Calculation of effective permeability for the BMP model in fractal porous media

In this work, a fractal model is developed for the effective permeability using the Bautista–Manero–Puig (BMP) model in porous media. The main assumptions of this analysis involve a bundle of tortuous capillaries whose size distribution and tortuosity follow the fractal scaling laws. The average flow velocity and the effective permeability for the BMP fluid flow in porous media are derived. The BMP model does not contain fitting parameters and every material constant in the model can be estimated from independent rheological measurements. This model consists in the upper-convected Maxwell equation coupled to a kinetic equation representing the structure modification that the complex liquid undergoes as it flows in the fractal porous media. Under simple shear, a first Newtonian viscosity plateau at low shear rates, a second plateau at high shear rates, a power-law region between both asymptotic regions, a real yield stress, thixotropy and elasticity are described by the model. Predictions of the proposed fractal model are compared with those of other models and with available experimental data.