Environ. Sci. Technol. 1997, 31, 1589-1596
Dynamic Model for Assessing 222Rn and Progeny Exposure from Showering with Radon-Bearing Water V. K. DATYE, P. K. HOPKE,* B. FITZGERALD, AND T. M. RAUNEMAA† Department of Chemistry, Clarkson University, Potsdam, New York 13699-5810
In homes supplied by water with a high radon content, inhalation exposure from the radon in the water may occur on two different time scales: (a) long-term exposure that occurs due to an increase in the background radon concentration from radon released during water use and (b) short-term exposure that occurs during actual radon use such as in the bath, kitchen, and laundry room. While the former mode has been the subject of several studies, not much is known about the latter mode of exposure. During water use, the radon concentration can be considerably higher than the background and varies rapidly with time. Most of the exposure occurs well before a steady state can be reached. The goal of this work was to develop a dynamic, size-dependent model for the radon progeny activity during showering. The model includes radon and progeny decay, attachment of progeny to the existing aerosol, recoil, ventilation, and surface deposition. The model is used to evaluate radon exposure during and subsequent to showering as a function of environmental and other parameters (such as aerosol profile, bathroom dimensions, ventilation rate, and shower duration). These results are used in conjunction with a recent dosimetric model to obtain the integrated lung dose as a function of time.
Introduction Radon and its decay products represent a potential health hazard to the population in their homes. When a home is supplied by radon-bearing groundwater, the radon that is released into the air during water use becomes another source of indoor inhalation exposure. To evaluate the significance of this contribution to the overall radon risk, it is necessary to examine each instance of water use (such as in the kitchen, bath, laundry room, and other areas) and to look at both the steady-state (long-term) as well as the dynamic (short-term) components of the exposure. The steady-state component has been studied in considerable detail (1-4), but little is known about the time-varying exposure. Unless the dynamic component is also evaluated, it is not possible to make a complete exposure assessment. One of the potentially important sources of short-term exposure is the release of radon from water during showering * Author to whom correspondence should be addressed. Telephone: (315)268-3861; fax: (315)268-6610; e-mail: hopkepk@draco. clarkson.edu. † On leave from the Department of Environmental Sciences, University of Kuopio, Kuopio, Finland.
S0013-936X(96)00154-X CCC: $14.00
1997 American Chemical Society
and the subsequent in-growth of the radon decay products. The main task of the work being reported here was the development of a model for the radon progeny activity size distribution as a function of time, during and subsequent to showering. It is necessary to have a size distribution, since the lung dose depends sensitively on the size of the inhaled particle carrying the activity. Existing steady-state models cannot be applied to this situation since the radon concentration varies rapidly with time when water is being used, and most of the exposure occurs well before a radiological or atmospheric steady-state can be reached. The experimental results for a field-study home as well as from measurements in a laboratory-installed shower stall are presented in our previous paper (5). The present work is not an analysis of the experimental data, but complements it. The goal of the model is to develop a conceptual framework for theoretical analysis in order to assess the relative importance of the variables that influence dynamic radon exposure and thus to extrapolate from limited experimental data to a range of possible exposure conditions. The essential features of the model are similar to the standard steady-state room model for indoor radon exposure (6-10). In this case, however, the source term for radon is inherently time dependent. Radon enters the bathroom from the water droplets when the shower is turned on, and a substantial fraction of it is released into the air. The airborne radon decays into its radioactive progeny [218Po, 214Pb, and 214Bi(214Po)], and the progeny attach to the existing aerosol to yield a size distribution of the activity. Some of the 214Pb becomes ‘unattached’ due to recoil during the R-decay of 218Po. Removal of activity from the air takes place by ventilation and by deposition onto walls and other surfaces. There is a competition between those factors that keep the activity airborne and those that remove the activity, and the relative effectiveness of the competing terms is a function of particle size. The model must keep track of this competition in each size range and update the activity size distribution at each time step. While the dynamic model is conceptually similar to the steady-state version, it is computationally more complex, and the integration in time is complicated by the large number of widely differing time scales. Phenomena such as coagulation, diffusiophoresis, thermophoresis, and removal of particles by the shower stream due to a scrubbing action can also influence the activity concentration. However, the contributions from these effects can be estimated to be small and are neglected in this model. For instance, the typical activity concentrations in the bathroom and the relatively short time during showering are not likely to produce a significant amount of coagulation. The concentration gradients are not expected to be large enough to make diffusiophoresis significant. Thermophoresis is likely to be present only as a transient immediately after the shower is turned on when there are significant thermal gradients between the shower stream and the walls. The scrubbing action will be confined to the volume of the shower stream, and the effect is expected to be small for the particle sizes involved. An important simplifying feature of the model is that it keeps track of the radioactive aerosol alone, and mass balance is applied only to this entity. This means that the ambient (non-radioactive) aerosol enters the model only when radioactive progeny atoms attach to it. In the dynamic equations, this is represented via the attachment rates. It is reasonable to assume that the ambient aerosol in the bathroom is in a steady state and that the aerosol that is removed by ventilation and deposition is balanced by that which is drawn into the bathroom from the rest of the home.
