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Modelling radon progeny concentration variations in thermal spas
Science of the Total Environment 373 (2007) 82 – 93 www.elsevier.com/locate/scitotenv
Modelling radon progeny concentration variations in thermal spas Dimitrios Nikolopoulos a,⁎, Efstratios Vogiannis b,⁎ a
Laboratory of Ionising Radiations, Department of Medical Instruments Technology, Technological Educational Institution of Athens, Agiou Spyridonos, Egaleo, 122 10, Athens, Greece b Waste Management Laboratory, School of Environment, Department of Environment, University of the Aegean, University Hill, 81100 Mytilene, Greece Received 26 June 2006; received in revised form 5 November 2006; accepted 15 November 2006 Available online 22 December 2006
Abstract Radon and its short-lived progenies (218Po, 214Pb, 214Bi and 214Po) are well known radioactive indoor pollutants identified as the major radiation burden component of the thermal spa users. Monitoring of short-lived progeny concentration is of great importance for short-term dose estimations both for bathers and working personnel. A prediction model of the short-lived progeny concentration variations was developed and applied on published data of the thermal spas of Lesvos Island. The physical procedures involved were modeled in a set of differential equations describing radon progeny concentration variations on the basis of radon measurements. Published daughter data were fitted on model predictions adjusting non-measured parameters, e.g. attachment and deposition rate constants for attached and unattached progenies. Attachment rate constants were estimated between 50 and 200 h− 1 while the deposition rate constants between 0.25 and 5 h− 1 for attached progenies and 0.5 and 170 h− 1 for the unattached ones. In addition, unattached 218Po, 214Pb and 214Bi progenies were found to be shifted forward in respect to radon approximately 0.001 h, 0.05 h and 0.40 h respectively, while attached 218Po, 214Pb and 214Bi progenies 0.05 h, 0.45 h and 0.65 h respectively. © 2006 Elsevier B.V. All rights reserved. Keywords: Radon; Daughter; Model; Spas PAEC
1. Introduction Radon is natural gas generated from the 226 Ra adecay (half-life 1600 years). It is a noble gas with 3.82 days half-life and high water solubility. In most cases, the major component of radon entrance in building structures is the underground soil followed by the exhalation from the building materials and the ⁎ Corresponding authors. Nikolopoulos is to be contacted at Tel.: +30 10 5385 375 (work), +30 10 6977208318 (Cellular) fax: +30 10 5910 975 (work). Vogiannis, Tel.: +30 22510 36214 (work), +30 10 6977072031 (Cellular) fax: +30 22510 26625 (work). E-mail addresses: [email protected] (D. Nikolopoulos), [email protected] (E. Vogiannis). 0048-9697/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.scitotenv.2006.11.017
emanation due to water and natural gas use. However, elevated radon concentrations in building structures due to entering water have been reported (Bernhardt and Hess, 1996). The radon concentrations in the entering water, the volume and the way of water usage, separated or in combination, could result in large amounts of radon in indoor air. It could be building structures, e.g. water stations and contextual workplaces, where the water usage is the dominant source of elevated indoor radon. Thermal spas have been identified as such places (Lettner et al., 1996; Song et al., 2005; Radolic et al., 2005). Moreover, acute radon and daughter peaks during bath filling have also been observed (Vogiannis et al., 2004a,b,c; Geranios et al., 2004), thus yielding to high radiation doses to workers and bathers.
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In this consensus and on the basis of previous studies (Vogiannis et al., 2004a,b,c) regarding concentration peak appearances in the thermal spas of Lesvos Island under controlled experiments, this paper aimed to model the behaviour of short-lived radon progeny in the indoor atmosphere of thermal spas, in an effort to describe the mechanism that allows the appearance of concentration peaks during filling and bath using. Such modeling could help in the quantification of physical parameters not easily measured and provide a guide for predicting concentrations on the basis of the determined parameters. The selection of the thermal spas of Lesvos Island was based on the geological background of Lesvos Island and mainly on the fact that these spas have been identified as areas presenting intense variations of radon and progeny concentrations and PAEC, thus imposing additional short-term health impact both to bathers and working personnel (Vogiannis et al., 2004a,b,c). 2. Materials and methods 2.1. Physical behaviour As a first step, a building structure of a thermal spa is considered comprising a treatment room (TR) with a bathtub of some m3 and a water supply system utilized both for thermal and non-thermal water filling of the bathtub. The TR is considered to be ventilated via window and door openings. The TR is considered under working conditions i.e. bath filling from personnel and usage from bathers. Radon entrance in the TR may be due to the underground soil, building materials and outdoor air, however, the main source is the supply of thermal water (Vogiannis et al., 2004a,b). After entrance, radon either resolves or decays to neutral or, at most, positively charged progeny, which in turn may neutralize. Positive or neutral progeny append to existing atmospheric trace gases and water vapour, forming clusters (Porstendörfer et al., 2000, 2005) in dynamic exchange between
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positive and neutral form. The clusters may attach to aerosol particles and in either form, airborne attached or airborne unattached–clustered, may deposit on surfaces (Fig. 1). Depending on atmospheric conditions, exchanges of short-lived progeny between the various forms may occur (Porstendörfer, 2001). However, in most circumstances only exchange from recoil between airborne attached and surface deposited 218 Po nuclides is considered (Nazaroff and Nero, 1988; Porstendörfer, 2001). Airborne attached and unattached short-lived progeny in a TR distribute in terms of size (often expressed by the particle Arithmetic Mean Diameter-AMD) and activity. Their indoor distribution depends on particle sources, ventilation and other parameters (El-Hussein and Ahmed, 1995; Paul and Keyser, 1996; El-Hussein et al., 1998; Kertesz et al., 1999; Rumburg et al., 2001; Ristimaki et al., 2002) and is, in combination, described by the activity size distribution. This size distribution consists of three lognormal distributions (modes) each one contributing differently to the total (Datye et al., 1997; El-Hussein et al., 1998; Porstendörfer, 2001; Jung et al., 2002; Voutilainen and Kaipio, 2002). According to Porstendörfer (2001), the three modes are the nucleation mode (AMD 30–40 nm), the accumulation mode (AMD 250–450 nm) and the coarse mode (AMD 2000– 6000 nm). Thermal spa indoor environments, however, are characterised by low concentration of coarse mode particles due to lack of such particle sources and because any existing coarse particles are drifted out by water vapour molecules (wash-out effect) and deposit on room surfaces or bathtub water (Fitzgerald et al., 1997). Hence, the indoor environments of thermal spas may be considered to consist, under working conditions, of aerosol particles mainly in the nucleation and accumulation mode. These modes are traditionally characterised (e.g. Nazaroff and Nero, 1988) as airborne-unattached (AMD < 50 nm) and airborne-attached daughter particles (AMD > 50 nm). In addition to these, another mode is considered; the surface deposited progenies (either in
Fig. 1. Physical behaviour of radon progeny in indoor environments.
