Nonlinear simulation of non-Newtonian viscous fingering instability in anisotropic porous media

The viscous fingering instability of miscible non-Newtonian flow displacements in anisotropic porous media is studied. This instability was studied in a rectilinear Hele-Shaw cell and the shear-thinning character of the fluids has been modeled using the Carreau-Yasuda constitutive equation. In particular, the role of anisotropic properties of porous media including permeability and dispersion and also rheological parameters of non-Newtonian fluid is investigated through nonlinear simulation. In non-linear simulations, a spectral method based on the Hartley transforms are conducted and allowed to compare several non-linear finger interactions were observed in simulation. In this paper, three types of displacement are considered. In the first one, the displacing fluid and the displaced one are Newtonian and in the next two types of displacement, one of the displacing fluids or the displaced one is non-Newtonian. The evaluation of mixing length, sweep efficiency and transversely average concentration are examined for two different types of displacement where the displacing or the displaced phase were shear-thinning fluids and also for different anisotropic scenarios. The results indicate that in three types of displacement, the flow is more stable by increasing the anisotropic permeability ratio and also is more unstable by increasing the anisotropic dispersion ratio. Moreover, it’s concluded that in the case of the non-Newtonian fluid displaced the Newtonian fluid, by increasing the Deborah number and the power-law index, the more stable flow is obtained, while in the case of the Newtonian displaced the non-Newtonian one, the more unstable flow is obtained.