Comptes Rendus
no. 10
Benchmark of different CFL conditions for IMPES
[Comparaison de différentes conditions CFL pour l' IMPES]
Jacques Franc1, 2  ; Pierre Horgue1, 2  ; Romain Guibert1, 2  ; Gerald Debenest1, 2
1 Université de Toulouse, INPT, UPS, IMFT (Institut de mécanique des fluides de Toulouse), 2, allée du Professeur-Camille-Soula, 31400 Toulouse, France
2 CNRS, IMFT, 31400 Toulouse, France
Comptes Rendus. Mécanique, Volume 344 (2016) no. 10, pp. 715-724.

L'IMplicit Pressure Explicit Saturation method (IMPES) est l'une des principales méthodes pour traiter les cas d'écoulements multiphasiques en milieu poreux. La stabilité numérique de cette méthode séquentielle implique des contraintes différentes sur le pas de temps selon le régime d'écoulement étudié. Dans cette note, les trois principaux critères de stabilité liés à l'IMPES sont testés sur des milieux homogènes et hétérogènes pour différents régimes (visqueux/capillaire/gravitaire). Cette étude montre qu'aucun critère optimal, réunissant stabilité et efficacité, ne se dégage. Pour les écoulements capillaires, la condition de Todd est la plus efficace, tandis que la condition standard de Coats est préférable pour les écoulements visqueux. Quand les effets gravitaires sont pris en compte, la condition de Coats doit être restreinte, mais demeure plus efficace que celle de Todd.

The IMplicit Pressure Explicit Saturation (IMPES) method is a prevalent way to simulate multiphase flows in porous media. The numerical stability of this sequential method implies limitations on the time step, which may depend on the flow regime studied. In this note, three stability criteria related to the IMPES method, that differ in their construction on the observed variables, are compared on homogeneous and heterogeneous configurations for different two-phase flow regimes (viscous/capillary/gravitational). This highlights that there is no single optimal criterion always ensuring stability and efficiency. For capillary dominated flows, the Todd's condition is the most efficient one, while the standard Coat condition should be preferred for viscous flows. When gravity effects are present, Coat's condition must be restricted, but remains more efficient than the Todd's condition.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2016.08.003
Keywords: IMPES, Stability criteria, CFL, Multiphase flow, Porous Media, Numerical Efficiency
Mot clés : IMPES, Critère de stabilité, CFL, Écoulements multiphasiques, Milieux Poreux, Efficacité numérique
Jacques Franc 1, 2 ; Pierre Horgue 1, 2 ; Romain Guibert 1, 2 ; Gerald Debenest 1, 2

1 Université de Toulouse, INPT, UPS, IMFT (Institut de mécanique des fluides de Toulouse), 2, allée du Professeur-Camille-Soula, 31400 Toulouse, France
2 CNRS, IMFT, 31400 Toulouse, France 
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Jacques Franc; Pierre Horgue; Romain Guibert; Gerald Debenest. Benchmark of different CFL conditions for IMPES. Comptes Rendus. Mécanique, Volume 344 (2016) no. 10, pp. 715-724. doi : 10.1016/j.crme.2016.08.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2016.08.003/

[1] K. Aziz; A. Settari Petroleum Reservoir Simulation, Applied Science Publishers Ltd., London, 1979

[2] H. Cao Development of Techniques for General Purpose Simulators, Stanford University Press, 2002

[3] M.G. Gerritsen; L.J. Durlofsky Modeling fluid flow in oil reservoirs, Annu. Rev. Fluid Mech., Volume 37 (2005), pp. 211-238

[4] P. Mostaghimi; J.R. Percival; D. Pavlidis; R.J. Ferrier; J.L.M.A. Gomes Anisotropic mesh adaptivity and control volume finite element methods for numerical simulation of multiphase flow in porous media, Math. Geosci., Volume 47 (2005) no. 4, pp. 417-440

[5] A. Negara; A. Salama; S. Sun Multiphase flow simulation with gravity effect in anisotropic porous media using multipoint flux approximation, Comput. Fluids, Volume 114 (2015), pp. 66-74

[6] J.W. Sheldon; W.T. Cardwell et al. One-Dimensional Incompressible Noncapillary Two-Phase Fluid Flow in a Porous Medium, Society of Petroleum Engineers, 1959

[7] T.F. Russell, et al. Stability analysis and switching criteria for adaptive implicit methods based on the CFL condition, in: SPE Symposium on Reservoir Simulation, 6–8 February 1989, Houston, TX, USA.

