2015 International Nuclear Atlantic Conference - INAC 2015 São Paulo, SP, Brazil, October 4-9, 2015 ASSOCIAÇÃO BRASILEIRA DE ENERGIA NUCLEAR - ABEN ISBN: 978-85-99141-06-9

MATHEMATICAL MODEL OF RADON ACTIVITY MEASUREMENTS

Sergei A. Paschuk1, Janine N. Corrêa1, Jaqueline Kappke1, Pedro Zambianchi1 and Valeriy Denyak2

1 Federal University of Technology - Paraná Av. Sete de Setembro, 3165 80230-901, Curitiba, PR [email protected], [email protected]

2 Pelé Pequeno Príncipe Research Institute, Av. Silva Jardim, 1632, Curitiba 80250-200, PR, Brazil [email protected]

ABSTRACT

Present work describes a mathematical model that quantifies the time dependent amount of 222Rn and 220Rn altogether and their activities within an ionization chamber as, for example, AlphaGUARD, which is used to measure activity concentration of Rn in soil gas. The differential equations take into account tree main processes, namely: the injection of Rn into the cavity of detector by the air pump including the effect of the traveling time Rn takes to reach the chamber; Rn release by the air exiting the chamber; and radioactive decay of Rn within the chamber. Developed code quantifies the activity of 222Rn and 220Rn isotopes separately. Following the standard methodology to measure Rn activity in soil gas, the air pump usually is turned off over a period of time in order to avoid the influx of Rn into the chamber. Since 220Rn has a short half-life time, approximately 56s, the model shows that after 7 minutes the activity concentration of this isotope is null. Consequently, the measured activity refers to 222Rn, only. Furthermore, the model also addresses the activity of 220Rn and 222Rn progeny, which being metals represent potential risk of ionization chamber contamination that could increase the background of further measurements. Some preliminary comparison of experimental data and theoretical calculations is presented. Obtained transient and steady-state solutions could be used for planning of Rn in soil gas measurements as well as for accuracy assessment of obtained results together with efficiency evaluation of chosen measurements procedure.

1. INTRODUCTION

It is well known that among three natural isotopes of radon, the isotope 222Rn, which is produced in the decay series of 238U and proceeds from the α-decay of 226Ra, is responsible for approximately half of the effective dose received by the population from natural radiation sources. The 222Rn is entering and mixing with the atmosphere of a dwelling being released from several sources, including its release and emanation from basement soil through breaks in the foundation, which is considered as a principle source.

In general, the entry of radon into the air of dwellings is affected by several physical parameters such as barometric pressure, ambient and outdoor temperature, differential pressure, wind speed, etc. Rather complete review of studies of physical, geological and meteorological factors that influence the indoor 222Rn concentrations and its progeny can be found in [1].

Despite the importance of radon activity in soil gas, safety limits and norms usually are not applied to this source of radon. This happens because soil gas radon has to be considered as only one from a number of sources, which efficiency is affected by different physical, geological, meteorological and evidently by construction parameters of planed or existed buildings, which gives a possibility to predict the radon activity in the air of dwelling. Such extremely complicated combination of conditions and parameters is making impossible to evaluate the radon concentration in the air of dwelling before it is built. More over, radon activity in soil gas can present significant variation even over relatively small distances, during the daytime and weather conditions. Nevertheless some countries of the European Union are discussing the necessity to establish the radon risk classification of foundation soils taking into account the soil radon activity together with soil and rocks permeability for gasses as it is described in [2, 3].

In the case of radon activity in the air of dwellings, there could be found rather big variety of norms and regulations as, for example, the documents of the US Environmental Protection Agency (EPA) [4] suggest practical intervention in residence where the concentration of radon reaches 148 Bq/m3, which coincide with conclusions of the World Health Organization report [5] that worldwide indoor average of radon remains below 148 Bq/m3 that is below 200 Bq/m3 recommended by UNSCEAR [6].

In the case of radon in soil risk evaluation, as it is suggested by [2, 3], the measurements of radon activity have to be performed following rather tight space grid of 10 meters, which has to cover the corresponding area of assumed construction. Such survey of radon in soils activity is generally performed using instant radon detector (RAD7, AlphaGUARD or similar) associated with gas probe, filter vessels and air pump. Following the recommendations of User Manual of such detectors for soil gas measurements procedure and practice protocols developed by CDTN as well as the results of Soil-Gas Radon Intercomparison Measurements frequently performed during last two decades at different countries of the world, such measurement consists usually of three main steps: 1) background appraisal, 2) measurements of total activity of 222Rn and 220Rn isotopes in soil gas streamflow of 1 L/min and 3) static activity measurements (with disconnected air pump) of soil gas accumulated within the cavity of instant radon detector with an objective to evaluate the contribution of short half-life isotope 220Rn in obtained data.

