Equilibrium factor

Values of K-equilibrium factors are usually associated with hydrocarbon systems for which most data have been developed. See following paragraph on K-factor charts. For systems of chemical components where such factors are not developed, the basic relation is ... 

This inverse relationship between equilibrium factor and "unattached" fraction and their relationship to the resulting dose is important in considering how to most efficiently and effectively monitor for exposure. This inverse relationship suggests that it is sufficient to determine the radon concentration. However, it is not clear how precisely this relationship holds and if the dose models are sufficiently accurate to fully support the use of only radon measurements to estimate population exposure and dose. 

As indicated above, there is a relationship between particle concentration, equilibrium factor and the amount of highly mobile radioactive particles. Removal of the accumulation mode particles may decrease the decay product exposure, but increase the dose because of the high effectiveness of the "unattached activity in dose deposition. Thus, air cleaning may not succeed in lower risk unless both factors are taken into account. Jonassen explores electrostatic filtration in this context. Finally, design considerations are presented for a possible alternative control system using activated carbon in an alternating bed system. 

From the measured indoor Rn-222 concentration during the heating season, measurements of equilibrium factors and assessments of the seasonal variations, it is possible to assess population averaged indoor concentrations of Rn-222 progeny in Norwegian dwellings. 

Here we have only discussed the concentration of the radon gas. This is because the measurements have been made of this nuclide. However, the health effects are referred to the short-lived decay products. The equilibrium factor depends on the ventilation rate and the particle concentrations. 

The ventilation rate has decreased since the 1950s indicating a higher equilibrium factor and thereby a higher radon daughter increase since the 1950s than the increase of the radon gas concentration. How the particle concentrations have changed is not known. 

Figure 1. Variations in the hourly mean alpha-energy concentration during an integrating radon gas measurement of three weeks The alpha-energy concentration calculated from the radon level (4860 Bq/m3) and the typical equilibrium factor (0.45) is also given.

A survey of the radon concentrations in a representative sample of more than 2000 dwellings in the UK has been completed and provisional results are now available. On average, concentrations are 29% lower in bedrooms than in living areas. The mean radon concentration weighted for room occupancy is 22 Bq m 3. Assuming an equilibrium factor of 0.35 and a mean occupancy of 75%, the mean annual exposure in UK homes is assessed as 0.08 Working Level Months (WLM) and the mean annual effective dose equivalent as 0.43 mSv. 

An equilibrium factor of 0.35, derived from measurements made during the local surveys, has been assumed to typify conditions in UK dwellings. This value has been used to convert the average radon concentrations measured in the national survey to potential alpha-energy concentration of radon decay-products. On average, persons in the UK spend 75% of their time in their homes and 15% of their time elsewhere indoors (Brown, 1983). The occupancy factor of 0.75, together with an equilibrium factor of 0.35, results in an annual exposure of 1.3 10"5 J h m"3 (0.0037 Working Level Months,... 

The average concentration of radon in outdoor air in the UK is 2.6 Bq m"3. Comprehensive data on the equilibrium factor in outdoor air in the UK is not available. Assuming equilibrium, the average exposure to radon decay products received by a member of the UK population during the 10% of time spent in the open is 0.0036 WLM, an annual effective dose equivalent of 0.02 mSv. 

In the radon surveys the primary quantity determined is the indoor air mean radon activity concentration. From a radiological health perspective it is the dose arising from the inhalation of radon daughters that is of interest. The conversion from radon exposure to annualised effective dose equivalent for the survey was carried out using the factors given in Table I which are similar to those being used in other European surveys. The occupancy and equilibrium factors given in this table are assumed mean values for Irish... 

Some of the 220 detectors recently recovered have been analysed not only for radon exposure but also to determine the value of F (the equilibrium factor) in the houses. A preliminary set of such F factor results, obtained by analysing the inner and outer LR- 115 track densities of each detector, are presented in Table III for 12 houses with mean indoor radon concentrations greater than 200 Bq/nP. In Table III are also presented radon daughter doses estimated using the individually determined equilibrium factor values F together with the doses estimated on the basis of an assumed mean F factor value of 0.45. 

The degree of equilibrium of the airborne daughter products with the radon in the air is characterized by the equilibrium factor, F... 

The effect of a given process such as plateout, filtration or field deposition on the PAEC is, however, better expressed by the ratio of the PAEC at a process level, r, to the PAEC at a process level of r =0. This quantity, which like the equilibrium factor is independent of the radon concentration, can adequately be named the ERF (energy- (or exposure) reduction factor)... 

