An Integration of Multilevel Local-Global Upscaling With Grid Adaptivity
James V. Lambers, Margot G. Gerritsen · SPE Annual Technical Conference and Exhibition · 2005
Abstract We present an iterative method for generating appropriate coarse scale models for adaptive flow simulation in highly heterogeneous reservoir formations. Our approach applies to any strategy for generating structured adaptive grids, but we will focus on Cartesian Cell-based Anisotropic Refinement (CCAR) grids due to their suitability for EOR processes that require aggressive refinement. We first construct an initial grid that captures the principal flow paths in the reservoir. Refinement is driven by regions of greater heterogeneity in the fine-scale permeability field, which are detected using a connected set approach1. Next, we generate a hierarchy of coarse-scale permeability fields, beginning with the finest scale on the simulation grid. Each field is computed using a local-global upscaling approach2, which employs generic global coarse scale simulations to determine the boundary conditions for the local calculation of upscaled transmissibilities or diagonal permeability tensors. An iteration procedure assures consistency between the local and global calculations. As we proceed to coarser scales, permeability values at finer scales are fixed in order to ensure that fine-scale high permeability flow paths are preserved. This is especially important when simulating gas injection processes because the highly mobile gas will preferentially flow through these paths. Thus we obtain a permeability field that yields an accurate global flow solution with sufficient local resolution where required. Adaptivity eliminates the need to represent permeability with full tensors; diagonal tensors are sufficient. Furthermore, the combination of adaptivity determined by the connected set approach, and the local-global upscaling (which introduces global connectivities) leads to accurate representation of potential flow paths. Because of this, we significantly reduce process dependency. For highly heterogeneous (e.g., channelized) systems, this new approach is shown to consistently provide more accurate coarse scale models for global flow in a variety of directions, relative to reference fine scale results, than do existing local, extended local, or local-global upscaling techniques applied to uniform grids.