Study of multispecies convection-dispersion transport equation with variable parameters

Multispecies pollutant migration is most natural phenomenon, frequently occurring in the polluted groundwater system and also evidently occurs in the nuclear repositories and sites having radioactive substances and chemical solvent. Modeling pollutant migration of reactive multispecies problem with variable transport parameters is quite a challenging issue, necessary for better sightedness of fate and transport of reactive solutes and their geochemical growth in the geological formations. At present most of the solutions for multispecies problem are corresponding to the constant parameters affecting the concentration distribution, not for variable transport parameters, because of the complexity of the modelled equation. This paper dealt with the comparative study of multispecies pollutant transport problem in porous structure to analyse the effect of spatially and temporally varying hydrodynamic dispersion coefficient and transport velocity terms in more general form. For mathematical elaboration, two-species transport problem is considered subjected to the concept of linear isotherm with both the parent and daughter species without using identical retardation factor and model is also incorporated with the first-order decay term under spatially varying initial conditions. Homotopy analysis method (HAM) is adopted to develop the series solution for the concentration segmentation of each species of the model. The advantage of this method is that it is capable to overcome the limitation of existing transform methods for some cases of complex modelled problems. The zeroth order deformation equation is derived by using HAM to generate the semi-analytical solution of the model under certain auxiliary linear operator. The impact of distinct retardation factor for different species and effect of diversity in dependency of modelled parameters over space and time are graphically depicted for both the species and illustrated that it has a valuable impact over multispecies pollutant migration. As there exist no analytical or numerical solution for such complex variable dependency of migration parameters over transport phenomenon, these solutions may be helpful to deliver a better significant about the concentration variation due to space and time dependent transport parameters, responsible for reactive multispecies migration, in more natural way.