The committee has used an extended-radiation-source program to estimate the annual gamma radiation dose from water treatment units containing granular activated carbon (GAC) for water-treatment-plant workers or for situations where point-of-entry (POE) units are used. The extended source accounts for the distribution of the radioactivity throughout the bed instead of assuming that the radioactivity is located at a single point. This program, MICRO-SHIELD (Grove Engineering Company, Rockville, MD), was used to compute gamma ray exposure rates at locations outside a volume containing radioactivity with a specified distribution of radioisotopes. The program accounts for both the source-receptor geometry and the attenuation of the gamma rays by the materials within the tank (such as water and carbon) and the tank wall. The program also contains several options to correct for the second-order effects of a thick source and attenuation; in this case, the Taylor approximation for build-up was used.

For the present calculations, the committee used a vertical, cylindrical tank with a 1-cm-thick iron wall. The radius and length of the tank were chosen based on standard engineering designs for the POE or water treatment plant flow rates. These water flow rates and tank dimensions are shown in table E.1. Flow rates for POE systems are typically 1 m^{3}/d, while flow rates for water treatment plants using GAC range from 11 to 981 m^{3}/d. Two entries are shown for the highest flow rate. The first represents a tank designed for a pressurized treatment system while the second is for a water treatment tank operating at atmospheric pressure with flow driven by gravity. All of the calculations assumed an input radon-in-water concentration of 185 kBq/m^{3} and an output concentration of 25 kBq/m^{3}.

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E Gamma Radiation Dose From Granular-Activated Carbon (GAC) Water Treatment Units
The committee has used an extended-radiation-source program to estimate the annual gamma radiation dose from water treatment units containing granular activated carbon (GAC) for water-treatment-plant workers or for situations where point-of-entry (POE) units are used. The extended source accounts for the distribution of the radioactivity throughout the bed instead of assuming that the radioactivity is located at a single point. This program, MICRO-SHIELD (Grove Engineering Company, Rockville, MD), was used to compute gamma ray exposure rates at locations outside a volume containing radioactivity with a specified distribution of radioisotopes. The program accounts for both the source-receptor geometry and the attenuation of the gamma rays by the materials within the tank (such as water and carbon) and the tank wall. The program also contains several options to correct for the second-order effects of a thick source and attenuation; in this case, the Taylor approximation for build-up was used.
For the present calculations, the committee used a vertical, cylindrical tank with a 1-cm-thick iron wall. The radius and length of the tank were chosen based on standard engineering designs for the POE or water treatment plant flow rates. These water flow rates and tank dimensions are shown in table E.1. Flow rates for POE systems are typically 1 m3/d, while flow rates for water treatment plants using GAC range from 11 to 981 m3/d. Two entries are shown for the highest flow rate. The first represents a tank designed for a pressurized treatment system while the second is for a water treatment tank operating at atmospheric pressure with flow driven by gravity. All of the calculations assumed an input radon-in-water concentration of 185 kBq/m3 and an output concentration of 25 kBq/m3.

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Table E.1
Estimated Equivalent Dose Rates and Dose at Water-Treatment Plants or in Point-Of-Entry Applications Using GAC to Remove Radon
Flow (m3 d-1)
Tank Radius (cm)
Tank Height (cm)
Case 1: Equivalent Dose at 1 m (µSv/h)
Case 1: Time to Acquire 1mSv (h)
Case 2: Equivalent Dosea at 1 m (µSv/h)
Case 3: Equivalent Dose at 1 m (µSv/h)
1 (POE)
12.7
54.5
0.124
8064
0.137
0.068
11
22.8
185
0.666
1488
0.725
0.387
981 (P)b
91.5
520
5.12
192
7.02
7.01
981 (G)b
152.5
186
4.69
216
6.35
4.01
a The radiation weighting factor of 1.0 was used for these gamma rays.
b P is pressure-driven while G is gravity fed.
The absorbed dose calculation was performed for a point 1 m from the outside of the tank wall and at the mid-point of the tank height. By specifying that the radiation source is Rn-222, the MICRO-SHIELD program computes the source strength for the various radon decay products, assuming that they are in equilibrium with the radon in the carbon bed. Sufficient time was allowed to elapse to permit the radon decay products to reach equilibrium with the radon. This calculation also ignores the very small contribution to the radiation field made by the longer-lived Pb-210 (22.3 years) and its subsequent decay products.
Doses and dose rates were calculated for several different source assumptions. The first case used a 50-50 (by mass) mixture of carbon and water (with a carbon density of 0.42 g/cm3) and assumed that the radioactivity was uniformly distributed throughout the cylinder. The results of these calculations are shown as Case 1 in table E.1. The equivalent dose rate is shown for the point at 1 m from the tank wall and at half the height of the tank. In addition, the total time to acquire an annual dose of 1 mSv is shown.
The second set of calculations were done using an ''idealized'' mixture of water and carbon to give a mixture density of 1.2 g/cm3 (based on the experiment of mixing water and carbon in a known volume and measuring the resultant density). Again, the table shows (as Case 2) the results of the model for the equivalent dose rate.
The assumption that the radioactivity is uniformly mixed within the cylinder is an oversimplification, as the distribution of radioactivity is higher near the entrance to the bed (assumed to be the top of the tank for this work) and diminishes with bed depth. In order to simulate this effect the cylinder was divided into five sections of equal height. The radioactivity in each section was uniform, but the assigned value for each section decreased exponentially from top to bottom according to the following relationship

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where C(z) is the concentration at depth z in the bed, C(Rn) is the input concentration of the radon in the water, Kss is the adsorption/decay constant (GAC-and water-specific; see Appendix C), V is the volume of the GAC and Q is the water flow rate. The resulting absorbed dose rate for this 'five-cylinder' model is shown in table E.1 as Case 3. As can be seen, the estimated dose rate is smaller for the two low-flow GAC units, compared with the single, well-mixed cylinder results. However, for the two examples of the high-flow case, the resulting dose rates are about the same.
Finally, calculations were also done with the CARBDOSE model (Rydell and Keene, 1993), which is intended for POE-type units only. Two calculations were done. The first assumes that the radioactive materials are confined to a point source; this yields an estimated equivalent dose of 0.148 µSv/h. The second is based on an extended radioactive source and gives an estimated equivalent dose of 0.173 µSv/h. These results are not very different and are essentially consistent with the results of Cases 1 and 2 shown in table E.1.