Radionuclide migration through fractured rock for arbitrary-length decay chain: Analytical solution and global sensitivity analysis

Shahkarami, Pirouz; Liu, Longcheng; Moreno, Luis; Neretnieks, Ivars

doi:10.1016/j.jhydrol.2014.10.060

Cited by 28 publications

(19 citation statements)

References 26 publications

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“…8 suggest that matrix diffusion (Neretnieks 1980) causes strong retardation of solute transport, due to the great capacity of the porous rock in retaining the solute (Mahmoudzadeh et al 2016), and therefore it dominates eventually over hydrodynamic dispersion in determining the spreading of a tracer pulse. Radioactive decay is, on the other hand, also an important factor decisive for the late tail of the breakthrough curves (Shahkarami et al 2015); however, the general features shown in Fig. 7 as to the spreading of the tracer pulse are still kept in Fig.…”

Section: Comparison Of the Model Predictionsmentioning

confidence: 95%

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Solute transport along a single fracture in a porous rock: a simple analytical solution and its extension for modeling velocity dispersion

et al. 2017

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A simple and robust solution is developed for the problem of solute transport along a single fracture in a porous rock. The solution is referred to as the solution to the singleflow-path model and takes the form of a convolution of two functions. The first function is the probability density function of residence-time distribution of a conservative solute in the fracture-only system as if the rock matrix is impermeable. The second function is the response of the fracture-matrix system to the input source when Fickian-type dispersion is completely neglected; thus, the effects of Fickian-type dispersion and matrix diffusion have been decoupled. It is also found that the solution can be understood in a way in line with the concept of velocity dispersion in fractured rocks. The solution is therefore extended into more general cases to also account for velocity variation between the channels. This leads to a development of the multi-channel model followed by detailed statistical descriptions of channel properties and sensitivity analysis of the model upon changes in the model key parameters. The simulation results obtained by the multi-channel model in this study fairly well agree with what is often observed in field experiments-i.e. the unchanged Peclet number with distance, which cannot be predicted by the classical advectiondispersion equation. In light of the findings from the aforementioned analysis, it is suggested that forced-gradient experiments can result in considerably different estimates of dispersivity compared to what can be found in naturalgradient systems for typical channel widths.

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Section: Comparison Of the Model Predictionsmentioning

confidence: 95%

“…Shahkarami et al (2015) and Mahmoudzadeh et al (2013). It suffices, however, for the need in the analysis of field tracer tests, and should be taken as the starting point before going deeper into complicated systems involving, e.g.…”

Section: Mathematical Model and Solution Proceduresmentioning

confidence: 99%

Solute transport along a single fracture in a porous rock: a simple analytical solution and its extension for modeling velocity dispersion

et al. 2017

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“…influencing the disposal facility (repository) and its surrounding environment necessitating a complex analysis of the processes and their interactions. Thus, the analyzed model output differs from study to study (i.e., peak flux [22], peak time [23], maximum concentration [5], peak dose [24], the amount of radionuclides being released at particular times after repository closure [25], dose over time [26], dose conversion factors [6]). The uncertainty and sensitivity of physical parameters that impact contaminant transport to the environment are considered as a model output to be analyzed (e.g., pressure in the borehole [27]).…”

Section: Radionuclide Transport Model For Rbmk-1500 Snf Disposalmentioning

confidence: 99%

Uncertainty and Sensitivity Analysis at Low Value of Determination Coefficient of Regression Analysis: Case of I-129 Release from RBMK-1500 SNF under Disposal Conditions

