Modeling and Numerical Simulations of Immiscible Compressible Two-Phase Flow in Porous Media by the Concept of Global Pressure
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A new formulation is presented for the modeling of immiscible compressible two-phase flow in porous media taking into account gravity, capillary effects, and heterogeneity. The formulation is intended for the numerical simulation of multidimensional flows and is fully equivalent to the original equations, contrary to the one introduced in Chavent and Jaffré (Mathematical Models and Finite Elements for Reservoir Simulation, 1986). The main feature of this formulation is the introduction of a global pressure. The resulting equations are written in a fractional flow formulation and lead to a coupled system which consists of a nonlinear parabolic (the global pressure equation) and a nonlinear diffusion–convection one (the saturation equation) which can be efficiently solved numerically. A finite volume method is used to solve the global pressure equation and the saturation equation for the water and gas phase in the context of gas migration through engineered and geological barriers for a deep repository for radioactive waste. Numerical results for the one-dimensional problem are presented. The accuracy of the fully equivalent fractional flow model is demonstrated through comparison with the simplified model already developed in Chavent and Jaffré (Mathematical Models and Finite Elements for Reservoir Simulation, 1986).
KeywordsImmiscible compressible two-phase flow Global pressure Porous media Water hydrogen
Mathematics Subject Classification (2000)76S05 35Q35
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- Amaziane B., Jurak M.: A new formulation of immiscible compressible two-phase flow in porous media. C. R. Mecanique 336, 600–605 (2008)Google Scholar
- ANDRA: Couplex-Gaz: http://www.gdrmomas.org/ex_qualifications.html (2006). Accessed 6 October 2009
- Antontsev S.N., Kazhikhov A.V., Monakhov V.N.: Boundary Value Problems in Mechanics of Nonhomogeneous Fluids. North-Holland, Amsterdam (1990)Google Scholar
- Bear J., Bachmat Y.: Introduction to Modeling of Transport Phenomena in Porous Media. Kluwer, London (1991)Google Scholar
- Chavent, G.: A fully equivalent global pressure formulation for three-phases compressible flows. Appl. Anal. (2009). doi: 10.1080/00036810902994276
- Chavent G., Jaffré J.: Mathematical Models and Finite Elements for Reservoir Simulation. North– Holland, Amsterdam (1986)Google Scholar
- Chen Z., Huan G., Ma Y.: Computational Methods for Multiphase Flows in Porous Media. SIAM, Philadelphia (2006)Google Scholar
- Galusinski C., Saad M.: Weak solutions for immiscible compressible multifluids flows in porous media. C. R. Acad. Sci. Paris Ser. I 347, 249–254 (2009)Google Scholar
- Helmig R.: Multiphase Flow and Transport Processes in the Subsurface. Springer, Berlin (1997)Google Scholar
- OECD/NEA: Safety of Geological Disposal of High-level and Long-lived Radioactive Waste in France. An International Peer Review of the “Dossier 2005 Argile” Concerning Disposal in the Callovo-Oxfordian Formation. OECD Publishing (2006). http://www.nea.fr/html/rwm/reports/2006/nea6178-argile.pdf. Accessed 6 October 2009