scenarios for Belgium, drier summers and wetter winters are expected. In this study, we focus on two multi-purpose reservoirs located in the Vesdre catchment, which is part of the Meuse basin. The current operation rules of the reservoirs are first analysed. Next, the impacts of two climate change scenarios are assessed and enhanced operation rules are proposed to mitigate these impacts. For this purpose, an integrated model of the catchment was used. It includes a hydrological model, one-dimensional and two-dimensional hydraulic models of the river and its main tributaries, a model of the reservoir system and a flood damage model. Five performance indicators of the reservoir system have been defined, reflecting its ability to provide sufficient drinking water, to control floods, to produce hydropower and to reduce low-flow conditions. As shown by the results, enhanced operation rules may improve the drinking water potential and the low-flow augmentation while the existing operation rules are efficient for flood control and for hydropower production.

Molecular Simulation towards Efficient and Representative Subsurface Reservoirs Modeling

KAUST Repository

Kadoura, Ahmad Salim

2016-01-01

This dissertation focuses on the application of Monte Carlo (MC) molecular simulation and Molecular Dynamics (MD) in modeling thermodynamics and flow of subsurface reservoir fluids. At first, MC molecular simulation is proposed as a promising method

Will building new reservoirs always help increase the water supply reliability? - insight from a modeling-based global study

Science.gov (United States)

Zhuang, Y.; Tian, F.; Yigzaw, W.; Hejazi, M. I.; Li, H. Y.; Turner, S. W. D.; Vernon, C. R.

2017-12-01

More and more reservoirs are being build or planned in order to help meet the increasing water demand all over the world. However, is building new reservoirs always helpful to water supply? To address this question, the river routing module of Global Change Assessment Model (GCAM) has been extended with a simple yet physical-based reservoir scheme accounting for irrigation, flood control and hydropower operations at each individual reservoir. The new GCAM river routing model has been applied over the global domain with the runoff inputs from the Variable Infiltration Capacity Model. The simulated streamflow is validated at 150 global river basins where the observed streamflow data are available. The model performance has been significantly improved at 77 basins and worsened at 35 basins. To facilitate the analysis of additional reservoir storage impacts at the basin level, a lumped version of GCAM reservoir model has been developed, representing a single lumped reservoir at each river basin which has the regulation capacity of all reservoir combined. A Sequent Peak Analysis is used to estimate how much additional reservoir storage is required to satisfy the current water demand. For basins with water deficit, the water supply reliability can be improved with additional storage. However, there is a threshold storage value at each basin beyond which the reliability stops increasing, suggesting that building new reservoirs will not help better relieve the water stress. Findings in the research can be helpful to the future planning and management of new reservoirs.

Mathematical models and accuracy of radioisotope gauges

International Nuclear Information System (INIS)

Urbanski, P.

1989-01-01

Mathematical expressions relating the variance and mean value of the intrinsic error with the parameters of one and multi-dimensional mathematical models of radioisotope gauges are given. Variance of the intrinsic error at the model's output is considered as a sum of the variances of the random error which is created in the first stages of the measuring chain and the random error of calibration procedure. The mean value of the intrinsic error (systematic error) appears always for nonlinear models. It was found that the optimal model of calibration procedure not always corresponds to the minimal value of the intrinsic error. The derived expressions are applied for the assessment of the mathematical models of some of the existing gauges (radioisotope belt weigher, XRF analyzer and coating thickness gauge). 7 refs., 5 figs., 1 tab. (author)

Leading Undergraduate Research Projects in Mathematical Modeling

Science.gov (United States)

Seshaiyer, Padmanabhan

2017-01-01

In this article, we provide some useful perspectives and experiences in mentoring students in undergraduate research (UR) in mathematical modeling using differential equations. To engage students in this topic, we present a systematic approach to the creation of rich problems from real-world phenomena; present mathematical models that are derived…

Scaffolding Mathematical Modelling with a Solution Plan

Science.gov (United States)

Schukajlow, Stanislaw; Kolter, Jana; Blum, Werner

2015-01-01

In the study presented in this paper, we examined the possibility to scaffold mathematical modelling with strategies. The strategies were prompted using an instrument called "solution plan" as a scaffold. The effects of this step by step instrument on mathematical modelling competency and on self-reported strategies were tested using…

Daily Reservoir Inflow Forecasting using Deep Learning with Downscaled Multi-General Circulation Models (GCMs) Platform

Science.gov (United States)

Li, D.; Fang, N. Z.

2017-12-01

Dallas-Fort Worth Metroplex (DFW) has a population of over 7 million depending on many water supply reservoirs. The reservoir inflow plays a vital role in water supply decision making process and long-term strategic planning for the region. This paper demonstrates a method of utilizing deep learning algorithms and multi-general circulation model (GCM) platform to forecast reservoir inflow for three reservoirs within the DFW: Eagle Mountain Lake, Lake Benbrook and Lake Arlington. Ensemble empirical mode decomposition was firstly employed to extract the features, which were then represented by the deep belief networks (DBNs). The first 75 years of the historical data (1940 -2015) were used to train the model, while the last 2 years of the data (2016-2017) were used for the model validation. The weights of each DBN gained from the training process were then applied to establish a neural network (NN) that was able to forecast reservoir inflow. Feature predictors used for the forecasting model were generated from weather forecast results of the downscaled multi-GCM platform for the North Texas region. By comparing root mean square error (RMSE) and mean bias error (MBE) with the observed data, the authors found that the deep learning with downscaled multi-GCM platform is an effective approach in the reservoir inflow forecasting.

Modeling interdisciplinary activities involving Mathematics

DEFF Research Database (Denmark)

Iversen, Steffen Møllegaard

2006-01-01

In this paper a didactical model is presented. The goal of the model is to work as a didactical tool, or conceptual frame, for developing, carrying through and evaluating interdisciplinary activities involving the subject of mathematics and philosophy in the high schools. Through the terms...... of Horizontal Intertwining, Vertical Structuring and Horizontal Propagation the model consists of three phases, each considering different aspects of the nature of interdisciplinary activities. The theoretical modelling is inspired by work which focuses on the students abilities to concept formation in expanded...... domains (Michelsen, 2001, 2005a, 2005b). Furthermore the theoretical description rest on a series of qualitative interviews with teachers from the Danish high school (grades 9-11) conducted recently. The special case of concrete interdisciplinary activities between mathematics and philosophy is also...

The Spectrum of Mathematical Models.

Science.gov (United States)

Karplus, Walter J.

1983-01-01

Mathematical modeling problems encountered in many disciplines are discussed in terms of the modeling process and applications of models. The models are classified according to three types of abstraction: continuous-space-continuous-time, discrete-space-continuous-time, and discrete-space-discrete-time. Limitations in different kinds of modeling…

Mathematical model in economic environmental problems

Energy Technology Data Exchange (ETDEWEB)

Nahorski, Z. [Polish Academy of Sciences, Systems Research Inst. (Poland); Ravn, H.F. [Risoe National Lab. (Denmark)

1996-12-31

The report contains a review of basic models and mathematical tools used in economic regulation problems. It starts with presentation of basic models of capital accumulation, resource depletion, pollution accumulation, and population growth, as well as construction of utility functions. Then the one-state variable model is discussed in details. The basic mathematical methods used consist of application of the maximum principle and phase plane analysis of the differential equations obtained as the necessary conditions of optimality. A summary of basic results connected with these methods is given in appendices. (au) 13 ills.; 17 refs.

Development of a Cerebrospinal Fluid Lateral Reservoir Model in Rhesus Monkeys (Macaca mulatta)

OpenAIRE

Lester McCully, Cynthia M; Bacher, John; MacAllister, Rhonda P; Steffen-Smith, Emilie A; Saleem, Kadharbatcha; Thomas, Marvin L; Cruz, Rafael; Warren, Katherine E

2015-01-01

Rapid, serial, and humane collection of cerebrospinal fluid (CSF) in nonhuman primates (NHP) is an essential element of numerous research studies and is currently accomplished via two different models. The CSF reservoir model (FR) combines a catheter in the 4th ventricle with a flexible silastic reservoir to permit circulating CSF flow. The CSF lateral port model (LP) consists of a lateral ventricular catheter and an IV port that provides static access to CSF and volume restrictions on sample...

Development of a Multidisciplinary Middle School Mathematics Infusion Model

Science.gov (United States)

Russo, Maria; Hecht, Deborah; Burghardt, M. David; Hacker, Michael; Saxman, Laura

2011-01-01

The National Science Foundation (NSF) funded project "Mathematics, Science, and Technology Partnership" (MSTP) developed a multidisciplinary instructional model for connecting mathematics to science, technology and engineering content areas at the middle school level. Specifically, the model infused mathematics into middle school curriculum…

A novel methodology improves reservoir characterization models using geologic fuzzy variables

Energy Technology Data Exchange (ETDEWEB)

Soto B, Rodolfo [DIGITOIL, Maracaibo (Venezuela); Soto O, David A. [Texas A and M University, College Station, TX (United States)

2004-07-01

One of the research projects carried out in Cusiana field to explain its rapid decline during the last years was to get better permeability models. The reservoir of this field has a complex layered system that it is not easy to model using conventional methods. The new technique included the development of porosity and permeability maps from cored wells following the same trend of the sand depositions for each facie or layer according to the sedimentary facie and the depositional system models. Then, we used fuzzy logic to reproduce those maps in three dimensions as geologic fuzzy variables. After multivariate statistical and factor analyses, we found independence and a good correlation coefficient between the geologic fuzzy variables and core permeability and porosity. This means, the geologic fuzzy variable could explain the fabric, the grain size and the pore geometry of the reservoir rock trough the field. Finally, we developed a neural network permeability model using porosity, gamma ray and the geologic fuzzy variable as input variables. This model has a cross-correlation coefficient of 0.873 and average absolute error of 33% compared with the actual model with a correlation coefficient of 0.511 and absolute error greater than 250%. We tested different methodologies, but this new one showed dramatically be a promiser way to get better permeability models. The use of the models have had a high impact in the explanation of well performance and workovers, and reservoir simulation models. (author)

Mathematical models in biology bringing mathematics to life

CERN Document Server

Ferraro, Maria; Guarracino, Mario

2015-01-01

This book presents an exciting collection of contributions based on the workshop “Bringing Maths to Life” held October 27-29, 2014 in Naples, Italy.  The state-of-the art research in biology and the statistical and analytical challenges facing huge masses of data collection are treated in this Work. Specific topics explored in depth surround the sessions and special invited sessions of the workshop and include genetic variability via differential expression, molecular dynamics and modeling, complex biological systems viewed from quantitative models, and microscopy images processing, to name several. In depth discussions of the mathematical analysis required to extract insights from complex bodies of biological datasets, to aid development in the field novel algorithms, methods and software tools for genetic variability, molecular dynamics, and complex biological systems are presented in this book. Researchers and graduate students in biology, life science, and mathematics/statistics will find the content...

Ocular hemodynamics and glaucoma: the role of mathematical modeling.

Science.gov (United States)

Harris, Alon; Guidoboni, Giovanna; Arciero, Julia C; Amireskandari, Annahita; Tobe, Leslie A; Siesky, Brent A

2013-01-01

To discuss the role of mathematical modeling in studying ocular hemodynamics, with a focus on glaucoma. We reviewed recent literature on glaucoma, ocular blood flow, autoregulation, the optic nerve head, and the use of mathematical modeling in ocular circulation. Many studies suggest that alterations in ocular hemodynamics play a significant role in the development, progression, and incidence of glaucoma. Although there is currently a limited number of studies involving mathematical modeling of ocular blood flow, regulation, and diseases (such as glaucoma), preliminary modeling work shows the potential of mathematical models to elucidate the mechanisms that contribute most significantly to glaucoma progression. Mathematical modeling is a useful tool when used synergistically with clinical and laboratory data in the study of ocular blood flow and glaucoma. The development of models to investigate the relationship between ocular hemodynamic alterations and glaucoma progression will provide a unique and useful method for studying the pathophysiology of glaucoma.

Influence of heat exchange of reservoir with rocks on hot gas injection via a single well

Science.gov (United States)

Nikolaev, Vladimir E.; Ivanov, Gavril I.

2017-11-01

In the computational experiment the influence of heat exchange through top and bottom of the gas-bearing reservoir on the dynamics of temperature and pressure fields during hot gas injection via a single well is investigated. The experiment was carried out within the framework of modified mathematical model of non-isothermal real gas filtration, obtained from the energy and mass conservation laws and the Darcy law. The physical and caloric equations of state together with the Newton-Riemann law of heat exchange of gas reservoir with surrounding rocks, are used as closing relations. It is shown that the influence of the heat exchange with environment on temperature field of the gas-bearing reservoir is localized in a narrow zone near its top and bottom, though the size of this zone is increased with time.

Dealing with dissatisfaction in mathematical modelling to integrate QFD and Kano’s model

Science.gov (United States)

Retno Sari Dewi, Dian; Debora, Joana; Edy Sianto, Martinus

2017-12-01

The purpose of the study is to implement the integration of Quality Function Deployment (QFD) and Kano’s Model into mathematical model. Voice of customer data in QFD was collected using questionnaire and the questionnaire was developed based on Kano’s model. Then the operational research methodology was applied to build the objective function and constraints in the mathematical model. The relationship between voice of customer and engineering characteristics was modelled using linier regression model. Output of the mathematical model would be detail of engineering characteristics. The objective function of this model is to maximize satisfaction and minimize dissatisfaction as well. Result of this model is 62% .The major contribution of this research is to implement the existing mathematical model to integrate QFD and Kano’s Model in the case study of shoe cabinet.

Integrating geologic and engineering data into 3-D reservoir models: an example from norman wells field, NWT, Canada

International Nuclear Information System (INIS)

Yose, L.A.

