Superposition Principle and Reciprocity for Pressure Transient Analysis of Data From Interfering Wells

Abstract

Summary 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 multiwell extension of the superposition principle and re-examine the question of reciprocity between wells that may be modeled as point sinks or as extended sinks. In the latter case, we find that the answer depends on the well-bore boundary conditions: Reciprocity holds for infinite conductivity wells but fails to hold for spatially uniform sink strength. We also derive a multiwell generalization of the fractional transformation 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.