Decay Helium - std301320000062

DOE-STD-3013-2000

which is the middle term of the equation in DOE-STD-3013-96, if the free gas volume, V1, is

defined as

V1 = (Vc - m/ρ)

where ρ is the density of the oxide.

B.2.4

Decay Helium

For a radioactive species, the decay rate (and, hence, the helium generation rate, h, for alpha

decay) is

h=λN

[14]

where λ is the decay constant and N is the number of atoms of the decaying material. As a

function of time, N is given by

-λt

N = N0e .

[15]

The total amount of helium generated, H, over a period of time τ is therefore

-λt

-λτ

H = h dt = λ N0e

dt = N0(1 - e ).

[16]

For values of λτ which are small, the term in parentheses can be replaced by its linear

-λτ

approximation, λτ. This approximation is conservative because λτ ≥ 1 - e . Also, since the units

of H are the same as the units of N0, it is possible to consider both as moles, rather than as

atoms, and the volume of helium thus produced (in liters at STP) is

H = 22.4(1000 m/271)λτ

[17]

where m is the oxide mass in kg, and 271 is the molecular weight of PuO2.

The pressure due to this volume of helium is

PHe = (14.7)[22.4(1000 m/271)λτ](T1/273)/V1

PHe= 4.4507mλτT1/V1.

[18]

239

If it is assumed that the radioactive species is

Pu with a half-life of 24,110 years, then

Equation [18] becomes

-4

PHe = 1.28x10 m τT1/V1.

[19]

Equation [19] is the same as the third term of the equation in DOE-STD-3013-96.