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Radon-in-water secondary standard preparation
842
Radon-in-water secondary standard preparation D.J. Karangelos, N.P. Petropoulos, E.P. Hinis, S.E. Simopoulos Nuclear Engineering Section, Mechanical Engineering Department, National Technical University of Athens, 15 780 Athens, Greece
This work presents a method to generate radon-in-water solutions of known concentration that can easily be applied in a laboratory that has access to a radon-in-air calibration facility. The method has been proven to be accurate enough for the solution produced to be usable as a secondary standard, traceable to the calibration of the original radon source. This fact, as well as other attractive features such as low running cost and ease of use, makes the method appropriate for purposes such as quality control, intercalibration of instruments and laboratory intercomparison. 1. Introduction Although radon-in-water standards are necessary for the calibration and quality control of instruments and methods, the short half-life of radon limits their availability. For measurement techniques that do not require the sample to come into physical contact with the detector, such as liquid scintillation, this problem can be addressed by adding 226 Ra to the standard to support 222 Rn. However, when using techniques that require the sample to be introduced in the measuring device and subsequently discarded, such as the method based on gas-transfer membranes described later on, the use of 226 Ra can be a source of potential cross-contamination, as well an added complication in terms of disposal. The method presented in this work was developed to avoid the problems of crosscontamination and disposal while not requiring an additional, dedicated 226 Ra source. It is based on bubbling radon-rich air through water, thus avoiding the addition of 226 Ra, while still not requiring any special encapsulation of the radon source. 2. Description of the method 2.1. The method in principle Consider a closed air–water–radon system, where the volume of the air phase is VA , the volume of the water phase is VW and the total radon activity is R. The concentration of radon in RADIOACTIVITY IN THE ENVIRONMENT VOLUME 7 ISSN 1569-4860/DOI 10.1016/S1569-4860(04)07105-0
© 2005 Elsevier Ltd. All rights reserved.
Radon-in-water secondary standard preparation
843
Fig. 1. The Ostwald coefficient.
the air phase (CA ) and the water phase (CW ) when the process of radon diffusion between the two phases has reached equilibrium is determined by the following equations: CA VA + CW VW = R,
(1)
CW (2) = k, CA where k is the dimensionless Ostwald coefficient for radon in water. The Ostwald coefficient determines the solubility of a gas in a liquid and depends on the specific gas–liquid pair as well as the temperature. As can be seen in Fig. 1, where the Ostwald coefficient for radon, determined from experimental solubility data [1,2], has been plotted against temperature, the variability for ordinary room temperatures is rather limited (∼ 1%/◦ C). We will therefore assume in the following that temperature is controlled to a sufficient degree, so that the value of k can be considered constant in the course of an experiment. If the volumes VA , VW of the system as well as the total radon activity R are known, equations (1) and (2) can be easily solved for the radon concentrations CA and CW : CA =
1 R , VA 1 + kVW /VA
(3)
CW =
k R . VA 1 + kVW /VA
(4)
This is the basis of our method for the generation of radon-in-water standards: A known quantity of radon is introduced in a closed circuit, part of which is a vessel containing water. An air pump is used to drive the air through the water, thus establishing equilibrium. Equation (4) can then be used to calculate the concentration of radon in the water. In particular, if the air volume is much greater than the water volume, VA VW , equation (4) can be simplified to R CW = k , (5) VA where the water volume VW does not enter the calculation. 2.2. Experimental apparatus The apparatus consists of three separate chambers, connected in series in a closed circuit (Fig. 2):
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D.J. Karangelos et al.
Fig. 2. Experimental apparatus.
• Chamber A is a radon concentration calibration chamber, in which known amounts of radon can be generated by means of a radon-emanating 226 Ra source. This can be part of an independent radon-in-air calibration facility, as long as inlet and outlet valves are provided. • Chamber B contains the water, into which radon will be dissolved. The air inlet is led to a perforated plastic tube below water level (c), while the outlet is well above the water level. Valves are provided at both the inlet and outlet, which allow this chamber to be removed from the circuit and its water content taken for measurement. • Chamber C is connected between the outlet of chamber B and the inlet of chamber A as a safety vessel, to collect any water droplets that might escape. A gas-tight air pump (a) is used to pump air from chamber A through the water in chamber B, while several measuring instruments – a flow meter (b) and pressure gauge (d) in particular – are also connected. Furthermore, active radon instrumentation can be used to monitor the air in the circuit, either included in chamber A, if space permits it, or connected in parallel with the circuit. 2.3. Standard generation procedure The method proceeds as follows: 1. A known amount of 222 Rn is introduced in chamber A. The secondary radon-in-water standard produced will be traceable to the certification of the 226 Ra source used, which in this sense will be the primary standard. Alternatively, a reference instrument can be used to quantify the concentration of 222 Rn in chamber A. In the later case, the radon-in-water standard produced will be traceable to the original calibration of the reference monitor. 2. Chamber B is partially filled with distilled water and connected to the circuit as in Fig. 2. For the experiments described in this work 4 L of water per run were used. It should however be noted that – depending on the volumes of chambers A and C – accurate determination of the water volume might not be critical, as explained previously 3. All connecting valves are opened and the air pump is operated for a time sufficient for the system to attain equilibrium with respect to the distribution of 222 Rn. Two processes occur simultaneously during this step: air with different radon concentrations is mixed across
Radon-in-water secondary standard preparation
845
Fig. 3. Sub-sampling of the radon-in-water standard.
