ORNL-4575.txt

 

    

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DR S  ORNL-4575, Volume 2
UC 25 Metols, Ceramics, qnd Materlols

 

 

 

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CORROSION IN POLYTHERMAL LOOP SYSTEMS

 

 

‘I A SOLID-STATE DIFFUSION 'MECHANISM
WITH AND WITHOUT LIQUID FILM EFFECTS

R B Evans III

J. W Koger " _‘ |
J H. DeVan s T

 

 

 

 

 

 

e s operaled by
UNION CARBIDE CORPORATlON

o dorthe .o
U S ATOM'C ENERGY COMMISS'ON :

 

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ORNL-4575, Volume 2

Contract No. W-7405-eng-26

METALS AND CERAMICS DIVISION

CORROSION IN POLYTHERMAL LOOP SYSTEMS
II. A SOLID-STATE DIFFUSION MECHANISM
WITH AND WITHOUT LIQUID FILM EFFECTS

R. B. Evans III
J. W. Koger
J. H. DeVan

 

 

This report was prepared as an -account of work
sponsored by the United States Government, Neither
-the United States nor the United States Atomic Energy
Commission, nor any of their employees, nor any of
their contractors, subcontractors, or their employees,
makes any warranty, express or implied, or assumes any
legal liability or responsibility for the accuracy, com-
pleteness or usefulness of any information, apparatus,
product or process disclosed, or represents that its use
would not infringe privately owned rights,

 

 

 

JUNE 1971

OAK RIDGE NATIONAL LABORATORY
Oak Ridge, Tennessee '
- operated by
UNION CARBIDE CORPORATION
for the _
U.S. ATOMIC ENERGY COMMISSION

, DISTRIBUTION OF THIS DOCUMENT IS UNLIMITED

 
 

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iii

CONTENTS

EEES

Abstract . . . . . . . . . . } e s e e s e s e e e e s e e e 1
NOmenclature « « « « « « o o s o o s o o o s o o o s v o o o o o o 2
Introduction . . . . + « ¢ ¢« ¢ s ¢« v e 4 e e e . e o 5
Fundamental Concepts « « ¢ « « &« 4 e b e e e e 4 e e 8
Basic Diffusion RelationshiDs . - « « « o o o o s o o o o o o 9
Surface BehaVIOr . v v v v o o+ ¢ o o o o o o o o 12

EqQuilibrium Ratio . « « « « ¢ o 4 o o o o 0 o o 0 a0 . 12
Reaction Rates . « ¢ « ¢ & o o o « s o o o o o o o & 14

Mass Transfer Across Liquid Films . . . . « « « « « « o+ = 16
Combined Reaction Rate-Film Resistances . . « « « . « . . 17

Surface Effects Referred to the Alloy . « . « + + « « & 18
Transient Solutions . . e e e e e e e e e e e e e e e e e e 19
Review of the Equations . . . . « « + ¢« ¢ ¢ ¢ ¢ o ¢ ¢ o o o & 19
Application to Sodium-Inconel 600 Systems . . . . . . . . . 24
Temperature Profiles and Loop Configurations e e e e e e e e e 26
Reference and Prototype Loops . . « « . .« & .-. « e s e e 26

The Reference LOOp . . « « ¢« ¢ o ¢ ¢ ¢ ¢ « o & . . 26

A Prototype LOOD « « « o « s o o o s o o o o o 0 o0 o . 28
Quasi-Steady-State Solution . . . . . . « o 4 o0 o 0o 0. 32
Statement of the Problem and Objectives . « + « « « « + + . . 32
Solution in Terms of the Prototype Loop . .'. e 8 e e e s 36

" Predicted Results for Sodium-Inconel 600 Systems . . . . . . . 43
Discussion of Sodium-Inconel 600 Results . - « « « ¢ o« s o« « o« » « 46
Application to Molten-Salt Systems . . . . R 1o
Thermal Convection LOOPS « « + + v « + « « « o « o « « s o o« » 50

Redox Corrosion Equilibria and Systems Selected for -
Di.SCU.SSiOn L v » . LI . '.. . . . * . v = . L) &« o @ - . . 54’

1 Transient FACEOTS + « « « + o « « o o s o o o o o o o o « o+ 55
Quasi-Steady-State Solutions . . . . . . o0 0. oo .o . 59
Discussion of Molten-Salt Results . . .+ « « « ¢ v v o o v v o . 64

SUMMAYY « « « o o o s o s s o o o s s o o o s s & o » » e e e . 69

 
 

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CORROSION IN POLYTHERMAI. LOOP SYSTEMS |
II. A SOLID-STATE DIFFUSION MECHANISM WITH AND
WITHOUT LIQUID FILM EFFECTS

R. B. Evans III J. W. Koger
J. H. DeVan

ABSTRACT

The corrosion resistance of alloys exposed to nonisothermal
circulating liquids is an important consideration in the design
of reactor systems that employ liquids as eilther coolants or
coolant-fuel combinations. Accordingly, several mathematical
descriptions have been developed to explain selective transport
of corrosion-labile constituents of nickel-base alloys. This
report is the second of a series to correlate results of corro-
sion behavior observed in polythermal loop systems. The present
report specializes to cases in which solid-state diffusion in the
alloy, as influenced by coolant characteristics and composition,
dominates the corrosion mechanism. Equations are derived for
both transient and steady-state cases. ' Since transients, which
are induced by liquid films, are negligible, analy31s of steady-
state behavior is of greatest 1mportance.‘

Applicability of the derived equations is demonstrated by
comparison of predicted values with experimental results for two
distinctly different systems. The first involves hot-to-cold-
zone transfer of nickel in Inconel 600 pumped loops circulating
liquid sodium. Comparisons revealed that actual corrosion is
much higher than predicted by the equations; this suggests that
the true corrosion reaction overrides a slow solid-state diffu-

- .8ion process. The second system considered is transfer of

chromium in Hastelloy N loops with molten salt flow induced by‘

.~thermal convection. Three hypothetical examples are considered,

namely: (1) chromium corrosion at all points, transfer tb salt

only; (2) hot-to-cold-zone chromium transfer; and finally

(3) cold-to-hot-zone chromium transfer. While complete data to
substantiate the results computed for the above cases are not
available, the success of early °Cr tracer experiments
(example 1) suggests that the solid-state diffusion mechanism
does apply to certain molten-salt systems when the salt con-
stituents (and 1mpur1t1es) are subaected to stringent control.

 

 
 

' e
OI-'-O 0 O‘N:D%i »—:lbgm o

o o

exp(7)

erf(v)
erfc(v)

E u;

()

Ei(uj)
Esoln

f

£(p)
?(w,s)

F(w,t)

5lE QR R

- Total liquid exposed area of loop alloy, cm®.

NOMENCIATURE

Subscript denoting alloy; superscript denoting activity.

Activity of alloy constituent M, no units.
2

Cross-sectional area of loop tubing, cm?.

Internal pgripheral area of loop tubing, em?.
Slope of a linear T versus z segment, °K/cm.

Subscript denoting cold zone.

Integration constant W1th respect tow, i =1, 2, wt. frac. sec.

Constant group, 4 Xapar’/Db“ g cm™! sec }/2.

Constant group, (Kb/KO)G, g cm™l sec=1/2,

- Symbol for dissolved metallic species.

Diffusion coefficient of M(s) in alloy, cm®/sec.
Preexponential term, D/exp(-E /RT), cm?/sec.

Mutuel diffusion coefficient of M(d) in liquid metal cmz/sec.

The transcendental number 2.71828.. ., no units.
The exponential function 3? T,zeT, no units.
The error function of v, é e”"  dr, no units.

The complementary error function of v, 1 — erf(v), no units.

! oo .
First-order exponential function of uj, J (7" /t)dr, no units.

uj
The "i" exponential function of u, 5 f /3 ( e”/r)dr, no units.

_Actlvatlon energy for solld-state diffu51on of M(fi), cal/mole.

Energy required to dissolve M in liquid metal, Cal/molé.

'FraCtion of AT;'when A is constant, f = z/L. |
,Location of balance point where j =0 and*gp‘= kT.

- !
Laplace transform of F(w,t) f F(w,t)e 57 447

An arbitrary function of w and t.

Symbol denoting gram mass.

Symbol denoting gas.

Gibb's potential or free energy, cal/mole.
Film coefficient for mass transfer, cm/sec.

Combined solution rate — film coefficient, cm/sec.

(w

i
 

at

)

hl

I, (aft

iy

)

W
N - .
N b P N”E?‘é? e

= B o s S

AM(t)

“Re

S

C

Sh

H

H

H O a0 J

T =

I

 

Subscript denoting hot zone.

The product kT(h/D)(Dz/pa)(ma/mM), cm™ !

Enthalpy difference, cal[mole.

Index 1 at £ = O for function below.

An integrated function along extended z coordinate from
§i to §j,,cm;' ‘

Index p or 2 at balance point or f = 1 for function above.
Mass flux of species M, g cm™? sec"l/2

Atomic or molecular flux of species M, mole cm™? sec‘l/z.
Boltzmann constant = 1.38 x 10716 g cm? sec™! °k~1,
Solution rate constant, cm/sec.

Solution rate constant, mole cm~2? sec~!.

Deposition rate constant, cm/sec.

Deposition rate constant, mole cm™2 sec~l.

Equilibrium constant, k a/k~a, no units.

Activity coefficient ratio, 7M(d)/7M(s)’ units depend on
choice of standard states for

Preexponential factor KT/exp( Esoln/RT)’ no units.
Balance point value of KT, no units.

Experimental solubility constant, no units.

Subscript denoting liquid.

Total loop length, cm.

Molecular or atomic weight, g/mole.

Symbol denoting metal constituent subaect to corr031on.
Mass or weight of M transferred, g. | '
Reynolds number, 2r'V p/n.

Schmidt number, u/pfimw, no units

Sherwood number for mass transfer, 2hr/'DNw, no units.
Symbol or subscript denoting balance point.

A transformation variable, (s/D):l/2 cm.

Volumetric flow rate in loop, cm cm?/sec.

Radial distance measured from the center of the loop tublng, cm.

Atomic radius of M(d) in liquid metal, cm.
Inside radius of loop tubing, cm.

 
 

 

 

4

Gas constant used in exponential terms, 1.987 cal mole™! °K 1.

Laplace transformation variable, sec~!.
Symbol denoting solid solution.

Time, sec. N

Temperature, °F, °C, or °K.

Temperature drop along.a segment of gz, °E, °c, or °K.
Dimensionless variable, a/t., no units.

The argument W/(4Dt)1/2, no units.

Liquid flow velocity, Q/Axs, cm/sec.

Distance of linear diffusion, normal to A , of M(s) in
alloy, cm.

Concentration of M(s) in alloy expressed as weight fraction,
no units. | | |

Concentration of M(s) in as-received alloy.

Surface concentration of M(s) as a function of T along z.
Concentration of M(s) in diffusion region as a function of

position and time.

Alloy concentration of M(s) equivalent to liquid concentration

of M(d) at the liquid side of the liquid film.

Alloy concentration of M(s) equivalent to equilibrium.liquid
concentration at liquid-solid interface. _ |
Concentration of M(E) in alloy expressed as afomic fraction,
no units. .

The concentration difference,'xh,(o,t) - x_, no units.

The concentration difference, x* — xa,vno units. .
Concentration of M(d) in bulk liquid expressed as weight

fraction; it corresponds to y* when transients are discussed,

no units.

Concentration of_M(g) at metal-film interface, no units.

Equilibrium or saturation concentration of M(d) in a unit
activity container. |

Concentration of M(d) in bulk 1iqfiid exprés#ed as weight

. fraction, no units.

n

-
 

-y

LD

 

z = Linear flow coordinate for v or Q, cm.
o = The factor (ED)/(2bR), cnm.
o = The factor (Ej —2E, ; )/2bR > 1, cm.
oat = The factor o’ <1, cm.
B(uj) = The factor u exp(u )El(u ), no units.
7 = Activity coefficients, units selected to make o
dimensionless. S
A = Symbol to denote difference.
t = Extended z coordinate = a/u ., CI.
L = Viscosity coefficient of the liquid metal, g cm~1 sec™?..
n = The transcendental number 3.1416..., no units.
p = Mass or weight density, g/cm?.
T = Dummy variable of integration, no units.
¢., = Concentration difference for hot zone, xh,(O t) —-xh,(w,t)

no units.

W = Concentration‘difference for hot zone when liquid film is
present, x¥, —-xh,(w,t) no units.
¢ = ¢* concentration difference for cold zone with and without

presence of liquid film, x (w;t) - x_, no units.

INTRODUCTION

In a previous report;'(nereafter referred to as Report I) atten-
tion.was'given to internretations of corrosion behavior,in'systems com-
posed‘of'liquid'sodium contained in the nickel-base alloy Inconel 600.
Speclfic 1nterest focused on experimental pumped lOOpS that gave definite
evidence that nickel and chromium moved from hot to cold regions of the

'loops. Only nickel transfer was considered because little Was known
._about the solubility of chromium in liquid sodium, furthermore, the magor

component undergoing corros1on and transfer was nickel Solubillty

1nformation is of major importance because the manner 1n'which solubility

 

1R. B. Evans III ana_Paui Nelson, Jr., Corrosion in Polythermal
Systems, I. Mass Transfer Limited by Surface and Interface Resistances
as Compared with Sodjum-Inconel Behavior, ORNL~4575, Vol. 1 (March 1971).

