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One-dimensional Analytical Solutions for Diffusion from a Low-permeability Layer
1차원 해석해를 이용한 저투수성 매체에서의 확산에 관한 연구
Econ. Environ. Geol. 2020 Feb;53(1):11-21
Published online February 28, 2020;
Copyright © 2020 the Korean society of economic and environmental gelology.

Seonggan Jang1 and Minjune Yang2*
장성간1 · 양민준2*

1Division of Earth Environmental System Sciences, Pukyong National University, Busan 48514, South Korea
2Department of Earth and Environmental Sciences, Pukyong National University, Busan 48514, South Korea
1부경대학교 지구환경시스템과학부, 2부경대학교 지구환경과학과
Received January 3, 2020; Revised January 31, 2020; Accepted February 1, 2020.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
One-dimensional analytical solutions were used for forward and back diffusion of trichloroethylene (TCE) and tetrachloroethylene (PCE) in a single system with high- and low-permeability layers. Concentration profiles in a lowpermeability layer, diffusive fluxes at the interface between the high- and low-permeability layers, and contaminant persistence in the high-permeability layer due to back diffusion were simulated with a comparison of semi-infinite and finite analytical solutions. In order to validate the analytical solutions used in this study, the results of onedimensional analytical solutions developed by Yang et al. (2015) were compared with Nash–Sutcliffe model efficiency coefficient (NSE). When compared with Yang et al. (2015), the analytical solutions used in this study showed good agreements (NSE = 0.99). When compared with semi-infinite analytical solutions, TCE and PCE concentration profiles in the low-permeability layer, the diffusive fluxes, and the contaminant tailings of the high-permeability layer were underestimated. In order to determine the appropriate analytical solutions based on the effective diffusion coefficient, the thickness of the low-permeability layer, and the diffusion time in the TCE and PCE contaminated site, a term of dimensionless diffusion length (Zd) was used. If the Zd is less than 0.7, the semi-infinite solutions can be used to simulate accurate concentration profiles in low-permeability layers. If the Zd is greater than 0.7, the reliability of simulations may be improved by using the finite solutions.
Keywords : analytical solution, DNAPL, diffusion, low-permeability layer, TCE


April 2020, 53 (2)