Rigorous Coupling of Geomechanics and Multiphase Flow with Strong Capillarity
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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 spaceis 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 energyis 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.
