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Semianalytic solution for transport of a two‐member decay chain in discrete parallel fractures
Author(s) -
Hansen Scott K.
Publication year - 2013
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1002/wrcr.20451
Subject(s) - decay chain , chain (unit) , parallel computing , computer science , mathematics , physics , nuclear physics , quantum mechanics
A wide variety of analytic solutions have been developed for 1‐D contaminant transport, but to date the author is aware of none modeling a decay chain in parallel discrete fractures in porous media. In this note, the derivation is presented for a two‐species first‐order decay chain in such an environment, with an arbitrary concentration history specified upgradient, fracture advection, and diffusion into the porous matrix. The solution is presented in brief, followed by corroboration of its numerical implementation against two different existing numerical codes. An appendix contains a detailed derivation of the solution, and a Mathematica notebook that implements it and may be used by practitioners is enclosed as supporting information.