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Fig. 2. Multi-compartmental diagram for radon and progeny in indoor environments of thermal spas. The symbols employed are described in Table 1.
attached or unattached form). In this traditional three mode manner the radon progenies are treated within this manuscript. 2.2. Model For modelling purposes an open multi-compartment system with reversible progeny flux is considered as shown in Fig. 2. The system's compartments represent Table 1 Parameters employed in system equations ((1.1)–(1.9)) Symbol Units λ0 C0 Á0 λi Cui Cai Csi Aui Aai Asi λv λa,i pl λad,i λud,i
Meaning
h− 1 m− 3 Bq m− 3 h− 1 m− 3 m− 3 m− 3
Decay constants (0.00755) Concentration of 222Rn Activity concentration of 222Rn Decay constants (λ1 = 13.37, λ2 = 1.552, λ3 = 2.111) Concentration of unattached progeny Concentration of attached progeny Surface (volume equivalent) concentration of deposited progeny Bq m− 3 Activity concentration of unattached progeny Bq m− 3 Activity concentration of attached progeny Bq m− 3 Surface (volume equivalent) activity concentration of deposited progeny h− 1 Ventilation rate h− 1 Attachment rate constant of progeny Unitless Recoil fraction of 218Po h− 1 Deposition rate constant of attached progeny h− 1 Deposition rate constant of unattached progeny
Index i equals 1,2,3 for 218Po, 214Pb and 214Bi respectively.
the various potential (traditional three mode) states of radon progeny in indoor environments of thermal spas under working conditions. 214Po is not included in Fig. 2 because it follows the state of 214Bi due to its short decay time (168 μs). All daughter nuclides terminate by decay to surface deposited 210 Pb. This is taken as the final compartment because 210 Pb is considered of no short-term health impact due to its long half-life (22.3 years). All progenies may be removed from indoor air by ventilation. Assuming that the variation of radon concentration (C0) with time is known, modelling of the behaviour of decay products may be achieved through the multicompartmental system ((1.1)–(1.9)) of linear differential equations, describing the variations of radon and radon progeny within a certain time interval dt (Fig. 2). The symbols employed together with their units are described in detail in Table 1. d u C1 ¼ k0 C0 k1 þ kv þ ka;1 þ kud;1 C1u ð1:1Þ dt d a C1 ¼ ka;1 C1u k1 þ kv þ ka;1 þ kad;1 C1a ð1:2Þ dt d s C ¼ kud;1 C1u þ kad;1 C1a þ k1 C1s ð1:3Þ dt 1 d u C2 ¼ k1 C1u þ p1 k1 C1a k2 þ kv þ ka;2 þ kud;2 C2u dt ð1:4Þ
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d a C ¼ ka;2 C2u þ ð1 p1 Þk1 C1a dt 2 k2 þ kv þ ka;2 þ kad;2 C2a d dt d dt d dt d dt
C2s ¼ k1 C1s þ kud;2 C2u þ kad;2 C2a k2 C2s C3u ¼ k2 C2u k3 þ kv þ ka;3 þ kud;3 C3u C3a ¼ k2 C2a þ ka;3 C3u k3 þ kv þ kad;3 C3a C3s ¼ k2 C2s þ kud;3 C3u þ kad;3 C3a k3 C3s
ð1:5Þ ð1:6Þ ð1:7Þ ð1:8Þ ð1:9Þ
In all equations the positive terms represent input from other compartments and the negative terms output to other compartments or atmosphere, which is considered to be only through ventilation (terms proportional to λv). The term λ0C0 represents the net input of the first compartment (218 Pou) via radon decay. The terms λiCix, x λd,i Cix , λa,iCix (i = 1,2,3; x = a,u) represent compartmental loss or input of radon progeny through decay, deposition and attachment to ambient aerosol respectively. In Eqs. (1.1)–(1.9) the activity size distribution is considered to be three mode, i.e. airborne-attached, airborne-unattached and surface-deposited. Moreover, a u the parameters λv, λa,i, λd,i and λd,i are considered to remain constant during dt. Attachment to ambient aerosols and deposition to surfaces is taken into account for all short-lived radon progeny and recoil only for 218 Po nuclides. System equations ((1.1)–(1.9)) represent a linear approximation of the involved phenomena in the assumed typical TR, accounting only for the first order derivatives and the proportional terms of the daughter concentrations. This approximation is applicable in temporal radon varying phenomena in thermal spas which do not exhibit very intense (second and higher order) temporal changes induced by external influences (e.g. human, ambient air acute activity). Eqs. (1.1)–(1.9) can be transformed to account for the activity concentration (Bq m− 3) changes which could be measured by employment of proper active measuring methodology. Conversion is achieved by substituting λi− 1Aix for each Cix (i = 1,2,3; x = a,u) and λ0− 1A0 for C0. By this substitution, system (2) may be written as: d u A1 ¼ k1 A0 k1 þ kv þ ka;1 þ kud;1 Au1 ð2:1Þ dt d a A1 ¼ ka;1 Au1 k1 þ kv þ ka;1 þ kad;1 Aa1 ð2:2Þ dt d s A ¼ kud;1 Au1 þ kad;1 Aa1 þ k1 As1 ð2:3Þ dt 1
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d u A2 ¼ k2 Au1 þ p1 k2 Aa1 k2 þ kv þ ka;2 þ kud;2 Au2 dt ð2:4Þ d a A ¼ ka;2 Au2 þ ð1 p1 Þk2 Aa1 dt 2 k2 þ kv þ ka;2 þ kad;2 Aa2 ð2:5Þ d dt d dt d dt d dt
As2 ¼ k2 As1 þ kud;2 Au2 þ kad;2 Aa2 k2 As2 Au3 ¼ k3 Au2 k3 þ kv þ ka;3 þ kud;3 Au3 Aa3 ¼ k3 Aa2 þ ka;3 Au3 k3 þ kv þ kad;3 Aa3 As3 ¼ k3 As2 þ kud;3 Au3 þ kad;3 Aa3 k3 As3
ð2:6Þ ð2:7Þ ð2:8Þ ð2:9Þ
Model equations ((2.1)–(2.9)) may provide the concentrations of all radon progeny on the basis of known radon activity concentration (A0) and model a u parameters λv, λa,i, λd,i and λd,i . As in Eqs. (1.1)–(1.9), there is a linear (first order) relation between time series activity concentrations and temporal rates of change, a u assuming model parameters λv, λa,i, λd,i and λd,i constant. Through measuring, radon activity concentration data may be modelled analytically, i.e. explicit mathematical equations, and hence, all daughter concentrations can be predicted either analytically, by solving system (2), or numerically. On the other hand, Eqs. (2.1)–(2.9) may be utilized a for the determination of model parameters λa,i, λd,i and u λd,i (considering these constant during measurement) assuming that the ventilation rate λv and the activity concentrations of radon and radon progeny A0, Aia and Aiu are experimentally determined, i.e. analytically expressed. In this manner, however, there is a nonlinear relation between time series concentrations and a u model parameters λa,i, λd,i and λd,i . This consideration could be the preceding one, at least in cases where the a u experimental determination of λa,i, λd,i and λd,i is not easily achievable. 2.3. Comparison to experimental data Model validity was checked in terms of comparison of model predictions with experimental data obtained from previous studies (Vogiannis et al., 2004a,b,c) in the lateral described model consideration, i.e. predicta u ing model parameters λa,i, λd,i and λd,i . The experimental data comprised time series radon and radon daughter (attached and unattached) activity concentration measurements collected through controlled experiments in the thermal spas of Lesvos Island. The
