Dispersion in Hyperporous Fractured Systems and the Impact of Matrix Permeability on Fracture Transmissivity

Abstract

Current studies of fractures generally assume purely diffusive transport in the matrix. Yet, this assumption is invalid for fractures embedded in hyperporous matrices that can be highly permeable to flow. By means of perturbation theory and asymptotic analysis, we derive a set of upscaled equations describing mass transport in a coupled fracture-matrix system and an analytical expression relating macro-scale dispersion coefficient and matrix permeability. Our analysis shows that its impact on dispersion coefficient strongly depends on the magnitude of the Peclet number, i.e. on the interplay between diffusive and advective mass transport. Additionally, we demonstrate different scaling behaviors of the dispersion coefficient for thin or thick porous matrices. Our analysis shows the possibility of controlling the dispersion coefficient, i.e. transversal mixing, by either active (i.e. changing the operating conditions) or passive mechanisms (i.e. controlling matrix effective properties) for a given Peclet number. We compare the upscaled model against experiments conducted on microchannels with surfaces patterned with different topologies. The experimental data are in agreement with the developed theory and quantitatively confirm the impact of the matrix geometry on dispersion at different Peclet numbers. Furthermore, we demonstrate that patterned microchannels can be used as benchmarks experiments to model flows in coupled channel/fracture-matrix systems.