Fractured–Injection–Well Performance Under Non–Newtonian, Power–Law Fluids

Abstract

Summary A new source function developed in this work is used to predict well responses to evaluate long-term injectivity and late-time responses of fractured wells after the injection of a non-Newtonian, pseudoplastic fluid. The source function yields integrals of modified Bessel functions of fractional order that are evaluated numerically by techniques developed by the authors. Consideration of well responses after the injection of pseudoplastic fluids into reservoirs through fractured wells requires the solution of a nonlinear differential equation and examination of flow fields in two dimensions. Consequently, numerical methods have been the only recourse. This work explores the applicability of new tools developed in recent times by analytical means. Calculating well injectivity accurately and rapidly for this complex situation by the methods outlined here is particularly convenient. The expressions we derive may be readily applied to concepts such as the Peaceman (1978) probe radius and transient well injectivity. Predictions by use of the new solution are compared with numerical solutions in the literature.