ORNL-CF-62-11-69.txt

UCN-2383
(3 11-60)

OAK RIDGE NATIONAL LABORATORY
Operated by

 

UNION CARBIDE NUCLEAR COMPANY
Division of Union Carbide Corporation 0 R N l
= CENTRAL FILES NUMBER
Oak Ridge, Tennessee | 6 2 l l 2

 

 

 

 

For Internal Use Only
DATE: November 12, 1962 | COPY NO. 2

SUBJECT: Preliminary Equations to Describe Jodine and Xenon
Behavior in the MSRE

TO: Distribution
FROM: J . R' mgel
ABSTRACT
. | Equations are presented to describe the behavior of iodine and

xenon in the primary loop of the MSRE at steady state. These equa-
tions may be programmed for machine solution to obtain the spatial

‘ distribution of xenon in the reactor from which the xenon poison frac-
tion can be estimated. An alternate use of the equations is to evalu-
ate physical parameters from observations made on the operating reactor.

An attempt has been made to include all of the important, or poten-
tially important, behavior mechanisms in the equations. Comments and
suggestions are solicited regarding the mechanisms treated, other pos-
sible mechanisms, and the mathematical representations thereof.

NOTICE

This document contains information of a preliminary nature

and was prepared primarily for internal use at the Oak Ridge

National Laboratory. It is subject to revision or correction

and therefore does not represent a final report. The information

is not to be abstracted, reprinted or otherwise given public

- dissemination without the approval of the ORNL patent branch,
Legal and Information Control Department.

 
INTRODUCTION

Xenon poisoning is a problem of significant interest in the MSRE.
A reasonably accurate evaluation of the xenon poison fraction requires
a detailed description of the xenon behavior in the entiré core loop.
Since most of the Xe is formed by decay of iodine, an equally detailed
description of the iodine behavior is also required. This memo presents
a set of steady~state equations which is intended to fulfill these re-
quirements. A number of effects which may or may not be important in
the reasctor are included while some, for which there is good evidence
that‘they are unimportant, are omitted. The equations describe the fis-
sion product behavior in terms of a number of physical properties of the
system, the fuel and the fission products, even though it may not be
possible at this time to assign accurate values to all of the properties.

This set of equations may be used in two ways. First, if values
are assigned to all of the physical parameters, the equations can pro-
vide an estimate of the xenon distribution and, hence, the poison frac-
tion in the reactor. Second, the equations may be used with the oper-
- ating reactor to evaluate those physical parameters which cannot otherwise
be evaluated. For the latter case it is hoped that the reactor can be
operated under a sufficiently wide variety of conditions to permit simul-
taneous evaluation of a number of the parameters. The use of time~-dependent
forms of the equations and observation of xenon tranSients may be used to
aid these evaluations. | |

The purpose of this memo is to solicit comments and suggestions re-
garding the mechanisms and their mathematical representations. To this
end the text describes all the assumptions and approximations that were
used in developing the equations as well as the equations themselves. It
is expected that revisions to the equations will be required after all
comments are received. The final equations will then be programmed for
solution on the IBM-7090 computer to predict the xenon poison fraction.
Ultimately, a program will be prepared to evaluate physical parameters
from information obtained from the operating reactor.

It is anticipated that the equations which are initially programmed
for computer solution will be simplified approximations of the ones pre-

sented here. Part of this simplification can be achieved by ignoring
behavior mechanisms of questionable importance. However, as a first step
it seems desirable to include all_mechanisms which might be important.
Then, if the simple approximation proves to be inadequate for evaluating
the reactor performance, a more refined analysis can be made omitting

the simplifications.

