Interfacial instabilities of immiscible non-Newtonian radial displacements in porous media

Abstract

Immiscible flows that involve radial displacements of shear-thinning or shear-thickening fluids by a Newtonian fluid in a homogeneous porous medium are modeled numerically. The interfacial instabilities are tracked in time for different values of the rheological parameters, namely, the Deborah number (De) and the power-law index (n), and are characterized through the effective number of fingers and the finger area density. The results of the study reveal that the effects of these two parameters on the instability are not monotonic, and it is found that the flow is least unstable for some critical value of either De or n. The dependence of these critical values, in particular, on the mobility ratio (M) and capillary number (Ca) is analyzed. It is found that when all other parameters are fixed, the critical Deborah number (Dec) increases as the power-law index increases in shear-thinning fluids or decreases in shear-thickening ones. Similarly, the critical power-law index (nc) increases with increasing (decreasing) Deborah number in shear-thinning (shear-thickening) flows. Furthermore, both critical parameters are found to vary monotonically with the mobility ratio, with the dependence most noticeable at small values of M. Their variation with the capillary number is however nonmonotonic reaching an extremum at an intermediate value of Ca. An examination of the rate of shear strain at the interface reveals that it consistently shows the smoothest variation and the smallest average value at the critical parameter.