Mathematical Modelling of One-Dimensional Solute Transport with an Exponentially Time-Varying Dispersion Coefficient in Porous Media

Groundwater contamination is influenced by the natural processes which involve dispersion, adsorption and advection. These processes determine the movement of solute either in liquid or solid phase. The governing equation was formulated with time dependent dispersion coefficient in an exponential form to reflect hydrological conditions. The model equation in a finite domain was shown to be locally asymptotically stable through matrix Lyapunov approach. Initial and boundary conditions were chosen while approximate analytical method was used to obtain the solution of the model. The results show that the exponential time dependent dispersion coefficient affects the particle concentration. An increase in parameters such as dispersion coefficient, first order decay rate and zero order coefficients reduce the concentration profile. Within the examined baseline regime, the local sensitivity analysis suggests dispersion coefficient exerts a relative greater influence on the other parameters. The findings are important for environmental protection in contaminated porous media.