Analytical modeling of spherical displacement for power-law fluids in porous media

We analyze the pressure transient due to the point injection of a non-Newtonian power-law fluid within an infinite homogeneous porous domain initially saturated with another non-Newtonian power-law fluid. Taking into account fluid and domain compressibility yields a displacement front propagating with finite velocity in spherical or semi-spherical geometry; considering two shear-thinning fluids with the same flow behavior index n allows derivation of a self-similar solution in closed form describing the propagation of the displacement front and demonstrating the existence of a compression front ahead of the interface between fluids. The positions of the displacement and compression fronts, and the pressure distributions in the two fluids, are derived in closed form for any value of n < 1/2. Sensitivity analysis of model responses indicates a strong direct dependence on mobility and compressibility ratios and on permeability; an inverse moderate dependence on porosity and a mixed, weaker dependence on flow behavior index.