We present a new finite element that incorporates a logarithmic shape function in the radial direction. The element was derived to be used when calculating flows near wells, where the single phase analytic solution has a logarithmic pressure distribution. Using this element, the well can be represented as a point in the mesh and the numerical calculation of pressures and flows near wells is ensured to be accurate.

For a single well test case, calculated pressures have an error of less than one tenth of one percent compared to the analytic solution. This demonstrates that it is possible to use large elements in the vicinity of the well, but still obtain an accurate result.

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