Exhalation rate

In areas where the highest indoor Rn-222 concentrations were measured, the source term was studied at the site. Houses with high concentration were inspected visually, especially the basement, and the heating and ventilation system was discussed with the householders. Field measurements of Rn-222 exhalation rates were perfored near the houses and at furture building sites in the municipality. 

The method for the exhalation rate measurements is based on the same activated charcoal/TLD combinations as the dosimeter for measurements of indoor Rn-222. Details on the method is published elsewhere. (Stranden et al, 1985.)... 

In Table I results of Rn-226 activity measurements cn geological samples are shewn together with measurements cn Rn exhalation rates from the sanples. The exhalation rates varies considerably with the moisture content of material. The exhalation rate is lew for dry samples and when the moisture content increases, the exhalation rate increases until it reaches a plateau. When the moisture content increases further, a rapid increase in radon exhalation occur. When the saturation level of moisture is reached, the exhalation rate drops dramatically. The exhalation rates given in Table I are obtained by assuming that the most probable moisture content is whithin the plateau of exhalation rate/moisture curve. (Stranden et al, 1984, Stranden et al, 1984a). 

Table I. Activity concentrations and exhalation rates from sanples...

Material No Of sanples Activity concentration of Ra-226 (Bq kg l) Exhalation rates from sanples + (Bq h l kg l)... 

Table II. Indoor Rn-222 concentration and exhalation rates from the ground surface in different areas...

In the granite and alum shale areas, exhalation measurements above the ground were well correlated with the indoor air measurements. In the esker area, the exhalation rates were normal, and the high indoor Rn-222 concentrations here are believed to be caused by convective flew due to underpresure in the houses. (Stranden et al, 1985). 

Building material Ra-226 activity concentration (Bq kg-1) Range and mean Exhalation rate per unit mass and unit Ra-226 activity concentration (Bqh lkg l)/(Bqkg l) Estimated range of exhalation rate frcm typical walls (Bqh l m 2) ++... 

Based on Ra-226 activity concentration, typical wall thickness and exhalation rate measurements frcm samples and walls. (Stranden and Berteig, 1980 Stranden 1983, Stranden et al, 1984 Stranden et al, 1984a.)... 

The highest indoor Rn-226 concentrations occur in areas with alum shale in the ground. Measurements in these areas yield a good agreement between exhalation rates and indoor Rn-222 concentrations. Even in granite areas, high indoor Rn-222 concentrations may occur, but no extreme values were found in such areas. These findings are also confirmed by the field studies. 

In order to simplify the situation, we assume that our porous sample under investigation covers the bottom of an open straight-walled can and fills it to a height d (Figure 1). Such a sample will exhibit the same areal exhalation rate as a free semi-infinite sample of thickness 2d, as long as the walls and the bottom of the can are impermeable and non-absorbant for radon. A one-dimensional analysis of the diffusion of radon from the sample is perfectly adequate under these conditions. To idealize the conditions a bit further we assume that diffusion is the only transport mechanism of radon out from the sample, and that this diffusive transport is governed by Fick s first law. Fick s law applied to a porous medium says that the areal exhalation rate is proportional to the (radon) concentration gradient in the pores at the sample-air interface... 

Figure 1. A semi-infinite slab of thickness 2d in open air has the same areal exhalation rate as the open surface of the subsample of thickness d in an open can. The height coordinate is denoted by z. When the can is closed the outer volume height is h.

From Figure 3 we have that the radon concentration after 4 minutes is about 6.5 Bq m 3 in the outer volume of the can. Let us assume that the can has a horizontal cross section area of 0.2 m. The outer volume is then 20 litres and the concentration 6.5 Bq m" corresponds to a mean exhalation rate of 2.7 mBq m 2 s l, which is lower than the free exhalation rate by a factor 3.15/2.7= 1.17. 

If our mission is an experimental determination of the free exhalation rate we are in difficulties. Still with the sample in Figure 2 as an illustration, we see that even if we take a grab... 

Figure 2. The areal exhalation rate as a function of time after closing the can. Sample geometry and data as shown (theory).

Figure 3 The internal radon concentration of the sample in Figure 2 at time of closure (corresponding to free exhalation rate) and four minutes after closure of the can (theory).

The conclusion from the experiment illustrated in Figures 2 and 3 is thus that the exhalation rate will change so rapidly after closure that only a mean exhalation rate, significantly lower than the free exhalation rate, can be measured. This problem can be solved if we choose our sample geometry differently or make another approach to the grab sampling from the can. These things will be dealt with in the next section. 

One, or actually two questions must be raised in connection with the exhalation behaviour exemplified in Figure 2. For how long will the exhalation decrease and what is the final steady-state exhalation value The latter question is the easier one, as the quotient free exhalation rate, Eq, to final steady-state exhalation with the can closed, E, is (cf. Figure 2 for the notation) ... 

For a thin sample (d<0.5L), like that in Figure 2, the quotient is equal to (1+a)/ a where a equals h/(pd), the outer to inner volume ratio. Applying Equation 2 to our case in Figure 2 the steady-state exhalation rate is simply half of the free exhalation rate. 

Table I. The 95% gradient reshaping times (see text) for different combinations of sample thickness, d, outer volume height, h, and diffusion length, L. The quotient free exhalation rate, Eq, and the final steady-state exhalation rate, E, is also given.

If we choose a much larger than 1 (thin samples d<0.5L) or h pL (thick samples d>>L), the final steady-state exhalation deviates very little from the free exhalation rate and we do not need to know the reshaping time or use Equation 2 for corrections. An air grab sample taken at any time (and corrected for radioactive decay if necessary) after closure, will yield the free exhalation rate to a good approximation, provided that the can is perfectly radon-tight. 

The thin sample case is illustrated in Figure 4, in which the time behavior of the exhalation rate is given with the outer volume height as parameter. 

Figure 6 displays exhalation rate curves versus time for the sample in Figure 2, with the leakage factory as the variable parameter. Large leaks make the final steady-state exhalation rate deviate less from the free exhalation rate, in accordance with Equation 4. It must be remembered, however, that the radon activity accumulating in the outer volume is dependent on y, the exhalation rate is only the strength of the radon source feeding this volume. 

What kind of experiments can be done to elucidate the special features of the time-dependent diffusion theory as applied above One of several possibilities is to choose a sample/can geometry in such a way that the initial change in slope of the outer volume concentration as a function of time is pronounced. This is equivalent to saying that the final exhalation rate should be significantly lower than the free exhalation rate and that the gradient reshaping time should be fairly short, of the order of hours. Results from such an experiment are displayed in Figure 7. Notice the characteristic constant slope (about 11 kBq m" h l) of... 

Figure 5. The areal exhalation rate from the porous sample in Figure 2, enclosed in three different exhalation cans. Two of them ( a1 and 0 ) are completely radon-tight and the third Cb1) has a radon leak rate constant v, numerically equal to the radon decay rate constant (v=A= 2.1 10" s" ). The cans are closed at time zero. The radon exhalation evolution as a function of time is discussed in the text (theory).

Figure 6. The areal exhalation rate during the first 200 hours after closure, from the porous sample in Figure 2, with the leakage factor yas the variable parameter (yis defined in Figure 2) (theory).

Jonassen N., The Determination of Radon Exhalation Rates, Health Physics 45 369-376 (1983). 

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