the circuit, leading to a homogeneous distribution of radon, while radon diffuses through the air–water interface, aided by the increased contact area created by bubbling. It was experimentally determined that, for the particular set-up used in the present work, 20 min of circulation at an airflow rate of 10 L min−1 are enough to guarantee equilibrium. 4. The connecting valves are closed and chamber B is removed from the circuit, while remaining closed to the atmosphere. Its water content can now be taken for measurement, either by tilting the chamber and drawing a sample of the water through the outlet valve (Fig. 3), or, if larger volumes are required, by opening the chamber lid, in accordance with the sampling protocol of the method to be used for measurement. 2.4. Uncertainty assessment According to equation (5), the uncertainty of the radon concentration in the water standard produced will be 2 2 δCW δk δR δV 2 (6) = + + . CW k R V The Ostwald coefficient has been calculated from experimental solubility data, with an uncertainty of about 2%, while the systematic uncertainty in the activity of the 226 Ra sources used for the present work is of the order of 4%. The total volume VA of the gas phases of the system is the sum of free volumes in all components of the circuit: VA = VCA + VCB + VCC + VCON where VCA , VCB , VCC are the free volumes of the three chambers and VCON is the free volume of all connecting tubing and associated instrumentation. In the system used for the present work, chamber A is a 1.9 m3 calibration chamber, whose volume has been determined with an uncertainty of about 2%. As the total volume of all connecting tubing is not greater than 5 L, while VCB = 6 L and VC = 4 L, it is reasonable to approximate V ∼ = VCA , within the uncertainty of 2%. Taking these parameters into account according to equation (6), the systematic uncertainty of the method as applied in the present work is seen to be equal to 5%.
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Table 1 Method validation results CW,0 (Bq L−1 )
CW (Bq L−1 )
3.1 3.2 4.7 6.6 8.3 13.8 16.9
3.4 ± 0.3 3.5 ± 0.5 4.6 ± 0.3 6.4 ± 0.4 8.5 ± 0.4 16.0 ± 1.1 16.4 ± 1.0
Fig. 4. Method validation results.
3. Validation of the method To validate the method, a set of water samples with radon concentrations ranging from 3 to 17 Bq L−1 were generated and measured using an ionisation chamber coupled to a bubbler. Nominal concentrations (CW,0 ), calculated according to equation (1), and measured values (CW ) for these samples are presented in Table 1. The intercept of the least-squares line for these data points, drawn in Fig. 4, is statistically insignificant, while the slope is not significantly different from unity. The RMS-deviation of measured values from the nominal concentrations is equal to 10%.
4. A calibration example As an example of the usefulness of the method, the quality control of the calibration of a radon-in-water measuring apparatus based on a gas-transfer membrane is presented. The apparatus under control consists of a special microporous membrane tube contained in an air-tight vessel, a magnetic stirrer and an active radon monitor based on a solid-state detector. The principle of operation of the apparatus is as follows: The membrane tube is submerged in the water sample, which is contained in the air-tight vessel and continuously stirred using the magnetic stirrer. Radon is allowed to diffuse through the membrane for a fixed time period and quantified by the active monitor. The radon quantity that diffuses through the membrane during the above fixed time period is proportional to the initial concentration in the water sample; therefore, a calibration factor f can be determined to calculate the initial concentration in the water sample CW from the concentration in the counting chamber of the instrument, CA . The manufacturer of the apparatus has determined a calibration factor f1 = 4 for 20 min of diffusion, while previous experiments at NES-NTUA, using a different methodology from that presented in this work and based on a theoretical calculation of the time evolution of the radon concentration, led to the value of f2 = 1.7 ± 0.1. A comparison of nominal values
Radon-in-water secondary standard preparation
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Table 2 Calibration control results CW,0 (Bq L−1 )
CA (kBq m−3 )
3.1 3.2 4.7 6.6 8.3 13.8 16.9
1.4 ± 0.1 1.3 ± 0.2 1.9 ± 0.2 2.8 ± 0.4 3.5 ± 0.1 6.7 ± 0.4 7.5 ± 0.3
CW,1 (Bq L−1 )
CW,2 (Bq L−1 )
5.6 ± 0.5 5.2 ± 0.6 7.6 ± 0.8 11.2 ± 1.6 26.0 ± 0.4 26.8 ± 1.4 30.0 ± 1.3
2.4 ± 0.2 2.2 ± 0.3 3.2 ± 0.3 4.8 ± 0.7 11.1 ± 0.2 11.4 ± 0.6 12.8 ± 0.5
Fig. 5. New calibration curve.
