Operator Splitting of Advection and Diffusion on Non-uniformly Coarsened Grids

High-resolution geological models of subsurface reservoirs typically contain much more details than can be used in conventional reservoir simulators. Geomodels are therefore upscaled before flow simulation is performed. Here, we present a non-uniform coarsening strategy to upscale geomodels, where the coarse grid is generated by grouping cells in the fine-scaled geomodel selectively into connected coarse blocks, with some minimum volume and with the total flow through each coarse block bounded above. Transport is then modeled on this simulation grid. For purely advective flow, the coarsening strategy has been shown to be robust, allowing for both accurate and fast transport simulations of highly heterogeneous and fractured reservoirs. Here, we consider advection-dominated two-phase flow, where the capillary diffusion is discretized separately from the advective and gravity terms using operator splitting. In particular, we investigate different damping strategies of the diffusive term to counteract overestimation of the diffusion operator on the coarse grid, this to ensure accurate diffusion modelling in the transport solver.