SUMMARY OF BEHAVIOR MECHANISMS

Several mechanisms are considered for the appearance and disappear-
ance of Xe and I in various parts of the reactor system. These mecha-

nisms may be summarized as follows:

Appearance of Xe in circulating fuel

1. Direct production by fission of uranium in the circulating fuel
2. Decay of I in the circulating fuel
3. Desorption from metal walls

Disappearance of Xe from circulating fuel
1. Radioactive decay
2. Neutron absorption
3. Stripping in the fuel-pump bowl
. Sorption in the graphite
Appearance of Xe in graphite
1. Direct production by fission of uranium in fuel soaked
into the graphite
2. Decay of I in the graphite
3. Sorption from the circulating fuel

Disappearance of Xe from graphite

1. Radioactive decay
2. Neutron absorption

Appearance of Xe on metal walls

1. Decay of I sorbed on the walls

Disappearance of Xe from metal walls
l. Radioactive decay
2. Desorption into the circulating fuel
Appearance of I in circulating fuel
1. Direct production by fission of uranium in the

circulating fuel

Disappearance of 1 from circulating’fuel
l. Radiocactive decay
2. Sorption in the graphite
3. Sorption on metal walls

Appearance of I in graphite
1. Direct production by fission of uranium in fuel soaked
into the graphite |
2. Sorption from the circulating fuel

Disappearance of I in graphite

1. Radioactive decay

Appearance of I on metal walls
1. Sorption from the circulating fuel

Disappearance of I from metal walls

l. Radioactive decay

It may be noted that all mechanisms are not applied equally to both
species. In the case of the sorption processes, only the net currents
are represented and the reverse processes of those given are taken into
account in the concentration gradients. Other mechanisms, neutron ab-
sorption in I and I-stripping, are omitted because they are expected to

be negligibly small.

DESCRIPTION OF EQUATIONS

The equations describing the behavior of iodine and xenon in the
reactor were derived from material balance considerations. In develop-
ing these equations, the reactor system was divided into two parts: a
core in which the detailed spatial distribution of xenon in both the
fuel and graphite was of primary interest and anlexternal loop where
the spatial distribution was less important. With this goal in mind,

the steady-state equations for the core were written in differential

 
form while simplified, integrated forms of the equations were used for

the external loop.

Core Equations

The MSRE core consists of fuel salt flowing through channels and
an array of graphite stringers; both of these materials were treated
separately. The flow pattern of the fuel makes a further division in
the mathematical treatment necessary. Although the established fluid
flow in most of the core channels is laminar, there are regions of high
turbulence at the channel inlets. In addition, turbulent flow may per-
sist over the entire length of some of the channels. Two sets of fuel
equations were developed to cover the different flow patterns. In solving
the xenon distribution problem, the fuel channels will be treated in two
parts, using the turbulent-flow equations for the lower parts and the
laminar-flow equations for the remsinder. Although the transition to
laminar flow does not occur at a sharp boundary, it is expected that a
reasonable approximation to the true condition can be obtained by judi-

cious selection of a fixed transition elevation.

Fuel in laminar Flow

Under laminar flow conditions it is necessary to consider variations
in concentration in both the radial and axial directions within individual
channels. To simplify the treatment the channels are regarded as circular
with a diameter equal to the hydraulic diameter of the MSRE channels and
the neutron flux is assumed constant in the transverse direction in any
given channel. Material balances may then be written for the volume ele-

ment,l 2nr'dr'dz. For xenon

, £ L ’

Y e zaf #(r,z)r'dr'dz - Ao Nke(r',z)r'dr'dz + KINI(r',z)r'dr'dz
£ £ . ¢ 2y a £

+ D, v Nke(r ,2) r'dr'dz - O o d(r,z) Nfie(r',z)r'dr'dz

o Nfie(r'z)
oz

 

- v(r,r') r'dr'dz = 0 . (1)

 

lSee Appendix for definitions of symbols.

 
The various terms represent differential changes in the xenon population
in the volume element due to the following mechanisms, in the order of
the terms: (1) direct production from fission; (2) loss by radioactive
decay; (3) production by decay of iodine; (4) net diffusion from the vol=-
ume element; (5) burnup; and (6) net transport by the flowing fluid.
The diffusion term, as written, includes diffusion in both the radial

and axial directions. In the actual reactor it is likely that axial 4if-
fusion will be much less important than axial transport by the flowing

stream. If this is assumed the diffusion term may be simplified as follows:

 

 

£, 4 £ ., |

Dfie‘v2 Nfie(r',z) r'dr'dz = ‘Dfie [ BEszf: %) + %3 BNie;:',z) ] r'dr'dz .
' (2)

The microscopic velocity, v(r'), varies about a mean, or macro-
scopic, velocity for the channel. In addition, the macroscopic velocity
varies with the radial position of the channel in the reactor. Axial
variations in velocity, both macroscopic and microscopic, are neglected.

