Previous literature work is generalized and expanded, providing a dimensionless formulation suitable for any geometry, and deriving similarity solutions to the nonlinear governing equations valid for pseudoplastic, Newtonian and dilatant fluids. A pressure front propagating with finite velocity is generated when the fluid is pseudoplastic; no such front exists for Newtonian or dilatant fluids. The front rate of advance depends directly on fluid flow behavior index and inversely on medium porosity and domain dimensionality.
The effects and relative importance of uncertain input parameters on the model outputs are investigated via Global Sensitivity Analysis by calculating the Sobol鈥?indices of (a) pressure front position and (b) domain pressure, by adopting the Polynomial Chaos Expansion technique. For the selected case study, the permeability is the most influential factor affecting the system responses.