Analytical Model for Three-Dimensional Reactive Transport of Coexisting Chlorinated Solvent Contaminants in Groundwater Under Time-Varying Source Discharge Concentrations Induced by Remediation Efforts

Chlorinated solvents, common groundwater contaminants, can cause coexistence of the original contaminant and its degradation products during the transport process. Practically applicable analytical models for reactive transport are essential for simulating the plume migration of chlorinated solvent contaminants and their degradation products within a complex chemical mixture. Although several analytical models have been developed to solve advection–dispersion equations coupled with a series of decay reactions for simulating transport of the coexisting chlorinated solvent contaminants, the majority assume static, time-invariant inlet boundary conditions. Such time-invariant inlet boundary conditions may fail to adequately represent the temporal evolution of dissolved source discharge concentration concerning mass reduction, especially in the context of diverse DNAPL source remediation strategies. This study seeks to derive analytical models for three-dimensional reactive transport of multiple contaminants, specifically addressing the challenges posed by dynamical, time-varying inlet boundary conditions. The model development incorporates two distinct inlet functions: exponentially decaying and piecewise constant. Analytical solutions are obtained using three integral transform techniques. The accuracy of the newly developed analytical models is verified by comparing them with solutions derived from existing literature using multiple illustrative examples. By incorporating two distinct time-varying inlet boundary conditions, the models exhibit strong capabilities in capturing the complex transport dynamics and fate of contaminants within groundwater systems. These features make the models valuable tools for improving the understanding of subsurface contaminant behavior and for quantitatively evaluating and optimizing a range of remediation strategies.