Analytical Solutions to Three-Dimensional Reactive Contaminant Transport Problems Involving Point, Line, and Area Sources

Screening tools such as BioScreen, BioChlor, ATRANS, AT123D-AT, ArcNLET, and Hydroscape are routinely employed to simulate the three-dimensional transport of reactive contaminants in groundwater. These tools estimate contaminant plume concentrations either using exact semi-analytical solutions or the approximate closed-form Domenico analytical solution. Semi-analytical solutions involve numerical integration procedures that can be mathematically challenging and computationally demanding. To overcome this, screening tools often use the approximate closed-form Domenico solution. However, the approximate Domenico solution introduces significant errors under realistic values of longitudinal dispersion, especially at plume locations beyond the advective front. Recently, an improved closed-form approximation to the three-dimensional reactive transport problem was developed using the concept of characteristic residence time. However, this solution was only applicable for a rectangular area source subject to a Dirichlet boundary condition. This severely restricts the use and applicability of the closed-form approximate solution to solve practically relevant simplified groundwater contaminant transport problems. Here, we present a library of six exact semi-analytical solutions for point, line, and area sources (three source geometries) under Dirichlet and Cauchy boundary conditions (two boundary conditions). Additionally, we develop approximate closed-form analytical solutions for all six solutions using the characteristic residence time concept. Our approximate solutions match well with the exact solutions under a wide range of parameter and domain conditions. We extend our analytical solutions to include the effects of linear equilibrium sorption, source decay, and pulse source input. Our analytical solution library facilitates the application of screening tools for a wide range of practically relevant simplified groundwater reactive contaminant transport problems.