Applicability of the closed-circuit accumulation chamber technique to measure radon surface exhalation rate under laboratory conditions

Radiation Measurements 133 (2020) 106284

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Applicability of the closed-circuit accumulation chamber technique to measure radon surface exhalation rate under laboratory conditions a, * � I. Guti�errez-Alvarez , J.E. Martín a, J.A. Adame b, C. Grossi c, A. Vargas c, J.P. Bolívar a a

Integrated Sciences Department, University of Huelva, Spain Atmospheric Sounding Station, El Arenosillo, Atmospheric Research and Instrumentation Branch, National Institute for Aerospace Technology, INTA, Mazag� on, Huelva, Spain c Institut de T�ecniques Energ�etiques, Universitat Polit�ecnica de Catalunya, Spain b

A R T I C L E I N F O

A B S T R A C T

Keywords: Radon Radon exhalation Phosphogypsum Linearity time

A layer of phosphogypsum was placed at the bottom of two large volume boxes. This system allowed to measure the surface radon exhalation from phosphogypsum without altering the emitting material. The limits and optimal setup of the closed-circuit accumulation chamber technique were thoroughly studied. More precisely, the per­ formance of different radon exhalation fitting methods was analyzed in the reference exhalation boxes, employing different measurement devices and three smaller operational accumulation chambers. As expected, the best approach to obtain the radon exhalation rate depends upon the effective decay constant of the mea­ surement system and the time employed to perform the measurement. The time until the linear approximation can no longer be applied was scrutinized. Although this approximation is usually applied routinely in the literature, the effective time constant of the chamber is often not low enough for the linear fit to be applied safely, providing statistically acceptable measurements that can lead to significative underestimations of the radon exhalation rate.

1. Introduction One of the main sources of natural exposure to ionizing radiation is due to natural radon gas and its decay products. The United Nations Scientific Committee on the Effects of Atomic Radiation (UNSCEAR) reported that the dose due to inhalation of this gas and the alpha-decay of its daughters represent more than 42% of the dose from all sources of radiation to the public. (UNSCEAR, 2008). In addition, radon can be a useful proxy to study atmospheric vertical stability variations and as an atmospheric tracer. Its half-life is short enough to avoid accumulation in the atmosphere, but sufficient to be a €rfer et al., 1991; Vargas conservative tracer during the night (Porstendo et al., 2015). It has also been used as a continental tracer because of the difference in radon generation between sea and land air masses (Schery and Huang, 2004) and as a tracer of air pollutants and aerosols (Arnold et al., 2010; Grossi et al., 2016). An important factor to consider is the radon exhalation from soils. The exhalation plays a significant role in the radon behavior and its systematic monitoring could be used to improve the atmospheric models and refine radon transport simulations. There exist several procedures to

measure the exhalation rate, such as passive methods like activated charcoal canisters (Alharbi and Akber, 2014; Tsapalov et al., 2016) and electrets (Grossi et al., 2008; Kotrappa, 2015), or active methods based on radon build up inside an accumulation chamber (Jonassen, 1983). This last method seems most suitable to perform continuous measure­ ments due to its potential automation (Mazur and Kozak, 2014). The accumulation chamber method allows to obtain the exhalation rate by fitting the radon growth to either an exponential or linear equation. The former is usually employed for longer accumulations periods while the latter is recommended only for the first hours of the accumulation. (ISO, 2012; Noverques et al., 2019; Seo et al., 2018; Yang et al., 2019). However, the linear fit is frequently used without exami­ nation of its range of applicability or verification of its accuracy. One of the main issues to consider is the strength of radon removal processes in the measurement system, which can restrict or even invalidate the usage of the linear fit (Abo-Elmagd, 2014). In this work, the closed-circuit accumulation chamber method was tested in laboratory with two reference exhalation soils, made with phosphogypsum (PG) from a nearby repository. The main goal of this work consisted in designing a laboratory setup to achieve a better

* Corresponding author. � E-mail address: [email protected] (I. Guti�errez-Alvarez). https://doi.org/10.1016/j.radmeas.2020.106284 Received 17 July 2019; Received in revised form 13 February 2020; Accepted 22 February 2020 Available online 24 February 2020 1350-4487/© 2020 Elsevier Ltd. All rights reserved.

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Radiation Measurements 133 (2020) 106284

As happened before, in laboratory conditions vertical radon trans­ port due to convection will be negligible as there is no significant pressure difference between air inside the chamber and outside the chamber. In these conditions and using Fick’s first law, equation (3) can be rewritten as:

∂CRnðtÞ S ¼ EðtÞ V ∂t

(4)

ðλRn þ λl ÞCRn ðtÞ

As described previously, the exhalation rate will not be constant in time due to the radon increase inside the chamber and the subsequent decrease in the diffusion transport from the soil to the accumulation chamber. Applying equations (2)–(4):

∂CRn ðtÞ S ¼ E0 V ∂t

Fig. 1. Scheme of the accumulation chamber method.