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measurements were derived with Alpha Guard PRO of Genitron Ltd (10 min radon time series) and EQF 3023 of Sarad Instruments, GmbH (2 h radon, attached and unattached progeny time series). The methodology of the experiments is described in detail in the above references. In general, it included TR ambient air atmosphere variations induced by controlled thermal water bath filling with simultaneous time series radon and radon progeny measurements together with ventilation rate estimation. For brevity, only results of model comparison to selected data of radon and daughter peaks of Eftalou and Thermi baths are presented. For comparison, model equations ((1.1)–(1.9)) were described in a Pentium (R)M PC using Microsoft FORTRAN specially developed codes employing iterative solving procedures (Press et al., 1990). At first, the published measured data were fitted to the minimum χ2 nonlinear curve functions by application of the Levenberg–Marquardt method (Press et al., 1990) and were used as inputs (A0, Aia, Aiu) of the model. The radon concentration curve functions from Alpha Guard were used as initial time series values (A0) for the prediction of the values of the input daughter activity concentration functions (estimated Aiu and Aia) according to model equations ((1.1)–(1.9)) by employing numerical equation solving. After solving, the predicted model daughter concentration values (predicted Aiu and Aia) were fitted to the corresponding values of the input daughter concentration functions (estimated Aiu and Aia) by application of the Levenberg–Marquardt method (Press et al., 1990). According to the method, the model a u parameters λa,i, λd,i and λd,i were allowed to vary until the difference between predicted and input values yielded to minimum χ2 for each daughter function. Goodness of fit was checked by means of application of the Wilcoxon signed ranks test (Mendenhall and Sincich, 1994) between predicted and estimated values of daughter concentrations (Aiu and Aia ) with critical alpha value of 0.10 for being a Levenberg–Marquardt fit acceptable. The adapted ventilation rate values (λv) in the model were constant and taken equal to those measured according to the available database (Vogiannis et al., 2004c). 3. Results and discussion Figs. 3 and 4 present characteristic cases of model predictions for the TRs of Eftalou and Thermi thermal spas together with measurements reported by Vogiannis et al. (2004a,b). The model seems to predict in a statistical manner the published results with few
outliers. Interesting is the fact that the predicted values of daughter concentrations (Aiu and Aia) present the peaks which had been attributed to the bath filling procedure (Vogiannis et al., 2004a,b). Fig. 5 present for the spas of Eftalou and Thermi model predictions and measurements of Potential Alpha Energy Concentration (PAEC), which is a measure of the maximum alpha energy that can be delivered to the bather's lungs during treatment. Agreement between predicted and measured data is achieved. PAEC peaks are detected implying peaks in radiation dose delivered to bathers and working personnel (Vogiannis et al., 2004a,b), thus providing physical and theoretical interpretations leading to the dose estimation at thermal spas. a u The estimated model parameters λa,i, λd,i and λd,i are summarized in Table 2. For reasons of uncertainty analysis, Table 2 also presents ranges of the abovementioned model parameters for varying ventilation rate values. These ranges were estimated by performing 30 iterative solutions of the model equations ((2.1)–(2.9)), by allowing the ventilation rate values (λv) to vary in ascending order from − 10% to +10% (range arbitrarily selected) in respect to the measured values (Vogiannis et al., 2004c). The model parameters were determined according to methods described earlier in text (paragraph 2.3) considering time series data of progeny concentrations and PAEC unchanged. Ventilation rate a u changes affect λa,i, λd,i and λd,i values in a non-linear manner. However, a change of ±10% in ventilation rate imposes lower relative deviation in the range of the a above model parameters (e.g. from 0% for λd,1 to 6% for λa,2). To our knowledge, no experimental data on the values of such parameters in thermal spas exist. Comparisons can only be performed in reference to published attachment and deposition rate constants (assumed equal for all progenies) estimated for dwellings or through controlled chamber environments (see e.g. Nazaroff and Nero, 1988). According to Nazaroff a and Nero (1988) typical range values for λa,i, λd,i and u λd,i for dwelling environments are 5–500, 0.1–0.4 and 10–40 h− 1 respectively. The λa,1 and λa,2 values both for Eftalou and Thermi baths lay in the above range. In addition, by interpretation of reported data by Datye et al. (1997) on dwelling baths, an attachment rate constant of approximately 50–100 h − 1 could be estimated assuming a diffusion coefficient (D) of approximately 0.02–0.04 cm2 s− 1 which is valid for clustering of progeny with 200 vapour molecules (Datye et al., 1997; Nazaroff and Nero, 1988). On the other hand, the estimated values and the corresponding ranges
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Fig. 3. Predicted and measured radon daughter activity concentration in Eftalou thermal baths: (a) 218Po, (b) 214Pb, (c) 214Bi. The measured data points are taken from Vogiannis et al. (2004a). a u for the parameters λd,i and λd,i are well above this range. This could be explained on the basis of the wash-out effect reported by Fitzgerald et al. (1997); due to the high humidity in the thermal baths during bath filling, more progenies are forced to deposit on surfaces or a u bathtub, causing increased λd,i and λd,i values. Worth to notice is the fact that the attachment and deposition of the 214 Bi nuclides is estimated to be significantly lower
when compared to that of 218Po and 214Pb. This could be attributed to an increased surface (volume equivalent) activity concentration of the 214 Bi nuclides caused mainly by the decay of surface deposited 218Po and 214 Pb activity. Since surface deposition includes also the one on the water surface, an increased wash-out effect of the 218Po and 214 Pb nuclides could result in increased surface (volume equivalent) activity concentration of
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Fig. 4. Predicted and measured radon daughter activity concentration in Thermi thermal baths: (a) 218Po, (b) 214Pb, (c) 214Bi. The measured data points are taken from Vogiannis et al. (2004a).
the 214Bi nuclides and, probably, thus, lower potentiality of deposition and attachment of airborne 214Bi nuclides, i.e. lower rate constant values. Fig. 6 presents the surface (volume equivalent) activity concentration of all progeny. High activity concentration values are detected implying, possible, increased wash-out effect as aforementioned. 214Bi surface activity is higher than that of 218 Po and 214Pb. Since no recoil is expected for surface deposited 214Pb and 214Bi nuclides, the excess activity between these two could be attributed to deposition of
airborne 214Bi nuclides. Being this excess activity low accordingly low rate constants are probably detected for the 214 Bi nuclides. Interpreting the present results, modelling of progeny concentrations, at least in the cases presented, could be achieved on the basis of only radon measurements. Such measurements are performed easily and can be done in small time steps. On estimations based on such (quick) measurements quick predictions of progeny concentrations and PAEC may be achieved. Such a case is
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Fig. 5. Predicted and measured values for the Potential Alpha Energy Concentration in Eftalou and Thermi baths: (a) Eftalou, (b) Thermi. The measured data points are taken from Vogiannis et al. (2004a).
presented for the Policnitos spas (Fig. 7) by applying present model to published results (Vogiannis et al., 2004a,b). To our knowledge, similar modelling of progeny concentrations or PAEC based on quick radon measurements has not been published previously. Moreover, well-known mathematical models for radon entrance (e.g. Font and Baixeras, 2003) and accumula-
tion indoors (e.g. Nazaroff and Nero, 1988) have not been applied in thermal spas, for which very intense increases in radon, radon progeny concentrations and PAEC occur during bath filling and using. It should be emphasized however, that such modelling could be applied only in cases were the second order derivatives of the concentrations are of low importance. Such cases
Table 2 Estimated model parameters λa,i, λad,i and λud,i for Eftalou and Thermi thermal spas λa,i (h− 1)
i = 1 Po-218 i = 2 Pb-214 i = 3 Bi-214
λad,i (h− 1)
λud,i (h− 1)
Eftalou
Range
Thermi
Range
Eftalou
Range
Thermi
Range
Eftalou
Range
Thermi
Range
50 105 0.5
50–52 105–112 0.5–0.8
200 90 0.8
200–203 90–96 0.8–0.9
5.0 1.0 4.3
4.9–5.0 0.9–1.0 3.7–4.0
1.0 0.25 2.0
0.9–1.1 0.25–0.26 1.8–2.1
102 125 0.7
102–103 112–120 0.6–0.7
170 100 0.5
169–171 98–105 0.5–0.6
Index i equals 1,2,3 for 218Po, 214Pb and 214Bi respectively.
