Correction of Stokes drag for non-Newtonian flow through pack of spheres

Non-Newtonian fluids have great relevance in a wide range of porous media applications, such as enhanced oil recovery and filtration processes. The estimation of the drag coefficient of power-law fluids flowing through simple porous media structures in the Stokes regime is typically modeled by adding a direct correction term to the Newtonian model. In this study, to calculate the non-dimensional drag for various fluid indices and volume fractions of packed spheres, extensive numerical simulations of the power-law fluid flow through single cubic, body-centered cubic, and face-centered cubic porous structures are conducted. The numerical results are used to develop a model function of the non-dimensional drag depending on the power-law fluid index and volume fraction of the sphere pack. Consequently, the drag force and coefficient of shear-thinning or shear-thickening fluid flowing through the investigated structures can be predicted. A correction is introduced for the Stokes drag correlation based on the generalized Reynolds number for non-Newtonian fluids. The results of the proposed model and numerical simulations are in excellent agreement with deviations not more than 1.2%. This implies that the modeled predictions are valid for all investigated structures.