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While a typical shower head is not expected to be a significantsource of particles, the ambient aerosol profile in the bathroom could vary during showering if particles are created elsewhere in the home and then drawn into the bathroom due to ventilation. Additionally, there could be hygroscopic growth (11) in the high humidity environment of the bathroom. However, the former situation is not typical, and hygroscopic growth is so rapid (compared with the duration of a typical shower) that it can be considered as a transient which occurs before progeny atoms attach to the existing aerosol. A dynamic treatment of the attachment rates is possible, but the ensuing computational complexity does not seem to be justified for an effect that is either small or not representative. A quasi-static approximation will therefore be made for the ambient aerosol. It is assumed that the sources and sinks (or phenomena such as hygroscopic growth) have been operating long enough for the ambient aerosol to have reached a steady state in the bathroom and that this steady state is maintained while radon builds up and decays. The bathroom could be modeled as two interconnected chambers consisting of the showering area and the rest of the bath. However, air circulation above the shower curtain (or shower stall) as well as the permeability of the shower curtain promote mixing. This is further enhanced by the buoyancy of hot air in the showering area. Therefore, a single chamber representation was considered to be adequate for this analysis. There are two approaches to the modeling. One approach is to use experimentally measured values as input parameters for quantities such as the deposition and attachment rates. The other approach is to develop the model using a semiempirical formalism for the underlying physical phenomena. The later approach was taken in the present analysis so that the model can serve as a predictive tool under different operating conditions. Attachment of the activity to the existing aerosol is relatively well understood and was modeled using Porstendo¨rfer’s formalism (12). Deposition is more complex. Even though diffusiophoresis and thermophoresis can be neglected, Brownian and turbulent diffusion, sedimentation, and laminar as well as convective flow exist to varying degrees and lead to particle deposition onto walls and other surfaces. Depending on the flow regime, different models have been proposed for particle deposition in a room. The turbulent flow paradigm appears to be best applicable to the showering scenario where ventilation (natural or forced) is the primary source of turbulence. Crump and Seinfeld’s deposition model (13), which is a refinement of Corner and Pendlebury’s (14) analysis, forms the basis of deposition studies in this class and was adopted in the present work. The time-dependent size distribution of activity from the dynamic model was combined with the ICRP66 lung dose model (15) for the size-dependent dose to obtain the integrated lung dose as a function of size. Even with identical concentrations of radon in the water, the exposure in different homes/bathrooms can vary due to factors such as bathroom size, ventilation rate, and aerosol profile in the home. Additionally, differences in the use patterns including duration of the shower, time spent in the bathroom after showering, and the number of consecutive showers also influence the exposure. The input parameters to the model were varied to correspond to these factors, and the model was applied to evaluate the range of possible exposures and doses. A comparison of these results with the dose contribution from the steady-state background exposure is presented.
