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Solute transport in variable‐aperture fractures: An investigation of the relative importance of Taylor dispersion and macrodispersion

Dispersion of solutes in a variable aperture fracture results from a combination of molecular diffusion and velocity variations in both the plane of the fracture (macrodispersion) and across the fracture aperture (Taylor dispersion). We use a combination of physical experiments and computational simulations to test a theoretical model in which the effective longitudinal dispersion coefficient DL is expressed as a sum of the contributions of these three dispersive mechanisms. The combined influence of Taylor dispersion and macrodispersion results in a nonlinear dependence of DL on the Peclet number (Pe = V〈b〉/Dm, where V is the mean solute velocity, 〈b〉 is the mean aperture, and Dm is the molecular diffusion coefficient). Three distinct dispersion regimes become evident: For small Pe (Pe ≪1), molecular diffusion dominates resulting in DL ∝ Pe0; for intermediate Pe, macrodispersion dominates (DL ∝ Pe); and for large Pe, Taylor dispersion dominates (DL ∝ Pe2). The Pe range corresponding to these different regimes is controlled by the statistics of the aperture field. In particular, the upper limit of Pe corresponding to the macrodispersion regime increases as the macrodispersivity increases. Physical experiments in an analog, rough‐walled fracture confirm the nonlinear Pe dependence of DL predicted by the theoretical model. However, the theoretical model underestimates the magnitude of DL. Computational simulations, using a particle‐tracking algorithm that incorporates all three dispersive mechanisms, agree very closely with the theoretical model predictions. The close agreement between the theoretical model and computational simulations is largely because, in both cases, the Reynolds equation describes the flow field in the fracture. The discrepancy between theoretical model predictions and DL estimated from the physical experiments appears to be largely due to deviations from the local cubic law assumed by the Reynolds equation.