Pore-network modeling of polymer flow in porous media

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 the complex fluid rheology and intricate pore structures. This study focuses on polymer fluids with shear-thinning rheology with the motivation of advancing understanding of polymer support fluids for ground engineering applications. 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. Our simulations reveal three distinct flow regimes, highlighting the impact of the rheology on flow dynamics. Notably, flow heterogeneity amplifies as the shear-thinning feature directs more flow through wider pores, where the effective viscosity decreases more significantly compared to narrower ones. A generalized Darcy's law is formulated for non-Newtonian fluids, validated through pore-network modeling on 60 distinct sphere packings. The proposed framework is adaptable to a broad range of non-Newtonian fluids, offering valuable insights for scaling up to field-scale applications. © 2025 The Authors