Anomalous transport for multispecies reactive system with first order decay: time-fractional model

Abstract

The prediction of pollutant migration and its concentration variation in the subsurface hydrology is vitally requisite for the assessment and restorative treatment of polluted groundwater system. Pollutant migration for the multispecies reactive system cannot be reliably investigated by classical form of convection-dispersion equation (CDE), due to the presence of more than one reactive species. This paper establishes a time-fractional model for multispecies reactive system under the first order sequential reaction network to understand the anomalous or non-Fickian migration phenomenon for reactive pollutants. At present, most of the fractional models are presented for the classical CDE to investigate migration phenomenon for single species system, not for the multispecies reactive system due to the complexity of the modelled framework. The impact of fractional derivative model is analysed for variable dependent migration parameters and constant parameters, both for the multispecies reactive migration phenomenon. The fractional derivative is expressed in the Caputo sense and to handle the non-linearity of problem, Homotopy perturbation method (HPM) is adopted. The advantage of this method, to get the solutions, is that the HPM is independent of small parameters required for the deformation process as used in other existing perturbation techniques, which make it much more convenient to use for non-linear systems. The impact of the fractional derivative index and other migration parameters is graphically depicted for the reactive species and significant influence of fractional term is observed. The derived solutions are then validated by using the corresponding solutions obtained by other existing well-established methods to ensure the convergence of the HPM solutions. As there do not exist any solutions for such fractional models for multispecies reactive system, this study may be advantageous to convey better understanding for the anomalous or non-Fickian migration for reactive pollutants and their remediation planning in the groundwater resources.