The development of a through-diffusion model with a parent–daughter decay chain

Chen, Chin-Lung; Wang, TsingHai; Lee, Ching-Hor; Teng, Shi-Ping

doi:10.1016/j.jconhyd.2012.06.002

Cited by 7 publications

(6 citation statements)

References 24 publications

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“…These prove that ( 17 ) is a semi-analytical solution of the CC–VC model, and that ( 18 ) is the concentration formula in the OR. Analytical solution Similar to the discussion by Chen et al [ 9 ], the multi-compartment (MC) model was used to develop the analytical solution of the CC–VC model with a decay effect. The derivation steps are presented below.…”

Section: Methodsmentioning

confidence: 99%

“…The VC–VC model with a decay effect can refer to the Ref. [ 9 ]. The semi-analytical solutions using the advection–dispersion (AD) model in the Laplace domain are as follows: where , , and .…”

Section: Methodsmentioning

confidence: 99%

“…Similarly, the concentration in the end term can be fixed or variable. The combinations involve a constant inlet concentration–constant outlet concentration model (CC–CC model) [ 3 , 4 ], a constant inlet concentration–variable outlet concentration model (CC–VC model) [ 5 , 6 ], a variable inlet concentration–constant outlet concentration model (VC–CC model) [ 3 ], and a variable inlet concentration–variable outlet concentration model (VC–VC model) [ 7 – 9 ]. The estimated methods of the diffusion coefficients corresponding to the models are termed the CC–CC method, CC–VC method, VC–CC method, and VC–VC method, respectively.…”

Section: Introductionmentioning

confidence: 99%

“…This is currently a resources waste. The literatures [ 7 – 9 ] did not apply those useful data. Thus, we develop the diffusion coefficient estimated methods from the concentration distributions of the IR and OR in the VC–VC model.…”

Section: Introductionmentioning

confidence: 99%

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Intercomparison of diffusion coefficient derived from the through-diffusion experiment using different numerical methods

Chen

Wang

Lee

et al. 2014

J Radioanal Nucl Chem

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Diffusion is a dominant mechanism regulating the transport of released nuclides. The through-diffusion method is typically applied to determine the diffusion coefficients (D). Depending on the design of the experiment, the concentrations in the source term [i.e., inlet reservoir (IR)] or the end term [i.e., outlet reservoir (OR)] can be fixed or vary. The combinations involve four distinct models (i.e., the CC–CC model, CC–VC model, VC–CC model, and the VC–VC model). Studies discussing the VC–CC model are scant. An analytical method considering the decay effect is required to accurately interpret the radioactive nuclide diffusion experiment results. Therefore, we developed a CC–CC model and a CC–VC model with a decay effect and the simplified formulas of these two models to determine the diffusion coefficient (i.e., the CC–CC method and CC–VC method). We also proposed two simplified methods using the VC–VC model to determine the diffusion coefficient straightforwardly based upon the concentration variation in IR and OR. More importantly, the best advantage of proposed method over others is that one can derive three diffusion coefficients based on one run of experiment. In addition, applying our CC–VC method to those data reported from Radiochemica Acta 96:111–117, 2008; and J Contam Hydrol 35:55–65, 1998, derived comparable diffusion coefficient lying in the identical order of magnitude. Furthermore, we proposed a formula to determine the conceptual critical time (Tc), which is particularly beneficial for the selection of using CC–VC or VC–VC method. Based on our proposed method, it becomes possible to calculate diffusion coefficient from a through-diffusion experiment in a shorter period of time.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Intercomparison of diffusion coefficient derived from the through-diffusion experiment using different numerical methods

Chen

Wang

Lee

et al. 2014

J Radioanal Nucl Chem

Self Cite

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show abstract

“…Chen et al (2012) found radioisotope concentrations and the diffusion coefficient using multi-compartment methods. Moridis (1999) obtained analytical solutions for the diffusion, sorption and decay equations of radioisotope concentrations in the Laplace domain.…”

Section: Introductionmentioning

confidence: 99%