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Abstract

Non-Newtonian fluid flow in porous media is encountered in a variety of applications. Aspects of single-phase flow of power-law fluids in porous media are examined. First, homogenization theory is used to derive a macroscopic law. It is shown that the single-capillary power law between flow rate and pressure gradient also applies at the macroscopic scale, provided that the Reynolds number is sufficiently small. Homogenization theory confirms the validity of the use of pore network models to describe flow of power-law fluids, although not necessarily of fluids of a more general rheology. Flow in pore networks is next used to explore various pore geometry effects. Numerical simulations show that approaches based on an effective medium or on the existence of a critical path, which carries most of the flow, are valid in narrow- or wide-pore-size distributions, respectively. The corresponding expressions agreed well with the numerical results in the respective ranges. An analysis presented for Bethe lattices leads to closed-form expressions in two limits: for an effective medium and near percolation. The behavior near percolation generalizes the results of Stinchcombe (1974) for the linear (Newtonian) case.