Kristian Holme

• Holme, Kristian; Lie, Knut-Andreas; Møyner, Olav & Johansson, August (2025). Grid-Orientation Effects in the 11th SPE Comparative Solution Project Using Unstructured Grids and Consistent Discretizations. SPE Journal. ISSN 1086-055X. 30(10), p. 6313–6328. doi: 10.2118/223885-PA. Full text in Research Archive Show summary

  We present a systematic investigation into how the choice of grid type and discretization scheme affects predictions in the 11th SPE Comparative Solution Project (SPE11). Focusing on Case B, we compare grid types with varying conformity with internal aquifer geometry: standard Cartesian grids, two types of cut-cell grids, perpendicular bisector (PEBI) grids, hybrid quadrilateral-triangle grids, and Delaunay-triangulated grids. These grids are coupled with state-of-the-art flux approximation schemes: The standard two-point flux approximation (TPFA) scheme, which is inconsistent on non-K-orthogonal grids, and three consistent schemes—multipoint flux approximation (MPFA), average multipoint flux approximation (AvgMPFA), and nonlinear two-point flux approximation (NTPFA). For transport terms, we evaluate a second-order weighted essentially nonoscillatory (WENO) scheme as an alternative to the standard single-point upstream-mobility weighting (SPU) scheme as a means to reduce numerical smearing and directional bias. Simulations are conducted using isothermal black oil and multicomponent K-value thermal flow models implemented in the open-source MRST and JutulDarcy simulators. (The thermal model assumes a constant thermal gradient for simplicity.) We also include results from Case C, emphasizing computational efficiency. We observe that variability in the prediction of overall plume migration and measurables used as proxies for assessing risk, such as pointwise pressure buildup, is modest across grid types and discretization schemes. However, the choice of grid type significantly affects the formation of the self-enhancing dissolution fingers that drive convective mixing beneath the CO2 plume—a key focus of the comparative solution project. These fingers form at locations where the discrete grid representation of the CO2-brine interface deviates from the true interface. The greater the number of deviation points, the more fingers will be triggered. Likewise, the more irregular the local representation of the interface, the stronger the fingers develop. In comparing different grid types and discretizations, we conclude that Cartesian grids with the standard TPFA/SPU discretization are likely the best choice for high-resolution simulations. Most simulators are optimized for this combination, and deviations from K-orthogonality are relatively minor for Case C and entirely absent in Case B. For simulations at more modest resolutions, we recommend using a grid type that better conforms to faults and facies boundaries, preferably a cut-cell grid. While such grids are generally not K-orthogonal, using a consistent discretization like AvgMPFA can help mitigate inconsistency errors that might otherwise compromise simulation accuracy.

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