A front-tracking method for efficient simulation of miscible gas injection processes

SPE Reservoir Simulation Symposium, Proceedings

Volumn , Issue , 2005, Pages 363-380

  Juanes, R ^a   Lie, K A ^b  

^a STANFORD UNIVERSITY   (United States)

^b SPE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

GAS INJECTION; RIEMANN PROBLEM; THERMODYNAMICAL EQUILIBRIUM; WAVE STRUCTURES;

BOUNDARY VALUE PROBLEMS; COMPUTER SIMULATION; HYDROCARBONS; MATHEMATICAL MODELS; THERMODYNAMICS; WELL FLOODING;

SOLUBILITY;

EID: 22244460510     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (42)

1. F. I. Stalkup Jr. Miscible Displacement, volume 8 of SPE Monograph Series. Society of Petroleum Engineers, Dallas, TX, 1983.
2. L. W. Lake. Enhanced Oil Recovery. Prentice-Hall, Englewood Cliffs, NJ, 1989.
3. F. M. Orr Jr. Theory of Gas Injection Processes. Stanford University, 2002.
4. G. A. Pope. The application of fractional flow theory to enhanced oil recovery. Soc. Pet. Eng. J., 20(3):191-205, June 1980.
5. Petrol. Trans. AIME, 269.
6. F. G. Helfferich. Theory of multicomponent, multiphase displacement in porous media. Soc. Pet. Eng. J., 21(1):5162, February 1981.
7. Petrol. Trans. AIME, 271.
8. G. J. Hirasaki. Application of the theory of multicomponent, multiphase displacement to three-component, two-phase surfactant flooding. Soc. Pet. Eng. J., 21(2):191-204, April 1981.
9. Petrol. Trans. AIME, 271.
10. Y. Wang and F. M. Orr Jr. Analytical calculation of the minimum miscibility pressure. Fluid Phase Equilib., 139:101-124, 1997.
11. K. Jessen, M. L. Michelsen, and E. H. Stenby. Global approach for calculation of the minimum miscibility pressure. Fluid Phase Equilib., 153:251-263, 1998.
12. K.-A. Lie and R. Juanes. A front-tracking method for the simulation of three-phase flow in porous media. Comput. Geosci., 2004. (In review).
13. R. Juanes, K.-A. Lie, and V. Kippe. A front-tracking method for hyperbolic three-phase models. In European Conference on the Mathematics of Oil Recovery, ECMOR IX, volume 2, paper B025, Cannes, France, August 30-September 2 2004.
14. E. L. Isaacson. Global solution of a Riemann problem for a non-strictly hyperbolic system of conservation laws arising in enhanced oil recovery. Technical report, The Rockefeller University, New York, 1980.
15. T. Johansen and R. Winther. The solution of the Riemann problem for a hyperbolic system of conservation laws modeling polymer flooding. SIAM J. Math. Anal., 19(3) :541-566, 1988.
16. T. Johansen and R. Winther. The Riemann problem for multicomponent polymer flooding. SIAM J. Math. Anal., 20(4):908-929, 1989.
17. T. Johansen, A. Tveito, and R. Winther. A Riemann solver for a two-phase multicomponent process. SIAM J. Sci. Comput., 10(5):846-879, 1989.
18. H. Holden and N. H. Risebro. Front Tracking for Hyperbolic Conservation Laws. Springer, New York, 2002.
19. N. H. Risebro. A front-tracking alternative to the random choice method. Proc. Amer. Math. Soc, 117(4): 1125-1129, 1993.
20. A. Bressan and P. LeFloch. Uniqueness of weak solutions to systems of conservation laws. Arch. Rational Mech. Anal., 140(4):301-317, 1997.
21. I.-L. Chern, J. Glimm, O. McBryan, B. Plohr, and S. Yaniv. Front tracking for gas dynamics. J. Comput. Phys., 62:83-110, 1986.
22. J. Glimm, B. Lindquist, O. McBryan, and L. Padmanabhan. A front tracking reservoir simulator, five-spot validation studies and the water-coning problem. In R. E. Ewing, editor, Mathematics of Reservoir Simulation, volume 1 of Frontiers in Applied Mathematics. SIAM, 1983.
23. N. H. Risebro and A. Tveito. Front tracking applied to a nonstrictly hyperbolic system of conservation laws. SIAM J. Sci. Stat. Comput., 12(6):1401-1419, 1991.
24. M. J. King and A. Datta-Gupta. Streamline simulation: A current perspective. In Situ, 22(1):91-140, 1998.
25. V. Haugse, K. H. Karlsen, K.-A. Lie, and J. R. Natvig. Numerical solution of the polymer system by front tracking. Transp. Porous Media, 44:63-83, 2001.
26. E. Zauderer. Partial Differential Equations of Applied Mathematics. Series in Pure and Applied Mathematics. John Wiley & Sons, New York, 1983.
27. P. D. Lax. Hyperbolic systems of conservation laws, II. Comm. Pure Appl. Math., 10:537-566, 1957.
28. F. Ancona and A. Marson. A note on the Riemann problem for general n × n conservation laws. J. Math. Anal. Appl., 260:279-293, 2001.
29. O. A. Oleinik. Discontinuous solutions of nonlinear differential equations. Usp. Mat. Nauk. (N.S.), 12:3-73, 1957.
30. English transl. in Amer. Math. Soc. Transl. Ser. 2, 26:95-172.
31. T.-P. Liu. The Riemann problem for general 2×2 conservation laws. Trans. Amer. Math. Soc., 199:89-112, 1974.
32. R. Juanes. Determination of the wave structure of the three-phase flow Riemann problem. Transp. Porous Media, 2005. (Accepted, in press).
33. E. Isaacson, D. Marchesin, and B. Plohr. Transitional waves for conservation laws. SIAM J. Math. Anal., 21(4):837-866, 1990.
34. S. Schecter, D. Marchesin, and B. J. Plohr. Structurally stable Riemann solutions. J. Differential Equations, 126:303-354, 1996.
35. K. Jessen, E. H. Stenby, and F. M. Orr. Interplay of phase behavior and numerical dispersion in finite-difference compositional simulation. Soc. Pet. Eng. J., 9(2):193-201, June 2004.
36. M. A. Christie and M. J. Blunt. Tenth SPE comparative solution project: A comparison of upscaling techniques. SPE Reserv. Eval. Eng., 4(4):308-317, 2001. url: www.spe.org/csp.
37. E. J. Koval. A method for predicting the performance of unstable miscible displacements in heterogeneous media. Soc. Pet. Eng. J., pages 145-150, June 1963.
38. Petrol. Trans. AIME, 219.
39. M. R. Todd and W. J. Longstaff. The development, testing and application of a numerical simulator for predicting miscible flood performance. J. Pet. Technol., pages 874-882, July 1972.
40. M. Blunt and M. Christie. How to predict viscous fingering in three component flow. Transp. Porous Media, 12:207-236, 1993.
41. B. L. O'Steen and E. T. S. Huang. Modeling of trapped and dendritic oil mobilization during miscible displacement. In Situ, 14(3):285-343, 1990.
42. T. LaForce and R. T. Johns. Analytical theory for three-phase partially miscible flow in ternary systems. In SPE/DOE Fourteenth Symposium on Improved Oil Recovery, Tulsa, OK, April 17-21, 2004. (SPE 89438).