The average pore-pressure, , defined as the sum of the product of the saturation and pressure of the fluid phases is widely used as the average pore-pressure of multiphase fluid systems in deformable porous media. Using the incremental formulation, Coussy (2004) shows that for systems with multiple fluid phases, the ‘equivalent’ pore-pressure, pE, defined as minus the interfacial energy is the appropriate quantity. We investigate the accuracy and stability of the fully implicit method (FIM) for multiphase flow and mechanical deformation based on and pE. We then study the convergence and stability properties of sequential-implicit coupling strategies. The findings from stability theory are verified using nonlinear simulation of two-phase flow with mechanical deformation. Our analysis of FIM for systems with strong capillarity indicates that using leads to serious numerical instabilities, and to significant deviations from the reference solution even when the solutions are stable. Our analysis and simulation results indicate that, in contrast, using pE leads to unconditional stability and accurate solutions.
For the sequential-implicit coupling strategies, our previously published results for single-phase flow carry over for multiphase systems when the equivalent pore-pressure, pE, is used in the conservation equations and constitutive relations. Specifically, the undrained and fixed-stress schemes are unconditionally stable. The fixed-stress split is superior to the undrained approach in terms of convergence behavior. Therefore, we recommend the incremental formulation based on the equivalent pore-pressure for coupled multiphase flow and mechanics. In terms of stability and convergence properties, we recommend the fixed-stress sequential-implicit scheme.