2. Experimental and methods

λRn CRn þ λRn CBS ¼ 0

� � � � � � �

(1)

(7)

CRn ðtÞ Radon concentration inside the chamber (Bq m 3 ) E0 Free exhalation rate (Bq m 2 h 1 ) S Chamber surface (m 2 ) V Accumulation volume (m 3 ) λRn Radon decay constant (s 1 ) λl Leakage rate constant (s 1 ) λb Bound exhalation constant (s 1 )

This equation describes a balance between radon generation, pro­ duced by exhalation from the soil, and several radon removal processes, such as radon decay, bound exhalation and possible leaks in the mea­ surement system. Considering λl and λb constant during the measurement, the solution of eq. (7) can be obtained:

In laboratory, diffusion is expected to be the main transport mech­ anism and convection effects can be considered negligible (Abo-Elmagd, �pez-Coto et al., 2009; Porstendo €rfer et al., 2014; Jonassen, 1983; Lo 1991; Ryzhakova, 2012; Sahoo and Mayya, 2010). In this situation the exhalation rate from the soil can be derived using Fick’s first law, obtaining the expression:

ωCRn ðtÞ

ðλRn þ λl þ λb ÞCðtÞ

where:

DB Diffusion coefficient (m2 s 1 ). CRn Radon concentration (Bq m 3 ). z Vertical position in the material (m). β Effective porosity. v Convective flow rate inside the material (m s 1 ). λRn Radon decay constant (s 1 ). CBS Radon concentration at maximum depth (Bq m 3 ).

EðtÞ ¼ E0

(6)

dCRn ðtÞ E0 S ¼ dt V

Where: � � � � � � �

(5)

This effect, called ‘bound exhalation’ (Aldenkamp et al., 1992; �pez-Coto et al., 2009), depends on the geometry of the accumulation Lo chamber, the radon diffusion constant within the soil, the radon diffu­ sion length and the depth of the soil. As a consequence, the balance equation (3) can be rewritten as:

The most common way to measure radon exhalation is based on the accumulation chamber method (Fig. 1). Radon exhaled from the ground enters the chamber and starts to build up inside. Then, the radon accumulation can be registered using a detector device, obtaining the radon exhalation rate by fitting the growth curve to a known equation. The steady-state of radon concentration within a homogeneous ma­ �pez-Coto et al., 2009; Mayya, terial is determined by the relation (Lo 2004; Onishchenko et al., 2015; Porstend€ orfer, 1994): 1 ∂ðvCRn Þ β ∂z

λl CRn ðtÞ

S ω ¼ λb V

2.1. Theoretical framework

∂2 CRn ∂z2

λRn CRn ðtÞ

The second term on the right side describes the reduction in the exhalation as the radon concentrations increase inside the chamber. This effect appears as a virtual radon sink in the balance equation and is commonly referred as ‘back-diffusion’, where:

understanding of the closed-circuit accumulation method and system­ atically study the capacity of the radon build up fitting models to obtain the exhalation rate.

DB

S ωCRn ðtÞ V

CðtÞ ¼ Csat þ ðC0

Csat Þe

λef t

(8)

being the effective decay constant, λef ¼ λRn þ λb þ λl , the saturation concentration, CSat ¼ E0 S=λef V, and the initial concentration inside the chamber, C0 . Typically, the initial concentration is several orders of magnitude lower than the saturation concentration. When this happens, the approximation C0 ≪Csat can be applied and (8) rewritten as:

(2)

Where E0 represents the ‘free’ exhalation rate that would exist on the material if no radon was present in the accumulation chamber, and ω represents the rate at which the radon exhalation will decrease as radon builds up within the chamber. Inside the accumulation chamber, there will be a balance between the radon sources, i.e. diffusion and convection from the soil, and removal processes such as radon decay and possible leakages in the system: � � �� � ∂CRnðtÞ S ∂CRn ðtÞ�� ðtÞC ðtÞj CRn t (3) þ v λ þ λ ¼ DB z Rn Rn l z¼0 V ∂t ∂z �z¼0

CðtÞ ¼ Csat ð1

e

λef t

Þ

(9)

which is a commonly used expression in the literature (Aldenkamp et al., 1992; Jonassen, 1983; Onishchenko et al., 2015; Seo et al., 2018). A fundamental parameter in equations (8) and (9) is the effective decay constant, λef , which dictates how much time the system will need to reach saturation. While the product λef t is low enough, radon grows lineally. Within this interval, the exponential term of equation (9) can be approximated by 1 λef t, obtaining:

2

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Radiation Measurements 133 (2020) 106284

Fig. 2. (a) Scheme of an operational chamber placed inside the reference exhalation box and (b) a hermetically closed reference exhalation box.

This parameter allows to establish the maximum acceptable devia­ tion between the two models. This is an alternate derivation of the �pez-Coto et al., 2009). For example, correction factor proposed by (Lo choosing a 10% variation as the maximum acceptable level (Elin =Eexp ¼ 0:9) equation (16) can be numerically solved, obtaining the following relation:

(10)

CðtÞjλef t≪1 � Csat λef t

Equations (2)–(4) represent three different models to fit the experi­ mental points obtained in an accumulation measurement: the general exponential fit (eq. (8)), the simplified exponential fit (eq. (9)) and the simplified linear fit (eq. (10)). Consequently, all the simplified fits per­ formed in this work considered the initial concentration to be exactly zero. In order to get the exhalation rate, it is necessary to apply the relation between the saturation concentration and the exhalation: E0 ¼ CSat λef

V S

λef tlin ¼ 0:21

where tlin is the time that an accumulation experiment, with λef as its effective decay constant, needs to show a 10% deviation between the exhalation predicted by the linear model with respect to the exponential model. More precisely, it is the maximum time where we can use the linear approximation to calculate the exhalation before it differs 10% from the real radon exhalation.

