Analytical solutions of contaminant transport from finite one-, two-, and three-dimensional sources in a finite-thickness aquifer

Analytical study of contaminant transport from a finite source in a finite-thickness aquifer is most useful in hydrological and environmental sciences and engineering but rarely investigated in previous studies. This paper provides analytical solutions of contaminant transport from one-, two-, and three-dimensional finite sources in a finite-thickness aquifer using Greenʹs function method. A library of unpublished analytical solutions with different finite source geometry is provided. A graphically integrated MATLAB® script is developed to calculate the temporal integrations in the analytical solutions and obtain the final solutions of concentration. The analytical solutions are examined by reproducing the solutions of some special cases discussed in previous studies. The sensitivities of the line source solutions to source geometry, dispersion coefficients, and distance to the source are tested. The contaminant concentration in the near field is found to be sensitive to the source geometry and anisotropy of the dispersion coefficients. The contaminant concentration in the far field is found to be much less sensitive to the source geometry. The physical insights of the analytical solutions are interpreted.