Polymer support fluids are increasingly used to stabilize slurry-supported excavations and bored piles, yet predicting their penetration into granular media and the associated pressure demand remains challenging because shear-thinning flow depends on pore-scale flow-path morphology and soil–polymer interactions. However, it remains unclear how void ratio and pore-network topology translate into changes in pressure drop and apparent permeability under shear-thinning flow. Polymer conductivity and fluid–particle interaction force were quantified while varying void ratio in periodic simple cubic (SC), body-centered cubic (BCC), and face-centered cubic (FCC) sphere packings, isolating how pore-throat topology influences hydraulic resistance and drag in polymer flow. Pore-resolved OpenFOAM simulations prescribed an inlet velocity and fixed outlet pressure in the x direction, applied no-slip conditions at particle surfaces, and imposed periodic boundaries in the y and z directions, with short inlet/outlet extensions to promote fully developed flow. The numerical framework was verified for Newtonian flow by matching drag coefficients of periodic sphere arrays to the Stokes-flow solutions of Zick and Homsy, and was then compared against polymer permeation experiments using an FCC packing representative of the tested granular medium, with shear-thinning represented using power-law and Carreau constitutive laws. Results were normalized as polymer-to-water ratios using water simulations for the same packing, void ratio, and inlet velocity. As discharge velocity increases from 10^-8 to 10^-4 m/s, the normalized fluid–particle interaction force decreases by about two orders of magnitude, while the normalized polymer hydraulic conductivity increases by roughly two orders of magnitude, consistent with shear-thinning behavior: higher shear rates reduce apparent viscosity and bring the response closer to the Newtonian baseline. For discharge velocities between 10^-7 and 10^-4 m/s, increasing void ratio modestly increases the normalized force and decreases the normalized conductivity before both trends level off; this void-ratio sensitivity is negligible at 10^-8 m/s. Differences among SC, BCC, and FCC packings mainly appear as small magnitude shifts at fixed void ratio, without changing the overall trends.