Improved Domenico solution for three-dimensional contaminant transport

The Domenico solution is a widely used analytical solution in screening tools such as BioScreen, FATE5, BioChlor, ART3D, ArcNLET, Quick-Domenico, etc., to simulate the three-dimensional transport of reactive contaminants in groundwater. While being approximate, this solution presents a convenient closed-form expression for computing plume contaminant concentrations without the need for numerical integration. Previous studies have mathematically shown that the Domenico solution provides correct estimates of contaminant plume concentrations when the value of longitudinal dispersivity is zero. However, under non-zero longitudinal dispersivity values, the errors in the Domenico solution increase, especially at plume locations beyond the advective front. The nature of these errors places severe limitations on the applicability of the Domenico solution in simulating realistic contaminant transport problems. Here, we present a new closed-form solution for three-dimensional (3D) reactive contaminant transport that overcomes this limitation. We introduce the concept of characteristic residence time, which represents the average time taken by a contaminant particle to reach a given (x, y, z) location. We show that along the plume centerline, the characteristic residence time exhibits three features, (i) initial linear response with a slope equal to the inverse of advection velocity, (ii) final saturation response with a maximum value of simulation time (iii) transition between the initial and final responses at the region surrounding the advective front, with sharper transitions at lower longitudinal dispersivities and smoother transitions at higher longitudinal dispersivities. We calibrate the Ramberg-Osgood function to fit the behavior of the characteristic residence time along the plume centerline and use this to develop a new and improved closed-form approximation for the Domenico solution. Without any additional computational effort, our new and improved solution better approximates the solute concentrations of a three-dimensional contaminant plume under realistic values of longitudinal dispersivity. Our improved solution closely matches the exact analytical solution, especially at plume locations beyond the advective front, where the Domenico solution performs poorly. Existing screening tools can be readily be retrofitted with the new and improved solution to provide more accurate estimates for plume concentrations.