Abstract
In this paper, we introduce a numerical study of the hydrocarbon system used for petroleum reservoir simulations. This system is a simplified model which describes a two-phase flow (oil and gas) with mass transfer in a porous medium, which leads to fluid compressibility. This kind of flow is modeled by a system of parabolic degenerated non-linear convection-diffusion equations. Under certain hypotheses, such as the validity of Darcy’s law, incompressibility of the porous medium, compressibility of the fluids, mass transfer between the oil and the gas, and negligible gravity, the global pressure formulation of Chavent (Mathematical Models and Finite Elements for Reservoir Simulation: Single Phase, Multiphase and Multicomponent Flows Through Porous Media, 1986) is formulated. This formulation allows the establishment of theoretical results on the existence and uniqueness of the solution (Gasmi and Nouri in Appl. Math. Sci. 7(42):2055-2064, 2013). Furthermore, different numerical schemes have been considered by many authors, among others we can refer the reader to (Chen in Finite element methods for the black oil model in petroleum reservoirs, 1994; Chen in Reservoir Simulation: Mathematical Techniques in Oil Recovery, 2007) and (Gagneux et al. in Rev. Mat. Univ. Complut. Madr. 2(1):119-148, 1989). Here we make use of a scheme based on the finite volume method and present numerical results for this simplified system.
Highlights
The fluids flow within porous media has an important role in various domains, such as geothermal studies, geotechnics, chemical engineering, ground water storage, hydrocarbon exploitation, etc
In this paper we introduce a finite volume method for solving the hydrocarbon system model often used for petroleum reservoir simulations
6 Conclusion In this paper we proposed a new scheme based on the finite volume method for solving the displacement of a fluid by another one, within a porous medium, while the displacing fluid is immiscible with the fluid being displaced
Summary
The fluids flow within porous media has an important role in various domains, such as geothermal studies, geotechnics (the mechanics of soils), chemical engineering, ground water storage, hydrocarbon exploitation (see references [ ] and [ ]), etc. This model, called a hydrocarbon system, is a simplified compositional model describing two-phase flow in a porous medium with mass interchange between them It can predict compressibility and mass transfer effects, in the sense that it is assumed that there is mass transfer between the oil and the gas phase. With constant dynamic viscosities and where the gravity effect is neglected Under these hypotheses, Darcy?s law combined with the mass conservation equations for each one of the component leads to the following system of partial differential equations of parabolic convection-diffusion type:. By adding the last two equations and noting that CGg + COg = , we obtain ρg The substitution of these mass fractions and densities into ( ) gives, for the gas and the oil components,.
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