A pore network modelling approach to investigate the interplay between local and Darcy viscosities during the flow of shear-thinning fluids in porous media.

During the flow of non-Newtonian fluids in porous media, the relationships between macroscopic quantities are governed by extremely complex microscopic fluid dynamics resulting from solid-fluid interactions. Consequently, the Darcy-scale viscosity exhibited by a shear-thinning fluid depends on the injection velocity, contrarily to the case of Newtonian fluids. In the present work, pore network modelling is used to investigate the relationships between local and macroscopic viscosities during the flow of shear-thinning fluids in 3D porous media. Special efforts are devoted to 1) identifying the influence of the viscosity exhibited by the fluid within the constrictions of the preferential flow paths on the value of Darcy-scale viscosity and 2) proposing an analytical expression to upscale viscosity from the local viscosity values. To go further, the reduction in average hydraulic tortuosity stemming from the directional nature of shear-thinning behavior in 3D porous media will also be quantified. The results of the present study show that Darcy-scale viscosity can be accurately calculated as the flow-rate weighted average of local viscosities in the investigated media. Moreover, the velocity maps provided by the proposed pore network flow simulations are suitable to assess hydraulic tortuosity reduction as compared to the flow of a Newtonian fluid.