2004-01-01

A case study of the Norman Wells field will be presented to highlight the work-flow and data integration steps associated with characterization and modeling of a complex hydrocarbon reservoir. Norman Wells is a Devonian-age carbonate bank ('reef') located in the Northwest Territories of Canada, 60 kilometers south of the Arctic Circle. The reservoir reaches a maximum thickness of 130 meters in the reef interior and thins toward the basin due to depositional pinch outs. Norman Wells is an oil reservoir and is currently under a 5-spot water injection scheme for enhanced oil recovery (EOR). EOR strategies require a detailed understanding of how reservoir flow units, flow barriers and flow baffles are distributed to optimize hydrocarbon sweep and recovery and to minimize water handling. Reservoir models are routinely used by industry to characterize the 3-D distribution of reservoir architecture (stratigraphic layers, depositional facies, faults) and rock properties (porosity. permeability). Reservoir models are validated by matching historical performance data (e.g., reservoir pressures, well production or injection rates). Geologic models are adjusted until they produce a history match, and model adjustments are focused on inputs that have the greatest geologic uncertainty. Flow simulation models are then used to optimize field development strategies and to forecast field performance under different development scenarios. (author)

Incorporating teleconnection information into reservoir operating policies using Stochastic Dynamic Programming and a Hidden Markov Model

Science.gov (United States)

Turner, Sean; Galelli, Stefano; Wilcox, Karen

2015-04-01

Water reservoir systems are often affected by recurring large-scale ocean-atmospheric anomalies, known as teleconnections, that cause prolonged periods of climatological drought. Accurate forecasts of these events -- at lead times in the order of weeks and months -- may enable reservoir operators to take more effective release decisions to improve the performance of their systems. In practice this might mean a more reliable water supply system, a more profitable hydropower plant or a more sustainable environmental release policy. To this end, climate indices, which represent the oscillation of the ocean-atmospheric system, might be gainfully employed within reservoir operating models that adapt the reservoir operation as a function of the climate condition. This study develops a Stochastic Dynamic Programming (SDP) approach that can incorporate climate indices using a Hidden Markov Model. The model simulates the climatic regime as a hidden state following a Markov chain, with the state transitions driven by variation in climatic indices, such as the Southern Oscillation Index. Time series analysis of recorded streamflow data reveals the parameters of separate autoregressive models that describe the inflow to the reservoir under three representative climate states ("normal", "wet", "dry"). These models then define inflow transition probabilities for use in a classic SDP approach. The key advantage of the Hidden Markov Model is that it allows conditioning the operating policy not only on the reservoir storage and the antecedent inflow, but also on the climate condition, thus potentially allowing adaptability to a broader range of climate conditions. In practice, the reservoir operator would effect a water release tailored to a specific climate state based on available teleconnection data and forecasts. The approach is demonstrated on the operation of a realistic, stylised water reservoir with carry-over capacity in South-East Australia. Here teleconnections relating

Fena Valley Reservoir watershed and water-balance model updates and expansion of watershed modeling to southern Guam

Science.gov (United States)

Rosa, Sarah N.; Hay, Lauren E.

2017-12-01

In 2014, the U.S. Geological Survey, in cooperation with the U.S. Department of Defense’s Strategic Environmental Research and Development Program, initiated a project to evaluate the potential impacts of projected climate-change on Department of Defense installations that rely on Guam’s water resources. A major task of that project was to develop a watershed model of southern Guam and a water-balance model for the Fena Valley Reservoir. The southern Guam watershed model provides a physically based tool to estimate surface-water availability in southern Guam. The U.S. Geological Survey’s Precipitation Runoff Modeling System, PRMS-IV, was used to construct the watershed model. The PRMS-IV code simulates different parts of the hydrologic cycle based on a set of user-defined modules. The southern Guam watershed model was constructed by updating a watershed model for the Fena Valley watersheds, and expanding the modeled area to include all of southern Guam. The Fena Valley watershed model was combined with a previously developed, but recently updated and recalibrated Fena Valley Reservoir water-balance model.Two important surface-water resources for the U.S. Navy and the citizens of Guam were modeled in this study; the extended model now includes the Ugum River watershed and improves upon the previous model of the Fena Valley watersheds. Surface water from the Ugum River watershed is diverted and treated for drinking water, and the Fena Valley watersheds feed the largest surface-water reservoir on Guam. The southern Guam watershed model performed “very good,” according to the criteria of Moriasi and others (2007), in the Ugum River watershed above Talofofo Falls with monthly Nash-Sutcliffe efficiency statistic values of 0.97 for the calibration period and 0.93 for the verification period (a value of 1.0 represents perfect model fit). In the Fena Valley watershed, monthly simulated streamflow volumes from the watershed model compared reasonably well with the

A new method in predicting productivity of multi-stage fractured horizontal well in tight gas reservoirs

Directory of Open Access Journals (Sweden)

Yunsheng Wei

2016-10-01

Full Text Available The generally accomplished technique for horizontal wells in tight gas reservoirs is by multi-stage hydraulic fracturing, not to mention, the flow characteristics of a horizontal well with multiple transverse fractures are very intricate. Conventional methods, well as an evaluation unit, are difficult to accurately predict production capacity of each fracture and productivity differences between wells with a different number of fractures. Thus, a single fracture sets the minimum evaluation unit, matrix, fractures, and lateral wellbore model that are then combined integrally to approximate horizontal well with multiple transverse hydraulic fractures in tight gas reservoirs. This paper presents a new semi-analytical methodology for predicting the production capacity of a horizontal well with multiple transverse hydraulic fractures in tight gas reservoirs. Firstly, a mathematical flow model used as a medium, which is disturbed by finite conductivity vertical fractures and rectangular shaped boundaries, is established and explained by the Fourier integral transform. Then the idea of a single stage fracture analysis is incorporated to establish linear flow model within a single fracture with a variable rate. The Fredholm integral numerical solution is applicable for the fracture conductivity function. Finally, the pipe flow model along the lateral wellbore is adapted to couple multi-stages fracture mathematical models, and the equation group of predicting productivity of a multi-stage fractured horizontal well. The whole flow process from the matrix to bottom-hole and production interference between adjacent fractures is also established. Meanwhile, the corresponding iterative algorithm of the equations is given. In this case analysis, the productions of each well and fracture are calculated under the different bottom-hole flowing pressure, and this method also contributes to obtaining the distribution of pressure drop and production for every

Transport of reservoir fines

DEFF Research Database (Denmark)

Yuan, Hao; Shapiro, Alexander; Stenby, Erling Halfdan

Modeling transport of reservoir fines is of great importance for evaluating the damage of production wells and infectivity decline. The conventional methodology accounts for neither the formation heterogeneity around the wells nor the reservoir fines’ heterogeneity. We have developed an integral...... dispersion equation in modeling the transport and the deposition of reservoir fines. It successfully predicts the unsymmetrical concentration profiles and the hyperexponential deposition in experiments....

Mathematical models for therapeutic approaches to control HIV disease transmission

CERN Document Server

Roy, Priti Kumar

2015-01-01

The book discusses different therapeutic approaches based on different mathematical models to control the HIV/AIDS disease transmission. It uses clinical data, collected from different cited sources, to formulate the deterministic as well as stochastic mathematical models of HIV/AIDS. It provides complementary approaches, from deterministic and stochastic points of view, to optimal control strategy with perfect drug adherence and also tries to seek viewpoints of the same issue from different angles with various mathematical models to computer simulations. The book presents essential methods and techniques for students who are interested in designing epidemiological models on HIV/AIDS. It also guides research scientists, working in the periphery of mathematical modeling, and helps them to explore a hypothetical method by examining its consequences in the form of a mathematical modelling and making some scientific predictions. The model equations, mathematical analysis and several numerical simulations that are...

Mathematical Modelling of Surfactant Self-assembly at Interfaces

KAUST Repository

Morgan, C. E.; Breward, C. J. W.; Griffiths, I. M.; Howell, P. D.

2015-01-01

© 2015 Society for Industrial and Applied Mathematics. We present a mathematical model to describe the distribution of surfactant pairs in a multilayer structure beneath an adsorbed monolayer. A mesoscopic model comprising a set of ordinary

Productivity Analysis of Volume Fractured Vertical Well Model in Tight Oil Reservoirs

Directory of Open Access Journals (Sweden)

Jiahang Wang

2017-01-01

Full Text Available This paper presents a semianalytical model to simulate the productivity of a volume fractured vertical well in tight oil reservoirs. In the proposed model, the reservoir is a composite system which contains two regions. The inner region is described as formation with finite conductivity hydraulic fracture network and the flow in fracture is assumed to be linear, while the outer region is simulated by the classical Warren-Root model where radial flow is applied. The transient rate is calculated, and flow patterns and characteristic flowing periods caused by volume fractured vertical well are analyzed. Combining the calculated results with actual production data at the decline stage shows a good fitting performance. Finally, the effects of some sensitive parameters on the type curves are also analyzed extensively. The results demonstrate that the effect of fracture length is more obvious than that of fracture conductivity on improving production in tight oil reservoirs. When the length and conductivity of main fracture are constant, the contribution of stimulated reservoir volume (SRV to the cumulative oil production is not obvious. When the SRV is constant, the length of fracture should also be increased so as to improve the fracture penetration and well production.

a Discrete Mathematical Model to Simulate Malware Spreading

Science.gov (United States)

Del Rey, A. Martin; Sánchez, G. Rodriguez

2012-10-01

With the advent and worldwide development of Internet, the study and control of malware spreading has become very important. In this sense, some mathematical models to simulate malware propagation have been proposed in the scientific literature, and usually they are based on differential equations exploiting the similarities with mathematical epidemiology. The great majority of these models study the behavior of a particular type of malware called computer worms; indeed, to the best of our knowledge, no model has been proposed to simulate the spreading of a computer virus (the traditional type of malware which differs from computer worms in several aspects). In this sense, the purpose of this work is to introduce a new mathematical model not based on continuous mathematics tools but on discrete ones, to analyze and study the epidemic behavior of computer virus. Specifically, cellular automata are used in order to design such model.

Use of mathematical modeling in nuclear measurements projects

International Nuclear Information System (INIS)

Toubon, H.; Menaa, N.; Mirolo, L.; Ducoux, X.; Khalil, R. A.; Chany, P.; Devita, A.

2011-01-01

Mathematical modeling of nuclear measurement systems is not a new concept. The response of the measurement system is described using a pre-defined mathematical model that depends on a set of parameters. These parameters are determined using a limited set of experimental measurement points e.g. efficiency curve, dose rates... etc. The model that agrees with the few experimental points is called an experimentally validated model. Once these models have been validated, we use mathematical interpolation to find the parameters of interest. Sometimes, when measurements are not practical or are impossible extrapolation is implemented but with care. CANBERRA has been extensively using mathematical modeling for the design and calibration of large and sophisticated systems to create and optimize designs that would be prohibitively expensive with only experimental tools. The case studies that will be presented here are primarily performed with MCNP, CANBERRA's MERCURAD/PASCALYS and ISOCS (In Situ Object Counting Software). For benchmarking purposes, both Monte Carlo and ray-tracing based codes are inter-compared to show models consistency and add a degree of reliability to modeling results. (authors)

Real-time management of a multipurpose water reservoir with a heteroscedastic inflow model

Science.gov (United States)

Pianosi, F.; Soncini-Sessa, R.

2009-10-01

Stochastic dynamic programming has been extensively used as a method for designing optimal regulation policies for water reservoirs. However, the potential of this method is dramatically reduced by its computational burden, which often forces to introduce strong approximations in the model of the system, especially in the description of the reservoir inflow. In this paper, an approach to partially remedy this problem is proposed and applied to a real world case study. It foresees solving the management problem on-line, using a reduced model of the system and the inflow forecast provided by a dynamic model. By doing so, all the hydrometeorological information that is available in real-time is fully exploited. The model here proposed for the inflow forecasting is a nonlinear, heteroscedastic model that provides both the expected value and the standard deviation of the inflow through dynamic relations. The effectiveness of such model for the purpose of the reservoir regulation is evaluated through simulation and comparison with the results provided by conventional homoscedastic inflow models.

Mathematical modelling of fracture hydrology

International Nuclear Information System (INIS)

Herbert, A.W.; Hodgkinson, D.P.; Lever, D.A.; Robinson, P.C.; Rae, J.

1985-06-01

This report summarises the work performed between January 1983 and December 1984 for the CEC/DOE contract 'Mathematical Modelling of Fracture Hydrology', under the following headings: 1) Statistical fracture network modelling, 2) Continuum models of flow and transport, 3) Simplified models, 4) Analysis of laboratory experiments and 5) Analysis of field experiments. (author)

[Hematophagous bats as reservoirs of rabies].

Science.gov (United States)

Scheffer, Karin Corrêa; Iamamoto, Keila; Asano, Karen Miyuki; Mori, Enio; Estevez Garcia, Andrea Isabel; Achkar, Samira M; Fahl, Williande Oliveira

2014-04-01

Rabies continues to be a challenge for public health authorities and a constraint to the livestock industry in Latin America. Wild and domestic canines and vampire bats are the main transmitter species and reservoirs of the disease. Currently, variations observed in the epidemiological profile of rabies, where the species of hematophagous bat Desmodus rotundus constitutes the main transmitting species. Over the years, knowledge has accumulated about the ecology, biology and behavior of this species and the natural history of rabies, which should lead to continuous development of methods of population control of d. Rotundus as well as prevention and diagnostic tools for rabies. Ecological relationships of this species with other hematophagous and non-hematophagous bats is unknown, and there is much room for improvement in reporting systems and surveillance, as well as creating greater awareness among the farming community. Understanding the impact of human-induced environmental changes on the rabies virus in bats should be cause for further investigation. This will require a combination of field studies with mathematical models and new diagnostic tools. This review aims to present the most relevant issues on the role of hematophagous bats as reservoirs and transmitters of the rabies virus.

Mathematical Modelling Plant Signalling Networks

KAUST Repository

Muraro, D.; Byrne, H.M.; King, J.R.; Bennett, M.J.

2013-01-01

methods for modelling gene and signalling networks and their application in plants. We then describe specific models of hormonal perception and cross-talk in plants. This mathematical analysis of sub-cellular molecular mechanisms paves the way for more

Performance modeling of an integral, self-regulating cesium reservoir for the ATI-TFE

International Nuclear Information System (INIS)

Thayer, K.L.; Ramalingam, M.L.; Young, T.J.

1993-01-01

This work covers the performance modeling of an integral metal-matrix cesium-graphite reservoir for operation in the Advanced Thermionic Initiative-Thermionic Fuel Element (ATI-TFE) converter configuration. The objectives of this task were to incorporate an intercalated cesium-graphite reservoir for the 3C 24 Cs→2C 36 Cs+Cs (g) two phase equilibrium reaction into the emitter lead region of the ATI-TFE. A semi two-dimensional, cylindrical TFE computer model was used to obtain thermal and electrical converter output characteristics for various reservoir locations. The results of this study are distributions for the interelectrode voltage, output current density, and output power density as a function of axial position along the TFE emitter. This analysis was accomplished by identifying an optimum cesium pressure for three representative pins in the ATI ''driverless'' reactor core and determining the corresponding position of the graphite reservoir in the ATI-TFE lead region. The position for placement of the graphite reservoir was determined by performing a first-order heat transfer analysis of the TFE lead region to determine its temperature distribution. The results of this analysis indicate that for the graphite reservoirs investigated the 3C 24 Cs→2C 36 Cs+Cs (g) equilibrium reaction reservoir is ideal for placement in the TFE emitter lead region. This reservoir can be directly coupled to the emitter, through conduction, to provide the desired cesium pressure for optimum performance. The cesium pressure corresponding to the optimum converter output performance was found to be 2.18 torr for the ATI core least power TFE, 2.92 torr for the average power TFE, and 4.93 torr for the maximum power TFE

Mathematical modeling and applications in nonlinear dynamics

CERN Document Server

Merdan, Hüseyin

2016-01-01

The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems. Provides methods for mathematical models with switching, thresholds, and impulses, each of particular importance for discontinuous processes Includes qualitative analysis of behaviors on Tumor-Immune Systems and methods of analysis for DNA, neural networks and epidemiology Introduces...

