Multiscale/Mimetic Pressure Solvers with Near-well Grid Adaptation

Multiscale methods have proved to be an efficient means to achieving fast simulations on large reservoir models. The main characteristic of these methods is high resolution flow fields obtained at relatively low computational cost. We are thus able to resolve large scale flow patterns as well as fine-scale details that would be impossible to obtain for models for which direct simulation using traditional methods would be prohibitive. However, there are still a number of open problems in applying these methods to reservoir simulation. In particular, we observe some discrepancy in the performance of wells when compared to direct simulation on the fine-scale grid. To improve the multiscale method's predictive power for individual wells, we consider two direct opposite strategies: First, by resolving the near-well flow in the coarse grid by adaptive grid refinement in regions near wells. Second, by ensuring that near-well flow is sufficiently captured in the corresponding multiscale basis functions. For the latter strategy, we consider both adaptive alignment of coarse pressure grid to well trajectories, and an oversampling method for the computation of the multiscale basis functions corresponding to wells. In this paper we will study the effects of such near-well grid adaptations, and state pros and cons for the approaches considered.