The question of whether exposure rates or doses should be used in evaluating all types of remedial procedures has so far received very little attention. For reasons of convenience the PAEC is normally used, sometimes even estimated from the radon concentration assuming a rather arbitrarily chosen value of the equilibrium factor. It seems reasonable to assume that this in certain cases may give a rather misleading description of the radiological conditions. 

The paper summerizes the experimental data on the equilibrium factor, F, the free fraction, fp, the attachment rate to the room air aerosol, X, the recoil factor,, and the plateout rates of the free, qf, and the attached, q3, radon daughters, determined in eight rooms of different houses. In each room several measurements were carried out at different times, with different aerosol sources (cigarette smoke, stove heating etc.) and under low (v<0.3 It1) and moderate (0.3[Pg.288]

The mean value of the equilibrium factor F measured in houses without aerosol sources was 0.3 t 0.1 and increased up to 0.3 by additional aerosol particles in the room air. The fraction of the free radon daughters had values between fp = 0.06-0.13 with a mean value near 0.1. Only additional aerosol sources led to a decrease of f - values below 0.05. 

The equilibrium factor F = ceq/c0(c0 radon concentration) describes the state of equilibrium between radon and its daughters. 

This paper will summerize our experimental data on the equilibrium factor (F), the free fraction (f ), the attachment rate to the room air aerosol (X), the recoil factor r and the plateout... 

The concentrations of radon (cj) and the free (c f, c2f ) and on aerosol attached (cja, cja, cja radon daughters vi/ere measured and with these data the equilibrium factor F and the free fraction of the radon daughters fp were calculated. The room parameters (e, v) and the parameters of radon daughter transport processes (X, qf, q3, ri) were evaluated by means of equations (3), (4), (8), (9), (10) and (11) using the measured data. 

The equilibrium factor F in low ventilated rooms without aerosol sources varied between 0.2 and 0.4 (Table la) with an average value near 0.30 a similar value as reported by Keller and Folkert, 1983, and by Wicke and Porstendorfer, 1982. In rooms with additional aerosol sources an average F-value between 0.4 and 0.5 was obtained (Table III). An error of about 20 % can be estimated for the equilibrium factor. 

Table lb. The equilibrium factor (F), the free fraction (fp), the attachment parameters (X,0,d), the plateout rates (qf, qa) and the recoil factor (r ), calculated from the measured data of Table la (lo i/ ventilation). 

The mean value of the equilibrium factor F in houses i/as 0.3 0.1 without aerosol sources and can increase up to 0.3 with cigarette smoke in the room air. 

The fraction of unattached daughters (fp), the equilibrium factor (F) and the activity median diameter (AMD) are plotted in Figure 6 for all the measurements. The AMD is derived from the aerosol measurements. These three parameters are important in the dosimetric models. At the top of Figure 6 the effective dose equivalent is plotted, computed with two models called the J-E (Jacobi-Eisfeld) and J-B (James-Birchall) models in the NEA-report (1983, table 2.9, linear interpolation between AMD=0.1 and 0.2 ym). The figure also shows the effective dose equivalent calculated from the equilibrium equivalent radon concentrations with the NEA dose conversion factor (NEA,1983, table 2.11). 

Figure 6a. Evolution of the activity median diameter (A.M.D.), the equilibrium factor (F), the unattached fraction and the effective dose equivalent (AJ-B, V J-E, + NEA) during the case studies.

In Figure 8 the doses per unit radon concentration are plotted as a function of the measured ventilation rate. The NEA conversion factor for low and moderate ventilation (NEA,1983, table 2.10) is multiplied by the appropriate equilibrium factor. In the figure no influence of the ventilation rate on the doses is found. 

In Figure 9 it is shown that the attachment rate is the dominating factor for the unattached fraction. The equilibrium factor however, is also strongly influenced by the deposition rate of the unattached daughters. The curves are calculated as in Figure 7. The limited fluctuations of the actual data illustrate the importance of the attachment rate. 

Figure 7. Effective dose equivalent per hour and per unit radon concentration (AJ-B, 7 J-E) as a function of the equilibrium factor. The full lines are calculated with the mean values of the 72 measurements (Xa -. 37/h, XVent . 41/h, P -. 53, A.M.D. —. 15 lJm) and changing attachment rates.

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