Similarity solutions for flow of non-Newtonian fluids in porous media revisited under parameter uncertainty

We analyze the transient motion of a non-Newtonian power-law fluid in a porous medium of infinite extent and given geometry (plane, cylindrical or spherical). The flow in the domain, initially at constant ambient pressure, is induced by fluid withdrawal or injection in the domain origin at prescribed pressure or injection rate.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’ 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.

► We revise and generalize analytical solutions for non-Newtonian flow in porous media. ► We consider power-law fluid flow in plane, radial, and spherical geometry. ► Solutions for 1-D transient motion are derived in terms of a self-similar variable. ► We analyze the solution sensitivity to parameter uncertainty. ► Sobol’ indices are evaluated via Polynomial Chaos Expansion technique.