Model Development Dynamic Equations. As in the standard room model, the bathroom is modeled as a well-mixed chamber. The activity is divided by size into an ultrafine mode ( 1; s(t) is the strength of the radon source at time t; λi is the decay constant of the ith species; λv is the ventilation rate; λa(k) is the (speciesindependent) attachment rate of the ultrafine progeny to particles in the kth size bin (λa(1) ) 0); λd(k) is the (speciesindependent) deposition rate of particles in the kth size bin; and ri is the recoil coefficient (non-zero only for i ) 1). Parametric forms for the source function and for the attachment and deposition rates are given in the following subsections. Source. The time-dependent source function, s(t), for radon is assumed to have the following functional form:
s(t) )
rwfwe g(t) V
(5)
where V is the volume of the bathroom, e is the fraction of the radon released from the water, fw is the flow rate of water,
rw is the radon concentration in the water, and
g(t) ) t - ton 1 toff + 1 - t 0
ton e t < ton + 1 ton + 1 e t < toff - 1 toff e t < toff + 1 t < ton or t > toff + 1
for for for for
(6)
where ton and toff are the times in minutes when the shower is turned on(off). The trapezoidal function, g(t), is a computational artifact that approximates the transients that occur when the shower is turned on and off. Any appropriate continuous function could be used here. Experiments performed in our laboratory shower stall (5) have shown that the radon release rate, e, was not particularly sensitive to the shower head design, nor was it found to vary significantly over the range of temperatures encountered in the bathroom. Hence, the release rate is held constant in this analysis. While the primary source of radon is that released by the airborne water droplets, the film of water that forms on the walls and the other surfaces as well as water that collects in the drain could be secondary sources. The contribution from these sources was calculated and was not found to be significant. Attachment. Porstendo¨rfer’s application (12) of Fuch’s attachment formalism yields the following expression for the probability of attachment, β(x), of a radionuclide to an airborne particle of diameter, x:
β(x) )
2πD0x
(7)
8D0 x + vj 0x x + 2∆
where D0 is the Brownian diffusion coefficient, v0 is the mean thermal velocity, and ∆ is the apparent mean free path of the radionuclide. The rate of attachment of the radionuclide to particles in the kth size bin, λa(k), is
λa(k) ) Z
∫
dk+1
dk
β(x)f(x) dx
[
1 1 exp x2π ln σg
]
(ln x - ln dg)2 2(ln σg)2
λd(x) )
[
1 π (2wh + 2lh) sin (keD(x)n-1)1/n + lwh n
[
d (ln x) (9)
with a geometric mean diameter equal to dg and a geometric standard deviation of σg. These parameters are varied to correspond to typical aerosol profiles found in indoor air. Experimentally measured particle size distributions could also be used as an input for the computation of the attachment rate. The results of Ramamurthi et al. (17) are used to estimate the size and the mass of the ultrafine progeny and hence to determine the diffusion coefficient and the mean thermal velocity of the ultrafine clusters. To keep the computation tractable, it is assumed that the attachment characteristics of the ultrafine clusters are species independent. There is some evidence of species dependence in the size of the ultrafine clusters (18), but in the relatively short time frame of showering, only 218Po has time to build in to a significant
]
(
wlvs(x) coth
)]
πvs(x) π 2n sin (keD(x)n-1)1/n n
(10)
where D(x) and vs(x) are the Brownian diffusion coefficient and the settling velocity of a particle of diameter x, respectively. The deposition rate is assumed to be species independent. The parameters n and ke are used to calculate the eddy diffusion coefficient. The length, width, and height of the bathroom are l, w, and h, respectively. The Brownian diffusion coefficient of a particle of diameter, x, is
D(x) )
kBTCslip 3πηx
(11)
where kB is the Boltzmann’s constant, T is the ambient temperature, η is the viscosity of air, and Cslip is the slip correction factor
(
Cslip ) 1 +
(
(
)))
λair x 2.514 + 0.8 exp -0.55 x λair
(12)
and λair is the mean free path of air. The sedimentation velocity of a particle of diameter, x, is
vs(x) )
(8)
where f(x) is the aerosol size distribution function, and Z is the total aerosol concentration. The total attachment rate is obtained by summing the contribution from all the bins. It is assumed that f(x) is lognormally distributed:
f(x) dx )
level, and it is computationally expedient to neglect changes that lead to higher order contributions. In the simulations that were performed, several different aerosol profiles were examined. However, as mentioned in the Introduction, the ambient aerosol profile was assumed to be time-independent during each individual simulation. Deposition. Application of the Crump and Seinfeld (13) formalism to a rectangular enclosure yields the following expression for the deposition rate, λd(x), of a particle of diameter, x:
Fgx2 C 18η slip
(13)
where F is the density of the particle and g is the gravitational acceleration. The deposition rate for the kth size bin (k g 2) is obtained by averaging eq 9 over the bin:
λd(k) )
1 dk+1 - dk
∫
dk+1
dk
λd(x) dx
(14)
The C-S formalism was developed for reactor vessels where turbulence is produced by stirring. The turbulence parameter, ke, was estimated by assuming complete turbulent dissipation of the input energy. This analysis was also applied to a chamber where mixing fans are present and a semiempirical expression derived for ke based on fan specifications (19). However, in the case of ventilation-induced turbulence, it is difficult to estimate ke. Nazaroff and co-workers (20, 21) have estimated the range of variation of ke in indoor air based on air flow velocities in the room. Those estimates are used in the present analysis. Numerical Issues. The system of equations in eqs 2 and 3 is a linear, first-order system of coupled differential equations. The number of independent variables in 3N + 1 where N is the number of bins in the size range of interest. Integration over time is straightforward in principle but is complicated by the existence of a large number of widely differing time scales. An IMSL implementation (22) of the fifth-sixth-order Runge-Kutta algorithm forms the core of our numerical integration scheme. The algorithm is stable provided the error and the convergence criterion are carefully monitored.
