ORNL-TM-0262.txt

 

  
  

f
E5h, N

OAK RIDGE NATIONAEL
operated by

UNION CARBIDE CORPORATION
for the

U.5. ATOMIC ENERGY COMMISSION

 

 

ORNL- TM~ 262

corvno. - 4

DATE - June 27, 1962

 

XENON DIFFUSION IN GRAPHITE: EFFECTS OF XENON ABSORPTION IN
MOLTEN SALT REACTORS CONTAINING GRAPHITE

G. M. Watson and R. B. Evans, IIT

ABSTRACT

Estimates have been made of the xenon poison fraction in a
hypothetical molten salt reactor operating at steady-state
conditions near those projected for the MSRE. The polson
fraction was expressed as a function of the Xe-135 concen-
tration in the molten salt fuel, the free gas space over the
fuel, the pores of the unclad graphite contacting the fuel,
and the corresponding volumes.

Xenon transport rates were considered the various combinations
of generation, burn-out, decay, removal via helium stripping,
and diffusion into graphite. Particular attention was given
to & discussion of the graphite porosity, permesbility, and
xenon diffusion coefficient. These parameters govern the rate
of xenon diffusion into the graphite moderator.

The computations established that permeability and/or porosity
reduction coupled with increased

NOTICE

This document contains information of o preliminary nature and was prepared
primarily for internal use at the Ock 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 dis-
semination without the approval of the ORNL patent branch, Legal and Infor-
mation Control Department.
stripping rates effectively decrease the xenon poison frac-
tion and increase neutron economy. Within the range of
graphites currently under consideration for the MSRE, in-
creased stripping rates appear to be the most effective
means of reducing the xenon poison fraction. At the circu-
lation rates considered, it was found that neutron economy
(with respect to xenon) could not be advanced through per-
meability reduction alone.

INTRODUCTION

The possibility of employing unclad graphite in direct
contact with the MSRE fuel leads to four contingencies,
which must undergo continual and thorough examination, as
conceptual designs approach specification form. These con-
tingencies are:

1. Deposition of solid U0, arising from oxygen in-
troduced via the graphite

2. Invasion of the graphite by the molten fuel

3. Variable reactivity resulting from a variable
Xe-135 concentration in the graphite

4. High xenon poison fraction

The first three items could result in erratic reactor
operation; the last item is of importance from a standpoint
of neutron economy. Research efforts, which are slanted to
yield information applicable for evaluating these difficul-
ties, involve: volatile impurity contents of graphites,l
molten salt absorbability of graphitesz (also UF, to UOQ,
conversion due to impurities), effects_of pore size distri-
bution of graphites and we&ting agents~ and studies of gas
transport in porous media.

In addition to the third and fourth difficulties
mentioned, it has been shown that Cs° for which Xe-135 is
a precursor, is not compatible with graphite. The role o
Cs° in gas cooled reactors has been discussed by Rosenthal
and Cantor.’

A comparison of proposed methods for xenon control has
been presented by Burch. More recent computations have
been made by Spie&wak.9 The results of both studies are
quite different with respect to xenon control and graphite
requirements as the earlier work was based on high circula-
tion rates and the presence of a large decay dome in series
with the pump. These features have been eliminated in pres-
ent designs which lead to increased driving forces for the
xenon absorption by the graphite.

The primary objective of this report was to extend the com-
putations by Burch to lower ranges of removal rates to de-
termine the feasibility of using low permeability graphites
under the more recently projected conditions, In view of
this objective, considerable discussions of the graphite
parameters of interest are presented.

BASIC CONSIDERATIONS

Xenon Poison Fraction

Maximum Poison Fraction

 

A maximum poison fraction indicates a low level of
neutron economy, and a relatively high rate of Cs® produc-
tion within the graphite. Since the maximum fraction ap-
pears as a limiting value for many of the curves presented,
a brief discussion of maximum poisoning follows.