 
 

 

increases with temperature governs the steady-state driving force for
mass transfer around the loop.
The major effort in Report I was to develop a simple system of

equatlons that might describe the mass transfer as observed experimentally.

The approach in Report I was to assume that the mass-transfer equations
would fall into the same patterns as those that describe heat transfer
from hot to cold zones under conditions of known external-temperature

profiles and rates of fluid flow around the loop. For heat flow, the

only resistances involved would be an overall coefficient that would com-

prise the thermal conductivity of the walls and a heat-transfer film.
An anslogous situation was assumed for mass transfer with the exception

that the thermal conductivity term was replaced by a reaction-rate con-

- stant that was presumed to be associated with a first-order dissolution

reaction.

Predictions of corrosion based on the heat-transfer analog showed

that transient mass transfer effects decayed after negligibly short

times (fractions of an hour). Steady-state corrosion rates calculated

from the film coefficient alone were much greater than measured values.
It was necessary to invoke the reaction-rate constant to increase the

resistances and lower the computed results in order to match experimen-

tal results. While this "matching" could be done for results of individ-

ual experiments, a consistent set of reaction constants for all results

that would lead to a general correlation could not be obtained. One of
the prime reasons for the failure of the mechanisms covered in Report I
is that the 1dop walls were not pure nickel. Rather, the walls were of
an alloy wherein solid-state diffusion effects influenced the overall
behavior. These effects were ignored in the equations of Report'I.'
The present report is devoted to another mathemetical treatment of
an idealized mass-transfer proeess wherein corrosion rates depend
directly on the rate at which consituents of alloys diffuse into or out
of container walls, as influenced by the condition of wall surfaces
exposed to a high-temperature liquid. Specifically, consideration is
given to cases for which solid-state diffusion controls mass transfer

at all poinfis in a polythermal loop system containing circulating

liquids. The container constituents of interest are nickel-base elloys.

3]

e
 

 

i

«

AP

 

We have also considered the contributions of liquid-film resistances
acting simultaneously with the solid-state mechanism to ascertain whether
or not a suitable combined mechanismn (our ultimate goal) could be
attained. Unfortunately, this approach was unsuccessful. ,

Three rather impbrtant'assumptions are made in our present deriva-
tions. 'First, effects of changes in wall dimensions can be neglected.
Second, the rate of diffusion is unaffected-by composition changes in
the'diffusion zone of the alloy; in other words, the diffusion coef-

ficient is not a function of concentration. Third, the circulating
 liquid is pre-equilibrated with respect to the amount of dissolved com-

ponents so that the concentrations in the liquid do not vary appreciably
with position or time. This latter boundary condition is embodied in

both the "transient" and "qua51-steady-state" conditions that are

covered in this report.

It should be mentioned that, although many llqulds have been studied
relative to reactor applicatlons, the basic approach in assessing corro-
sion properties remains the same. One employs either thermal convection
loops or pumped systems to collect the data required. At the time of
thie"writing, sOdiumrsystems,'wnich are of interest to the Liquid Metal

' Fast Breeder Reactor,?s3 are under intensive study. We should note a

treatment simildr to that to be covered here was initially roughed out

in 1957 under'the auspices of the Aircraft'Nuclear‘PrOPulsion (ANP)

Project.* The liqulds of interest in thls early effbrt were molten

.fluoride salts.”’

The obgectlve of the work leadlng to the present report has been

to carry out refinements of the early ANP treatments, and to generalize

- the results to permit their application to many systemsnthat ndght

 

" GRNL-2440, Pp- 104-113.

2Argonne National Laboratory, Liquld Metal Fast Breeder Reactor
(LMFBR) Program Plan. Volume 1. Overall Plan, WASH-1101 (August 1968) .

3A1kali Metal Coolants (Proceedings of & Symposium, Vienna,
28 November — 2 December, 1966), International Atomic Energy Agency,
Vienna, 1967.

“R. B. Evans III ANP Program.Quart Progr Rept Dec. 31 1957

5R. C. Briant and A. M. Weinberg, "Molten Fluorides &s Power Fuels,"
Nucl. Sci. Eng. 2, 797-803 (1957).

 
 

 

operate within the solid-state mechanism under consideration. A short-

term and immediate objective is to determine whether a mechanism of this

type applies to the migration of nickel in the sodium-Inconel system in
high-velocity pumped loops. | -

One of the central conclusions of the present study is that the
solid-state mechanism clearly does not explain the observed corrosion
behavior of the sodium~Inconel 600 system. On the positive side, how-
ever, the analytical work that was done is immediately and directly
applicable to Hastelloy N-molten salt thermal convection loops, in which
this solid-state mechanism clearly does operate. Thus, the present work
includes two separate topics: one covering corrosion induced by liquid

metals, another covering corrosion induced by constituents in molten-

- salt systems

- For ease of presentatlon, a rather unorthodox outline has been

adopted for this report. First, we discuss basic diffusion relatlonshlps

variables, and the type of transients one might encounter. Then we turn
to a discussion of liquid mass-transfer films and their effects on the
corrosion rates. Next, we derive and present equations for the cumule-
tive corrosion at quasi-steady-state (i.e., when the transient effect
associated with liquid film resistance hes diminished). The term "quasi“
appears because the predicted corrosion varies with the square root of
time. These make up the most important aspect of the report. However,
to emphasize the meaning of the analytical results, detailed "example
calculations" are given. Separate discussions are'presented for the
liquid-metal application and three molten-salt applications. The final
section is a summary of the more important features of the equations and

their applications.

FUNDAMENTAL CONCEPTS

Tt would be most convenient, from the authors' standpoint, to
proceed directly to the task of setting up the diffusion relationships
that take liquid phase mass transfer into account, show this to be of
little importance, and proceed d1rectly to the qu331-steady-state solu-

tion based on the diffusion relationships. This is the conventional

(o

3 ]
 

ot

“h

4y

 

method of presentation, but one immediately encounters fractional-
approach variables introduced by the nature of the alloys and chemistry
of the liquids. Accordingly, we shall jump ahead of the film part of-
the problem.end start by writing down some of the well-known expressions
for solid-state diffusion in order to introduce the ideas behind
fractional-approach variables and to enable recognltlon of integrated

forms that emerge when film re81stances are encountered

Basic Diff'usion Relationships

The basic relationships required are the concentration-profile
equations that express the weight or mass fraction x(w,t) of an alloy
constituent as a. functlon of position across the wall, W) and time, t.
We let w = r — r’', where r’ is the inner radius of the 100p tubing.

The relationships derive from Fick's second law of diffusion, sometimes
called the Fourier'equetion,_and apply to both hot and cold zones of-
the system. These relationships are developed elsewhere.®s?7 It is suf-

- ficient here to point out just a few importantdfeatures of the equations

involving x(w,t). First x(0,t) is aSSfimed to be constant with time.®

Only linear diffusion along a s1ngle coordinate, 'w, shall be cons1dered.

The direction of w is normal to the llquid exposed surface, Az,‘where

.w = 0. The contalner walls are inflnitely thick relative to the effec-

tive depth of the profile; thus x(w,t) = x,, the bulk concentration of
the constituent, for all times. -

 

6R. V. Churchill, Modern Operational Mathematics in'Engineering;'
1st ed., pp. 109—112 McGraw-Hill, New York, 1950. |

7H. 8. Carslaw and J. C. Jaeger, Conduction of Heat in Solids,
2nd ed., pp. 58-61, Oxford University Press, New York, 1959.

8The Justiflcation for this assumption will become evident as we

'_dlscuss the relationship between the concentration of an element at the
" metal surface and its concentration in the corrosion medlum '

9The reader should not infer that use of w = r — r’ means that a
radial flow system is to be employed; we use w as a linear flow coordi-
nate, even though the container is a cylindrical tube, because most of
the alphabet has been reserved for other notation. '

 
 

 

10

Two functions evolve from the solution of the Fourier equation;

these hold for the hot and cold zones , respectively:

¢ x(0,t) — x(w,t)

 

_h o = erf(v) , (1)
AX | X(O,t)- - X, .
x(w,t) — x o
fE= —(————.——a = erfe(v) , (2)
Ax x(0,t) - X - -
‘where
v = w/(4Dt)1/2 . - | - (3)

Consider now a hypothetical case (somewhat implausible for an actual
lbop) in which given points in the hot and cold legs have the same v.
A rather imp'orta.nt identity can be demonstrated by adding Egs. (1) and
(2), na.mely,: (¢h, + ¢c)'/Ax = 1. This happens because the definitions
of the error functions take the form shown below:

v 00

_ 2 2 a2 7 . |
?f(v) + erfe(v) [[e | ar + Je T dT:I, 1 (4)

8

As v approaches zero, ¢h’ /Ax approaches un_ity, and as v approaches
infinity, o, /Ax spproaches zero. The reverse is true for ¢c/Ax. This

means that

x(w,») = x(0,t) - X, » x(w,t) = x(w,0)

in the hot zone, and

x(w,») = x(0,t) , } x(=,t) = x(w,0) -» X,

in the cold zone.
The necessity of introducing variables like ¢ and parameters like
Ax should begin to emerge at this point. From a physical point o;f iriew,

the concentration of a constituent in the alloy can never be unity in a

"compatible" alloy-liquid system. The purity of the liquid should be

high while its ability to dissolve a.‘lldy constituents should be minimal.

Thus, values like x(w,») = 1 or 0, and x(0,t) = O or 1, are seldom
 

 

)

&)

11

encountered in practice. Yet, from a mathematical point of view, the

- solution must vanish at all boundaries except one. Stated in the

language of partial differential equations, the heat equation must be
homogeneous; the same is true for all but one of the boundary condi-
tions1%s11 unless an additional equation is involved. The nonhomogeneous
conditions usually concern an initial or particular surface condition.
For these reasons, fractional-approach variables are employed.

The problem at hand requires use of x(w,t) as prescribed for Fick's

. first law, the latter being evaluated at the surface to obtain an expres-

sion for the flux traver81ng'w = O:

Iy - —Dp'aéxéi—’t)= —p, Ax (p/nt)2/2 | (5)

If we assign z as the directional flow coordinate of the circulating
liquid normal to w, then Ax at each point is a function of z and of tem-
perature, and Eq. (5) with x(O t) = xp, takes the form '

Iy = Pe¥, (1 = xT»/xa)(n/:rol/z : (e

- The flux JM is pos1tive for the hot zone and negative for the cold zone.
' One of the basic assumptions stated in the Introduction, namely, that

the concentration of the circulatlng liquid remains fixed with time,
means that the ratio xT/x varies with related tlme-temperature points
in a speC1a1 way. This is the reason Eq. (5) has been cast into the
form of Eq. (6). Irrespectlve of this, Eq. (6) may be 1ntegrated'w1th

respect to time without concern about the XT/X relationship, since

x(0,t) and, therefore, XT/xa do not vary with time. One obtains:
o | & | N
o s A4 = — - '1/2 |
AM(t) /AZ_ f Jy at 2p,x,_ (1 xT/xa)(Dt/fi)r . (7)

0

 

1°R E. Gaskell, Englneering Mathematlcs, 1st. ed., p. 358,

‘Dryden- Press, ‘New York 1958.

11g,s. Carslew and J. C. Jaeger, Conduction of Heat in ‘Solids,
2nd - ed., pp. 99—101 Oxford Unlvers1ty Press, New York 1959 '

 

 
 

12

Under the usual sign'convention,‘a positive value of AM/A means
that the metal constituent diffuses into the alloy (cold zone); negative
values mean outward diffusion (hot zone). We shéll reverse this conven-
tion, since we desire & balance of M with respect to the liquid. The
solution behavior of most acceptable systems is such that the liquid

- gains material in the hot zone and loses material in the cold zone. In

other words, X, > Xp in the hot zone; x, < x,, in the cold zone; notice
that Egs. (6) and (7) follow the adopted convention automatically. The

-~ next mathematical operation involves integration along z, but this

requires some knowledge of the manner in which z varies with T and, of
greater importance, the mammer in which T varieS'with_x(O,t). The lat-
ter is a problem in chemistry to which we now turn.

Surface Behavior

Equilibrium Ratio

 

A good example is the reaction that gives rise to chromium migra-
tion in Inconel 600 loops circulating UF,-bearing molten salts.12,13

The reaction of interest is
Cr(s) + 2 UF,(d) = 2 UF3(d) + CrF.(a) . (8)

The symbols (s) and (d) are intended to denote the respective states:
"solution in the alloy" and "solution in the ligquid." The equilibrium

constant is

_ [CI‘Fz][UFgng

’ 9
[crl{ur,]? | - ()

whereby

 

12R. B. Evans III, ANP Program Quart. Progr. Rept Dec. 31, 1957,
ORNI~-2440, pp. 104-113.

13y, R. Grimes, G. M. Watson, J. H. DeVan, and R. B. Evans, "Radio-
Tracer Techniques in the Study of Corrosion by Molten Fluorides,"
pp. 559-574 in Conference on the Use of Radioisotopes in the Physical
Sciences and Industry, September 6—~17, 1960, Proceedings, Vol. III,
International Atomic Energy Agency, Vienna, 1962.