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Dosimetric Conversion Factors. The radioactive decay of inhaled short-lived radon progeny in the respiratory tract results in the deposition of R-energy in the cells of epithelial tissue. This energy deposition may result in the special damage to the nuclear DNA that will lead to the transformation of a normal cell into a malignant cell. The ICRP66 lung model (15) was used to evaluate the equivalent lung dose as a function of the radon progeny activity-size distribution using the standard ICRP66 parameters for adult males. Details of the dosimetric calculations and a figure presenting the sizedependent dosimetric conversion factors from ICRP66 (15) for 218Po, 214Pb, and 214Bi are found in Hopke et al. (23).
Input Parameters The values (ranges) of all the input parameters appearing in the model are listed below. Source Parameters. In the field-study home, the concentration of radon in the water (rw) was 555 kBq m-3. The rate of flow of water through the shower head (fw) was 8 L/min, and the fraction of radon released from the water to air (e) was 0.7. In all other simulations, rw was 370 kBq m-3 (10 000 pCi L-1), fw was 10 L/min, and e equaled 0.7. These parameters were held constant since the exposure and dose scale linearly as a product of these terms. Decay Constants. The decay constants in eqs 2 and 3 for Rn and its radioactive progeny are λ0 ) 3.823 days, λ1 ) 3.05 min, λ2 ) 26.8 min, and λ3 ) 19.7 min. Ventilation Rate. Two different ventilation rates were considered. A ventilation rate of 0.5 ACH (air changes h-1) corresponding to the low end of the range for natural ventilation and 4.0 ACH corresponding to forced ventilation with the exhaust fan turned on in the bathroom. Unless otherwise stated, the simulations reported were done with a ventilation rate of 0.5 ACH, so as to obtain a conservative estimate for the exposure. Ambient Temperature. The ambient temperature was held fixed at 20 °C (68 °F). Computation of the attachment and deposition rates indicate no significant variation in these quantities as a function of temperature in the range 20-30 °C. Parameters for the Ultrafine Clusters. The diffusion coefficient, D0, of the ultrafine clusters was taken to be 0.044 cm2 s-1 at 20 °C (16). Assuming that a hydrated cluster contains six water molecules (24) around a 218Po ion, its mean thermal velocity at 20 °C is 1.39 × 10-4 cm s-1. Bathroom Dimensions. The dimensions of the field study bathroom are 4.2 m × 2 m × 2.2 m. Three other cases were considered. A ‘small’ bathroom of 1.5 m × 2 m × 2.2 m, a ‘typical’ bathroom of 2.5 m × 2 m × 2.2 m, and a ‘large’ bathroom of 4.0 m × 2.5 m × 2.2 m. As shown below, the dose is inversely proportional to the bathroom volume. Therefore, the results can be easily scaled for different bathroom sizes. Number of Bins and Size Range. The size range, 0.5-2 nm, was chosen to represent the ultrafine mode. The size range from 2-1000 nm was divided into nine geometrically equal size bins. Particles larger than 1000 nm were not considered since at typical indoor concentrations the dosimetric weight for such particles is too small to make a significant contribution (23). Aerosol Profile. To study a sampling of aerosols produced by particle sources found in homes, three different log-normal aerosol number size distributions were considered: A 167nm geometric mean diameter (gmd) aerosol with a geometric standard deviation (gsd) of 2.5 having 1700 particles cm-3 as measured in the field-study home, a 20-nm 1.4 gsd aerosol corresponding to emissions from a natural gas flame (25), and a 140-nm 1.6 gsd aerosol observed for side stream tobacco smoke (25). In the latter two cases, a particle concentration of 20 000 cm-3 was assumed. The distribution for the 20-nm gmd aerosol is comparable with the smallest activity-weighted
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size distribution we have observed in normally occupied homes (23). Parameters in the Crump-Seinfeld Model. There is some controversy (19, 26) regarding the value of the exponent (n) in the Crump-Seinfeld model. In this study, n was chosen to be 2. The value of the turbulence intensity parameter, ke, was set equal to 0.1 s-1 to correspond to the low end of the range in indoor air in a room without an operating fan (20, 21). There will be some coupling between the rate of ventilation and the degree of turbulence. However, this coupling is expected to be small for ventilation-induced turbulence and was neglected in the model. It is also possible to have increased turbulence without increasing the ventilation rate, such as when a blow dryer is turned on. It was not possible to estimate the change in ke in such a situation, and that scenario was not considered. The values of the remaining parameters needed for deposition are well known. They are included here for completeness: η ) 1.81 × 10-4 P, Fair ) 1.2 × 10-3 g cm-3, λair ) 0.66 × 10-5 cm. The density of the particles (F) was assumed to be 1 g cm-3. Initial Conditions. The radon (and consequently the progeny) activity concentration at the start of all the simulations (at t ) 0) was assumed to be zero, since the goal of this work is to examine the incremental dynamic contribution to the dose from showering. Since the dynamic equations are linear, this dose can be added to the contribution from the background radon to obtain the total dose. In most of the cases that are reported here, the shower is turned on at the start of the simulation and turned off 15 min into the simulation. The period spent in the bathroom after showering was taken to be 15 min. While these times are greater than typical, they were chosen to obtain an upper limit for the dose.
