A semi-analytical solution for a two-dimensional capacitance model in solute transport

Journal of Petroleum Science and Engineering

Volumn 22, Issue 4, 1999, Pages 275-295

  Bai, M ^a   Shu, Z ^a   Cao, J ^a   Zaman, M ^a   Roegiers, J C ^a  

^a UNIVERSITY OF OKLAHOMA   (United States)

Author keywords

Capacitance model; Heterogeneous media; Solute transport

Indexed keywords

SEMI ANALYTICAL SOLUTION; SOLUTE TRANSPORT; TWO DIMENSIONAL CAPACITANCE MODEL;

LAPLACE TRANSFORMS; MATHEMATICAL MODELS; ONE DIMENSIONAL; POROUS MATERIALS; PROBLEM SOLVING; TWO DIMENSIONAL;

TRANSPORT PROPERTIES;

HETEROGENEOUS MEDIUM; MASS TRANSFER; MATHEMATICAL MODELING; POROUS MEDIUM; SOLUTE TRANSPORT;

HETEROGENEOUS MEDIUM; MASS TRANSFER; NUMERICAL MODEL; POROUS MEDIUM; SOLUTE TRANSPORT;

EID: 0033084157     PISSN: 09204105     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0920-4105(98)00089-8     Document Type: Article

References (32)

1. Aifantis E.C., Beskos D.E. Heat extraction from hot fry rock. Mech. Res. Comm. 7:1980;165-170.
2. Arbogast, T., Douglas, J.R., Hornung, U., 1990. Derivation of the double porosity model of single phase flow via homogenization theory. SIAM J. Math. Anal., 823-836.
3. Atkin R.J., Craine R.E. Continuum theories of mixtures: basic theory and historical development. Q. J. Mech. Appl. Math. 29:1976;209-244.
4. Auriault J.-L. Effective macroscopic description for heat conduction in periodic composite. Int. J. Heat Mass Transfer. 26:1983;861-869.
5. Auriault J.-L., Lewandowska J. Non-Gaussian diffusion modeling in composite porous media by homogenization: tail effect. Transport in Porous Media. 21:1995;47-70.
6. Bai M., Bouhroum A., Civan F., Roegiers J.-C. Improved model of solute transport in heterogeneous porous media. J. Petroleum Sci. Eng. 14:1995;65-78.
7. Baker L.E. Effects of dispersion and dead-end pore volume in miscible flooding. Soc. Pet. Eng. J. 17:1977;219-227.
8. Batycky J.P., Maini B.B., Fisher D.B. Simulation of miscible displacement in full-diameter carbonate cores. Soc. Pet. Eng. J. 22:1982;647-657.
9. Bouhroum A., Bai M. Experimental and numerical simulation of solute transport in heterogeneous porous media. Int. J. Num. Anal. Meth. Geomech. 20:1996;155-171.
10. Bretz R.E., Orr F.M. Jr. Interpretation of miscible displacements in laboratory cores. SPE Reser. Eng. 2:1987;492-500.
11. Bretz, R.E., Specter, R.M., Orr, F.M. Jr., 1986. Effect of pore structure on miscible displacements in laboratory cores. SPE 15017, Proc. Permian Basin Oil and Gas Recor., Midland, TX, pp. 263-278.
12. Coats K.H., Smith B.D. Dead-end pore volume and dispersion in porous media. SPEJ. 4:1964;73-84.
13. Correa A.C., Pande K.K., Ramey H.J., Brigham W.E. Computation and interpretation of miscible displacement performance in heterogeneous porous media. SPE Reser. Eng. 5:1990;69-78.
14. Crochet M.J., Naghdi P.M. On constitutive equations for flow of fluid through an elastic solid. Int. J. Eng. Sci. 4:1966;383-401.
15. Deans H.A. A mathematical model for dispersion in the direction of flow in porous media. J. Soc. Pet. Eng. 3:1963;49-52.
16. Goltz M.N., Roberts P.V. Using method of moments to analyze three-dimensional diffusion-limited solute transport from temporal and spatial perspectives. Water Resour. Res. 23:1987;1575-1585.
17. Goode D.J., Konikow L.F. Apparent dispersion in transient groundwater flow. Water Resour. Res. 26:1991;2339-2351.
18. Gwo J.P., Jardine P.M., Wilson G.V., Yeh G.T. A multiple-pore-region concept to modeling mass transfer in subsurface media. J. Hydrology. 164:1995;217-237.
19. Johns R.A., Roberts P.V. A solute transport model for channelized flow in a fracture. Water Resour. Res. 27:1991;1797-1808.
20. Lapidus, L., Pinder, G.F., 1982. Numerical solution of partial differential equations in science and engineering. Wiley, New York, 677 pp.
21. Mannhardt K., Nasr-El-Din H.A. A review of one-dimensional convection-dispersion models and their applications to miscible displacement in porous media. In Situ. 18:1994;277-345.
22. Patel K.M., Greaves M. Surfactant dispersion in porous media. Chem. Eng. Res. Des. 65:1987;12-22.
23. Ramirez W.F., Shuler P.J., Friedman F. Convection, dispersion, and adsorption of surfactants in porous media. J. Soc. Pet. Eng. 20:1980;430-438.
24. Salter, S.J., Mohanty, K.K., 1982. Multiphase flow in porous media: I. Macroscopic observations and modeling. SPE 11017, presented at the Pet. Eng. Annual Tech. Conf. and Exhib., New Orleans, LA, pp. 26-29.
25. Shearn, R.B., Wakeman, R.J., 1978. Theoretical mass transfer models for assessing tertiary recovery by miscible fluid displacement. Presented at the European Symp. on EOR, Edinburgh, UK, pp. 253-269.
26. Skopp J., Gardner W.R., Taylor E.J. Solute movement in structured soils: two-region model with small interaction. Soil Sci. Soc. Am. J. 45:1981;837-842.
27. Sorbie, K.S., Parker, A., Clifford, P.J., 1985. Experimental and theoretical study of polymer flow in porous media. SPE 14231, presented at the Pet. Eng. Annual Tech. Conf. and Exhib., Las Vegas, NV, pp. 22-25.
28. Spence, A.P. Jr., Watkins, R.W., 1980. The effect of microscopic core heterogeneity on miscible flood residual oil saturation. SPE 9229, presented at the Pet. Eng. Annual Tech. Conf. and Exhib., Dallas, TX, pp. 21-24.
29. Stalkup F.I. Displacement of oil by solvent at high water saturation. Soc. Pet. Eng. J. 10:1970;337-348.
30. Stehfest H. Numerical inversion of Laplace transforms algorithm 368. Commun. Assoc. Comput. Mach. 13:1970;47-49.
31. van Genuchten M.Th., Wierenga P.J. Mass transfer studies in sorbing porous media: I. Analytical solutions. Soil Sci. Soc. Am. J. 40:1976;473-480.
32. Warren J.E., Root P.J. The behavior of naturally fractured reservoirs. J. Soc. Pet. Eng. 3:1963;245-255.