Predicting Non-Darcy Inertial Resistance from Darcy Regime Characterization and Pore-Scale Structural Descriptors

High-velocity fluid flow in porous media frequently exhibits non-Darcy behavior, where inertial losses lead to nonlinear pressure gradient velocity behavior. Predicting the Forchheimer coefficient β remains challenging because β varies sensitively with pore geometry and is often not constrained by porosity and permeability alone. This study develops a structure-based method to estimate β using intrinsic descriptors obtained from the Darcy regime flow characterization and image-based geometry analysis. A set of two-dimensional granular porous media was generated with controlled variations in porosity, particle size distribution, and grain size variability. Single phase simulations are simulated with a body-force multiple-relaxation-time lattice Boltzmann method. The transition from Darcy flow to non-Darcy flow is identified from the velocity and pressure gradient response, and β is determined by fitting the inertial flow regime. Two tortuosity responses were observed. In uniform media, hydraulic tortuosity remained nearly constant in the Darcy regime and then gradually decreased. In disordered media, hydraulic tortuosity first increased with the onset of recirculation and then decreased as dominant flow paths became stable. Based on these results, a dimensionless inertial factor was correlated with porosity, intrinsic hydraulic tortuosity, and a pore structure index derived from specific surface area and hydraulic pore size. The resulting model predicts β from permeability and structural descriptors. The resulting correlation provides β estimates from Darcy permeability and geometry descriptors. Validation with quasi-two-dimensional microfluidic pillar array data showed that the model captured both the magnitude and relative ordering of β for the tested geometries. The proposed framework should be regarded as a proof of concept for idealized granular porous media and quasi-two-dimensional structured systems.