Multiphysics and multiscale methods for modeling fluid flow through naturally fractured vuggy carbonate reservoirs

We present a novel approach for flow simulations through naturally-fractured vuggy carbonate reservoirs. This approach generalizes upscaling methods which have been successfully used to perform reservoir simulations on geological (fine) scales. Typically, vugular porous media is described using both Stokes and Darcy's equations at the fine-scale. We propose the use of simplified model based on Stokes-Brinkman equations. Stokes and Darcy equations can be obtained from these equations by appropriate choice of parameters. Moreover, in the presence of damaged zones between vugular regions and Darcy regions, Stokes-Brinkman equations allow a seamless transition. The upscaling of fine-scale equations is addressed within homogenization theory. Appropriate local problems are solved to compute the effective permeabilities, which are further used for the simulations on the field scale. We present numerical results for homogeneous and heterogeneous background permeability fields. Our results show that the coarse-scale permeability field is greatly affected when the background permeability is heterogeneous. This is due to the fact that the high flow channels connecting some of the vugs significantly alter the upscaled permeability. We compare the coarse-scale pressure obtained from upscaled equations with the averaged fine-scale pressure. The results are in agreement which indicates that the upscaled models are accurate for practical purposes.