Finite Volume Methods for Coupled Stress/Fluid Flow in a Commercial Reservoir Simulator

Abstract

Abstract The flow equations in commercial reservoir simulators are generally discretized using the finite difference method, whereas for stress equations it is more common to use the finite element approach. In a reservoir simulator designed to include geomechanical effects, these two distinct types of equations must be solved with some degree of coupling. It is therefore natural to ask whether suitable finite volume methods can be derived for the stress equations - so that the stress and fluid flow models can share a common derivation, and what are the relative merits of finite volume and finite element methods for these coupled systems. In this paper we present a finite volume discretization of the stress equations as implemented in a commercial reservoir simulator with an option to couple the stress with the fluid flow. We demonstrate that the method is locally conservative and retains second order accuracy on general threedimensional grids. We discuss the imposition of various types of boundary condition and describe the implementation of special features such as faults, pinch-outs and local grid refinements. We also present a comparison with other approaches based on finite differences1,2 and finite elements3. The relative accuracy, efficiency and robustness of these three different approaches are discussed. Finally the paper presents some case studies demonstrating the suitability of the finite volume approach for realistic geomechanical simulations.