Analytical solution to pressure transient analysis in non-Newtonian/Newtonian fluids in naturally fractured composite reservoirs

Abstract

During polymer flooding into the reservoir using shear-thinning non-Newtonian fluids, an interface exists between the in situ Newtonian crude oil in the reservoir and the injected polymer solution. This paper examines the application of non-Newtonian well test analysis techniques to develop an analytical solution to non-Newtonian/Newtonian fluids with different flow index composite reservoirs for estimating the interface boundary conditions in such reservoirs. Mathematical models were presented and solved analytically using the Laplace transform. The solution was inverted to real domain with the Stehfest algorithm (Stehfest Commun ACM, 1970). Solutions were obtained for three boundary conditions that are infinite acting, constant pressure and no-flow boundaries. New pressure and pressure derivative type curves are developed for naturally fractured reservoirs. A general solution was obtained, which is adaptable to the case of non-Newtonian/Newtonian fluid interface. Numerical examples are used to estimate the radius of investigation, reservoir and power-law flow parameters using type curve matching and Tiab’s direct synthesis technique.