Stochastic Finite Element Analysis for Multiphase Flow in Heterogeneous Porous Media

Transport in Porous Media

Volumn 32, Issue 3, 1998, Pages 239-262

  Ghanem, R ^a   Dham, S ^a  

^a Johns Hopkins University   (United States)

Author keywords

Mathematical model; Multiphase flow; Stochastic media

Indexed keywords

DIFFERENTIAL EQUATIONS; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; POROUS MATERIALS; PROBABILITY; RANDOM PROCESSES; SATURATION (MATERIALS COMPOSITION); TWO DIMENSIONAL;

KARHUNEN-LOEVE EXPANSION; RANDOM VARIABLES; RELATIVE PERMEABILITIES;

MULTIPHASE FLOW;

AQUIFER; MULTIPHASE FLOW; POROUS MEDIUM;

EID: 0032173318     PISSN: 01693913     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1006514109327     Document Type: Article

References (26)

1. Adler, P. M.: Transport in materials with fractal microstructure, in: J. P. Lamb (ed), Proc. 10th U.S. National Congress of Applied Mechanics, ASME, 1986, pp. 141-143.
2. Allen, M. B., Behie, G. A. and Trangenstein, J. A.: 1998, Multiphase Flow in Porous Media, Springer-Verlag, New York.
3. Baker, L. E.: 1995, Three-phase relative permeability of water-wet, intermediate-wet and oil-wet sandstone, in: H. J. de Haan (ed.), New Developments in Improved Oil Recovery, The Geological Society, London, pp. 51-60.
4. Bear, J.: 1972, Dynamics of Fluids in Porous Media, Dover.
5. Cameron, R. H. and Martin, W. T.: 1947, The orthogonal development of nonlinear functionals in series of Fourier-Hermite functional, Ann. Math. 48, 385-392.
6. Chavent, G. and Jaffre, J.: 1986, Mathematical Models and Finite Elements for Reservoir Simulation, North-Holland, Amsterdam, New York, Oxford, Tokyo.
7. Cushman, J. H.: 1984, On unifying the concepts of scale, instrumentation, and stochastics in the development of multiphase transport theory, Water Resour. Res. 20(11), 1668-1676.
8. Ghanem, R. and Spanos, P.: 1991, Stochastic Finite Elements: A Spectral Approach, Springer Verlag, New York.
9. Ghanem, R. and Kruger, R.: 1996a, Numerical solution of spectral stochastic finite element systems, Computer Meth. Appl. Mech. Engng. 129, 289-303.
10. Ghanem, R. and Brzkala, V.: 1996b Stochastic finite element analysis for randomly layered media, ASCE J. Engng. Mech. 122(4), 361-369.
11. Ghanem, R.: 1997, Hybrid stochastic finite elements: coupling of spectral expansions with Monte Carlo simulations. J. Appl. Mech. (to appear).
12. Ghanem, R.: The nonlinear Gaussian spectrum of log-normal stochastic processes and variables, ASME J. Appl. Mech. (submitted for review).
13. Glimm, J., Lindquist, B., McBryan, O. and Padmanabhan, L.: 1983, A front tracking reservoir simulator, five-spot validation studies and the water coning problem, in: R. Ewing (ed.), The Mathematics of Reservoir Simulation, SIAM, Philadelphia.
14. Kallianpur, G.: 1980, Stochastic Filtering Theory, Springer-Verlag, Berlin.
15. Kemblowski, M. W. and Wen, J.-C.: 1993, Contaminant spreading in stratified soils with fractal permeability. Water Resour. Res. 29(2), 419-425.
16. Kueper, B. H. and Frind, E. O.: 1991, Two-phase flow in heterogeneous porous-media: I. Model development, Water Resour. Res. 27, 1059.
17. Li, R. and Ghanem, R.: Adaptive polynomial chaos simulation applied to statistics of extremes in nonlinear random vibration, Probab. Engng. Mech. (to appear).
18. Loeve, M.: 1977, Probability Theory, 4th ed., Springer-Verlag, New York.
19. Muskat, M.: 1949, Physical Principles of Oil Production, McGraw-Hill, New York, Toronto, London.
20. Russell, T. F. and Wheeler, M. F.: 1983, Finite element and finite difference methods for continuous flows in porous media, in: R. E. Ewing (ed.), The Mathematics of Reservoir Simulation, SIAM, Philadelphia, pp. 35-106.
21. Sagar, B.: 1997, Galerkin finite element procedure for analyzing flow through random media, Water Resour. Res. 14(6), 1035-1044.
22. Spanos, P. D. and Ghanem, R.: 1989, Stochastic finite element expansion for random media, J. Engng. Mech. Div., ASCE 115(5), 1035-1053.
23. Spanos, P. D. and Ghanem, R.: 1991, Boundary element formulation for random vibration problems, J. Engng. Mech. Div., ASCE 117(409-423), 1035-1053.
24. Sposito, G., Jury, W. and Gupta V. K.: 1986, Fundamental problems in the stochastic convection-dispersion model of solute transport in aquifers and field soils, Water Resour. Res. 22(1), 77-88.
25. "State-of-the-art review on computational stochastic mechanics", prepared by the Sub-Committee on Computational Stochastic Mechanics, IASSAR, Probab. Engng. Mechanics, 1997 (to appear).
26. Wiener, N.: 1938, The homogeneous chaos, Amer. J. Math. 60, 897-936.