A parsimonious analytical model for simulating multispecies plume migration
Abstract. A parsimonious analytical model for rapidly predicting the long-term plume behavior of decaying contaminant such as radionuclide and dissolved chlorinated solvent is presented in this study. Generalized analytical solutions in compact format are derived for the two-dimensional advection-dispersion equations coupled with sequential first-order decay reactions involving an arbitrary number of species in groundwater system. The solution techniques involve the sequential applications of the Laplace, finite Fourier cosine, and generalized integral transforms 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 verified against the numerical solutions. The analytical results indicate that the parsimonious analytical solutions are robust and accurate. The solutions are useful for serving as simulation or screening tools for assessing plume behaviors of decaying contaminants including the radionuclides and dissolved chlorinated solvents in groundwater systems.