An equation similar to (1) can be written for iodine except that
fewer terms are required because fewer mechanisms are involved in the

iodine behavior. Thus:
2
f I I

Ni(rt,z)
- v(r,r') 5 r'dr'dz = 0 . (3)

All of the comments on the xenon equation, including an expression sim-
ilar to (2) apply to the iodine equation.

Fuel in Turbulent Flow

The microscopic radial variations in concentration and velocity
disappear in those channels, or parts of channels, where the fluid flow
is turbulent. As a result the diffusion terms do not appear in the mate-
rial balance equations for this condition. However, a new term must be
included to describe the transport of xenon (or iodine) through the fluid
film, at the channel wall, to the graphite. The volume element for this

condition is nR'adz. Then, for xenon
2
Z ¢(r)z) dz - xe Nx (Z) dz + A NI(z) dz - X hXe *

L L (z) |
[Nie(z) - NxéR"z)] dz - 0' ¢(r z) - v(r) ——3———- dz = 0 . (%)

The quantity, N (R',z), is the concentratlon of xenon in the lig-
uid on the graphite 31de of the fluid film and N (z) is the bulk con-
centration in the liquid. The difference between these quantities is
the driving force for mass transfer across the film.

The equation for iodine which corresponds to (4) is

, .
Y Z #(r,2) dz - A Np(z) - 2, hg [Nf(z) - Nf(a',z)] az

ant (z)
-v(r)T——-— dz = 0O . (5)

Graphite

In order to simplify the mathematics somewhat, the graphite stringers
are regarded as cylinders with an equivalent radius, R", to be assigned on
the basis of the physical dimensions. This treatment is equivalent to re-
garding the reactor as an array of graphite and fuel cylinders in a medium
which has infinite resistance to mass transfer in the axial direction and
zero resistance in the radial direction. The material balance equations
for the graphite are written on the assumption that, if fuel soaks into
the graphite (providing a direct source of fission products), it will be
uniformly distributed in all respects. As with the fuel channels, a uni-
form transverse neutron flux is assumed for the individual stringers.

For a graphite volume element, 2mr"dr'"dz, the material balance for

xenon gives

Y oo Zi @(r,z) r'"dar"daz - A N (r",z)r"dr"dz + 7\I N%(r",z) r'dr"dz

xe ~ xe
. BeNie(r"z)
r'dr'dz + D° r" ar" dz
xe 322

 

 

 

O’ Mlyz) ) A ("e)
3" T or"

- oie d(r,z) Nié(?",z) r"dr" dz = 0 . (6)

+ poF [
Xe
This equation is similar to (1) except that the transport term does not
appear because the graphite is stationary. The diffusion in graphite is
represented as two separate terms and different symbols are used for the
diffusion coefficient in the terms; it has been suggested that the wvalues
of the diffusion coefficient may be significantly different for the two
directions.

The material balance for iodine in the graphite volume element gives

g
"t 1! " " "
Yi‘}af #(r,z) r'"dr"dz - kI N%(r ,2) r'dr"dz

 

 

 

Befig(r",z) 0 Ng(r" z )
+ D%I‘[ I 5 + _:_L_" I I ]r"d.r"dz
dr" - r dr "
- Ng(r" 2 )
+ DE* 612 L rtar'az . _ (7)
z

As before, the comments on the xenon equation also apply for iodine.

Boundary Conditions

A number of boundary conditions are required to fill out the set
of equations for the core. Some of thése are intuitively obviocus while
others require assumptions about the behavior mechanisms. Some boundary

conditions also depend on the nature of the flow in the fuel channels.

