Stabilized finite element methods for coupled geomechanics and multiphase flow

Geomechanical models are needed to account for rock deformation resulting from flow-induced pressure changes in stress sensitive reservoirs. There are, however, several numerical issues that must be resolved before these coupled models can be used reliably. In addition, the stability, convergence and accuracy for these coupled procedures have not been considered in detail.; In the 1980's, the phenomenon of intensified spatial oscillations of the pore pressure in consolidation problems was examined. It was shown that the causes of this problem are the saddle point mechanism in the coupled equations as well as a violation of the Babuška-Brezzi condition. This condition stipulates that only certain combinations of finite element base functions can be used for pressure and displacement in standard Galerkin techniques. A new numerical scheme using a discontinuous Galerkin method in time and a stabilized finite element method in space was developed to circumvent the difficulties observed with standard approaches. Numerical calculations clearly show that the stabilized method can improve stability while maintaining consistency.; There are several types of coupled methods in the literature, mainly iteratively coupled and fully coupled methods. We developed a fully coupled method by using the Galerkin Method for the force balance equations and the finite difference methods for the mass balance equations. However, this fully coupled method is also subject to the Babuška-Brezzi condition. To solve large scale reservoir problems, a novel framework is proposed which combines a stabilized finite element method to solve the force balance and pressure equations and a control-volume finite difference method to solve the remaining component mass balance equations. All of the equations are solved in a fully coupled fashion. This framework is applicable for different finite element techniques appropriate for geomechanics, while still tightly coupling the geomechanics with state-of-the-art reservoir flow models. In this way, we are able to prevent pressure oscillation and numerical instability. This method is also compared with existing fully coupled and iteratively coupled methods. These comparisons demonstrate consistent results on homogeneous reservoirs with compressible fluids, and the stabilized methods provide improved stability at early times and for reservoirs with very low permeability barriers.