Analytical and numerical techniques have been routinely employed to solve the fate and transport of reactive three-dimensional groundwater contaminants governed by one-dimensional advection, three-dimensional dispersion, linear equilibrium sorption, and first-order decay reaction. While computationally intensive numerical models are used to simulate contaminant plumes for heterogeneous real-world scenarios, analytical models are used as validation tools for numerical models and also as screening tools for initial estimates of plumes in simplified concept models. The exact analytical solution (Wexler solution) to three-dimensional groundwater transport is not closed-form and requires numerical integration to compute the final solution. To overcome this, an approximate analytical solution (Domenico solution) was developed that was closed-form. The Domenico approach approximates the characteristic residence time in the transverse dispersion terms of the solution using the advection travel time. The Domenico solution has been widely used in several screening tools such as BioScreen, FATE5, BioChlor, ART3D, ArcNLET, Quick-Domenico. However, the Domenico solution has been shown to be accurate only when the longitudinal dispersivity is small. For larger values of longitudinal dispersivities and at plume locations beyond the advective front, the Domenico approximate solution has been shown to introduce significant errors. The nature of these errors places severe limitations on the applicability of the Domenico solution in realistic contaminant transport scenarios. Here we use inverse numerical techniques (fminbnd, MATLAB) to estimate the true characteristic residence time for transverse dispersion. Our results show that the characteristic residence time approximation by the Domenico solution is valid only within the advective front and for small longitudinal dispersion values. We conclude that a better approximation of the characteristic residence time that includes the effect of longitudinal dispersive transport will help improve the accuracy of the Domenico solution.