Hydraulic characterization and modeling of water diffusivity through direct neutron radiography measurement on unsaturated cracked sandstone

Water diffusivity in cracked rocks is of great importance in the recovery of conventional and unconventional resources and in the sequestration of carbon dioxide and nuclear wastes. However, the mechanism of water diffusivity is not clearly revealed in the unsaturated fractured sandstone due to the limitation of accurately identifying the dynamic wetting front and water content in the conventional methods. Based on a set of self-designed coupling loading device, the novel neutron radiography imaging is used to visualize the dynamic diffusivity process of forced water from a horizontal rough crack vertically imbibed into an unsaturated sandstone matrix with nonuniform boundary in real time. As a result, an anomalous diffusivity phenomenon, namely the time exponent less than 0.5 is discovered. The anomalous diffusivity may be mainly caused by the heterogeneity and anisotropy of matrix and complicated 3-D water imbibition due to nonuniform geometric boundary. The nonstandard imbibition experiment condition may be an additional important factor. The anomalous diffusivity was calculated by three methods, including the Generalized Fickian law, Lockington and Parlange (L-P) model and the developed Meyer-Warwick (M-W) model. The value of the diffusivity increases non-linearly with the increase of normalized water content θ_n. The diffusivity calculated by the developed M-W model increases rapidly with increasing θ_n from 0 to 0.2 mm³mm⁻³, which is almost the same as that calculated by L-P model. When θ_n> 0.2 mm³mm⁻³, the L-P model obviously overestimates the diffusivity, but the diffusivity calculated by the developed M-W model is closest to that obtained by the Generalized Fickian law. The developed M-W model provides an effective way to quantitatively describe the diffusivity of water in the sandstone matrix.