Single-phase Near-well Permeability Upscaling and Productivity Index Calculation Methods

Reservoir models with many grid blocks suffer from long run time; it is hence important to deliberate a method to remedy this drawback. Usual upscaling methods are proved to fail to reproduce fine grid model behaviors in coarse grid models in well proximity. This is attributed to rapid pressure changes in the near-well region. Standard permeability upscaling methods are limited to systems with linear pressure changes; therefore, special near-well upscaling approaches based on the well index concept are proposed for these regions with non-linear pressure profile. No general rule is available to calculate the proper well index in different heterogeneity patterns and coarsening levels. In this paper, the available near-well upscaling methods are investigated for homogeneous and heterogeneous permeability models at different coarsening levels. It is observed that the existing well index methods have limited success in reproducing the well flow and pressure behavior of the reference fine grid models as the heterogeneity or coarsening level increases. Coarse-scale well indexes are determined such that fine and coarse scale results for pressure are in agreement. Both vertical and horizontal wells are investigated and, for the case of vertical homogeneous wells, a linear relationship between the default (Peaceman) well index and the true (matched) well index is obtained, which considerably reduces the error of the Peaceman well index. For the case of heterogeneous vertical wells, a multiplier remedies the error. Similar results are obtained for horizontal wells (both heterogeneous and homogeneous models).