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Nuclear Reactor Digitization Project

Raymond L. Murray Reactor Project Notebook

Prepared for the North Carolina State University Science and Technology Electronic Text Center

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Since you pointed out that it was impractical to exhaust the contaminated
gases from the reactor continuously (over a 24 hr. period.), it has been necessary

to reconsider the analysis reported earlier. In addition, an alternative "transit

time" method of estimating necessary holding volumes was proposed by

that gave, a quite different form to the theory and calculated result. In this

note it is shown that such qualitative approaches to the problem do not give the

correct answer. An extension of the previous theory to the case of interrupted

The final conclusion that is reached is that a factor of Xe concentration
attenuation of greater than 10 is achieved by 8 tanks of 100 gallon capacity,

assuming 6 hours per day 10 Kw reactor operation with 100 ml/hr air flow. A smaller

total volume could be used if the number of tanks was increased and the individual

Transit Time Treatment Of Holding System.

Assumptions: Fluid is discharged at a rate v into and out of a container of volume
V. Two possible modes of transfer through the container are (a) steady flow,

Case (a) Regardless of the dimensions of the system, the time ¯t for a given
sample of fluid to traverse the system is given by V/v. (Assume a length of total

path L, area A, then ¯t = L/u where u is the flow speed. However u A = v, so ¯t =

Case (b) The rate at which particles of fluid leave the system is dN/dt=-ρv
where ρ is the no. per unit volume of the selected group, and is N/V. Thus dN/dt = -Nf

where f = v/V. Let ψ(t)dt =

|dN|/N o be the distribution function for transit times.

Extension to Radioactive Deacy: The concentration of exhaust fluid would be

The transit time analysis is applicable to a case in which the radioactive gas
decays into a stable gas which also continues through the system of containers.

In the actual situation, the Xe decays into Cs, which will be largely trapped by

the water chamber walls, etc. The fallacy that is embodied in the transit time

approach is thus readily seen. The average transit time would have to include

all those Cs atoms which are stopped; ie., have infinite lifetime in the system.

Thus it appears that the differential equations approach is more realistic, and so

far as is determined, correct. The revision in calculation by the latter method

REVISED METHOD OF CALCULATION OF SERIES HOLDING EFFECTS

In an earlier report
holding tanks was calculated on the assumption that the discharge was continuous.

system, at a concentration C

o, at a rate v liters per day, for the reactor
ration

o = A/vτ
l of discharge from the first tank during the period τ
is governed by the equation

dC l/

Thus B =
l = 0.511lτ = 0.128

In order to achieve en attenuation of 10, the number of tanks must be that for
which (0.728)

n = 0.1 or

It is interesting to note that the predicted attenuation by transit time theory
is attained only by an infinite array of infinitesimal tanks, as shown below:

Fix the total volume VT = n V, so that the above ratio becomes

One other case besides that of continuous discharge may be analyzed by the same
method: Assume that contaminated air is let in for a period τ, but the system

is flushed with pure air for a period 1 - τ.

λ

l = λ + f in the denominator rather then just λ. The attenuation per tank