(11)

Equation (11) provides a way to obtain the radon exhalation rate after fitting the radon growth to one of the three different models provided.

2.3. Reference exhalation soil

2.2. Linearity time

With the objective of testing different accumulation models and accumulation chambers, two reference exhalation soils were designed. Seven bags with several tenths of kilograms of PG from the repository were used to create a homogenized PG layer of several centimeters in the bottom of two polypropylene rectangular boxes with 0.44 m2 of bottom area and a volume of 172 L. The polypropylene was chosen to minimize leakages while the dimensions allow measuring inside the boxes with accumulation chambers of different sizes (Fig. 2, a). Two covers were also built to hermetically close the reference boxes and force the radon to stay inside (Fig. 2, b). This setup allows to use the whole boxes as accumulation chambers, providing a way to measure reference exhala­ tion rates by forcing all the radon exhaled by the PG to stay inside the corresponding accumulation volume. To ensure that the exhalation rate is uniform it is essential to obtain a homogenous reference soil. For this reason, the first step was to ho­ mogenize separately every PG bag taken from the NORM repository. Then, 900 g were extracted from each bag and mixed inside one box, homogenizing it once again. This process was repeated for each box until 35 and 73 kg of PG were inside each one, respectively, thoroughly mixing their content every time new PG was added. After the addition of the phosphogypsum, the first reference box, RB1, had 148.1 L of accu­ mulation volume and the second one, RB2, 117.2 L. The PG layer reached 6.0 cm on RB1 and 13.0 cm on RB2. Once the reference exhalation boxes were finished, its exhalation was monitorized to verify the stability of the measurements. Initially, exhalation rates decreased over time on both boxes due to the drying of the emitting material. This behavior was expected due to the phospho­ gypsum water content. Routine measurements were performed until the exhalation values stabilized, which took approximately 1 month for RB1 and 3 for RB2. All measurements used in the present work were made

Considering that λef remains constant during the accumulation, the most precise procedure to obtain the radon exhalation rate requires experiments with a duration of several hours, until the curvature of the radon growth can be observed. On the other hand, the linear approxi­ mation only requires the first moments of the accumulation. However, the applicability of equation (10) must be stablished, because its sys­ tematic application may lead to erroneous estimations of the exhalation rates. To better approach these situations, a parameter can be defined as the ratio between the exhalation predicted by the simplified linear and exponential models: Elin Eexp

(12)

The value of this parameter can be deduced from the concentrations anticipated by the simplified models, which are: Cexp ðtÞ ¼ CSat ð1

e

Clin ðtÞ ¼ CSat λef t ¼

λef t

Þ¼

Eexp S ð1 λef V

e

λef t

Þ

Elin S t V

(13) (14)

Since the measured concentrations are the same for both cases: Eexp S ð1 λef V

e

λef t

Þ¼

Elin ð1 e λef t Þ ¼ λef t Eexp

Elin S t V

(17)

(15) (16)

3

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Radiation Measurements 133 (2020) 106284

Table 1 Dimensions of the operational chambers. In order: inner short side (a), inner long side (b), inner height not including insertion depth (h), inner covered area (S) and accumulation volume (V). Chamber Code

a (cm)

b (cm)

h (cm)

S (m2)

V (L)

V10 V14 V30

26.9 26.7 37.0

36.8 36.8 56.7

10.0 14.0 14.0

0.10 0.10 0.21

9.9 13.8 29.4

Table 3 p-value obtained by applying student’s t-test between results of each device for each reference box. A value closer to 1 represents more probability that there is no difference between devices. Ref. Exhalation Box 1 (RB1)

Table 2 Number of valid experiments (N) and average exhalation rates, obtained by fitting to equation (8), for each measurement device: Alphaguard 1 (AG1), Alphaguard 2 (AG2), Rad 7 (R7) and Radon Scout (RS). Uncertainties are calculated using 1σ. Ref. Exhalation Box 1 (RB1) Device

N

Exhalation (Bq m

AG1

11

AG2 R7 RS

Exhalation (Bq m

46:9 � 1:2

9

83:7 � 0:8

12

48:4 � 1:3

20

85:4 � 0:9

14

46:2 � 1:6

10

83 � 3

11

49:5 � 1:2

5

85 � 3

h

1

)