U

1

i
oy

 

) ]

 

[CI‘Fz] L '
—-—-—l— . 5
UF;] (KT) S (%)

Brackets are used to denote concentration variables. If the concentra-
tions can be related to appropriste activity values, one may write, in

terms of the standard free energy change for the reaction above,

AG° = —RT £n K. . | - (10)

. Values of X~ or KT'may be computed with the aid of information summa-

rized by Baes.l%
We have assumed that all points along Z are exposed to the same
concentration of dissolved species of interest. Thus [Cr] = ~ X adjusts

to éompensate for temperature-induced changes in KT' Furthermore,

balance points f(p) and f(p’) exist along z and have the property

Jyy = 0. These points delineate the boundaries of the hot and cold zones.
Clearly, then [Cr] , ~ X, at f(p), and an equation equivalent to
Eq. (9a) can be wrltten'W1th KT replaced by K when quasi-steady-state

conditions are attained. The ratio in Eg. (7) is
xT/xa = Kfi/KT . - (11)

Units of the concentrations in this ratio cancel out; those of X, which

is factored out to form the Py Xy product, should be weight fraction

because jM is a mass flux.

- We shall now consider nickel migration in Inconel 600 1odps con-

'talning liquid sodium. Although it is generally accepted that the -

nickel reaction is & simple dlssolutlon process, very few rellable data

exist on the solubility of nickel in sodium. About the best one can do

 at this time is to write an equation of the form:

Ni(s) = Ni(d)

"andflthéfi.assume a reasonable temperature relationship of the form:

KT K, exp( Esoln/RT) ‘ . (12)

 

| 14C F. Baes, "The Chemlstry and Thermodynamlcs of Molten-Salt-
Reactor Fluoride Solutions," pp. 409433 in Thermodynamics, Vol. I,
International Atomic Energy Agency, Vienna, 1966.

 

 
 

 

 

Values for KO and ESO

14

1n used in fhe present report are, respectively,
6.79% x 10™% weight fraction and 6.985 keal/mole. With these values
Eq. (12), cast in the form of Eq. (9), passes through a set of solubility

data reported by Singer.l”’ It is clear that
KT=Y/7§, | - (13)

wfiere we assume the activity coefficient ¥ to be unity and the mole
fraction X of nickel to be unity, since the solubility experiments were
conducted in a pure nickel pot.16 1In this case, Y (the saturation value
in the pot experiments) is~equivalent to the experimental KT. In a |
loop, x = (mM/ma)Y/KT. Thus once again the form of Eq. (11) holds true.

- We might point out by way of conclusion that we really don't know
what reaction Esoln represents, as we did for the fluoride case, Eq. (10).

In certain ideal cases, E__, would be nearly equivalent to the heat of

soln
fusion of nickel (=~ 4 kcal/mole), but in the present case the solubili-
ties are so low and the data are so scattered it would seem difficult to

attach definite physical significance to this‘variable. Note also that

‘hot-to-cold-zone transfer requires the energy term to be positivé. Ir

it is negative, material would tend to move from the cold to the hot

Zone.

Reaction Rates

Consider an alloy with constituent M that tends to undergo a revers--
ible solution reaction governed by a positive solution energy — namely,
ky

M(s) = M(d) .
k,

 

15R. M. Singer and J. R. Weeks, "On the Solubility of Copper, Nickel,
and Iron in Liquid Sodium," pp. 309-318 in Proceedings of the International
Conference on Sodium Technology and large Fast Reactor Design, November 7-
9, 1968, ANL-7520, Part I.

16We have written Eq. (13) in terms of a selected standard state for
dissolved nickel in the saturated solution with the concentration expressed
as ppm (by'weight). A more conventional choice would have been to express

Y in terms of mole fraction such that the corresponding activity would be

unit¥ at saturation. This choice would have avoided a "split" definition
f XK', which appears later. -v ,

>

>
 

ot

¥

 

15

As stated earlier the symbols (s) and (d4) dencte the respective states
solution in the salloy and solution in the liquid. One may set forth
the classical rate expression for the net amount of M that reacts in
terms of the molecular or atomic flux as

(14)

iA JM=k1 *M(s) ~ k2 M(d)

The units of k™ must take on those of Iy (mole cm™?

ec™l) because By
must be dimenS1onless according to establlshed conventions. The units
cm® refer to a unit or peripheral ares along z.

At equilibrium, J,, = O, and one obtains the correct thermodynamic

 

M _
expression for the equilibrium constant, which is
"mid) k* . (15)
= - 2 ——, _ 15
a |
*M(s) ko

Although Egs. (14) and (15) are classical expressions — in a thermo-
dynamic sense — for first-order reactions, they seldom appear in this
form in corrosion practice. Mass fluxes are most frequently used, and
the concentrations and eqnilibfium constants involve weight or mass
fractions. Furthermore, the constants usually have velocity units.
These conventions fequire the use Of’mass density'tefmSQ Therefore,
additional modifications of Egs. (14) and (15) are clearly in order.

It is convenient for present purposes to take & ., as the product

M
of an activity coefficient and the mole fraction. Then

~ jM = mM‘TM_-': [kl%M(E) - kf%(a)} oy, - (1)

where x and y represent mole fractions in the solid and liquid, respec-

tively. wa if new rate constants are defined such that,

= kf?mg)mmf%,'f and X = 2a7M(d)mz/pz ;o ()

| thenrthe expression for the'mass flux becomes

 
 

16

The superscriptiC>appears as & reminder that the liquid concentration
that governs the dissolution reaction is the value that exists between
the metal and mass transfer film. Assuming the absence of a film,

h e, with j, = O (equilibrium); then X+ ¥, and the relationship
between Kéxp and Kg'may be readily found. It turns out that

iR n e 09)

Notice that the units of k, and k, are cm/sec.

Mass Transfer Across Liquid Films

The accepted and usual approach for explanations of the mass-
transfer phenomenon is to invoke the close analogies that exist for
various modes of heat and mass tranéfer. In this case we are interested
in the mass-transfer analog of heat transfer as it occurs under Newton's
law of cooling. In terms of the concentrations in the liquid, one may

write,
Iy = b=, , N (20)
and if‘surface reactions are fast — k, = kl/KT'> h —

dy = h(Y — -3}-)91a . (20a,)

The interested reader is referred to discussions given by Bird et al.l7
of particular importance is the analogous way in which h's for mass and
heat transfer are COm.pu.ted.l8 Many think of h as a representative of
a diffusion parameter because a binary diffusion coefficient (for
example, Ni(d) in sodium) appears in the correlations concerning b for

mass transfer.

 

*"R. B. Bird, W. E. Stewerd, and E. N. Lightfoot, Transport
Phenomena, pp. 267, 522, Wiley, New York, 1960. | |

181bid., pp. 636647, 681.

"

U
 

 

wl

wy

3y

 

17

Combined Reaction Rate~Film Resistances’

In some instances, a'Cdmplete description of surface effects may
require coupling of the effects of both chemical kinetics and liquid

film transport such that the associated resistences to flow act in

- series. The relationships sought are not new.1® We repeat them here

to gain generality and camplefieness. We note that the coupled resis-
tance is a most importent aspect of the following presentation regarding
corrosion in liquid-metal systems. |

Since a large portion of the combined surface effects involve
liquid behaviof; we shali develop & rate term that éives the wall-
related input to an increment of fluid passing a unit area of wall. '
This term will be altered to conform to solid-state diffusion convention

by changing certain liquid concentrations to pseudo-wall concentrations.

‘Three reference concentrations, each referred to the liquid, are

involved. These are: Y, fci and y. Consider a unit area in the hot
zone. The same jM:passesfboth the resistances associated with the

reaction-rate equation,

Jy = (kyx = 11235))9,1Z , | (18)

and the film equation,
i w O T .
Jy = by _y)pz o (20)

Thus, one may solve for jC>using Eq;3(20),,substitute'this'result in

Eq. (18), and, using manipulations allowed by Eq. (19),'obtain:

Iy = B(Y = ¥le, , (21)
where

- 1m =1/ +'1/k2 . (22)

 

193, Hopenfeld and D. Darley, Dynamic Mass Transfer of Stainless
Steel in Sodium under High-Heat-Flux Conditions, NAA-SR=-12447 {July

- e, —

 
 

18

Surface Effects Referred to the Alloy

The next point to consider is the application of Eg. (21) to solve
a solid-state diffusion problem. Equation (21) may be altered as
follows with Y = KTEO : ' - |

= B —y/egde, . (212)

The superscript < appears on the X as & reminder that this is a true
alloy concentration at the surface. We have also substituted subscript T
for subs'cript exp. (experimental) as a r_eminder that kexp = KT varies
with temperature. A basic assumption stated in the Introduction permits
one to treat y as independent of temperature. If we are at a balance
pc_a;i.nt, ,jM #Q,'>c<> = X5, and KT = Kp, where subscript p denotes balance

point. Thus, y = Kp':?a, and for all other points along z other than p we

-may write

3y = BRy(m /) = 2o, (210)
where

<&

x¥ = xa.Kp/KT . (23)
Before writing down the final forms, one will recall that Eqs. (21)
through (21b) were set up in terms of positive flow into a salt volume.
This is opposite to the direction of flow into the metal, so the sign

of Eq. (21b) must be reversed. Then, |

dx(0,t)

Jy = Doy -TW-— = 'EK(ma;/xpM) -(:vc<> - x*)pz . (21c)

The surface condition can be set forth in terms of a derivative

‘where | 7 | |
H=Kr(h/D)(%/pa)(_ma/mM) . @

o
 

-}

¥

N

 

19

The varisble £C>is to be treated in general as x, so we shall drop the
superscript & in Eq. (24)' from this point on. It is of some interest
to note that, if k, in Eq. (17) had been defined as k,"- M(d)mM/ s
Eq. (18) would have involved only weight fractions and the ratio m [mM
would not have appeared in Eq. (25).

TRANSTENT SOLUTIONS

The Introduction stated that the loop operation was to be initiated
with the y'corresponding to the quasi-steady state. Quasi-steady'state
invokes two conditions: (1) that the bulk concentration of the liquid
and, hence, the concentration 6f surface elements, x(0,t), remain fixed
with time, and (2) that the effects of the liquid film resistance on
mass transfer remain fixed with time. From the results of Report I, we
conclude that the bulk concentration of the liquid will have a constant
value in some small fraction of an hour. We now wish to examine the
point in time that the second transient condition, X — x* £ £(t), will
be realized. To find the answer, we must solve a somewhat complicated
solid-state diffusion problem. |

Review of the Equations

A succinct statement of the problem is as follows: First, find a

solution, x(w,t), of the Fourier equation,

% :"»i]; éf , (26)

incorporating Eq. (24) and other appropriate boundary conditions; then
manipulate the results to produce an expression like Eg. (7).

- Solutions for Eq. (26) with (24) have been given for the hot

zones®® using classical techniques, and for the cold zone alone?! using

 

204, 5. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, |

2nd ed., pp. 70-73, Oxford Unlversity Press, New York 1959

21Ib1d., PP 305-306

 
 

20

Laplace transforms. We could start with these results; however, little
would be gained and complete familiarity would be lost if this approach
were followed. In fact, it is Just about as easy to start from the -
beginning, since the flux expressions turn out to be the same (with the
exception of different signs) for both zones. Attention may be
restricted to one zone; and we shall choose the cold zone. Boundary
conditions are x(w,0) = X, x(,t) = x_, x(0,0) = x*; finally, x(0,t)
must setisfy Eq. (24). let

o(w,t) = x(w,t) —

a ’
and
M:X*—Xa.
We have
2 B
ow?® ‘Dot

to be solved with the boundary conditions:??

¢(W,O) = 0 » (a')
¢(oo,t) -0, (b)
6(0,@) = Ax* , (c)

and
"—(0 t) = H(¢ - AX*) (d) (249-)
aW’ ? ’

Notice that nothing is said sbout X at this point. -

Figure 1 presents the variables involved for both the simple con-
stant potential and the present prbblems. We shall not use the subscript c

 

22with the variable change indicated, the solution for the concen-
tration profile could be written in a form analogous to Eqs. (1) and (2);
of course Ax*¥ would replace Ax. Tt turns out that this solution will be
bypassed in passing directly to the expression for AM(t)/Az.
 

w)

~F

Ly}

21

ORNL~DWG €9-10089

 

    
  
  

 

 

 

 

 

 

 

1.0 _
#*" xe=agf (M) —m—m— - — — — 3
. ,
S - x¥= x (o) ———m————— ——— g —————
oo N _ ., L
2 ' '
= Jwt®) - ax ax*
= —_— e
= COLD ZONE $. (%, 7) AND
2 0.6 - wu Lt ¢ (w,7)
a - g| <
z IlE . o :
S log————— e m= e Xg= x{w,#)——|
o 3 é i
g 07+ HOT ZONE
P T ALLOY Ax
o jM(-)
: Ax*
@ ) ———— - ———— ==
g 0'6 — ¢n (W,f)
h
- =x (o) —— X o — X
$o (0 1)
S y_____ N _
0.5

w, DIRECTION OF LINEAR DIFFUSION —»

Fig. 1. The Relatlve Positions of Various Concentration Parameters
and Variables. These quantities govern the concentration profiles in
the tubing walls under transient, then steady-state conditions; they
control concentration profiles and the migration rates in the alloy. An
individual representation of reaction rate contributions is not shown;
thus the difference, Ax* — Ax, relates directly to h or h.

for cold zone in the expressions to follow since we have already stated

this restr:.ct:l.on ‘ ,
We now turn to tra.nsformed versions, starting with the notation of

Churchill?3 and then converting to that of Carslaw and Jaeger.?* In

view of boundary condition (a), the transform of Eq. (26a) is

9%0(w,8) _ 8 5w,s) ~0 =0, o (=6e)
- aw D _ :

 

23R, V. Church:l.ll Modern Operationa.l Mathematics in Engineering ,

1st ed., pp. 109-112, McGraw—H:.ll New York, 1950.

