Pressure transient analysis of non-Newtonian power-law fluid flow in fractal reservoirs

Analytical modelling of heterogeneous and, especially, fractured reservoir systems constitutes an important aspect of petroleum reservoir engineering and formation evaluation and environmental engineering studies. Fractal geometry has been used in some recent studies to help define hydrologic conceptual models for a certain class of fractured systems. However, transient pressure behaviour during the flow of non-Newtonian power-law fluids in homogeneous systems has often been misinterpreted as flow in fractures when using Newtonian-based theory. Thus, use of the existing fractal pressure transient models may not be appropriate when analyzing pressure transient data during non-Newtonian fluid flow through a network of fractures.;Transient pressure behaviour for finite reservoir cases is studied. Analytical solutions are also presented for the case of a two-zone composite reservoir, with the inner zone being completely fractal and the outer zone homogeneous. Finally, an analytical model is presented for Newtonian fluid flow in a "double-porosity" situation where the fracture network is characterized by a particular type of fractal geometry and the matrix is homogeneous. The sensitivity of the system response to the various relevant parameters is also examined in detail.;The principal objective of the present study is to examine the basic characteristics of transient flow of non-Newtonian power-law fluids in a fractal network of fractures. The theoretical basis for analyzing transient pressure and rate data under such situations are presented. Analytical and finite-difference solutions of the partial differential equations describing the single-phase flow of a slightly compressible, power-law fluid in an infinitely large fractal reservoir are obtained.