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

摘要

The flow equations in commercial reservoir simulators aregenerally discretized using the finite difference method,whereas for stress equations it is more common to use thefinite element approach. In a reservoir simulator designed toinclude geomechanical effects, these two distinct types ofequations must be solved with some degree of coupling. It istherefore natural to ask whether suitable finite volumemethods can be derived for the stress equations - so that thestress and fluid flow models can share a common derivation,and what are the relative merits of finite volume and finiteelement methods for these coupled systems.In this paper we present a finite volume discretization of thestress equations as implemented in a commercial reservoirsimulator with an option to couple the stress with the fluidflow. We demonstrate that the method is locally conservativeand retains second order accuracy on general threedimensionalgrids. We discuss the imposition of various typesof boundary condition and describe the implementation ofspecial features such as faults, pinch-outs and local gridrefinements. We also present a comparison with otherapproaches based on finite differences1,2 and finite elements3.The relative accuracy, efficiency and robustness of these threedifferent approaches are discussed.Finally the paper presents some case studies demonstrating thesuitability of the finite volume approach for realisticgeomechanical simulations.