Pressure Behavior for Spherical Flow in a Reservoir of Non-Newtonian Power-Law Fluids

Abstract

The pressure variations during polymer flooding of oil reservoirs for oil recovery projects can be used to analyze the flow in the reservoir which is especially useful for the partially perforated reservoirs. This paper presents a relationship between the viscosity and the shear rate which is similar to forms developed for radial flow (Odeh, A. S., Yang, H. T. ([1979]). SPEJ. AIME (Jun.) 155). The power-law viscosity model is used to give the variation of the fluid viscosity with the spherical radius for a mathematical model of unsteady spherical flow for non-Newtonian fluids with wellbore storage and skin. An analytical solution for the wellbore pressure responses derived in Laplace space is used to analyze the behavior characteristics at early and later times to interpret the well-test parameters. The pressure variations are similar to those for a Newtonian fluid at the early times, but at later times, the variation of the viscosity with the power-law exponent is important, so the pressure response differs from that for a Newtonian fluid. The solution has significance for interpreting well test parameters for non-Newtonian spherical flow.