Analytical Solution to Pressure Transient Analysis in Non-Newtonian/Newtonian Fluids Composite Reservoirs

Abstract

During polymer flooding in the reservoir using shear-thinning non-Newtonian fluids, an interface exists between the in-situ Newtonian crude in the reservoir and the injected polymer solution. This work examines application of well test analysis techniques to develop an analytical solution to investigate the interface boundary conditions for non-Newtonian/Newtonian fluids in composite reservoirs. Mathematical models were presented and solved analytically using Laplace transform method. The solution was inverted to real domain with the Stehfest algorithm and extended to obtain equations for the three boundary conditions which are: infinite-acting, constant pressure, and no-flow boundaries. New pressure and pressure derivative type curves are developed for homogeneous and naturally fractured reservoirs (NFRs). Cases of non-Newtonian/non-Newtonian and Newtonian/non Newtonian fluid interface were also considered. Numerical examples are used to estimate reservoir and power-law flow parameters using type curve matching and Tiab’s Direct Synthesis (TDS) technique.