The maximum poison fraction is the product of three
factors: the ratio of Xe-135 burn-out to total Xe-135 loss,
i.e., ($p0)/($,0 + Axe)s the moles of Xe-135 formed per
fission, and the ratio of neutrons causing fission to the
total number absorbed by U-233. Thus,

O 2.21
P.F. | = [_,,.._;..E___.,.._% (6.2:10™%) g ) - (1)
ax. ¢cc + RXe .5

This expression is based on the assumption that all the
Xe-135 which does not decay 1is burned out in. the reactor
core. Since Ay, is the decay constant, (sec)™, the power
level contribution is contained in the Xe-135 destruction
constant ¢eo, (sec)~l. To show the effects of Xe-135 re-~
moval by stripping and Xe-135 absorption by graphite, one
must employ a destruction ratio which is more complex than
that appearing in Eq. 1.

Poison Fraction with Removal Rates

The complete destruction ratio may be developed by con-
sidering a steady-state Xe-135 mass balance and the total
neutron captures by Xe-135, Let: np be the diffusion rate
of Xe-135 into the graphite, fis be the removal rate at the
primary pump, nj, be the Xe-135 dissolved in 211 the salt,
and nyp,. be the amount of Xe-135 dissolved in the core salt.
The poilson fraction is given by

$e0

on —————— « N
P.F. (%) = (éc Le ¥ ¢.0 + xe D ) (5.48) (2)
écOnLc + kX@nL + nS + nD

The variables, n;, DLcs and ng can be expressed in terms of

reactor parameters through the use of the noble gas solu-
bility relationship, that is,

n, = Cg (KPRT)VL, (3a)
nj, = C, (KpRT)VLc, (3b)
A, = C, (KpRT}QS, (3¢)

where V and Qg are volume and volumetric strip rate, re-
spectively, and C, is the gas phase xenon concentration in
equilibrium with the dissolved concentration, nL/VL. The
Henry's law constant is given by Kp.

Typical plotslo?ll’lz of Kp versus temperature for
various mixtures are shown in Fig. 1.

Only one stripping term, ng or Qg, appears in Eq. 2 as
current plans for the MSRE call for one free gas space at
the primary pump bowl. The bowl will be swept with helium
and will see Xenon-saturated salt at a rate equivalent to
Qg, which is (0.04) (circulating pump rate). A rough sketch
salt-atm)

[
o

Xenon Solubility Constant (molie Xe/cc

NaF-BeF,
x\x\\\\\ N (57-43)
\ \.
- LiF-BeF, \\\\\\\\ -
(64-36) \

(x10
11

 

 

 

 

 

 

 

- 5 - ORNL~L.i-Dwg. 56196
o Tnelgssified
emperature, C

800 750 700 650 600 550 500

{ | | K i | N

I i I { ¥ I 1
Ets\

‘\\\\\\\\\

NaF-ZrF, -UF,
NN (50-46-4)

 

L

 

X

X

 

 

 

 

 

 

 

 

 

™~

 

 

 

Proportion in mole %

 

 

 

 

 

 

 

 

«5

10,

Fig,

0

10.5

11.0

1

\ N
1.5 12.0 1

Reciprocal Temperature, (°K)-!

1.

Molten S8alt Mixtures

AN
2.5 13.

Xenon Solubility Constants for Various
of the pump configuration is presented as Fig. 2. Use of
Eq. 2 and Eq. 3 implies the assumptions that (a) Henry's
law holds (equilibrium is maintained between the dissolved
gas, the gases entering the pump bowl, and the graphite-
salt interface); also that (b) diffusion rates across films
and through the salt are negligible as compared to the
rates of absorption by graphite and removal at the pump.

Hypothetical Reactor Conditions

 

The following reactor conditions and related para-
metric values were utilized to carry out the poison fraction
computations.

Xe-~135 decay constant, AXe’ = 2,11 x 10“5 sec™! .

Xe-135 destruction constant, ¢_0ge, = 7.4 x 107° sec™ .
Average reactor temperature, T, = 936°9K.

Gas constant, R, = 82.05 cm®-atm/mole-°K.

Xe solubility constant, Ky =3 % 107% moles Xe/cm® salt-atm.

Total salt volume, Vi, = 66.5 ft3= 1.88 x 10% cm®.
Le’ 20 ft° = 5,66 x 10°cm3.

