Mathematical Modeling for Flow and Transport Through Porous Media

1. Front Matter

   Pages i-iii

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2. International Workshop on Mathematical Modeling for Flow and Transport Through Porous Media

   • Gedeon Dagan, Ulrich Hornung, Peter Knabner

   Pages 473-473

3. International Workshop on Mathematical Modeling for Flow and Transport Through Porous Media

   • Gedeon Dagan, Ulrich Hornung, Peter Knabner

   Pages 475-477

4. Simulation of Multiphase Flows in Porous Media

   • Richard E. Ewing

   Pages 479-499

5. Geometric properties of two phase flow in geothermal reservoirs

   • Graham J. Weir

   Pages 501-517

6. Numerical Simulation and Homogenization of Two-Phase Flow in Heterogeneous Porous Media

   • Brahim Amaziane, Alain Bourgeat, Joe Koebbe

   Pages 519-547

7. A Limit Form of the Equations for Immiscible Displacement in a Fractured Reservoir

   • Jim Douglas Jr., Paulo Jorge Paes-Leme, Jeffrey L. Hensley

   Pages 549-565

8. Diffusion Models with Microstructure

   • R. E. Showalter

   Pages 567-580

9. Characterization of Porous Media — Pore Level

   • F. A. L. Dullien

   Pages 581-606

10. Scaling Mixing during Miscible Displacement in Heterogeneous Porous Media

    • Robert A. Greenkorn, John S. Haselow

    Pages 607-626

11. Fixed Domain Methods for Free and Moving Boundary Flows in Porous Media

    • J. C. Bruch Jr.

    Pages 627-649

12. Qualitative Mathematical Analysis of the Richards Equation

    • B. H. Gilding

    Pages 651-666

13. Modeling of In-Situ Biorestoration of Organic Compounds in Groundwater

    • Chen Y. Chiang, Clint N. Dawson, Mary F. Wheeler

    Pages 667-702

14. Reaction Kinetics and Transport in Soil: Compatibility and Differences between Some Simple Models

    • Sjoerd E. A. T. M. van der Zee

    Pages 703-737

15. A Perturbation Solution for Nonlinear Solute Transport in Porous Media

    • D. O. Lomen, A. L. Islas, X. Fan, A. W. Warrick

    Pages 739-744

16. Trace Type Functional Differential Equations and the Identification of Hydraulic Properties of Porous Media

    • J. R. Cannon, Paul DuChateau, Ken Steube

    Pages 745-758

17. Parameter Identification in a Soil with Constant Diffusivity

    • David Zachmann, Ian White

    Pages 759-769

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.

• Simulation
• calculus
• geotechnical engineering
• mathematical modeling
• modeling
• multiphase flow
• optimization
• porous media
• fluid- and aerodynamics

• Tel Aviv, Israel

  Gedeon Dagan

• Neubiberg, Germany

  Ulrich Hornung

• Augsburg, Germany

  Peter Knabner

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