Can Geometric Parameters Enable Direct Prediction of Non-Fickian Transport in Rock Fractures Across Diverse Flow Regimes?

Abstract

<p>Anomalous solute migrations in fractured rocks are governed by geometric characteristics and flow regimes. Although existing inverse models can describe this behavior, the underlying physics for quantifying key transport coefficients remains largely unexplored. Here, we investigate the quantitative impacts of geometric heterogeneity and flow regimes on solute transport in rock fractures. We conduct numerical experiments to simulate water flow and conservative solute transport in 3D fractures with varying geometric features and Reynolds numbers. Our results show that the non-Fickian transport is prevalent across the entire flow regime, with Darcy flows attributed to geometric heterogeneity and non-Darcian flows influenced by additional eddy zones. We employ the mobile-immobile (MIM) domain model and continuous time random walk (CTRW) model to inversely model simulated breakthrough curves. Inverse analyses demonstrate that both models effectively characterize anomalous transport behaviors. The fitted transport coefficients of the MIM model exhibit stronger quantitative relationships with aperture and roughness parameters, as well as Reynolds number, compared to the CTRW model. By incorporating parameterized transport coefficients, we propose physics- and statistics-based models to directly predict anomalous transport behaviors under different flow regimes. These prediction models accurately reproduce solute transport processes of all simulated cases with acceptable errors. The feasibility of directly predicting solute transport under varying flow regimes using geometric information is thus validated. Our study not only supports the study of substance migration based on geometric structure features, but also serves as a foundation for investigating geological activities based on substance migration information.</p>