Solute transport in a single fracture with negligible matrix permeability: 2. mathematical formalism

This report provides an overview of the mathematical expressions for modeling fundamental solute transport mechanisms at the fracture scale. It focuses on low-permeability rocks where advection in the matrix is negligible as compared to that in fractures. The following processes are considered: (1) advective transport in fractures, (2) hydrodynamic dispersion along the fracture axis, (3) molecular diffusion from the fracture to the porous matrix, (4) sorption reactions on the fracture walls and within the matrix, and (5) decay reactions. The aim of this review is to gather in a single article the transport equations and their analytical solutions, using a homogeneous notation to facilitate comparison and exploitation.