Fingering instabilities in miscible displacement flows of non-Newtonian fluids

Full nonlinear simulation of the viscous fingering instability of miscible flow displacements in porous media that involve two non-Newtonian fluids has been conducted. The development of the fingering instability was studied in a rectilinear Hele-Shaw cell that models fluid flow in a porous media of constant permeability, and both the displacing and displaced fluids are considered to be non-Newtonian. The non-Newtonian fluids are assumed to be pseudo-plastic and are modeled using the Carreau-Yasuda model. A modified Darcy's law is derived and is solved numerically using a pseudo-spectral method based on the Hartley transform. New mechanisms of viscous fingering not previously observed in the case of similar Newtonian flow displacements have been identified These mechanisms, which are reminiscent of the fractal patterns observed in experimental studies, were interpreted in terms of the velocity-dependent mobility of the flow.