2

h

1

Device

AG1

AG2

R7

RS

AG1

AG2

R7

RS

AG1 AG2 R7 RS

1 0.41 0.73 0.16

0.41 1 0.29 0.59

0.73 0.29 1 0.12

0.16 0.59 0.12 1

1 0.17 0.84 0.63

0.17 1 0.50 0.95

0.84 0.50 1 0.62

0.63 0.95 0.62 1

The general exponential model, eq. (8), was considered the reference model to obtain the reference exhalation rate of each reference box. For every experimental fit, the R2 adjusted coefficient along with the χ2 goodness of fit test and its associated p-value were calculated. In general, an experiment was considered valid if its R2 coefficient was above 0.5 and its p-value was higher than 0.05. In Table 2 the valid results for RB1 and RB2 are shown. All the experiments performed on the reference exhalation boxes fulfilled the quality criteria imposed. In addition, the uncertainties of the estimated exhalation rates derived from the fittings were checked to be consistent with the observed variability. The results show that measurements on each reference box are similar and independent on the device used. However, there is an apparent difference for average exhalation rates on both reference boxes between AG1 and R7, and AG2 and RS. Looking at the uncertainties, these differences should not be considered statistically significant as they stay under 2 time the standard deviation. To evaluate the importance of the differences between devices, a student’s t-test was employed. From the results of this test, its p-value score was computed. In this case, the p-value represents the probability that there is no difference between the results of the two compared samples. It is assumed that there is no statistical difference between samples if the p-value is above 0.05. The results can be seen in Table 3. The results show that there is no statistically significant difference be­ tween the devices employed. To characterize the performance of the different operational accu­ mulation chambers, a reference exhalation rate was calculated doing the average over all the valid experiments performed on each box. As stated previously, those measurements were done routinely during the exper­ imentation period to ensure the constancy of the exhalation rates. Using 48 experiments done over RB1, its reference exhalation rate was E0 jRB1 ¼ 47:7 � 0:7 Bq m 2 h 1 . On the other hand, for the 44 valid experiments performed over RB2, the reference exhalation rate was E0 jRB2 ¼ 84:5 � 0:9 Bq m 2 h 1 . From now on, the ratio between the measured exhalation rate and the corresponding reference exhalation rate will be used. Several methods have been reported in the literature to calculate the theoretical radon exhalation using the characteristics of the emitting €rfer, 1994; Zhuo et al., 2006). The reference exha­ material (Porstendo lation boxes, RB1 and RB2, have a thin layer of material compared to the radon diffusion length, which can be considered to be 1 m in materials like PG when is dry enough, as this parameter might vary with the hu­ midity content (Keller et al., 2001; Rogers and Nielson, 1991). In these �pez-Coto et al. (2009) proposed the following equation to cases, Lo calculate the radon exhalation rate:

Ref. Exhalation Box 2 (RB2) N

2

Ref. Exhalation Box 2 (RB2)

)

after the stabilization was reached. In addition, the reference exhalation rate on both boxes were routinely tested every weekend to ensure its constancy. 2.4. Operational chambers and measurement devices Three smaller boxes, operational chambers from now on, were remodeled to be placed directly over the PG layers of the reference boxes (Fig. 2 a). These chambers were rectangular-shaped, with different volumes and made of polypropylene (Table 1). The operational cham­ bers were inserted 2.6 cm into the PG layer. To perform radon concentration measurements, four different radon devices were used: two Alphaguards (AG1 and AG2), a Rad 7 (R7) and a Radon Scout (RS). The Alphaguards and Rad 7 were configured to work in flow-through mode, performing measurements every 10 min. Radon Scout works by diffusion and was programmed to take one measurement every hour. Due to space limitations, the Radon Scout were only used in the reference boxes. Upon calculation of the exhalation rates, the measurement system volume, i.e. tubes, pumping and measurement devices, needed to be taken into account as well. Following the guidelines of ISO, 2012, they were designed trying not to exceed 10% of the effective accumulation volume. The measurement system, i.e. tubes and pump, used for each measurement device was always the same to reduce its influence on the measurements. The measurement system volume of both Alphaguards added 0.6 L to the effective volume while the Rad 7 added volume was 1.2 L. 3. Results and discussion 3.1. Estimation of the reference exhalation rate Almost 100 accumulation experiments were made on the reference exhalation boxes, RB1 and RB2. This experiments lasted between 3 and 14 days, enough time to ensure the development of the exponential curve. For RB1, the saturation concentration reached values between 8 and 13 kBq m 3 . RB2 showed results between 13 and 40 kBq m 3 . These ranges reflect differences in the effective decay constant, exhalation rate and accumulation volume. The average radon concentration in the laboratory, identified as the initial radon concentration, C0 , was found to be 32 � 12 Bq m 3 . This value confirms that the simplified exponen­ tial equation can be applied.

