Buckley-Leverett mathematical and numerical models describing vertical equilibrium process in porous media

International Journal of Engineering Science

Volumn 42, Issue 11-12, 2004, Pages 1289-1303

  Cunha, M C C ^a   Santos, M M ^a   Bonet, J E ^a  

^a UNIVERSITY OF CAMPINAS   (Brazil)

Author keywords

Conservation laws; Godunov method; Hysteresis; Porous media; Riemann problem; Stationary discontinuity; Two phase flow; Vertical equilibrium

Indexed keywords

APPROXIMATION THEORY; HYSTERESIS; MATHEMATICAL MODELS; NUMERICAL METHODS; POROUS MATERIALS; PROBLEM SOLVING;

CONSERVATION LAWS; GODUNOV METHOD; RIEMANN PROBLEMS; STATIONARY DISCONTINUITY; TWO-PHASE FLOW; VERTICAL EQUILIBRIUM;

MULTIPHASE FLOW;

EID: 3142563150     PISSN: 00207225     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijengsci.2003.10.005     Document Type: Article

References (19)

1. Bear J., Ryzhik V. On the displacement of NAPL lenses and plumes in a phreatic aquifer. Transp. Porous Media. 33:1998;227-255.
2. Braun E.M., Holland R.F. Relative permeability hysteresis: laboratory measurements and a conceptual model. SPE Reservoir Eng. 1995;222-228.
3. Brggs J.E., Katz D.L. Drainage of water from sand in developing aquifer storage. Tech. Rep. SPE, Soc. Pet. Eng. 1502:1996.
4. Coats K.H., Henderson J.H. The use of vertical equilibrium in two-dimensional simulation of three-dimensional reservoir performance. Soc. Pet. Eng. J. 1971;63-71.
5. Colonna J., Brissaud F., Millet J.L. Evolution of capillary and relative permeability hysteresis. Soc. Pet. Eng. J. 1972;28-37.
6. Dafermos C.M. Hyperbolic Conservation Laws in Continuous Physics. 2000;Springer-Verlag.
7. Furati K. Effects of relative permeability hysteresis dependence on two-phase flow in porous media. Trans. Porous Media. 28:1997;181-203.
8. Furati K. The solution of the Riemann problem for a hyperbolic system modeling polymer flooding with hysteresis. J. Math. Anal. Appl. 206:1997;205-233.
9. Gladfelter R.E., Gupta S.P. Effect of fractional flow hysteresis on recovery of tertiary oil. Soc. Pet. Eng. J. 1980;508-520.
10. E. Isaacson, Global solution of a Riemann problem for a non-strictly hyperbolic system of conservation laws arising in enhanced oil recovery, Rockefeller University, NY, (1984) preprint.
11. Johansen T., Winther R. The solution of the Riemann problem for a hyperbolic system of conservation laws modeling polymer flooding. SIAM J. Math. Anal. 19(3):1988;541-566.
12. Lake L.W. Enhanced Oil Recovery. 1989;Prentice Hall.
13. LeVeque R. Numerical Methods for Conservation laws. 1990;Birkhauser- Verlag.
14. Philip J. Horizontal redistribution with capillary hysteresis. Water Resour. Res. 1991;1459-1469.
15. D. Serre, Systems of conservation laws, vol. 1, Cambridge University Press, Cambridge, 1996.
16. F. Siddiqui, L. Lake, A comprehensive dynamical theory of hydrocarbon migration and trapping, Tech. Rep. SPE 38682 Soc. Pet. Eng., 1997.
17. J. Smoller, Shock waves and reaction-diffusion equations, second ed., Grundlehren der Mathematischen Wissenschaften (Fundamental Principles of Mathematical Sciences), vol. 258, Springer-Verlag, New York, 1994.
18. Templeton E.E., Nielsen R.F., Stahl C.D. A study of gravity counterflow segregation. Soc. Pet. Eng. J. 1962;185-193.
19. Van Dijke M., Zee S.V.D. A similarity solution for oil lens redistribution including capillary forces and oil entrapment. Transp. Porous Media. 29(1):1997;99-125.