Mathematical structure of compositional reservoir simulation

Abstract

In this paper multicomponent two-phase isothermal fluid flow in petroleum reservoirs is described. The fluid-flow model consists of component conservation equations, Darcy's law for the volumetric flow rates, balance between the fluid volume and the rock void, and the conditions of thermodynamic equilibrium that determine the distribution of the chemical components into phases. Thermodynamic equilibrium is described by means of a mathematical model for the chemical potentials of each component in each phase of the fluid. The flow equations are manipulated to form a pressure equation and a modified component-conservation equation; these form the basis for the sequential method. It is shown that the pressure equation is parabolic under reasonable assumptions on the thermodynamic equilibrium model, and that the component-conservation equations are hyperbolic in the absence of diffusive forces such as capillary pressure and mixing. A numerical method based on the sequential formulation of the flow equations is outlined and used to illustrate the kinds of flow behavior that occur during miscible gas injection.