PROBABILISTIC ASSESSMENT OF A CRITICALITY IN A WASTE CONTAINER AT SRS Page: 3 of 3
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WSRC-STI-2006-00378
The integral limits range from the minimum critical
mass to the maximum credible fissile mass. The minimum
integral limit chosen for this assessment is one kilogram
of 239Pu. Although a criticality is possible with a lower
fissile mass, the probabilities of the events necessary for
the criticality are so low that inclusion in equation 1 is
insignificant. It is noted that the probability of a criticality
is not very sensitive to the upper fissile mass limit
because of the rapid decrease in the probability of having
a container with a large fissile mass. A credible but
unlikely upper mass limit was assumed to be three
kilograms 239Pu.
The probability of having a drum with a specific
fissile mass was estimated using the assay results of 500
drums whose originally assigned inventory values were
suspect. These drums came from a period in the 1980s in
which human errors are believed to be a major contributor
in generating waste drums with high fissile mass content.
The probability for having a particular fissile mass in a
drum was determined using a log-normal distribution
described by the probability density function (pdf)
presented in equation 2 [1].
1 -0.5 )
pdf e (2)
where x is the natural logarithm of the fissile mass, p is
the mean of the natural logarithm of the fissile mass
values, and 6 is the standard deviation of the natural
logarithm of the fissile mass values for the 500 suspect
drums. The cumulative distribution function (cdf) is then
obtained by integrating equation 2 over the limits of the
mass interval.
From the assayed drum data, the probability of a
drum containing a specific fissile mass was obtained by
dividing the number of drums in a mass interval by the
total number of drums assayed. For the log-normal
distribution, the probability for having a drum containing
a specific fissile mass was obtained from the difference of
the values of the cdf as shown in equation 3.
Probability =cdf KU -cdf KL (3)
where U and L are the upper and lower mass limits,
respectively, of the fissile mass interval. The fissile mass
probabilities are compared in Figure 1.
The probability for enough moderator in a drum to
support a criticality was estimated based on the
radiography of the 500 suspect drums contents. The
probability for optimum fissile material concentration was
estimated based on the required height of a critical fissile
pancake at the bottom of a drum divided by the totalheight of the drum. The probability for sufficiently low
leakage geometry was estimated as a function of fissile
mass in the drum. A larger fissile mass provides more
source neutrons to compensate for a higher neutron
leakage geometry. The probability of the neutron
absorber content was estimated based on the historical
operational data and waste packaging practices.
1 E+OO
a 1 E-02
1 E-0-
a 1 E-04
Pu-2SflMass (g)
Figure 1. Comparison of Assay Results with Log-Normal
Distribution Predictions
The probability of a criticality in a drum having
between 1 and 3 kg plutonium is the product of event
probabilities and the fissile mass probability. Equation 1
may be integrated using the trapezoidal rule to estimate
the probability of criticality. The conditional probability
term, P(Elm), is the average of the product of the event
probabilities at the end points of the mass intervals.
CONCLUSION
The probabilistic assessment study concluded that the
probability of a criticality in a drum at the SRS solid
waste management facility is acceptably low.
REFERENCES
1. R. 0. Gilbert, "Statistical Methods for Environental
Pollution Monitoring," Van Nostmand Reinhold, New
York, 1987.
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Eghbali, D. PROBABILISTIC ASSESSMENT OF A CRITICALITY IN A WASTE CONTAINER AT SRS, article, December 26, 2006; [Aiken, South Carolina]. (https://digital.library.unt.edu/ark:/67531/metadc889453/m1/3/: accessed April 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.