Salt circulation rate (reactor pump rate), Qp, = 2.67 ft?/sec
= 7.56 x 10¢cm® /sec.

(0.04)(7.56 x 10%)
3.02 x 10° cm3/sec.

Xenon concentration in salt entering bowl = np/Vy; at exit = 0.

Total salt volume in the core, V

Salt circulation rate through pump bowl, st

i

When these values are combined with Eq. 2a and Eq. 3, one
obtains

/N
5.29-10~% + 4.26°10 2<§E>
PF (%) = G.

1.88-10-% + 0.174r + (fin

 

. (2b)

The by=-pass or recycle rate, 0,04 OQp, has been replaced by
(in Eq. 2b) to show the effect of stripping in subse-

quent computations.
-7 - ORNL-LR-Dwg. S6197
Unclassified

Drive

Helium
+ KRéenon

 

Helium

 
   

 

 

 

 

 

 

Liguid Level

 

 

 

 

o Ol Recycle

 

 

 

 

 

 

 

“'fi\ A L eI e .

- S
(:::::jmwt::;;:ZD galt
Bowl Out

 

 

 

 

Impellier Upper Shell

 

 

 

Salt In

Fig. 2

Schematic Diagram of Primary Circulating Pump
The only factor remaining to be discussed is n /co,
which introduces the contributions of the rate of xenon
diffusion into the pores of the graphite-moderator blocks.
P@rtinentlgraphite dimensions, as presently envisioned for

the MSRE, are tabulated below:
total graphite volume - 77 ft?,
total number of blocks - 565,
exposed area per block - 545 in.?,

3.08-10° in.2? ~ 2¢10° cm?.

and total exposed area
A cross-sectional sketch of the blocks may be found on
Fig. 3.

Xenon Diffusion in Graphite

Permeability and Diffusion Coefficients

 

It should be clear, at this point, that low permeability,
high density graphites are most applicable for advanced
molten salt reactors. This statement is made in view of the
problems associated with graphites as outlined in the
Introduction. The discussion here will center on graphites
with ?ermeability coefficients ranging from 1°10~° to
1107 cm?/sec. Gaseous diffusion rates within such materials
are governed by wall collisions - not by intermolecular
collisions. The xenon rates should not be influenced by the
presence of other gases, (e.g., helium) in the same passages.
When these conditions exist, each gas possesses its own dif-
fusion coefficient, D, which is closely approximated by
the permeability coefficient, K. The definitions of the
coefficients may be obtained from the steady-state equations:

fif RT = KXe

and nD RT = DXe

where fif is the forced flow rate, Pye 1s partial pressure,

and L is the length of graphite. Essentially, the above
argument implies that the gas does not differentiate between

AP, (3)

= i

AP (4)
- 9 - ORNL~LR-Dwg. 56198

Unclassified
1
!
.f’ ‘\
r’ h
i i
i
) |
T e T T T T T ~ |
m; / ZHR uZ”R ‘ !mm___'m___‘
s T \
j\ // N

 

 

 

 

 

 

 

tY
< 2 ]

Fig., 3

Tentative Cross-~Section of MSRE Moderator Blocks
- 10 -

P and Py, in small passa%es. An equation applicable to all
porous media 1is given by 4,15

4
3
where B, and K, are_characteristics of the medium, p is the
gas viscosity, and Vv is the mean thermal velocity or

_  /8RT\z
v =) (6)
M
Py is the mean pressure of the flowing gas.
When Bo is large, viscous flow controls.

K=B, m4+ 2KV, (5)
L

Also,

1.5
D -p_ Yo (EW\ : (7)
He-Xe °p \T,/

When B, — 0, Knudsen flow prevails.

Then,
D, ~ =2k ¥ (8)
xe “ Ke 3KV .

