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Model of kinematic waves for gas–liquid segregation with phase transition in porous media

  • Stephane Zaleski (a1) and Mikhail Panfilov (a1) (a2)
Abstract

We consider the problem of gas–liquid flow with phase transition in a porous medium, governed by the buoyancy force. Free gas releases due to continuous pressure decrease. We take into account the gas expansion and the dissolution of chemical components in both phases controlled by the local phase equilibrium. We have developed an asymptotic model of flow for low pressure gradients in the form of a nonlinear hyperbolic system of first order with respect to the liquid saturation and the total flow velocity, which is the extended non-homogeneous Buckley–Leverett model. In two asymptotic cases determined by two different ratios between the characteristic times, this model is completely decoupled from pressure, i.e. the pressure enters in this model as a parameter determined through an independent formula. The segregation problem with phase transition in a bounded domain is solved for two cases of boundary conditions. The saturation behaviour is described in terms of nonlinear kinematic waves, whose evolution follows a complex segregation scenario, which includes the wave reflection and formation of shocks. The macroscopic gas–liquid interfaces are described in terms of shock waves. The comparison with numerical simulations shows satisfactory results.

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Corresponding author
Email address for correspondence: michel.panfilov@dalembert.upmc.fr
References
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Bank, R., Rose, D. & Fichtner, W. 1983 Numerical methods for semiconductor device simulation. IEEE Trans. Electron Devices 30 (9), 10311041.
Bastian, P., Blatt, M., Dedner, A., Engwer, C., Klofkorn, R., Kornhuber, R., Ohlberger, M. & Sander, O. 2008 A generic grid interface for parallel and adaptive scientific computing. part II: Implementation and tests in DUNE. Computing 82 (23), 121138.
Bedrikovetsky, P. 1993 Mathematical Theory of Oil and Gas Recovery. Kluwer Academic Publishers.
Buckley, S. E., Leverett, M. C. et al. 1942 Mechanism of fluid displacement in sands. Trans. AIME 146, 107116.
Chraïbi, M.2008 Modélisation de l’expasion de gaz dissout dans les huiles lourdes en milieux poreux. PhD thesis, Université Pirerre et Marie Curie, 31 janvier (thesis director S. Zaleski).
Entov, V. M. 2000 Nonlinear waves in physicochemical hydrodynamics of enhanced oil recovery. Multicomponent flows. In Porous Media: Physics, Models, Simulation: Proceedings of the International Conference, Moscow, Russia, pp. 1921. World Scientific Publishing Co Inc., p. 33.
Entov, V. M. & Zazovsky, A. 1989 Hydrodynamics of Enhanced Oil Recovery (ed. Nedra Moscow) (in Russian).
Flemisch, B., Darcis, M., Erbertseder, K., Faigle, B., Lauser, A., Mosthaf, K., Muthing, S., Nuske, P., Tatomir, A., Wolff, M. et al. 2011 DuMux: DUNE for multi-phase, component, scale, physics, … flow and transport in porous media. Adv. Water Resour. 34 (9), 11021112.
Kalisch, H., Mitrovic, D. & Nordbotten, J. M. 2015 Non-standard shocks in the Buckley–Leverett equation. J. Math. Anal. Appl. 428, 882895.
Kramer, K., Nicholas, G. & Hitchon, W. 1997 Semiconductor Devices, a Simulation Approach. Prentice Hall Professional Technical Reference.
Orr, F. M. 2002 Theory of Gas Injection Processes. Stanford University.
Panfilov, M. 1986 Quasi-equilibrium asymptotics of the depletion of subsurface petroleum and gas strata. Dokl. Acad. Nauk SSSR 31 (5), 225227.
Panfilov, M., Zaleski, S. & Josserand, C. 2016 Mechanisms of formation of natural hydrogen reservoirs in thermal aquifers: impact of methanogen bacteria and the non equilibrium of gas bubble dynamics. In Procs. ECMOR-15: 15th European Conference on Mathematics of Oil Recovery, Amsterdam, the Netherlands, August 29–Septembre 1, paper WE GRA 06.
Patankar, S. V. 1980 Numerical Heat Transfer and Fluid Flow. McGraw-Hill Book Company.
Rhee, H., Aris, R. & Amundson, N. R. 1986 First-Order Partial Differential Equations, vol. 1. Prentice-Hall.
Young, R. 1993 Two-phase geothermal flows with conduction and the connection with Buckley–Leverett theory. Trans. Porous Med. 12 (3), 261278.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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