In the present article, we study the temperature effects on two-phase immiscible incompressible flow through a porous medium. The mathematical model is given by a coupled system of 2-phase flow equations and an energy balance equation. The model consists of the usual equations derived from the mass conservation of both fluids along with the Darcy-Muskat and the capillary pressure laws. The problem is written in terms of the phase formulation; ie, the saturation of one phase, the pressure of the second phase, and the temperature are primary unknowns. The major difficulties related to this model are in the nonlinear degenerate structure of the equations, as well as in the coupling in the system. Under some realistic assumptions on the data, we show the existence of weak solutions with the help of an appropriate regularization and a time discretization. We use suitable test functions to obtain a priori estimates. We prove a new compactness result to pass to the limit in nonlinear terms.
KEYWORDSimmiscible incompressible, nonisothermal two-phase flow, nonlinear degenerate system, existence, porous media
INTRODUCTIONModeling 2-phase flow through porous media is an important topic that spans a broad spectrum of engineering disciplines. Examples include geothermal systems, oil reservoir engineering, ground-water hydrology, and thermal energy storage. More recently, modeling multiphase flow received an increasing attention in connection with gas migration in a nuclear waste repository and sequestration of CO 2 .This work aims to incorporate the temperature effects into immiscible incompressible 2-phase flow in heterogeneous porous media. The basic equations for nonisothermal 2-phase flow in a porous medium involve mass conservation, Darcy's law, energy conservation, saturation, and capillary pressure constraint equations. The governing fluid and heat transport equations used to model thermal recovery processes are highly nonlinear. As fluid properties are defined as a function of temperature and pressure, there is a strong coupling between the mass balance and energy balance equations.
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