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In-situ measurement via the flow-through method and numerical simulations for radon exhalation during measurements of the radon exhalation rate

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Abstract

Small-scale measurements of the radon exhalation rate using the flow-through and closed-loop methods were conducted on the surface of a uranium tailing pond to better understand the differences between the two methods. An abnormal radon exhalation behavior was observed, leading to computational fluid dynamics (CFD)-based simulations in which dynamic radon migration in a porous medium and accumulation chamber was considered. Based on the in-situ experimental and numerical simulation results, variations in the radon exhalation rate subject to permeability, flow rate, and insertion depth were quantified and analyzed. The in-situ radon exhalation rates measured using the flow-through method were higher than those measured using the closed-loop method, which could be explained by the negative pressure difference between the inside and outside of the chamber during the measurements. The consistency of the variations in the radon exhalation rate between the experiments and simulations suggests the reliability of CFD-based techniques in obtaining the dynamic evolution of transient radon exhalation rates for diffusion and convection at the porous medium-air interface. The synergistic effects of the three factors (insertion depth, flow rate, and permeability) on the negative pressure difference and measured exhalation rate were quantified, and multivariate regression models were established, with positive correlations in most cases; the exhalation rate decreased with increasing insertion depth at a permeability of 1 × 10−11 m2. CFD-based simulations can provide theoretical guidance for improving the flow-through method and thus achieve accurate measurements.

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Data availibility

The data that support the findings of this study are openly available in Science Data Bank at https://cstr.cn/31253.11.sciencedb.j00186.00538 and https://doi.org/10.57760/sciencedb.j00186.00538.

Abbreviations

\({A}_\text {Ra}\) :

Radium activity concentration, Bq kg−1

C :

Radon concentration in the air, Bq m−3

\({C_0}\) :

Initial radon concentration, Bq m−3

\({C_\text {a}}\) :

Radon concentration in the atmosphere, Bq m−3

\({C_\text {b}}\) :

Radon concentration at the porous medium-air interface, Bq m−3

\(C_\text {v-avg}\) :

The volume-averaged radon concentration in the chamber, Bq m−3

D :

Radon diffusion coefficient in porous medium, m2 s−1

\({D_\text {m}}\) :

Molecular diffusion coefficient of radon in air, 1.05 × 10−5 m2 s−1

\(D_\text {p}\) :

Average grain size, mm

\(D_\text {t}\) :

Effective turbulent diffusion coefficient, m2 s−1

E :

Radon exhalation rate, Bq m−2 s−1

\({E_\text {a}}\) :

Initial radon exhalation rate equivalent to the analytical solution in diffusion, Bq m−2 s−1

E a–c :

Initial radon exhalation rate equivalent to the analytical solution in diffusion and convection, Bq m−2 s−1

\(E_\text {f}\) :

Fitted radon exhalation rate, Bq m−2 s−1

\(E_\text {f-exp}\) :

Radon exhalation rate by exponential fit, Bq m−2 s−1

\(E_\text {f-lin}\) :

Radon exhalation rate by linear fit, Bq m−2 s−1

\(E_\text {mf}\) :

Radon exhalation rate obtained by the fitted multivariate function, Bq m−2 s−1

E n :

Transient radon exhalation rate (En-d + En-c), Bq m−2 s−1

E n-d :

Transient radon exhalation rate for diffusion, Bq m−2 s−1

E n-c :

Transient radon exhalation rate for convection, Bq m−2 s−1

\(E_\text {Rn}\) :

Radon emanation coefficient of porous medium, dimensionless

F :

Source term of external body forces, N m−3

FVM:

Finite volume method

H1,  H3, and  H5:

The insertion depth of the accumulation chamber into porous medium

k :

Turbulent kinetic energy, m2 s−2

K :

Permeability, m2

\(\Delta P\) :

The pressure difference, Pa

P :

Static pressure, Pa

\(P_\text {s}\) :

The volume-averaged static pressure in the accumulation chamber, Pa

\(P_\text {mf}\) :

The fitted negative differential pressure, Pa

\(Q_\text {out}\)  and  \(Q_\text {in}\) :

Flow rate during measurements at the outlet and inlet, respectively, of the chamber, L min−1

\(S_\text {a}\) :

The area of the surface where radon exhales, m2

Sct :

Schmidt number

\(S_\text {Rn}\) :

Source term of governing equation of radon migration in numerical simulation, Bq m−3 s−1

t :

Time, s

v :

Superficial velocity of gas flowing in porous medium, m s−1

V :

Volume of the accumulation chamber, m3

u :

Physical velocity of gas flowing in porous medium, m s−1

x :

Vertical depth of porous medium, m

\(\alpha\) :

Free radon production rate, Bq m−3 s−1

\(\varepsilon\) :

Turbulent dissipation rate, m2 s−3

\(\eta\) :

Porosity, %

\(\lambda\) :

Radon decay constant, 2.1 × 10−6 s−1

\(\lambda _\text {b}\) :

Back-diffusion coefficient, s−1

\(\lambda _\text {e}\) :

Equal to \(\lambda\) + \(\lambda _\text {b}\) + \(\lambda _\text {l}\), s−1

\(\lambda _\text {l}\) :

The leakage rate for radon in the accumulation chamber, s−1

\(\mu\) :

Dynamic viscosity, Pa s

\(\mu _\text {t}\) :

Turbulent viscosity, Pa s

\(\rho _\text {s}\) :

Porous medium density, kg m−3

\(\rho _\text {a}\) :

Air density, kg m−3

\(\tau\) :

Tortuosity factor, dimensionless

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Authors and Affiliations

  1. School of Resources Environment and Safety Engineering, University of South China, Hengyang, 421001, China

    Ming **a, Yong-Jun Ye, Shan-Wei Shang, Ting Yu & Dai-Jia Chen

  2. Key Discipline Laboratory for National Defense for Biotechnology in Uranium Mining and Hydrometallurgy, University of South China, Hengyang, 421001, China

    Yong-Jun Ye

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Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Ming **a, Yong-Jun Ye, Shan-Wei Shang, Ting Yu, and Dai-Jia Chen. The first draft of the manuscript was written by Ming **a and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Yong-Jun Ye.

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Additional information

This work was supported by the National Natural Science Foundation of China (No. 11575080), Hunan Provincial Natural Science Foundation of China (No. 2022JJ30482), and Hunan Provincial Innovation Foundation for Postgraduate (No. QL20220206).

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**a, M., Ye, YJ., Shang, SW. et al. In-situ measurement via the flow-through method and numerical simulations for radon exhalation during measurements of the radon exhalation rate. NUCL SCI TECH 35, 112 (2024). https://doi.org/10.1007/s41365-024-01491-5

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