(CW,0 ) for a set of samples generated using the method presented in this work with instrument readings (CA ) and values calculated according to the calibration factors f1 and f2 mentioned above (CW,1 , CW,2 ) is shown in Table 2. It is obvious that neither f1 nor f2 is a valid calibration factor, and a new one needs to be determined. This discrepancy may be attributed to ageing and wear of the membrane over a period of years, which might have an effect on its properties with respect to the diffusion of radon. The instrument reading CA has been plotted against the nominal concentration CW,0 in Fig. 5, along with a least-squares line, which in fact is the new calibration curve. As can be seen, the radon concentration in the water sample is indeed reproducible from the amount that diffuses through the membrane (R2 = 0.99), for the range of concentrations tested. The calibration factor was estimated by the least-squares fit to be equal to f3 = 2.22 ± 0.05, which is significantly different from both the value given by the manufacturer (f1 = 4), and that previously estimated at NES-NTUA (f2 = 1.7). 5. Conclusions The method presented in this paper has been successfully applied to the calibration of radonin-water measuring instrumentation. It is easy to apply as well as inexpensive, and is therefore very useful for the periodic control of instruments and methods, as in the example presented in this work.
References [1] H.L. Clever (Ed.), Krypton, Xenon and Radon, IUPAC Solubility Data Series, vol. 2, Pergamon Press, Oxford, 1979. [2] D.R. Lide (Ed.), Handbook of Chemistry and Physics, 74th ed., CRC Press, Boca Raton, 1994.
Radon-in-water secondary standard preparation D.J. Karangelos, N.P. Petropoulos, E.P. Hinis, S.E. Simopoulos Nuclear Engineering Section, Mechanical Engineering Department, National Technical University of Athens, 15 780 Athens, Greece
This work presents a method to generate radon-in-water solutions of known concentration that can easily be applied in a laboratory that has access to a radon-in-air calibration facility. The method has been proven to be accurate enough for the solution produced to be usable as a secondary standard, traceable to the calibration of the original radon source. This fact, as well as other attractive features such as low running cost and ease of use, makes the method appropriate for purposes such as quality control, intercalibration of instruments and laboratory intercomparison. 1. Introduction Although radon-in-water standards are necessary for the calibration and quality control of instruments and methods, the short half-life of radon limits their availability. For measurement techniques that do not require the sample to come into physical contact with the detector, such as liquid scintillation, this problem can be addressed by adding 226 Ra to the standard to support 222 Rn. However, when using techniques that require the sample to be introduced in the measuring device and subsequently discarded, such as the method based on gas-transfer membranes described later on, the use of 226 Ra can be a source of potential cross-contamination, as well an added complication in terms of disposal. The method presented in this work was developed to avoid the problems of crosscontamination and disposal while not requiring an additional, dedicated 226 Ra source. It is based on bubbling radon-rich air through water, thus avoiding the addition of 226 Ra, while still not requiring any special encapsulation of the radon source. 2. Description of the method 2.1. The method in principle Consider a closed air–water–radon system, where the volume of the air phase is VA , the volume of the water phase is VW and the total radon activity is R. The concentration of radon in RADIOACTIVITY IN THE ENVIRONMENT VOLUME 7 ISSN 1569-4860/DOI 10.1016/S1569-4860(04)07105-0
© 2005 Elsevier Ltd. All rights reserved.