EOS simulation and GRNN modeling of the constant volume depletion behavior of gas condensate reservoirs

Energy Technology Data Exchange (ETDEWEB)

Elsharkawy, A.M.; Foda, S.G. [Kuwait University, Safat (Kuwait). Petroleum Engineering Dept.

1998-03-01

Currently, two approaches are being used to predict the changes in retrograde gas condensate composition and estimate the pressure depletion behavior of gas condensate reservoirs. The first approach uses the equation of states whereas the second uses empirical correlations. Equations of states (EOS) are poor predictive tools for complex hydrocarbon systems. The EOS needs adjustment against phase behavior data of reservoir fluid of known composition. The empirical correlation does not involve numerous numerical computations but their accuracy is limited. This study presents two general regression neural network (GRNN) models. The first model, GRNNM1, is developed to predict dew point pressure and gas compressibility at dew point using initial composition of numerous samples while the second model, GRNNM2, is developed to predict the changes in well stream effluent composition at any stages of pressure depletion. GRNNM2 can also be used to determine the initial reservoir fluid composition using dew point pressure, gas compressibility at dew point, and reservoir temperature. These models are based on analysis of 142 sample of laboratory studies of constant volume depletion (CVD) for gas condensate systems forming a total of 1082 depletion stages. The database represents a wide range of gas condensate systems obtained worldwide. The performance of the GRNN models has been compared to simulation results of the equation of state. The study shows that the proposed general regression neural network models are accurate, valid, and reliable. These models can be used to forecast CVD data needed for many reservoir engineering calculations in case laboratory data is unavailable. The GRNN models save computer time involved in EOS calculations. The study also show that once these models are properly trained they can be used to cut expenses of frequent sampling and laborious experimental CVD tests required for gas condensate reservoirs. 55 refs., 13 figs., 6 tabs.

The Real and the Mathematical in Quantum Modeling: From Principles to Models and from Models to Principles

Science.gov (United States)

Plotnitsky, Arkady

2017-06-01

The history of mathematical modeling outside physics has been dominated by the use of classical mathematical models, C-models, primarily those of a probabilistic or statistical nature. More recently, however, quantum mathematical models, Q-models, based in the mathematical formalism of quantum theory have become more prominent in psychology, economics, and decision science. The use of Q-models in these fields remains controversial, in part because it is not entirely clear whether Q-models are necessary for dealing with the phenomena in question or whether C-models would still suffice. My aim, however, is not to assess the necessity of Q-models in these fields, but instead to reflect on what the possible applicability of Q-models may tell us about the corresponding phenomena there, vis-à-vis quantum phenomena in physics. In order to do so, I shall first discuss the key reasons for the use of Q-models in physics. In particular, I shall examine the fundamental principles that led to the development of quantum mechanics. Then I shall consider a possible role of similar principles in using Q-models outside physics. Psychology, economics, and decision science borrow already available Q-models from quantum theory, rather than derive them from their own internal principles, while quantum mechanics was derived from such principles, because there was no readily available mathematical model to handle quantum phenomena, although the mathematics ultimately used in quantum did in fact exist then. I shall argue, however, that the principle perspective on mathematical modeling outside physics might help us to understand better the role of Q-models in these fields and possibly to envision new models, conceptually analogous to but mathematically different from those of quantum theory, helpful or even necessary there or in physics itself. I shall suggest one possible type of such models, singularized probabilistic, SP, models, some of which are time-dependent, TDSP-models. The

FEMME, a flexible environment for mathematically modelling the environment

NARCIS (Netherlands)

Soetaert, K.E.R.; DeClippele, V.; Herman, P.M.J.

2002-01-01

A new, FORTRAN-based, simulation environment called FEMME (Flexible Environment for Mathematically Modelling the Environment), designed for implementing, solving and analysing mathematical models in ecology is presented. Three separate phases in ecological modelling are distinguished: (1) the model

Influence of pH on dynamics of microbial enhanced oil recovery processes using biosurfactant producing Pseudomonas putida: Mathematical modelling and numerical simulation.

Science.gov (United States)

Sivasankar, P; Suresh Kumar, G

2017-01-01

In present work, the influence of reservoir pH conditions on dynamics of microbial enhanced oil recovery (MEOR) processes using Pseudomonas putida was analysed numerically from the developed mathematical model for MEOR processes. Further, a new strategy to improve the MEOR performance has also been proposed. It is concluded from present study that by reversing the reservoir pH from highly acidic to low alkaline condition (pH 5-8), flow and mobility of displaced oil, displacement efficiency, and original oil in place (OOIP) recovered gets significantly enhanced, resulting from improved interfacial tension (IFT) reduction by biosurfactants. At pH 8, maximum of 26.1% of OOIP was recovered with higher displacement efficiency. The present study introduces a new strategy to increase the recovery efficiency of MEOR technique by characterizing the biosurfactants for IFT min /IFT max values for different pH conditions and subsequently, reversing the reservoir pH conditions at which the IFT min /IFT max value is minimum. Copyright © 2016 Elsevier Ltd. All rights reserved.

SILTATION IN RESERVOIRS

African Journals Online (AJOL)

Keywords: reservoir model, siltation, sediment, catchment, sediment transport. 1. Introduction. Sediment ... rendered water storage structures useless in less than 25 years. ... reservoir, thus reducing the space available for water storage and ...

mathematical models for estimating radio channels utilization

African Journals Online (AJOL)

2017-08-08

Aug 8, 2017 ... Mathematical models for radio channels utilization assessment by real-time flows transfer in ... data transmission networks application having dynamic topology ..... Journal of Applied Mathematics and Statistics, 56(2): 85–90.

Numerical solution of fractured horizontal wells in shale gas reservoirs considering multiple transport mechanisms

Science.gov (United States)

Zhao, Yu-long; Tang, Xu-chuan; Zhang, Lie-hui; Tang, Hong-ming; Tao, Zheng-Wu

2018-06-01

The multiscale pore size and specific gas storage mechanism in organic-rich shale gas reservoirs make gas transport in such reservoirs complicated. Therefore, a model that fully incorporates all transport mechanisms and employs an accurate numerical method is urgently needed to simulate the gas production process. In this paper, a unified model of apparent permeability was first developed, which took into account multiple influential factors including slip flow, Knudsen diffusion (KD), surface diffusion, effects of the adsorbed layer, permeability stress sensitivity, and ad-/desorption phenomena. Subsequently, a comprehensive mathematical model, which included the model of apparent permeability, was derived to describe gas production behaviors. Thereafter, on the basis of unstructured perpendicular bisection grids and finite volume method, a fully implicit numerical simulator was developed using Matlab software. The validation and application of the new model were confirmed using a field case reported in the literature. Finally, the impacts of related influencing factors on gas production were analyzed. The results showed that KD resulted in a negligible impact on gas production in the proposed model. The smaller the pore size was, the more obvious the effects of the adsorbed layer on the well production rate would be. Permeability stress sensitivity had a slight effect on well cumulative production in shale gas reservoirs. Adsorbed gas made a major contribution to the later flow period of the well; the greater the adsorbed gas content, the greater the well production rate would be. This paper can improve the understanding of gas production in shale gas reservoirs for petroleum engineers.

River Stream-Flow and Zayanderoud Reservoir Operation Modeling Using the Fuzzy Inference System

Directory of Open Access Journals (Sweden)

Saeed Jamali

2007-12-01

Full Text Available The Zayanderoud basin is located in the central plateau of Iran. As a result of population increase and agricultural and industrial developments, water demand on this basin has increased extensively. Given the importance of reservoir operation in water resource and management studies, the performance of fuzzy inference system (FIS for Zayanderoud reservoir operation is investigated in this paper. The model of operation consists of two parts. In the first part, the seasonal river stream-flow is forecasted using the fuzzy rule-based system. The southern oscillated index, rain, snow, and discharge are inputs of the model and the seasonal river stream-flow its output. In the second part, the operation model is constructed. The amount of releases is first optimized by a nonlinear optimization model and then the rule curves are extracted using the fuzzy inference system. This model operates on an "if-then" principle, where the "if" is a vector of fuzzy permits and "then" is the fuzzy result. The reservoir storage capacity, inflow, demand, and year condition factor are used as permits. Monthly release is taken as the consequence. The Zayanderoud basin is investigated as a case study. Different performance indices such as reliability, resiliency, and vulnerability are calculated. According to results, FIS works more effectively than the traditional reservoir operation methods such as standard operation policy (SOP or linear regression.

ECMOR 4. 4th European conference on the mathematics of oil recovery. Topic B: Heterogeneity description and assessment of uncertainty. Proceedings

Energy Technology Data Exchange (ETDEWEB)

1994-01-01

The report with collected proceedings from a conference, deals with mathematics of oil recovery with the focus on heterogeneity description and assessment of uncertainty. Topics of proceedings are as follow: Reservoir engineering and uncertainty - how much we know about what we don't know; sampling from Bayesian models in reservoir characterization; improvement in the truncated Gaussian method - combining several Gaussian functions; Levy stochastic model for the variations in the properties in sedimentary rock; modelling sub-seismic fault patterns using a marked point process; marked point models with complex conditioning used for modelling of shales; integration of large- and small-scale data using Fourier transforms; ranking of production performance from detailed geological models; direct solution reservoir flow equations with uncertain parameters. Nine papers are prepared. 83 refs., 58 figs., 1 tab.

Terahertz-dependent identification of simulated hole shapes in oil-gas reservoirs

Science.gov (United States)

Bao, Ri-Ma; Zhan, Hong-Lei; Miao, Xin-Yang; Zhao, Kun; Feng, Cheng-Jing; Dong, Chen; Li, Yi-Zhang; Xiao, Li-Zhi

2016-10-01

Detecting holes in oil-gas reservoirs is vital to the evaluation of reservoir potential. The main objective of this study is to demonstrate the feasibility of identifying general micro-hole shapes, including triangular, circular, and square shapes, in oil-gas reservoirs by adopting terahertz time-domain spectroscopy (THz-TDS). We evaluate the THz absorption responses of punched silicon (Si) wafers having micro-holes with sizes of 20 μm-500 μm. Principal component analysis (PCA) is used to establish a model between THz absorbance and hole shapes. The positions of samples in three-dimensional spaces for three principal components are used to determine the differences among diverse hole shapes and the homogeneity of similar shapes. In addition, a new Si wafer with the unknown hole shapes, including triangular, circular, and square, can be qualitatively identified by combining THz-TDS and PCA. Therefore, the combination of THz-TDS with mathematical statistical methods can serve as an effective approach to the rapid identification of micro-hole shapes in oil-gas reservoirs. Project supported by the National Natural Science Foundation of China (Grant No. 61405259), the National Basic Research Program of China (Grant No. 2014CB744302), and the Specially Founded Program on National Key Scientific Instruments and Equipment Development, China (Grant No. 2012YQ140005).

Mathematical modelling in solid mechanics

CERN Document Server

Sofonea, Mircea; Steigmann, David

2017-01-01

This book presents new research results in multidisciplinary fields of mathematical and numerical modelling in mechanics. The chapters treat the topics: mathematical modelling in solid, fluid and contact mechanics nonconvex variational analysis with emphasis to nonlinear solid and structural mechanics numerical modelling of problems with non-smooth constitutive laws, approximation of variational and hemivariational inequalities, numerical analysis of discrete schemes, numerical methods and the corresponding algorithms, applications to mechanical engineering numerical aspects of non-smooth mechanics, with emphasis on developing accurate and reliable computational tools mechanics of fibre-reinforced materials behaviour of elasto-plastic materials accounting for the microstructural defects definition of structural defects based on the differential geometry concepts or on the atomistic basis interaction between phase transformation and dislocations at nano-scale energetic arguments bifurcation and post-buckling a...

Interfacial Fluid Mechanics A Mathematical Modeling Approach

CERN Document Server

Ajaev, Vladimir S

2012-01-01

Interfacial Fluid Mechanics: A Mathematical Modeling Approach provides an introduction to mathematical models of viscous flow used in rapidly developing fields of microfluidics and microscale heat transfer. The basic physical effects are first introduced in the context of simple configurations and their relative importance in typical microscale applications is discussed. Then,several configurations of importance to microfluidics, most notably thin films/droplets on substrates and confined bubbles, are discussed in detail.  Topics from current research on electrokinetic phenomena, liquid flow near structured solid surfaces, evaporation/condensation, and surfactant phenomena are discussed in the later chapters. This book also:  Discusses mathematical models in the context of actual applications such as electrowetting Includes unique material on fluid flow near structured surfaces and phase change phenomena Shows readers how to solve modeling problems related to microscale multiphase flows Interfacial Fluid Me...

Mathematical Models of Tuberculosis Reactivation and Relapse

Directory of Open Access Journals (Sweden)

Robert Steven Wallis

2016-05-01

Full Text Available The natural history of human infection with Mycobacterium tuberculosis (Mtb is highly variable, as is the response to treatment of active tuberculosis. There is presently no direct means to identify individuals in whom Mtb infection has been eradicated, whether by a bactericidal immune response or sterilizing antimicrobial chemotherapy. Mathematical models can assist in such circumstances by measuring or predicting events that cannot be directly observed. The 3 models discussed in this review illustrate instances in which mathematical models were used to identify individuals with innate resistance to Mtb infection, determine the etiology of tuberculosis in patients treated with tumor necrosis factor antagonists, and predict the risk of relapse in persons undergoing tuberculosis treatment. These examples illustrate the power of various types of mathematic models to increase knowledge and thereby inform interventions in the present global tuberculosis epidemic.

Using outcrop data for geological well test modelling in fractured reservoirs

NARCIS (Netherlands)

Aljuboori, F.; Corbett, P.; Bisdom, K.; Bertotti, G.; Geiger, S.

