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Mathematical Model of Radon Activity Measurements

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Mathematical Model of Radon Activity Measurements 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, INAC 2015, São Paulo, SP, Brazil. 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. INAC 2015, São Paulo, SP, Brazil. 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.
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