By Eq. 6 and Eq. 8,

o

T
= He
RN N

The pf%nts under discussion are reflected in the following
data:

 

D, Apparent Diffusion K, Permeability
Type Graphite Coefficient, cm2/sec Coefficient, cm?/sec
Helium Argon Helium Argon

 

 

 

AGOT  (National 7.2 x 10™% 2.3 x 10~ 1.6 x 10° 1.2 x 10°
Carbon Company)

CEY Coated Pipe 1.3 x 10~ 0.4 x 10-° 7.6 x 105 2.6 x 10~°
(National Carbon
Company)

 

* Data referred to 25°9C and 1 atm.
It may be noted that the K/D ratio for the permeable graphite
is 400; whereas that for the low permeability graphite is 6.
This tends to verify the approximation indicated at Eq. 8.
For materials with a K lower than that of CEY graphite, K/D
should approach unjty. Another point of interest involves
the ratio (My/Myx.)z = 3.16. Both K and D for CEY graphite
appear to follow this relationship (Eq. 9). DxXe at 936°K is
estimated to be 3.86-10"%cm?/sec, zs based on the Dj cited
and Eg. 9.

Porosity

I1f one considers two graphites with equal permeability
coefficients and unequal porosities, it is apparent that the
specimen with the highest porosity value will contain the
largest amount of gas at equilibrium saturation and during
steady flow. Low porosity graphites have a low absorption
capacity with respect to gaseous fission products. Thus, a
discussion of porosity is pertinent.

Two definitions of porosity are often employed in dis-
cussions of gaseous flow through graphites. One is the total
porosity, which is based on a comparison of the measured
density and a theoretical density (2.26 gm/cc). The other
is the effective porosity or open porosity as measured by
helium cbsorption. The total value is greater than the ef-
fective value, which indicates the presence of completely
closed voids. The effective value is of primary importance
regarding the Xe-135 problem,

Another point of interest involves the relationship be-
tween the porosity and permeability of graphites. From the
standpoint of graphite fabrication, porosity reduction is
not a necessary condition for permeability reduction; how-
ever, the former is a sufficient condition for the iatter.

It is possible to partially plug the channels within a graph-
ite without markedly decreasing the porosity; on the other hand,
a treatment which reduces the porosity of a graphite will
reduce the permeability coefficient. One may generalize thus:
graphites having low porosity values also have low permea-
bility coefficients. The degree to which this generalization
hoids is illustrated by nominal permeability-porosity values,
which are tabulated below.
- 12 -

 

Helium
Effective Permeability
Graphite Vendor Grade or Type Porosity, € Coefficient, K Notes

 

(%) (em? /sec)
National Carbon AGOT 22 2 X 100 a
Speer Carbon Moderator No. 1 17 7 X 10'1 a
Unknown Experimental 17 3 x 1074 b
National Carbon CEY (coated pipe) 11 5 x 107 a
National Carbon CEY 5 4 x 107° c
Hawker Siddeley HS-143-9 1 4 x 1077 c
Raytheon Pyrolytic 0.02 3 x 107° c

 

a. ORNL Data™'

b. Data from HutcheanlS
¢. General Atomic Datal8

From a2 standpoint of product improvement, the data suggest that
treatments to reduce permeability would be far more successful than
efforts to reduce porosity.

Pore Diffusion Equation

 

When consideration is given to a gas-cooled reactor which
utilizes coated particles or pyrolytic-graphite coated fuel elements,
the primary problem involves fission product release and resultant
coolant stream contamination. The rate controlling step (slowest
step) of release is, to a large degree, dependent on surface and
lattice diffusion mechanisms, as the fissioning process occurs in
the solid state within a ceramic shell or matrix.
This philosophy is reversed when consideration is given to
a moiten salt reactor. In this case, the fission process takes
place in the liquid and one is concerned with the fastest mode
of xanon absorption as a gas - not as a nuclide recoiled into a
lattice. Lattice and surface diffusion of xenon are of secondary
importance in molten-salt reactors._ The equation most applicable
is the pore diffusion equation, 2?2

2 N 8C
Dye V' C = € (¢ 05, + KXQ)C + €5 - (10)

The symbol C, mole/cc, represents free gas concentration - in
this case Xe-~135; t, sec, represents time. All other symbols
have been defined. The porosity term, €, appears, since xXenon
can accumulate or deplete (also burn-out or decay) only within
the pores of the graphite. It may be recalled that Dy, 1s re-

ferred to the external graphite geometry and to steady-state flow
which do not depend on porosity.

