Direct computation of critical plume quantities required for initial assessment of contaminated sites. (March 2023)

• Record Type: Journal Article
• Authors: Yadav, P.K.; Ibrahim, S.I.; Liedl, R.; Chahar, B.R.; Grischek, T.
• Is Part Of: Computers & geosciences. Volume 172(2023)
• Publication Date: 2023-03
• Subjects: Maximum plume width -- Maximum plume area -- Non-linear solver -- Contamination management; Environmental policy -- Periodicals; 550.5
• DOI: 10.1016/j.cageo.2023.105299
• Languages: English
• ISSNs: 0098-3004

Abstract

Abstract: Estimates of plume extremes such as maximum plume width ( W m a x ) and its location ( X w m a x ), maximum plume area ( A m a x ), and maximum plume length ( L m a x ), 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 W m a x and X w m a x, and their characterization with respect to source geometry (source width S w and source thickness S t ) for estimating A m a x . A direct computation of W m a x and X w m a x 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 W m a x and X w m a x 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 L m a x /8 ¡ X w m a x ¡ L m a x /8 and 1 × S w ¡ W m a x ¡ 1 . 4 × S w . These limiting results simplify the finding of initial guesses for W m a x and X w m a x . Further characterization of W m a x and X w m a x with L m a x, S t, and S w provided an empirical relation between plume and source areas, in addition to an approximation of A m a x . A field site data illustrate the potential applications of the methods developed in this work. Highlights: Identifying challenges for estimating maximum plume width ( W m a x ) and plume area ( A m a x ). Finding of most appropriate non-linear system solver for computing W m a x and A m a x . Analyzing and exploring the practicality of W m a x and A m a x .