Application of diffuse source functions for improved flow upscaling

A novel upscaling approach was previously introduced using pressure transient concepts which allowed us to distinguish between well-connected, weakly connected, and disconnected pay in the local upscaling region. The current work applies these same concepts to benchmark the upscaling formulation against existing upscaling techniques to test the impact of localization. The local flow field generated for transmissibility calculation is based on transients approaching pseudo steady state in a sub volume as opposed to steady state or pseudo steady state in the entire volume. Identification of well-connected sub volume allows us to assess the impact of localization and degree of local connectivity on overall coarse simulation performance. The upscaling step draws upon its similarity to pressure transient well testing concepts to set up local flow problems and obtain coarse transmissibilities. The concept of diffusive time of flight together with diffuse source functions allows us to assess the error in localization for a particular local flow problem. A large error in localization may require adaptive grid resolution as a possible solution by separating the well-connected and weakly connected pay. The transient methodology has also allowed us to generalize the flow diagnostics designed for incompressible flow to compressible flow. The diagnostics are used to evaluate the quality of coarsening and upscaling.