Multicomponent reactive transport in discrete fractures: I. Controls on reaction front geometry

Abstract

A multicomponent reactive transport model with mixed equilibrium and kinetic reactions is presented for a dual porosity system. The model is used to analyze alteration front geometry in discrete fractures and adjacent rock matrix. An analytical solution for a dual porosity system is used to verify the numerical model and to obtain an expression for mineral reaction front geometry under quasi-stationary state conditions. Both the analytical solution and numerical results suggest that the geometry of reaction fronts in a dual porosity system can be characterized by the sum of two dimensionless parameters: φD′/ δv ( φ=porosity, D′=effective diffusion coefficient in rock matrix, δ=fracture aperture, and v=fluid velocity in the fracture) and λ m/ λ 0 f ( λ m=equilibration length scale in rock matrix and λ 0 f=equilibration length scale in the fracture in the absence of matrix diffusion). In the case where the system is surface reaction-controlled, the first dimensionless parameter, which is independent of the reaction rate constants, dominates. From an analysis of a system described by linear reaction rates, this parameter can be used to predict quasi-stationary state concentration profiles and the distribution of minerals along the length of a fracture based on the one-dimensional diffusion-reaction profile in the rock matrix bordering the fracture. Numerical simulations of a multi-component problem involving dedolomitization resulting from the infiltration of hyperalkaline groundwater demonstrate that the dimensionless parameter φD′/ δv applies in more complicated multicomponent systems as well. This result suggests that field observations of matrix alteration perpendicular to the fracture may be used to predict mineralization along the fracture itself.