Novel Unified Model for Geofluid Nonlinear Flows in Rock Fractures

Abstract

In this study, we numerically investigated the multi-scale flow features of 43 types of geofluids (including 18 real geofluids and 25 parametric fluids) within rock fractures under different roughness and hydrodynamic conditions. Our findings demonstrate that the generalized Forchheimer equation, an extension of Darcy's law for nonlinear flows, effectively captures the nonlinear flow features of these diverse fluids. While changes in fluid properties have minimal impact on Darcy's viscous permeability, they significantly influence Forchheimer inertial permeability and the critical Reynolds number. These dependencies are mechanistically attributed to the regulation of eddy growth rate in fractures by fluid properties. Building on these mechanistic insights, we developed two types of models for predicting inertial permeability and critical Reynolds number across various geofluids within a unified framework. One model extrapolates predictions from the results of classical standard water flow, while another enables direct prediction based on the mean and variance of the fracture aperture field.