24H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids s
2nd. ed., pp. 58-61, Oxford University Press, New York, 1959.

 
 

22
where

[+ +]
- r—
¢(w,s) = f o8 o(w,t’) at’ .
0

The general solution of Eq. (268) is
o(w,s) = cie"qW + c2e+qW ,
where q = (s/D)l/z. To satisfy condition (b), c, must be zero.

derivative of the particular solution with respect to w is

o (w,s) = --qc:le_':IW .
At the surface,

3  (0,s)

$(0,s) = c, —qc, -

0 is

I

Thus the transform of Eq. (24a) evaluated at w

]

3’(0,5) H[®(0,s) — Ax*/s] .

This may be rewritten as

—qc, = H(e, —~ ax*/s) ,
whereby

¢, = Hax*/s(q + H) .

The inverse of ¢(w,s) = cle"'quill demonstrate that condition (¢) is

satisfied. This implies that Ax* - Ax as t » ». In other words,

x* » X in view of the associated film condition _(d).

Now, since

dx(0,t)
)
Jy = Do, ——=
it is clear that . | |
Dp AX*Hq

= R T e
-}

 

-y

 

 

Y

 

23

The stated goal is a form like Eq. (7). In transformed coordinates
this will be '

Afi:t) {f 3,(0,%") dt'}- 5ls - (27)

Thus

 

. 27)
-. Az . Sq(q + H) ( ’

The inverse®® transform of Eq. (27) is

 

 

M) | op a2} 2B - {1 — exp(-H?Dt) erfe [(IiaDt)l/z:l } . (278)

To go back to sign conventions associated with the corrosion medium, we

merely reverse signs by redefining Ax* to be

e = x, - x* ='xa(1 - KP/KT) .

Equation (23) was used to write the last form.
- Comparison of the first term of Eq.‘ (27a) — including the new ver-

‘sion of Ax* — with the right side of Eq. (7) reveals that both forms

are equivalent. One may recell that Eq. (7) was developed on the basis

* of negligible film or surface effects, whereby *O - x*. This actually

happens over a period of time, depending on the H value, because

exp(—u?) erfe(u) = 0 as u —» 0 (t-0). ""Ciaz"ific'ation is gained by

forming the ratio of AM/A (Where His accounted) to AM/A (where H is

B neglected) The ratio is

._ AX&}(ID?J) = (21{)( )1/2 {1 - exp(-H’-’Dt) erfe [(HaDt)l/z]} : (28)‘

 

257pe inversion formule in this case is ta.bulated as item 15,
Appendix V, p. 405, in H. S. Carslaew and J. C. Jaeger, Conduction of Heat
in Solids, 2nd. ed , Oxford University Press, New York, 1959.

 
 

 

e

Several somewhat fortuitous distinctions evolve when the results
are put forth as a ratio. The results come out in compact form as
1 minus & remainder; the remainder obviously fades out as time increases.
This clearly demonstrates that surface effects, relative to diffusive
effects, are important only in the initial phases of the loop operation.

' An attractive feature of Eq. (28) is the cancellation of Ax*. This

means that specification of the balance point (manifest through Ki) is
not required to preparé a plot showing the effects of h or H. The

reader will discover in later sections that determination of the balance
points is an involved procedure, even under quasi-steady-state conditioms.

Furthermore, we have no idea as to where the balance points reside at

various times during the transient period. Thus, elimination of Ki con-

stitutes an important simplification at this point in the report. Whether
M is lost or gained by the alloy makes no différence when the ratio is

used. The plots of the ratio versus time are always positive.

Application to Sodium-Inconel 600 Systems

For demonstrative purposes, we have concocted an illustrative
exemple fqr the Inconel-sodium system showing rates and degrees of
approach to equilibrium, assuming that the only surface effects of impor-
tance are those associated with the liquid film. In other words, we
assume that k, - o3 thus h - h. This is assumed because no information
exists as to the values of k, and k, for the system. In fact, the values
of KT are not above question. Details of the computation of H are given
later. We have compared two values of H corresponding to typical maxi-
mm and minimum temperatuies for'experiment5=with Inconel 600 loops con-
taining sodium, namely, 1089°K (1500°F) and 922°K (1200°F).

The example'is presented in Fig. 2. Note that the film coefficient,

- h, in this example was assumed to bé the same at all surface points

around the loop, while D and'KT in H were assumed to vary according to
the local liquid (actuslly wall) temperatures. A comparison of these

 

curves clearly indicates that film coefficients are of greatest impor-
tance in the hot zone where solid-state diffusion rates are relatively

 

high. Nevertheless, transient effects associated with the liquid-film
 

 

)]

i3

25

ORNL-DWG 69-10090

 

1.00 ,
0.95
0.20

0.85"

   

0.80

       

CONDITIONS
(°F) 1200 1500 .

[AM (1, 0,1/8M (0,0] - o

 

 

 

075 H _
ah tem®/sec)  7.52x 1077 2.67x10°1
0.70 1 (cm/sec) 4.27x40°2  4.27x10°2
' : ' (wl frac)  $.51x90°%  2,702107®
_{_ {emy?  7.89x107 3.98x10%
0.65 ‘ _
i
0.60 — —
055 |- o '_ A —
. ] L L | | |- ] i |
o 05 10 45 20 25 30 35 40 45 50
EXPOSUR| r '
[EXPOSURE TIME (h 172

Fig. 2. Predicted Transient Behavior in a Sodium-Inconel 600 Loop
Operating at Typica.l Forced-Convection Conditions. The transient feature
results from the presence of a constant liquid-film resistance that
becomes less :unportant as solid-sta.te diffusion resistances incresse
with t:lme. :

resistance become diminishingly small after sbout 24 hr. Since oper-

‘ating times for pump loops cu_rrently range from 1000 hr to one year,
we may neglect ‘such ‘transient effects without significantly affecting
the caleulation of the overa.ll transfer of M from one zone to another.
'This greatly simplifies the problem, ‘only the quasi-steady-state
solution need be consideréd._ The major task is integration of j

" along. z. Of course the work required is minimized if one selects a

" simple, yet reasonable, temperature profile (variation of T with z).

 
 

 

 

26
TEMPERATURE PROFILES AND LOOP CONFIGURATIONS

Reference and Prototype Loops

Our ultimate goal is to develop steady-state solutions for a vari-
ety of loops haviné arbitrary temperature profiles along z. For reasons
of mathematical tractability, we assume that the tempefature profile may
be approximated by several straight4line segménts. The number of seg-
ments is of no importance in the finsl analysis. However, for conve-
nience the connected segments should be drawn such that the overall
profile will exhibit only one maximum and one minimum. A "typical"
pump~loop configuration and profile will be considered for practical
reasons; this will be called the reference loop. Next we shall consider
a very simple profile designed to possess a fair degree of equivalence
to the reference loop; this will be called the prototyfie loop. A Simple
and symmetrical prototype is desirable to minimize the necessary mathe-
matical calisthenics, particularly with regard to the numerical exsmples.

The Reference Loop

 

Figure 3 shows a schematic disgram of the reference forCed;con#ection
loops used in early ligquid-metal corrosion tesfs. Eachvloop consisted of
a pump and cold trap with a heat exchanger between the coid and hot legs
(surge tank attached). The inner tube of the heat exchanger contained
the hot liquid while the cold liquid traveled through the annulus. Thus
the cold liquid was contained between two walls eachrat & slightly dif-
ferent temperature. The cold trap was used to remove traces of oxide
impurities, mainly Na20; from the sodium. Only & smell portion of the
main flow was diverted to the cold trap. The trap design along fiith_this
low flow, coupled with return-line heaters, mitigated major tefipérature
perturbations in the main flow stream. Furthermore, the trap did not -
materially affect the deposition of metal constituents in the cold leg.

" The maximum and minimum loop temperatures were 816°C (1500°F) and
649°C (1200°F), respectively, with a flow rate of 2.5 gpm and a typical
operating time of 1000 hr. The temperéture profile and dimensional

information for the experimental (reference) loop are given in Table 1.
 

) )

»

n

 

27

| — SURGE TANK ORNL-LR-DWG 15353R

    

 

ELECTROMAGNETIC
PUMP

    
   

  

2 = o ‘1' ¥
ELECTROMAGNETIC L
FLOWMETER [}

5 COLD TRAP

TO SUMP
™~
TRAP PACKED WITH INCONEL

NOTE : DIMENSIONS IN INCHES WIRE MESH

Fig. 3. Reference Pung)ed TLoop Used in Corrosion Experments.
Most of the acceptable sodium-Inconel 600 results were obtained with

. loops as shown a.bove s elthough different conflgurations were sometimes

used

 
 

 

 

28

Teble 1. Geometrical-Temperature Characteristics of Forced-Convection
Pump Loops for Liquid-Metal Corrosion Experiments

 

Wall Fraction Cumulative
Flow Section Area. of Ares, Fraction,

(in.?) A/AT Z(A/A'T) (°F) (°c)

Exit Temperature

 

 

 

Economizer® 263.9  0.3367 0.3367 1%50° 788
Annulus
Hot leg loop>  222.1 0.2832 0.6197 1500 816
Economizer - 108.4 ° 0.1382 - 0.7581 1230 666
Central tube ' _ | :
Cold leg loop® 189.7  0.2419 © 1.0000 1200 649
TorAL® 784.1 1.0000
a

Shell and loop tubing: 0.75 in. OD X 0.065 in. wall.
bEn.tra.nce temperature: 1200°F.

®Central tubing: 0.5 in. OD X 0.020 in. wall.
dneludes pump area of 7.05 in.?; see Fig. 3.

€potal length: 349 in.

Before operation, the loop was flushed with sodium at about 650°C
for several hours to remove surface oxides.  The‘cold trap was not used
durihg this operation. For the actual run, fresh sodium was introduced.
After operation, sections of the loop were cut and analyzed by various
methods.

 

A Prototype Loop

Table 1 illustrates that the temperature profile and geometridal
characteriétics of the referencé looP are Quite complicated) especially
~if one wishes to apply a mathematical treatment of the diffusion process
using numericel examples. Work of this type reqfiires a more simplified
configuration, which we shall call a prototype loop. (We employ the
designation "prototype" to suggest that future designs of forced-
convection loops incorporate less complicated flow paths and temperature
profiles.) As stressed in Report I, we again avoid the overworked word

"model," as this might suggest that calculations of the overall corrosion

-t
 

 

4y

b))

29

rate, AM(t), depend on the flow characteristics of the prototype.
Except for transients, which are handled in these reports, the solid-
state diffusion mechanism depends only on the wall temperature and the
concentration of dissolved alloy constituents. We care nothing about
the flow itself or its direction.

Our purpose here is to propose a simplified configuration'whereby
all the geometrical complexities engineered into early forced-convection
loops will be removed; yet the features important to the mechanism
under teSt'will be retained. Actually, we are striving for a maximum
degree of equivalence between the refErence and prototype loops. The
most logical prototype that is easily envisioned is the "tent- shaped”
profile over a constant-diameter loop used by Keyes.?® This "tent-
shaped" profile appears to display the utility desired, although it is
somewhat awkward when applied to other mechanisms, where perhaps a saw-
tooth profile might be most appropriate. The idea that a tent-shaped
profile composed of two straight-line segments cannot be experimentally
obtained has been dispelled by DeVan and Sessions.?27 They used profiles
that were tent-shaped but showed some asymmetry

In long-term.pump loop experimentS'we shall eventually establish
that liquid-film.contributions are not of great importance; thus, the
primary consideration is acQuisition.of alloop with an equivalent area.

‘In Table 1 we see that the total area exposed to liquid is 784 in.? or

5050 cm?. If we assume a constant diameter of 0.70 in. all around the

~loop, the total length will be 906 cm, which is not too far removed

from the actual value of 886 cm for the reference loop" The average
Reynolds number, (N ) weighted according to the fractional areas
involved, is 5.06 X lO4 | S ,

Thus, we inquire as to the (N ) for the prototype loop. Based on

‘5 D , V., p,, and p values of 0.89 em, 3.3 X 10~% cm?/sec,
Ni-Na z® T4 T T TR OTT : L ’

 

263, 7. Keyes, Ji., Some Calculations of Diffusion-Controlled

Thermal Gradient Transfer, CF-57-7-115 (July 1957).

273, H. DeVan and C, E. Sessions, "Mass Transfer of Niobium-Base

Alloys in Flowing Nonisothermal Lithium," Nucl. Appl. 3, 102-109 (1967).

