Theory of anomalous chemical transport in random fracture networks

Abstract

We show that dominant aspects of chemical (particle) transport in fracture networks---non-Gaussian propagation---result from subtle features of the steady flow-field distribution through the network. This is an outcome of a theory, based on a continuous time random walk formalism, structured to retain the key space-time correlations of particles as they are advected across each fracture segment. The approach is designed to treat the complex geometries of a large variety of fracture networks and multiscale interactions. Monte Carlo simulations of steady flow in these networks are used to determine the distribution of velocities in individual fractures as a function of their orientation. The geometry and velocity distributions are used, in conjunction with particle mixing rules, to map the particle movement between fracture intersections onto a joint probability density $\ensuremath{\psi}(\mathbf{r},t).$ The chemical concentration plume and breakthrough curves can then be calculated analytically. Particle tracking simulations on these networks exhibit the same non-Gaussian profiles, demonstrating quantitative agreement with the theory. The analytic plume shapes display the same basic behavior as extensive field observations at the Columbus Air Force Base, Mississippi. The quantitative correlation between the time dependence of the mean and standard deviation of the field plumes, and their shape, is predicted by the theory.