2015-01-01

Outcrop fracture data sets can now be acquired with ever more accuracy using drone technology augmented by field observations. These models can be used to form realistic, deterministic models of fractured reservoirs. Fractured well test models are traditionally seen to be finite or infinite

Triple-porosity/permeability flow in faulted geothermal reservoirs: Two-dimensional effects

Energy Technology Data Exchange (ETDEWEB)

Cesar Suarez Arriaga, M. [Michoacan Univ. & CFE, Mich. (Mexico); Samaniego Verduzco, F. [National Autonomous Univ. of Mexico, Coyoacan (Mexico)

1995-03-01

An essential characteristic of some fractured geothermal reservoirs is noticeable when the drilled wells intersect an open fault or macrofracture. Several evidences observed, suggest that the fluid transport into this type of systems, occurs at least in three stages: flow between rock matrix and microfractures, flow between fractures and faults and flow between faults and wells. This pattern flow could define, by analogy to the classical double-porosity model, a triple-porosity, triple-permeability concept. From a mathematical modeling point of view, the non-linearity of the heterogeneous transport processes, occurring with abrupt changes on the petrophysical properties of the rock, makes impossible their exact or analytic solution. To simulate this phenomenon, a detailed two-dimensional geometric model was developed representing the matrix-fracture-fault system. The model was solved numerically using MULKOM with a H{sub 2}O=CO{sub 2} equation of state module. This approach helps to understand some real processes involved. Results obtained from this study, exhibit the importance of considering the triple porosity/permeability concept as a dominant mechanism producing, for example, strong pressure gradients between the reservoir and the bottom hole of some wells.

Development of a cerebrospinal fluid lateral reservoir model in rhesus monkeys (Macaca mulatta).

Science.gov (United States)

Lester McCully, Cynthia M; Bacher, John; MacAllister, Rhonda P; Steffen-Smith, Emilie A; Saleem, Kadharbatcha; Thomas, Marvin L; Cruz, Rafael; Warren, Katherine E

2015-02-01

Rapid, serial, and humane collection of cerebrospinal fluid (CSF) in nonhuman primates (NHP) is an essential element of numerous research studies and is currently accomplished via two different models. The CSF reservoir model (FR) combines a catheter in the 4th ventricle with a flexible silastic reservoir to permit circulating CSF flow. The CSF lateral port model (LP) consists of a lateral ventricular catheter and an IV port that provides static access to CSF and volume restrictions on sample collection. The FR model is associated with an intensive, prolonged recovery and frequent postsurgical hydrocephalus and nonpatency, whereas the LP model is associated with an easier recovery. To maximize the advantages of both systems, we developed the CSF lateral reservoir model (LR), which combines the beneficial features of the 2 previous models but avoids their limitations by using a reservoir for circulating CSF flow combined with catheter placement in the lateral ventricle. Nine adult male rhesus monkeys were utilized in this study. Pre-surgical MRI was performed to determine the coordinates of the lateral ventricle and location of choroid plexus (CP). The coordinates were determined to avoid the CP and major blood vessels. The predetermined coordinates were 100% accurate, according to MRI validation. The LR system functioned successfully in 67% of cases for 221 d, and 44% remain functional at 426 to 510 d postoperatively. Compared with established models, our LR model markedly reduced postoperative complications and recovery time. Development of the LR model was successful in rhesus macaques and is a useful alternative to the FR and LP methods of CSF collection from nonhuman primates.

Exploring the Relationship between Mathematical Modelling and Classroom Discourse

Science.gov (United States)

Redmond, Trevor; Sheehy, Joanne; Brown, Raymond

2010-01-01

This paper explores the notion that the discourse of the mathematics classroom impacts on the practices that students engage when modelling mathematics. Using excerpts of a Year 12 student's report on modelling Newton's law of cooling, this paper argues that when students engage with the discourse of their mathematics classroom in a manner that…

PROJECT CASCADES OF SMALL DRY RESERVOIRS FOR FLOOD PROTECTION OF URBAN AREAS

Directory of Open Access Journals (Sweden)

Rafał Antoszewski

2017-02-01

Full Text Available The paper presents the problem of designing an open reservoirs with a capacity of about 100 000 m3 in heavily urbanized areas of anthropogenically transformed natural watercourses with numerous outlets drainage and large sealed surfaces runoff. In particular the issues of the hydrological basics design based on the meteorological data in the catchment uncontrolled water level checkpoints with particular emphasis on the tools of computer-aided modeling of hydrological processes (HEC-HMS, HEC-RAS and available for use mathematical models and statistical rainfall-runoff, this practical the method SCS-CN and linear model cascade tanks Nash to transform the effective precipitation in surface runoff.

Mathematical model of compact type evaporator

Science.gov (United States)

Borovička, Martin; Hyhlík, Tomáš

2018-06-01

In this paper, development of the mathematical model for evaporator used in heat pump circuits is covered, with focus on air dehumidification application. Main target of this ad-hoc numerical model is to simulate heat and mass transfer in evaporator for prescribed inlet conditions and different geometrical parameters. Simplified 2D mathematical model is developed in MATLAB SW. Solvers for multiple heat and mass transfer problems - plate surface temperature, condensate film temperature, local heat and mass transfer coefficients, refrigerant temperature distribution, humid air enthalpy change are included as subprocedures of this model. An automatic procedure of data transfer is developed in order to use results of MATLAB model in more complex simulation within commercial CFD code. In the end, Proper Orthogonal Decomposition (POD) method is introduced and implemented into MATLAB model.

Modellus: Learning Physics with Mathematical Modelling

Science.gov (United States)

Teodoro, Vitor

Computers are now a major tool in research and development in almost all scientific and technological fields. Despite recent developments, this is far from true for learning environments in schools and most undergraduate studies. This thesis proposes a framework for designing curricula where computers, and computer modelling in particular, are a major tool for learning. The framework, based on research on learning science and mathematics and on computer user interface, assumes that: 1) learning is an active process of creating meaning from representations; 2) learning takes place in a community of practice where students learn both from their own effort and from external guidance; 3) learning is a process of becoming familiar with concepts, with links between concepts, and with representations; 4) direct manipulation user interfaces allow students to explore concrete-abstract objects such as those of physics and can be used by students with minimal computer knowledge. Physics is the science of constructing models and explanations about the physical world. And mathematical models are an important type of models that are difficult for many students. These difficulties can be rooted in the fact that most students do not have an environment where they can explore functions, differential equations and iterations as primary objects that model physical phenomena--as objects-to-think-with, reifying the formal objects of physics. The framework proposes that students should be introduced to modelling in a very early stage of learning physics and mathematics, two scientific areas that must be taught in very closely related way, as they were developed since Galileo and Newton until the beginning of our century, before the rise of overspecialisation in science. At an early stage, functions are the main type of objects used to model real phenomena, such as motions. At a later stage, rates of change and equations with rates of change play an important role. This type of equations

Simulating cold production by a coupled reservoir-geomechanics model with sand erosion

Energy Technology Data Exchange (ETDEWEB)

Wang, Y.; Xue, S. [Petro-Geotech Inc., Calgary, AB (Canada)

2002-06-01

This paper presents a newly developed fully coupled reservoir-geomechanics model with sand erosion. Sand production occurs during aggressive production induced by the impact of viscous fluid flow and the in situ stress concentration near a wellbore, as well as by perforation tips in poorly consolidated formations. This compromises oil production, increases well completion costs, and reduces the life cycles of equipment down hole and on the surface. The proposed model can be used for sand production studies in conventional oil/gas reservoirs such as the North Sea as well as in heavy oil reservoirs such as in northwestern Canada. Instead of generating a high permeability network in reservoirs, the enhanced oil production is determined by the increase in the effective wellbore radius. This paper presents the general model. A detailed study on the capillary pressure and the impact of multiphase flow on sanding and erosion will be conducted at a later date. It appears that 2 phase flow can be important to elastoplasticity if no significant sand erosion has occurred. It was determined that high porosity is induced by erosion and capillary pressure. Two phase flow can be important when the built-up drag force carries sand-fluid slurry into the well. It is concluded that viscosity and flow velocity can help estimate the slurry transport, sand rate and enhanced oil production. 22 refs., 3 tabs., 11 figs.

On the effects of adaptive reservoir operating rules in hydrological physically-based models

Science.gov (United States)

Giudici, Federico; Anghileri, Daniela; Castelletti, Andrea; Burlando, Paolo

2017-04-01

Recent years have seen a significant increase of the human influence on the natural systems both at the global and local scale. Accurately modeling the human component and its interaction with the natural environment is key to characterize the real system dynamics and anticipate future potential changes to the hydrological regimes. Modern distributed, physically-based hydrological models are able to describe hydrological processes with high level of detail and high spatiotemporal resolution. Yet, they lack in sophistication for the behavior component and human decisions are usually described by very simplistic rules, which might underperform in reproducing the catchment dynamics. In the case of water reservoir operators, these simplistic rules usually consist of target-level rule curves, which represent the average historical level trajectory. Whilst these rules can reasonably reproduce the average seasonal water volume shifts due to the reservoirs' operation, they cannot properly represent peculiar conditions, which influence the actual reservoirs' operation, e.g., variations in energy price or water demand, dry or wet meteorological conditions. Moreover, target-level rule curves are not suitable to explore the water system response to climate and socio economic changing contexts, because they assume a business-as-usual operation. In this work, we quantitatively assess how the inclusion of adaptive reservoirs' operating rules into physically-based hydrological models contribute to the proper representation of the hydrological regime at the catchment scale. In particular, we contrast target-level rule curves and detailed optimization-based behavioral models. We, first, perform the comparison on past observational records, showing that target-level rule curves underperform in representing the hydrological regime over multiple time scales (e.g., weekly, seasonal, inter-annual). Then, we compare how future hydrological changes are affected by the two modeling

Boundary element analysis of earthquake induced hydrodynamic pressures in a water reservoir

International Nuclear Information System (INIS)

Jablonski, A.M.

1988-11-01

The seismic analysis of concrete gravity and arch dams is affected by the hydrodynamic pressures in the water reservoir. Boundary element method (BEM) formulations are derived for the hydrodynamic pressures arising in a gravity dam-reservoir-foundation system, treating both 2- and 3-dimensional cases. The formulations are based on the respective mathematical models which are governed by two- and three-dimensional Helmholtz equations with appropriate boundary conditions. For infinite reservoirs, loss of energy due to pressure waves moving away toward infinity strongly influence response. Since it is not possible to discretize an infinite extent, the radiation damping due to outgoing waves is accounted for by incorporating special boundary conditions at the far end, and in a similar manner the loss of energy due to absorption of waves by a flexible bottom of reservoir and banks can be accounted for by a special condition along the boundaries. Numerical results are obtained and compared with available classical solutions and convergence of numerical results with the size and number of boundary elements is studied. It is concluded that the direct boundary element method is an effective tool for the evaluation of the hydrodynamic pressures in finite and infinite dam-reservoir-foundation systems subjected to harmonic-type motion, and can easily be extended to any type of random motion with fast Fourier transform techniques. 82 refs., 65 figs., 25 tabs

Stochastic reservoir simulation for the modeling of uncertainty in coal seam degasification

Science.gov (United States)

Karacan, C. Özgen; Olea, Ricardo A.

2015-01-01

Coal seam degasification improves coal mine safety by reducing the gas content of coal seams and also by generating added value as an energy source. Coal seam reservoir simulation is one of the most effective ways to help with these two main objectives. As in all modeling and simulation studies, how the reservoir is defined and whether observed productions can be predicted are important considerations.

On the mathematical modeling of memristors

KAUST Repository

Radwan, Ahmed G.

2012-10-06

Since the fourth fundamental element (Memristor) became a reality by HP labs, and due to its huge potential, its mathematical models became a necessity. In this paper, we provide a simple mathematical model of Memristors characterized by linear dopant drift for sinusoidal input voltage, showing a high matching with the nonlinear SPICE simulations. The frequency response of the Memristor\\'s resistance and its bounding conditions are derived. The fundamentals of the pinched i-v hysteresis, such as the critical resistances, the hysteresis power and the maximum operating current, are derived for the first time.

Mathematical Properties Relevant to Geomagnetic Field Modeling

DEFF Research Database (Denmark)

Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils

2010-01-01

be directly measured. In this chapter, the mathematical foundation of global (as opposed to regional) geomagnetic field modeling is reviewed, and the spatial modeling of the field in spherical coordinates is focussed. Time can be dealt with as an independent variable and is not explicitly considered......Geomagnetic field modeling consists in converting large numbers of magnetic observations into a linear combination of elementary mathematical functions that best describes those observations.The set of numerical coefficients defining this linear combination is then what one refers.......The relevant elementary mathematical functions are introduced, their properties are reviewed, and how they can be used to describe the magnetic field in a source-free (such as the Earth’s neutral atmosphere) or source-dense (such as the ionosphere) environment is explained. Completeness and uniqueness...

Mathematical Properties Relevant to Geomagnetic Field Modeling

DEFF Research Database (Denmark)

Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils

2014-01-01

be directly measured. In this chapter, the mathematical foundation of global (as opposed to regional) geomagnetic field modeling is reviewed, and the spatial modeling of the field in spherical coordinates is focused. Time can be dealt with as an independent variable and is not explicitly considered......Geomagnetic field modeling consists in converting large numbers of magnetic observations into a linear combination of elementary mathematical functions that best describes those observations. The set of numerical coefficients defining this linear combination is then what one refers....... The relevant elementary mathematical functions are introduced, their properties are reviewed, and how they can be used to describe the magnetic field in a source-free (such as the Earth’s neutral atmosphere) or source-dense (such as the ionosphere) environment is explained. Completeness and uniqueness...

Mathematical modeling and optimization of complex structures

CERN Document Server

Repin, Sergey; Tuovinen, Tero

2016-01-01

This volume contains selected papers in three closely related areas: mathematical modeling in mechanics, numerical analysis, and optimization methods. The papers are based upon talks presented  on the International Conference for Mathematical Modeling and Optimization in Mechanics, held in Jyväskylä, Finland, March 6-7, 2014 dedicated to Prof. N. Banichuk on the occasion of his 70th birthday. The articles are written by well-known scientists working in computational mechanics and in optimization of complicated technical models. Also, the volume contains papers discussing the historical development, the state of the art, new ideas, and open problems arising in  modern continuum mechanics and applied optimization problems. Several papers are concerned with mathematical problems in numerical analysis, which are also closely related to important mechanical models. The main topics treated include:  * Computer simulation methods in mechanics, physics, and biology;  * Variational problems and methods; minimiz...