 
 

 

30

63.5 cm/sec, 0.772 g/em®, and 1.80 X 10~% g em™! sec™l, respectively,
one may compute the h as well as the (Nfie) using

- 0.8 0.33
Ny, = 0.023(NRe) Ngo ,

elong with the variables that make up the dimensionless constants,
whose definitions may be found in the Nomenclature. The results ere
that h = 4.27 X 10~2 em/sec and (Nhe) = 4.85 x 10% for the prototype.
Deteils appear in Appendix A of Report I. The value of (N ) compares
favorably with that calculated above for the reference loop Figure 4
compares the temperature profiles for_the prototype and reference loops.

o ORNL-DWG 69-1009¢
T I 1 il — 825

 

 

 

 

1500 |~ A
/ _
\ ‘ — 800
1450 | / \\
// \ -~ 775
L 1400 - /I &
| %J / N\ —{ 750 Eg’
e I’PROTOTYPE \ E
% 1350 | / PROFILE \ | &
s \ 725 =
o / &
- / \\
- /
/  PUMP-LOOP \ '
/ PROFILE S\
1250 |— / | \\'— 675
A\
. \ -
1200 1 | ' ' 650
0 02 04 0.6 0.8 1.0

f, FRACTION OF TOTAL AREA

Fig. 4. Comparison of Tempersture Profiles for Pumped Loops. The
solid curve approximetes temperatures around the "reference" loop; the
dotted curve represents a "tent-shaped" prototype loop.
 

-

2

31

We now wish to calculate the H's of Fig. 2, since these quantities
are based on the geometry of the prototype. .We recall that

 

 

= -lgr(hzfpm)(p‘e/pa)(ma/mM) | .(25)
At 816°C | |
- (270 x 107¢) (421X igj;)(gm)(g 7) < 5.9 x 10%/en
At 649°C .
= (3.98 x :105) ; :; : 10_6> (2'67 X 10-”): 7.89 x 107 Jen .

7.52 X 10~17

The density end viscosity of liquid sodium were‘ based on extrapolation
of appropria.te hendbook values.2® The equilibrium ratios were estimated
from date assembled by Singer and Weeks.2® The diffusion coefficients
for nickel were obta.ined from work done by K. .Monma. et 2l.?® The den-
sity of the Inconel 600 was é.cquired from a vendor'.s handbook?! and the
molecular weight of the ailoy'wa.s compfi’ced from the information presented
in Table 2, which is based on data'reported by DeVan.32 The D used

Ni-Na
in the computa.tion of h was obta.ined from the Stokes-Einstein equa.t:l.on,

 

28R. R. Miller, “Physica.l Properties of quuid Metals," pp. 42-43

in Liquid Metals Ha.ndbook 2nd ed. > TEV., ed. by R. N. Lyon, NAVEXOS-

P-733(Rev.) (June 1952)..

29R. M. Singer and J. R Weeks, "On the Solubility of Copper, Nickel,
and Iron in Liquid Sodium," pp. 309—318 in Proceedings of the Inter-
national Conference on Sodium Technology and Large Fa.st Reactor Design,

- November /-9, 1968, ANL-7520, Part I.

30K. Monma, H. Suto, and H. Oikewa, Nippon Kinzoku Gakkaishi 28
188 (1964); as cited by J. Askill, A Bibliograpny on Tracer Diffus::.on
in Metals: Part III. Self and Impurity D:Lf:f‘usion in Alloys s ORNL~3795
Part III (February 1967), p. 15. ,

| 317ne Huntington Plant Staff, Hendbook of Huntington Alloys, 4th ed.,

Bulletin T-7 (Inconel 600), the Internationa.l Nickel Company, Inc. 3
Hunt:.ngton, W. V., Jenuary 1968, |

32J H. DeVa.n,- "Corros:.on of Iron- and Nlckel-Base Alloys in High
Temperature Na and NaK," pp. 643-659 in Alkali Metal Coolants (Proceedings

- of a Symposium, Vienna, 28 November — 2 December 1966), International

Atomic Energy Agency, Vienna, 1967.

 
 

 

32

" Table 2. Nominal Composition of Inconel 600

 

 

cit - Weight Ty Mole™ Atom

Constituent ;;agiizn (g/mole) 100 g _ Fraction
Ni 0.7635 58.71 1.3000 0.7377
cr 0.1500 52.00 0.2885 0.1637
Fe 0.0700 55.85 0.1253 0.0711
Mn 0.0100 54 .90 0.0182 0.0103
si 0.0050 28,09 0.0178 - 0.0101
c 0.0015 12.00 0.0125 0.0057

 

,(a‘)ma = 100/z(col. 4) = 100/1.7623 =~ 56.7.

: 1 kT
Ni-Na Mye 6:urrNi ’

where r.., =~ 1.24 x 108 cm.
Ni

 

- QUAST-STEADY-STATE SOLUTION

Statement of the Problem and Objectives

We seek a relationship that will permit computation of the amount
of M migrating from the hot zone to the cold zone of the loop, assuming,

of course, that Eso is endothermic; if not we seek the transfer in

1n

- the opposite direction. Diffusion out of and into the container wall

is expected to be slow, and, if the liquid is pretreated to eliminate
transients associated with buildup of M in the liquid, all that remains
is a transient induced by the mass transfer film resistance.

We have previously shown that film transients become negligible
after a day or less. It follows then that our steadyhstate'conditions-
mean that the M concentrations in‘the liquid and the positions of the
balance fioints separating the fiot and cold zones are both steady‘(do not
vary) with time. The term "quasi” steady state must be employed, how-

ever, because the point rates are proportional to t+1/2,'and the gross
 

4y

2N

33

transfer is proportional to t-1/2, ‘Therefore, both the rates and their
time'integrals vary with time. However, in view of the quasi-steady-
state features of the problem, the timeé and position integrations may
be performed 1ndependently of one another. This constitutes a great
simplification of the tasks that lie ahead.

Our starting point is Eq. (7) in which the time integration has
already been performed for single points along z. The next step 1s
integration along z. Since dA_ = 21y’ dz and xi/xa = Ep/KT [Eq. (11)],
we may integrate Eq. (7) as

| AM'(t)- = le Pg ( - "T> (2nr’ L) (Dt>1/ dz’  (7a)

The KT and D are functions of temperature, and z’ is a dummy variable
of integration. A differential form of Eg. (72) is

.ad? G%Mfla :_.e.%xa;pé’ (1 - ]—I:};) (pm)2/2 B (70)

where £ = 2z’ /L. The integrand evaluated at several points around the

loop is plotted in Fig. 5;, Notice ‘that Flg. 5 refers to the prototype
loop, which is actually an ad hoc device for the present. d1scuss1on. :
One could stop here, insofar as the mathematics is concerned, and

integrate graphically as was done in the original work.?? The procedure

adopted at that time was to assume a balance point, prepare_,a plot of

- the integrand as indicated in Fig. 5, and then ascertain the area under
~¢the.hot'zone:portion of . the curve. The~procedfire was repeated for the
. cold zone. Unfortunately'it'was,necessary to iterate until the two.
| -areas. balaheed.:‘USe of'plots;similar to those in Fig. 6 speeded'the ,

work; but this approach requlred many trials, and it was tedious and

- Vborlng to say the least.

The only magor difference ‘between the earlier and present problems

;was/utilizatlon of a sinusoidal temperature proflle inrthe_earller'work.

 

33R B. Evans III, ANP Program Quart. Progr. Rept Dec. 31, 1957,
ORNLF244O, PP. 104—113 |

 

 
 

 

Feb. 28, 1969, ORNL-4396, p. 249.

ORNL-DWG €9-2953A

 

 

 

 

 

IOV T 7T T T A 1 T T 1
| 1080
12
— 1060
_§“ 10 <
g , 1040 &
S ! —1020 2
~— . i é
l: °r | 1000 &
h o 1 p—
: = ° 2
X 4r | -
S . — 980 4
2L : g
1 .
M : ~ 960
| » B
> / 5 | ! \\ - 940
1 i
5 f{p) i - f(p)
2 ; , / ..
r | L1 | 11 1 1 920

 

0O O 02 03 04 05 06 O7 08 09 10
f, FRACTION OF WALL AREA AND/OR LOOP LENGTH

Fig. 5. Profile of Cumulative Mass Transfer Contributions Expressed
as 8 Ratio Involving Loop Length and Time. The profile applies to the
rototype loop operating under quasi-steady-state conditions. Aress
?integrals) corresponding to hot and cold zones are equal; thus, the
balence points are properly located. -

This same approach was used by Epstein.?* This difference is of con-

siderable importance because after ten years it is still quite difficult
to achieve a sinusoidal profile in the laboratory. About the most mathe-
matically tractable profile seen to date by the authors was that obtained

‘recently by DeVan and Sessions3’ and by Koger and Litman.?6:37 Yet even

this profile was slightly skewed. In other words, a series of straight

 

341, F. Epstein, "Static and Dynemic Corrosion and Mess Transfer.
in Liquid Metal Systems," Chem. Eng. Progr. Symp. Ser. 53, 67-81 (1956).

33J. H. DeVan and C. E. Sessions, "Mass Transfer of Niobium-Base
Alloys in FlOW1ng Nonisothermal Lithium," Nucl. Appl. 3, 102-109 (1967).

36J. W. Koger and A. P. Litman, MSR Program Semiann. Progr. Rept.
Feb. 29, 1968, ORNL~4254, p. 224.

373, W. Koger and A. P. L:Ltma.n, MSR Program Semiann. Progr. Rept

 

 

- %
 

»

 

35

. ORNL—DWG 89-10092
- TEMPERATURE (°C) .
" 850 675 700 725 750 775 800
(x10™%) I [ T T | —
2.8

26

 

24
2,2

20

SOLUBILITY OF MIGRATING METAL IN
CIRCULATING LIQUID (wt frac)

 

 

. 14

 

(x10™9) - | i | 7 1 _ I {

  

FTTT]
L1

    

]
|

I
i

SQUARE ROOT OF DIFFUSION COEFFICIENT
FOR MIGRATING METAL IN WALL (cm/vSec)
o

 

 

|1

1 | l | :
1200 1250 300 ' 1350 1400 1450 1500
* TEMPERATURE (°F)

 

Fig. 6. Graphical Presentation of Temperature-Dependent Parameters
That Control the Idealized Diffusion Process at Quasi-SteadyaState

Conditions.

| line segments represents the most realistic epproximation,to experimen-

tal cases. Of greater importance, straight-line‘profiles are the

'easiest to. integrate* 1n fact, the results using straight-line segments

are exact in an analytical sense No serious compromises, such as

straight-line approximation of exponential functions over extended ranges,

are required.

Our problem_divides 1tself into two distinct parts:,'(l) find the

" balance points and (2) compute the amount of material entering or leaving

either zone. Both parts depend on obtaining the position integral. Our

 
 

 

 

36

approach will be to carry out the manipulations using the prototype
loop; present computations for the prototype loop using numerical
examples, hopefully to clarify the overall procedure and nomenclature;

and finally, discuss extension to cases like the reference loop.

Solution in Terms of the Prototype Loop

Equation (7a) is our starting point for the 1ntegrat10ns that'w1ll

produce a solution

_AM(8)] _ f4x o 2" (D, )1/2 1 _ %}) exp ("'ED az . (7¢)

2t1/2 2RT

 

The reader will recall that the time integration was performed‘earlier.
A factor of 1/2 appears on the left side as the symmetry of the tent.
profile permits consideration of only half the loop. Also we have |

introduced the expression for the diffusion coefficient in the form of

(1)).1/2 = (Do)l/é exp (—-—Eg/zmt) . | (30)

The equilibrium constant may be written similarly as either

Kp = K, exp(?Esoln/Ré> , - (31)
or |

=1 _ -1 |

(Kp)™? = (Ko)~1 exp +Esoln/R?> . | (B;a)
Thus Eq. (7c¢) can be divided conveniently into two parts:
A[M(t)] = ( )dzr —-— cl exp [_ D soln az’ , (7d)
2£1/2 - 2RT T

where

C= 4xapar’(flbb)?/2 S (32)
 

.and

37

and
¢’ = CK /K . (33)

The next part of the problem is the key'to the whole solution. It
concerns the relationship between T end z. In terms of °C (or °F) en

obvious relationship is
- ?(z) = T, + bz, °c, (34)
where z runs from O to 0.5; thus
" b—2(T - )/L—ZAT/L. -  (34a)

This would be an ideal form if the exponential terms in Eq. (7c)'were
not present. However, they are indeed present; also they demand values
of T expressed in °K. Consider an extension of the segments on the pro-
files in Fig. 5 whereby the. distance.g would be zero at absolute zero
(=273°C or 0°K). What will happen is not difficult to visualize if one
recalle the trivial relationship, AT(°K) = AT(°C), which means that &

is valid for both temperature scales. One immediately envisions the
possibilities of an extended eoordinate § such that

= (L/2a1)(273 + T°C) = b"3(273 + T, + AT) ,

E = §0'+;Z ) cm., . (35)
which in turn simply means that we have adopted the relationship

| T= BE, °K, o (358)

for the extension. From Eq (35) dé¢ = dz, and the new variable ¢t may
be introduced into Egq. (70) with this and following definitions. Let

=FTD/2bR_'{" L o L (36)

(ED 2E_ 10 // 2bR . - (36a)

 
 

38

Then the right side of Eq. (7d) becomes

Es £,
Cf exp (-a/g) dg’ — ¢’ f exp (—a’ /§’_> de’

£ &

or, in abbreviated form,

0112<a/§> — ¢ i12<°" /g) .

We are now ready for integration. Whether one operates on the

unprimed or primed term is of no consequence as long as & or &’ > 1.

Thus we choose the former. However, a change of variable is useful at

this point. Let u

ore)

a/t or £ = afu; then at = —(a/u?)au;

i

4,

Integration in terms of u can be performed by parts with the formula

f‘l’dw=!fw—fwd\f.

