Applying the boundary layer concept to model transport of dissolved chemicals in preferential flow paths

The exchange of dissolved chemicals between preferential flow paths and the surrounding matrix has a major effect on the concentration at the flow pat h outlet and, on a larger scale, on contaminant transport in structured soi ls and fractured rock systems. A model for dissolved chemical transport in a discrete fracture accompanied by simultaneous exchange with the surroundi ng porous matrix is presented and solved analytically. The fracture transpo rt is modeled by a kinematic wave equation which ignores longitudinal dispe rsion, and the lateral solute transport in the matrix, where fluid is stagn ant, is modeled by a diffusion equation. The exchange of dissolved chemical s between the fracture and matrix is assumed to take place through a bounda ry layer along the fracture-matrix interface. The analytical solution to th e equations is a convergent series, even for large Values of the characteri stic dimensionless parameter epsilon = kb(2)/(D theta(2)), (where k is mass transfer coefficient, b is half the fracture width, and D and theta are th e matrix diffusion coefficient and porosity, respectively) the column lengt h, and long time periods. The number of terms in the series depends on the parameter values and desired accuracy. The model was successfully verified by fitting its output to breakthrough curves measured for highly fractured clay-till soils. The role of the boundary layer (also known as film resista nce) was studied by comparing breakthrough curves predicted by the current model (boundary layer (BL) model) and by a model that assumes a uniform con centration across the fracture-matrix interface (local equilibrium (LE) mod el). Analyses of the model equations and simulations revealed that solute d isplacement from a fracture surrounded by a matrix with immobile solute can be divided into two stages with respect to the boundary layer's effect on breakthrough curve shape. Soon after the initiation of displacement, the bo undary layer controls the solute flux to the matrix and the rate of concent ration increase at the fracture outlet. The BL model predicts lower fluxes into the matrix than the LE model, and use of the latter for this stage und erestimates the displaced solute mass at the fracture outlet. The duration of this stage and the deviation between breakthrough curves predicted by th e current and LE models depend on epsilon, how velocity, and column length. During the following stage, the boundary layer's effect on the rate-limite d exchange steadily diminishes, and the solute flux is controlled by matrix diffusion. At this latter stage, both models predict similar breakthrough curves at the fracture outlet.