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 deliberatea method to remedy this drawback. usual upscaling methods are proved to fail to reproduce fine gridmodel behaviors in coarse grid models in well proximity. this is attributed to rapid pressure changesin the near-well region. standard permeability upscaling methods are limited to systems with linearpressure changes; therefore, special near-well upscaling approaches based on the well index conceptare proposed for these regions with non-linear pressure profile. no general rule is available tocalculate 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 heterogeneouspermeability models at different coarsening levels. it is observed that the existing well index methodshave limited success in reproducing the well flow and pressure behavior of the reference fine gridmodels as the heterogeneity or coarsening level increases. coarse-scale well indexes are determinedsuch that fine and coarse scale results for pressure are in agreement. both vertical and horizontal wellsare investigated and, for the case of vertical homogeneous wells, a linear relationship between thedefault (peaceman) well index and the true (matched) well index is obtained, which considerablyreduces the error of the peaceman well index. for the case of heterogeneous vertical wells, amultiplier remedies the error. similar results are obtained for horizontal wells (both heterogeneousand homogeneous models).