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