Multiscale finite-volume formulation for multiphase flow in porous media: Black oil formulation of compressible, three-phase flow with gravity

Computational Geosciences

Volumn 12, Issue 3, 2008, Pages 351-366

  Lee, S H ^a   Wolfsteiner, C ^a   Tchelepi, H A ^b  

^a CHEVRON ENERGY TECHNOLOGY COMPANY   (United States)

^b STANFORD UNIVERSITY   (United States)

Author keywords

Blackoil; Compressibility; Gravity; Multiscale finite volume; Operator split; Reservoir simulation

Indexed keywords

ALGORITHMS; COMPRESSIBLE FLOW; COMPUTER SIMULATION; MULTIPHASE FLOW; PETROLEUM RESERVOIRS; POROUS MATERIALS; SOLUBILITY;

ALGORITHM; CAPILLARITY; COMPRESSIBLE FLOW; CONFERENCE PROCEEDING; FINITE VOLUME METHOD; GRAVITY FIELD; HETEROGENEITY; HETEROGENEOUS MEDIUM; IMMISCIBILITY; MASS BALANCE; MULTIPHASE FLOW; POROUS MEDIUM; THREE PHASE FLOW;

EID: 51549112746     PISSN: 14200597     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10596-007-9069-3     Document Type: Conference Paper

References (25)

1. Aarnes, J.E.: On the use of a mixed multiscale finite element method for greater flexibility and increased speed or improved accuracy in reservoir simulation. Multiscale Model. Simul. 2 (3), 421-439 (2004)
2. Arbogast, T.: Implementation of a locally conservative numerical subgrid upscaling scheme for two-phase darcy flow. Comput. Geosci. 6, 453-481 (2002)
3. Arbogast, T., Bryant, S.L.: A two-scale numerical subgrid technique for waterflood simulations. SPE J. 7, 446-457 (2002)
4. Aziz, K., Settari, A.: Petroleum Reservoir Simulation. Elsevier, Amsterdam (1979)
5. Chen, Y., Durlofsky, L.J., Gerritsen, M., Wen, X.H.: A coupled local-global upscaling approach for simulating flow in highly heterogeneous formations. Adv. Water Resour. 26, 1041-1060 (2003)
6. Chen, Z., Hou, T.Y.: A mixed finite element method for elliptic problems with rapidly oscillating coefficients. Math. Comput. 72, 541-576 (2002)
7. Chen, Z., Yue, X.: Numerical homogenization of well singularities in the flow transport through heterogeneous porous media. Multiscale Model. Simul. 1 (2), 260-303 (2003)
8. Christie, M.A., Blunt, M.J.: TenthASPE Comparative solution project: a comparison of upscaling techniques. SPE Reserv. Eng. 4 (4), 308-317 (2001)
9. Craft, B., Hawkins, M.F.: Petroleum Reservoir Engineering. Prentice-Hall, Englewood Cliffs (1959)
10. Dagan, G.: Flow and Transport in Porous Formations. Springer, New York (1989)
11. Deutsch, C.V., Journel, A.G.: GSLIB: Geostatistical Software Library and User's Guide. Oxford University Press, New York (1998)
12. Efendiev, Y., Wu, X.: Multiscale finite element methods for the problems with highly oscillatory coefficients. Numer. Math. 90, 459-486 (2001)
13. Gautier, Y., Blunt, M.J., Christie, M.A.: Nested gridding and streamline-based simulation for fast reservoir performance predicition. Comput. Geosci. 4, 295-320 (1999)
14. Hou, T., Wu, X.H.: A multiscale finite element method for elliptic problems in composite materials and porous media. J. Comp. Phys. 134, 169-189 (1997)
15. Jenny, P., Lee, S.H., Tchelepi, H.A.: Multi-scale finite-volume method for elliptic problems in subsurface flow simulation. J. Comput. Phys. 187, 47-67 (2003)
16. Jenny, P., Lee, S.H., Tchelepi, H.A.: Adaptive multiscale finite volume method for multi-phase flow and transport. Multiscale Model. Simul. 3, 50-64 (2004)
17. Jenny, P., Lee, S.H., Tchelepi, H.A.: Adaptive fully implicit multi-scale finite-volume method for multi-phase flow and transport in heterogeneous porous media. J. Comput. Phys. 217, 627-641 (2006)
18. Juanes, R., Dub, F.-X.: A locally-conservative variational multiscale method for the simulation of porous media flow with multiscale source terms. Comput. Geosci. (2008) doi: 10.1007/s10596-007-9070-x
19. Lee, S.H., Tchelepi, H.A., Jenny, P., DeChant, L.J.: Implementation of a flux-continuous finite difference method for stratigraphic, hexahedron grids. SPE J. 7, 267-277 (2002)
20. Lunati, I., Jenny, P.: Multi-scale finite-volume method for multi-phase flow with gravity. Comput. Geosci. (2008) doi: 10.1007/s10596-007-9071-9
21. Lunati, I., Jenny, P.: Multi-scale finite-volume method for compressible multi-phase flow in porous media. J. Comput. Phys. 216, 616-636 (2006)
22. Peaceman, D.W.: Fundamentals of Numerical Reservoir Simulation. Elsevier, Amsterdam (1977)
23. Tchelepi, H.A., Jenny, P., Lee, S.H., Wolfsteiner, C.: Adaptive multiscale finite volume framework for reservoir simulation. SPE J. 12, 188-195 (2007)
24. Watts, J.W.: A compositional formulation of the pressure and saturation equations. In: Proceedings of 7th SPE Symposium on Reservoir Simulation: SPE 12244, pp. 113-122, San Francisco, CA, 15-18 November 1983
25. Wolfsteiner, C., Lee, S.H., Tchelepi, H.A.: Modeling of wells in the multiscale finite volume method for subsurface flow simultion. Multiscale Model. Simul. 5 (3), 900-917 (2006)