We let
Y= exp(-u) and dw = du/u® ;
then
dy = —exp(—u) du and W= - l/i:. .

Also we note that uy - @ as Ej + 0. The result is

| -~y | e"'ul uze—u' .
I laft)=allE - > + f du']
12 u u u’
2 1 3
' 1
- A —uy A=
= a e 2 — f e - d'll’) _ e -— f e - — duf
u u Uy u
| up | W

 

 

 

 

 

2

)

£z w2 o
fexp(—cx/g'> dg’ = -f -9—2- exp(—uw’ ) dauw’ . (37)
u’

£, )

(37a)
 

| J]

39

Notice, via Egs. (35a) and (36), that u =_ED/2RT in this case. Clearly
the integration does not involve position — only temperature. However,

'L does enter the results through the factor 0. The integral term was

broken up into two parts, each with infinite limits , to cast the results
into a form that brings forth the so-called exponential integrals of the
first order. These are tabulated in the literature.?® In our work,
velues of the argument are large, end in this cese the tabulations are

in the form
+u

where
w .

f e ' aT/T .
u,
Uy
The T in this case is the dimensionless dummy varisble of integration

T=vw =aft. One can show, using W = a/g"; that

ms) - f @ [=t# ](5-)

The minus sign is accounted 'for by suitable a.rra.ngement of terms. As
suggested by the form of the tabulated values, the final result may be

wr:.tten as

I \a/§> = §,e uz[l l B(uz)] _§1e ul[l - (u1):| 3. . . '(37b).

_ wh:.ch clearly shows the contributlon of the pos ition va.ria.bles

Values of B(u ) are plotted on Fig. 7. An accurate interpolation
of the values is clea.rly requ:Lred because the results contain the dif-
ference 1 - fi(u ), and fi(u ) values are not too far removed from unity

:'when u, is la.rge

.

 

38y. Gautschi end W. F. Cehill, "Exponential Integral and Related
Functions,"” pp. 228231 and p. 243 in Handbook of Mathematical Functions,
ed. by M. Abramowitz and I. A. Stegun, U.S. Dept. of Commerce, NBS
publication AMS-55 (June 1964 ). :

 
 

40 | . Y

- ORNL-DWG 69-10093 , ’i
| | | r — o/

 

 

 

 

0.960 (— | , . .
Blu=vje'l £ (y)
FOR vj = a/¢; OR a'/¢
a “ZoR . ’ -
Ep-2E,,
+_ -0 soln >4
_ 2R
__ 0.94s |— | ' —
3 .
Q
0.940 |— ]
Elyy) = f dr, >
0.935 [— /- | ]
0.930 - i — »
I l I ] |
12 14 16 18 20 22 24

Hj -

Fig. 7. Plot of B(u;) for Large Values of us:. The function B(uj)
carries contributions of “E;(us); the interval of u; is dictated by
values of parameters peculiar to the sodium-Inconel 600 system.

Thus far we have outlined a solution for all cases where the reac-
tions leading to mass transfer are exothermic, also cases where the
reaction is endothermic up to the point where Esoln-= ED/Z. 'At this
point the second term in Eq. (7c¢) is simply | |

cxuw)_cg —g> - (38)

which states that the second term in Eq. (7¢) or (7b) is . a constant.
The probability of this happening is quite low in practice, so we shall

- pass 1mmedlate1y to the cases where the solution reactlon 1s endothermlc '

§

enough to bring about the 1nequa11ty

solhl> Eb/2 L , ,  . (hs)

E
 

 

41

When - the energy of solution overrides the contribution of the enefgy
of activation for diffusion, the second term in Eq. (7c¢c) becomes

4xpr'(K/K)(1tD )1/2 exp[ 2E ln—E)/ZRT dz’. .

Note that C’ remains the same. In terms of & coordinates s using the

 same substitutions, one obtains the following:

£, : 4 |
" — 'a” 3 ! = i” ’ ‘ ’
112(0 /§> = fexp <+ ;) dg’ = --f " e:cp(fu ) dw , (39)
£ oy

~ where it ma.y be helpful to th:.nk in terms of the: equa.llty Q’ = =0 .
| -Integratlon y::.elds '

 

 

 

)l ).

which ma.y be rea.rra.nged to coni‘o_rm to tabulated functions as

12<a"/§) a"K u"’::;' - 9—:—;3] | . (39a)

Collection and rearrangement of terms permits one to write

    

     

      

12<a"/§> = 51 {A(u ) - 1:| - 52 [k(uz) - 1] , (39b)
Where_ o | -
L ?‘(fi;i'j - uje;u'jEi(uj')
" and
e My
- Ei(“J) =. f _efld"'/"f. ) fi_'> 0

-0

" The last fimction, E (u ) 1s the exponential 1ntegral, va.lues of
7\(u ) appear in the same ta.bless'8 ‘as those for B(uJ) The presence of

 
 

42

uy fUnctions before u, functions should be expected in Eq. (39b)

because ui > u, and exponentials with positive arguments appear. A plot

of k(uj) egainst uy for large values of the argument appears in Fig. 8.
The balance point is located by integrating over the entire loop.

One assigns 1 and 2 in Eq. (7d) as the terminal points of the loop. A

mass balance requires that this integral be zero if the liquid is

essentially pre-equilibrated. Thus, Eq. (74) can be rearranged to yield

or

145

1144 .

143

1.42

141

1.08

.07

1.05

on,@) = ¢ L,) |

 

I,,(c) .C’ K  Esoln\
me e wlw) ol

ORNL-DWG 6§9-10094 i

 

F

 

    
 

[ T 1T 1 | | I I

Mup=v; ™ Eitep) -]
FOR v = a"/£| |
':——————ZE”".-E" >‘

a 207 —

vy
Ef'(ufi"f "-;dr.rfl
- %o

  

 

1 | | | | | 1

 

9

10 i 12 13 14 15 16 7 {8 {9 20
Ui ’

Fig. 8. Plot of A(u:;) for Large Values of u;. _Application of this

plot is required when 2E

soln exceeds ED. This si% tion is encountered

vhen molten-salt systems are discussed in sections to follow.
 

 

 

43

One may back calculate to find T and then successively z, T, § , and
finally, u- The AMimay'be evaluated by application of Eq. (7d) using

either the limits (1,p) over the cold zone or (p,2) over the hot zone.
Details concerning these manipulations appear in the next section.

Predicted Results for ScdifimeInconel 600 Systems

Two objectives are associsted with this section of the report.
First, we hope to attach some physical reality to equations developed
in the previous section through presentation'of numerical exemples,
thereby demonstrating thet the equations are easy to use in spite of
their formidable appearance. Second, we desire to predict corrosion
rates under our assumed condition that diffusion controls both in the
hot and cold zones and that a predictable balance point does exist, as
suggested by the mlcr0probe data shown in Report I. To parallel the
procedures for the preceding derivatlons, we may specialize to the case
of the prototype for simpllcity'W1thout too much loss in generality.

One may start by considering the first and third columns of
Table 3. The first computation requlred involves b. One finds, using
Bq. (34a):

b=l = L/sm =- 906/2 X 167 = 2.71 em/°K .
Related eqaations give _‘ B N |
£, = (2.715 cm/°K) (922°K) = 2503 em
and | )
g = (2.715 em/°k)(1089°K) = 2956 em .

z
Ccm@fitation.of'u and u, 'requires e knowledge of @ and &'. But these,

1n turn, require parameters associated'W1th the curves of Fig. 6.

 
 

44

 

 

 

Table 3. Values Used to Compute Balance Points and
Mass Transfer in Prototype Loop ' '
. Ej,' cm
Functions of gj §2 = 2956 gn - 28126 gl = 2503
u, = a/gga-) 16.22¢ 17.05 19.165
u’j = o /ggb) 13,000 13.66¢ 13.35,
exp(-u,) 8.98, x 1078 3.92, X 1078 4.77, x 1077
-~ exp(-u}) 2.26, X 10=6 1,172, x 1076  2.160 x 10~7
1- B(u.) 5.52 X 1072 5.28 X 1072 4.76 x 10~2
1 - B(d)) .\ 6.73 x 10°2 6.43 X 1072 5.82 x 102
‘ua[l ~ B(uj)]  1.466 X 1077 5.83 x 1076 5.69 x 1077
| e W1 -p(u;)]  4.509 x 1074 2.120 x 10~  3.15 x 10~5

 

(a)a = ED/ZbR = 4.797 X 10~* cm.

(b) ’  _ . 2 -41
o = (ED 2E501n)/2bR = 3.842 X 10™% cn.

For & and related computations, diffusion parameters for nickel,
in an alloy similar to Inconel 600, as reported by Monma et al.39
appear adequate, namely: D, = 3.3 cm®/sec and E, = 70.2 keal/mole.
For o/ and related computations, estimates of parameters based on
solubility data for nickel in sodium &as reported by Singer and Weeks4°
were employed. Pertinent values here are K, = 6.79% X 1077 weight frac-
tion and E soln = = 6.985 kecal/mole. Application of all these values &s

indicated in the footnotes of Table 3 produces the values shown Thus,

 

39K. Monma, H. Suto, and H. Oikawa, Nippon Kinzoku Gakkaishi 28,
188 (1964); as cited by J. Askill, A Bibliography on Tracer lefu51on
in Metals: Part IIT. Self and Impurity Diffusion in Alloys ORNL-3795
Part III (February 1967), p. 15.

“0R. M. Singer and J. R. Weeks, "On the Solubility of Copper, Nlckel

~and Iron in Liquid Sodium,"” pp. 309-318 in Proceedings of the Internatlonal,

Conference on Sodium Technology and large Fast Reactor Design, November /-
9, 1968, ANL-7520, Part I.

 
 

 

45

various values of §j'could be converted to the corresponding u, values.
The latter allowed calculation of the exponential functions; they also
allowed acquisition of appropriate 1 —-B(u ) values with the aid of
enlarged versions of Fig. 7. 1In this regard note that both a and o
‘are positive; thus, functions related to the El(u ) values apply here.
The operations necessary to complete the first and third columns are
straightforward and require no additional comment.
" The next and perhaps most importent task is a computetion of the

“balance points (the points at which Jy = 0). Since the prototype is
under consideration, just one point is needed because symmetry permits
treatment of only half the loop. The criterion is to set AM(t) = O in
Eq. (7). Thus the appropriate sum of the integral terms must also be
zero when the integratlon is carried out over the entire loop. This
facet of the solution is discussed around Eq. (40), reference to which
clearly 1ndicates the method of approach° namely,'we seek TP or f(p)

__through K% The 1atter is given by:

K, = Kollz(d/§)/1i2(a' /&) = (6.79 X 1073)(1.46 — 0.0565) X 1073 /(4.509

- 0.315) X 10-4 ~ (6.69 X 10'5)(3 .37 X 1072) = 2,28 x 106

The temperature correspondlng to K_ is 1036°K, thus § ~ (2.715)(1036°)
= 2813, and f(p) (of L/2) is O. 683. Computation of the values in the

middle column corresponds to & information
Finally a value for AM(t) may be.found by use of integral terms for

the cold zone (limits: 1,p) and for the hot zone (limits: p,2). Values
for both zones were computed and averaged since all the differences ;
involved introduced some uncertainties in "hand calculations.” Every-
thing required,todcalefil&te AM(t)'appears in Table 3 except_valfies_offc
and C’. The latter are evaluated through Egs. (32) and (33). Thus |

= (4)(0.763,)(9.111)(0.350 x 2.54)(3.3 x 3.141,)}/2 = 70.9 ,
and o

= (3.37 x 10~2)(70.9) = 2.39 .

For the cold zone, using Eg. (7¢) again,

 
 

 

46

mM(t)/261/2 = (70.9)(5.83 ~ 0.569) x 1076 — (2.39)(2.12 — 0.315) x 1074
= (3.73 - 4.31) X 10°% = 5,8 x 1077 g/Sec1/2 .
Fer the hot zone, _ |
AM(t) [2£1/2 = (70.9)(14.66 — 5.83) x 107° — (2.39)(4.509 — 2.12) x 10™%
| = (6.-26 - 5.71) X 107% = 45.5 x 1077 g/sec?/?—
The different signs mean that the liquid sodium-loses nickel in the cold
zone, but it gains nickel (in principle, an equal amount) in the hot

zone. The test period of interest is 1000 hr, 2t1/2 = 3.8 x 10*? secl/z;
therefore: | |

AM(t = 1000 hr) = (3.8 x 1072)(5.65) = 0.215 g Ni .

A very high value of transport could be obtained by assuming that
no balance point would exist because all the liquid could be forced
through a 100%-efficient nickel trep placed at the coldest point of the
loop. In other words, the entire loop would be & hot zone. One obtains

(3.8 x 103)(70.9)(14.66 — 0.57) X 10~°

I

Am/mx(t = 1000 hr)

3.8 g Ni .

This value was computed for comparative discussion.

