A stratified channel model with local longitudinal dispersion

Modifications have been made to an existing stratified channel contaminant transport model by incorporating hydrodynamic dispersion in each channel. The integrals in the modified model are solved by a numeric method. Gaussian quadrature integration formulas were used to solve the equation, including the Gauss-Laguerre quadrature to deal with the upper infinite limit of the integral. This approach proved to be both accurate and efficient. The effects of physicochemical parameters on the elution breakthrough curve have been studied with this model. The parameters that were considered were (a) the standard deviation of a lognormal distribution of the channel width, (b) longitudinal dispersivity, (c) water velocity (d) fracture length, (e) surface sorption coefficient, and (f) rock matrix diffusivity. Results from the calculations showed that the hydrodynamic dispersion in each channel caused additional dispersion in the elution profile. A new parameter which quantifies rock matrix diffusion and residence time of the solute in the fracture simultaneously, and its reference value are presented. This parameter is useful to determine numerically if the diffusion into the rock matrix is a significant contribution to the transport of the tracer through the fracture. This parameter can also be used in the design of migration experiments intended to observe diffusion into the rock matrix. The modified model has been used to analyze two independent experimental data sets obtained for a conservative tracer one obtained in an artificial fracture and the other in a natural fracture. The results obtained with this modified model were in good agreement with both sets of experimental results. The dispersivities for both experimental systems were determined by curve fitting, and similar values were obtained for both types of fracture. The values obtained for the natural fracture especially indicated that both local hydrodynamic and channeling dispersion occurred.