Present calculations were stimulated by evident problem concerning the contamination of instant radon detector as, for example, AlphaGUARD by radioactive progeny. Participating in radon in soil survey, one has to answer the following the questions that affect the interpretation of obtained results: how much the measurements of radon activity in soil gas of 100 – 200 kBq/m3 or even bigger can affect the results of consequent measurements?, how much time it is necessary to wait for reduction of radon progeny activity before to initiate the consequent measurements?, how many measurements of radon in soil gas activity it is possible to perform during one day of field measurements?, etc.

Usually such questions are answered on the basis of general knowledge of radon progeny isotopes and their half-life notwithstanding the measured instant activity of radon. But taking into account that mentioned above Regulation of Radon Risk Classification [2, 3] is considering the activity of 1 kBq/m3 as significant (which cannot be neglected), it appeared very important to perform any measurement with background below this value as well as to elaborate an adequate planning of radon in soil measurements considering that after two,

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three or four consequent measurements the detector would be unsuitable for further measurements for at least during few days.

2. MATHEMATICAL MODEL

Some sort of similar mathematical model was developed more then 35 years ago for calculations of radon and its progeny concentrations in ventilated spaces of buildings with low-level ventilation and air leakage rates [7]. In that work time-dependent solutions, which account for ventilation, were obtained for indoor radon and daughter concentrations for tightened buildings.

Our mathematical model of instant radon detector operation considered three main physical phenomena described using the system of linear differential equations. Physical processes that were included in the model are: a) injection of radon into the cavity of detector by the air flux due to the air pump operation including the effect of Rn transportation by connection hoses; b) after the measurement the gas is liberated into external atmosphere by extinguishing hose; and c) radioactive decay of radon isotopes and its progeny within detector cavity, which detection efficiency was considered of 100%.

Figure 1: Schematic diagram of mathematical model for radon in soil gas measurements.

As it could be seen in Figure 1, it was considered that initial radon concentration in soil is 222 220 C0,222 and C0,220 for Rn and Rn isotopes respectively. But considering the time of transportation of gas through the hose of length L by air flux q, it is injected into the cavity of detector with activity concentration of C1,222 or C1,220 for considered isotopes. Being mixed with the air of volume V0 already present in the cavity, both isotopes reach the detection level of Cx,222 or Cx,220 respectively and possibly undergoing the decay emitting alpha particles, which are detected with efficiency of 100%. Figure 1 is showing the exit of gases with concentration of Cx,220 or Cx,220 for both studied isotopes respectively. At the top of the Figure are shown used differential equation and its solution where y(t) is the function of detected radon activity (Cx,222 or Cx,220), t is time of measurements and λ is decay constant for considered isotope of radon.

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Among other physical parameters included in present analysis it has to be mentioned that air flux q produced by air pump was considered of 1 L/min, initial radon activity was considered equal 103 Bq/L, the sensitive volume of instant radon detector was considered equal 1 L, the length and diameter of connection hoses were considered of 2 m and 6 mm respectively.

All described calculations together with output plots were performed using Wolfram Mathematica® package. We didn’t intend to simplify the obtained solutions as well as there were not excluded from obtained functions any terms, which contribution could be considered as negligible. In other words, the obtained results are shown as is nevertheless some terms could be reduced from further consideration and analysis.

3. OBTAINED RESULTS AND DISCUSSION

Obtained results are shown in Figure 2. One can see that under considered parameters of radon in soil measurements, detected activity of 220Rn isotope reaches only 55% of efficiency even during active phase of 10 min when air pump is injected both isotopes in the cavity of detector. It can be seen also that stable level for both radon isotopes is reached after 5 min of active measurements when in case of 222Rn could be observed the efficiency of 100%, which means that detected activity became equal to real activity of this isotope in soil gas.

Figure 2: Calculated activity of 222Rn and 220Rn isotopes during the measurements of radon in soil gas measurements following suggested combination of active (10 min) and passive (7 min) phases.

After active phase of radon in soil measurements, it is recommended to turn off the air pump over a period of time in order to avoid the further injection of gas mixture from soil. Since 220Rn has a short half-life of approximately 56 s, it is expected that after 7 – 10 min of such passive measurements the detected activity of radon will refer to 222Rn only. Such approach is completely supported by the results of calculations. One can see in Figure 2 that after 7 min of passive phase the activity of 220Rn is practically extinguished.