DISCUSSION OF SODIUM-INCONEL 600 RESULTS

- The manner in which the material has been presented up to this

- point almost demands that some comparisons be made between predicted

(computed) results for the prototype loop and those for the reference
loop. 1In this connection, we digress to note that extension of the
mathematics to actual lOops_withvtemperature'profiles as indicated by
the solid iine segments in Fig. 4 is relatively simple in principle,

but tedious in practlce —-because symmetry is. lost and several straight-

line segments (each with 1ts owvn b, O, and @ values) are present. Of
 

 

»

)

4

 

47

course, each must be accounted{ Accordingly, a computer program*! was
@eveloped to handle all cases where E, 2:2Eséln'

There were several reasons whereby use of a program could be
justified. As shown in our illustrative calculations, the balance
point is difficult to determine precisely by hand; we might add that
acquisition of predicted corrosion and deposition profiles is also
desired. The program permits an'accuréte prediction of these because
the computer can evaluate fiany:"poin " Jy's quite rapidly after locating
the balance points [and evaluating AM(t) in passing].

The reader is invitéd.to Inspect Fig. 9, in which computer program
results for the actual loop and the profotype are presented together.

‘The 1000-hr AM(t)'s computed from the integral forms are 0.232 g for the

actual profile and 0.213 g for the prototype. Recall that the hand
calculations based on Table 3 gave a value of 0.215 g for the prototype.
The locations of the balance points for each case are also in close

agreement. Thus we may conclude that the prototype is an excellent

- device for estimating AM, even though the proflles themselves turn out

to be somewhat different in appearance.

- The point of greatest 1mportance is whether or not the mechanism
under discussion here gives a reasonable representatibn of what‘happens
in an eggerlmental loop. The answer to the question, as was the case
for Report I, is, "No, it does not!" The amount we must account for
ranges between 10 to 14 g Ni. The computations produce values consider-
ably less then 1 g Ni if one asstmes that a balance point exists and

about 4 g if one assumes»thatithe entire loop ects as a hot zone under’

the dominance of the mechanism;pfoPoSed. In regard to the latter; micro-
. probe data show that deposition occurs in at least half the loop.
- Deposition tendencies are, in fact, so great that a region of nickel

deposits appears, and furthermore samples of loop sodium suggést that
the- liquid is either supersaturated or contains suspended metal particu-
letes all around the circuit. Thus we can forget about the value of

 

“lmhe camputer program-was ‘devised by D. E. Arnurius and
V. A. Singletary of the Mathematics Division at ORNL. - The authors
acknowledge thls 1mportant contributlon to the present study

 
 

 

~
0

ORNL-DWG 69-2953

 

(x107)

12

(AM/LVF) (gem sec2)

Z
df

— 1080

. —1 1060

1040
1020
. 1000
980

960

 

940

920

 

 

fi (Aam/L ’\/l‘_) (g cmit )

- 1080
1060
1040
1020
1000
980

960

 

 

 

|
Hp}
R S

e o e - ——— i —

940

 

N 920

 

4 g and base our conclusions on a predicted value renging about 0.242 g.
Other shortcomings of thé mechanism described hére stem from the initial
aésumptions that AM is not a function of fluid velocity — only of wall
temperature — and that AM should be directly proportional to the square

root of time. Both assumptions are in opposition to experimehtal behav-

ot 02 03 04 05 06 07 08 09
f, FRACTION OF WALL AREA AND/OR LOOP LENGTH

Fig. 9. Profiles for Cumulative Chromium Corrosion as Computed for
the Reference Loop, at Top, and the Prototype Loop Below.

ior as described in Report I.

At this point we must consider which of the two limiting.casés
(treated individually in Report I and in the present report) might be

most responsive to alterations td form the basis for an empirical

1.0

WALL TEMPERATURE (°K)

WALL TEMPERATURE (°K)

U
 

 

£

&

 

49

correlation. In other words, if we wefe to concoct a combined mechanism
accounting solid-state and liquid-film diffusion effects together, where
should we start? Intuitively, we lean toward the idea of going to work
on the liquid-film mechanism, simply because it is the faster of the two
considered thus far. We are attracted to this point of view because

resistances associated with a fast mechanism can always be reduced by

addition of a time-variable resistance that acts in series with the
liquid film. On the other hand, it would be most difficult to justify

‘decreasing the resistance of the slower mechanism. We should mention

here that inclusion of & film resistance in the usu2l manner gives rise
to a transient effect, which decays:with time. Although such an effect
is fortuitous, the overall result was to reduce further the already low
value of material transported. | |

Two possibilities for altering the diffusion mechanisms under dis-

cussion might seem feasible. The first would involve increasing the

‘value of D.. such that the prédicted results and experimental‘data

Ni ,
would coincide. The factor of increase would have to be about 10°, but

this might be tempered by the use of higher solubility values. Never-
theless, increases of this msgnitude do not appear reasonable, and one
tends to rule out this possibility. |

A second possibility for increasing the predicted values would be
to invoke solid-state diffusion equations where the point at which w = O
moves around the loop. In other words, assume that the walls grow
slightly thicker in cold regions and slightly thinner in the hot zones.

This would accrue from corrosion reactions that will not "wait for" a
'diffusiOn-contrOlléd procesS' However, the solution x(w,t), even for
 the case where the w = 0 boundary moves at & constant rate (a simple
| case) 42 15 too complex to be effectively spplied to & mathematical

treatment of the ma.ss transfer process.

 

42p solution of this kind is given by E. G. Brush, Sodium Mass

- Transfer; XVI. The Selective Corrosion Component of Steel Exposed to
Flowing Sodium, GEAP-4832 (March 1965), Appendix II, pp. 105-110. More

general forms of this solution appear on pp. 388-389 of H. S. Carslaw
and J. C. Jaeger, Conduction of Heat in Solids, 2nd ed., Oxford
University Press, New York, 1959, along with citations of the original
work (in 1955), which also involved diffusion in liquid metals.

 
 

50

For both possibilities, a large amount of experimental data would
be required to justify the selection of the approach and the evaluation

of the parameters required. It would seem that, on the basis of the

date available, the best approach is to resort to an empirical treatment.

This is the objective of the next repbrt. We may now turn to an applica-

tion of the solid-state diffusion mechanisms to molten-salt systems, for

~which the corrosion reactions are well understood and the diffusion

mechanism appears to apply — as demonstrated in early experiments.
APPLICATION TO MOLTEN-SALT SYSTEMS

The results of experiments carried out over the past few years on
the temperature gradient migration of metal 1n a molten-salt environment
1nd1cate that the overall rate of movement is controlled by diffusion
rates within the metal. Hence, we will apply the equatlons derlved '

earlier to several molten-salt systems to demonstrate the usefulness of

the method. .

At the beginning of the qperatlon of a molten—salt loop that con-
tains UF; as reactant, chromium will be removed from the entlre loqp
until the CrF, concentration in the circulating salt reaches equilibrium

with the chromium concentration of the wall surface at the coldest

. position of the loop. At this time this position is the balance poifit.

Then, as the concentration of CrF, in the circulating salt increases
even more, this initial balance poiht develops into a growing deposition
ares bounded by two balance points. Steady state is attained when the
balance points become stationary and the CrF, concentration in the cir-
culating salt ceases to vary with time. Our mathematical analyéis is
valid for this laSt condition we call the quasi steady state. Quasi
steady state can also be obtained by pre-equilibrating the salt before
loop operation — that is, adding the amount of CrF; required so that

the concentration will be constant.

Thermal Convection Loops

A schematic diagram of the reference thermal convectlon loop used

in molten-salt experiments, particularly the °lCr tracer experiments,-
 

by

4,‘

 

51

is shown in Fig. 10. The thermal convection loop differs from the pump
loops mentioned in the earlier sections in that flow is achieved by.
convection forces resulting'fram‘heating one leg and an adjacent side
of the loop while'expoéing the other portions of the loop to embient
conditions. The flow velocities in the thermal convection loop are 2
to 10 fpm, depending on the temperature difference and dimensions of

 the vertical sections. The total tubing léngth'of the loop under dis-

cussion is 254.0 cm and the diameter is_l.383 cn.

ORNL-LR-DWG 49844 A

¥a-in. SWAGELOK TEE

3-in. SCHED, 10 PIPE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

%-in. SWAGELOK l
! <
SAMPLING POT l
,fi@
P .
© = "_T I o
_/’ . . ?\le‘
B®-
/o
! “lhp ‘ &.L_::’ 1 4s
+ ] 1
el
? <
? , i 8
i [=—3%-in. SCHED. 10 PIPE —---‘
g |H+—@ o 2=0
| | n
: , T
) o %
: . i Kl
| T 2
W p o e i, .
.l‘ . ' _-f’”’_ ‘_:,—" 2
\ “' - “’;:: ':‘-”/A
THET e
NG
H e THERMOCOUPLE

%4-in, SWAGELOK (INCONEL)
Fig. 10. ‘Thermal-Convection Loop Used in 51Cr Tracer Experiments.

Circled numbers and letters denote thermocouple designations and
locations. :

 
 

52

The maximum temperature of the two actual (reference).thermal con-

vection loops in which our calculations are based was 860°C (1580°F)
‘and the minimum 685°C (1265°F). Both loops were constructed of

Hastelloy N, whose nominal composition is given in Table_4. As noted
in an earlier section, the actual loop temperature profiles were not
conducive to a simple analytical expression, so we have proposed a
simplified configuration ("tent-shape" profile), which we designate the
prototype profile. Figure 11 shows the average temperature profile for
the two loops and the profile assumed for the prototype. ' The prototype

profile was constructed by drawing straight lines from the minimum tem-

- perature at £ = 0 and 1.0 to the maximum temperature at £ = 0.5. This

construction provided the same maximum temperature for the actual and
prototype loop while allowing some small difference in the areas under
the curves.

The diffusion coefficient of chromium in Hastelloy N as & function
of temperature is given in Fig. 12. These values are based on determina-
tions#3s44 of the self-diffusion of chromium in Hastelloy N using the
tracer °1Cr in thermal convection loops like those previously mentioned.’

The appropriate Arrhenius relation constants are

D, = 6.068 x 107° em?/sec
and

Ep = 41.48 kcal/mole .

 

43§. R. Grimes, G. M. Watson, J. H. DeVan, and R. B. Evans, "Radio-
Tracer Techniques in the Study of Corrosion by Molten Fluorides,"
Pp. 559-574 in Conference on the Use of Radioisotopes in the Physical
Sciences and Industry, September 6—17, 1960, Proceedings, Vol. III,
International Atomic Energy Agency, Vienna, 1962.

44R. B. Evans III, J. H. DeVan, and G. M. Watson, Self-Diffusion
of Chromium in Nickel-Base Alloys, ORNL-2982 (January 1961).
)

 

53

 Table 4.

 

 

M

Typical Composition of Hastelloy I\Ta
Weight M Mole or
Constituent or Mass Atom
Fraction  (&/mole) Fraction
Cr 0.0741  52.00 10.088
Ni 0.7270 58.71 0.765
Mo 0.1500 94.95 0.096
Fe 0.0472 55.85 0.051
c 0.0017 |

 

®Density of Hastelloy N = 8.878 g/cm’.

ORNL-DWG 69-10095

 

  
 
 
 

  

 

   

   

  

 

   

 

 

1600 ] I I I 1
LOOP NUMBER o — 860
s 1248 \
1550 - ° 1249 .
ACTUAL 840
| MOLTEIg SéxLT _
: PROFIL _
1500 | \ \ 820
- | \

. g: S © — 800 ;5
W 4450 \ w
5 \ — 780 &
— -
g \ g
& ya00 | — 760 g
& =
= —{ 740 F

1350 : T(°F) T(°C) T{°K)
: £=0 1265 6850 958.2
© F=0.25 1310 T710.0 9832 \ 720
f=053 {580 8600 1133.2 \
1300 F=090 410 765.6 10388 7
f=1{00 1265 €850 9582 . | 700
1250 ! I T S R NOU NS 680
0O 04 02 03 04 05 0.6 07 0.8 09 10
f, FRACTION OF WALL AND/OR LOOP LENGTH
Fig. 11. Temperature Profiles for Two Experiments with L00ps as

Illustrated in Fig. 10. The "average" curve (solid line) drawn through
the two sets of data was taken as a reference for all molten-salt
examples considered. The dashed line represents the s1.mplif1ed "proto-
- type" loop more amensble. to ma.thema.tica.l treatment . o

 
 

24

ORNL-LR-DWG 46403
TEMPERATURE (°C)
850 800 70 700

B T

A COEFFICIENTS BASED ON TOTAL SPECIMEN COUNTS

@ COEFFICIENTS BASED ON Cr3' CONCENTRATION ——
GRADIENT MEASURED BY COUNTING ELECTROLYTE

O COEFFICIENTS BASED ON Cr®' CONCENTRATION

° GRADIENT MEASURED BY COUNTING SPECIMEN

 

 

 

>
/
®
oe
o®

1090 £ {cm?/sec)
>
b

>
>
b.
bfl
ce
L

 

|~

 

 

 

 

 

 

 

 

 

 

 

-173 ]
. N A o
© a
A

OBTAINED UNDER NON-CORROSIVE CONDITIONS o o8-

BY ADDITION OF Cr*F, TO NaF -ZrF,
a L |

8.75 9.00 9.25 9.50 9.75 1000 10.25 10.50

10,000/1 (oic-1)

Fig. 12. Diffusion Coefficients of °lCr Obtained from a Tracer
Loop Experiment (1248 on Fig. 11). The average curve was the basis for
Dy and ED used in all computations relative to molten-salt examples.