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Fig. 6. Surface (volume equivalent) daughter activity concentration in (a) Eftalou and (b) Thermi thermal baths.
may be found in spas where the ventilation is rather poor and constant with time, the bath is filled once and the bather receives treatment without inducing acute changes in bath surface, i.e. stays rather calm during treatment. It may not apply in spas for which thermal water enters continuously with flux abnormalities or in cases where the bather changes, unpredictably, the indoor atmosphere by opening windows or thermal water supplies. It may also not apply in the cases for which thermal water induces entering of trace gases (e.g. CO2) which alter indoor atmosphere. Fig. 8 presents time series modelled radon and airborne daughter activity concentration data for the Eftalou baths. Similar is the case for the Thermi baths. Since modelling is based on pure radon time series data the curve shapes for all progeny are identical, however, time-shifted. The time shift of each curve (in respect to the one of radon) is attributed to the different decay, deposition and attachment rate constants of the progeny. In general, unattached 218Po, 214Pb and 214Bi nuclides are shifted forward approximately 0.001 h, 0.05 h and 0.40 h respectively, while attached 218Po, 214 Pb and 214 Bi nuclides 0.05 h, 0.45 h and 0.65 h respectively. It should be mentioned that, time series radon curves detected by EQF3023 and Alpha Guard present
differences originating from the different radon detection methodology followed by the two instruments (Genitron, 1998; Sarad Instruments, 1998). However, the instruments were cross calibrated and, thus, the curve peaks were of the same order. Yet, the 10-min Alpha Guard time interval allows for quicker time series monitoring, though of lower statistical accuracy. Although quicker radon monitoring could result in quicker progeny activity predictions, the experimental verifications still remain under the longer time needed for daughter activity determination. Worth to mention is that the estimation of PAEC based on quick radon measurements is affected by the multiple a u model parameters (λa,i, λd,i , λd,i and λv). Characteristic uncertainty analysis for the case of Eftalou thermal baths is shown in Table 3. Mean, maximum and standard deviation of PAEC were calculated from the predicted time series PAEC values according to model equations ((2.1)–(2.9)). This was achieved by performing, for each parameter, 30 iterative solutions of Eqs. (2.1)–(2.9) by allowing ascending variation of the parameter from its minimum to its maximum value, while considering all other parameters unchanged. The exposure (integration of PAEC with time) was calculated from the predicted PAEC time series data. The ranges of the model parameters (λa,i,
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Fig. 7. Predicted radon daughter activity concentration in Polichnitos thermal baths: (a) Attached radon progeny, (b) Radon and potential alpha energy concentration.
a u λd,i and λd,i ) were those estimated to correspond to the arbitrarily ±10% change of ventilation rate (see Table 2), while on the other hand, the ventilation rate was allowed to change to within ±1% of its measured value (according to Vogiannis et al., 2004c), considering this change as acceptable for the certain experimental conditions. Changes in model parameters (λv, λa,i, a u λd,i and λd,i ) induce subsequent changes in mean, peak (maximum) PAEC, PAEC standard deviation and exposure (Table 3). As is well known (e.g. Nazaroff and Nero, 1988), the ventilation rate affects PAEC and exposure significantly, since (according to model predictions) it reduces both peak PAEC and exposure about thirty to forty (30–40) times in percentage (e.g. ±1% change in λv induces about 30–33% change in peak PAEC and about 35–38% in exposure). On the other hand, bias in some model parameters affects model predictions significantly (e.g. about 9 times in a u percentage for λd,1 and 28 times in percentage for λd,1 ),
while bias in others (e.g. λa,3) has little influence on model estimations. However, it should be emphasized that the present modelling was done for the purpose of dose estimation at thermal spas during filling and bath using and not for the evaluation of the attachment rate constants of 218Po, 214 Pb and 214Bi, although an estimation of these rates was, more or less, achieved. Under this perspective the present model provides physical and theoretical analysis that could be useful in studies regarding dose estimation at spa areas. Nevertheless, model predictions are affected by the experimental accuracy in the determination of the attachment and deposition rate constants of radon progeny. The present analysis was based on reported data taken under controlled experiments by application of certain fitting procedures. In this manner, the selection of applying the Levenberg–Marquardt method to the estimated daughter concentration functions instead of
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Fig. 8. Time series predicted radon and airborne daughter activity concentration for the Eftalou baths: (a) Radon and attached progeny, (b) Unattached progeny. The lines indicate the time-shift between radon and daughter activity concentration.
applying to the corresponding measured values was based on the fact that concentration functions were considered as more efficient predictors of the daughter
concentration variations during measurement. Similar consideration was also taken by Vogiannis et al. (2004c). Although in the above reference polynomial
Table 3 Uncertainty analysis of model outputs for Eftalou thermal spas Model parameter Symbol
PAEC
Range
Mean value −1
λv λa,1 λa,2 λa,3 λud,1 λad,1
Exposure Maximum value
Standard deviation
Value (h )
(%)
Min (%)
Max (%)
Min (%)
Max (%)
Min (%)
Max (%)
0.59–0.60 50–52 105–112 0.5–0.8 102–103 4.9–5.0
1.0 2.0 3.2 23.1 0.5 1.0
1.2 − 1.3 − 0.6 0.1 0.4 0.3
1.2 − 1.3 − 0.6 0.1 0.4 0.3
− 30.7 − 36.8 − 17.1 −1.4 − 11.8 −9.0
33.0 33.7 15.9 1.5 12.8 9.6
−30.7 −36.8 −17.1 −1.3 − 11.9 −9.0
33.1 33.7 15.9 1.6 12.8 9.7
Min (%)
Max (%)
−35.4 −36.2 −17.9 − 1.8 −14.1 − 8.7
38.3 32.6 16.1 2.1 9.5 9.4
Columns 1–3 present the value and relative range of the various model parameters (λa,i, λad,i and λud,i) corresponding to ±10% change of ventilation rate according to Table 2 and of the ventilation rate (λv).Columns 4–11 present the relative (%) range (min–max) of PAEC mean value, PAEC peak (maximum) value, PAEC standard deviation and of exposure (integration of PAEC over time). Index equals 1,2,3 for 218Po, 214Pb and 214Bi respectively.
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least square fitting was adopted, the non-linear Levenberg–Marquardt fitting was considered here as more adequate. Moreover, it optimized for numerical solving. In the near future, more measurements are programmed for further checking model validity to experimental data. Emphasis will be taken on a possible different deposition of 214Bi nuclides and on the factors that affect the whole physical behaviour. Acknowledgments We would like to thank Professor Ioannis Kandarakis for his help in editing the manuscript of this paper. We would also like to thank Associate Professor Anna Louizi for her overall assistance at the initiatory stage of this work. References Bernhardt GP, Hess CT. Acute exposure from 222Rn and aerosols in drinking water. Environ Int 1996;22(Suppl. 1):S753–9. Datye VK, Hopke K, Fitzerland B, Raunemaa M. Dynamic model for assessing 222-Rn and progeny exposure from showering with radon-bearing water. Environ Sci Technol 1997;31:1589–96. El-Hussein A, Ahmed AA. Unattached fraction and size distribution of aerosol-attached radon progeny in the open air. Appl Radiat Isot 1995;46(12):1393–9. El-Hussein A, Ahmed AA, Mohammed A. Radiation dose to the human respiratory tract from inhalation of radon-222 and its progeny. Appl Radiat Isot 1998;49(7):783–90. Fitzgerald B, Hopke K, Datye V, Raunemaa T, Kuuspalo K. Experimental assessment of the short- and long-term effects of 222-Rn from domestic shower water on the dose burden incurred in normally occupied homes. Environ Sci Technol 1997;31(6):1822–9. Font L, Baixeras C. The RAGENA dynamic model of radon generation, entry and accumulation indoors. Sci Total Environ 2003;307:55–69. Genitron Instruments, Ltd. Alpha guard PQ2000/MC50, multiparameter radon monitor. Frankfurt: Genitron Instruments; 1998. 12 pp. Geranios A, Nikolopoulos D, Louizi A, Karatzi A. Multiple radon survey in spa of Loutra Edipsou (Greece). Radiat Prot Dosimetry 2004;112(2):251–8. Jung CH, Kim YP, Lee KW. Simulation of the influence of coarse particles on the properties of fine mode particles. J Aerosol Sci 2002;34(8):1201–16. Kertesz Z, Borbely-Kiss I, Hunyadi I. Study of aerosols collected in a speleotherapeutic cave situated below Budapest, Hungary. Nucl Instrum Methods B 1999;150:384–91.