As a further step of radon in soil gas activity modeling, it was calculated the activity of radon progeny, namely the isotopes of 216Po, 212Pb and 212Bi considering that their half-live is 0.15s, 10.6 h and 61 min respectively. In this case it was considered that produced during the decay of 220Rn isotope 216Po as being metal is totally maintained within the cavity of detector. Such assumption is more or less realistic in the case of AlphaGUARD detector since its operation

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(ionization chamber) is related to usage of high voltage potential that effectively stimulate the transport and deposition/accumulation of produced atoms of metals at the surface of electrodes, which could provoke the undesirable radioactive contamination of instant radon detector.

As an example, the equations (1) and (2) are showing the activity functions for 216Po obtained for the active and passive phases of the measurements:

(1)

(2)

220 216 Where λ1 and λ2 are decay constants for Rn and Po isotopes respectively.

Obtained results for mentioned above three isotopes are shown in Figures 3 – 5. One can see that the activity of 216Po reaches secular equilibrium after first few seconds of described measurements protocol and during the rest of time perfectly reproduce the activity of 220Rn, which means that emitted at this stage alpha particles could double the evaluation of 220Rn activity in the air if no special measures were taken.

Figure 3: Calculated activity of 216Po isotope during the measurements of radon in soil gas measurements following suggested combination of active (10 min) and passive (7 min) phases.

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Obtained results for 212Pb presents very long side effect of detector contamination of 1 day approximately, which doesn’t represent any possible mislead of alpha activity measurements since this isotope is undergoing beta decay. Anyway, its presence within the sensitive volume of instant radon detector generates 212Bi isotope, which undergoing alpha decay (66%) characterized by half-life of 61 min (212Bi  208Tl). After few first hours produced 208Tl isotope reaches the secular equilibrium and reproduce the activity of 212Pb. Other possible channel of 212Bi beta decay (33%) results in production of 212Po, which undergoing alpha decay with extremely short half-life of 0.3 μs, immediately reaches secular equilibrium and perfectly reproduce the activity of 212Bi and consequently of 212Pb.

Figure 4: Calculated activity of 212Pb isotope during the measurements of radon in soil gas measurements following suggested combination of active (10 min) and passive (7 min) phases.

Figure 5: Calculated activity of 212Bi isotope during the measurements of radon in soil gas measurements following suggested combination of active (10 min) and passive (7 min) phases.

In the case of 222Rn progeny and its activity it has to be evaluated the activity of 218Po, 214Pb and 210Pb considering that the activity of the last isotope represents some sort of permanent detector contamination since its half-life is 22 years approximately. Such analysis and calculations are actually in progress and we expect to get the results within next few months.

3. CONCLUSIONS

Performed numerical calculations of 220Rn isotope activity in soil gas unexpectedly presented rather low efficiency of its detection of 55% using suggested measurements protocol and taking into account the sensitive volume of instant radon detector of 1 L. Obtained transient

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and steady-state solutions of differential equations for activity measurements of radon isotopes in soil gas and its progeny using instant detector could be used for planning of radon survey measurements as well as for accuracy assessment of obtained results together with efficiency evaluation of chosen measurements procedure.

ACKNOWLEDGMENTS

The authors are very thankful to CNPq and CNEN for financial support for this work as well as to colleagues from the Center of Nuclear Technology Development (CDTN/CNEN) for permanent positive discussions and assistance in the calculations.

REFERENCES

1. M. Eisenbud, T. F. Gesell, Environmental Radioactivity From Natural, Industrial and Military Sources, Academic Press, California (1997). 2. “Radon Risk Classification,” http://www.radon-vos.cz (2009) 3. “The New Method for Assessing the Radon Risk of Building Sites,” http://www.radon- vos.cz/pdf/metodika.pdf (2000). 4. EPA - Environmental protection Agency, http://www.epa.gov/radon/pubs/ (2011). 5. WHO - World Health Organization, Handbook on Indoor Radon: A Public Health Perspective, WHO press, Switzerland (2009). 6. UNSCEAR - United Nations Scientific Committee on the Effects of Atomic Radiation, "Sources and Effects of Ionizing Radiation", annex I. UNSCEAR Reported to the United Nations General Assembly, (2000). 7. T. Kusuda, S. Silberstein & P. E. McNall Jr. “Concentrations in Ventilated Spaces”, Journal of the Air Pollution Control Association, 30, pp.1201-1207 (1980).

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