ANALYTICAL MODEL FOR THREE-DIMENSIONAL MULTISPECIES PLUME MIGRATION SUBJECT TO FIRST- AND THIRD-TYPE INLET BOUNDARY CONDITIONS

This study presents analytical solutions to the three-dimensional advection-dispersion equations coupled with sequential first-order decay reactions involving arbitrary number of species in groundwater system. The analytical solutions are derived for both first- and third-type inlet boundary conditions. The solutions can be used to predict the three-dimensional plume behavior of decaying contaminant such as radionuclide and dissolved chlorinated solvent. Solutiions are derived through the sequential application of the Laplace, double finite Fourier cosine, and generalized integral transform to transform a set of coupled partial differential equations to a linear algebraic equation system. The algebraic equation system is subquently solved for each species in the transformed domain. Utimately, the solutions in the original domain are then obtained through consecutive inverse integral transforms. The new derived solutions are useful for simulating plume behaviors of decaying contaminants.