Abstract
In this paper, the linear stability of a certain class of miscible displacement processes in porous media is examined. Specifically, the stability features of processes with viscosity profiles that either decay algebraically upstream or exhibit percolation-like characteristics downstream are discussed. The latter pertains to viscosity profiles of the form: μ( z )=μ 0 for z>0; μ continuous at z =0; dμ/d z ∼const·(− z ) − ml (m+1) , with m>0, for 0<− z ≪1; μ( z ) otherwise arbitrary for z<0. Compared to the case of exponentially decaying viscosity profiles, two novel results are obtained. Viscosity profiles with algebraic decay induce a logarithmic contribution to the rate of growth at small wavenumbers of the disturbance. For percolation-like profiles, the rate of growth displays a power-law dependence on the wavenumber; thus it becomes unbounded at large wavenumbers.
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