A location-based multiple point statistics method: modelling the reservoir with non-stationary characteristics

Directory of Open Access Journals (Sweden)

Yin Yanshu

2017-12-01

Full Text Available In this paper, a location-based multiple point statistics method is developed to model a non-stationary reservoir. The proposed method characterizes the relationship between the sedimentary pattern and the deposit location using the relative central position distance function, which alleviates the requirement that the training image and the simulated grids have the same dimension. The weights in every direction of the distance function can be changed to characterize the reservoir heterogeneity in various directions. The local integral replacements of data events, structured random path, distance tolerance and multi-grid strategy are applied to reproduce the sedimentary patterns and obtain a more realistic result. This method is compared with the traditional Snesim method using a synthesized 3-D training image of Poyang Lake and a reservoir model of Shengli Oilfield in China. The results indicate that the new method can reproduce the non-stationary characteristics better than the traditional method and is more suitable for simulation of delta-front deposits. These results show that the new method is a powerful tool for modelling a reservoir with non-stationary characteristics.

Reservoir Inflow Prediction under GCM Scenario Downscaled by Wavelet Transform and Support Vector Machine Hybrid Models

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Gusfan Halik

2015-01-01

Full Text Available Climate change has significant impacts on changing precipitation patterns causing the variation of the reservoir inflow. Nowadays, Indonesian hydrologist performs reservoir inflow prediction according to the technical guideline of Pd-T-25-2004-A. This technical guideline does not consider the climate variables directly, resulting in significant deviation to the observation results. This research intends to predict the reservoir inflow using the statistical downscaling (SD of General Circulation Model (GCM outputs. The GCM outputs are obtained from the National Center for Environmental Prediction/National Center for Atmospheric Research Reanalysis (NCEP/NCAR Reanalysis. A new proposed hybrid SD model named Wavelet Support Vector Machine (WSVM was utilized. It is a combination of the Multiscale Principal Components Analysis (MSPCA and nonlinear Support Vector Machine regression. The model was validated at Sutami Reservoir, Indonesia. Training and testing were carried out using data of 1991–2008 and 2008–2012, respectively. The results showed that MSPCA produced better extracting data than PCA. The WSVM generated better reservoir inflow prediction than the one of technical guideline. Moreover, this research also applied WSVM for future reservoir inflow prediction based on GCM ECHAM5 and scenario SRES A1B.

Mathematical Modelling of Unmanned Aerial Vehicles with Four Rotors

Directory of Open Access Journals (Sweden)

Zoran Benić

2016-01-01

Full Text Available Mathematical model of an unmanned aerial vehicle with four propulsors (quadcopter is indispensable in quadcopter movement simulation and later modelling of the control algorithm. Mathematical model is, at the same time, the first step in comprehending the mathematical principles and physical laws which are applied to the quadcopter system. The objective is to define the mathematical model which will describe the quadcopter behavior with satisfactory accuracy and which can be, with certain modifications, applicable for the similar configurations of multirotor aerial vehicles. At the beginning of mathematical model derivation, coordinate systems are defined and explained. By using those coordinate systems, relations between parameters defined in the earth coordinate system and in the body coordinate system are defined. Further, the quadcopter kinematic is described which enables setting those relations. Also, quadcopter dynamics is used to introduce forces and torques to the model through usage of Newton-Euler method. Final derived equation is Newton’s second law in the matrix notation. For the sake of model simplification, hybrid coordinate system is defined, and quadcopter dynamic equations derived with the respect to it. Those equations are implemented in the simulation. Results of behavior of quadcopter mathematical model are graphically shown for four cases. For each of the cases the propellers revolutions per minute (RPM are set in a way that results in the occurrence of the controllable variables which causes one of four basic quadcopter movements in space.

Experimental and numerical modeling of sulfur plugging in a carbonate oil reservoir

Energy Technology Data Exchange (ETDEWEB)

Al-Awadhy, F. [ADMA-OPCO, Abudhabi (United Arab Emirates); Kocabas, I.; Abou-Kassem, J.H. [UAE University, Al Ain (United Arab Emirates); Islam, M.R. [Dalhousie University, Halifax, NS (United States)

2005-01-15

Many oil and gas reservoirs in the United Arab Emirates produce large amounts of sour gas, mainly in the form of hydrogen sulfide. In addition to creating problems in the production line, wellbore damage is often reported due to the precipitation of elemental sulfur in the vicinity of the wellbore. While there have been several studies performed on the role of solid deposition in a gas reservoir, the role of sulfur deposition in oil reservoirs has not been investigated. This article presents experimental results along with a comprehensive wellbore model that predicts sulfur precipitation as well as plugging. The experiments were conducted in a core (linear) system. Both analytical and numerical modelings were performed in a linear coordinate system. Data for the numerical model was obtained from both test tube and coreflood experiments. By using a phenomenological model, the wellbore plugging was modeled with an excellent match (with experimental results). The crude oil was de-asphalted prior to conducting the experiment in order to isolate the effect of asphaltene plugging. A series of coreflood tests was carried out to observe sulfur precipitation and plugging in a carbonate rock. Significant plugging was observed and was found to be dependent on flow rate and initial sulfur concentration. This information was used in the phenomenological model and can be incorporated in the wellbore numerical model. (author)

Integrated 3D Reservoir/Fault Property Modelling Aided Well Planning and Improved Hydrocarbon Recovery in a Niger Delta Field

International Nuclear Information System (INIS)

Onyeagoro, U. O.; Ebong, U. E.; Nworie, E. A.

2002-01-01

The large and varied portfolio of assets managed by oil companies requires quick decision-making and the deployment of best in class technologies in asset management. Timely decision making and the application of the best technologies in reservoir management are however sometimes in conflict due to large time requirements of the latter.Optimizing the location of development wells is critical to account for variable fluid contact movements and pressure interference effects between wells, which can be significant because of the high permeability (Darcy range) of Niger Delta reservoirs. With relatively high drilling costs, the optimization of well locations necessitates a good realistic static and dynamic 3D reservoir description, especially in the recovery of remaining oil and oil rim type of reservoirs.A detailed 3D reservoir model with fault properties was constructed for a Niger delta producing field. This involved the integration of high quality 3D seismic, core, petrophysics, reservoir engineering, production and structural geology data to construct a realistic 3D reservoir/fault property model for the field. The key parameters considered during the construction of the internal architecture of the model were the vertical and horizontal reservoir heterogeneities-this controls the fluid flow within the reservoir. In the production realm, the fault thickness and fault permeabilities are factors that control the impedance of fluid flow across the fault-fault transmissibility. These key internal and external reservoir/structural variables were explicitly modeled in a 3D modeling software to produce different realizations and manage the uncertainties.The resulting 3D reservoir/fault property model was upscaled for simulation purpose such that grid blocks along the fault planes have realistic transmissibility multipliers of 0 to 1 attached to them. The model was also used in the well planner to optimize the positioning of a high angle deviated well that penetrated

Mathematical Modeling of Loop Heat Pipes

Science.gov (United States)

Kaya, Tarik; Ku, Jentung; Hoang, Triem T.; Cheung, Mark L.

1998-01-01

The primary focus of this study is to model steady-state performance of a Loop Heat Pipe (LHP). The mathematical model is based on the steady-state energy balance equations at each component of the LHP. The heat exchange between each LHP component and the surrounding is taken into account. Both convection and radiation environments are modeled. The loop operating temperature is calculated as a function of the applied power at a given loop condition. Experimental validation of the model is attempted by using two different LHP designs. The mathematical model is tested at different sink temperatures and at different elevations of the loop. Tbc comparison of the calculations and experimental results showed very good agreement (within 3%). This method proved to be a useful tool in studying steady-state LHP performance characteristics.

Mathematical Modelling Plant Signalling Networks

KAUST Repository

Muraro, D.

2013-01-01

During the last two decades, molecular genetic studies and the completion of the sequencing of the Arabidopsis thaliana genome have increased knowledge of hormonal regulation in plants. These signal transduction pathways act in concert through gene regulatory and signalling networks whose main components have begun to be elucidated. Our understanding of the resulting cellular processes is hindered by the complex, and sometimes counter-intuitive, dynamics of the networks, which may be interconnected through feedback controls and cross-regulation. Mathematical modelling provides a valuable tool to investigate such dynamics and to perform in silico experiments that may not be easily carried out in a laboratory. In this article, we firstly review general methods for modelling gene and signalling networks and their application in plants. We then describe specific models of hormonal perception and cross-talk in plants. This mathematical analysis of sub-cellular molecular mechanisms paves the way for more comprehensive modelling studies of hormonal transport and signalling in a multi-scale setting. © EDP Sciences, 2013.

Building Mathematical Models of Simple Harmonic and Damped Motion.

Science.gov (United States)

Edwards, Thomas

1995-01-01

By developing a sequence of mathematical models of harmonic motion, shows that mathematical models are not right or wrong, but instead are better or poorer representations of the problem situation. (MKR)

Fourth SIAM conference on mathematical and computational issues in the geosciences: Final program and abstracts

Energy Technology Data Exchange (ETDEWEB)

NONE

1997-12-31

The conference focused on computational and modeling issues in the geosciences. Of the geosciences, problems associated with phenomena occurring in the earth`s subsurface were best represented. Topics in this area included petroleum recovery, ground water contamination and remediation, seismic imaging, parameter estimation, upscaling, geostatistical heterogeneity, reservoir and aquifer characterization, optimal well placement and pumping strategies, and geochemistry. Additional sessions were devoted to the atmosphere, surface water and oceans. The central mathematical themes included computational algorithms and numerical analysis, parallel computing, mathematical analysis of partial differential equations, statistical and stochastic methods, optimization, inversion, homogenization and renormalization. The problem areas discussed at this conference are of considerable national importance, with the increasing importance of environmental issues, global change, remediation of waste sites, declining domestic energy sources and an increasing reliance on producing the most out of established oil reservoirs.

Simple mathematical models of symmetry breaking. Application to particle physics

International Nuclear Information System (INIS)

Michel, L.

1976-01-01

Some mathematical facts relevant to symmetry breaking are presented. A first mathematical model deals with the smooth action of compact Lie groups on real manifolds, a second model considers linear action of any group on real or complex finite dimensional vector spaces. Application of the mathematical models to particle physics is considered. (B.R.H.)

Mathematical modeling of dissolved oxygen in fish ponds ...

African Journals Online (AJOL)

Mathematical modeling of dissolved oxygen in fish ponds. WJS Mwegoha, ME Kaseva, SMM Sabai. Abstract. A mathematical model was developed to predict the effects of wind speed, light, pH, Temperature, dissolved carbon dioxide and chemical oxygen demand (COD) on Dissolved Oxygen (DO) in fish ponds. The effects ...

Structured Mathematical Modeling of Industrial Boiler

Directory of Open Access Journals (Sweden)

Abdullah Nur Aziz

2014-04-01

Full Text Available As a major utility system in industry, boilers consume a large portion of the total energy and costs. Significant reduction of boiler cost operation can be gained through improvements in efficiency. In accomplishing such a goal, an adequate dynamic model that comprehensively reflects boiler characteristics is required. This paper outlines the idea of developing a mathematical model of a water-tube industrial boiler based on first principles guided by the bond graph method in its derivation. The model describes the temperature dynamics of the boiler subsystems such as economizer, steam drum, desuperheater, and superheater. The mathematical model was examined using industrial boiler performance test data.It can be used to build a boiler simulator or help operators run a boiler effectively.

Geological modeling for methane hydrate reservoir characterization in the eastern Nankai Trough, offshore Japan

Science.gov (United States)

Tamaki, M.; Komatsu, Y.; Suzuki, K.; Takayama, T.; Fujii, T.

2012-12-01

The eastern Nankai trough, which is located offshore of central Japan, is considered as an attractive potential resource field of methane hydrates. Japan Oil, Gas and Metals National Corporation is planning to conduct a production test in early 2013 at the AT1 site in the north slope of Daini-Atsumi Knoll in the eastern Nankai Trough. The depositional environment of methane hydrate-bearing sediments around the production test site is a deep submarine-fan turbidite system, and it is considered that the reservoir properties should show lateral as well as vertical heterogeneity. Since the variations in the reservoir heterogeneity have an impact on the methane hydrate dissociation and gas production performance, precise geological models describing reservoir heterogeneity would be required for the evaluation of reservoir potentials. In preparation for the production test, 3 wells; two monitoring boreholes (AT1-MC and AT1-MT1) and a coring well (AT1-C), were newly acquired in 2012. In addition to a geotechnical hole drilling survey in 2011 (AT1-GT), totally log data from 2 wells and core data from 2 wells were obtained around the production test site. In this study, we conducted well correlations between AT1 and A1 wells drilled in 2003 and then, 3D geological models were updated including AT1 well data in order to refine hydrate reservoir characterization around the production test site. The results of the well correlations show that turbidite sand layers are characterized by good lateral continuity, and give significant information for the distribution morphology of sand-rich channel fills. We also reviewed previously conducted 3D geological models which consist of facies distributions and petrophysical properties distributions constructed from integration of 3D seismic data and a well data (A1 site) adopting a geostatistical approach. In order to test the practical validity of the previously generated models, cross-validation was conducted using AT1 well data. The

The role of reservoir characterization in the reservoir management process (as reflected in the Department of Energy`s reservoir management demonstration program)

Energy Technology Data Exchange (ETDEWEB)

Fowler, M.L. [BDM-Petroleum Technologies, Bartlesville, OK (United States); Young, M.A.; Madden, M.P. [BDM-Oklahoma, Bartlesville, OK (United States)] [and others

1997-08-01

Optimum reservoir recovery and profitability result from guidance of reservoir practices provided by an effective reservoir management plan. Success in developing the best, most appropriate reservoir management plan requires knowledge and consideration of (1) the reservoir system including rocks, and rock-fluid interactions (i.e., a characterization of the reservoir) as well as wellbores and associated equipment and surface facilities; (2) the technologies available to describe, analyze, and exploit the reservoir; and (3) the business environment under which the plan will be developed and implemented. Reservoir characterization is the essential to gain needed knowledge of the reservoir for reservoir management plan building. Reservoir characterization efforts can be appropriately scaled by considering the reservoir management context under which the plan is being built. Reservoir management plans de-optimize with time as technology and the business environment change or as new reservoir information indicates the reservoir characterization models on which the current plan is based are inadequate. BDM-Oklahoma and the Department of Energy have implemented a program of reservoir management demonstrations to encourage operators with limited resources and experience to learn, implement, and disperse sound reservoir management techniques through cooperative research and development projects whose objectives are to develop reservoir management plans. In each of the three projects currently underway, careful attention to reservoir management context assures a reservoir characterization approach that is sufficient, but not in excess of what is necessary, to devise and implement an effective reservoir management plan.

