High-order upwind schemes for two-phase, multicomponent flow

SPE Journal

Volumn 10, Issue 3, 2005, Pages 297-311

  Mallison, Brad T ^a,b   Gerritsen, Margot G ^a   Jessen, Kristian ^a   Orr, Franklin M ^a  

^a STANFORD UNIVERSITY   (United States)

^b CHEVRON ENERGY TECHNOLOGY COMPANY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; EIGENVALUES AND EIGENFUNCTIONS; FINITE DIFFERENCE METHOD; OPTIMIZATION; RUNGE KUTTA METHODS;

COMPOSITIONAL SIMULATION; HIGH ORDER FINITE DIFFERENCE SCHEMES; UPWIND SCHEMES;

PETROLEUM RESERVOIRS;

EID: 26844487489     PISSN: 1086055X     EISSN: None     Source Type: Journal    
DOI: 10.2118/79691-PA     Document Type: Article

References (28)

1. Aziz, K. and Settari, A.: Petroleum Reservoir Simulation, Applied Science Publishers, Essex, U.K. (1979).
2. King, M.J. and Datta-Gupta, A.: "Streamline Simulation" A Current Perspective," In Situ (1998) 22, No. 1, 91.
3. Wang, Y. and Orr, F.M. Jr.: "Analytical Calculation of Minimum Miscibility Pressure," Fluid Phase Equilibria (1997) 139, 151.
4. Johns, R.T. and Orr, F.M. Jr.: "Miscible Gas Displacement of Multicomponent Oils," SPEJ (1996) 1, 39.
5. Jessen, K. et al.: "Fast, Approximate Solutions for 1D Multicomponent Gas-Injection Problems," SPEJ (December 2001) 442.
6. Jessen, K. and Orr, F.M. Jr.: "Gas Cycling and the Development of Miscibility in Condensate Reservoirs," SPEREE (October 2004) 334.
7. LeVeque, R.J.: Numerical Methods for Conservation Laws, Birkhauser Verlag, Basel, Switzerland (1992).
8. Van Leer, B.: "Towards the Ultimate Conservative Finite Difference Scheme, V: A Second Order Sequel to Godunov's Method," J. Comput. Phys. (1979) 32, 101.
9. Harten, A. et al.: "Uniformly High Order Accurate Essentially Non-Oscillatory Schemes III," J. Comput. Phys. (1987) 71, 231.
10. Jiang, G.-S. and Shu, C.-W.: "Efficient Implementation of Weighted ENO Schemes," J. Comput. Phys. (1996) 126, -202.
11. Rubin, B. and Blunt, M.J.: "Higher-Order Implicit Flux Limiting Schemes for Black Oil Simulation," paper SPE 21222 presented at the 1991 SPE Symposium on Reservoir Simulation, Anaheim, California, 17-20 February.
12. Rubin, B. and Edwards, M.: "Extension of the TVD Midpoint Scheme to Higher-Order Accuracy in Time," SPE 25265 presented at the 1993 SPE Symposium on Reservoir Simulation, New Orleans, 28 February-3 March.
13. Peddibhotla, S., Datta-Gupta, A., and Xue, G.: "Multiphase Streamline Modeling in Three Dimensions: Further Generalizations and a Field Application," paper SPE 38003 presented at the 1997 SPE Reservoir Simulation Symposium, Dallas, 8-11 June.
14. Chen, W.H. et al.: "Minimization of Grid Orientation Effects Through Use of Higher-Order Finite Difference Methods," SPE Advanced Technology Series (July 1993) 43.
15. Thiele, M.R. and Edwards, M.: "Physically Based Higher-Order Godunov Schemes for Compositional Simulation," paper SPE 66403 presented at the 2001 SPE Reservoir Simulation Symposium, Houston, 11-14 February.
16. Bell, J.B. and Trangenstein, J.: "Mathematical Structure of Compositional Reservoir Simulation," SIAM J. Sci. Stat. Comput. (1989) 10, 817.
17. Peng, D.Y. and Robinson, D.B.: "A New Two-Constant Equation of State," Ind. Eng. Chem. Fund (1976) 15, 59.
18. Michelsen, MIL.: "Speeding up the Two-Phase PT-Flash, With Application for Calculation of Miscible Displacements," Fluid Phase Equilibria (1998) 1, 143.
19. Lohrenz, J., Bray, B.G., and Clark, C.R.: "Calculating Viscosities of Reservoir Fluids From Their Compositions," JPT (October 1964) 1171; Trans., AIME, 231.
20. Helferich, F.G.: "General Theory of Multicomponent, Multiphase Displacement in Porous Media," SPEJ (February 1981) 21, 51.
21. Jessen, K., Stenby, E.H., and Orr, F.M. Jr.: "Interplay of Phase Behavior and Numerical Dispersion in Finite-Difference Compositional Simulation," SPEJ (June 2004) 193.
22. Sweby, P.K.: "High-Resolution Schemes Using Flux Limiters for Hyperbolie Conservation Laws," SIAM J. Numerical Analysis (1984) 21, 995.
23. Nessyahu, H. and Tadmor, N.: "Non-Oscillatory Central Differencing for Hyperbolic Conservation Laws," J. Comput. Phys. (1990) 87, 408.
24. Levy, D., Puppo G., and Russo, G.: "Central WENO Schemes for Hyperbolic Systems of Conservation Laws," Mathematical Modeling and Numerical Analysis (1999) 33, No. 3, 547.
25. Qiu, J. and Shu C.-W.: "On the Construction, Comparison, and Local Characteristic Decomposition for High-Order Central WENO Schemes," J. Comput. Phys. (2002) 183, No. 1, 187.
26. Godunov, S.K.: "A Difference Scheme for Computation of Discontinuous Solutions of Equations of Fluid Dynamics," Mat. Sb. (1959) 47, 271 (in Russian).
27. Shu, C.-W. and Osher, S.: "Efficient Implementation of Essentially Non-Oscillatory Shock-Capturing Schemes," J. Comput. Phys. (1988) 77, 439.
28. Dindoruk, B.: "Analytical Theory of Multiphase, Multicomponent Displacement in Porous Media," PhD dissertation, Stanford U., Stanford, California (1992).