Mathematical properties of three-phase flow equations

SPE Journal

Volumn 2, Issue 3, 1997, Pages 291-300

  Guzmán, Rafael E ^a,b,c   Fayers, F John ^d,e  

^a BP AMERICA INC   (United States)

^b Universidad de América   (Colombia)

^c STANFORD UNIVERSITY   (United States)

^d 8 The Dell ^*  (United Kingdom)

^e UNIVERSITY OF READING   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EQUATIONS OF MOTION; GRAVITATIONAL EFFECTS; MATHEMATICAL MODELS; MECHANICAL PERMEABILITY; VISCOSITY OF LIQUIDS;

COREY RELATIVE PERMEABILITIES; THREE PHASE FLOW EQUATIONS;

MULTIPHASE FLOW;

EID: 0031232695     PISSN: 1086055X     EISSN: None     Source Type: Journal    
DOI: 10.2118/35154-PA     Document Type: Article

References (27)

1. Aanonsen, S.I.: "Application of Fractional-Flow Theory to 3-Phase, 1-Dimensional Surfactant Flooding," Proceedings of the First European Conference on the Mathematics of Oil Recovery, Cambridge, July, 1989, P. King (ed.), Cambridge University Press, Cambridge (1992).
2. Aziz, K., and Settari, A.: Petroleum Reservoir Simulation, Applied Science Publisher Ltd., London (1979).
3. Baker, L.E.: "Three-Phase Relative Permeabilities," paper SPE 17369 presented at the 1988 SPE/DOE Symposium on Enhanced Oil Recovery, Tulsa, Oklahoma, April 17-20.
4. Bell, J.B., Trangenstein, J.A., and Shubin, G.R.: "Conservation Laws of Mixed Type Describing Three-Phase Flow in Porous Media," SIAM J. Applied Math. (December 1986) 46, No. 6, 1000-1017.
5. Buckley, S.E. and Leverett, M.C.: "Mechanism of Fluid Displacement in Sands," Trans., AIME (1941) 249, 107-116.
6. Chierici, G.L.: "Novel Relations for Drainage and Imbibition Relative Permeabilities," Soc. Pet. Eng. J. (June 1984) 275-276.
7. Delshad, M., and Pope, G.A.: "Comparison of the Three-Phase Oil Relative Permeability Models," Transport in Porous Media (1989) 4, 59-83.
8. Falls, A.M., and Schulte, W.M.: "Theory of Three-Component, Three-Phase Displacement in Porous Media," Soc. Pet. Eng. Res. Eng. (August 1992a) 377-384.
9. Falls, A.H., and Schulte, W.M.: "Features of Three-Component, Three-Phase Displacement in Porous Media," Soc. Pet. Eng. Res. Eng. (November 1992b) 426-432.
10. Fayers, F.J.: "Extension of Stone's Method 1 and Conditions for Real Characteristics in Three-Phase Flow," Soc. Pet. Eng. Res. Eng. (November 1989) 437-445.
11. Fayers, F.J., and Matthews, J.D.: "Evaluation of Normalized Stone's Methods for Estimating Three-Phase Relative Permeabilities," Soc. Pet. Eng. J. (April 1984) 224-232.
12. Guzmán, R.E.: Mathematics of Three-Phase Flow, PhD dissertation, Stanford University, Stanford, CA (July 1995).
13. Guzmán, R.E. and Fayers, F.J.: "Solutions to the Three-Phase Buckley-Leverett Problem," (1997) 2, SPE 35156, Soc. Pet. Eng. J. (this issue).
14. Holden, L.: "On the Strict Hyperbolicity of the Buckley-Leverett Equations for Three-Phase Flow in a Porous Medium," SIAM J. Applied Math. (June 1990) 50, No. 3, 667-682.
15. Hosain, A.: "Three-Phase Relative Permeability Measurements," Master's thesis, University of Birmingham, Birmingham, U.K. (1961).
16. Isaacson, E.L., Marchesin, D., and Plohr, B.J.: "The Structure of the Riemann Solution for Non-Strictly Hyperbolic Conservation Laws," (March, 14-18 1988a) Second International Conference on Nonlinear Hyperbolic Problems, Aachen, FGR.
17. Marchesin, D., and Madeiros, H.B.,: "A Note on the Stability of Eigenvalue Degeneracy in Nonlinear Conservation Laws of Multiphase Flow," Contemporary Mathematics (1989) 100, 215-224.
18. Saraf, D.N., and Fatt, I.: "Three-Phase Relative Permeability Measurement Using a Nuclear Magnetic Resonance Technique for Estimating Fluid Saturation," J. Pet. Tech., Trans., AIME (September 1967) 240, 235-242.
19. Saraf, D.N., Batycky, J.P., Jackson, C.H., and Fisher, D.B.: "An Experimental Investigation of Three-Phase Flow to Water/Oil/Gas Mixtures Through Water-Wet Sandstones," paper SPE 10671 presented at the 1982 SPE California Regional Meeting, San Francisco, CA, March 24-26.
20. Schaeffer, D.G., and Shearer, M.: "The Classification of 2×2 Systems of Non-strictly Hyperbolic Conservation Laws, With Application to Oil Recovery," Comm. Pure and Applied Math. (1987) 40, 141-178, Appendix with Marchesin, D., and Paes-Leme, P.J.
21. Shalimov, B.V.: "Flow of a Three-Phase Fluid in a Porous Medium (Buckley-Leverett Model)," Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza (1972) 39, No. 1, 39-44.
22. Shearer, M.: "The Riemann Problem for 2 × 2 Systems of Hyperbolic Conservation Laws with Case I Quadratic Nonlinearities," J. Diff. Eqs. (1989) 80, 343-362.
23. Shearer, M., and Trangenstein, J.A.: "Loss of Strict Hyperbolicity of the Buckley-Leverett Equations for Three-Phase Flow in a Porous Medium," Transport in Porous Media (1989) 4, 499-525.
24. Stone, H.L.: "Probability Model for Estimating Three-Phase Relative Permeability," J. Pet. Tech., Trans., AIME (February 1970) 249, 214-218.
25. Stone, H.L.: "Estimation of Three-Phase Relative Permeability and Residual Oil Data," J. Cdn. Pet. Tech. (Oct.-Dec. 1973) 12, 53-61.
26. Trangenstein, J.A.: "Three-Phase Flow with Gravity," Contemporary Mathematics (1989) 100, 147-159.
27. Zauderer, E.: Partial Differential Equations of Applied Mathematics, second edition, Wiley-Interscience, New York, NY (1989).