Mathematical Model-Based Temperature Preparation of Liquid-Propellant Components Cooled by Liquid Nitrogen in the Heat Exchanger with a Coolant

Directory of Open Access Journals (Sweden)

S. K. Pavlov

2014-01-01

Full Text Available Before fuelling the tanks of missiles, boosters, and spacecraft with liquid-propellant components (LPC their temperature preparation is needed. The missile-system ground equipment performs this operation during prelaunch processing of space-purpose missiles (SPM. Usually, the fuel cooling is necessary to increase its density and provide heat compensation during prelaunch operation of SPM. The fuel temperature control systems (FTCS using different principles of operation and types of coolants are applied for fuel cooling.To determine parameters of LPC cooling process through the fuel heat exchange in the heat exchanger with coolant, which is cooled by liquid nitrogen upon contact heat exchange in the coolant reservoir, a mathematical model of this process and a design technique are necessary. Both allow us to determine design parameters of the cooling system and the required liquid nitrogen reserve to cool LPC to the appropriate temperature.The article presents an overview of foreign and domestic publications on cooling processes research and implementation using cryogenic products such as liquid nitrogen. The article draws a conclusion that it is necessary to determine the parameters of LPC cooling process through the fuel heat exchange in the heat exchanger with coolant, which is liquid nitrogen-cooled upon contact heat exchange in the coolant reservoir allowing to define rational propellant cooling conditions to the specified temperature.The mathematical model describes the set task on the assumption that a heat exchange between the LPC and the coolant in the heat exchanger and with the environment through the walls of tanks and pipelines of circulation loops is quasi-stationary.The obtained curves allow us to calculate temperature changes of LPC and coolant, cooling time and liquid nitrogen consumption, depending on the process parameters such as a flow rate of liquid nitrogen, initial coolant temperature, pump characteristics, thermal

The possibilities of a modelling perspective for school mathematics

Directory of Open Access Journals (Sweden)

Dirk Wessels

2009-09-01

complex teaching methodology requires in-depth thinking about the role of the teacher, the role of the learner, the nature of the classroom culture, the nature of the negotiation of meaning between the teacher and individuals or groups, the nature of selected problems and material, as well as the kind of integrative assessment used in the mathematics classroom. Modelling is closely related to the problem-centred teaching approach, but it also smoothly relates to bigger and longer mathematical tasks. This article gives a theoretical exposition of the scope and depth of mathematical modelling. It is possible to introduce modelling at every school phase in our educational sytem. Modelling in school mathematics seems to make the learning of mathematics more effective. The mastering of problem solving and modelling strategies has definitely changed the orientation, the competencies and performances of learners at each school level. It would appear from research that learners like the application side of mathematics and that they want to see it in action. Genuine real life problems should be selected, which is why a modelling perspective is so important for the teaching and mastering of mathematics. Modelling should be integrated into the present curriculum because learners will then get full access to involvement in the classroom, to mathematisation, to doing problems, to criticising arguments, to finding proofs, to recognising concepts and to obtaining the ability to abstract these from the realistic situation. Modelling should be given a full opportunity in mathematics teacher education so that our learners can get the full benefit of it. This will put the mathematical performances of learners in our country on a more solid base, which will make our learners more competitive at all levels in the future. 

Optimal Operation of Hydropower Reservoirs under Climate Change: The Case of Tekeze Reservoir, Eastern Nile

Directory of Open Access Journals (Sweden)

Fikru Fentaw Abera

2018-03-01

Full Text Available Optimal operation of reservoirs is very essential for water resource planning and management, but it is very challenging and complicated when dealing with climate change impacts. The objective of this paper was to assess existing and future hydropower operation at the Tekeze reservoir in the face of climate change. In this study, a calibrated and validated Soil and Water Assessment Tool (SWAT was used to model runoff inflow into the Tekeze hydropower reservoir under present and future climate scenarios. Inflow to the reservoir was simulated using hydro-climatic data from an ensemble of downscaled climate data based on the Coordinated Regional climate Downscaling Experiment over African domain (CORDEX-Africa with Coupled Intercomparison Project Phase 5 (CMIP5 simulations under Representative Concentration Pathway (RCP4.5 and RCP8.5 climate scenarios. Observed and projected inflows to Tekeze hydropower reservoir were used as input to the US Army Corps of Engineer’s Reservoir Evaluation System Perspective Reservoir Model (HEC-ResPRM, a reservoir operation model, to optimize hydropower reservoir release, storage and pool level. Results indicated that climate change has a clear impact on reservoir inflow and showed increase in annual and monthly inflow into the reservoir except in dry months from May to June under RCP4.5 and RCP8.5 climate scenarios. HEC-ResPRM optimal operation results showed an increase in Tekeze reservoir power storage potential up to 25% and 30% under RCP4.5 and RCP8.5 climate scenarios, respectively. This implies that Tekeze hydropower production will be affected by climate change. This analysis can be used by water resources planners and mangers to develop reservoir operation techniques considering climate change impact to increase power production.

Full field reservoir modeling of shale assets using advanced data-driven analytics

Directory of Open Access Journals (Sweden)

Soodabeh Esmaili

2016-01-01

Full Text Available Hydrocarbon production from shale has attracted much attention in the recent years. When applied to this prolific and hydrocarbon rich resource plays, our understanding of the complexities of the flow mechanism (sorption process and flow behavior in complex fracture systems - induced or natural leaves much to be desired. In this paper, we present and discuss a novel approach to modeling, history matching of hydrocarbon production from a Marcellus shale asset in southwestern Pennsylvania using advanced data mining, pattern recognition and machine learning technologies. In this new approach instead of imposing our understanding of the flow mechanism, the impact of multi-stage hydraulic fractures, and the production process on the reservoir model, we allow the production history, well log, completion and hydraulic fracturing data to guide our model and determine its behavior. The uniqueness of this technology is that it incorporates the so-called “hard data” directly into the reservoir model, so that the model can be used to optimize the hydraulic fracture process. The “hard data” refers to field measurements during the hydraulic fracturing process such as fluid and proppant type and amount, injection pressure and rate as well as proppant concentration. This novel approach contrasts with the current industry focus on the use of “soft data” (non-measured, interpretive data such as frac length, width, height and conductivity in the reservoir models. The study focuses on a Marcellus shale asset that includes 135 wells with multiple pads, different landing targets, well length and reservoir properties. The full field history matching process was successfully completed using this data driven approach thus capturing the production behavior with acceptable accuracy for individual wells and for the entire asset.

GPU-Based Computation of Formation Pressure for Multistage Hydraulically Fractured Horizontal Wells in Tight Oil and Gas Reservoirs

Directory of Open Access Journals (Sweden)

Rongwang Yin

2018-01-01

Full Text Available A mathematical model for multistage hydraulically fractured horizontal wells (MFHWs in tight oil and gas reservoirs was derived by considering the variations in the permeability and porosity of tight oil and gas reservoirs that depend on formation pressure and mixed fluid properties and introducing the pseudo-pressure; analytical solutions were presented using the Newman superposition principle. The CPU-GPU asynchronous computing model was designed based on the CUDA platform, and the analytic solution was decomposed into infinite summation and integral forms for parallel computation. Implementation of this algorithm on an Intel i5 4590 CPU and NVIDIA GT 730 GPU demonstrates that computation speed increased by almost 80 times, which meets the requirement for real-time calculation of the formation pressure of MFHWs.

Reservoir inflow forecasting with a modified coactive neuro-fuzzy inference system: a case study for a semi-arid region

Science.gov (United States)

Allawi, Mohammed Falah; Jaafar, Othman; Mohamad Hamzah, Firdaus; Mohd, Nuruol Syuhadaa; Deo, Ravinesh C.; El-Shafie, Ahmed

2017-10-01

Existing forecast models applied for reservoir inflow forecasting encounter several drawbacks, due to the difficulty of the underlying mathematical procedures being to cope with and to mimic the naturalization and stochasticity of the inflow data patterns. In this study, appropriate adjustments to the conventional coactive neuro-fuzzy inference system (CANFIS) method are proposed to improve the mathematical procedure, thus enabling a better detection of the high nonlinearity patterns found in the reservoir inflow training data. This modification includes the updating of the back propagation algorithm, leading to a consequent update of the membership rules and the induction of the centre-weighted set rather than the global weighted set used in feature extraction. The modification also aids in constructing an integrated model that is able to not only detect the nonlinearity in the training data but also the wide range of features within the training data records used to simulate the forecasting model. To demonstrate the model's efficacy, the proposed CANFIS method has been applied to forecast monthly inflow data at Aswan High Dam (AHD), located in southern Egypt. Comparative analyses of the forecasting skill of the modified CANFIS and the conventional ANFIS model are carried out with statistical score indicators to assess the reliability of the developed method. The statistical metrics support the better performance of the developed CANFIS model, which significantly outperforms the ANFIS model to attain a low relative error value (23%), mean absolute error (1.4 BCM month-1), root mean square error (1.14 BCM month-1), and a relative large coefficient of determination (0.94). The present study ascertains the better utility of the modified CANFIS model in respect to the traditional ANFIS model applied in reservoir inflow forecasting for a semi-arid region.

iSTEM: Promoting Fifth Graders' Mathematical Modeling

Science.gov (United States)

Yanik, H. Bahadir; Karabas, Celil

2014-01-01

Modeling requires that people develop representations or procedures to address particular problem situations (Lesh et al. 2000). Mathematical modeling is used to describe essential characteristics of a phenomenon or a situation that one intends to study in the real world through building mathematical objects. This article describes how fifth-grade…

Experimental and numerical modeling of sulfur plugging in carbonate reservoirs

Energy Technology Data Exchange (ETDEWEB)

Abou-Kassem, J.H. [Chemical and Petroleum Engineering Department, UAE University, PO Box 17555, Al-Ain (United Arab Emirates)

2000-05-01

Sour gas, mainly in the form of hydrogen sulfide, is produced in large amounts from many oil and gas reservoirs in the United Arab Emirates. In addition to creating problems in production lines, the precipitation of elemental sulfur in vicinity of the wellbore is often reported to cause wellbore damage. While there have been several studies performed on the role of solid deposition in gas reservoirs, the role of sulfur deposition in oil reservoirs has not been investigated. This paper presents experimental results along with a comprehensive wellbore model that predicts sulfur precipitation as well as plugging. Two separate sets of experiments, one for a gas phase system and another for a crude oil system, were conducted to investigate the deposition of elemental sulfur in (linear) carbonate cores. The gas flow tests were conducted with elemental sulfur being carried with nitrogen through limestone cores. Changes in gas flow rate were monitored while the injection pressure was held constant. A series of experiments generated valuable data for plugging with elemental sulfur. X-ray diffraction tests provided evidence of sulfur deposition along the cores. The oil flow tests were carried out to observe sulfur precipitation and plugging in a carbonate core. The crude oil was de-asphalted before conducting these tests in order to isolate the effect of asphaltene plugging. Significant plugging was observed and was found to be dependent on flow rate and initial sulfur concentration. This information was used in a phenomenological model that was incorporated in the wellbore numerical model. The data for the numerical model were obtained from both test tube and oil flow experiments. By using a phenomenological model, the wellbore plugging was modeled with an excellent match (with experimental results)

Exploration and reservoir characterization; Technology Target Areas; TTA2 - Exploration and reservoir characterisation

Energy Technology Data Exchange (ETDEWEB)

2008-07-01

In future, research within exploration and reservoir characterization will play an even more important role for Norway since resources are decreasing and new challenges like deep sea, harsh environment and last but not least environmental issues have to be considered. There are two major fields which have to be addressed within exploration and reservoir characterization: First, replacement of reserves by new discoveries and ultimate field recoveries in mature basins at the Norwegian Continental shelf, e.g. at the Halten Terrace has to be addressed. A wealth of data exists in the more mature areas. Interdisciplinary integration is a key feature of reservoir characterization, where available data and specialist knowledge need to be combined into a consistent reservoir description. A systematic approach for handling both uncertainties in data sources and uncertainties in basic models is needed. Fast simulation techniques are necessary to generate models spanning the event space, covering both underground based and model-based uncertainties. Second, exploration in frontier areas like the Barents Sea region and the deeper Voering Basin has to be addressed. The scarcity of wells in these frontier areas leads to uncertainties in the geological understanding. Basin- and depositional modelling are essential for predicting where source rocks and reservoir rocks are deposited, and if, when and which hydrocarbons are generated and trapped. Predictive models and improved process understanding is therefore crucial to meet these issues. Especially the challenges related to the salt deposits e.g. sub-salt/sub-basalt reservoir definitions in the Nordkapp Basin demands up-front research and technology developments. TTA2 stresses the need to focus on the development of new talents. We also see a strong need to push cooperation as far as possible in the present competitive environment. Projects that may require a substantial financial commitment have been identified. The following

Qualitative mathematics for the social sciences mathematical models for research on cultural dynamics

CERN Document Server

Rudolph, Lee

2012-01-01

In this book Lee Rudolph brings together international contributors who combine psychological and mathematical perspectives to analyse how qualitative mathematics can be used to create models of social and psychological processes. Bridging the gap between the fields with an imaginative and stimulating collection of contributed chapters, the volume updates the current research on the subject, which until now has been rather limited, focussing largely on the use of statistics. Qualitative Mathematics for the Social Sciences contains a variety of useful illustrative figures, in

Mathematical modeling of biological processes

CERN Document Server

Friedman, Avner

2014-01-01

This book on mathematical modeling of biological processes includes a wide selection of biological topics that demonstrate the power of mathematics and computational codes in setting up biological processes with a rigorous and predictive framework. Topics include: enzyme dynamics, spread of disease, harvesting bacteria, competition among live species, neuronal oscillations, transport of neurofilaments in axon, cancer and cancer therapy, and granulomas. Complete with a description of the biological background and biological question that requires the use of mathematics, this book is developed for graduate students and advanced undergraduate students with only basic knowledge of ordinary differential equations and partial differential equations; background in biology is not required. Students will gain knowledge on how to program with MATLAB without previous programming experience and how to use codes in order to test biological hypothesis.

