An ELLAM approximation for highly compressible multicomponent flows in porous media

Computational Geosciences

Volumn 6, Issue 3-4, 2002, Pages 227-251

  Wang, H ^a   Liang, D ^b   Ewing, R E ^a,c   Lyons, S L ^d   Qin, G ^d  

^a UNIVERSITY OF SOUTH CAROLINA   (United States)

^b TEXAS A AND M UNIVERSITY   (United States)

^c SHANDONG UNIVERSITY   (China)

^d EXXONMOBIL UPSTREAM RESEARCH COMPANY   (United States)

Author keywords

Advection diffusion equations; Characteristics methods; Compressible flows; Eulerian Lagrangian methods; Multicomponent flow in porous media; Peng Robinson equation of state; Point sources and sinks

Indexed keywords

COMPRESSIBLE FLOW; FLUID FLOW; MATHEMATICAL METHOD; MULTIPHASE FLOW; POROUS MEDIUM;

ADVECTION-DIFFUSION EQUATION; COMPRESSIBLE FLOW; FLUID FLOW; MULTIPHASE FLOW; NUMERICAL METHOD; POROUS MEDIUM;

EID: 0036931645     PISSN: 14200597     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021262308114     Document Type: Article

References (36)

1. M.B. Allen III, G.A. Behie and J.A. Trangenstein, Multiphase Flow in Porous Media, Lecture Notes in Engineering, Vol. 34 (Springer, Berlin, 1988).
2. H. Aziz and A. Settari, Petroleum Reservoir Simulation (Applied Science Publishers, 1979).
3. J.P. Benque and J. Ronat, Quelques difficulties des modeles numeriques en hydraulique, in: Computing Methods in Applied Sciences and Engineering, eds. Glowinski and Lions (North-Holland, Amsterdam, 1982) pp. 471-494.
4. P.J. Binning and M.A. Celia, A three-dimensional forward particle tracking Eulerian-Lagrangian localized adjoint method for solution of the contaminant transport equation, in: Computational Methods in Water Resources, Vol. XIII, eds. L.R. Bentley, J.F. Sykes, C.A. Brebbia, W.G. Gray and G.F. Pinder (Balkema, Rotterdam, 2000) pp. 611-618.
5. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, Springer Series in Computational Mathematics, Vol. 15 (Springer, New York, 1991).
6. M.A. Celia and L.A. Ferrand, A comparison of ELLAM formulations for simulation of reactive transport in groundwater, in: Advances in Hydro-Science and Engineering, Vol. 1(B), ed. S.Y. Wang (Univ. of Mississippi Press, 1993) pp. 1829-1836.
7. M.A. Celia, T.F. Russell, I. Herrera and R.E. Ewing, An Eulerian-Lagrangian localized adjoint method for the advection-diffusion equation, Adv. in Water Resource. 13 (1990) 187-206.
8. H. Chen, R.E. Ewing, S.L. Lyons, G. Qin, T. Sun and D.P. Yale, Numerical solution of coupled geomechanics and fluid flow in elastic porous media, in: Numerical Treatment of Multiphase Flows in Porous Media, eds. Z. Chen, R.E. Ewing and Z. Shi, Lecture Notes in Physics, Vol. 552 (Springer, Berlin, 2000) pp. 80-92.
9. J. Douglas, Jr., R.E. Ewing and M.F. Wheeler, A time-discretization procedure for a mixed finite element approximation of miscible displacement in porous media, RAIRO Modél. Math. Anal. Numér. 17 (1983) 249-265.
10. J. Douglas, Jr., F. Furtado and F. Pereira, On the numerical simulation of waterflooding of heterogeneous petroleum reservoirs, Comput. Geosci. 1 (1997) 155-190.
11. J. Douglas, Jr. and T.F. Russell, Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures, SIAM J. Numer. Anal. 19 (1982) 871-885.
12. R.E. Ewing, ed., The Mathematics of Reservoir Simulation, Research Frontiers in Applied Mathematics, Vol. 1 (SIAM, Philadelphia, PA, 1984).
13. R.E. Ewing, T.F. Russell and M.F. Wheeler, Simulation of miscible displacement using mixed methods and a modified method of characteristics, SPE 12241 (1983) 71-81.
14. B.A. Finlayson, Numerical Methods for Problems with Moving Fronts (Ravenna Park, Seattle, 1992).
15. R.W. Healy and T.F. Russell, Solution of the advection-dispersion equation in two dimensions by a finite-volume Eulerian-Lagrangian localized adjoint method, Adv. in Water Resourc. 21 (1998) 11-26.
