Modeling and Numerical Simulations of Immiscible Compressible Two-Phase Flow in Porous Media by the Concept of Global Pressure |
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Authors: | Brahim Amaziane Mladen Jurak Ana ?galji? Keko |
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Institution: | 1.Laboratoire de Mathématiques et de leurs Applications, CNRS-UMR 5142,Université de Pau,Pau,France;2.Department of Mathematics,University of Zagreb,Zagreb,Croatia;3.Faculty of Electrical Engineering and Computing,University of Zagreb,Zagreb,Croatia |
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Abstract: | 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). |
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