Analytical Solutions of Three-Dimensional Contaminant Transport Models with Exponential Source Decay

Despite the availability of numerical models, interest in analytical solutions of multidimensional advection-dispersion systems remains high. Such models are commonly used for performing Tier I risk analysis and are embedded in many regulatory frameworks dealing with groundwater contamination. In this work, we develop a closed-form solution of the three-dimensional advection-dispersion equation with exponential source decay, first-order reaction, and retardation, and present an approach based on some ease of use diagrams to compare it with the integral open form solution and with earlier versions of the closed-form solution. The comparison approach focuses on the relative differences associated with source decay and the effect of simulation time. The analysis of concentration contours, longitudinal sections, and transverse sections confirms that the closed-form solutions studied can be used with acceptable approximation in the central area of a plume bound transversely within the source width, both behind and beyond the advective front and for concentration values up to two orders of magnitude less than the initial source concentration. As the proposed closed-form model can be evaluated without nested numerical computations and with simple mathematical functions, it can be very useful in risk assessment procedures.