Groundwater is a vital source for domestic, industrial, and agricultural purposes contributing to 31% of global freshwater use. However, this resource is increasingly being threatened by contamination from natural as well as anthropocentric causes. Common sources of groundwater contamination include industrial and municipal wastes, agricultural runoff, and mining waste. Computational modelling tools such as MT3D, RT3D, and PHREQ-C are often employed to delineate the contaminant source, monitor the extent contaminant plume, and suggest remedial measures. These tools numerically solve the groundwater transport equation that includes advection, dispersion, reaction, and adsorption under heterogeneous, anisotropic and unsteady conditions with complex source boundaries. However, they also require extensive input data, model parameters, and significant computational resources. While these tools are suited for long-term detailed studies, they are ineffective for use as screening tools which are often used to obtain quick initial estimates of plume concentrations. Screening tools such as BioScreen, FATE5, BioChlor, ART3D, ArcNLET, Quick-Domenico, etc. employ analytical solutions since they do not require much computation time. Additionally they can be run using a small set of input data and parameters since they solve a simplified transport problem with homogeneous aquifer characteristics under uniform flow conditions. These characteristics make screening tools ideal for use in rapid contaminant assessment and multi-scenario analysis. Most screening tools employ the closed-form Domenico approximate analytical solution for computing transient contaminant plume concentrations emanating from a rectangular Dirichlet area source in a 3D domain. While the Domenico solution gives reasonable estimates of contaminant plume concentrations for advection dominant transport conditions, the errors are high under longitudinal dispersion dominant transport especially at plume locations beyond the advective front. This places severe restrictions on the applicability of the Domenico solution.
Here we introduce the concept of characteristic time (Timp) to derive a more accurate solution for the 3D transient transport problem. Our improved approximation matches well with the exact solution (which is 50 times more computationally expensive) under a wide range of parameter values that occurs in the groundwater contaminant transport. We extend the solution for the rectangular Dirichelt area source problem to include contaminant sources with point, line and area dimensions under both Dirichlet and Cauchy boundary conditions with decaying contaminant plume and decaying contaminant source. Additionally, we apply the superposition principle to derive solutions for a pulse boundary condition. These additions broadens the applicability of screening tools in solving a wide range of practical groundwater contaminant transport problems.