Non-Newtonian fluid flows in porous media are critical in various subsurface and geotechnical engineering applications. However, accurately predicting such flows remains challenging due to complex fluid rheology and intricate pore structures. This study focuses on polymer fluids with shear-thinning rheology. To address the limitations of existing models, we derive a theoretical conductance model for polymer flow in a capillary tube, based on which a customized pore-network method is developed. Simulations reveals three distinct flow regimes, highlighting the impact of complex rheology on flow dynamics. Notably, flow heterogeneity amplifies as the shear-thinning feature directs more flows through wider pores, where the effective viscosity decreases more significantly compared to narrower ones. The conductance model also enables formulating a generalized Darcy's law for non-Newtonian fluids, validated through Pore-network modeling. The proposed framework is adaptable to a broad range of non-Newtonian fluids, offering valuable insights for scaling up to field-scale applications.

The semi-resolved CFD-DEM method has emerged as a prominent tool for modelling particle-fluid interactions in granular materials with high particle size ratios. However, challenges arise from conflicting requirements regarding the CFD grid size, which must adequately resolve fluid flow in the pore space while maintaining a physically meaningful porosity field. This study addresses these challenges by introducing a two-grid mapping approach. Initially, the porosity field associated with fine particles is estimated using a coarse CFD grid, which is then mapped to a dynamically refined grid. To ensure conservation of total solid volume, a volume compensation procedure is implemented. The proposed method has been rigorously validated using benchmark cases, showing its high computational efficiency and accurate handling of complex porosity calculations near the surface of coarse particles. Moreover, the previously unreported impact of the empirical drag correlation on fluid-particle force calculations for both coarse and fine particles has been revealed.