Fuel~-Graphite Interfacé -~ Two boundary conditions can be specified at
the fuel-graphite interface. The first of these requires that the net
currents in the two media at the interface be equal; the form of this
expression depends on the type of fluid flow. For xenon, where the

channel flow is laminar

awie (R",2) 2 amie(R'yz)

gr =
D or" = Die or' | (8)

Xe

 

 

For iodine at the same condition

INE(R", z) iR, z)
Dir I _ D:fi I - i (9)

 

gA. Taboada, personal communication

 
10

For turbulent flow in the channels

 

e (R", z)
Diz Xeafu = h_, [Nfie(z) - Nfie(R',z)J (10)
and

NE(R",z)
D%r -Eg;fl—-—- = h [Nf(z) - Nf(a,z) ] : (11)

Expressions may also be written to relate the absolute concentra-
tions in the two media at the interface. For a liquid metal in contact
with graphite at high temperature, it has been found experimentally3
that xenon béhaves as if it were an ideal gas in contact with the liq-
uid when the void volume of the graphite is used as the gas phase. If
the same type of behavior is assumed for molten salt systems, the con-
centrations in the two media can be related by'the Henry's Law constant, H,

for the gas. Thus, for xenon

 

N (R",z) RT
Y (r',z) = X ‘ . | (12)
*e Hee S

Tt seems reasonable to assign the same type of behavior to iodine by

*
using an "effective" Henry's law constant, H . Then

N8(R",z) RT
Nfi(R',z) = z - ) : (13)

HI £

 

Center of Fuel Channels =-- For laminar flow in the fuel channels, an

 

additional boundary condition can be written for the center of the chan-

nel. That is, for xenon

d Nfie(r'=0,z)

S’ = 0 , (1k4)

 

 

3F° J. Salzano and A. M. Eshaya, "Sorption of Xenon in High Density
Graphite at High Temperatures," Nuclear Sci. and Eng., 12, 1-3, (Jan. 1962).

 
11
and for iodine

o Nf (r'=0,z)
o =

 

o . | | @)

Similar expressions could be written for the turbulent-flow condition
but they are not required;because the concentration is assumed constent
across the channel (except in the boundary layer).

Center of Graphite Stringers -- Equations similar to (14%) and (15)

can be written for the center of the graphite stringers. For xenon

 

 

d N8 (r"=0,z)
xear" = 0 , (16)
and for iodine
o N%(r"=0,z) | o
= 0 . | | (17)

or"

Core Inlet -~ The concentration of xenon (or iodine) at the chan-

nel inlet is assumed constant for all chamnels. For xenon

£ L |
Nie(r', z=0) = N ) ’ (18)
and for iodine
Nfi(r',z=0) = Nf Q@ . | (19)

External-loop Equations

The distribution of xenon (or iodine) in the reactor is described
by the core equations presented above for a given core inlet concentra-
tion. However, the concentration at the core inlet is related to that
at the outlet through the processes which occur in the external loop.
Since the detailed fission-product distribution in the external loop
1s not of primary interest, the equations can be greatly simplified by
s set of assumptions which have little effect on the relation between
the concentrations at the outlet and inlet of the core. First it is
12

assumed that the xenon (or iodine) concentration in the fuel does not
change drastically in the external loop. This leads to the treatment
of all of the rate processes in the external loop as constants which
are governed by the mean concentration at the core outlet. Then the
concentration of a species at the core inlet can be expressed as the
corresponding concentration at the core outlet plus or minus the var-
ious small changes that occur in the external loop.

The concentration change due to radioactive decay of an isotope
in an element of fuel as it traverses the external loop is proportional
to 1 - e;kt. However, since the half-lives of xenon and iodine are long
compared to the loop transit time, this term can be represented ade-
quately by At, using the appropriate decay constant for each sPecies.

