Richard E. Ewing
Institute for Scientific Computation
Texas A&M University
ewing@science.tamu.edu

The purpose of mathematical reservoir simulation models in petroleum applications is to try to optimize the recovery of hydrocarbon from permeable underground reservoirs. In order to accomplish this, one must be able to predict the performance of the reservoir under various production schemes. Models must be constructed to describe the complex geochemical, physical, and multiphase flow processes that accompany the various recovery techniques. The models require the estimation and modeling of various rock and fluid properties that influence the flow. Upscaling must be utilized to provide effective flow properties for coarse-grid models used for field-scale simulations. However, localized flow regimes at sub-coarse grid scales must often be resolved using local grid refinement, possibly coupled with local time-stepping techniques. Patch grid-refinement strategies coupled with domain-decomposition methods can be incorporated in existing reservoir simulators. Finite volume element methods for accurate resolution of localized geometrics can be coupled with cell-centered finite difference methods used in many existing simulators. Aspects of coupling different grids, different discretization schemes and different physical equations via mortar techniques will be presented. Numerical results will be discussed.