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Mathematical Models on Diffusive Loss of Non-Aqueous Phase Organic Solvents from a Disk Source  

Yoon, In-Taek (GeoSystem Research Corp.)
S.E., Dickson (Department of Civil Engineering, McMaster University)
Publication Information
Journal of Soil and Groundwater Environment / v.13, no.6, 2008 , pp. 40-49 More about this Journal
Abstract
Matrix diffusion from planar fractures was studied mathematically and through physical model experiments. Mathematical models were developed to simulate diffusion from 2D and 3D instantaneous disk sources and a 3D continuous disk source. The models were based on analytical solutions previously developed by Carslaw and Jaeger (1959). The mathematical simulations indicated that the 2D scenario produces significantly different results from the 3D scenario, the time for mass disappearance is significantly larger for continuous sources than for instantaneous sources, the normalized concentration generally decreased over time for instantaneous sources while it increased over time for continuous sources, diffusion rates decrease significantly over time and space, and the normalized mass loss from the source zone never reaches 1 for continuous sources due to the semi-infinite integral. The simulations also showed that disappearance times increase exponentially with increasing source radii and matrix porosity, and decrease with increasing aqueous-phase NAPL solubilities.
Keywords
Fracture; Matrix diffusion; Disk source; Mathematical model; NAPL;
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