Transient Solutions.-- Having written Eqg. 10, it is con-
venient to touch on methods of employing this relationship for
the determination of the ¢ and X (and D) of low permeability
graphites. The destruction term becomes zero, since noble gases
other than Xe-135 are employed in the experiments. Eq. 10 takes
the form:

 

 

2
:xf = ¢ %% n (10b)

The solution of Eqg. 10b, P(x,t), which involves K and €, is used
to obtain (8P/8X)yx fixeq; this is multiplied by -D-A and in-
tegrated with respect to time. The P(t) thus obtained is uti-
iized to correlate pressure build-up data for specimens of known
geometry. When P(t) varies with time, the build-up is in-
fluenced by X and e; when AP(t) /At is constant, P(t) depends on
K alone. One obtains K through the steady-state data -~ then
employs this value and the transient data to obtain e.18,22 1p
many cases, the transient period is brief due to the material
and specimen geometry employed; thus ¢ must be measured via gas
absorption methods or estimated via the gross density measurements.
- 14 -

Steady~State Solutions.-- The form of Eq. 10 applicable
to the poison fraction expression (Eq. 2b) is

 

Dy, V% (C) = € (§ 09, + Axe)C . (10¢)

A rigorous solution for the graphite blocks (see Fig. 3) would
be cumbersome in that two variables related to geometry would

be present. In lieu of the rigorous solution, there are two
solutions of Eq. 10c (representing simpler geometries) that
yield convenient rate expressions. These equations should
closely approximate the rigorous equation within certain

ranges of D and ¢. For very low values of D and ¢, the solution
corresponding to a semi-infinite geometry is applicable, i.e.,

C =D_e , (1l1ia)

which leads to the rate expression:

fiD/Co = fiDXel , (12a)
where
1
A= [(E)(qfico‘xe + Ay )/ (D)]2 cm™ , and
X = penetration distance, cm.

Cylindrical geometry is applicable for nearly all values of D
and € since the back-pressure of xenon in the center of the
graphite blocks is taken into account. The corresponding
equations are:

1, (Ar)
and I, (Ar)

Plots corresponding to Eq. 11 and Eq. 12 are shown on Fig. 4a

and Fig. 4b, respectively. The curves indicate that the concentra-
tion profiles and rates for the two geometries merge as values of

D decrease. Based on the profiles at low values of D (Fig. 4a)
- 15 - ORNL~LR-Dwg. 56199

Unclassified

  
   
   

 

 

 

 

 

|

Cylindrical Sclution _—

Legend:

 

 

-~ —— Semi~-infinite Soluticn
e = 10.52%

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
Penetration Distance, ¢cm

Fig. 4a. Computed Concentration Proiiles for Xe-135 in Various
Graphites with MSRE Moderator Geometry

 

fiXe cm 20 T l

 

 

 

 

 

 

 

 

 

 

 

 

—"
" sec "
Co " Legend: ‘//,/”
—~—— Cylindrical P A/”/”’/’
15 b L L =
—— Seml—lnflnlggf’
e —
~
~
7~
10 < ]
’//b//ICondiiions
/ e = 10.52% .
5 / DA = 3.16 x 10"3])":’f cn/sec
// A= 2x 106 cm®
/ t
O | - -6
0 2 4 6 8 10(x1077)

Xenon Diffusion Coefficient cm®/sec

Fig. 4b. Steady State Diffusion Rates
- 16 -

it was concluded that most of the xenon is near the surface in
promising cases; thus the external area of the cylinders was
taken as the external area of the blocks (2 x 10%cm?). The
equivalent cylinder radius was taken as 3,603 cm. Geometry ef-
fects with respect to poison fraction computations are pursued
in the section to follow.

RESULTS AND DISCUSSION OF XENON POISON FRACTION COMPUTATIONS
Equivalent Graphite Geometry

The poison fraction was computed utilizing both diffusion
rate expressions (Eq. 12a and Eq. 12b) under assumed recycle
values of 4 and 100%. The curves arising from the cylindrical
case are shown as solid lines on Fig. 5; those arising from the
semi~infinite case are shown as dotted lines on Fig. 5.