16. R. Helmig, Multiphase Flow and Transport Processes in the Subsurface (Springer, Berlin, 1997).
17. R.W. Lewis and B.A. Schrefler, The Finite Element Methods in the Static and Dynamic Deformation and Consolidation of Porous Media (Wiley, New York, 1998).
18. N. Lu, A semianalytical method of path line computation for transient finite-difference groundwater flow models, Water Resour. Res. 30 (1994) 2449-2459.
19. J. Lohrenz, B. Bray and C. Clark, Calculating viscosities of reservoir fluids from their composition, J. Petrol. Tech. 16 (1964) 1171-1176.
20. K.W. Morton, A. Priestley and E. Süli, Stability of the Lagrangian-Galerkin method with nonexact integration, RAIRO Modél. Math. Anal. Numer. 22 (1988) 123-151.
21. D.Y. Peng and D.B. Robinson, A new two-constant equation of state, Indian Engrg. Chem. Fundam. 15 (1976) 59-64.
22. O. Pironneau, On the transport-diffusion algorithm and its application to the Navier-Stokes equations, Numer. Math. 38 (1982) 309-332.
23. D.W. Pollock, Semianalytical computation of path lines for finite-difference models, Ground Water 26 (1988) 743-750.
24. P.A. Raviart and J.M. Thomas, A mixed finite element method for second order elliptic problems, in: Mathematical Aspects of Finite Element Methods, eds. Galligani and Magenes, Lecture Notes in Mathematics, Vol. 606 (Springer, Berlin, 1977) pp. 292-315.
25. R.C. Reid, J.M. Prausnitz and B.E. Poling, The Properties of Gases and Liquids, 4th ed. (McGraw-Hill, New York, 1987).
26. T.F. Russell, Eulerian-Lagrangian localized adjoint methods for advection-dominated problems, in: Pitmann Research Notes in Mathematics Series, Vol. 228, eds. Griffiths and Watson (Longman Scientific & Technical, Harlow, UK, 1990) pp. 206-228.
27. T.F. Russell, and R. W. Healy, Analytical tracking along streamlines in temporally linear Ravirt-Thomas velocity fields, in: Computational Methods in Water Resources, Vol. XIII, eds. L.R. Bentley, J.F. Sykes, C.A. Brebbia, W.G. Gray and G.F. Pinder (Balkema, Rotterdam, 2000) pp. 631-638.
28. T.F. Russell and R.V. Trujillo, Eulerian-Lagrangian localized adjoint methods with variable coefficients in multiple dimensions, in: Computational Methods in Surface Hydrology, eds. Gambolati et al. (Springer, Berlin, 1990) pp. 357-363.
29. T.F. Russell and M.F. Wheeler, Finite element and finite difference methods for continuous flows in porous media, in: The Mathematics of Reservoir Simulation, ed. R.E. Ewing (SIAM, Philadelphia, PA, 1984) pp. 35-106.
30. A.L. Schafer-Perini and J.L. Wilson, Efficient and accurate front tracking for two-dimensional groundwater flow models, Water Resources Res. 27 (1991) 1471-1485.
31. E. Varoglu and W.D.L. Finn, Finite elements incorporating characteristics for one-dimensional diffusion-convection equation, J. Comput. Phys. 34 (1980) 371-389.
32. H. Wang, An optimal-order error estimate for an ELLAM scheme for two-dimensional linear advection-diffusion equations, SIAM J. Numer. Anal. 37 (2000) 1338-1368.
33. H. Wang, H.K. Dahle, R.E. Ewing, M.S. Espedal, R.C. Sharpley and S. Man, An ELLAM scheme for advection-diffusion equations in two dimensions, SIAM J. Sci. Comput. 20 (1999) 2160-2194.
34. H. Wang, R.E. Ewing, G. Qin, S.L. Lyons, M. Al-Lawatia and S. Man, A family of Eulerian-Lagrangian localized adjoint methods for multi-dimensional advection-reaction equations, J. Comput. Phys. 152 (1999) 120-163.
35. H. Wang, R.E. Ewing and T.F. Russell, Eulerian-Lagrangian localized methods for convection-diffusion equations and their convergence analysis, IMA J. Numer. Anal. 15 (1995) 405-459.
36. H. Wang, D. Liang, R.E. Ewing, S.L. Lyons and G. Gin, An approximation to miscible fluid flows in porous media with point sources and sinks by an Eulerian-Lagrangian localized adjoint method and mixed finite element methods, SIAM J. Sci. Comput. 22 (2000) 561-581.