Reservoir simulations are limited to large-scale gridblocks because of prohibitive computational costs of fine-grid simulations. Rock properties, such as permeability, are measured on a scale smaller than coarse-scale simulation gridblocks. Therefore, the properties defined on a smaller scale are upscaled to a coarser scale. Few prior studies on permeability upscaling paid special attention to the problem of radial flow in the vicinity of a wellbore. This study presents an analytical method to calculate effective permeability of a coarse-grid wellblock from its constituent fine gridblocks. The method uses the incomplete-layer upscaling procedure, which is modified for radial flow around wellbore but applied to permeability heterogeneity defined in a Cartesian grid scheme. The method is validated by numerical simulations of primary and secondary recovery processes involving two-dimensional (2D) and three-dimensional (3D) systems. The simulation results with permeabilities from radial flow upscaling for wellblocks agreed better with the simulation results with the original permeabilities than results from linear-flow upscaling.

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