Transient flow of non-Newtonian power-law fluids in porous media

Abstract

A study of the transient flow behavior of non-Newtonian fluids in petroleum reservoirs has been made. A new partial differential equation has been derived. The diffusivity equation is a special case of this new equation. The new partial differential equation describes the flow of a slightly compressible, non-Newtonian, power-law fluid in a homogeneous porous medium. This equation should govern the flow of most non-Newtonian oil displacement agents used in secondary and tertiary oil recovery projects, e.g., polymer solutions, micellar solutions, and foams. Analytical solutions of the new partial differential equation were obtained. The solutions permit new methods of well test analysis for non-Newtonian fluids. An example of the use of the new techniques to analyze injection well-test data in a polymer injection project is presented. Graphs of the dimensionless pressure function are also presented. These may be used to investigate the error in using Newtonian fluid flow equations to model the flow of non-Newtonian fluids in porous media.