E0 ¼ ερλRn CRa z0

(18)

where ε is the emanation factor, ρ is the density, CRa is the radium concentration in the soil and z0 is the height of the layer of emitting material. On one hand, the density was obtained by dividing the PG mass employed for each reference box over its volume. This values were ρjRB1 ¼ 1080 � 10 kg m 3 and ρjRB2 ¼ 1011 � 3 kg m 3 . On the other hand, the radium content of each reference box was computed by gamma spectroscopy from four samples of each box, extracted from 4

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Radiation Measurements 133 (2020) 106284

another set of experiments on the field. The saturation concentration on the operational chambers showed values between 700 and 1000 Bq m 3 on RB1 and among 1200 and 1700 Bq m 3 for RB2. The laboratory radon concentration, 32 � 12 Bq m 3 , represents less than a 5% with respect to the saturation concentration, allowing the use of the simplified fits. The results for the general exponential fit (eq. (8)) and simplified exponential fit (eq. (9)), are shown in Fig. 3. As it happened in the reference boxes, the uncertainties of the exhalation rates obtained by the fittings were consistent with the observed variability. This set of experimental fits used all the available points in the accumulation curve. Since all the measurement devices had a sample period of 10 min and lasted a minimum of 18 h, around 100 points were used for each fit. For this reason, the linear fit was not tested as its main assumption would not be fulfilled. The general behavior of the operational chambers may be considered satisfactory, since most of the results stay within 25% of the reference value, with over half of them within 10%. The higher scattering in some of the chambers might be due to the lower saturation concentration values. This is supported by the results for chamber V30, which presents the closest results to reference independently of the measurement device used. It is noticeable that there is some consistent overestimation in V10 results when applied on RB2. A potential explanation would be a misplacement while inserting the accumulation chamber, which would imply that the effective volume is higher than it actually is, artificially increasing the exhalation result. There seems to be no significant

Table 4 Number of total experiments performed with each combination of measurement device, accumulation chamber and reference box. Device AG1 AG2 R7 TOTAL

Ref. Exhalation Box 1 (RB1)

Ref. Exhalation Box 2 (RB2)

RB1

V10

V14

V30

RB2

V10

V14

V30

11 12 14 37

6 5 10 21

8 8 11 27

5 5 5 21

9 20 10 39

– 5 5 10

– 16 5 21

– 6 7 13

different points of the PG layer, and averaging the results. The obtained values were CRa jRB1 ¼ 451 � 7 Bq kg 1 and CRa jRB2 ¼ 420� 8 Bq kg 1 . Finally, the emanation factor considered was ε ¼ 0:20� 0:04, which was �pez-Coto et al., 2014). After characterizing the PG the obtained from (Lo theoretical exhalation rates obtained were Eth jRB1 ¼ 44 � 9 Bq m 2 h 1 and Eth jRB2 ¼ 82 � 16 Bq m 2 h 1 . 3.2. Operational accumulation chambers Once a reference exhalation rate to compare with was obtained, the operational chambers presented in the previous section (V10, V14, V30), were evaluated. Each experiment lasted a minimum of 18 h. The total number of experiments performed with each device on every chamber is shown in Table 4. The device AG1 was not employed with the operational chambers on the reference box RB2 as it was being used in

Fig. 3. Relative exhalation rate applying the general exponential fit on RB1 (a) and RB2 (b), and applying the simplified exponential fit on RB1 (c) and RB2 (d), grouped by operational chamber. The number inside of each bar represents the number of valid experiments. The gray dashed line represents a 10% variation from unity. The error bars are calculated using 1σ. 5

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Radiation Measurements 133 (2020) 106284

Fig. 4. Relative exhalation rate applying the general exponential fit for RB1 (a) and RB2 (b), applying the simplified exponential fit on RB1 (c) and RB2 (d) and applying the simplified linear fit on RB1 (e) and RB2 (f), sorted by fit duration. The number inside of each bar represents the number of valid experiments. The gray dashed line represent a 10% variation from unity. The full length of some set of experiments is not shown to facilitate the comparison with other fits.

distinction between the general and simplified exponential fits.

computed do not distinguish between measurement devices. The results for the general exponential fit with the durations mentioned above can be seen in Fig. 4(a and b). It is clear that, for short durations, the general exponential fit is not reliable. For every opera­ tional chamber tested, this fit could not provide good results using the first 60, 90 nor 120 min of accumulation. This can be seen in the number of valid experiments, which is lower for the shorter accumulation pe­ riods. It is also noticeable that the fits on the reference boxes did not provide good results for all the accumulation periods except for the longest one. This was expected since for short accumulation times (λef t < e5) the curvature of the accumulation curve is not yet well

3.3. Comparison of fitting models with different measurement periods To monitor the radon exhalation rates in the PG repository, it would be necessary to perform measurements with durations shorter than 18 h. For this reason, we repeated the fits to the models using the first 60, 90, 120, 240, 300 and 600 min of accumulation, as shown in Fig. 4. This way, the reliability of the exponentials and linear fits with different accumulation periods was tested. Since there has been proved that there is not statistical difference between devices, the relative exhalation rates 6

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Radiation Measurements 133 (2020) 106284

