Scale dependence of sorption coefficients for contaminant transport in saturated fractured rock

Abstract

A significant challenge in contaminant transport modeling is to obtain a mechanistic understanding of transport parameter scaling that accurately addresses the combined influence of physical and chemical heterogeneities at different scales. In this paper, we have developed a scaling methodology to upscale matrix sorption coefficients for fractured‐rock systems by characterizing both the tortuosity field (physical heterogeneity) and retardation factor field (chemical heterogeneity) in the rock matrix. We compute the effective tortuosity with a conservative tracer (e.g., tritium), and then using a sorbing tracer (e.g., uranium), we derive the equations for upscaling the sorption coefficients in a saturated, fractured rock system. The derived upscaling equations for the sorption coefficients are verified with Monte Carlo simulations, which are based on a generalized dual‐porosity model to enable highly efficient and accurate numerical simulations of diffusive concentration fronts moving between the fractures and matrix material. The scientific results from this study will provide a theoretical and practical link between controlled experimental results at scales increasing from the laboratory bench to the field scale at which risk assessment and contaminant remediation are actually conducted.