Pressure Transient Analysis for Relaxation Model of Non-Newtonian Visco-elastic Flow in Fractal Reservoir with Wellbore Storage and Skin Effect

Abstract

Abstract The majority of the conventional pressure-transient models assume that permeability and porosity of a formation is invariant in space. Moreover, fluid flow in reservoir is Newtonian fluids or non-Newtonian power-law fluids. Such an assumption gives good results in many situations; but the geological complexity of units and/or non-Newtonian relaxation characteristics of visco-elastic fluids may make these assumptions of dubious value. The purpose of this study is to explore flow analysis of non-Newtonian visco-elastic fluids with relaxation property in reservoir that are not amenable to the conventional approach. In the study, we present a pressure-transient radial relaxation flow model of non-Newtonian visco-elastic fluids in fractal reservoir considering the effect of wellbore storage and skin factor. Analytical solution and asymptotic solution in real space are obtained by using Laplace transform for a constant- rate condition at a single well in an infinite reservoir. The flow behavior of non-Newtonian visco-elastic fluids is also analyzed by using numerical inversion scheme of Laplace transform. We discuss pressure response of changing spectral dimension and rheological parameters. Conventional model (hornogenous reservoir, Newtonian fluids) is a special case of above model. The results obtained in the study extend previous pressure transient analysis for single phase Newtonian flow in a 2-D cylindrical system to reservoir of arbitrary fractal dimension and visco-elastic fluids of rheological parameters. P. 343