where C(z) is the concentration at depth z in the bed, C(Rn) is the input concentration of the radon in the water, K_ss 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.