Generalized flow analysis of non-Newtonian visco-elastic fluid flow through fractal reservoir

Abstract

In this paper, fractal geometry theory is used to combine with the seepage flow mechanics to establish the relaxation models of non-Newtonian visco-elastic fluid flow in fractal reservoirs. A method to scale the fractal properties of a fractal reservoir by the double parameters (df, ds) and to describe the generalized flow characteristics of visco-elastic fluid by four parameters (df, ds, λ y , λ p ) are presented. Exact solutions and asymptotic solutions have been obtained by using the Laplace-Weber and Laplace-orthogonal transforms with both infinite and finite reservoirs. The pressure transient behavior of non-Newtonian visco-elastic fluid flow through a fractal reservoir are studied by using the numerical Laplace transform inversion and asymptotic solutions. The law of pressure change for various fractal parameters is obtained.