Modeling Compositional Compressible Two-phase Flow in Porous Media by the Concept of the Global Pressure

Abstract

The modeling of multiphase flow in porous formations is important for both the management of petroleum reservoirs and environmental remediation. More recently, modeling multiphase flow received an increasing attention in connection with the disposal of radioactive waste and sequestration of CO2. In this talk, we will discuss a new formulation for modeling compositional compressible two-phase flow in porous media such as immiscible gas injection in oil reservoirs or gas migration through engineered and geological barriers in a deep repository for radioactive waste . The focus is on the problems arising due to Newton-Raphson's flash calculations and the phase appearance and disappearance . Compositional compressible two-phase flows in porous media are usually modeled by the mass balance law written for each component, Darcy-Muscat's law, and the thermodynamic equilibrium between the phases . The obtained equations represent a set of highly coupled nonlinear partial differential equations. In order to model both saturated and unsaturated zones, one has to change the main unknowns of the system. In the saturated zones, the pressure and the saturation of one of the phases are commonly chosen as the main unknowns, whereas in the unsaturated zones the saturation may be replaced by the mass density of one of the component in its phase. To avoid changing the main unknowns, and to make the system coupling weaker, we derive a new formulation of the compositional compressible liquid and gas flow. The formulation considers gravity, capillary effects and diffusivity of each component. The main feature of this formulation is the introduction of a new variable called the global pressure. The derived system is written in terms of the global pressure and the total gas mass density that partially decouples the equations and is able to model the flows both in the saturated and unsaturated zones with no changes of the primary unknowns. The mathematical structure is well defined: the system consists of two nonlinear degenerate parabolic equations. The derived formulation is fully equivalent to the original equations and is more suitable for mathematical and numerical analysis. The accuracy and effectiveness of the new formulation is demonstrated through numerical results.