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Lettner H, Humber AK, Rolle R, Steinhäusler F. Occupational exposure to radon in treatment facilities of the radon-spa Badgastein, Austria. Environ Int 1996;22(suppl. 1):S399–407. Mendenhall W and Sincich T. Statistics for engineering and the sciences. Prentice Hall, Inc., New Jersey, USA 1994, ISBN 0-02380581-1, pp. 919–981. Nazaroff W.W, Nero A.V. Radon and its Decay Products in Indoor Air. John Wiley & Sons, Inc., USA, 1988, ISBN 0-471-62810-7, 518 pp. Paul A, Keyser U. A reference aerosol for a radon reference chamber. Nucl Instrum Methods A 1996;368:819–24. Porstendörfer J. Physical parameters and dose factors of the radon and thoron decay products. Radiat Prot Dosimetry 2001;94(4):365–73. Porstendörfer J, Zock C, Reineking A. Aerosol size distribution of the radon progeny in outdoor air. J Environ Radioact 2000;51: 37–48. Porstendörfer J, Pagelkopf P, Grundel M. Fraction of the positive 218Po and 214Pb clusters in indoor air. Radiat Prot Dosimetry 2005;113 (3):342–51. Press,W.H, Flannery B.P, Teukolsky S.A, Vetterling W.T. Numerical recipes in C: the art of scientific computing. Cambridge University Press, Cambridge, 1990, ISBN 0-521-43108-5, pp. 633–777. Radolic V, Vukovic B, Smit G, Stanic D, Planinic J. Radon in the spas of Croatia. J Environ Radioact 2005;83:191–8. Ristimaki J, Virtanen A, Marjamaki M, Rostedt A, Keskinen J. On-line measurement of size distribution and effective density of submicron aerosol particles. J Aerosol Sci 2002;33:1541–57. Rumburg B, Alldredge R, Claiborn C. Statistical distributions of particulate matter and the error associated with sampling frequency. Atmos Environ 2001;35:2907–20. Sarad Instruments. EQF3023 user manual. Dresden: Sarad Gbmh; 1998. 25 pp. Song G, Zhang B, Wang X, Gong J, Chan D, Bernett J, Lee SC. Indoor radon levels in selected hot spring hotels in Guangdong, China. Sci Total Environ 2005;339:63–70. Vogiannis E, Niaounakis M, Halvadakis CP. Contribution of 222Rnbearing water to the occupational exposure in thermal baths. Environ Int 2004a;30:621–9. Vogiannis E, Nikolopoulos D, Louizi A, Halvadakis CP. Radon variations during treatment in thermal spas of Lesvos Island (Greece). J Environ Radioact 2004b;75:159–70. Vogiannis E, Nikolopoulos D, Louizi A, Halvadakis CP. Radon exposure in the thermal spas of Lesvos Island — Greece. Radiat Prot Dosimetry 2004c;111(1):121–7. Voutilainen A, Kaipio JP. Estimation of time-varying aerosol size distributions — exploitation of modal aerosol dynamic models. J Aerosol Sci 2002;33(8):1181–200.
Modelling radon progeny concentration variations in thermal spas Dimitrios Nikolopoulos a,⁎, Efstratios Vogiannis b,⁎ a
Laboratory of Ionising Radiations, Department of Medical Instruments Technology, Technological Educational Institution of Athens, Agiou Spyridonos, Egaleo, 122 10, Athens, Greece b Waste Management Laboratory, School of Environment, Department of Environment, University of the Aegean, University Hill, 81100 Mytilene, Greece Received 26 June 2006; received in revised form 5 November 2006; accepted 15 November 2006 Available online 22 December 2006
Abstract Radon and its short-lived progenies (218Po, 214Pb, 214Bi and 214Po) are well known radioactive indoor pollutants identified as the major radiation burden component of the thermal spa users. Monitoring of short-lived progeny concentration is of great importance for short-term dose estimations both for bathers and working personnel. A prediction model of the short-lived progeny concentration variations was developed and applied on published data of the thermal spas of Lesvos Island. The physical procedures involved were modeled in a set of differential equations describing radon progeny concentration variations on the basis of radon measurements. Published daughter data were fitted on model predictions adjusting non-measured parameters, e.g. attachment and deposition rate constants for attached and unattached progenies. Attachment rate constants were estimated between 50 and 200 h− 1 while the deposition rate constants between 0.25 and 5 h− 1 for attached progenies and 0.5 and 170 h− 1 for the unattached ones. In addition, unattached 218Po, 214Pb and 214Bi progenies were found to be shifted forward in respect to radon approximately 0.001 h, 0.05 h and 0.40 h respectively, while attached 218Po, 214Pb and 214Bi progenies 0.05 h, 0.45 h and 0.65 h respectively. © 2006 Elsevier B.V. All rights reserved. Keywords: Radon; Daughter; Model; Spas PAEC
1. Introduction Radon is natural gas generated from the 226 Ra adecay (half-life 1600 years). It is a noble gas with 3.82 days half-life and high water solubility. In most cases, the major component of radon entrance in building structures is the underground soil followed by the exhalation from the building materials and the ⁎ Corresponding authors. Nikolopoulos is to be contacted at Tel.: +30 10 5385 375 (work), +30 10 6977208318 (Cellular) fax: +30 10 5910 975 (work). Vogiannis, Tel.: +30 22510 36214 (work), +30 10 6977072031 (Cellular) fax: +30 22510 26625 (work). E-mail addresses: [email protected] (D. Nikolopoulos), [email protected] (E. Vogiannis). 0048-9697/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.scitotenv.2006.11.017
emanation due to water and natural gas use. However, elevated radon concentrations in building structures due to entering water have been reported (Bernhardt and Hess, 1996). The radon concentrations in the entering water, the volume and the way of water usage, separated or in combination, could result in large amounts of radon in indoor air. It could be building structures, e.g. water stations and contextual workplaces, where the water usage is the dominant source of elevated indoor radon. Thermal spas have been identified as such places (Lettner et al., 1996; Song et al., 2005; Radolic et al., 2005). Moreover, acute radon and daughter peaks during bath filling have also been observed (Vogiannis et al., 2004a,b,c; Geranios et al., 2004), thus yielding to high radiation doses to workers and bathers.
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In this consensus and on the basis of previous studies (Vogiannis et al., 2004a,b,c) regarding concentration peak appearances in the thermal spas of Lesvos Island under controlled experiments, this paper aimed to model the behaviour of short-lived radon progeny in the indoor atmosphere of thermal spas, in an effort to describe the mechanism that allows the appearance of concentration peaks during filling and bath using. Such modeling could help in the quantification of physical parameters not easily measured and provide a guide for predicting concentrations on the basis of the determined parameters. The selection of the thermal spas of Lesvos Island was based on the geological background of Lesvos Island and mainly on the fact that these spas have been identified as areas presenting intense variations of radon and progeny concentrations and PAEC, thus imposing additional short-term health impact both to bathers and working personnel (Vogiannis et al., 2004a,b,c). 2. Materials and methods 2.1. Physical behaviour As a first step, a building structure of a thermal spa is considered comprising a treatment room (TR) with a bathtub of some m3 and a water supply system utilized both for thermal and non-thermal water filling of the bathtub. The TR is considered to be ventilated via window and door openings. The TR is considered under working conditions i.e. bath filling from personnel and usage from bathers. Radon entrance in the TR may be due to the underground soil, building materials and outdoor air, however, the main source is the supply of thermal water (Vogiannis et al., 2004a,b). After entrance, radon either resolves or decays to neutral or, at most, positively charged progeny, which in turn may neutralize. Positive or neutral progeny append to existing atmospheric trace gases and water vapour, forming clusters (Porstendörfer et al., 2000, 2005) in dynamic exchange between
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positive and neutral form. The clusters may attach to aerosol particles and in either form, airborne attached or airborne unattached–clustered, may deposit on surfaces (Fig. 1). Depending on atmospheric conditions, exchanges of short-lived progeny between the various forms may occur (Porstendörfer, 2001). However, in most circumstances only exchange from recoil between airborne attached and surface deposited 218 Po nuclides is considered (Nazaroff and Nero, 1988; Porstendörfer, 2001). Airborne attached and unattached short-lived progeny in a TR distribute in terms of size (often expressed by the particle Arithmetic Mean Diameter-AMD) and activity. Their indoor distribution depends on particle sources, ventilation and other parameters (El-Hussein and Ahmed, 1995; Paul and Keyser, 1996; El-Hussein et al., 1998; Kertesz et al., 1999; Rumburg et al., 2001; Ristimaki et al., 2002) and is, in combination, described by the activity size distribution. This size distribution consists of three lognormal distributions (modes) each one contributing differently to the total (Datye et al., 1997; El-Hussein et al., 1998; Porstendörfer, 2001; Jung et al., 2002; Voutilainen and Kaipio, 2002). According to Porstendörfer (2001), the three modes are the nucleation mode (AMD 30–40 nm), the accumulation mode (AMD 250–450 nm) and the coarse mode (AMD 2000– 6000 nm). Thermal spa indoor environments, however, are characterised by low concentration of coarse mode particles due to lack of such particle sources and because any existing coarse particles are drifted out by water vapour molecules (wash-out effect) and deposit on room surfaces or bathtub water (Fitzgerald et al., 1997). Hence, the indoor environments of thermal spas may be considered to consist, under working conditions, of aerosol particles mainly in the nucleation and accumulation mode. These modes are traditionally characterised (e.g. Nazaroff and Nero, 1988) as airborne-unattached (AMD < 50 nm) and airborne-attached daughter particles (AMD > 50 nm). In addition to these, another mode is considered; the surface deposited progenies (either in
Fig. 1. Physical behaviour of radon progeny in indoor environments.
