Flow through porous media of a shear‐thinning liquid with yield stress

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Abstract
Darcy's law for the laminar flow of Newtonian fluids through porous media has been modified to a more general form which will describe the flow through porous media of fluids whose flow behavior can be characterized by the Herschel‐Bulkley model. The model covers the flow of homogeneous fluids with a yield value and a power law flow behavior.Experiments in packed beds of sand were carried out with solutions of paraffin wax in two oils and with a crude oil from the Peace River area of Canada. The model fitted the data well.A sensitivity analysis of the fitting parameters showed that the model fit was very sensitive to errors in the flow behavior index, n, of the Herschel‐Bulkley model. A comparison of the “n” values calculated from viscometer measurements and from flow measurements agreed well.A more general Reynolds number for flow through porous media, which includes a fluid yield value, was developed. The data were fitted to a Kozeny‐Carman type equation using this Reynolds number. The constant in the Kozeny‐Carman equation was determined for the two packed beds studied using Newtonian oils.The data could all be represented, within the experimental error, by the relationship f* = 150/Re*. Since the mean volume to surface diameter of the packing was determined by the measurement of its permeability to a Newtonian oil, assuming C' = 150, the new definition of the Reynolds number allows the direct use of the Kozeny‐Carman equation with Herschel‐Bulkley type fluids.

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