Results In the results presented below, the units for the dose rate are nSv min-1 since it is convenient to express the shower duration in minutes. However, the units for the dose rate normalized for radon are nSv h-1 Bq-1 m3 for comparison with measured steady-state values of this parameter (23). Since values of the input parameters are given in the previous section, they will be quoted below only where additional clarification is needed. Simulation for the Field-Study Home. Figure 1 shows the result of a simulation of the radon activity as a function of time for the field-study bathroom. The radon activity rises while the shower is running, peaks at about the time the shower is turned off, and then falls with a decay rate dictated by the ventilation rate. Also shown are snapshots of the progeny activity 5 min (Figure 1b) and 20 min (Figure 1c) into the simulation. At 5 min, some 218Po is present due to its shorter half-life. It is largely in the ultrafine mode. At 15 min into the simulation, the other, longer lived species are also seen, and the fraction of the attached activity is greater. The main difference from a steady-state scenario is that the progeny activity concentration is considerably smaller than its steady-state value for the same radon level. Also, the progeny activity concentration grows while the radon activity is falling. Figure 2 is a plot of the equivalent dose rate as a function of time. The contribution to the dose rate from each size bin is shown. The total dose rate (circles) is also shown. The dose rate continues to grow for a considerable period after the shower is turned off. This feature makes the time spent in the bathroom after showering an important parameter to be considered in dose reduction. Since the number of particles is relatively small (1700 cm-3), attachment is low and the dominant contribution to the dose is from the ultrafine mode. The dash dot line shows the equivalent dose rate computed by making an instantaneous steady-state
FIGURE 1. (a) Time evolution of radon gas concentration from simulation of the field study home. The radon concentration of the water (rw) is 555 kBq m-3; the rate of flow of water (fw) is 8 L/min, the bathroom dimensions are 4.2 m × 2 m × 2.2 m; and the ventilation rate is 0.5 ACH. (b and c) Progeny activity size distribution corresponding to the above radon profile at 5 (b) and 20 min (c) into the simulation for a 167-nm aerosol with a gsd of 2.5 and 1700 particles cm-3.
