A Generalized Analytical Model for Multispecies Reactive Solute Transport with Scale?Dependent Dispersion Subject to First- and Third-Type Inlet Boundary Conditions

Analytical models for a set of advection-dispersion equations of multispecies transport coupled with aseries of first-order sequential decay reactions are essential and efficient tools for synchronous prediction ofthe fate and transport of the parent and daughter species of decaying contaminants such as radionuclides,chlorinated organic compounds, pesticides and nitrogen. Although several researchers proposed various typesof mathematical methods for analytically solving this coupled advection-dispersion equation system ofmultispecies transport, the currently available solutions in the literature are mostly derived based on advectiondispersionequations with constant dispersion coefficients. It has been known for a couple of decades thatdispersion coefficient increases with solute displacement distance in the subsurface. The increase of dispersioncoefficient with solute travel distance results from significant variation in hydraulic properties of porous mediaand was identified in the relevant literature as scale-dependent dispersion. An analytical model for the coupledmultispecies transport problem associated with scale-dependent dispersion coefficients is not currentlyavailable in the published literature.In this project, we target to develop a novel analytical model for coupled multispecies transport with scaledependentcoefficients. First, sequential applications of the Laplace transform with respect to time and thegeneralized integral transform with respect to spatial variable will be executed to reduce the coupled partialdifferential equation system to a set of linear algebraic equations for the species concentrations in thetransformed domain. Subsequently, the system of algebraic equations will be easily solved using operation ofalgebra to obtain each species concentration in the transformed domain, and the solutions in the original domainwill be then obtained through consecutive integral transform inversions. The developed analytical model willbe compared with a numerical model that solves a set of coupled advection-dispersion equations using Laplacetransform finite difference method to test the correctness of the derived solution and the computation accuracyof the corresponding computer code developed for the derived solution. We will compare the new analyticalmodel derived for scale-dependent dispersion coefficient against the published analytical solutions derived forconstant dispersion coefficients to illustrate the effect of the dispersion coefficients on the coupled multispeciestransport of decaying contaminants.