Interpretation of Wellblock Pressures in Numerical Reservoir Simulations Part 3—Off-Center and Multiple Wells Within a Wellblock

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Abstract
Summary: In reservoir simulation by finite differences, well models are used to relate the wellblock pressure, the actual wellbore pressure, and the flow rate of the well. These well models are based on an "equivalent wellblock radius, " r0. Two methods for obtaining r0 exist: (1) by numerical experiments, and (2) by an approximate analytical approach that assumes that the pressures of the blocks surrounding the wellblock satisfy the exact radial solution. By definition, the numerical approach gives the correct r0. The more commonly used analytical approach frequently gives a good approximation but, in some cases, it does not. Hence, an analytically derived r0 should always be checked by a numerical calculation. In this paper, two important well geometries are investigated numerically: a single well arbitrarily located within an isolated wellblock and two or more wells within a single wellblock. The numerical r0 for a single well is found to be independent of location, a result that contradicts the prediction of the analytical approach.

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