FIGURE 2. Plot of the equivalent dose rate as function of time for the field study home corresponding to the simulation shown in Figure 1. The contribution to the dose rate from each size bin is shown as well as the total equivalent dose rate and its value in the instantaneous steady-state approximation. approximation. In this approximation, it assumed that as the radon activity concentration changes, the progeny activity size distribution adjusts instantaneously its steady-state value, and hence the radon profile is representative of the dose rate. Since the progeny are still growing in, this approximation overestimates the dose. The equivalent dose from a 15-min shower followed by 15 min in the bathroom, corresponding to the dose rate shown in Figure 2, is 31 µSv. For a more typical showering time of
FIGURE 3. Equilibrium factor (a) and equivalent dose rate normalized for radon (b) for two test aerosols in a 2.5 m × 2 m × 2.2 m bathroom with rw equal to 370 kBq m-3, a fw of 10 L/min, and a ventilation rate of 0.5 ACH. The circles correspond to the 20-nm aerosol, while the triangles represents the 140-nm aerosol. The particle concentration is 20 000 cm-3 in both cases. 10 min followed by 10 min in the bathroom, the equivalent dose is about 12 µSv. This 10 min/10 min simulation is sufficiently similar in its general characteristics to the 15 min/ 15 min one that these additional figures are not presented here. They are available elsewhere (27). Effect of Aerosol Profile. Figure 3 shows simulations performed for two different aerosols in an average bathroom with a ventilation rate of 0.5 ACH. Figure 3a is a plot of the equilibrium factor as a function of time. The larger diameter aerosol leads to greater attachment, which keeps the activity airborne. The smaller particles are more effectively removed by deposition. Therefore, the equilibrium factor is greater for the 140-nm aerosol and grows proportionately larger as the progeny grow in. The progeny activity grows while the radon level is falling, resulting in higher values for the equilibrium factor than have been reported from steady-state analyses. The equilibrium factor was also found to have higher values in the field-study home and in measurements done in the laboratory shower stall (5). Figure 3b shows the equivalent dose rate, normalized for radon, as a function of time for the two aerosols. Due to the lower dosimetric weight attached to larger particles, there is an inverse relationship between the equilibrium factor and the dose rate. The kink in the curves in Figure 3 corresponds to the time the shower is turned off and is a computational artifact of the radon source function. The horizontal lines are the values that would be obtained assuming that a steady state has been and is continuously achieved. These values are lower than the corresponding median value of 130 nSv h-1 Bq-1 m3 reported for U.S. homes (23). This is not surprising. The smaller confining volume for the bathroom results in a higher surface/volume ratio (than for the entire home) and consequently a higher deposition rate of particles. This in turn reduces the concentration of airborne progeny and, consequently, yields a lower dose rate. Effect of Ventilation. Figure 4 shows a simulation where the ventilation rate was varied from 0.5 to 4.0 ACH in the average bathroom for two different aerosols. As expected, the maximum dose rate is smaller at the higher ventilation rate. Additionally, the peak occurs earlier as the ventilation rate increases. This pattern was also seen in the showering experiments (5). The equivalent dose found by integrating the dose rate for 30 min (15 min in the shower followed by
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FIGURE 4. (a) Effect on the radon concentration of changing the ventilation rate from 0.5 to 4.0 ACH. The bathroom dimensions are 2.5 m × 2 m × 2.2 m, rw is 370 kBq m-3, and fw is 10 L/min. (b) Corresponding variation in the equivalent dose rate for two test aerosols. The particle concentration for both aerosols is 20 000 cm-3. 15 min in the bathroom) is reduced from 69 to 34 µSv for the 20-nm aerosol. Ventilation reduces the corresponding equivalent dose for the 140-nm aerosol from 31 to 14 µSv. Effect of Bathroom Dimensions. Simulations were performed for the three different size bathrooms listed in the section on input parameters. It was found that, to a very good level of approximation, the equivalent dose rate varies inversely as the volume of the bathroom. This is to be expected since the radon concentration is inversely proportional to the bathroom volume. However, there is an additional factor. As the bathroom volume decreases, its surface to volume ratio increases, and this leads to a higher rate of deposition of particles. The consequent reduction in activity concentration works against a purely volumetric increase in dose. The correction is however small for the expected variation in bathroom volume. For reasons of space, those simulations are not presented here but are in Hopke et al. (27). Shower Duration and Time Spent in the Bathroom Subsequent to Showering. Figure 5 shows the result of simulations performed for the two test aerosols by varying the shower duration and the time spent in the bathroom after showering. Each symbol corresponds to a fixed shower duration. Even though the dose rate is initially nonlinear as a function of time (Figure 2), a few minutes after the shower is turned off it is linear to a good approximation. Hence, the doses are linear with respect to the time spent in the bathroom after showering. As noted earlier (Figure 2), the dose rate continues to rise after the shower is turned off. As a