Radon-in-water secondary standard preparation
843
Fig. 1. The Ostwald coefficient.
the air phase (CA ) and the water phase (CW ) when the process of radon diffusion between the two phases has reached equilibrium is determined by the following equations: CA VA + CW VW = R,
(1)
CW (2) = k, CA where k is the dimensionless Ostwald coefficient for radon in water. The Ostwald coefficient determines the solubility of a gas in a liquid and depends on the specific gas–liquid pair as well as the temperature. As can be seen in Fig. 1, where the Ostwald coefficient for radon, determined from experimental solubility data [1,2], has been plotted against temperature, the variability for ordinary room temperatures is rather limited (∼ 1%/◦ C). We will therefore assume in the following that temperature is controlled to a sufficient degree, so that the value of k can be considered constant in the course of an experiment. If the volumes VA , VW of the system as well as the total radon activity R are known, equations (1) and (2) can be easily solved for the radon concentrations CA and CW : CA =
1 R , VA 1 + kVW /VA
(3)
CW =
k R . VA 1 + kVW /VA
(4)
This is the basis of our method for the generation of radon-in-water standards: A known quantity of radon is introduced in a closed circuit, part of which is a vessel containing water. An air pump is used to drive the air through the water, thus establishing equilibrium. Equation (4) can then be used to calculate the concentration of radon in the water. In particular, if the air volume is much greater than the water volume, VA VW , equation (4) can be simplified to R CW = k , (5) VA where the water volume VW does not enter the calculation. 2.2. Experimental apparatus The apparatus consists of three separate chambers, connected in series in a closed circuit (Fig. 2):
844
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Fig. 2. Experimental apparatus.
• Chamber A is a radon concentration calibration chamber, in which known amounts of radon can be generated by means of a radon-emanating 226 Ra source. This can be part of an independent radon-in-air calibration facility, as long as inlet and outlet valves are provided. • Chamber B contains the water, into which radon will be dissolved. The air inlet is led to a perforated plastic tube below water level (c), while the outlet is well above the water level. Valves are provided at both the inlet and outlet, which allow this chamber to be removed from the circuit and its water content taken for measurement. • Chamber C is connected between the outlet of chamber B and the inlet of chamber A as a safety vessel, to collect any water droplets that might escape. A gas-tight air pump (a) is used to pump air from chamber A through the water in chamber B, while several measuring instruments – a flow meter (b) and pressure gauge (d) in particular – are also connected. Furthermore, active radon instrumentation can be used to monitor the air in the circuit, either included in chamber A, if space permits it, or connected in parallel with the circuit. 2.3. Standard generation procedure The method proceeds as follows: 1. A known amount of 222 Rn is introduced in chamber A. The secondary radon-in-water standard produced will be traceable to the certification of the 226 Ra source used, which in this sense will be the primary standard. Alternatively, a reference instrument can be used to quantify the concentration of 222 Rn in chamber A. In the later case, the radon-in-water standard produced will be traceable to the original calibration of the reference monitor. 2. Chamber B is partially filled with distilled water and connected to the circuit as in Fig. 2. For the experiments described in this work 4 L of water per run were used. It should however be noted that – depending on the volumes of chambers A and C – accurate determination of the water volume might not be critical, as explained previously 3. All connecting valves are opened and the air pump is operated for a time sufficient for the system to attain equilibrium with respect to the distribution of 222 Rn. Two processes occur simultaneously during this step: air with different radon concentrations is mixed across
Radon-in-water secondary standard preparation
845
Fig. 3. Sub-sampling of the radon-in-water standard.
the circuit, leading to a homogeneous distribution of radon, while radon diffuses through the air–water interface, aided by the increased contact area created by bubbling. It was experimentally determined that, for the particular set-up used in the present work, 20 min of circulation at an airflow rate of 10 L min−1 are enough to guarantee equilibrium. 4. The connecting valves are closed and chamber B is removed from the circuit, while remaining closed to the atmosphere. Its water content can now be taken for measurement, either by tilting the chamber and drawing a sample of the water through the outlet valve (Fig. 3), or, if larger volumes are required, by opening the chamber lid, in accordance with the sampling protocol of the method to be used for measurement. 2.4. Uncertainty assessment According to equation (5), the uncertainty of the radon concentration in the water standard produced will be 2 2 δCW δk δR δV 2 (6) = + + . CW k R V The Ostwald coefficient has been calculated from experimental solubility data, with an uncertainty of about 2%, while the systematic uncertainty in the activity of the 226 Ra sources used for the present work is of the order of 4%. The total volume VA of the gas phases of the system is the sum of free volumes in all components of the circuit: VA = VCA + VCB + VCC + VCON where VCA , VCB , VCC are the free volumes of the three chambers and VCON is the free volume of all connecting tubing and associated instrumentation. In the system used for the present work, chamber A is a 1.9 m3 calibration chamber, whose volume has been determined with an uncertainty of about 2%. As the total volume of all connecting tubing is not greater than 5 L, while VCB = 6 L and VC = 4 L, it is reasonable to approximate V ∼ = VCA , within the uncertainty of 2%. Taking these parameters into account according to equation (6), the systematic uncertainty of the method as applied in the present work is seen to be equal to 5%.