Fig. 5. Effective decay constant for RB1 (left) and RB2 (right), sorted by accumulation chamber, applying the general exponential fit equation. The red dashed line represents the value for the radon decay constant (λRn ¼ 2:1⋅10 6 s 1 ). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

defined, causing spurious results in the fitting. Simplified exponential fit results are shown in Fig. 4(c and d). In general, this approach shows results similar to the general version. However, the number of valid experiments using short durations is higher for the simplified fit. V14 and V30 on RB1 presents good results for accumulation periods over 120 min, which also happens on RB2 for V30. As it happened before, measurements on RB1 and RB2 need about 600 min to get close to unity. Finally, the results for the simplified linear fit appear in Fig. 4(e and f). This case is significantly different from the exponential models. RB1 and RB2 results show good agreement to the reference, improving with the higher accumulation periods. However, the operational chambers results go further away from the reference as more time is used to perform the fit. This behaviour is expected as the linear approximation can only be used in the first moments of accumulation. In that sense, the linearity time seems to be less than 60 min for the operational chambers used since all operational chambers show underestimations of the exhalation rate even for the shorter accumulation periods. It is important to note that in all cases the number of valid experi­ ments is lower for the shorter durations. This is due to the lower number of experimental points available to perform the curve fit. Moreover, the dispersion of the results is slightly inferior on RB2 than on RB1. This could be related to the higher exhalation rate of the former. Larger exhalation rates ensure that radon reach higher concentrations, allowing the measurement devices to achieve more precise radon readings.

measurement system. The value of this parameter for the different chambers and devices can be seen in Fig. 5. There is a variation of two orders of magnitude between the reference boxes, RB1 and RB2, and the operational chambers, V10, V14 and V30. This situation implies that saturation will be reached slower in the reference chambers, allowing to perform the linear fit for a longer period. On the other hand, the expo­ nential curve will take longer to appear in the reference chambers, making it harder to find the adequate parameters for the exponential models without the use of extensive accumulation periods. It is worth noting that the effective decay constant seems to increase with the perimeter to effective volume ratio for the operational cham­ bers. V10 has slightly higher decay constant and ratio (13 cm L 1) than V14 (9 cm L 1) and both V10 and V14 have higher values than V30 (6 cm L 1). The higher difference between the reference and the operation chambers suggests that leaks in the latter chambers are significantly higher than in the former. The difference between measurement devices is clearer in the reference box than in the operational chambers, prob­ ably due to the lower leaks present in the reference box. As introduced in section 2.2, a parameter might be defined to mea­ sure how long the linear approximation can be considered valid. This parameter was defined as the “linearity time” and its value for each device and chamber for the two reference boxes is shown in Table 5. As expected, the linearity time shows a clear distinction between the reference boxes and the operational chambers. The former can hold the linear approximation for several hours while in the latter this approxi­ mation cannot be applied for periods longer than 20–40 min, for 10% deviation, and 40–90 min, for 20% deviation, depending on the opera­ tional chamber used. The higher linearity time, superior to 600 min, presented by the reference boxes allows using the linear fit on longer experiments. This

3.4. Effective decay constant and short-accumulation linear fits The performance of the different models with respect to fit duration may be explained using the effective decay constant of each

Table 5 Results for the linearity time in minutes assuming a deviation of 10% (applying λef tlin ¼ 0:21) and assuming a deviation of 20% (applying λef tlin ¼ 0:46), computed for every device, chamber and reference box. The effective time constant was obtained using the general exponential fit. Uncertainties are calculated using 1σ. Elin Eexp

Device

RB1

V10

V14

V30

RB2

V10

V14

V30

10%

AG1

710 � 90

20 � 2

25 � 3

40 � 3

520 � 13

–

–

–

AG2

1140 � 70

21 � 3

32 � 3

39 � 3

1280 � 80

18 � 2

27 � 2

37 � 3

R7

610 � 90

20 � 5

24 � 7

37 � 7

800 � 80

18 � 3

20 � 4

36 � 5

AG1

1260 � 180

43 � 5

55 � 7

87 � 7

1140 � 30

–

–

–

AG2

2480 � 150

46 � 7

70 � 7

87 � 7

2800 � 170

40 � 4

60 � 5

82 � 6

R7

1340 � 190

43 � 12

53 � 15

80 � 16

1760 � 180

38 � 7

44 � 9

80 � 12

20%

Ref. Exhalation Box 1 (RB1)

Ref. Exhalation Box 2 (RB2)

7

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Radiation Measurements 133 (2020) 106284

Fig. 6. Average relative exhalation rate applying the simplified linear fit for the different chambers excluding no points in RB1 (a) and RB2 (b), excluding the first 10 min in RB1 (c) and RB2 (d) and excluding the first 20 min in RB1 (e) and RB2 (f), sorted by fit duration. The gray dashed line represent a 10% variation from unity.

situation also suggests that there is an intermediate zone for reference boxes where both exponential and linear models can be applied suc­ cessfully. This does not happen for operational chambers due to the low linearity time. Looking at the results for operational chambers and Fig. 4, it is concluded that linear fits with shorter durations would perform better than exponential ones, e.g. 30 min fits with V30 operation chamber. Unfortunately, when fit durations shorter than 60 min were tried, they did not verify the quality criteria imposed on R2 and the p-value ob­ tained by the χ2 goodness of fit due to the lower number of points available and the higher uncertainty of the initial points of the accumulation.