2019

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As in other nuclear countries, the operation of the Ignalina nuclear power plant in Lithuania has led to the accumulation of around 22 thousand assemblies of spent nuclear fuel (SNF). The development of geological disposal program involves an iterative assessment of the system safety supported by scientific research on radionuclides migration and related processes. This study focused on the application of Contribution to the Sample Mean (CSM) and Contribution to Sample Variance (CSV) methods to complement the uncertainty and sensitivity analyses of the time-dependent flux of I-129 from the engineered barriers of a conceptual disposal facility for RBMK-1500 SNF (RBMK is abbreviation of "High Power Channel-type Reactor" (in Russian)). The analysis was performed using a MATLAB platform (8.0.0.783 (R2012b), MathWorks, MA, USA). The mean and variance ratios derived from CSM and CSV plots were applied to estimate the effect of reduced uncertainty range on mean flux and its variance, and the uncertainty analysis was also complimented. Increasing the lower bounding value of defect size enlargement time range to 4.6 × 10 4 years would lead to a lower mean flux until 5 × 10 4 years after repository closure. Later on (up to 1 million years after repository closure), the only reduction of the upper bounding value of the SNF dissolution rate range would affect a decreased mean flux.Keywords: RBMK-1500 spent nuclear fuel; deep geological repository; uncertainty and sensitivity; CSM; CSV; radionuclide migration 3 × 10 −12 (p = 0.15) 1 × 10 −11 (p = 0.7) 3 × 10 −11 (p = 0.15) Discrete 1 Probability density function. SNF: spent nuclear fuel.Minerals 2019, 9, 521 5 of 26 Characterization of Model BehaviorThe model realized using the computer code AMBER [34] assessed time-dependent radionuclide release from the SNF matrix, dissolution, radioactive decay, and contaminant transport by diffusion through engineered barriers. The uncertainty of the main transport-related parameters, including defect size enlargement time, was characterized by probability density function for each parameter. The model output was a large number of the time-dependent flux values over an extended period (10 3 -10 6 years after repository closure), which allowed for the evaluation of the mean flux, the quantiles, and the distribution of the peak flux, as illustrated in Figure 2.

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“…Despite the advances in numerical modeling, the development of analytical solutions is still necessary to verify the computer models and to perform scoping calculations (e.g. Bolster et al, 2007;Chen et al, 2012;Hayek et 5 al., 2012;Shahkarami et al, 2015;Parker and Kim, 2015). Analytical solutions are ideally suited for the interpretation of the physical processes.…”

Section: Introductionmentioning

confidence: 99%

Semianalytical solutions for contaminant transport under variable velocity field in a coastal aquifer

Koohbor

Fahs

Ataie-Ashtiani

et al. 2018

Journal of Hydrology

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Existing closed-form solutions of contaminant transport problems are limited by the mathematically convenient assumption of uniform flow. These solutions cannot be used to investigate contaminant transport in coastal aquifers where seawater intrusion induces a variable velocity field. An adaptation of the Fourier-Galerkin method is introduced to obtain semianalytical solutions for contaminant transport in a confined coastal aquifer in which the saltwater wedge is in equilibrium with a freshwater discharge flow. Two scenarios dealing with contaminant leakage from the aquifer top surface and contaminant migration from a source at the landward boundary are considered. Robust implementation of the Fourier-Galerkin method is developed to efficiently solve the coupled flow, salt and contaminant transport equations. Various illustrative examples are generated and the semi-analytical solutions are compared against an in-house numerical code. The Fourier series are used to evaluate relevant metrics characterizing contaminant transport such as the discharge flux to the sea, amount of contaminant persisting in the groundwater and solute flux from the source. These metrics represent quantitative data for numerical code validation and are relevant to understand the effect of seawater intrusion on contaminant transport. It is observed that, for the surface contamination scenario, seawater intrusion limits the spread of the contaminant but intensifies the contaminant discharge to the sea. For the landward contamination scenario, moderate seawater intrusion affects only the spatial distribution of the contaminant plume while extreme seawater intrusion can increase the contaminant discharge to the sea. The developed semi-analytical solution presents an efficient tool for the verification of numerical models. It provides a clear interpretation of the contaminant transport processes in coastal aquifers subject to seawater 3 intrusion. For practical usage in further studies, the full open source semi-analytical codes are made available at the website https://lhyges.unistra.fr/FAHS-Marwan.

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Radionuclide migration through fractured rock for arbitrary-length decay chain: Analytical solution and global sensitivity analysis

Cited by 28 publications

References 26 publications

Solute transport along a single fracture in a porous rock: a simple analytical solution and its extension for modeling velocity dispersion

Solute transport along a single fracture in a porous rock: a simple analytical solution and its extension for modeling velocity dispersion

Uncertainty and Sensitivity Analysis at Low Value of Determination Coefficient of Regression Analysis: Case of I-129 Release from RBMK-1500 SNF under Disposal Conditions

Semianalytical solutions for contaminant transport under variable velocity field in a coastal aquifer

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