Applied Mathematics, Modelling and Computational Science

CERN Document Server

Kotsireas, Ilias; Makarov, Roman; Melnik, Roderick; Shodiev, Hasan

2015-01-01

The Applied Mathematics, Modelling, and Computational Science (AMMCS) conference aims to promote interdisciplinary research and collaboration. The contributions in this volume cover the latest research in mathematical and computational sciences, modeling, and simulation as well as their applications in natural and social sciences, engineering and technology, industry, and finance. The 2013 conference, the second in a series of AMMCS meetings, was held August 26–30 and organized in cooperation with AIMS and SIAM, with support from the Fields Institute in Toronto, and Wilfrid Laurier University. There were many young scientists at AMMCS-2013, both as presenters and as organizers. This proceedings contains refereed papers contributed by the participants of the AMMCS-2013 after the conference. This volume is suitable for researchers and graduate students, mathematicians and engineers, industrialists, and anyone who would like to delve into the interdisciplinary research of applied and computational mathematics ...

Vibratory gyroscopes : identification of mathematical model from test data

CSIR Research Space (South Africa)

Shatalov, MY

2007-05-01

Full Text Available Simple mathematical model of vibratory gyroscopes imperfections is formulated, which includes anisotropic damping and variation of mass-stiffness parameters and their harmonics. The method of identification of parameters of the mathematical model...

Сontrol systems using mathematical models of technological objects ...

African Journals Online (AJOL)

Сontrol systems using mathematical models of technological objects in the control loop. ... Journal of Fundamental and Applied Sciences ... Such mathematical models make it possible to specify the optimal operating modes of the considered ...

Large reservoirs: Chapter 17

Science.gov (United States)

Miranda, Leandro E.; Bettoli, Phillip William

2010-01-01

expressed effects, such as turbidity and water quality, zooplankton density and size composition, or fish growth rates and assemblage composition, are the upshot of large-scale factors operating outside reservoirs and not under the direct control of reservoir managers. Realistically, abiotic and biotic conditions in reservoirs are shaped by factors working inside and outside reservoirs, with the relative importance of external factors differing among reservoirs. With this perspective, large reservoirs are viewed from a habitat standpoint within the framework of a conceptual model in which individual reservoir characteristics are influenced by both local- and landscape-scale factors (Figure 17.1). In the sections that follow, how each element of this hierarchical model influences habitat and fish assemblages in reservoirs is considered. Important in-reservoir habitat issues and reservoirs as part of larger systems, where reservoir management requires looking for real solutions outside individual reservoirs are described.

Modeling a distributed environment for a petroleum reservoir engineering application with software product line

International Nuclear Information System (INIS)

Scheidt, Rafael de Faria; Vilain, Patrícia; Dantas, M A R

2014-01-01

Petroleum reservoir engineering is a complex and interesting field that requires large amount of computational facilities to achieve successful results. Usually, software environments for this field are developed without taking care out of possible interactions and extensibilities required by reservoir engineers. In this paper, we present a research work which it is characterized by the design and implementation based on a software product line model for a real distributed reservoir engineering environment. Experimental results indicate successfully the utilization of this approach for the design of distributed software architecture. In addition, all components from the proposal provided greater visibility of the organization and processes for the reservoir engineers

Modeling a distributed environment for a petroleum reservoir engineering application with software product line

Science.gov (United States)

de Faria Scheidt, Rafael; Vilain, Patrícia; Dantas, M. A. R.

2014-10-01

Petroleum reservoir engineering is a complex and interesting field that requires large amount of computational facilities to achieve successful results. Usually, software environments for this field are developed without taking care out of possible interactions and extensibilities required by reservoir engineers. In this paper, we present a research work which it is characterized by the design and implementation based on a software product line model for a real distributed reservoir engineering environment. Experimental results indicate successfully the utilization of this approach for the design of distributed software architecture. In addition, all components from the proposal provided greater visibility of the organization and processes for the reservoir engineers.

Modeling Study of High Pressure and High Temperature Reservoir Fluids

DEFF Research Database (Denmark)

Varzandeh, Farhad

properties like saturation pressures, densities at reservoir temperature and Stock TankviOil (STO) densities, while keeping the n-alkane limit of the correlations unchanged. Apart from applying this general approach to PC-SAFT, we have also shown that the approach can be applied to classical cubic models...... approach to characterizing reservoir fluids for any EoS. The approach consists in developing correlations of model parameters first with a database for well-defined components and then adjusting the correlations with a large PVT database. The adjustment is made to minimize the deviation in key PVT...... method to SRK and PR improved the saturation pressure calculation in comparisonto the original characterization method for SRK and PR. Using volume translationtogether with the new characterization approach for SRK and PR gives comparable results for density and STO density to that of original...

Energy optimization through probabilistic annual forecast water release technique for major storage hydroelectric reservoir

International Nuclear Information System (INIS)

Abdul Bahari Othman; Mohd Zamri Yusoff

2006-01-01

One of the important decisions to be made by the management of hydroelectric power plant associated with major storage reservoir is to determine the best turbine water release decision for the next financial year. The water release decision enables firm energy generated estimation for the coming financial year to be done. This task is usually a simple and straightforward task provided that the amount of turbine water release is known. The more challenging task is to determine the best water release decision that is able to resolve the two conflicting operational objectives which are minimizing the drop of turbine gross head and maximizing upper reserve margin of the reservoir. Most techniques from literature emphasize on utilizing the statistical simulations approach. Markovians models, for example, are a class of statistical model that utilizes the past and the present system states as a basis for predicting the future [1]. This paper illustrates that rigorous solution criterion can be mathematically proven to resolve those two conflicting operational objectives. Thus, best water release decision that maximizes potential energy for the prevailing natural inflow is met. It is shown that the annual water release decision shall be made in such a manner that annual return inflow that has return frequency smaller than critical return frequency (f c ) should not be considered. This criterion enables target turbine gross head to be set to the well-defined elevation. In the other words, upper storage margin of the reservoir shall be made available to capture magnitude of future inflow that has return frequency greater than or equal to f c. A case study is shown to demonstrate practical application of the derived mathematical formulas

The Relationship between Big Data and Mathematical Modeling: A Discussion in a Mathematical Education Scenario

Science.gov (United States)

Dalla Vecchia, Rodrigo

2015-01-01

This study discusses aspects of the association between Mathematical Modeling (MM) and Big Data in the scope of mathematical education. We present an example of an activity to discuss two ontological factors that involve MM. The first is linked to the modeling stages. The second involves the idea of pedagogical objectives. The main findings…

Prospective Mathematics Teachers' Opinions about Mathematical Modeling Method and Applicability of This Method

Science.gov (United States)

Akgün, Levent

2015-01-01

The aim of this study is to identify prospective secondary mathematics teachers' opinions about the mathematical modeling method and the applicability of this method in high schools. The case study design, which is among the qualitative research methods, was used in the study. The study was conducted with six prospective secondary mathematics…

Mathematical modelling of the process of quality control of construction products

Directory of Open Access Journals (Sweden)

Pogorelov Vadim

2017-01-01

Full Text Available The study presents the results of years of research in the field of quality management of industrial production construction production, based on mathematical modelling techniques, process and results of implementing the developed programme of monitoring and quality control in the production process of the enterprise. The aim of this work is the presentation of scientific community of the practical results of mathematical modelling in application programs. In the course of the research addressed the description of the applied mathematical models, views, practical results of its application in the applied field to assess quality control. The authors used this mathematical model in practice. The article presents the results of applying this model. The authors developed the experimental software management and quality assessment by using mathematical modeling methods. The authors continue research in this direction to improve the diagnostic systems and quality management systems based on mathematical modeling methods prognostic and diagnostic processes.

Mathematical modeling of rainwater runoff over catchment surface ...

African Journals Online (AJOL)

The subject of an article is the mathematical modeling of the rainwater runoff along the surface catchment taking account the transport of pollution which permeates into the water flow from a porous media of soil at the certain areas of this surface. The developed mathematical model consists of two types of equations: the ...

Developing Understanding of Mathematical Modeling in Secondary Teacher Preparation

Science.gov (United States)

Anhalt, Cynthia Oropesa; Cortez, Ricardo

2016-01-01

This study examines the evolution of 11 prospective teachers' understanding of mathematical modeling through the implementation of a modeling module within a curriculum course in a secondary teacher preparation program. While the prospective teachers had not previously taken a course on mathematical modeling, they will be expected to include…

Ethnophysics, Mathematical Modeling, Geometry... All in the same Manzuá

Directory of Open Access Journals (Sweden)

Ednilson Sergio Ramalho de Souza

2013-06-01

Full Text Available The objective this is paper is to show partial results of research for project of doctorate whose intention is to analyze the Ethnophysics of the amazon fisherman end to develop innovative didactic resources for the conceptual approach in Physics and Mathematics in the classroom of the high school and higher education in environment of Mathematical Modeling. The research question was: How the build the Manzuá can contextualize lessons of Physics and Mathematics in high school? The methodology used was ethnographicresearch. The theoretical foundations were Ethnomathematics (D’AMBROSIO, 2008, Mental Models (JONHSON-LAIRD, 1983, Mathematical Modeling (CHAVES e ESPÍRITO SANTO, 2008 end Conceptual Field ((VERGNAUD, 2007. The initial results suggest which the traditional physical knowledge is strongly related to mental models formed in function long years practice in the construction of the Manzuá end the operational invariants take part in the mental models. The situations lived during the construction of the Manzuá can base situations-problem in the classes of Physics and Mathematics in environment of Mathematical Modeling. We can, therefore, develop didactics resources that relate the traditional knowledge to the school knowledge

A mathematical model for iodine kinetics

International Nuclear Information System (INIS)

Silva, E.A.T. da.

1976-01-01

A mathematical model for the iodine kinetics in thyroid is presented followed by its analytical solution. An eletroanalogical model is also developed for a simplified stage and another is proposed for the main case [pt

Wastewater injection and slip triggering: Results from a 3D coupled reservoir/rate-and-state model

Science.gov (United States)

Babazadeh, M.; Olson, J. E.; Schultz, R.

2017-12-01

Seismicity induced by fluid injection is controlled by parameters related to injection conditions, reservoir properties, and fault frictional behavior. We present results from a combined model that brings together injection physics, reservoir dynamics, and fault physics to better explain the primary controls on induced seismicity. We created a 3D fluid flow simulator using the embedded discrete fracture technique and then coupled it with a 3D displacement discontinuity model that uses rate and state friction to model slip events. The model is composed of three layers, including the top-seal, the injection reservoir, and the basement. Permeability is anisotropic (vertical vs horizontal) and along with porosity varies by layer. Injection control can be either rate or pressure. Fault properties include size, 2D permeability, and frictional properties. Several suites of simulations were run to evaluate the relative importance of each of the factors from all three parameter groups. We find that the injection parameters interact with the reservoir parameters in the context of the fault physics and these relations change for different reservoir and fault characteristics, leading to the need to examine the injection parameters only within the context of a particular faulted reservoir. For a reservoir with no flow boundaries, low permeability (5 md), and a fault with high fault-parallel permeability and critical stress, injection rate exerts the strongest control on magnitude and frequency of earthquakes. However, for a higher permeability reservoir (80 md), injection volume becomes the more important factor. Fault permeability structure is a key factor in inducing earthquakes in basement rocks below the injection reservoir. The initial failure state of the fault, which is challenging to assess, can have a big effect on the size and timing of events. For a fault 2 MPa below critical state, we were able to induce a slip event, but it occurred late in the injection history

Mathematical Modelling of Unmanned Aerial Vehicles

Directory of Open Access Journals (Sweden)

Saeed Sarwar

2013-04-01

Full Text Available UAVs (Unmanned Arial Vehicleis UAVs are emerging as requirement of time and it is expected that in next five to ten years, complete air space will be flooded with UAVs, committed in varied assignments ranging from military, scientific and commercial usage. Non availability of human pilot inside UAV necessitates the requirement of an onboard autopilot in order to maintain desired flight profile against any unexpected disturbance and/or parameter variations. Design of such an autopilot requires an accurate mathematical model of UAV. The aim of this paper is to present a consolidated picture of UAV model. This paper first consolidates complete 6 DOF Degree of Freedom equations of motion into a nonlinear mathematical model and its simulation using model parameters of a real UAV. Model is then linearized into longitudinal and lateral modes. State space models of linearized modes are simulated and analyzed for stability parameters. The developed model can be used to design autopilot for UAV

Mathematical modelling of unmanned aerial vehicles

International Nuclear Information System (INIS)

Sarwar, S.; Rehman, S.U.

2013-01-01

UAVs (Unmanned Aerial Vehicles) UAVs are emerging as requirement of time and it is expected that in next five to ten years, complete air space will be flooded with UAVs, committed in varied assignments ranging from military, scientific and commercial usage. Non availability of human pilot inside UAV necessitates the requirement of an onboard auto pilot in order to maintain desired flight profile against any unexpected disturbance and/or parameter variations. Design of such an auto pilot requires an accurate mathematical model of UAV. The aim of this paper is to present a consolidated picture of UAV model. This paper first consolidates complete 6 DOF Degree of Freedom) equations of motion into a nonlinear mathematical model and its simulation using model parameters of a real UAV. Model is then linearized into longitudinal and lateral modes. State space models of linearized modes are simulated and analyzed for stability parameters. The developed model can be used to design auto pilot for UAV. (author)

Molecular modeling: An open invitation for applied mathematics

Science.gov (United States)

Mezey, Paul G.

2013-10-01

Molecular modeling methods provide a very wide range of challenges for innovative mathematical and computational techniques, where often high dimensionality, large sets of data, and complicated interrelations imply a multitude of iterative approximations. The physical and chemical basis of these methodologies involves quantum mechanics with several non-intuitive aspects, where classical interpretation and classical analogies are often misleading or outright wrong. Hence, instead of the everyday, common sense approaches which work so well in engineering, in molecular modeling one often needs to rely on rather abstract mathematical constraints and conditions, again emphasizing the high level of reliance on applied mathematics. Yet, the interdisciplinary aspects of the field of molecular modeling also generates some inertia and perhaps too conservative reliance on tried and tested methodologies, that is at least partially caused by the less than up-to-date involvement in the newest developments in applied mathematics. It is expected that as more applied mathematicians take up the challenge of employing the latest advances of their field in molecular modeling, important breakthroughs may follow. In this presentation some of the current challenges of molecular modeling are discussed.

Statistical modeling of geopressured geothermal reservoirs

Science.gov (United States)

Ansari, Esmail; Hughes, Richard; White, Christopher D.