The retention of iodine and xenon on surfaces in the external loop
is included in this treatment even though the significance of this mech-
anism has not been established for the MSRE.h If iodine, in whatever
form it exists, is strongly held on the metal surfaces the transport to
the surface will be governed by the concentration of iodine in the salt.
It is assumed that xenon (formed by the decay of iodine) will tend to
escape from the surface. This escape tendency can be expressed in terms
of a mean residence time or an "escape" constant, K#, which is similar
to a decay constant. An alternative method might be to use the xenon
concentration difference between the wall and the fuel as a driving force
for mass transfer. The former method is used here because it leads to a
simpler expression.

Xenon stripping in the pump bowl is included with a factor to de-

scribe the efficiency of the stripper configuration.

 

 

- Q Q
£ £ £ s S
Need/ = Nkéé>" e [Axefiéy:)+'égg(}'- H :) ]
Q + 1 g7 e
*
h_ A A
£ [ IAW xe ] _
+ N ALt + e (20)
I® I@ QT(}\ +)\* ) ’
xe xe

 

hR.etention of iodine and xenon in metal scales was an important factor
in the HRT. The predicted absence of such scales in the MSRE may eliminate
this mechanism.

caag
13

and for iodine

£ | £ £ hI A'w |
MO - 5O - 1O N gt St | - (21)
The change terms in the xenon equation represent, in order of thelr ap-
pearance: loss by radioactive decay, loss due to stripping in the pump
bowl, production by iodine decay in the fuel and gain by xenon escape
from surfaces. The terms in the iodine equation represent loss by radio-

active decay and loss to metal surfaces.

Supplementary Equations

The mass transfer coefficients used in the material balance equa-
tions are calculated from the fluid properties and the flow parameters.
As a typical example, the coefficient for xenon is

| o pf (0-67 |
h = 0.023 (Re)©2 v ( ———-—’-E?-) . (22)
xe b

The external-loop equations describe the core inlet concentrations
in terms of the core outlet concentrations which must, in turn, be ob-

tained from the individusl-channel results. For xenon

*

R R!
z 5 . ! !
f0 f(r)fo N (r',L) r'ar' rar | .

 

 

L 2
:qmeifibzz

R'2 R
| jfl f(r) r ar
o

geb

 
O =2 ¢+ =3 P = O P

H

14
APPENDIX
Definitions of Symbols

area
diffusivity

fuel fraction in core

mass transfer coefficient
Henry's law constant

core length

concentration

volumetric flow rate

radial position in core

radial position in fuel channel
radial position in graphite stringer
core radius

fuel channel radius

graphite stringer radius
universal gas constant

Reynolds number

absolute temperature

time

fluid mean velocity

fission yield

axial position

macroscopic cross section

microscopic cross section

(l/
|.’1

>, > =

Subscripts

Xe

He
W

@D

Superscripts

g
L

15

Definitions of Symbols - contd

neutron flux

decay constant

"escape' constant

accessible void fraction of graphite
contactor efficiency in pump bowl
viscosity of fuel

fuel density

of xenon

of iodine

for fission

of stripped liquid (through pump bowl)
of total liquid (in loop)

of helium sweep gas (in pump bowl)

of metal wall outside active core

from position (@) to position (T)(core outlet
to core inlet)

in graphite

in liquid (fuel)

for neutron absorption
in radial direction

in axial direction

at core inlet

at core outlet
s

a)

 
()

e ® * * ® . e

\O O~ O\ FW ~

10.

o E

13.
k.
15.
16.
17.
18.
19.
20.
21,
22,
23.

24 -25,
26.

27-29.
30.

L7

Distribution

MSRP Director's Office,
Rm. 219, 9204-1

S. E. Beall

E. S. Bettis

F. P. Blankenship

W. D. Burch

J. L. Crowley

J. R. Engel

W. R. Grimes

R. H. Guymon

P. N. Haubenreich
P. R. Kasten

R. B. Lindauer

H. G. MacPherson
W. B. McDonald

H. F. McDuffie

R. L. Moore

‘A. M. Perry

B. E. Prince

D. Scott

M. J. Skinner

I. Spiewak

A. Taboada

J. R. Tallackson

Central Research Library
Document Reference Section
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