Impact of grid non-K-orthogonality on CO2 migration and pressure prediction using two-point and multi-point flux approximation methods

Accurate simulation of multiphase flow is essential for predicting pressure buildup and CO2 plume migration in geological carbon storage. The two-point flux approximation (TPFA) method is widely used in reservoir simulation due to its simplicity, but it is only consistent on K-orthogonal grids. Realistic subsurface models, however, often involve non-K-orthogonal grids caused by geological features such as faults and fractures, where TPFA may introduce significant errors. This study systematically quantifies the numerical error associated with using TPFA on non-K-orthogonal grids in the context of CO2 storage in saline aquifers. Based on the formalism of the TPFA method, a numerical index is proposed in this work for the first time to quantify the degree of grid non-K-orthogonality. A series of numerical experiments are presented to compare the TPFA and multi-point flux approximation (MPFA) methods, with high-resolution reference solutions used as benchmarks. Results show that grid non-K-orthogonality can impact the accuracy of both TPFA and MPFA solutions with larger degree of grid non-K-orthogonality leading to larger solution errors in general. The magnitude of solution errors of the MPFA method is significantly smaller than that of TPFA in terms of both pressure solution and CO2 saturation as it is much more robust against grid non-K-orthogonality effect. In particular, the TPFA method can produce substantial deviations in CO2 saturation distributions when grid non-K-orthogonality is present, indicating the necessity of more advanced discretization methods such as MPFA for modeling the CO2 plume migration behavior more accurately. These findings highlight the importance of selecting appropriate discretization methods for geologically complex reservoirs and the proposed grid non-K-orthogonality index can help evaluate the solution accuracy in a general simulation study. Our results offer practical guidance on the tradeoffs between computational efficiency and physical accuracy in carbon storage modeling.