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D.J. Karangelos et al.
Table 1 Method validation results CW,0 (Bq L−1 )
CW (Bq L−1 )
3.1 3.2 4.7 6.6 8.3 13.8 16.9
3.4 ± 0.3 3.5 ± 0.5 4.6 ± 0.3 6.4 ± 0.4 8.5 ± 0.4 16.0 ± 1.1 16.4 ± 1.0
Fig. 4. Method validation results.
3. Validation of the method To validate the method, a set of water samples with radon concentrations ranging from 3 to 17 Bq L−1 were generated and measured using an ionisation chamber coupled to a bubbler. Nominal concentrations (CW,0 ), calculated according to equation (1), and measured values (CW ) for these samples are presented in Table 1. The intercept of the least-squares line for these data points, drawn in Fig. 4, is statistically insignificant, while the slope is not significantly different from unity. The RMS-deviation of measured values from the nominal concentrations is equal to 10%.
4. A calibration example As an example of the usefulness of the method, the quality control of the calibration of a radon-in-water measuring apparatus based on a gas-transfer membrane is presented. The apparatus under control consists of a special microporous membrane tube contained in an air-tight vessel, a magnetic stirrer and an active radon monitor based on a solid-state detector. The principle of operation of the apparatus is as follows: The membrane tube is submerged in the water sample, which is contained in the air-tight vessel and continuously stirred using the magnetic stirrer. Radon is allowed to diffuse through the membrane for a fixed time period and quantified by the active monitor. The radon quantity that diffuses through the membrane during the above fixed time period is proportional to the initial concentration in the water sample; therefore, a calibration factor f can be determined to calculate the initial concentration in the water sample CW from the concentration in the counting chamber of the instrument, CA . The manufacturer of the apparatus has determined a calibration factor f1 = 4 for 20 min of diffusion, while previous experiments at NES-NTUA, using a different methodology from that presented in this work and based on a theoretical calculation of the time evolution of the radon concentration, led to the value of f2 = 1.7 ± 0.1. A comparison of nominal values
Radon-in-water secondary standard preparation
847
Table 2 Calibration control results CW,0 (Bq L−1 )
CA (kBq m−3 )
3.1 3.2 4.7 6.6 8.3 13.8 16.9
1.4 ± 0.1 1.3 ± 0.2 1.9 ± 0.2 2.8 ± 0.4 3.5 ± 0.1 6.7 ± 0.4 7.5 ± 0.3
CW,1 (Bq L−1 )
CW,2 (Bq L−1 )
5.6 ± 0.5 5.2 ± 0.6 7.6 ± 0.8 11.2 ± 1.6 26.0 ± 0.4 26.8 ± 1.4 30.0 ± 1.3
2.4 ± 0.2 2.2 ± 0.3 3.2 ± 0.3 4.8 ± 0.7 11.1 ± 0.2 11.4 ± 0.6 12.8 ± 0.5
Fig. 5. New calibration curve.
(CW,0 ) for a set of samples generated using the method presented in this work with instrument readings (CA ) and values calculated according to the calibration factors f1 and f2 mentioned above (CW,1 , CW,2 ) is shown in Table 2. It is obvious that neither f1 nor f2 is a valid calibration factor, and a new one needs to be determined. This discrepancy may be attributed to ageing and wear of the membrane over a period of years, which might have an effect on its properties with respect to the diffusion of radon. The instrument reading CA has been plotted against the nominal concentration CW,0 in Fig. 5, along with a least-squares line, which in fact is the new calibration curve. As can be seen, the radon concentration in the water sample is indeed reproducible from the amount that diffuses through the membrane (R2 = 0.99), for the range of concentrations tested. The calibration factor was estimated by the least-squares fit to be equal to f3 = 2.22 ± 0.05, which is significantly different from both the value given by the manufacturer (f1 = 4), and that previously estimated at NES-NTUA (f2 = 1.7). 5. Conclusions The method presented in this paper has been successfully applied to the calibration of radonin-water measuring instrumentation. It is easy to apply as well as inexpensive, and is therefore very useful for the periodic control of instruments and methods, as in the example presented in this work.
References [1] H.L. Clever (Ed.), Krypton, Xenon and Radon, IUPAC Solubility Data Series, vol. 2, Pergamon Press, Oxford, 1979. [2] D.R. Lide (Ed.), Handbook of Chemistry and Physics, 74th ed., CRC Press, Boca Raton, 1994.