result, the dose for a short shower followed by a long stay in the bathroom can equal that of a long shower followed by short subsequent exposure. Reduction of both the shower duration and/or subsequent time in the bathroom are highly effective in dose reduction. For instance, it can be seen from Figure 5 that for the small diameter aerosol the equivalent dose for a 15-min shower followed by 15 min in the bathroom is about 69 µSv, while that for a 10-min shower followed by 10 min in the bathroom is about 26 µSv. For the large diameter aerosol, the corresponding reduction is from 31 to 11 µSv. Sequential Showers. Figure 6 is a simulation of three sequential showers. Figure 6a shows the radon activity as a function of time for three showers lasting from 0 to 15 min, from 30 to 45 min, and from 60 to 75 min. It is not uncommon to have only one bathroom in the home, making such a scenario likely. The field-study home is a case in point. Each successive shower leads to an additional buildup of radon
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FIGURE 5. Results of simulations performed for the 20-nm aerosol (b) and 140-nm aerosol (a) by varying the shower duration and the time spent in the bathroom after showering. Each symbol corresponds to a fixed shower duration. The time axis is time spent in the bathroom following the shower. The ventilation rate is 0.5 ACH, the bathroom dimensions are 2.5 m × 2 m × 2.2 m, rw is 370 kBq m-3, and fw is 10 L/min. The particle concentration is 20 000 cm-3 in both cases. since ventilation only partially removes radon from the previous shower. Figure 6b is a plot of the equivalent dose rate as a function of time for the two test aerosols. The integrated equivalent dose is successively 69, 184, and 289 µSv for the smaller diameter aerosol and 33, 103, and 183 µSv for the larger diameter aerosol. The integrated dose for the nth shower is roughly (2n - 1) times the integrated dose for the first shower. Worst Case Scenario. A simulation such as the one described in Figure 6 was performed for a small bathroom (1.5 m × 2 m × 2.2 m) with no exhaust fan (ventilation rate 0.5 ACH), a small diameter aerosol (20 nm gmd, 20 000 particles cm-3) with three sequential showers. This simulation is the worst scenario among the possibilities that were considered. The integrated dose for the third shower was found to be 482 µSv. Comparison with the Long-Term (Steady-State) Exposure. The average increment in the background dose from radon in the water is given below. [For reference, the average daily background radon dose (non-water) in U.S. homes (23) is 108 µSv]. Using a coefficient of 10-4 (1) for the transfer of radon from the water to the air, the increment in the average background (steady-state) airborne radon concentration in the field-study home is 55.5 Bq m-3, from 555 kBq m-3 of radon in the water. The median equivalent dose rate for U.S. homes was found by Hopke et al. (23) to be 130 nSv h-1 Bq-1 m3. Assuming a 75% occupancy, the average increase in the daily background dose from radon in the water is 130 µSv (55.5 Bq m-3 × 130 nSv h-1 Bq-1 m3 × 24 h × 0.75). The daily
and a reduction in the duration of the shower are both found to be highly effective in dose reduction. A shorter shower also reduces the radon that is released into the rest of the home and so does an exhaust fan that vents to the outside of the home and is operated with the door closed. Thus, both of the above measures additionally reduce the average incremental background radon concentration in the home from water use. The concentration of radon during showering is considerably higher than the background level. However, the short duration of showering and the lower dose rate per unit radon concentration during showering result in the typical showering dose being a relatively small fraction of the incremental background dose. At the same time, the modeling analysis shows that there can be a large variability in the dose, depending on the exposure conditions. In some cases, the dose from showering can exceed the average incremental background dose if the radon concentration in the water is high. It should also be noted that showering is only one of the dynamic components, and when the other dynamic contributions, such as from the kitchen (dishwasher) and laundry room, are considered, the total dynamic contribution to the dose could be significant.
Acknowledgments This work was primarily supported by the American Water Works Association (AWWA) under Research Contract RAD 93-1. It was also partially assisted by the support of the U.S. Department of Energy under Grant DE FG02 80ER61029. The authors would also like to thank Dr. A. C. James for assistance with the 222Rn decay product dosimetry.
Literature Cited FIGURE 6. Simulation of three sequential showers for a 2.5 m × 2 m × 2.2 m bathroom with rw equal to 370 kBq m-3, fw of 10 L/min, and a ventilation rate of 0.5 ACH. Panel a shows the radon activity as a function of time for three showers lasting from 0 to 15 min, from 30 to 45 min, and from 60 to 75 min. Panel b shows the equivalent dose rate as a function of time for the two test aerosols.
(1) Nazaroff, W. W.; Doyle, S. M.; Nero, A. V.; Sextro, R. G. Health Phys. 1987, 52, 281-295. (2) Pritchard, H. M. J. Am. Water Works Assoc. 1987, 79, 159-161. (3) Hess, C. T.; Vietti, M. A.; Mage, D. T. Environ. Geochem. Health 1987, 9, 68-73. (4) Folger, P. F.; Nyberg, P.; Wanty, R. B.; Poeter, A. Health Phys. 1994, 67 (3), 245-253.
increment in the background dose for 370 kBq m-3 of radon in the water is 87 µSv.
(5) Fitzgerald, B.; Hopke, P. K.; Datye, V.; Raunemaa, T.; Kuuspalo, K. Environ. Sci. Technol. 1997, 31, 1822-1829.
