12.160. In calculating the expected radiation doses received from any airborne radioactive material that might escape from the reactor contain­ment structure, it is assumed that the material forms a plume similar to that from a smokestack but closer to the ground. The plume is carried forward by the wind while diffusion causes it to spread in two perpendicular directions, i. e., laterally (crosswind) and vertically. Observations made on small plumes indicate that diffusion would result in a Gaussian distribution (§9.165) of the radioactivity concentration about a centerline. According to the Gauss plume model, assuming that the containment vessel constitutes a continuous point source, the distribution of the radioactivity on the ground, from a specific radionuclide, would be represented by

(12.3)

where x(*, y) Bq/m3 is the ground-level concentration of radioactivity at a point x, y; Q Bq/s is the source strength of the given nuclide, и m/s is the wind speed, assumed to be uniform in the x direction, h m is the effective release height of the radioactivity, and у m is the lateral distance of the receptor from the plume centerline; ay and az are the standard deviations of the distribution in the plume in the у (lateral) and z (vertical) directions, respectively.

12.161. The values of ay and a2, which are functions of the distance x of the receptor from the source, have been determined from experimental studies; they are presented in graphical form in Figs. 12.12 and 12.13, for various atmospheric conditions, designated Pasquill categories A through F. Pasquill A refers to an extremely unstable atmosphere whereas Pasquill F is a moderately stable condition. Thus, if Q, w, and h are known, x(*, y) can be determined for various atmospheric conditions from equation

12.162.

The source strength Q for a particular radionuclide is deter­mined in the following manner. The saturation (or equilibrium) activity in a reactor which has been operating at a specified thermal power can be calculated along the lines indicated in §2.122. Values for the radioiodines obtained in this manner are given in Table 12.2. From the equilibrium activity of a particular radionuclide, the assumed release fraction, the di­mensions of the containment structure, and the maximum design leakage rate from the containment vessel, the source strength Q in Bq/s can be readily evaluated.

12.163. In making radiation dose calculations, у in equation (12.3) is

set equal to zero; the result

then applies to the radioactivity concentration on the ground along the plume centerline where the dose would be a maximum for a given value of x. This expression is assumed to hold for the first 8 hours after a presumed release of radioactive material, e. g., after an LOCA. For times greater than 8 hours, the wind is supposed to vary somewhat in direction so that the plume is spread uniformly over a 22.5° sector; the resulting equation is then

Fig. 12.13. Vertical dispersion coefficients for various atmospheric conditions.

12.164. For radioactivity escaping from a containment structure, the release is fairly close to ground level; hence h in equations (12.4) and (12.5) is taken as zero and the exponential terms are then equal to unity. The atmospheric conditions for the first 24 hours are assumed to correspond

TABLE 12.2. Equilibrium Activities of Fission-Product Radioiodines Nuclide Radioactive Half-Life Effective Fission Yield Equilibrium Activity flO13 Bq/MW (thermal)] Iodine-131 8.05 d 0.028 89 Iodine-132 2.3 h 0.041 130 Iodine-133 21 h 0.068 211 Iodine-134 52 min 0.072 226 Iodine-135 6.7 h 0.064 200

to Pasquill F with a wind speed of 2 m/s (about 4.5 mph); under these conservative conditions the calculated doses will be much larger than would be generally expected. More realistic atmospheric conditions are postulated for later times.

12.165. In the case of a release near ground level, allowance must be made of the turbulent wake resulting from the presence of the reactor building. The wake will cause additional dispersion of the radioactivity, thereby reducing the concentration on the ground. For the first 8 hours after a release, a dispersion factor, not exceeding 3, is introduced into the denominator of equation (12.4) with h = 0; the factor decreases with the (minimum) cross-sectional area of the building (at a given distance from the source) and with the distance (for a given area). After 8 hours, the effect of the building wake is ignored, i. e., the factor is unity.

12.166. Examination of equations (12.4) and (12.5) shows that, for a given (or zero) release height h, the quantity x(x)u/Q is a function only of the distance in the x direction from the release point and of the Pasquill criterion. Curves of x(x)u/Q versus x for various release heights and at­mospheric conditions have been published. These curves greatly facilitate the evaluation of x([24]) from a known source.

Whole-body dose

12.167. For a radioactive cloud (or plume) with dimensions that are small relative to the effective range of the gamma rays emitted from the cloud, the dose at a given point will include radiations received from various parts of the cloud. Calculations of the dose rate (or dose) are then very complex. If, however, the cloud is large and uniform, an equilibrium con­dition exists, and the rate of energy absorption per unit volume of air will be the same as the rate of energy release. Suppose that the concentration of a given radionuclide in a large uniform cloud is x Bq/m3,_i. e., x dis/s • m3, and the average gamma-ray energy per disintegration is Ey MeV, i. e., 1.60 x 10~13 Ey J/dis, then

Rate of energy release (or absorption) in air = 1.6 x 10~13

where p is the density of air in kg/m3. In soft-body tissue, the energy absorption would be 1.1 times that in air;* hence, upon taking p as about 1.3 kg/m3 and recalling that 1 rad represents the absorption of 10~2 J/kg,

it follows that

Absorbed dose rate in body tissue ~ 1.2 x 10-11 Ey rad/s. (12.6)

12.168. The value of x obtained from equation (12.4) or (12.5) is for a receptor at ground level. The gamma-ray dose received by an individual on the ground at the center of an “infinite” cloud would be roughly half that given by equation (12.6) owing to the presence of the ground which limits the source to a 2tt solid angle. The gamma-ray dose rate in body tissue (or the whole body) would then be

Whole-body dose rate ~ 0.6 x 10~n Ey rem/s,

where rems have been used in place of rads since they are essentially equivalent for gamma rays (§6.37). If the radionuclide concentration is assumed to remain constant over the exposure period of t s, the gamma — ray dose received in that time is

Dy ~ 0.6 x 10-11 XEy t rem.

In view of the various assumptions and approximations made, this expres­sion gives doses that are substantially larger than would realistically be expected.

Thyroid dose

12.169. The dose to the thyroid would arise mainly from breathing air containing radioiodines (see Table 12.2). If x, Bq/m3 is the average con­centration of radioiodine in the air, В m3/s is the breathing rate, and t s is the time during which the iodine-laden air is breathed, the initial amount C0(l) Bq of radioiodine taken into the lung is given by

Q)(0 = XiBt Bq.

For a conservative calculation, no allowance would be made for depletion of radioactivity from the plume as a result of deposition on the ground or for radioactive decay in transit from the reactor site to the point at which C0(z) is to be determined. In a realistic calculation, however, such factors would be taken into account.

12.170. Hence, in a conservative calculation, x,- is obtained from equa­tion (12.3), etc., with Qt Bq/s equal to the rate of escape of radioiodine from the containment vessel (cf. §12.159). For the first 8 hours after a postulated accident, В is assumed to be 3.47 x 10“4 m3/s, and from 8 to 24 hours it is 1.75 x 10"4 m3/s. Subsequently, until the plume has passed, the normal breathing rate of 2.32 x 10-4 m3/s is assumed. From these data, the value of C0(/) for a particular radioiodine can be determined. For iodine-131, this is related to the thyroid dose commitment by equation (6.8) in the form

Doo (in rem) = C0(i) (in Bq) x 4.1 x 10~5,

where rads are replaced by rems because they are essentially equivalent in this instance. Similar evaluations may be made for the other radioiodines or, more simply, the dose from iodine-131 may be multiplied by 1.9 to obtain the total iodine dose. The factor 1.9 takes into account the equilib­rium amounts (Table 12.2) and the dose equivalents per becquerel of the various isotopes.