The control-volume schemes are discussed for the modelling of vertical wells. The key problem of the well modelling is the accurate fluid flow calculation in the well vicinity. In this paper, the flux truncation errors are analyzed on the gridblocks in the near well region. It is shown that truncation errors of the standard approach might be large in the near well region due to the well singularity, and new numerical scheme is needed to be developed to reduce these errors. In this paper, a multi-point flux approximation scheme is presented for the flow modelling in the well vicinity. This scheme can take into account the particular well flow pattern, grid distortion and heterogeneity. It is suitable for any kinds of grids and heterogeneous media


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