Simulation of single-phase multicomponent flow problems in gas reservoirs by Eulerian-Lagrangian techniques

Transport in Porous Media

Volumn 50, Issue 3, 2003, Pages 307-342

  Douglas Jr , Jim ^a   Frías, Diego ^b   Henderson, Nélio ^c   Pereira, Felipe ^c  

^a PURDUE UNIVERSITY   (United States)

^b LABORATÓRIO NACIONAL DE COMPUTAÇÃO CIENTÍFICA   (Brazil)

^c STATE UNIVERSITY OF RIO DE JANEIRO   (Brazil)

Author keywords

Compressible flow; Miscible displacement; Modified method of characteristics

Indexed keywords

INCOMPRESSIBLE FLOW; ISOTHERMS;

MISCIBLE FLUIDS;

POROUS MATERIALS;

EULERIAN-LAGRANGIAN ALGORITHM; GAS FIELD; MULTIPHASE FLOW;

EULERIAN ANALYSIS; GAS FIELD; LAGRANGIAN ANALYSIS; MULTIPHASE FLOW;

EID: 0037372263     PISSN: 01693913     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021138131367     Document Type: Article

References (47)

1. de Almeida, C. G.: 2000, Escoamentos miscíveis em formaçōes heterogêneas: novos métodos numéricos e modelagem estocástica, PhD Dissertation, Instituto de Matemática, Estatística e Computaçāo Científica, UNICAMP, Campinas, Brazil.
2. Arbogast, T., Chilikapati, A. and Wheeler, M. F.: 1992, A characteristics-mixed finite element for contaminant transport and miscible displacement, in: T. F. Russel et al. (eds), Computational Methods in Water Resources IX, Vol. 1: Numerical Methods in Water Resources, Elsevier Applied Science, London, New York, pp. 77-84.
3. Batycky, R. P., Blunt, M. J. and Thiele, M. R.: 1996a, A 3D field scale streamline simulator with gravity and changing well conditions, SPE 36726, Oct.
4. Bratvedt, F., Gimse, T. and Tegnander, C.: 1996b, Streamline computations for porous media flow including gravity, Transport in Porous Media 25, 63-78.
5. Brezzi, F. and Fortin, M.: 1991, Mixed and Hybrid Finite Element Methods, Springer-Verlag, New York.
6. Chavent, G. and Jaffré, J.: 1986, Mathematical Models and Finite Elements for Reservoir Simulation, North-Holland, Amsterdam.
7. Dafermos, C. M.: 1972, Polygonal approximations of solutions of the initial value problem for a conservation law, J. Math. Anal. Appl. 38, 33-41.
8. Douglas Jr., J.: 1982, Simulation of miscible displacement in porous media by a modified method of characteristics procedure, in: Numerical Analysis, Lecture Notes in Mathematics, Vol. 912, Springer-Verlag, Berlin.
9. Douglas, Jr., J.: 1983, Finite difference methods for two-phase incompressible ow in porous media, SIAM J. Numer. Anal. 20, 681-696.
10. Douglas, Jr., J.: 1984, Numerical methods for the flow of miscible fluids in porous media, in: R. W. Lewis, P. Bettess and E. Hinton (eds), Numerical Methods in Coupled Systems, Wiley, London, pp. 405-439.
11. Douglas, Jr., J., Hensley, J. L., Wei, Y., Yeh, L., Jaffré, J., Paes Leme, P. J., Ramakrishnam, T. S. and Wilkinson, D. J.: 1992, A derivation for Darcy's law for miscible fluids and a revised model for miscible displacement in porous media, in: T. F. Russell, R. E. Ewing, C. A. Brebbia, W. G. Gray and G. F. Pinder (eds), Mathematical Modeling in Water Resources, Vol. 2, Computational Mechanics Publications, Elsevier Applied Science, Southhampton, Boston, pp. 165-178.
12. Douglas, Jr., J., Ewing, R. E. and Wheeler, M. F.: 1983a, The approximation of the pressure by a mixed method in the simulation of miscible displacement, R.A.I.R.O. Anal. Numér. 17, 17-33.
