Analytical multispecies chemical mixture transport model comprising degradable byproducts subject to scale-dependent dispersion

Although efforts to analytically model multispecies reactive transport have already been reported, most of the studies utilized the advection-dispersion equations coupled with sequential decay chain reactions with a constant dispersion coefficient. Over the past 30 or 40 years, however, some studies have demonstrated that the dispersivity increases with the distance the solute travels, which is an outcome of variation in the hydraulic characteristics of the subsurface environment. The numerical modelling of multispecies reactive transport associated with a scale-dependent solute dispersion process has been discussed in the literature. In this study, an analytical model for plume migration of a chemical mixture comprised of the original pollutant and its degradation-related byproducts, subject to a scale-dependent dispersion process, is developed by taking advantage of the Laplace transform technique for the temporal variable and the generalized integral transform technique for the spatial variable. The correctness of the developed model is evaluated by comparisons with a numerical model in which the same set of governing equations are solved using the Laplace transform finite difference (LTFD) technique. The computational results obtained with the analytical and LTFD numerical models agree perfectly. To illustrate the impact of a scale-dependent dispersion process on the multispecies plume migration of the original contaminant and its degradation-related byproducts, this paper makes a comparison of the developed multispecies model with a model of the constant dispersion coefficient.