Characterizing the impact of finite matrix block size on conservative particle transport through three-dimensional fracture networks

Mass transfer of solutes between fractures and the surrounding rock matrix exerts a noticeable signature on the tail of travel time distributions. When the width of the matrix is assumed to be infinite and advective transport through the fracture is sufficiently fast, the tails of the travel time distributions exhibit a classically expected slope of (t) proportional to t -3/2 . However, studies have yet to characterize how solute transfer between fractures via diffusion through finite matrix blocks influences the tail's slope in three-dimensional fractured media. In this study, we assess the impact of finite matrix block size on breakthrough curve shape at different spatio-temporal scales by conducting particle tracking simulations in three-dimensional discrete fracture networks. We consider a variety of hydrodynamic and geostructural properties to determine their relative impact on the resulting travel time distributions. We observe that the impact of matrix diffusion through a finite block on travel time distributions is similar to that of an infinite matrix block when the fracture spacing is sufficiently large, matrix diffusion is relatively weak, or transport is considered at an early control plane distance. We observe that the converse of these conditions, results in deviations from the classical (t) proportional to t -3/2 scaling. These results provide a first step toward developing a metric to assess when finite block size effects are expected to significantly influence transport.