Statistical analysis of liquid seepage in partially saturated heterogeneous fracture systems

Field evidence suggests that water flow in unsaturated fracture systems may occur along fast preferential flow paths. However, conventional macroscale continuum approaches generally predict the downward migration of water as a spatially uniform wetting front subjected to strong inhibition into the partially saturated rock matrix. One possible cause of this discrepancy may be the spatially random geometry of the fracture surfaces, and hence, the irregular fracture aperture. Therefore, a numerical model was developed in this study to investigate the effects of geometric features of natural rock fractures on liquid seepage and solute transport in 2-D planar fractures under isothermal, partially saturated conditions. The fractures were conceptualized as 2-D heterogeneous porous media that are characterized by their spatially correlated permeability fields. A statistical simulator, which uses a simulated annealing (SA) algorithm, was employed to generate synthetic permeability fields. Hypothesized geometric features that are expected to be relevant for seepage behavior, such as spatially correlated asperity contacts, were considered in the SA algorithm. Most importantly, a new perturbation mechanism for SA was developed in order to consider specifically the spatial correlation near conditioning asperity contacts. Numerical simulations of fluid flow and solute transport were then performed in these synthetic fractures by the flow simulator TOUGH2, assuming that the effects of matrix permeability, gas phase pressure, capillary/permeability hysteresis, and molecular diffusion can be neglected. Results of flow simulation showed that liquid seepage in partially saturated fractures is characterized by localized preferential flow, along with bypassing, funneling, and localized ponding. Seepage pattern is dominated by the fraction of asperity contracts, and their shape, size, and spatial correlation. However, the correlation structure of permeability field is less important than the spatial correlation of asperity contacts. A faster breakthrough was observed in fractures subjected to higher normal stress, accompanied with a nonlinearly decreasing trend of the effective permeability. Interestingly, seepage dispersion is generally higher in fractures with intermediate fraction of asperity contacts; but it is lower for small or large fractions of asperity contacts. However, it may become higher if the ponding becomes significant. Transport simulations indicate that tracers bypass dead-end pores and travel along flow paths that have less flow resistance. Accordingly, tracer breakthrough curves generally show more spreading than breakthrough curves for water. Further analyses suggest that the log-normal time model generally fails to fit the breakthrough curves for water, but it is a good approximation for breakthrough curves for the tracer