Simplified Expressions for Spatial Moments of Ground-Water Contaminant Plumes

Abstract

Ground-water aquifers are an important source of water for domestic, agricultural, and industrial use, but they are often contaminated by hazardous chemicals. In this note, the writers consider the transport of a sorbing contaminant in an infinite, macroscopically homogeneous aquifer. Nonequilibrium sorption is controlled by diffusion into the grains of the porous medium. For this problem, previous work by Goltz and Roberts has presented analytical solutions for the spatial moments of the contaminant plume. The solutions of Goltz and Roberts are given in terms of infinite integrals that can be difficult to evaluate. In this note, the writers demonstrate that the zeroth spatial moment can be represented as an infinite sum rather than as an infinite integral; in most cases, the sum is more easily evaluated than the integral. Also, we show a method for simplifying the expression for the first spatial moment. The modified expression still requires the evaluation of an infinite integral, but the new integral is much better behaved than the previous expression, greatly simplifying the numerical evaluation of the first moment.