Rigorous Coupling of Geomechanics and Multiphase Flow with Strong Capillarity Academic Article uri icon

abstract

  • Summary We 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.

author list (cited authors)

  • Kim, J., Tchelepi, H., & Juanes, R.

citation count

  • 51

publication date

  • December 2013