As the concentration in the chamber builds up, more radon is present in the accumulation volume and the precision of the radon measurement increases, i.e. the concentration measured 30–40 min after the start of the accumulation is more precise than measurements performed on the first 10 min. Therefore, for measurements systems with linearity times under 60 min, it would be interesting to analyse the determination of the exhalation rate excluding measurements taken in the first minutes of the accumulation. To investigate this approach, Fig. 6 shows the results of applying the simplified linear model using the first 10, 20, 30, 40 and 50 min of accumulation after excluding some of the initial measurements. This graph show the results after removing no points (Fig. 6 a-b), after 8

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Radiation Measurements 133 (2020) 106284

removing the first 10 min (Fig. 6 c-d) and after removing the first 20 min (Fig. 6 e-f). The quality criteria were not applied on this set of fits as the lower number of points did not allow to do so. In general, averaged mean exhalation rates are close to the reference, within 20%. There is a consistent underestimation in almost all cases, especially for operational chambers on RB1. This is probably due to the lower effective decay constant of the operational chambers which imply that these chambers have lower linearity times. Hence, in these cases the linear fit will underestimate the exhalation rate. This effect is not observed in the reference boxes, where the exhalation rates stay within 10% when using enough points to perform the linear fit. As happened before, RB2 results show lower dispersion than those for RB1 for all measurements. This reflects again that higher exhalation rates increase the radon measurements precision. Additionally, experi­ ments with more measurement points available for the curve fit increase the precision of exhalation measurements. The precision is also increased by removing the first measurements due to the increase in the counting rates as the radon concentration in the chamber build up. This effect is positive but should be used with caution, as the linear fit might be more precise at a first glance, but the exhalation measurement could be underestimated if the linearity time is exceeded.

R). Special thanks to Antonio Padilla for his invaluable technical support and know-how, without which it would have been impossible to carry out this work. References Abo-Elmagd, M., 2014. Radon exhalation rates corrected for leakage and back diffusion – evaluation of radon chambers and radon sources with application to ceramic tile. J. Radiat. Res. Appl. Sci. 7, 390–398. https://doi.org/10.1016/j.jrras.2014.07.001. Aldenkamp, F.J., Kernfysisch, V.I., de Meijer, R.K., Kernfysisch, V.I., Put, L.W., Kernfysisch, V.I., Stoop, P., Kernfysisch, V.I., 1992. An assesment of in situ radon exhalation measurements and the relation between free and bound exhalation rates. Radiat. Protect. Dosim. 45, 449–453. Alharbi, S.H., Akber, R.A., 2014. Radon-222 activity flux measurement using activated charcoal canisters: revisiting the methodology. J. Environ. Radioact. 129, 94–99. https://doi.org/10.1016/j.jenvrad.2013.12.021. Arnold, D., Vargas, A., Vermeulen, A.T., Verheggen, B., Seibert, P., 2010. Analysis of radon origin by backward atmospheric transport modelling. Atmos. Environ. 44, 494–502. https://doi.org/10.1016/j.atmosenv.2009.11.003. � Grossi, C., Agueda, A., Vogel, F.R., Vargas, A., Zimnoch, M., Wach, P., Martín, J.E., L� opez-Coto, I., Bolívar, J.P., Morguí, J.A., Rod� o, X., 2016. Analysis of ground-based 222 Rn measurements over Spain: filling the gap in southwestern Europe. J. Geophys. Res. Atmos. 121, 11021–11037. https://doi.org/10.1002/ 2016JD025196. Grossi, C., Vargas, A., Arnold, D., 2008. C. Grossi et al. Quality study of electret radon flux monitors by an in situ intercomparison campaign in Spain. In: Sources and Measurements of Radon and Radon Progeny Applied to Climate and Air Quality Studies. International Atomic Energy Agency, Vienna, pp. 39–48. ISO, 2012. 11665-7:2012 - Measurement of Radioactivity in the Environment - Air: Radon-222 - Part 7: Accumulation Method for Estimating Surface Exhalation Rate. Jonassen, N., 1983. The determination of radon exhalation rates. Health Phys. 45, 369–376. https://doi.org/10.1097/00004032-198308000-00009. Keller, G., Hoffmann, B., Feigenspan, T., 2001. Radon permeability and radon exhalation of building materials. Sci. Total Environ. 272, 85–89. Kotrappa, P., 2015. Electret Ion Chambers for Characterizing Indoor, Outdoor, Geologic and Other Sourced of Radon. Nova Sciencie Publishers. L� opez-Coto, I., Mas, J.L., Bolívar, J.P., García-Tenorio, R., 2009. A short-time method to measure the radon potential of porous materials. Appl. Radiat. Isot. 67, 133–138. L� opez-Coto, I., Mas, J.L., Vargas, A., Bolívar, J.P., 2014. Studying radon exhalation rates variability from phosphogypsum piles in the SW of Spain. J. Hazard Mater. 280, 464–471. https://doi.org/10.1016/j.jhazmat.2014.07.025. Mayya, Y.S., 2004. Theory of radon exhalation into accumulators placed at the soilatmosphere interface. Radiat. Protect. Dosim. 111, 305–318. https://doi.org/ 10.1093/rpd/nch346. Mazur, J., Kozak, K., 2014. Complementary system for long term measurements of radon exhalation rate from soil. Rev. Sci. Instrum. 85, 1–7. https://doi.org/10.1063/ 1.4865156. Noverques, A., Verdú, G., Juste, B., Sancho, M., 2019. Experimental radon exhalation measurements: comparison of different techniques. Radiat. Phys. Chem. 155, 319–322. https://doi.org/10.1016/j.radphyschem.2018.08.002. Onishchenko, A., Zhukovsky, M., Bastrikov, V., 2015. Calibration system for measuring the radon flux density. Radiat. Protect. Dosim. 164, 582–586. https://doi.org/ 10.1093/rpd/ncv315. Porstend€ orfer, J., 1994. Properties and behaviour of radon and thoron and their decay products in the air. J. Aerosol Sci. 25, 219–263. https://doi.org/10.1016/0021-8502 (94)90077-9. Porstend€ orfer, J., Butterweck, G., Reineking, A., 1991. Diurnal variation of the concentrations of radon and its short-lived daughters in the atmosphere near the ground. Atmos. Environ. Part A, Gen. Top. https://doi.org/10.1016/0960-1686(91) 90069-J. Rogers, V.C., Nielson, K.K., 1991. Multiphase radon generation and transport in porous materials. Health Phys. 60, 807–815. Ryzhakova, N.K., 2012. Parameters of modeling radon transfer through soil and methods of their determination. J. Appl. Geophys. 80, 151–157. https://doi.org/10.1016/j. jappgeo.2012.01.010. Sahoo, B.K., Mayya, Y.S., 2010. Two dimensional diffusion theory of trace gas emission into soil chambers for flux measurements. Agric. For. Meteorol. 150, 1211–1224. https://doi.org/10.1016/j.agrformet.2010.05.009. Schery, S.D., Huang, S., 2004. An estimate of the global distribution of radon emissions from the ocean. Geophys. Res. Lett. 31, L19104. https://doi.org/10.1029/ 2004GL021051. Seo, J., Nirwono, M.M., Park, S.J., Lee, S.H., 2018. Standard measurement procedure for soil radon exhalation rate and its uncertainty. J. Radiat. Prot. Res. 43, 29–38. https://doi.org/10.14407/jrpr.2018.43.1.29. Tsapalov, A., Kovler, K., Miklyaev, P., 2016. Open charcoal chamber method for mass measurements of radon exhalation rate from soil surface. J. Environ. Radioact. 160, 28–35. https://doi.org/10.1016/j.jenvrad.2016.04.016. UNSCEAR, 2008. Sources, Effects and Risks of Ionizing Radiation, vol I. https://doi.org/ 10.2307/3577647. Radiation Research. Vargas, A., Arnold, D., Adame, J.A., Grossi, C., Hern� andez-Ceballos, M.A., Bolívar, J.P., 2015. Analysis of the vertical radon structure at the Spanish “El arenosillo” tower