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Fig. 2. Multi-compartmental diagram for radon and progeny in indoor environments of thermal spas. The symbols employed are described in Table 1.
attached or unattached form). In this traditional three mode manner the radon progenies are treated within this manuscript. 2.2. Model For modelling purposes an open multi-compartment system with reversible progeny flux is considered as shown in Fig. 2. The system's compartments represent Table 1 Parameters employed in system equations ((1.1)–(1.9)) Symbol Units λ0 C0 Á0 λi Cui Cai Csi Aui Aai Asi λv λa,i pl λad,i λud,i
Meaning
h− 1 m− 3 Bq m− 3 h− 1 m− 3 m− 3 m− 3
Decay constants (0.00755) Concentration of 222Rn Activity concentration of 222Rn Decay constants (λ1 = 13.37, λ2 = 1.552, λ3 = 2.111) Concentration of unattached progeny Concentration of attached progeny Surface (volume equivalent) concentration of deposited progeny Bq m− 3 Activity concentration of unattached progeny Bq m− 3 Activity concentration of attached progeny Bq m− 3 Surface (volume equivalent) activity concentration of deposited progeny h− 1 Ventilation rate h− 1 Attachment rate constant of progeny Unitless Recoil fraction of 218Po h− 1 Deposition rate constant of attached progeny h− 1 Deposition rate constant of unattached progeny
Index i equals 1,2,3 for 218Po, 214Pb and 214Bi respectively.
the various potential (traditional three mode) states of radon progeny in indoor environments of thermal spas under working conditions. 214Po is not included in Fig. 2 because it follows the state of 214Bi due to its short decay time (168 μs). All daughter nuclides terminate by decay to surface deposited 210 Pb. This is taken as the final compartment because 210 Pb is considered of no short-term health impact due to its long half-life (22.3 years). All progenies may be removed from indoor air by ventilation. Assuming that the variation of radon concentration (C0) with time is known, modelling of the behaviour of decay products may be achieved through the multicompartmental system ((1.1)–(1.9)) of linear differential equations, describing the variations of radon and radon progeny within a certain time interval dt (Fig. 2). The symbols employed together with their units are described in detail in Table 1. d u C1 ¼ k0 C0 k1 þ kv þ ka;1 þ kud;1 C1u ð1:1Þ dt d a C1 ¼ ka;1 C1u k1 þ kv þ ka;1 þ kad;1 C1a ð1:2Þ dt d s C ¼ kud;1 C1u þ kad;1 C1a þ k1 C1s ð1:3Þ dt 1 d u C2 ¼ k1 C1u þ p1 k1 C1a k2 þ kv þ ka;2 þ kud;2 C2u dt ð1:4Þ
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d a C ¼ ka;2 C2u þ ð1 p1 Þk1 C1a dt 2 k2 þ kv þ ka;2 þ kad;2 C2a d dt d dt d dt d dt
C2s ¼ k1 C1s þ kud;2 C2u þ kad;2 C2a k2 C2s C3u ¼ k2 C2u k3 þ kv þ ka;3 þ kud;3 C3u C3a ¼ k2 C2a þ ka;3 C3u k3 þ kv þ kad;3 C3a C3s ¼ k2 C2s þ kud;3 C3u þ kad;3 C3a k3 C3s
ð1:5Þ ð1:6Þ ð1:7Þ ð1:8Þ ð1:9Þ
In all equations the positive terms represent input from other compartments and the negative terms output to other compartments or atmosphere, which is considered to be only through ventilation (terms proportional to λv). The term λ0C0 represents the net input of the first compartment (218 Pou) via radon decay. The terms λiCix, x λd,i Cix , λa,iCix (i = 1,2,3; x = a,u) represent compartmental loss or input of radon progeny through decay, deposition and attachment to ambient aerosol respectively. In Eqs. (1.1)–(1.9) the activity size distribution is considered to be three mode, i.e. airborne-attached, airborne-unattached and surface-deposited. Moreover, a u the parameters λv, λa,i, λd,i and λd,i are considered to remain constant during dt. Attachment to ambient aerosols and deposition to surfaces is taken into account for all short-lived radon progeny and recoil only for 218 Po nuclides. System equations ((1.1)–(1.9)) represent a linear approximation of the involved phenomena in the assumed typical TR, accounting only for the first order derivatives and the proportional terms of the daughter concentrations. This approximation is applicable in temporal radon varying phenomena in thermal spas which do not exhibit very intense (second and higher order) temporal changes induced by external influences (e.g. human, ambient air acute activity). Eqs. (1.1)–(1.9) can be transformed to account for the activity concentration (Bq m− 3) changes which could be measured by employment of proper active measuring methodology. Conversion is achieved by substituting λi− 1Aix for each Cix (i = 1,2,3; x = a,u) and λ0− 1A0 for C0. By this substitution, system (2) may be written as: d u A1 ¼ k1 A0 k1 þ kv þ ka;1 þ kud;1 Au1 ð2:1Þ dt d a A1 ¼ ka;1 Au1 k1 þ kv þ ka;1 þ kad;1 Aa1 ð2:2Þ dt d s A ¼ kud;1 Au1 þ kad;1 Aa1 þ k1 As1 ð2:3Þ dt 1
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d u A2 ¼ k2 Au1 þ p1 k2 Aa1 k2 þ kv þ ka;2 þ kud;2 Au2 dt ð2:4Þ d a A ¼ ka;2 Au2 þ ð1 p1 Þk2 Aa1 dt 2 k2 þ kv þ ka;2 þ kad;2 Aa2 ð2:5Þ d dt d dt d dt d dt
As2 ¼ k2 As1 þ kud;2 Au2 þ kad;2 Aa2 k2 As2 Au3 ¼ k3 Au2 k3 þ kv þ ka;3 þ kud;3 Au3 Aa3 ¼ k3 Aa2 þ ka;3 Au3 k3 þ kv þ kad;3 Aa3 As3 ¼ k3 As2 þ kud;3 Au3 þ kad;3 Aa3 k3 As3
ð2:6Þ ð2:7Þ ð2:8Þ ð2:9Þ
Model equations ((2.1)–(2.9)) may provide the concentrations of all radon progeny on the basis of known radon activity concentration (A0) and model a u parameters λv, λa,i, λd,i and λd,i . As in Eqs. (1.1)–(1.9), there is a linear (first order) relation between time series activity concentrations and temporal rates of change, a u assuming model parameters λv, λa,i, λd,i and λd,i constant. Through measuring, radon activity concentration data may be modelled analytically, i.e. explicit mathematical equations, and hence, all daughter concentrations can be predicted either analytically, by solving system (2), or numerically. On the other hand, Eqs. (2.1)–(2.9) may be utilized a for the determination of model parameters λa,i, λd,i and u λd,i (considering these constant during measurement) assuming that the ventilation rate λv and the activity concentrations of radon and radon progeny A0, Aia and Aiu are experimentally determined, i.e. analytically expressed. In this manner, however, there is a nonlinear relation between time series concentrations and a u model parameters λa,i, λd,i and λd,i . This consideration could be the preceding one, at least in cases where the a u experimental determination of λa,i, λd,i and λd,i is not easily achievable. 2.3. Comparison to experimental data Model validity was checked in terms of comparison of model predictions with experimental data obtained from previous studies (Vogiannis et al., 2004a,b,c) in the lateral described model consideration, i.e. predicta u ing model parameters λa,i, λd,i and λd,i . The experimental data comprised time series radon and radon daughter (attached and unattached) activity concentration measurements collected through controlled experiments in the thermal spas of Lesvos Island. The
