In reservoir simulation, a proper treatment of wells is crucial for the performance of fluid flow models. Important well parameters such as the well flow rate and the wellbore pressure are highly sensitive to the computational accuracy of near-well flow models. Near-well regions are characterised as high flow density regions, and the dominating flow pattern exhibits a radial-like nature with large pressure gradients and, for multiphase flow, large saturation gradients. Skew or horizontal wells will also in general imply a strong effect of anisotropy and heterogeneities due to geological layering of the reservoirs. Due to difference in the reservoir scale and the wellbore radius, reservoir flow models do not capture the true flow behavior in the well vicinity. Thus, more flexible models with local grid refinement in near-well regions are needed. The models should also be adapted to handle complex geological near-well structures and multiphase flow simulations. Existing near-well models are in general based on homogeneous media in the well vicinity. Anisotropies and strong heterogeneities are less accounted for in near-well flow simulations. In this work, we construct analytical solutions for near-well flow which is not aligned with a radial inflow pattern. These solutions resemble strongly heterogeneous, possible anisotropic media. We compare different control volume discretisation schemes and radial-type grids for such cases and give their convergence behavior. The objective is to obtain a clearer view on the accuracy of the near-well grids and discretisation schemes for large contrast in permeability, and hence, to determine which is the preferable grid and a suitable numerical scheme given certain near-well conditions. The simulations are performed for singlephase flow, however, the results will also have relevance for multiphase flow simulations.


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