Application of diffuse source basis functions for improved near well upscaling

摘要

Abstract Near well flow can have a significant impact on the accuracy of the upscaling of geologic models. A recent benchmark study has shown that these errors may dominate over other aspects of upscaling in commercial reservoir simulators. This same study showed the advantage of “Diffuse Source” (DS) upscaling over previous approaches. We now demonstrate the application of the DS basis functions to the calculation of the upscaled well index and the well cell intercell transmissibilities. DS upscaling is an extension of pseudo-steady-state (PSS) flow based upscaling that utilizes the diffusive time of flight to distinguish well-connected and weakly-connected sub-volumes. DS upscaling retains the localization advantage of a PSS calculation: unlike steady state flow, the local upscaling problem does not couple to adjacent regions, and local-global iterations are not required. DS upscaling has been developed and utilized for the calculation of the intercell transmissibility, but we now apply it to the calculation of the upscaled well index. Consistent with other researchers, we adjust the intercell transmissibilities in the near well region. We also consider the upscaling of the well index for a reservoir model in which the well trajectory and the high resolution geologic model are not simultaneously available. For many practitioners, this remains the most common reservoir modeling workflow. The result is an algebraic well index upscaling calculation, which also improves upon commercial applications. The industry standard for the well index follows Peaceman. We show that PSS/DS upscaling reduces to Peaceman’s well index on a coarse grid, and is consistent with Peaceman’s numerical convergence analysis. (In contrast, steady state upscaling for the well index reduces to the Dietz well index.) The current approach is a generalization of Peaceman’s well index, but now extended to represent near well reservoir heterogeneity and with the arbitrary placement of a well perforation within a simulation well cell. Consistent with steady state upscaling, we find an advantage in adjusting the intercell transmissibility in the near well region. However, we have found that it is only necessary to do so for the well cell itself, which may be a consequence of the improved localization of the current calculation. The new methodology performs very well. It is tested for two models, including the SPE10 reference model and the Amellago carbonate outcrop model. We compare the results to steady state flow based upscaling, the algebraic well index upscaling described above, and algorithms found in commercial applications.