Based on a linearized model for the isothermal flow of a single, compressible phase through a reservoir of arbitrary shape with impermeable or constant-pressure boundaries and spatially varying, anisotropic rock properties, we develop a multi-well extension of the superposition principle and re-examine the question of reciprocity between wells which may be modelled as point sinks or as extended sinks. In the latter case, we find that the answer depends on the wellbore boundary conditions: Reciprocity holds for infinite conductivity wells, but fails to hold for spatially uniform sink strength. We also derive a multi-well generalization of the fractional transform in the Laplace domain which adds skin and wellbore storage to a reservoir model and find that its impact on reciprocity is neutral: It preserves reciprocity if it holds for the reservoir model.
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