A multilevel multiscale mimetic (M3) method for two-phase flows in porous media

Flow simulations in porous media involve a wide range of strongly coupled scales. The length scale of short and narrow channels is on the order of millimeters, while the size of a simulation domain may be several kilometers (the richest oil reservoir in Saudi Arabia, Ghawar, is 280 km ×30 km). The permeability of rock formations is highly heterogeneous and may span several orders of magnitude, from nearly impermeable barriers to high-permeable flow channels. For such complex systems fully resolved simulations become computationally intractable. To address this problem we developed the new Multilevel Multiscale Mimetic (M3) method [1]. This method posseses several distinctive features that lead to more reliable, robust, and efficient simulations of subsurface flows: Upscaled model. Using the same mathematical model with averaged parameters to perform simulations at a much coarser scale does not adequately capture the influence of the fine-scale structure. In contrast, the M3 method constructs a hierarchical sequence of coarse-scale models, which provides a framework to capture fine-scale effects more accurately. Multilevel hierarchy. Many different model upscaling approaches have been proposed (cf. [2, 3]). All of these methods, except the Multilevel Upscaling (MLUPS) method [3], consider a two-level structure: coarseand fine-scale grids. Using a two-level structure most multiscale methods achieve a coarsening factor of approximately 10 in each coThe absolute permeability, K, of the 68th layer in an SPE benchmark model (left). Locations of the injector (×) and the producers (◦) (right).