13. Douglas Jr., J., Ewing, R. E. and Wheeler, M. F.: 1983b, A time-discretization procedure for a mixed finite element approximation of miscible displacement in porous media, R.A.I.R.O. Anal. Numér. 17, 249-265.
14. Douglas Jr., J., Furtado, F. and Pereira, F.: 1997, On the numerical simulation of waterflooding of heterogeneous petroleum reservoirs, Comput. Geosci. 1, 155-190.
15. Douglas Jr., J., Huang, C.-S. and Pereira, F.: 1999a, The modified method of characteristics with adjusted advection, Numer. Math. 83, 353-369.
16. Douglas Jr., J., Huang, C.-S. and Pereira, F.: 1999b, The modified method of characteristics with adjusted advection for an immiscible displacement problem, in: Z. Chen, Y. Li, C. A. Micchelli, Y. Xu (eds), Advances in Computational Mathematics, Lecture Notes in Pure and Applied Mathematics 202, Marcel Dekker, Inc., New York, Basel, Hong Kong, pp. 53-73.
17. Douglas Jr., J., Paes Leme, P. J., Roberts, J. E. and Wang, J.: 1993, A parallel iterative procedure applicable to the approximate solution of second order partial differential equations by mixed finite element methods. Numer. Math. 65, 95-108.
18. Douglas Jr., J., Pereira, F. and Yeh, L. M.: 2000a, A locally conservative Eulerian-Lagrangian method for flow in a porous medium of a mixture of two components having different densities, in: Z. Chen, R. Ewing and Z.-C. Shi (eds), Numerical Treatment of Multiphase Flows in Porous Media, Lecture Notes in Physics 552, pp. 138-155.
19. Douglas Jr., J., Pereira, F. and Yeh, L. M.: 2000b, A locally conservative Eulerian-Lagrangian method and its application to nonlinear transport in porous media, Comp. Geosci. 4, 1-40.
20. Douglas Jr., J. and Roberts, J. E.: 1983, Numerical methods for a model for compressible miscble displacement in porous media, Math. Comp. 41, 441-459.
21. Douglas Jr., J. and Russell, T. F.: 1982, Numerical methods for convection-dominated diffussion problems based on combining the method of characteristics with finite element or finite difference procedures, SIAM J. Numer. Anal. 19, 871-885.
22. Douglas Jr., J. and Spagnuolo, A. M.: (to appear), The transport of nuclear contamination in fractured porous media, Korean J. Math.
23. Douglas Jr., J. and Yuan, Y.: 1988, Numerical simulation of immiscible flow in porous media based on combining the method of characteristics with mixed finite element procedures, in: M. F. Wheeler (ed.), Numerical Simulation in Oil Recovery, The IMA Volumes in Mathematics and its Applications, Vol. 11, Springer-Verlag, Berlin, New York, pp. 119-131.
24. Ewing, R. E. and Russell, T. F.: 1982, Efficient time-stepping methods for miscible displacement problems in porous media, SIAM J. Numer. Anal. 19, 1-67.
25. Ewing, R. E., Russell, T. F. and Wheeler, M. F.: 1983, Simulation of miscible displacement using mixed methods and a modified method of characteristics, in: Proceedings, Seventh SPE Symposium on Reservoir Simulation, Paper SPE 12241, Society of Petroleum Engineers, Dallas, Texas, pp. 71-81.
26. Ewing, R. E., Russell, T. F. and Wheeler, M. F.: 1984, Convergence analysis of an approximation of miscible displacement in porous media by mixed finite elements and a modified method of characteristics, Comp. Meth. Appl. Mech. Eng. 47, 73-92.
27. Ewing, R. E., Wang, H. and Weekes, S. L.: 1999, On the simulation of multicomponent gas flow in porous media, Appl. Num. Math. 31, 405-427.
28. Ewing, R. E. and Wheeler, M. F.: 1980, Galerkin methods for miscible displacement problems in porous media, SIAM J. Numer. Anal. 17, 351-365.
