Stochastic model for mixing interface evolution through three-dimensional fracture networks.

Abstract

We study effective mixing behavior of solutes in steady flows through three-dimensional random fracture networks and find that mixing in these systems is characterized by phenomena distinct from continuous porous media. Network-scale heterogeneity leads to the complex spatio-temporal organization of the flow-field that determines a mixing interface between transported solutes. The growth of the mixing interface is characterized by splitting events as it crosses between fracture intersections, which does not occur in a continuous porous medium. We derive an analytical model for growth of the mixing interface, which is a function of network properties. Agreement of the model with high-fidelity simulations of flow and transport indicates a link between network topology and mixing dynamics unique to fractured media. The model also provides asymptotic predictions that are intractable with current numerical simulations. Moreover, we do not observe the chaotic exponential growth of the mixing interface that is commonly observed in porous media. The observations and model development indicate a foundational difference in mixing behavior between fractured and porous media.