Methods for Determining the Energy Release in Hypothetical Reactor Meltdown Accidents Page: 30
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30
to give.
Qi dQ(o) 2
dt dt 5
and once again to give
t
Q(t) - dQ( ) fexp(a t'/Z]dt' + Q( O) .~ (16)
dt 0
Equation (16) gives the time dependence of the energy generation
during Phase I in terms of the values d ) and Q() at prompt
critical. To apply the equation, it is necessary to know these quanti-
ties, whereas one would normally know instead the corresponding
quantities at delayed critical or even at some subcritical point.
However, if the equations are applied only for high rates of reactivity
increase, there is not time. for large changes in power level until
prompt critical is reached and the period becomes very short. It is
therefore sometimes satisfactory to just use the subcritical power
level for t , I. e., assume the power has not increased at all
between delayed critical and prompt critical. Alternatively, one can
make an estimate of the increase in power. 29 It is shown in the cal-
culations of Chapter IV that this is necessary for low rates of
reactivity increase. In the calculations it has been found that the
results are not sensitive to the precise value of dtQ( 0 Q( 0) is
the total energy content at time zero and we are free to set it equalto hero, thus establishing the reference point of the energy scale.
The end of Phase I was said to come at a time t1 such that
Q(ts) was sufficiently large to begin to produce pressure, and hence
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Nicholson, Richard Benjamin. Methods for Determining the Energy Release in Hypothetical Reactor Meltdown Accidents, report, December 1962; Detroit, Michigan. (https://digital.library.unt.edu/ark:/67531/metadc38363/m1/42/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.