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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
The lineation of the manuscript has been maintained and all end-of-line hyphens have been preserved.
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The principle of operation of the system sketched in Figure I is as follows:
1. An active gas such as Xe is introduced into the first of a sequence of
chambers. Initially, the tank is full of air only. A water seal isolates
the tanks.
2. The discharge to the next tank is composed of air and Xe in the proportions
characteristic of the mixture at that particular time.
3. The gas exhausted to the stack by the pressure due to air flow is at a low
concentration. Since the air diluent volume is conserved, the absolute amount
Theory of Approach to Equilibrium.
Let v be the volume of air containinr the discharged active material that is
introduced per second to the system. This must be the same as the volume sent
Let V be the volume of a given tank, of which a number n may be used.
Let C1 be the concontration of Xe (number of atoms/unit volume) in air at any
point in the system. That sent in initially is taken as C
o.
Set up the differential equation for Xe added and removed on a concentration
basis. (See Appendix 1)
Considor also decay, which adds a term -C1λ
It is assumed that the Xe itself is of negligible volume in comparison with the
air at any time and does not perturb the volume from which concentration is
computed. Thus
The balance equation for the second tank is
As shown in the appendix 2, the solution is
In general, for the nth tank, as shown in appendix 3,
Numerical Example
Assume that 12 curies of Xe are available for discharge by the time one day
These will decay negligibly during the discharge period of one full day, and
Assume that a set of n tanks of volume V are arranged to accept this; let the
ratio of daily volume v of air that comes from the recombines to dilute the
Xe to the tank volume
be f = v/V.
The concentration of material exhausted to the stack is at time t large
The maximum value of the ratio at time t Cn/Co can be no larger than the
Evaluate λ + f for a typical example:
10 cc/min for 6 hours gives 10 x 360 = 3600 cc = 3.6 liters.
This is to be released over a day's period.
Assume the tanks have a volume of 10 gallons,
~ 40 liters, then f ~ 0.1.
Derivation of Differential Equations
Let N be the total number of Xe atoms in a container of volume V, and define
the concentration C
1, as N/V. The number added par unit time is CoV where
C
o is the number per unit volume in the intake; the number removed per unit
time is Cv. Thus
Solution of equation for C 2
Solution of equation for C 3