Although the curves are plotted with DA as the independent
variable, it was necessary to specify a fixed value of porosity
to define the cylindrical values. This was required since
np/ce is proportional to the product of D-A and the ratio of
modified Bessel functions; D*A is proportional to (De)z. The
arguments of the Bessel functions are proportional to (e/D)=.

A convenient ¢hoice for ¢ was 10,52%, yhich fixed DA at
3.16°1072.(D)> and A as 3,16-10"3-(D)~2,

The curves of Fig. 5 show that the semi-infinite solution
is adequate for all values of R~r or x if DA < approximately
1 x 10-5 cm/sec or D is less than 1 x 10~®> cm2/sec. The curves
also show the effects of the back pressure at high values of DA
which are introduced by the cylindrical solution. Both curves
for the semi-infinite case approach the maximum poison fraction;
whereas, the curves derived from the cylindrical case approach
a constant value arising from a saturation effect which depends
only on the relative rate of Xe-135 production and removal at
the pump.
Percent

Xenon Poison-~Fraction,

- 17 -

ORNL~LR-Dwg. 55200

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Unclassified
Legend:
——— Cylindrical Solution
— —— Semi~infinite Solution
e = 10.52% .
DA = (D x 10™°)2, cm/sec
i
r = {
PR S M#_’,"‘
" //
////#/ % ~
* ~
T = 4% //
7~
Y // r = 100%
/
/ /
{/
/
/‘f’/
/’/
/
Vv
/
¢ //
)¢/
A
/
// ‘
|
6 1 2 4 6 1 2 4 6 1 2 4
(x10-%) (x1075) (x10~%)

DA, cm/sec

Fig. 5. Effect of Geometry on Computed Poison Fractions

 
Effect of Porosity

As pointed out previously, there is a slight trend be-
tween porosity and permeability, in that large decreases in
permeability (or diffusibility) are often accompanied by
slight decreaseg in porosity. The diffusion rate is propor-
tional to (D:e)z at low values of D. Within this region,
which is the region of interest, the effects of varying e¢
are the same as those of varying D. Curves showing the ef-
fects of varying ¢ are presented on Fig. 6.

Improved Graphites Versus Removal Rates

A family of poison fraction curves as a function of re-
cycle rate, r, and DA (actually Dz since ¢ is fixed) is shown
on Fig. 7. The estimated DA for CEY* graphite js
[ (9.51:10-5 sec-1)(6.9°107%)(3.9°10"% cm2/sec)]z or
5:10-% cm/sec, and that for AGOT* graphite is 6°107% cm/sec.
These grades represent the best, and perhaps the worst, grades
of non-pyrolytic graphites which are commercially available
in large quantities at the present time. Within the region of
6°10-*% cm/sec<DA>5:10"% cm?/sec the curves of Fig. 7. indicate
that increasing the recycle rate (i.e., the stripping or re-
moval rate) is the most effective means of reducing the poison
fraction. For example, at DA of 1:10"°® cm/sec increasing the
recycle rate from 4 to 10 percent will reduce the poison frac-
tion from 4.1% to 3.85%. To achieve the same reduction while
holding the rate at 4%, one must obtain a graphite with a DX
of 3.5-10~¢ cm/sec. This corresponds to a reduction in D
from 1-10-° cm2/sec to 1.2°10-% cm2/sec. In other words,
doubling the recycle rate is equivalent to decreasing the
permeability of the graphite by a factor of 7. With graphites
similar to AGOT, poison fraction reduction can be achieved
only through increased recycle rates,

 

* CEY and AGOT are National Carbon Company products.
Percent

Xenon Poison Fraction,

ORNL~LR-Dwz. 56201
Unclassified

Condition:

6 :
D=2 x 10 cmz/sec

 

 

 

 

 

 

 

\
|
\

 

 

\

 

 

 

 

 

 

 

 

 

 

 

 

 

Fig. 6.

