Effects of Relative Permeability History Dependence on Two-Phase Flow in Porous Media

Transport in Porous Media

Volumn 28, Issue 2, 1997, Pages 181-203

  Furati, Khaled M ^a  

^a KING FAHD UNIVERSITY OF PETROLEUM AND MINERALS   (Saudi Arabia)

Author keywords

Conservation law; Flow prediction; Fractional flow; History; Hysteresis; Immiscible displacement; Modelling; Relative permeability; Riemann problem; Two phase flow

Indexed keywords

HYSTERESIS; MATHEMATICAL MODELS; MECHANICAL PERMEABILITY; POROUS MATERIALS; SATURATION (MATERIALS COMPOSITION); SOLUBILITY;

FRACTIONAL FLOW; NONDIFFUSIVE FLOW; RIEMANN PROBLEM;

TWO PHASE FLOW;

PERMEABILITY; POROUS MEDIUM; TWO-PHASE FLOW;

HYSTERESIS; MODEL; MULTIPHASE FLOW; PERMEABILITY; POROUS MEDIUM; TWO PHASE FLOW;

EID: 0031201013     PISSN: 01693913     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1006556018950     Document Type: Article

References (32)

1. Amaefule, H. O., and Handy, L. L., 1982: The effect of interfacial tension on relative oil/water permabilities of consolidated porous media, Soc. Petrol. Engrs. J. 371-381.
2. Barenblatt, G. I., Entov, V. M. and Ryzhik, V. M., 1990: Theory of Fluid Flows Through Natural Rocks, Kluwer Academic Publishers, Dordrecht.
3. Buckley, S. E. and Leverett, M. C., 1942: Mechanisms of fluid displacement in sands, Trans. Amer. Inst. Min. Meta. Engrs. 146, 107-116.
4. Carlson, Francis M., 1981: Simulation of relative permeability hysteresis to the nonwetting phase, Paper SPE 10157 presented at the 56th Annual Fall Technical Conference and Exhibition of the Society of Petroleum Engineers of AIME, San Antonio, TX.
5. Colonna, J., Brissaud, F. and Millet, J. L., 1972: Evolution of capillarity and relative permeability hysteresis, SPEJ Trans. 253, 28-38.
6. Craig, Forrest F., 1971: The Resenoir Engineering Aspects of Waterflooding, Monograph Series, Society of Petroleum Engineers, Dallas.
7. Evrenos, Attila I. and Comer, A. G., 1969: Numerical simulation of hysteretic flow in porous media, Paper SPE 2693 prepared for the 44th Annual Fall Meeting of SPE of AIME, Denver, Co.
8. Furati, Khaled M.: The solution of the Riemann problem for a hyperbolic system modeling polymer flooding with hysteresis, J. Math. Anal. Appl. (to appear.).
9. Geffen, T. M., Owens, W. W. Parrish, D. R. and Morse, R. A., 1951: Experimental investigation of factors affecting laboratory relative permeability measurements. Trans. AIME 192, 99-110.
10. Gladfelter, Robert E. and Gupta, Surendra P., 1980: Effect of fractional flow hysteresis on recovery of tertiary oil, Soc. Petrol. Engrs. J. 20, 508-520.
11. Isaacson, Eli L.: Global solution of a Riemann problem for a non-strictly hyperbolic system of conservation laws arising in enhanced oil recovery, unpublished.
12. Thormod Johansen and Ragnar Winther, 1988: The solution of the Riemann problem for a hyperbolic system of conservation laws modeling polymer flooding, SIAM J. Math. Anal. 19(3), 541-566.
13. Jones, S. C and Roszell, W. O., 1978: Graphical techniques for determining relative permeability from displacement experiments, J. Petrol. Technol., 807-816.
14. Killough, J. E., 1976: Reservoir simulation with history-dependent saturation functions, Soc. Petrol. Engrs. J. 16, 37-48.
15. Land, Carlon S., 1968: Calculation of imbibition relative permeability for two- and three-phase flow from rock properties, Soc. Petrol. Engrs. J., 149-156.
16. Land, Carlon S., 1968: The optimum gas saturation for maximum oil recovery from displacement by water, Paper SPE 2216 prepared for the 43rd Annual Fall Meeting of SPE of AIME, Houston, TX.
17. Land, Carlon S., 1971: Comparison of calculated with experimental imbibition relative permeability, Soc. Petrol. Engrs. J., 419-425.
18. Lenhard, R. J. and Parker, J. C., 1987: A model for hysteretic constitutive relations governing multiphase flow, 2, permeability-saturation relations, Water Resour. Res. 23(12), 2197-2206.
19. Marchesin, D., Medeiros, H. B. and Paes-Leme, P. J., 1987: A model for two phase flow with hysteresis, Contemp. Math. 60, 89-107.
20. Naar, J. and Henderson, J. H., 1961: An imbibition model - its application to flow behavior and the prediction of oil recovery, Soc. Petrol. Engrs. J. 222, 61-70.
21. Naar, J. and Wygal, R. J., 1961: Three-phase imbibition relative permeability, Soc. Petrol. Engrs. J., 254-258.
22. Naar, J., Wygal, R. J. and Hende, J. H., 1962: Imbibition relative permeability in unconsolidated porous media, Soc. Petrol. Engrs. J. 225, 13-17.
23. Oleinik, O. A., 1959: Uniqueness and a stability of the generalized solution of the Cauchy problem for a quasilinear equation, Uspekhi Mat. Nauk 14, 165-170. English translation in Amer. Math. Soc. Transl. Ser. 2, 33, (1964), 285-290.
24. Oleinik, O. A., 1959: Uniqueness and a stability of the generalized solution of the Cauchy problem for a quasilinear equation, Uspekhi Mat. Nauk 14, 165-170. English translation in Amer. Math. Soc. Transl. Ser. 2, 33, (1964), 285-290.
25. Osoba, J. S., Richardson, J. G., Kerver, J. K., Hafford, J. A. and Blair, P. M., 1951: Laboratory measurements of relative permeability, Trans. AIME 192, 47-56.
26. Pope, Gary A., 1980: The application of fractional flow theory to enhanced oil recovery, Soc. Petrol. Engrs. J. 20, 191-205.
27. Pietro Raimondi and Torcaso, Michael A., 1964: Distribution of the oil phase obtained upon imbibition of water, Soc. Petrol. Engrs. J., 49-55.
28. Sandberg, C. R., Gournay, L. S. and Sippel, R. F., 1958: The effect of fluid-flow rate and viscosity on laboratory determinations of oil-water relative permeabilities, Trans. AIME 213, 36-43.
29. Snell, R. W., 1962: Three-phase relative permeability in an unconsolidated sand, J. Inst. Pet. 48(459), 80-88.
30. Welge, H. J., 1952: A simplified method for computing oil recovery by gas or water drive, Trans. Amer. Inst. Min. Meta. Engrs. 195, 91-98.
31. Wyllie, M. R. J. and Gardner, G. H. F., 1958: The generalized Kozeny-Carman equation: Part 1 - review of existing theories, World Oil 146, 121-127.
32. Wyllie, M. R. J. and Gardner, G. H. F., 1958: The generalized Kozeny-Carman equation: Part 2 - a novel approach to problems of fluid flow, World Oil 146, 210-227.