The effect of mobility gradients on viscous instabilities in miscible flows in porous media

Abstract

The onset of viscous instability and the subsequent fingering have been mostly studied under conditions of a sharp mobility contrast. In stable miscible flows in porous media, however, mobility gradients of variable extent can develop due to hydrodynamic dispersion. Graded mobility and density profiles will affect instabilities, either by mitigating (in the case of a monotonic variation) or by enhancing (nonmonotonic variation) the rates of growth. The mitigating effect was exploited by Claridge and Gorrel and Homsy for the optimal design of graded mobility banks. Hickernell and Yortsos showed that in the linear stability limit, the growth rate is controlled by the maximum of the logarithmic derivative of the mobility profile. We present an experimental study of miscible displacements in porous media to study effects of mobility gradients in viscous instability. We take advantage of molecular diffusion in miscible displacements to create a mobility gradient zone and subsequently initiate the instability by increasing the displacement velocity. A theoretical analysis based on linear stability is used to analyze the experimental results.