An analytical model for simulating two-dimensional multispecies plume migration

The two-dimensional advection-dispersion equations coupled with sequential first-order decay reactions involving arbitrary number of species in groundwater system is considered to predict the two-dimensional plume behavior of decaying contaminant such as radionuclide and dissolved chlorinated solvent. Generalized analytical solutions in compact format are derived through the sequential application of the Laplace, finite Fourier cosine, and generalized integral transform to reduce the coupled partial differential equation system to a set of linear algebraic equations. The system of algebraic equations is next solved for each species in the transformed domain, and the solutions in the original domain are then obtained through consecutive integral transform inversions. Explicit form solutions for a special case are derived using the generalized analytical solutions and are compared with the numerical solutions. The analytical results indicate that the analytical solutions are robust, accurate and useful for simulation or screening tools to assess plume behaviors of decaying contaminants.