The influence of surface sorption on dispersion in parallel plate fractures

Abstract

Solute transport in a parallel plate fracture is simulated using a random walk model which accounts explicitly for sorption onto the fracture walls. With the hypothesis that solute must move into the vicinity of the fracture wall in order to participate in the sorption process, three implications follow. (1) In comparison to a nonreactive solute, a sorbing solute requires a greater entrance length along the fracture before transverse homogenization is established. The increase in this entrance length is proportional to the surface retardation factor. (2) At short transport distances, surface sorption leads to a high degree of non-uniform retardation. The transport distance required to establish uniform retardation of the entire solute mass varies greatly with geometric conditions and sorption strength. (3) Surface sorption results in enhanced longitudinal spreading of the solute mass in transport regimes which favor advective transport along the fracture relative to transverse diffusion across the fracture aperture. At distances greater than that required for transverse homogenization, an effective longitudinal dispersion coefficient can be defined that describes this enhanced dispersion for a wide range of fluid velocities. The magnitude of enhanced dispersion increases with sorption strength.