Lie group symmetry analysis of transport in porous media with variable transmissivity
We determine the Lie group symmetries of the coupled partial differential equations governing a novel problem for the transient flow of a fluid containing a solidifiable gel, through a hydraulically isotropic porous medium. Assuming that the permeability ($K^*$) of the porous medium is a function of the gel concentration ($c^*$), we determine a number of exact solutions corresponding to the cases where the concentration-dependent permeability is either arbitrary or has a power law variation or is a constant. Each case admits a number of distinct Lie symmetries and the solutions corresponding to the optimal systems are determined. Some typical concentration and pressure profiles are illustrated and a specific moving boundary problem is solved and the concentration and pressure profiles are displayed.