2017-06-01

Identifying attractive candidate reservoirs for producing geothermal energy requires predictive models. In this work, inspectional analysis and statistical modeling are used to create simple predictive models for a line drive design. Inspectional analysis on the partial differential equations governing this design yields a minimum number of fifteen dimensionless groups required to describe the physics of the system. These dimensionless groups are explained and confirmed using models with similar dimensionless groups but different dimensional parameters. This study models dimensionless production temperature and thermal recovery factor as the responses of a numerical model. These responses are obtained by a Box-Behnken experimental design. An uncertainty plot is used to segment the dimensionless time and develop a model for each segment. The important dimensionless numbers for each segment of the dimensionless time are identified using the Boosting method. These selected numbers are used in the regression models. The developed models are reduced to have a minimum number of predictors and interactions. The reduced final models are then presented and assessed using testing runs. Finally, applications of these models are offered. The presented workflow is generic and can be used to translate the output of a numerical simulator into simple predictive models in other research areas involving numerical simulation.

Application of mathematical modeling in sustained release delivery systems.

Science.gov (United States)

Grassi, Mario; Grassi, Gabriele

2014-08-01

This review, presenting as starting point the concept of the mathematical modeling, is aimed at the physical and mathematical description of the most important mechanisms regulating drug delivery from matrix systems. The precise knowledge of the delivery mechanisms allows us to set up powerful mathematical models which, in turn, are essential for the design and optimization of appropriate drug delivery systems. The fundamental mechanisms for drug delivery from matrices are represented by drug diffusion, matrix swelling, matrix erosion, drug dissolution with possible recrystallization (e.g., as in the case of amorphous and nanocrystalline drugs), initial drug distribution inside the matrix, matrix geometry, matrix size distribution (in the case of spherical matrices of different diameter) and osmotic pressure. Depending on matrix characteristics, the above-reported variables may play a different role in drug delivery; thus the mathematical model needs to be built solely on the most relevant mechanisms of the particular matrix considered. Despite the somewhat diffident behavior of the industrial world, in the light of the most recent findings, we believe that mathematical modeling may have a tremendous potential impact in the pharmaceutical field. We do believe that mathematical modeling will be more and more important in the future especially in the light of the rapid advent of personalized medicine, a novel therapeutic approach intended to treat each single patient instead of the 'average' patient.

Reservoir Characterization using geostatistical and numerical modeling in GIS with noble gas geochemistry

Science.gov (United States)

Vasquez, D. A.; Swift, J. N.; Tan, S.; Darrah, T. H.

2013-12-01

The integration of precise geochemical analyses with quantitative engineering modeling into an interactive GIS system allows for a sophisticated and efficient method of reservoir engineering and characterization. Geographic Information Systems (GIS) is utilized as an advanced technique for oil field reservoir analysis by combining field engineering and geological/geochemical spatial datasets with the available systematic modeling and mapping methods to integrate the information into a spatially correlated first-hand approach in defining surface and subsurface characteristics. Three key methods of analysis include: 1) Geostatistical modeling to create a static and volumetric 3-dimensional representation of the geological body, 2) Numerical modeling to develop a dynamic and interactive 2-dimensional model of fluid flow across the reservoir and 3) Noble gas geochemistry to further define the physical conditions, components and history of the geologic system. Results thus far include using engineering algorithms for interpolating electrical well log properties across the field (spontaneous potential, resistivity) yielding a highly accurate and high-resolution 3D model of rock properties. Results so far also include using numerical finite difference methods (crank-nicholson) to solve for equations describing the distribution of pressure across field yielding a 2D simulation model of fluid flow across reservoir. Ongoing noble gas geochemistry results will also include determination of the source, thermal maturity and the extent/style of fluid migration (connectivity, continuity and directionality). Future work will include developing an inverse engineering algorithm to model for permeability, porosity and water saturation.This combination of new and efficient technological and analytical capabilities is geared to provide a better understanding of the field geology and hydrocarbon dynamics system with applications to determine the presence of hydrocarbon pay zones (or

Design and modeling of reservoir operation strategies for sediment management

NARCIS (Netherlands)

Sloff, C.J.; Omer, A.Y.A.; Heynert, K.V.; Mohamed, Y.A.

2015-01-01

Appropriate operation strategies that allow for sediment flushing and sluicing (sediment routing) can reduce rapid storage losses of (hydropower and water-supply) reservoirs. In this study we have shown, using field observations and computational models, that the efficiency of these operations

Developing an integrated 3D-hydrodynamic and emerging contaminant model for assessing water quality in a Yangtze Estuary Reservoir.

Science.gov (United States)

Xu, Cong; Zhang, Jingjie; Bi, Xiaowei; Xu, Zheng; He, Yiliang; Gin, Karina Yew-Hoong

2017-12-01

An integrated 3D-hydrodynamic and emerging contaminant model was developed for better understanding of the fate and transport of emerging contaminants in Qingcaosha Reservoir. The reservoir, which supplies drinking water for nearly half of Shanghai's population, is located in Yangtze Delta. The integrated model was built by Delft3D suite, a fully integrated multidimensional modeling software. Atrazine and Bisphenol A (BPA) were selected as two representative emerging contaminants for the study in this reservoir. The hydrodynamic model was calibrated and validated against observations from 2011 to 2015 while the integrated model was calibrated against observations from 2014 to 2015 and then applied to explore the potential risk of high atrazine concentrations in the reservoir driven by agriculture activities. Our results show that the model is capable of describing the spatial and temporal patterns of water temperature, salinity and the dynamic distributions of two representative emerging contaminants (i.e. atrazine and BPA) in the reservoir. The physical and biodegradation processes in this study were found to play a crucial role in determining the fate and transport of atrazine and BPA in the reservoir. The model also provides an insight into the potential risk of emerging contaminants and possible mitigation thresholds. The integrated approach can be a very useful tool to support policy-makers in the future management of Qingcaosha Reservoir. Copyright © 2017 Elsevier Ltd. All rights reserved.

Mathematical modeling for novel cancer drug discovery and development.

Science.gov (United States)

Zhang, Ping; Brusic, Vladimir

2014-10-01

Mathematical modeling enables: the in silico classification of cancers, the prediction of disease outcomes, optimization of therapy, identification of promising drug targets and prediction of resistance to anticancer drugs. In silico pre-screened drug targets can be validated by a small number of carefully selected experiments. This review discusses the basics of mathematical modeling in cancer drug discovery and development. The topics include in silico discovery of novel molecular drug targets, optimization of immunotherapies, personalized medicine and guiding preclinical and clinical trials. Breast cancer has been used to demonstrate the applications of mathematical modeling in cancer diagnostics, the identification of high-risk population, cancer screening strategies, prediction of tumor growth and guiding cancer treatment. Mathematical models are the key components of the toolkit used in the fight against cancer. The combinatorial complexity of new drugs discovery is enormous, making systematic drug discovery, by experimentation, alone difficult if not impossible. The biggest challenges include seamless integration of growing data, information and knowledge, and making them available for a multiplicity of analyses. Mathematical models are essential for bringing cancer drug discovery into the era of Omics, Big Data and personalized medicine.

The use of mathematical models in teaching wastewater treatment engineering

DEFF Research Database (Denmark)

Morgenroth, Eberhard Friedrich; Arvin, Erik; Vanrolleghem, P.

2002-01-01

Mathematical modeling of wastewater treatment processes has become increasingly popular in recent years. To prepare students for their future careers, environmental engineering education should provide students with sufficient background and experiences to understand and apply mathematical models...... efficiently and responsibly. Approaches for introducing mathematical modeling into courses on wastewater treatment engineering are discussed depending on the learning objectives, level of the course and the time available....

Mathematical modeling of swirled flows in industrial applications

Science.gov (United States)

Dekterev, A. A.; Gavrilov, A. A.; Sentyabov, A. V.

2018-03-01

Swirled flows are widely used in technological devices. Swirling flows are characterized by a wide range of flow regimes. 3D mathematical modeling of flows is widely used in research and design. For correct mathematical modeling of such a flow, it is necessary to use turbulence models, which take into account important features of the flow. Based on the experience of computational modeling of a wide class of problems with swirling flows, recommendations on the use of turbulence models for calculating the applied problems are proposed.

A mathematical model for postirradiation immunity

International Nuclear Information System (INIS)

Smirnova, O.A.

1988-01-01

A mathematical model of autoimmune processes in exposed mammals was developed. In terms of this model a study was made of the dependence of the autoimmunity kinetics on radiation dose and radiosensitivity of autologous tissues. The model simulates the experimentally observed dynamics of autoimmune diseases

Mathematical modelling of anisotropy of illite-rich shale

Science.gov (United States)

Chesnokov, E.M.; Tiwary, D.K.; Bayuk, I.O.; Sparkman, M.A.; Brown, R.L.

2009-01-01

The estimation of illite-rich shale anisotropy to account for the alignment of clays and gas- or brine-filled cracks is presented via mathematical modelling. Such estimation requires analysis to interpret the dominance of one effect over another. This knowledge can help to evaluate the permeability in the unconventional reservoir, stress orientation, and the seal capacity for the conventional reservoir. Effective media modelling is used to predict the elastic properties of the illite-rich shale and to identify the dominant contributions to the shale anisotropy. We consider two principal reasons of the shale anisotropy: orientation of clay platelets and orientation of fluid-filled cracks. In reality, both of these two factors affect the shale anisotropy. The goal of this study is, first, to separately analyse the effect of these two factors to reveal the specific features in P- and S-wave velocity behaviour typical of each of the factors, and, then, consider a combined effect of the factors when the cracks are horizontally or vertically aligned. To do this, we construct four models of shale. The behaviour of P- and S-wave velocities is analysed when gas- and water-filled cracks embedded in a host matrix are randomly oriented, or horizontally or vertically aligned. The host matrix can be either isotropic or anisotropic (of VTI symmetry). In such a modelling, we use published data on mineralogy and clay platelet alignment along with other micromechanical measurements. In the model, where the host matrix is isotropic, the presence of a singularity point (when the difference VS1 - VS2 changes its sign) in shear wave velocities is an indicator of brine-filled aligned cracks. In the model with the VTI host matrix and horizontally aligned cracks filled with gas, an increase in their volume concentration leads to that the azimuth at which the singularity is observed moves toward the symmetry axis. In this case, if the clay content is small (around 20 per cent), the

Study on detailed geological modelling for fluvial sandstone reservoir in Daqing oil field

Energy Technology Data Exchange (ETDEWEB)

Zhao Hanqing; Fu Zhiguo; Lu Xiaoguang [Institute of Petroleum Exploration and Development, Daqing (China)

1997-08-01

Guided by the sedimentation theory and knowledge of modern and ancient fluvial deposition and utilizing the abundant information of sedimentary series, microfacies type and petrophysical parameters from well logging curves of close spaced thousands of wells located in a large area. A new method for establishing detailed sedimentation and permeability distribution models for fluvial reservoirs have been developed successfully. This study aimed at the geometry and internal architecture of sandbodies, in accordance to their hierarchical levels of heterogeneity and building up sedimentation and permeability distribution models of fluvial reservoirs, describing the reservoir heterogeneity on the light of the river sedimentary rules. The results and methods obtained in outcrop and modem sedimentation studies have successfully supported the study. Taking advantage of this method, the major producing layers (PI{sub 1-2}), which have been considered as heterogeneous and thick fluvial reservoirs extending widely in lateral are researched in detail. These layers are subdivided into single sedimentary units vertically and the microfacies are identified horizontally. Furthermore, a complex system is recognized according to their hierarchical levels from large to small, meander belt, single channel sandbody, meander scroll, point bar, and lateral accretion bodies of point bar. The achieved results improved the description of areal distribution of point bar sandbodies, provide an accurate and detailed framework model for establishing high resolution predicting model. By using geostatistic technique, it also plays an important role in searching for enriched zone of residual oil distribution.

Modelling and applications in mathematics education the 14th ICMI study

CERN Document Server

Galbraith, Peter L; Niss, Mogens

2007-01-01

The book aims at showing the state-of-the-art in the field of modeling and applications in mathematics education. This is the first volume to do this. The book deals with the question of how key competencies of applications and modeling at the heart of mathematical literacy may be developed; with the roles that applications and modeling may play in mathematics teaching, making mathematics more relevant for students.

Hybrid modelling framework by using mathematics-based and information-based methods

International Nuclear Information System (INIS)

Ghaboussi, J; Kim, J; Elnashai, A

2010-01-01

Mathematics-based computational mechanics involves idealization in going from the observed behaviour of a system into mathematical equations representing the underlying mechanics of that behaviour. Idealization may lead mathematical models that exclude certain aspects of the complex behaviour that may be significant. An alternative approach is data-centric modelling that constitutes a fundamental shift from mathematical equations to data that contain the required information about the underlying mechanics. However, purely data-centric methods often fail for infrequent events and large state changes. In this article, a new hybrid modelling framework is proposed to improve accuracy in simulation of real-world systems. In the hybrid framework, a mathematical model is complemented by information-based components. The role of informational components is to model aspects which the mathematical model leaves out. The missing aspects are extracted and identified through Autoprogressive Algorithms. The proposed hybrid modelling framework has a wide range of potential applications for natural and engineered systems. The potential of the hybrid methodology is illustrated through modelling highly pinched hysteretic behaviour of beam-to-column connections in steel frames.

Mathematics of epidemics on networks from exact to approximate models

CERN Document Server

Kiss, István Z; Simon, Péter L

2017-01-01

This textbook provides an exciting new addition to the area of network science featuring a stronger and more methodical link of models to their mathematical origin and explains how these relate to each other with special focus on epidemic spread on networks. The content of the book is at the interface of graph theory, stochastic processes and dynamical systems. The authors set out to make a significant contribution to closing the gap between model development and the supporting mathematics. This is done by: Summarising and presenting the state-of-the-art in modeling epidemics on networks with results and readily usable models signposted throughout the book; Presenting different mathematical approaches to formulate exact and solvable models; Identifying the concrete links between approximate models and their rigorous mathematical representation; Presenting a model hierarchy and clearly highlighting the links between model assumptions and model complexity; Providing a reference source for advanced undergraduate...

Mathematical models of natural gas consumption

International Nuclear Information System (INIS)

Sabo, Kristian; Scitovski, Rudolf; Vazler, Ivan; Zekic-Susac, Marijana

2011-01-01

In this paper we consider the problem of natural gas consumption hourly forecast on the basis of hourly movement of temperature and natural gas consumption in the preceding period. There are various methods and approaches for solving this problem in the literature. Some mathematical models with linear and nonlinear model functions relating to natural gas consumption forecast with the past natural gas consumption data, temperature data and temperature forecast data are mentioned. The methods are tested on concrete examples referring to temperature and natural gas consumption for the area of the city of Osijek (Croatia) from the beginning of the year 2008. The results show that most acceptable forecast is provided by mathematical models in which natural gas consumption and temperature are related explicitly.

Mathematical modeling in wound healing, bone regeneration and tissue engineering.