Analysis of point-source and boundary-source solutions of one-dimensional groundwater transport equation

The solute transport equation is commonly used to describe the migration and fate of solutes in a groundwater flow system. Depending on the problem nature, the source of the solute may be represented as a point source term in the equation or specified as the first-type or third-type boundary condition. The solutions derived under the condition that the solute introduced into the flow system is from the boundary is herein considered as the boundary-source solutions. The solution obtained when solving the transport equation with a point-source term is considered as the point-source solution. The Laplace transform technique is employed to derive the formulas for those solutions expressed in terms of the normalized mass release rate. The underlying nature of different source release modes and the differences among those boundary-source solutions and the constant point-source solution can be easily and clearly differentiated based on the derived formulas for one-dimensional transport. The methodology could, however, be easily extended to two- and three-dimensional problems.