The dynamic contribution has to be added to these longterm contribution values to obtain the total increase in the dose from radon in the water. For instance, for a typical 10-min shower followed by 10 min in the bathroom for the field-study home, the model yields a dose of 12 µSv, which would add about 9% to the incremental background dose. For the large diameter aerosol in an average bath with low ventilation, the dose for a typical shower was found to be 11 µSv or a 8% addition to the incremental background dose. Thus, the short-term exposure and dose effects are small as compared to the effect of radon release from the domestic water on the long-term average radon concentration in the home.
(6) Jacobi, W. Health Phys. 1972, 22, 1163-1174. (7) Porstendo¨rfer, J.; Wicke, A.; Schraub, A. Health Phys. 1978, 34, 465-473. (8) Porstendo¨rfer, J. Radiat. Prot. Dosim. 1978, 7, 107-113. (9) Porstendo¨rfer, J.; Reineking, A.; Becker, K. H. In Radon and its Decay Products: Occurrence, Properties, and Health Effects; Hopke, P. K., Ed.; American Chemical Society: Washington, DC, 1987; pp 285-300. (10) Porstendo¨rfer, J.; Reineking, A. Radiat. Prot. Dosim. 1992, 45, 303-311. (11) Dua, S. K.; Hopke, P. K. Aerosol Sci Technol. 1996, 24, 151-160 (12) Porstendo¨rfer, J.; Ro¨big, G.; Ahmed, A. J. Aerosol Sci. 1979, 10, 21-28. (13) Crump, J. G.; Seinfeld, J. H. J. Aerosol Sci. 1981, 12, 405-415.
Discussion While the modeling study draws upon experimental work, it has not been possible to make a direct comparison with an experiment since dynamic measurements are not available for the size distribution of the radon progeny activity concentration. At this point, the model provides a framework to extrapolate beyond the immediate experimental results. Its main strength lies in its ability to simulate a wide range of exposure conditions. The modeling study has examined the influence of parameters such as the aerosol profile, bathroom dimensions, ventilation rate, and shower duration. Increased ventilation
(14) Corner, J.; Pendlebury, E. D. Proc. R. Soc. 1951, B64, 645-654. (15) International Commission on Radiological Protection. Human Respiratory Tract Model for Radiological Protection; ICRP Publication 66; ICRP: 1994; 482 pp. (16) Hopke, P. K. J. Radioanal. Nucl. Chem. 1996, 203, 353-375. (17) Ramamurthi, M.; Strydom, R.; Hopke, P. K.; Holub, R. F. J. Aerosol Sci. 1993, 24, 393-407. (18) Vanmarcke, H.; Landsheere, C.; Van Dingenen, R.; Poffijn, A. Aerosol Sci. Technol. 1991, 14, 257-265. (19) Okuyama, K.; Kousaka, Y.; Yamamota, S.; Hosokawa, T. J. Colloid Interface Sci. 1986, 110, 214-223. (20) Nazaroff, W. W.; Logocki, M. P.; Ma, T.; Cass, G. R. Aerosol Sci. Technol. 1990, 13, 332-348.
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(21) Nazaroff, W. W.; Cass, G. R. Environ. Int. 1988, 15, 567584. (22) IMSL Inc. In IMSL Math/Library; IMSL, Inc.: Houston, TX, 1986; Vol. 1, Chapter 5. (23) Hopke, P. K.; Jensen, B.; Li, C. S.; Montassier, N.; Wasiolek, P.; Cavallo, A. J.; Gatsby, K.; Socolow, R. H.; James, A. C. Environ. Sci. Technol. 1995, 29, 1359-1364. (24) Olawoyin, O. O.; Raunemaa, T. M.; Hopke, P. K. Aerosol Sci. Technol. 1995, 23, 121-130. (25) Li, W.; Hopke, P. K. Aerosol Sci. Technol. 1993, 19, 305-316. (26) Holub, R. F.; Raes, F.; Van Dingenen, R.; Vanmarcke, H. Radiat. Prot. Dosim. 1988, 24, 217-220.
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(27) Hopke, P. K.; Datye, V. K.; Fitzgerald, B.; Raunemaa, T. M.; Kuuspalo, K., Critical Assessment of radon Progeny Exposure While Showering in Radon-Laden Water; Report 90697; American Water Works Association Research Foundation: Denver, CO, 1996; 73 pp.
Received for review February 19, 1996. Revised manuscript received January 6, 1997. Accepted February 10, 1997.X ES9601548 X
Abstract published in Advance ACS Abstracts, April 15, 1997.
