The dose at any point may be calculated according to the following equa­tion

dose = (total inventory) (fraction released) BR J (%IQ) Q(t)DCF dt (5.2)

where BR is the breathing rate (3.47-10-4 m3/sec), DCF is the dose con­version factor (disintegrations/Ci), and xlQ is the meteorological dispersion factor.

The release rate is Q(t), taking leakage from the containment into account as well as plate-out, filtration, agglomeration, and decay removal mecha­nisms. Also included in Q{t) is allowance for any hold-up due to a double barrier containment, so it is a sum of a set of exponentials, each with a different removal decay time constant.

Q(0 = E Qoi ех-Р(—(/Т() (5.3)

і

The integral in Eq. (5.2) will be integrated over 2 hr for the site boundary dose and over 30 days for the low population zone boundary does. As the dose conversion factor (DCF) and Q(t) are both dependent on the isotope involved, the integral will also be integrated over the isotopes of interest (the iodines for the thyroid dose and all isotopes for the whole body dose).

For a double containment design in which leakages from the inner and outer barriers are typified by the inverse time constants A* and A2, Q(t) is given by

6(0 = AjA2C0[exp(—AjO — exp(— A2t)]/(A2 — Aj) (5.4)

where C0 is the inner containment fission product concentration.

The calculation of C0 is a critical part of the dose calculation.

Codes have been produced (10a, b) which, starting with an initial aerosol distribution and concentration within a containment volume, model and calculate the agglomeration and plate-out of the aerosol to derive its chang­ing concentration as a function of time (10c). The methods are also used in following the behavior of a sodium aerosol as a function of time. The assumption of agglomeration is critical because, for larger aerosol concen­trations, the rate of agglomeration increases and the ensuing concentration at any given time thereafter reaches a maximum. Thus the dose calculated as a function of the initial aerosol concentration saturates as the agglomera­tion removes more and more of the initial material. Thus C0 is obtained from these agglomeration calculations which are checked by experimental settling data.