[8] M.R. Todd; P.M. O'dell; G.J. Hirasaki et al. Methods for Increased Ac curacy in Numerical Reservoir Simulators, Society of Petroleum Engineers, 1972

[9] K.H. Coats et al. IMPES stability: selection of stable timesteps, SPE J., Volume 8 (2003) no. 02, pp. 181-187 (Society of Petroleum Engineers)

[10] R. Courant; K. Friedrichs; H. Lewy Über die partiellen Differenzengleichungen der mathematischen Physik, Math. Ann., Volume 100 (1928), pp. 32-74

[11] P.H. Sammon et al. An analysis of upstream differencing, SPE Reserv. Eng., Volume 3 (1988) no. 3, pp. 1053-1056

[12] P.A. Forsyth Adaptive implicit criteria for two-phase flow with gravity and capillary pressure, SIAM J. Sci. Stat. Comput., Volume 10 (1989) no. 2, pp. 227-252

[13] J. Wan, P. Sarma, A.K. Usadi, B.L. Beckner, et al., General stability criteria for compositional and black-oil models, in: SPE Reservoir Simulation Symposium, 31 January–2 Feburary 2005, The Woodlands, TX, USA.

[14] G.M. Homsy Viscous fingering in porous media, Annu. Rev. Fluid Mech., Volume 19 (1987), pp. 271-311

[15] P. Horgue; C. Soulaine; J. Franc; R. Guibert; G. Debenest An open-source toolbox for multiphase flow in porous media, Comput. Phys. Commun., Volume 187 (2014), pp. 217-226

[16] J. Hrvoje Error analysis and estimation for the finite volume method with applications to fluid flows, Department of Mechanical Engineering Imperial College of Science, Technology and Medicine, London, 1996 (PhD thesis)

[17] H.G. Weller; G. Tabor; H. Jasak; C. Fureby A tensorial approach to computational continuum mechanics using object-oriented techniques, Comput. Phys., Volume 12 (1998), pp. 620-631

[18] C. Soulaine; P. Horgue; J. Franc; M. Quintard Gas–liquid flow modeling in columns equipped with structured packing, AIChE J., Volume 60 (2014) no. 10, pp. 3665-3674

[19] A. Shewani; P. Horgue; S. Pommier; G. Debenest; X. Lefebvre; E. Gandon; E. Paul Assessment of percolation through a solid leach bed in dry batch anaerobic digestion processes, Bioresour. Technol., Volume 178 (2015), pp. 209-216

[20] M. Muskat Physical Principles of Oil Production, McGraw Hill, New York, 1949

[21] S.E. Buckley; M.C. Leverett Mechanism of fluid displacement in sands, Trans. AIME, Volume 146 (1941) no. 1

[22] J.H.M. Thomeer et al. Introduction of a pore geometrical factor defined by the capillary pressure curve, J. Pet. Technol., Volume 12 (1960) no. 3

[23] A.T. Corey; R.H. Brooks Drainage characteristics of soils, Soil Sci. Soc. Am. J., Volume 39 (1975) no. 2, pp. 251-255

[24] M.T. Van Genuchten A closed-form equation for predicting the hydraulic conductivity of unsaturated soils, Soil Sci. Soc. Am. J., Volume 44 (1980) no. 5, pp. 892-898

[25] H.J. Morel-Seytoux; P.D. Meyer; M. Nachabe; J. Tourna; M.Th. Van Genuchten; R.J. Lenhard Parameter equivalence for the Brooks–Corey and van Genuchten soil characteristics: preserving the effective capillary drive, Water Resour. Res., Volume 32 (1996) no. 5, pp. 1251-1258

[26] M.A. Christie; M.J. Blunt et al. Tenth SPE comparative solution project: a comparison of upscaling techniques, SPE Reserv. Eval. Eng. (2001), pp. 308-317

[27] K.H. Coats et al. IMPES stability: the CFL limit, SPE J., Volume 8 (2003) no. 3

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