6 10 20
€, Porosity, %

Effect of Porosity on Xenon Poison Fraction

 
Percent

Xenon Poison Fraction,

- 20 -
ORNL-~LR-Dwg. 56202

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Unclassified
Conditions:
e = 10.52% L
DA = (D x 10"5)2 cm/sec
o ! ! | “"é
Kge = 1 T 107 cEy AGOT
5 ; Y y
4 --—"""-—_'*w r = 0070 M—MM:WW
r = 2// ///
i //’/j.=“§// 4///////’//// .
///f 4 = 10 ///
3 r L % //
u : r = 20 // / -
//f r =‘%O ////f/
2 / / / / A //
/ / / / / /
//// r = 100%
e A ’ |
1 / A / /
< VLY
r///////////////// ,/’/// -
1
//M”'/
o —F—]
1 2 4 6 1 2 4 6 1 2 4 6 1
(x10-7) (x10-%) (x10-5) x10-%)
DA, cm/sec
Fig. 7. Xenon Poison Fraction at Various Values of Recycle

Rates and Diffusion Coefficients
- 21 -

In view of the relative importance of Xe-135 removal at
the pump, a series of curves were prepared (see Fig. 8),
which show the effect of increasing the circulation rate while
holding the recycle rate constant. An increase in the
circulation rate has the same effect as increasing the recycle
rate. This would also be true for any additional stripping
devices in the reactor.

The curves of Fig. 7 clearly demonstrate that decreasing
DA from 6-107* cm/sec (AGOT graphite) to 5-107% cm/sec (CEY
graphite) offers no advantages with respect to Xe-135 poisoning
particularly when the recycle rate (r) is 4%. Proceeding
further down the 4% curve, one finds that the Xe poison fraction
is 3.4% (max. 4.15%) for a graphite with a Kyge = 1:107°% cm?/sec
(DA = 1.4°10"%). An increase in r from 4 to 8% (at this D)
yields a poison fraction of 2.8%. Addition of a separate
stripping section would be required at this point, as r = 8%
represents %he minimum pump efficiency (92%) which can be
tolerated.z When one considers the combined effects of a
Kge = 1°107° cm?/sec graphite and the presence of a stripping
section comparable to a 50% recycle rate, it is apparent that
the poison fraction would be 1%. Adequate stripping coupled
with the utilization of low permeability graphites affords an
effective combination for reducing Xe-135 poisoning. On the
other hand, it is evident that the Xe-135 poison problem cannot
be solved through graphite improvement alone.

Another aspect of Xe~135 poisoning, which is not related
to neutron economy, involves intermittent operation of the
reactor.%44 A shut-down and fuel-drainage operation would allow
the graphite to de-saturate with respect to Xe-135. Resumption
of operation with the same fuel could result in a special
control problem (before the xenon content of the graphite
reached normal levels). This problem arises since fractional
removal of dissolved UF, is difficult to accomplish. Thus, low
Xe~135 concentrations in the reactor prior to shutdown would be
desirable. This might suggest further justification for ade-
quate stripping and permeability reduction.

Diffusion in Liquid-Graphite Systems

Comparison of experiments, wherein helium and argon were
allowed to interdiffuse through a dry CEY graphite specimen -
then interdiffuse with the specimen surrounded by a liquid phase
Xenon Poison Fraction, Percent

Wh

- 22 -

ORNL-LR-Dwg. 56203

 

Unclassified
{
Conditions:
e = 10.52%
r = 10%

 

N
N

 

 

2 X lg:imifi/sec

 

 

 

 

 

 

 

 

 

 

D = 2 X\lo"? \\
5 10 15 20 25 30
Pump Rate, ft’/sec
Fig. 8. Effect of Pump Rate on Xenon Poison Fraction
- 23 -

(water on the argon side) reveal that the rates are decreased
when the liquid phase 1is present. This was to be expected as
the specimen face was water-wet and 1% of the effective porosity
was occupied by water, although the water diffusion rate was
below the limit of detection. The argon and helium data, which
are referred to two atmospheres total pressure (on each side of
the specimen) and ZSOC, are shown below:

 

 

Type D, Apparent Diffusion Coefficients cm’/sec
Experiment Helium Argon
(x 10”6) (x 10'5)
dry 10.5 3.4
with water 2.2 1.9

 

Based on the argon data (which are analogous to xenon and
krypton), the rate of xenon absorption with liqujd at zero flow
rate would be decreased by a factor of (1.9/3.4)Z as compared
to the dry case. Films induced by liquid flow and resistance
resulting from higher liquid saturations of the porous material
would decrease the value of the ratio shown.
- 24 -

CONCLUSIONS

Experimental data have verified that the diffusion coeffi-
cient and the permeability coefficient of a given gas-
graphite system approach equality when the coefficients of
the systems under consideration are very low, i.e., approx-
imately 1-1077 cm?/sec.