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measurements were derived with Alpha Guard PRO of Genitron Ltd (10 min radon time series) and EQF 3023 of Sarad Instruments, GmbH (2 h radon, attached and unattached progeny time series). The methodology of the experiments is described in detail in the above references. In general, it included TR ambient air atmosphere variations induced by controlled thermal water bath filling with simultaneous time series radon and radon progeny measurements together with ventilation rate estimation. For brevity, only results of model comparison to selected data of radon and daughter peaks of Eftalou and Thermi baths are presented. For comparison, model equations ((1.1)–(1.9)) were described in a Pentium (R)M PC using Microsoft FORTRAN specially developed codes employing iterative solving procedures (Press et al., 1990). At first, the published measured data were fitted to the minimum χ2 nonlinear curve functions by application of the Levenberg–Marquardt method (Press et al., 1990) and were used as inputs (A0, Aia, Aiu) of the model. The radon concentration curve functions from Alpha Guard were used as initial time series values (A0) for the prediction of the values of the input daughter activity concentration functions (estimated Aiu and Aia) according to model equations ((1.1)–(1.9)) by employing numerical equation solving. After solving, the predicted model daughter concentration values (predicted Aiu and Aia) were fitted to the corresponding values of the input daughter concentration functions (estimated Aiu and Aia) by application of the Levenberg–Marquardt method (Press et al., 1990). According to the method, the model a u parameters λa,i, λd,i and λd,i were allowed to vary until the difference between predicted and input values yielded to minimum χ2 for each daughter function. Goodness of fit was checked by means of application of the Wilcoxon signed ranks test (Mendenhall and Sincich, 1994) between predicted and estimated values of daughter concentrations (Aiu and Aia ) with critical alpha value of 0.10 for being a Levenberg–Marquardt fit acceptable. The adapted ventilation rate values (λv) in the model were constant and taken equal to those measured according to the available database (Vogiannis et al., 2004c). 3. Results and discussion Figs. 3 and 4 present characteristic cases of model predictions for the TRs of Eftalou and Thermi thermal spas together with measurements reported by Vogiannis et al. (2004a,b). The model seems to predict in a statistical manner the published results with few
outliers. Interesting is the fact that the predicted values of daughter concentrations (Aiu and Aia) present the peaks which had been attributed to the bath filling procedure (Vogiannis et al., 2004a,b). Fig. 5 present for the spas of Eftalou and Thermi model predictions and measurements of Potential Alpha Energy Concentration (PAEC), which is a measure of the maximum alpha energy that can be delivered to the bather's lungs during treatment. Agreement between predicted and measured data is achieved. PAEC peaks are detected implying peaks in radiation dose delivered to bathers and working personnel (Vogiannis et al., 2004a,b), thus providing physical and theoretical interpretations leading to the dose estimation at thermal spas. a u The estimated model parameters λa,i, λd,i and λd,i are summarized in Table 2. For reasons of uncertainty analysis, Table 2 also presents ranges of the abovementioned model parameters for varying ventilation rate values. These ranges were estimated by performing 30 iterative solutions of the model equations ((2.1)–(2.9)), by allowing the ventilation rate values (λv) to vary in ascending order from − 10% to +10% (range arbitrarily selected) in respect to the measured values (Vogiannis et al., 2004c). The model parameters were determined according to methods described earlier in text (paragraph 2.3) considering time series data of progeny concentrations and PAEC unchanged. Ventilation rate a u changes affect λa,i, λd,i and λd,i values in a non-linear manner. However, a change of ±10% in ventilation rate imposes lower relative deviation in the range of the a above model parameters (e.g. from 0% for λd,1 to 6% for λa,2). To our knowledge, no experimental data on the values of such parameters in thermal spas exist. Comparisons can only be performed in reference to published attachment and deposition rate constants (assumed equal for all progenies) estimated for dwellings or through controlled chamber environments (see e.g. Nazaroff and Nero, 1988). According to Nazaroff a and Nero (1988) typical range values for λa,i, λd,i and u λd,i for dwelling environments are 5–500, 0.1–0.4 and 10–40 h− 1 respectively. The λa,1 and λa,2 values both for Eftalou and Thermi baths lay in the above range. In addition, by interpretation of reported data by Datye et al. (1997) on dwelling baths, an attachment rate constant of approximately 50–100 h − 1 could be estimated assuming a diffusion coefficient (D) of approximately 0.02–0.04 cm2 s− 1 which is valid for clustering of progeny with 200 vapour molecules (Datye et al., 1997; Nazaroff and Nero, 1988). On the other hand, the estimated values and the corresponding ranges
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Fig. 3. Predicted and measured radon daughter activity concentration in Eftalou thermal baths: (a) 218Po, (b) 214Pb, (c) 214Bi. The measured data points are taken from Vogiannis et al. (2004a). a u for the parameters λd,i and λd,i are well above this range. This could be explained on the basis of the wash-out effect reported by Fitzgerald et al. (1997); due to the high humidity in the thermal baths during bath filling, more progenies are forced to deposit on surfaces or a u bathtub, causing increased λd,i and λd,i values. Worth to notice is the fact that the attachment and deposition of the 214 Bi nuclides is estimated to be significantly lower
when compared to that of 218Po and 214Pb. This could be attributed to an increased surface (volume equivalent) activity concentration of the 214 Bi nuclides caused mainly by the decay of surface deposited 218Po and 214 Pb activity. Since surface deposition includes also the one on the water surface, an increased wash-out effect of the 218Po and 214 Pb nuclides could result in increased surface (volume equivalent) activity concentration of
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Fig. 4. Predicted and measured radon daughter activity concentration in Thermi thermal baths: (a) 218Po, (b) 214Pb, (c) 214Bi. The measured data points are taken from Vogiannis et al. (2004a).
the 214Bi nuclides and, probably, thus, lower potentiality of deposition and attachment of airborne 214Bi nuclides, i.e. lower rate constant values. Fig. 6 presents the surface (volume equivalent) activity concentration of all progeny. High activity concentration values are detected implying, possible, increased wash-out effect as aforementioned. 214Bi surface activity is higher than that of 218 Po and 214Pb. Since no recoil is expected for surface deposited 214Pb and 214Bi nuclides, the excess activity between these two could be attributed to deposition of
airborne 214Bi nuclides. Being this excess activity low accordingly low rate constants are probably detected for the 214 Bi nuclides. Interpreting the present results, modelling of progeny concentrations, at least in the cases presented, could be achieved on the basis of only radon measurements. Such measurements are performed easily and can be done in small time steps. On estimations based on such (quick) measurements quick predictions of progeny concentrations and PAEC may be achieved. Such a case is
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Fig. 5. Predicted and measured values for the Potential Alpha Energy Concentration in Eftalou and Thermi baths: (a) Eftalou, (b) Thermi. The measured data points are taken from Vogiannis et al. (2004a).
