MODELING TRANSPORT IN A SINGLE CRACK BY THE DUAL-POROSITY CONCEPT WITH A BOUNDARY-LAYER AT THE INTERFACE

A model for contaminant transport along a discrete fracture in a porou s rock matrix is developed and solved analytically. The focus here is on the dynamics of solute exchange between the matrix and a single cra ck and its effect on solute transport within the crack and the chemica l distribution with time at any depth. A laminar boundary layer of nea r stagnant fluid exists at the interface between the fracture and the matrix through which a rate-limited mass transfer takes place. The flo w and the dissolved chemical concentration normal to the flow directio n are essentially uniform in the crack except for the boundary layer. Chemical concentration in the immobile porosity varies with time and s pace in the lateral direction. The driving force for the dissolved che mical exchange through this layer is the difference between the fluid concentration in the crack and the matrix concentration at the interfa ce, both varying with time and space. The dissolved chemical concentra tion in the crack is modeled by the kinematic wave equation and the di ffusion equation is used to model the dissolved chemical transport in the matrix. Exact analytical solutions far the matrix and crack equati ons are obtained in the Laplace domain and an approximate solution in the time domain for the case where zeta epsilon/s is sufficiently smal l. zeta is the dimensionless distance along the crack, epsilon is a di mensionless parameter obtained when dimensionless variables were intro duced into the differential equations and boundary conditions, and s i s the Laplace transformation variable. The deviations between the appr oximate and exact solutions for different values of epsilon and other variables, calculated in the Laplace domain, enable us to evaluate the cases where the approximate solution can be satisfactorily used. The solution obtained by the current model was verified by its comparison with BTCs measured by Neretnieks et al. (Neretnieks, I., Eriksen, T., Tahtinen, P., 1982. Tracer movement in a single fissure in granitic ro ck: some experimental results and their interpretation. Water Resour. Res. 18, 4, pp. 849-858) for a granite core with a natural fissure par allel to its axis. A very good agreement was obtained between the meas ured and predicted BTCs. The physical meaning of the fitted parameters has been discussed. The relative role of the two rate-limited process es, namely film transfer and diffusion in the stagnant matrix solute, on the overall chemical exchange and BTC shape was analyzed by the non dimensional version of the mass balance equations. The displacement d uration has been divided into two stages, Soon after its initiation, t he chemical transfer through the stagnant film controls the chemical e xchange between the preferential path and matrix. The duration of this stage depends on different properties of the system. Subsequently, th e matrix-diffusion controls the chemical exchange between the two doma ins and the model can then be simplified by replacing the rate-limited transfer by a local equilibrium. For cases for which the current stud y is dealing with, the preferential flow is very fast and the rate-lim ited transfer through the stagnant film dominates the BTC shape. (C) 1 998 Elsevier Science B.V. All rights reserved.