Stabilized Finite Element Methods for Coupled Geomechanics – Reservoir Flow Simulations

Abstract

Abstract Coupled geomechanical-fluid flow models are needed to account for rock deformation resulting from flow-induced pressure changes in stress sensitive reservoirs. There are, however, issues of numerical stability that must be addressed before these coupled models can be used reliably. Specifically, it is known that standard procedures can lead to pressure oscillations as a result of the violation of the Babuška-Brezzi (B-B) condition, which requires unequal order interpolation of the displacement and pore-pressure variables. In this paper, a number of different types of coupled models are considered. A novel finite element method is developed to circumvent the B-B condition. The method applies a stabilized finite element technique to solve the force balance and pressure equations along with a finite volume method to solve the remaining component mass balance equations. All of the equations are solved in a fully coupled fashion. This method is compared with fully coupled and iteratively coupled models developed using non-stabilized finite elements for the force balance with finite volume methods for all of the component mass balance equations. These comparisons demonstrate that all methods perform reliably on homogeneous reservoirs over long time scales. The stabilized method is shown to provide improved stability at early times and for reservoirs with very low permeability barriers.