Ebook: Mathematical Modeling for Flow and Transport Through Porous Media

The main aim of this paper is to present some new and general results, ap­ plicable to the the equations of two phase flow, as formulated in geothermal reservoir engineering. Two phase regions are important in many geothermal reservoirs, especially at depths of order several hundred metres, where ris­ ing, essentially isothermal single phase liquid first begins to boil. The fluid then continues to rise, with its temperature and pressure closely following the saturation (boiling) curve appropriate to the fluid composition. Perhaps the two most interesting theoretical aspects of the (idealised) two phase flow equations in geothermal reservoir engineering are that firstly, only one component (water) is involved; and secondly, that the densities of the two phases are so different. This has led to the approximation of ignoring capillary pressure. The main aim of this paper is to analyse some of the consequences of this assumption, especially in relation to saturation changes within a uniform porous medium. A general analytic treatment of three dimensional flow is considered. Pre­ viously, three dimensional modelling in geothermal reservoirs have relied on numerical simulators. In contrast, most of the past analytic work has been restricted to one dimensional examples.

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This book contains a selection of articles presented at an International Workshop on `Mathematical Modeling for Flow and Transport Through Porous Media'.
The major topics of the meeting were free and moving boundary problems, structured media, multiphase flow, scale problems, stochastic aspects, parameter identification and optimization problems. The volume also represents a few contributions on the incorporation of chemical and biological processes in mathematical models for transport in porous media.
The book is directed at researchers active in porous media, mathematical modeling, petroleum and geotechnical engineering and environmental sciences.

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This book contains a selection of articles presented at an International Workshop on `Mathematical Modeling for Flow and Transport Through Porous Media'.
The major topics of the meeting were free and moving boundary problems, structured media, multiphase flow, scale problems, stochastic aspects, parameter identification and optimization problems. The volume also represents a few contributions on the incorporation of chemical and biological processes in mathematical models for transport in porous media.
The book is directed at researchers active in porous media, mathematical modeling, petroleum and geotechnical engineering and environmental sciences.
Content:
Front Matter....Pages i-iii
International Workshop on Mathematical Modeling for Flow and Transport Through Porous Media....Pages 473-473
International Workshop on Mathematical Modeling for Flow and Transport Through Porous Media....Pages 475-477
Simulation of Multiphase Flows in Porous Media....Pages 479-499
Geometric properties of two phase flow in geothermal reservoirs....Pages 501-517
Numerical Simulation and Homogenization of Two-Phase Flow in Heterogeneous Porous Media....Pages 519-547
A Limit Form of the Equations for Immiscible Displacement in a Fractured Reservoir....Pages 549-565
Diffusion Models with Microstructure....Pages 567-580
Characterization of Porous Media — Pore Level....Pages 581-606
Scaling Mixing during Miscible Displacement in Heterogeneous Porous Media....Pages 607-626
Fixed Domain Methods for Free and Moving Boundary Flows in Porous Media....Pages 627-649
Qualitative Mathematical Analysis of the Richards Equation....Pages 651-666
Modeling of In-Situ Biorestoration of Organic Compounds in Groundwater....Pages 667-702
Reaction Kinetics and Transport in Soil: Compatibility and Differences between Some Simple Models....Pages 703-737
A Perturbation Solution for Nonlinear Solute Transport in Porous Media....Pages 739-744
Trace Type Functional Differential Equations and the Identification of Hydraulic Properties of Porous Media....Pages 745-758
Parameter Identification in a Soil with Constant Diffusivity....Pages 759-769

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This book contains a selection of articles presented at an International Workshop on `Mathematical Modeling for Flow and Transport Through Porous Media'.
The major topics of the meeting were free and moving boundary problems, structured media, multiphase flow, scale problems, stochastic aspects, parameter identification and optimization problems. The volume also represents a few contributions on the incorporation of chemical and biological processes in mathematical models for transport in porous media.
The book is directed at researchers active in porous media, mathematical modeling, petroleum and geotechnical engineering and environmental sciences.
Content:
Front Matter....Pages i-iii
International Workshop on Mathematical Modeling for Flow and Transport Through Porous Media....Pages 473-473
International Workshop on Mathematical Modeling for Flow and Transport Through Porous Media....Pages 475-477
Simulation of Multiphase Flows in Porous Media....Pages 479-499
Geometric properties of two phase flow in geothermal reservoirs....Pages 501-517
Numerical Simulation and Homogenization of Two-Phase Flow in Heterogeneous Porous Media....Pages 519-547
A Limit Form of the Equations for Immiscible Displacement in a Fractured Reservoir....Pages 549-565
Diffusion Models with Microstructure....Pages 567-580
Characterization of Porous Media — Pore Level....Pages 581-606
Scaling Mixing during Miscible Displacement in Heterogeneous Porous Media....Pages 607-626
Fixed Domain Methods for Free and Moving Boundary Flows in Porous Media....Pages 627-649
Qualitative Mathematical Analysis of the Richards Equation....Pages 651-666
Modeling of In-Situ Biorestoration of Organic Compounds in Groundwater....Pages 667-702
Reaction Kinetics and Transport in Soil: Compatibility and Differences between Some Simple Models....Pages 703-737
A Perturbation Solution for Nonlinear Solute Transport in Porous Media....Pages 739-744
Trace Type Functional Differential Equations and the Identification of Hydraulic Properties of Porous Media....Pages 745-758
Parameter Identification in a Soil with Constant Diffusivity....Pages 759-769
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