Flow-Dependent Inertial Permeability Defines Crossover Between Darcy and Forchheimer Flow Regimes

Abstract

We present mechanistic evidence that the Forchheimer inertial permeability coefficient ((Formula presented.)) is flow-dependent in the weak-to-intermediate inertia crossover regime, governed by pore-scale eddy growth-to-confinement dynamics. In contrast to classical theory, (Formula presented.) attains steady-state ((Formula presented.)) asymptotically in the dominant inertial regime, marking the validity of Forchheimer law. This highlights a hydrodynamic gap between Darcy and Forchheimer regimes, which is addressed using a physics-based Eddy-Growth Dynamics–Inertial Permeability (EG-DIP) model. The EG-DIP model contributes to ongoing discussions on inertial permeability by providing a framework to determine (Formula presented.), integrate it into Forchheimer law, and suggest a physical basis for estimating (Formula presented.). This supports predictive modeling of flow across regimes and identifies (Formula presented.) as the characteristic medium-specific property for reliable correlation with porosity, permeability, and grain size. By unifying inertial flow theory through eddy growth dynamics, the EG-DIP model has direct implications for injection-induced seismicity, CO2 storage security, and geothermal energy recovery.