29. Glimm, J., Lindquist, B., Pereira, F. and Zhang, Q.: 1993, A theory of macro-dispersion for the scale up problem, Transport in Porous Media 13, 97-122.
30. Holden, H., Holden, L. and Hφegh-Krohn, R.: 1988, A numerical method for first order nonlinear conservation laws in one dimension, Comput. Math. Appl. 15, 595-602.
31. Huang, C.-S.: (to appear), Convergence analysis of a mass-conserving approximation of immiscible displacement in porous media by mixed finite elements and a modified method of characteristics with adjusted advection, in Computational Geosciences; currently available as Technical Report #318, Center for Applied Mathematics, Purdue University.
32. Joseph, D. D. and Renardy, Y. Y.: 1993, Fundamentals of Two-Fluid Dynamics. Part II: Lubricated Transport, Drops and Miscible Liquids, Interdisciplinary Applied Mathematics, Vol. 4, Springer-Verlag, New York.
33. Lohrenz, J., Bray, B. G. and Clark, C. R.: 1964, Calculating viscosities of reservoir fluids from their compositions, J. Pet. Tech., 1171-1176.
34. Martin, J. J.: 1979, Cubic equations of state-Which? Ind. Chem. Fundam. 18(2), 81-97.
35. Peaceman, D. W.: 1966, Improved treatment of dispersion in numerical calculation of multidimensional miscible displacements, Soc. Pet. Eng. J. 6, 213-216.
36. Peaceman, D. W.: 1997, Fundamentals of Numerical Reservoir Simulation, Elsevier, New York.
37. Raviart, P.-A. and Thomas, J. M.: 1977, A mixed finite element method for second order elliptic problems, in: I. Galligani and E. Magenes (eds), Mathematical Aspects of the Finite Element Method, Lecture Notes in Mathematics, 606, Springer-Verlag, Berlin, New York, pp. 292-315.
38. Reid, R. C., Prausnitz, J. M. and Poling, B. E.: 1987, The Properties of Gases and Liquids, McGraw-Hill, New York.
39. Renard, G.: 1990, A 2D reservoir streamtube EOR model with periodical automatic regeneration of streamlines, In Situ 14.
40. Russell, T. F.: 1985, Time stepping along characteristics with incomplete iteration for a Galerkin approximation of miscible displacement in porous media, SIAM J. Numer. Anal. 22, 970-1013.
41. Russell, T. F. and Wheeler, M. F.: 1983, Finite element and finite difference methods for continuous flows in porous media, in: The Mathematics of Reservoir Simulation, SIAM, Philadelphia.
42. Smith, J. M. and Van Ness, H. C.: 1975, Introduction to Chemical Engineering Thermodynamics, McGraw-Hill, New York.
43. Spagnuolo, A. M.: (to appear), The approximation of contaminant transport in porous media by mixed finite elements and a modified method of characteristics with adjusted advection.
44. Thiele, M. R.: 1994, Modeling multiphase flow in heterogeneous media using streamtubes, PhD Dissertation, Dept. of Petroleum Eng., Stanford Univ.
45. Thiele, M. R., Batycky, R. P., Blunt, M. J. and Orr Jr., F. M.: 1996, Simulating flow in heterogeneous sysytems using streamtubes and streamlines, SPE Resrvoir Engineering.
46. Wang, H., Liang, D., Ewing, R. E., Lyons, S. L. and Qin, G.: 2000a, An ELLAM-MFEM solution technique for compressible fluid flows in porous media with point sources and sinks, J. Comput. Phys. 159, 344-376.
47. Wang, H., Liang, D., Ewing, R. E., Lyons, S. L. and Qin, G.: 2000b, An accurate simulator to compressible flow in porous media with wells, in: L. R. Bentley, J. F. Sykes, C. A. Brebbia, W. G. Gray and G. F. Pinder (eds), Computational Methods in Surface-Water Systems with Hydrology, Computational Methods in Water Resources, Balkema, Rotterdam, pp. 623-630.