Mass arrival of reactive solute in single fractures

Abstract

Transport of reactive solute in individual fractures is investigated. Solute advection is coupled with matrix diffusion that is assumed perpendicular to the fracture plane. Fluid advection in the fracture is viewed as intersecting flow paths, whereby the advection velocity of a solute particle varies along individual streamlines. Solute mass arrival at a fixed position averaged in the direction perpendicular to the mean flow is examined. The dispersion in the solute breakthrough arises because of the different advection travel times and varying mass flux along individual streamlines. The fracture is conceptualized as a two‐dimensional porous medium with a statistically anisotropic, spatially varying transmissivity with a given correlation structure; the assumed anisotropy condition is consistent with elongated, channel‐like flow paths that have been observed in single fractures. Approximate expressions for the first two moments of solute travel time are used to illustrate the sensitivity to different correlation models for the fracture transmissivity. In particular, the finite correlation scale model, the self‐similar (fGn) model, and the channel model are considered. The expected cumulative mass arrival is more sensitive to the assumed correlation model for lower rates of matrix diffusion. The derived expression for the mass arrival can also be used for analyzing the effect of nonequilibrium sorption‐desorption reactions in single fractures.