Direct computation of critical plume quantities required for initial assessment of contaminated sites

Abstract

Estimates of plume extremes such as maximum plume width (Wmax) and its location (Xwmax), maximum plume area (Amax), and maximum plume length (Lmax), which are vital indicators of any site assessment work, mostly requires the use of rather complicated numerical approaches and a large number of site information. This paper focuses on simpler (semi)analytical quantification of Wmax and Xwmax, and their characterization with respect to source geometry (source width Sw and source thickness St) for estimating Amax. A direct computation of Wmax and Xwmax rather becomes a multi-dimensional nonlinear system problem for which only a few iterative methods are available. The challenge magnifies further as limited information on Wmax and Xwmax are available for obtaining an initial guess of the solution. Solving over 1000 synthetic problems, this work finds the Newton–Krylov method as the most suitable nonlinear system solver. Among the most important were the limiting results such as Lmax/8 ¡Xwmax¡Lmax/8 and 1×Sw¡Wmax¡1.4×Sw. These limiting results simplify the finding of initial guesses for Wmax and Xwmax. Further characterization of Wmax and Xwmax with Lmax, St, and Sw provided an empirical relation between plume and source areas, in addition to an approximation of Amax. A field site data illustrate the potential applications of the methods developed in this work.