Analytical Solution to the Advective-Dispersive Equation with a Decaying Source and Contaminant

We present an analytical solution of the one-dimensional contaminant transport undergoing advection, dispersion, sorption, and first-order decay, subject to a first-order decaying contaminant concentration at the source and a Type I, Dirichlet, boundary at infinity. This solution is unique because of the boundary conditions imposed, but similar to other published solutions. We briefly describe the governing equations, boundary and initial conditions, and the solution techniques used to develop the analytical solution. We provide and discuss the analytic solution using examples with source decay less than, equal to, and greater than contaminant decay during transport. Then we compare the results to several published solutions in the fields of radioactive waste disposal and recalcitrant nonaqueous phase liquid modeling. The other analytical solution results are similar to ours, but the RT3D solution shows more numerical dispersion than our solution.