Abstract: Non-reactive and Reactive transport in fractured rock are strongly influenced by fracture-matrix interactions (specifically matrix diffusion). The simple model problem of non-reactive mass transport or energy transport in a fracture adjacent to a finite or semi-infinite matrix is amenable to analytical solutions, and these analytical solutions have been employed extensively for interpretation of field experiments. In field scale transport in complex fractured rock systems, significant heterogeneity in advective velocities complicates the application of these analytical solutions. I present extensions of the analytical solutions to populations of streamlines with variable advective travel times as a measure of heterogeneity. These analytical solutions employ a travel-time coordinate transformation and reveal different scaling regimes for breakthrough curve tails. I also present an application of this analytical framework to interpretation of transit time distributions in mountain catchments.

The problem of reactive transport with progressive depletion of a reactive mineral in the rock matrix arises in the context of both subsurface energy systems and weathering in the critical zone. The essential feature of this problem is the formation of a sharp reaction front in the rock matrix. I present analytical solutions to capture the behavior of this reaction front. This analytical solution is readily extended to complex non-uniform flows within a fracture network using a travel-time coordinate transformation. I will also present some computational results for fracture networks.