Abstract
Grid generation for reservoir simulation must honor classical key constraints and be boundary aligned such that control-volume boundaries are aligned with geological features such as layers, shale barriers, fractures, faults, pinch-outs, and multilateral wells. An unstructured grid generation procedure is proposed that automates control-volume and/or control point boundary alignment and yields a PEBI-mesh both with respect to primal and dual (essentially PEBI) cells. In order to honor geological features in the primal configuration, we introduce the idea of protection circles, and to generate a dual-cell feature based grid, we construct halos around key geological features. The grids generated are employed to study comparative performance of cell-centred versus cell-vertex control-volume distributed multi-point flux approximation (CVD-MPFA) finite-volume formulations using equivalent degrees of freedom. The formulation of CVD-MPFA schemes in cell-centred and cell-vertex modes is analogous and requires switching control volume from primal to dual or vice versa together with appropriate data structures and boundary conditions. The relative benefits of both types of approximation, i.e., cell-centred versus vertex-centred, are made clear in terms of flow resolution and degrees of freedom required.
Highlights
Subsurface reservoirs are often comprised of complex geometric and geologic objects and features
In order to construct primal-cell Boundary-aligned grids (BAGs), we introduce the idea of protection circles build around key geological features, this ensures integrity of features in the final Delaunay triangulation
In order to avoid swapping and to preserve integrity of features honoured in the empty mesh, we introduce the idea of protection circles that pass through the simplices constituting geological features
Summary
Subsurface reservoirs are often comprised of complex geometric and geologic objects and features. The schemes employed here have been designed to overcome the TPFA limitations and involve families of control-volume distributed multi-point flux approximations (CVD-MPFA), with flow variables and rock properties being controlvolume distributed and assigned to share the same controlvolume locations Both cell-vertex and cell-centred CVDMPFA formulations [19,20,21,22,23,24,25,26,27,28] are compared in this work on unstructured grids. The actual grid is generated such that dual-cell boundaries are aligned with key internal constraint boundaries and the cell-vertex approximation becomes the natural choice In this case, flow variables and rock properties are associated with grid cell vertices and their associated control-volumes resulting from the dual mesh. A comparison between the cell-centred and cell-vertex CVD-MPFA results and corresponding grids is presented, followed by conclusions
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