Heterogeneity characteristics of flow and transport fields through rough-walled fractures

Due to the impact of rock surface roughness, fracture flow and transport fields are always heterogeneous with tortuous flow-lines. Typically as fracture apertures decrease, fracture flow tends to concentrate at preferential channels. Difficulty in studying fracture flow lies in the quantitative description of the evolution of preferential channels. In this study statistical measures are defined to capture the distributed characteristics of flow tortuosity and concentration. Tortuosity is defined as a ratio of flow-line length to some constant characteristic length of flow field, and the concentration is defined as spatial entropy of local parameters like local apertures, velocities or fluxes. Moreover, the spatial entropy production of local apertures is defined as the preferential channel maturity, which quantitatively indicates the evolution of preferential channels. Results suggest the tortuosity and spatial entropies of local flow field are all of significant positive relationships with preferential channel maturity. A similar positive relationship is found between solute transport contours' tortuosity and preferential channel maturity as well, which suggests the preferential channels bring additional dispersion to solute transport. At last a simple conceptual model is discussed to show how fracture roughness and preferential channels affect the fracture flow and solute transport.