presented for the Policnitos spas (Fig. 7) by applying present model to published results (Vogiannis et al., 2004a,b). To our knowledge, similar modelling of progeny concentrations or PAEC based on quick radon measurements has not been published previously. Moreover, well-known mathematical models for radon entrance (e.g. Font and Baixeras, 2003) and accumula-
tion indoors (e.g. Nazaroff and Nero, 1988) have not been applied in thermal spas, for which very intense increases in radon, radon progeny concentrations and PAEC occur during bath filling and using. It should be emphasized however, that such modelling could be applied only in cases were the second order derivatives of the concentrations are of low importance. Such cases
Table 2 Estimated model parameters λa,i, λad,i and λud,i for Eftalou and Thermi thermal spas λa,i (h− 1)
i = 1 Po-218 i = 2 Pb-214 i = 3 Bi-214
λad,i (h− 1)
λud,i (h− 1)
Eftalou
Range
Thermi
Range
Eftalou
Range
Thermi
Range
Eftalou
Range
Thermi
Range
50 105 0.5
50–52 105–112 0.5–0.8
200 90 0.8
200–203 90–96 0.8–0.9
5.0 1.0 4.3
4.9–5.0 0.9–1.0 3.7–4.0
1.0 0.25 2.0
0.9–1.1 0.25–0.26 1.8–2.1
102 125 0.7
102–103 112–120 0.6–0.7
170 100 0.5
169–171 98–105 0.5–0.6
Index i equals 1,2,3 for 218Po, 214Pb and 214Bi respectively.
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Fig. 6. Surface (volume equivalent) daughter activity concentration in (a) Eftalou and (b) Thermi thermal baths.
may be found in spas where the ventilation is rather poor and constant with time, the bath is filled once and the bather receives treatment without inducing acute changes in bath surface, i.e. stays rather calm during treatment. It may not apply in spas for which thermal water enters continuously with flux abnormalities or in cases where the bather changes, unpredictably, the indoor atmosphere by opening windows or thermal water supplies. It may also not apply in the cases for which thermal water induces entering of trace gases (e.g. CO2) which alter indoor atmosphere. Fig. 8 presents time series modelled radon and airborne daughter activity concentration data for the Eftalou baths. Similar is the case for the Thermi baths. Since modelling is based on pure radon time series data the curve shapes for all progeny are identical, however, time-shifted. The time shift of each curve (in respect to the one of radon) is attributed to the different decay, deposition and attachment rate constants of the progeny. In general, unattached 218Po, 214Pb and 214Bi nuclides are shifted forward approximately 0.001 h, 0.05 h and 0.40 h respectively, while attached 218Po, 214 Pb and 214 Bi nuclides 0.05 h, 0.45 h and 0.65 h respectively. It should be mentioned that, time series radon curves detected by EQF3023 and Alpha Guard present
differences originating from the different radon detection methodology followed by the two instruments (Genitron, 1998; Sarad Instruments, 1998). However, the instruments were cross calibrated and, thus, the curve peaks were of the same order. Yet, the 10-min Alpha Guard time interval allows for quicker time series monitoring, though of lower statistical accuracy. Although quicker radon monitoring could result in quicker progeny activity predictions, the experimental verifications still remain under the longer time needed for daughter activity determination. Worth to mention is that the estimation of PAEC based on quick radon measurements is affected by the multiple a u model parameters (λa,i, λd,i , λd,i and λv). Characteristic uncertainty analysis for the case of Eftalou thermal baths is shown in Table 3. Mean, maximum and standard deviation of PAEC were calculated from the predicted time series PAEC values according to model equations ((2.1)–(2.9)). This was achieved by performing, for each parameter, 30 iterative solutions of Eqs. (2.1)–(2.9) by allowing ascending variation of the parameter from its minimum to its maximum value, while considering all other parameters unchanged. The exposure (integration of PAEC with time) was calculated from the predicted PAEC time series data. The ranges of the model parameters (λa,i,
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Fig. 7. Predicted radon daughter activity concentration in Polichnitos thermal baths: (a) Attached radon progeny, (b) Radon and potential alpha energy concentration.
a u λd,i and λd,i ) were those estimated to correspond to the arbitrarily ±10% change of ventilation rate (see Table 2), while on the other hand, the ventilation rate was allowed to change to within ±1% of its measured value (according to Vogiannis et al., 2004c), considering this change as acceptable for the certain experimental conditions. Changes in model parameters (λv, λa,i, a u λd,i and λd,i ) induce subsequent changes in mean, peak (maximum) PAEC, PAEC standard deviation and exposure (Table 3). As is well known (e.g. Nazaroff and Nero, 1988), the ventilation rate affects PAEC and exposure significantly, since (according to model predictions) it reduces both peak PAEC and exposure about thirty to forty (30–40) times in percentage (e.g. ±1% change in λv induces about 30–33% change in peak PAEC and about 35–38% in exposure). On the other hand, bias in some model parameters affects model predictions significantly (e.g. about 9 times in a u percentage for λd,1 and 28 times in percentage for λd,1 ),
while bias in others (e.g. λa,3) has little influence on model estimations. However, it should be emphasized that the present modelling was done for the purpose of dose estimation at thermal spas during filling and bath using and not for the evaluation of the attachment rate constants of 218Po, 214 Pb and 214Bi, although an estimation of these rates was, more or less, achieved. Under this perspective the present model provides physical and theoretical analysis that could be useful in studies regarding dose estimation at spa areas. Nevertheless, model predictions are affected by the experimental accuracy in the determination of the attachment and deposition rate constants of radon progeny. The present analysis was based on reported data taken under controlled experiments by application of certain fitting procedures. In this manner, the selection of applying the Levenberg–Marquardt method to the estimated daughter concentration functions instead of
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Fig. 8. Time series predicted radon and airborne daughter activity concentration for the Eftalou baths: (a) Radon and attached progeny, (b) Unattached progeny. The lines indicate the time-shift between radon and daughter activity concentration.
applying to the corresponding measured values was based on the fact that concentration functions were considered as more efficient predictors of the daughter
concentration variations during measurement. Similar consideration was also taken by Vogiannis et al. (2004c). Although in the above reference polynomial
Table 3 Uncertainty analysis of model outputs for Eftalou thermal spas Model parameter Symbol
PAEC
Range
Mean value −1
λv λa,1 λa,2 λa,3 λud,1 λad,1
Exposure Maximum value
Standard deviation
Value (h )
(%)
Min (%)
Max (%)
Min (%)
Max (%)
Min (%)
Max (%)
0.59–0.60 50–52 105–112 0.5–0.8 102–103 4.9–5.0
1.0 2.0 3.2 23.1 0.5 1.0
1.2 − 1.3 − 0.6 0.1 0.4 0.3
1.2 − 1.3 − 0.6 0.1 0.4 0.3
− 30.7 − 36.8 − 17.1 −1.4 − 11.8 −9.0
33.0 33.7 15.9 1.5 12.8 9.6
−30.7 −36.8 −17.1 −1.3 − 11.9 −9.0
33.1 33.7 15.9 1.6 12.8 9.7
Min (%)
Max (%)
−35.4 −36.2 −17.9 − 1.8 −14.1 − 8.7
38.3 32.6 16.1 2.1 9.5 9.4
Columns 1–3 present the value and relative range of the various model parameters (λa,i, λad,i and λud,i) corresponding to ±10% change of ventilation rate according to Table 2 and of the ventilation rate (λv).Columns 4–11 present the relative (%) range (min–max) of PAEC mean value, PAEC peak (maximum) value, PAEC standard deviation and of exposure (integration of PAEC over time). Index equals 1,2,3 for 218Po, 214Pb and 214Bi respectively.
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