Effects of Intra-REV Pore Distribution Modeling in the Flow of Non-Newtonian Fluids in Porous Media

Motivated by some discrepancies in the comparison between the rheometric viscosity function of shear-thinning fluids and the apparent Darcy viscosity function obtained in porous media simulations/experiments, we propose a model for the flow in porous media with a non-uniform pore distribution in the pore scale, i.e., inside the Representative Elementary Volume (REV). Since different pore sizes inside the REV would lead to different characteristic shear rates, the heterogeneity of the pores in the elementary scale can be responsible for the mentioned discrepancies. Indeed, simulations in a plug of a porous medium have shown that the apparent viscosity function decreases as we increase the standard deviation distribution of the diameter of idealized cylindrical pores. The ratio of the mobility of the heterogeneous pore distribution to the mobility of the homogeneous one is plotted as a function of the power-law index of the non-Newtonian viscosity function. The dimensionless analysis has shown to be a powerful tool in the investigation, collapsing the information in several cases. In addition, our results reveal that a non-uniform pore size distribution can be an important source of the discrepancy between the viscosity function obtained in a rheometric device and the one obtained from the Darcy equation, as reported in the literature.

Automated summary

This paper proposes a flow model considering the non-uniform pore distribution in porous media, and through simulation and analysis, it is found that the non-uniform pore size distribution may be an important factor causing discrepancies between the viscosity functions obtained from rheometric devices and the Darcy equation.