4. Conclusions To test the applicability of the radon accumulation chamber tech­ nique, two reference exhalation soils were made with homogenized phosphogypsum from a nearby repository. Three operational chambers were sequentially placed on both reference soils and numerous experi­ ments were carried out with several radon measurement devices. Three radon growth models were used to extract the radon exhalation rate from the radon accumulation curves. The exhalation rate of the refer­ ence exhalation boxes was monitorized during the experimentation period to ensure its stability. This setup allowed to compare the measured exhalation rates with a reliable reference. As expected, exponential fits worked best when experiment dura­ tions were above 3 h, i.e. long enough to observe the curvature of the radon growth. The simplified exponential fit had better performance for shorter accumulation times. It is advisable to use the simplified expo­ nential fit as long as the initial concentration is low enough. Conversely, linear fit was applicable only within the first hour of accumulation. Even though its accuracy was improved by removing the first radon mea­ surements, hence reducing the counting errors, accumulation chambers with high effective decay constant systematically provided under­ estimated radon exhalation measurements. Therefore, the applicability of the linear fit cannot be assumed beforehand and should be assessed evaluating the effective decay constant first. Overall, we can learn from the present work that large effective decay constants reduce the concentration in the chamber and increase the counting errors to the point that the linear fit cannot be applied successfully. Leaks may vary significantly for different measurement systems, preventing the practitioner from accurately knowing them beforehand, and requiring preliminary measurements to verify the optimal approach for each case. In conclusion, it is critical to ensure the usage of accumulation chambers with low effective decay constants in order to increase the reproducibility of the accumulation chamber technique and allow the linear fit to be applied with enough reliability. Regardless, an initial assessment of the effective decay constant using the exponential models should be performed for each application. Acknowledgements This research was supported by the Spanish Ministry of Science, Innovation and Universities, by the project ‘‘Fluxes of radionuclides emitted by the PG piles located at Huelva; assessment of the dispersion, radiological risks and remediation proposals” (Ref.: CTM2015-686289

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station. J. Environ. Radioact. 139, 1–17. https://doi.org/10.1016/j. jenvrad.2014.09.018. Yang, J., Busen, H., Scherb, H., Hürkamp, K., Guo, Q., Tschiersch, J., 2019. Modeling of radon exhalation from soil influenced by environmental parameters. Sci. Total Environ. 656, 1304–1311. https://doi.org/10.1016/j.scitotenv.2018.11.464.

Zhuo, W., Iida, T., Furukawa, M., 2006. Modeling radon flux density from the earth’s surface. J. Nucl. Sci. Technol. 43, 479–482. https://doi.org/10.1080/ 18811248.2006.9711127.

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