Analytical solutions for transport in porous media with Gaussian source terms

Abstract

Analytical solutions for the advective‐dispersion equation for solute transport in porous media commonly assume a uniform distribution of mass within the source term. This paper derives an analytical solution for transport in porous media for a source term whose mass is distributed as a bivariate Gaussian spatial function. The solution is an extension of existing analytical solutions using a Green's function approach to separate out one‐dimensional terms in a manner similar to previous authors. This approach illustrates the relationship of the bivariate Gaussian source term solution to other Green's function solutions and thus leads to a set of solutions for advective‐dispersive transport with various source term and domain geometries. Comparison of point, bivariate Gaussian, and uniform source term solutions finds the greatest differences near the source, with discrepancies decreasing with travel distance.