The effective porosity, as well as the diffusion coefficient
for a given graphite, influences the steady-state rate at
which xenon is absorbed by graphite under conditions of
burn-out. Low porosity and transport coefficients (diffu-
sion and permeability) lead to low Xe-135 absorption rates.

Low porosity graphites generally possess low transport coef-
ficients; however, low porosity values are not necessary
indicia for low values of the transport coefficients.

For an approximate geometry for diffusion equations in-
volving the graphite moderator, one may utilize the semi-
infinite case when Dgxe<1:107° cm?/sec., At higher D values,
the cylindrical case appears to be most suitable.

O0f all the Xe-~135 control variables studied, the rate at
which xenon is removed from the reactor appears to be of
primary importance.

Adequate stripping coupled with graphite permeability {(and
porosity) reduction affords an effective combination for de-
creasing the xenon poison fraction. The latter cannot be
controlled through permeability reduction alone.
1.

10,

11.

12.

13.

14,

- 25 —

BIBLIOGRAPHY

L.. G. Overholser and J. P. Blakely, Reac. Chem. Div. Ann.
Prog. Rep. Jan. 31, 1960, ORNL-2931, p 139-148.

 

W. H. Cook and D. H. Jansen, A Preliminary Summary of
Studies of INOR-8, Inconel-Graphite and Fluoride Systems
for the MSRP for the Period from May, 1958 to December 31,
1958, ORNL CF-59-1-4 (January 30, 1959).

S. S. Kirslis and F. F. Blankenship, MSRP Semiannual Prog,
Rep. Feb., 28, 1961 (in preparation).

 

 

R. B. Evans, III, J. Truitt, and G. M. Watson, Interdiffu-
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CF 60-11-102 {(Nov. 23, 1960).

 

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I. Spiewak, (private communication via Intra-Qffice
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W. R. Grimes, N. V. Smith, and G. M. Watson, J. Phys. Chemn,
62, 862 (1958).

 

M. Blander, et al., J. Phys. Chem. 63, 1164 (1959).

 

N. V. Smith, W, T. Ward, g}_g}}, Reactor Chem, Div. Ann,
Prog. Rep. Jan. 31, 1960, ORNL-2931l, p 28-31.

 

 

J. H., Westsik, private communication.

P. C. Carman, Flow of Gases Through Porous Media, p 69,
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¥ w

15!

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19«

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21.

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24 .

- 26 -

J. M. Hutcheon, B. Longstaff and R. K. Warner, "The Flow
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1957,

GCR Monthly Prog. Rep. Jan. 20, 1961, p 5.
GCR Monthly Prog. Rep. Nov. 20, 1960, p 11-12.
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Characteristics of Graphite Materials for Use in Gas-
Cooled Reactors. (General Atomic Report) GA-1361 (April, 1960).

 

J. A. Lane, et al., A Study of Problems Associated with
Release of Fission Products from Ceramic TFuels in Gas-—
Cooled Reactors, ORNL-2851 (Oct. 27, 1959),

 

M. Muskat, Physical Principles of 0il Production, p 178-179,
McGraw-Hill, New York, 1949.

J. L. Scott and D. F. Toner, Consolidated Graphite Projects
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J. Crank, The Mathematics of Diffusion, p 47-48, Oxford
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A. Taboada, private communication.

I. Spiewak, private communication.
a4

- e

¥

Distribution

l-3. DTIE, AEC
4. M. J. Skinner
5. Prof. P. L. Walker, Jr.
Pennsylvania State Univ.