Rigorous Coupling of Geomechanics and Multiphase Flow with Strong Capillarity

Abstract

SummaryWe study sequential formulations for coupled multiphase flow and reservoir geomechanics. First, we identify the proper definition of effective stress in multiphase-fluid systems. Although the average pore-pressure p¯ —defined as the sum of the product of saturation and pressure of all the fluid phases that occupy the pore space—is commonly used to describe multiphase-fluid flow in deformable porous media, it can be shown that the "equivalent" pore pressure pE —defined as p¯ minus the interfacial energy—is the appropriate quantity (Coussy 2004). We show, by means of a fully implicit analysis of the system, that only the equivalent pore pressure pE leads to a continuum problem that is thermodynamically stable (thus, numerical discretizations on the basis of the average pore pressure p¯ cannot render unconditionally stable and convergent schemes). We then study the convergence and stability properties of sequential-implicit coupling strategies. We show that the stability and convergence properties of sequential-implicit coupling strategies for single-phase flow carry over for multiphase systems if the equivalent pore pressure pE is used. Specifically, the undrained and fixed-stress schemes are unconditionally stable, and the fixed-stress split is superior to the undrained approach in terms of convergence rate. The findings from stability theory are verified by use of nonlinear simulations of two-phase flow in deformable reservoirs.