Stochastic simulations of steady state unsaturated flow in a three-layer, heterogeneous, dual continuum model of fractured rock

Abstract

Unsaturated flow through fractured rocks is a concern in the siting and performance of waste disposal facilities such as the proposed geological repository at Yucca Mountain, Nevada. We simulated a small two-dimensional cross-section of welded volcanic tuff, representative of Yucca Mountain stratigraphy, using spatially correlated, randomly heterogeneous fracture permeability fields and homogeneous matrix permeability continua representing various degrees of welding. Ten realizations each of fracture permeability fields for four different variances ( σ 2=0.5, 1.0, 1.5, and 2.0) were generated by the direct Fourier transform method (Robin, M.J.L., Gutjahr, A.L., Sudicky, E.A., Wilson, J.L., 1993. Cross-correlated random field generation with the direct Fourier transform method, Water Resour. Res. 29(7)2385–2398) independently for the welded Tiva Canyon Tuff (TCw), the non-welded Paintbrush Tuff (PTn), and the welded Topopah Spring Tuff (TSw), the latter being the proposed primary repository horizon. Numerical simulations were run for steady state flow at three different uniform water flux boundary conditions. Boundary conditions along the sides were impermeable and the base was open to gas and liquid flow. Numerical simulations were performed using the dual-continuum, two-phase flow simulator METRA, which represents matrix and fractures as dual overlapping continua, where liquid flux between continua can be restricted by a uniform factor. Fracture–matrix interaction was modeled as being less restricted in the PTn as compared to the TCw/TSw. Heterogeneous fracture permeability fields generated strong preferential flow in the TCw/TSw fracture continuum and significant preferential flow in the uniformly permeable, PTn matrix continuum. Flow focusing led to a local increase in saturation, which in turn increased relative permeability to water along the preferential pathways, causing water to flow faster. The development of the preferential pathways reduced the wetted surface area for fracture–matrix interaction leaving a large volume of the rock isolated from the preferential flow pathways. Statistical analysis of water flux values in the three units showed that the magnitude of the ensemble variance, indicating preferential flow pathways, increased with both the variance of fracture permeability and the water flux boundary condition, reaching a plateau in the TCw/TSw fracture continuum units after flowing approximately 10 correlation scales of the vertical fracture permeability. Ensemble covariance of water flux normal to the layering revealed long range correlations in all units, which is longer than the correlation length of the fracture permeability fields. This suggests that the water flux boundary condition influences preferential flow in unsaturated dual continua media. These results suggest that careful analysis of information on fracture permeability variability obtained from pneumatic and hydraulic tests is an important component in understanding deep percolation processes.