The mathematical structure of multiphase thermal models of flow in porous media

Abstract

This paper is concerned with the formulation and numerical solution of equations for modelling multicomponent, two-phase, thermal fluid flow in porous media. The fluid model consists of individual chemical component (species) conservation equations, Darcy's law for volumetric flow rates and an energy equation in terms of enthalpy. The model is closed with an equation of state and phase equilibrium conditions that determine the distribution of the chemical components into phases. It is shown that, in the absence of diffusive forces, the flow equations can be split into a system of hyperbolic conservation laws for the species and enthalpy and a parabolic equation for pressure. This decomposition forms the basis of a sequential formulation where the pressure equation is solved implicitly and then the component and enthalpy conservation laws are solved explicitly. A numerical method based on this sequential formulation is presented and used to demonstrate some typical flow behaviour that occurs during fluid injection into a reservoir.