%MurNBholdingtanks000053; %MurNBholdingtanks000053forms; ]> Memorandum from Raymond L. Murray to Clifford K. Beck Machine readable transcription Murray, Raymond L. Creation of machine-readable version: Russell S. Koonts Creation of digital images: Russell S. Koonts Conversion to TEI.2-conformant markup: Russell S. Koonts ca. 20 kilobytes NCSU Libraries Raleigh, NC Modern English, MurNBholdingtanks000053

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 15 November, 2000

Nuclear Reactor Digitization Project

Raymond L. Murray Reactor Project Notebook

 Illustrations have been included from the print version. Scanned by Russell Koonts with Photoshop 5.0 software. Memorandum from Raymond L. Murray to Clifford K. Beck Raymond L. Murray

4 pp. Manuscript copy consulted UA 105.16

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Library of Congress Subject Headings 1953 English LCSH manuscript 24-bit color: 400 dpi Memorandum from Raymond L. Murray to Clifford K. Beck Typescript 4 pp. 1953 MurNBholdingtanks000053

Murray TO: Clifford K. Beck FROM: Raymond L. Murray SUBJECT: Effectiveness of Series Holding System for Radioactive Gases.

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 of Xe discharged is correspondingly small.

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 to the stack, for steady operation.

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 Co.

Set up the differential equation for Xe added and removed on a concentration basis. (See Appendix 1)

Where C is the ratio v/V

Considor also decay, which adds a term -C1λ

and let λ1 be an "effective" decay constant = λ + f.

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

For which the solution is, by the usual methods,
The highest concentration is
smaller than that injected, even at
.

The balance equation for the second tank is

or

As shown in the appendix 2, the solution is

In general, for the nth tank, as shown in appendix 3,

which is soon to involve the first n terms of the series expansion of eλ1t. That the concentration goes to zero for all times in an infinite sequence of tanks is verified. The drop is made more rapid by virtue of pa rtial cancel- lation of terms on the right side of the equation.

Numerical Example

Assume that 12 curies of Xe are available for discharge by the time one day has elapsed from the termination of a six hour operting period of the reactor.

These will decay negligibly during the discharge period of one full day, and in fact it is conservative to take the maxime value.

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 coef- ficient

, so it may be used for calculation purposes.

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.

The discharged activity is of concentration
, which is tabulated along with the activity itself for various numbers of tanks, No. of tanks, nCn/CoCuries/day 10.4355.320.1892.330.0821.040.0360.4450.0160.19

Appendix 1

Derivation of Differential Equations

Let N be the total number of Xe atoms in a container of volume V, and define the concentration C1, as N/V. The number added par unit time is CoV where Co is the number per unit volume in the intake; the number removed per unit time is Cv. Thus

or
the effect of decay is to bring in a term -Nλ in the first equation of -Cλ in the second

Appendix 2

Solution of equation for C2
∴
At

Appendix 3

Solution of equation for C3
∴
By extension it is clear that the solution for n tanks is