A Simulation of One Dimensional Contaminant Transport

In this note we present some simulations and some analytical solutions, in closed form, of the advection dispersion equation in one-dimensional domain. These solutions are obtained for not-conservative solutes by considering time-dependent, third type (Robin) boundary condition for first order reaction and linear equilibrium absorption. The Robin boundary condition models a combined production-decay function. The model is useful to describe sources as the contaminant release due to the failure of an underground pipelines or radioactive decay series. The developed analytical model gives rise to analytical solutions not present in the literature. Further, we remark that, for particular values of the rate constants involved in the model, our results furnish values which are in agreement with results present in the literature.