Mathematical Modeling, Numerical Techniques, and Computer Simulation of Flows and Transport in Porous Media (original) (raw)

Abstract

this paper we present a variety of models in groundwater hydrology that have been used in computer simulation for design of remediation and clean-up technologies. We also discuss the important question of the choice of the approximation method for the corresponding mathematical problem. In fluid reservoirs (aquifer and petroleum reservoirs) there are two imperative practical requirements: the method should conserve the mass locally and should produce accurate velocities (fluxes) even for highly nonhomogeneous media with large jumps in the physical properties. This is the reason that the finite volume method with harmonic averaging of the coefficients has been very popular and successful in computer simulation of flows in porous media. However, when the problem requires accurate description of the topography and the hydrological structure, a more general technique based on the finite element approximation is needed. The mixed finite element method has these properties. Since its intr...

Key takeaways

sparkles

AI

  1. The paper presents models for groundwater hydrology used in remediation technology simulations.
  2. Finite volume method with harmonic averaging is crucial for accurate flow simulation in porous media.
  3. Mixed finite element method accurately models complex topography and hydrological structures.
  4. Numerical simulations demonstrate contaminant transport dynamics influenced by geometry and medium properties.
  5. The study utilizes a 136x128x10 grid on a 56-processor Intel Paragon for 15-year simulations.

Loading...

Loading Preview

Sorry, preview is currently unavailable. You can download the paper by clicking the button above.

References (27)

  1. Allen, M., Behie, G., and Trangenstein, G., Multiphase Flows in Porous Media, Lecture Notes in Engineering, editors S. Brebia and S. Orszag, Springer-Verlag, 1992.
  2. Bear, J., Dynamics of Fluids in Porous Media, Dover Publications, Inc., 1988.
  3. Binning, P., Modeling Unsaturated Zone Flow and Contaminant Transport in the Air and Water Phases, PhD thesis, Princeton University, 1994.
  4. Bramble, J. and Pasciak, J., A Preconditioning Technique for Inde nite Systems Re- sulting from Mixed Approximations of Elliptic Problems, Math. Comp., 50, 1988, 1-18.
  5. Bramble, J., Pasciak, J., and Vassilev, A., Analysis of the Inexact Uzawa Algorithm for Saddle Point Problems, Technical Report ISC{94{09{MATH, Institute for Scienti c Computation, Texas A& M University, 1994.
  6. Bramble, J., Pasciak, J., Wang, J., and Xu, J., Convergence Estimates for Product Iterative Methods with Applications to Domain Decomposition, Math. Comp., 57, 1991, 1{21.
  7. Brezzi, F. and Fortin, M., Mixed and Hybrid Finite Element Methods, Springer-Verlag, New York, 1991.
  8. Celia, M. and Binning, P., Two-phase unsaturated ow: one dimensional simulation and air phase velocities, Water Resources Research, 28, 1992, 2819-2828.
  9. Celia, M., Russell, T., Herrera, I., and Ewing, R., An Eulerian-Lagrangian Localized Adjoint Method for Advection Di usion Equation, Advances in Water Resources, 13, 1990, 187{206.
  10. Chavent, G. and Ja re J., Mathematical Models and Finite Elements for Reservoir Simulation: Single Phase, Multiphase and Multicomponent Flows Through Porous Me- dia, North-Holland, Amsterdam, 1986.
  11. Chen, Z., Espedal, M., and Ewing, R., Continuous-time Finite Element Analysis of Multiphase Flow in Groundwater Hydrology, Technical Report ISC{94{11{MATH, Institute for Scienti c Computation, Texas A& M University, 1994.
  12. Cowsar, L., Mandel, J., and Wheeler, M., Balancing Domain Decomposition for Mixed Finite Elements, Math. Comp., (to appear).
  13. Douglas, J. Jr. and Russell, T., Numerical Methods for Convection-Dominated Di u- sion Problems Based on Combining the Method of Characteristics with Finite Element or Finite Di erence Procedures, SIAM J. Numer. Anal., 19, 1982, 871{885.
  14. Elman, H., Multigrid and Krylov Subspace Methods for the Discrete Stokes Equations, Proc. Copper Mountain Conference on Multigrid Methods, 1995.
  15. Espedal, M. and Ewing, R., Characteristic Petrov-Galerkin Subdomain Methods for Two-Phase Immiscible Flow, Comp. Meth. Appl. Mech. and Eng., 64, 1987, 113{135.
  16. Ewing, R., Russell, T., and Wheeler, M., Convergence Analysis of an Approximation of Miscible Displacement in Porous Media by Mixed Finite Elements and a Modi ed Method of Characteristics, Computer Methods in Applied Mechanics and Engineering, 47, 1984, 73{92.
  17. Ewing, R.E. and Wheeler, M.F., Computational Aspects of Mixed Finite Element Methods, Numerical Methods for Scienti c Computing (R. Steelman, ed.), 1983, 163{ 172, North-Holland, Amsterdam.
  18. Ja re, J., Flux calculations at the Interface Between Two Rock Types for Two-Phase Flow in Porous Media, Preprint 2075, INRIA, 1994.
  19. Hittel, D., Fundamentals of Soil Physics, Academic Press, 1980.
  20. Krauskopf, K., Radioactive Waste Disposal Geology, Chapman & Hill, London, 1988.
  21. Marr, R., Pasciak, J., and R. Peierls, R., IPX { Preemptive Remote Procedure Execu- tion for Concurrent Applications, Brookhaven National Laboratory, 1994.
  22. Nedelec, J., Mixed Finite Elements in R 3 , Numer. Math., 35, 1980, 315{341.
  23. Raviart, R. and Thomas, J.M., A Mixed Finite Element Method for Second Order Elliptic Problems, Mathematical Aspect of the Finite Element Method. Lecture Notes Math., 606, 1977, 292-315.
  24. Rusten, T. and Winther, R., A Preconditioned Iterative Method for Saddle Point Problems, SIAM J. Matrix Anal. Appl., 13, 1992, 887{904.
  25. van Genuchten, M., A Closed Form Equation for predicting the Hydraulic Conductivity in Soils, Soils, Soil Sci. Soc. Am. J., 44, 1980, 892{898.
  26. Williams, M., Stochastic Problems in the Transport of Radioactive Nuclides in Frac- tured Rock, Nuclear Sci. Eng. 112, 1992, 215{230.
  27. Young, L. and Stephenson, R., A generalized compositional approach for reservoir simulation, SPE Paper 10516, 1983, 727{742.