Redox Corrosion Equilibria and Systems Selected for Discussion

' In our examples we shall consider three different molten-salt
systems. Table 5 lists the significant reacting components of the salt
and also the alloy constituents sensitive to oxidation by the salt.
Also shown are the equilibrium values and constents of the corrosion
reactions. The three corrosion reactions have been designated as
examples I, II, and III. |

In example I the salt was composed of NaF—7 mole % ZrF; with
6720 ppm FeF,. The salt of example II is assumed to be primarily a’
LiF-BeF,-UF;, mixture typical of a fuel salt for a reactor wifih ho’impfiri-
ties such as FeF, present. Example III involves the same basic-salt as
example I but with HF present instead of uranium or iron fluorides.

In molten-salt mixtures HF can be formed by a reaction with water or
 

®}

»

 

55

Table 5. Equilibrium Constants for Molten-Salt
Corrosion Reactions

 

 

Salt : L coe
. - Reacting AH
1 : L
Example (ifizef;) Species o | %o (cal/mole)
I NeF—47 ZrF cr(s),FeF>(4d) [rellCrr,] 53,7 . =9,470
e T i —— - i
s 4 PIBLESAL TorllFers] ’

. 2 - V
II LiF-29 BeFr  cr(s),UFsi(d) [erR]IURsI® ) gy x 102 443,920

—5 ZrF;~L UF, . - [crl[HF,)?
IIT Example II cr(s),HF(g) LorF, K] 7.586 X 1076 41,450

salt | [_Cr][HF]2

 

other hydrogenous impurities and is usually present to some extent in
all fluoride salt mixtures at the start of loop operation. In regard to
the ZrF; present in the selts'of exemplesiII end III, certain amounts of
ZrF,; were added to LiF-Ber.mixtnres:that contain UF; to prevent precip-
itation of UO; through inadvertent contamination of.thelsystem'with

oxygen.

Transient Factors

Certain transient factors that are associated with surface condi-
tions, even with a quasi steady state, were discussed earlier for the

sodium-~-Inconel pump loop system. We will now perform calculations and

,discuss these transient factors for the molten-salt systems.

, The conditions under which the calculations, -both transient and
quasi-steady-state cese,'were_made for example I were realized experi-
mentally in an actuel,thermal convection loop, designated as loop 1249.
In this loop an excess of FeF@xwes added.to the salt g0 that the entire
loop acted.as & hot zone. No balance point existed since chromium was
removed from the alloy at all positlons. | T

For example I, the controlling corrosion reaction is

| Cr(s) + Fng(d)-v-Cng(d) + Fe(s)

 
 

56

On a mass basis Eq. (21b) becomes

Tre Torp [FeF, ] )
o G ) ) (e o

 

Where
[crF;] = x

and

| dler(0,t)] _ h e mch2> ([Fng]) ( _ )_
— 3% (mF ——=) (ler 7,1 — [CrF2]

mFe’mFeF are the molecular we:.ghts of the respective species; [ FeF- ]
and [Fe] are the concentrations, 6720 ppm and 5%, respect:wely From

Eq. (25),
w%$®%F%%

As in the liquid metal case, H was calculated for the ma.xurmm and mimi-

 

 

mum loop temperatures, 1133 and 958°K.

- 0—
y 03( ) 3.045 X 10 )( )(572x1 )
Hyy330g = 3-63 X L 8.90 6.06 X 10~13/ \93.84% X 10-%

= 4.83 X 10%/cn .

; = 12
! H958°K = 3.0 x 10'%/cm .

 

 

K, was calculated from the equation, log K = 1.73 + 2.07 X 103/r, which

i | was obteined from combining experimental equiln.brium quotients of the

reactions4’

CrF2(d) + Ha(g) ==cr(s) + 2 HF(g)
and

FeFp(d) + Ha(g) =Fe(s) + 2 HF(g)'

 

450, M. Blood et al., Reactor Chem. Div. Ann. Progr. Rept. Jan. 31,

1960, ORNI~-2931, pp. 39—43._

[—.,,4- T
 

»

n

 

57

in NaF—47 mole % ZrF,. We used. Py(salt) = 3.71 - 8.90 X 10’4'T(°C)
= 2.945 g/em® at 1133°K, p, from Table 4, and D from Fig. 12.

The liquid film coefflcient, h, is obtained.from 8 cafibination of
dimensionless groups, and'wé have calculated it for both turbulent and
laminasr flow. :

For turbulent flow, N, = 0.023N_ 0:8Ny_ 0:33  yhere N, = dh/D,

Sh Re Sc Sh

Ne, = DVo/u, Ny = u/pD, and d = 1.383 cm.

1.383h

o 1.383(1.422) (2.945) T8 2.62 x 10-2 0.33
4.166 X 10°° )

= 0.023[ _
2.62 X 10~2 .945(4.166 x 10™7)

or h = 3.045 X 10~%. The viscosity, u, was extrapolated from experimen-

tal values“S:

T, °C 600 700 800
1L, centipoise 7.5 4.6 3.2

- The liquid difquiofi-cCefficientjis calculated from the Stokes-

Einstein equation, where

1 kT(°K)
Hsalt 61trCr

 

flér(g)-salyle =

11,38 x 10-16(1133)
2.62 X 10~2(6)(3.142)(0.76 x 10~8)

 

Per(d)-salt, [1133°K

4.17 x 10~% cm 2 [sec

and the velocity of the sait = 2.8 fpm = 1m422 cm/sec is taken from the
loop operating conditions. ." _ ' _

There is always the questlon of whether the flow in a thermal con-
vection loop is leminar or turbulent. For the case of laminar flow, a
mass transfer equation can be written and h can be calculated. Its

 value is sufficiently close to the h calculated with the eqnatlon for
turbulent flow so that the former h will be used in subsequent

calculations.

 

463, Cantor, ORNL, personal communication.

 
 

 

58

The transient calculation for éxample IT is made somewhat differ-

ently because of the pre~equilibration and the presence of balance points.

The corrosion resction is

Cr(s) + 2 UF,(d)=> 2 UF3(d) + CrFp(d)

and |
- m KN 3lcr(0,t)]
2 2 - ) -, 2L
oler(0,6)] _KpPpMa 1 ([Cr]o—[()r]) h
ow | Ké P, ™M, ferl \ D

 

EEEEE

5 _3.53 x 107°¢ G 994) C:l 'Dc .308 x 10-4\
1133°K  1.26 x 10-¢ 06 x 10-13/

= 3.777 x 10° .

 

 

Kp and Kl‘) were calculated from the equation log K = 3.02 — 9.6 x 103/7,
which was obtained from combining experimental equilibrium quotients47

- of the reactions

Ha(g) + CrFa(d) == Cr(s) + 2 HF(g)
1/2 Ha(g) + UF.(d) = UFs(a) + HF(g)

in LiP-33 mole % BeF,. Values of these quotients are tabulated later.

Also, py(ca1y) = 2.575 — 5.13 X 10"4¢(°C) (ref. 46), p, is from Table 4,
m,, W, are the molecular weights of the alloy and salt, respectively,

D is from Fig. 12, h is calculated as before and = 2.308 X 1074,
d = 1.383 cm, and = 0.0916 exp(4098/T) centipoise (ref. 46).

Again the diffusion coefficient in the liquid is calculated from
the Stokes-Einstein equation: |

 

“7C. F. Baes, "The Chemistry and Thermodynamics of Molten-Salt-
Reactor Fluoride Solutions," pp. 409433 in Thermodynamics, Vol. I,
Internstional Atomic Energy Agency, Vienns, 1966.
 

 

 

59

1 1.38 X 10~16(1133)

9 = = 3.21 x 1073,
Cr(d)-salt,[1133°K ~ 5, 1072 6(3.1416)(0.76 X 10-8)

 

end the velocifiy of the salt is 1.422 em/sec from loqp opergting data.
We calculated H to develop a curve such as Fig. 2 for the molten salts.
However, it became quite evident that, because of the high value of H
for each example, the transient effect would be'even less than that
seen for the liquid metals. Thus, we again show that the transient
effects may be neglected and that only the quesi-steady-state solution

need be considered.

Quesi-Steady-State Solutions

Agein, as in the liquid metal case, we are required to find the
balance points (in examples II and III) and the amount of material
entering or 1eaving.the hot and cold,zones.' The calculations will be
made for the actual and prototype loops using the equations derived
earlier. The variables affecting the results of these calculations will
then be discussed. We will present'comfiuter‘calculatiofis for two of
the exemples and will show the details of a "hand" calculation for
example II to demonstrate the usefulness of the equations.

As filready noted, the conditiqns under which the calculations were
made for example I repreéent actual conditions encountered in loop 1249,
namely, an excess of FeF, was added to the salt so that the entire loop
acted as a hot zone. No balance point existed, and chromium was depleted
from all surfaces. 'Figure 13 shows the positional dependence of mass
transfer rates in the reference and prototype loops as determined by .

. computer calculations."Thé total mass removed in 1000 hr is 0.595 g in
the reference lbop, compared_fiith_0.6122 g in the prototype. '

In example II, balance points exist,fand, as in the liquid metal
" section, we have tabulated thé values of the various variables and will
demonstrate the arithmetic involved for,thé prototype loop. The obvious
difference between this moltenysalt calculation and the liquid metal
_calculation is the fact that E_, > E /2. This necessitates the use
of the Eqs. (39), (392), and (39b). We did not compile a computer
program to handle the Esoln'> ED/Z case, so we have used the &pproach

 
 

 

60

ORNL-DOWG 63-9929

 

 

      

 

 

 

 

 

 

xigH b T 1 17 17 1 1 (x1o o T T T T 1 | L
— 140 — 140
° _ .
Cro+ FeFy {xs) N Cro+ FeF, (xs)
— ' & | & - =
& 200 — ”  \\ oo o ' 200 "o g
W \ - @ s
§ / \ g 7 ¢
i / \\ 2 e 2
5 Il \ — 1060 o 1060 -
< 150 |- / N - L3
L: -——,— i illE l’ -
N 1 \ a 32 -
X ! \ 10203 X 1020
g / \ z 2 g
bk 1.00 — ! \‘ §I§ 1.00 —
- M 980 | 980
. ' \ 7/
L~ _ \ y \
0.50 0.50
0O 04 02 03 04 05 06 07 08 09 10 0O 04 02 03 04 05 06 07 08 09 10
f, FRACTION OF WALL AREA AND/OR LOOP LENGTH £, FRACTION OF WALL AREA AND/OR LOOP LENGTH

Fig. 13. Profiles for Computed Chromium Corrosion of Hastelloy N
when High: Fng/Cng Ratios are Present in & Molten-Salt Mixture. Pro-
files are based on wall temperatures shown by dashed lines. The salt
was NaF—47 mole % ZrF,. Reference loop results are at left; prototype
results are at right. - |

of itorative balance point calculations. The terms used in these
calculations are listed in the first and third colummns of Table 6.
The value b is computed with Eq. (34a):

= 2AT/L = 2(1133 — 958)/127 = 1.38°K/cm ,
and £ is computed with Eq. (35a):
£

i

958/1.38 = 695 cm ,
and 7 |
£, = 1133/1.38 = 822 cm .

Next we calculate u, and u,, which require values of O and o”.

For these next calculations, we use the values for the dlffu51on
of chromium in Hastelloy N as given in Fig. 12: Dy = 6.068 x 10™° cm?®/sec,
ED = 41.48 keal/mole. The values of ¢ and @” are shown in the footnote
of Table 6 and are used along with the &€'s to obtain ua and vw”. From
the 1atter we acquire the exponentials and thus can obtain the 1 — fi(u )
values from Fig. 1l4. The values of'k(u ) are found in Fig. 8. One is

now able to complete the calculations of the last two functions.

C,
 

 

 

61

Table 6. Values Used to Compute Balance Points and
Mass Transfer in Prototype Loop

 

 

 

 

| tp 1

Funetlons of &5 ¢ . 822.55 £ = 755.44 £, = 695.36
u = a/gg‘?) 9.211 ~10.027 ~10.893

uj = a"/ggb) 10.281 11.1916 12,175
exp(—uj) 1 x 10-% 4.427 X 1072 1.862 x 107°
exp(-&—u’j’) 2.912 x 10+4 7.238 x 10%4 11.935 x 10%?
1 - 8(u,) 0.005 0.08418 . 0.078
7\(u") -1 0.1265 -~ 0.1116 - 0.1011

£ e Wl - fi(u )] 7.4445 x 1072 2.810 X 1072 1.0151 x 102
§je 3[7\(11 ) - 1] 0.3032 X 107 6.1022 x 106 1.3604 X 107
(a), - E,/2bR = 8.2321.

(®)_, _ 4
‘o = (2E_,  ~ Ep)/2bR = 8.4566.

We next calculate the balance point, wfiére Jm = 0 or, more simply,
where material is neither removed nor deposited. Since we have delib-
erately constructed a symmetrical prototype 1odp, only one point need
be calculated. The approach for the'CalCfilatiOn‘of the balance point
was discussed earlier, and in this case a form of Eq. (40) was used;

nanely,
KOIl?_(a/g)/Ilz(a"/fl = 1.047 X 102(7 45 x 1072

- 1.015 X 10-3)/(1 360 X 107 - 0.303 X 107) 6 368 x 1077

The temperature corresponfling to Kp is 1041°K; thus § = 755 and
f(p) = 0.233. The values corresponding to the ‘balance p01nt tempera-
ture are given in column 2 of Table 6. o - '

| To calculate the total amount. of material transported AAM(t) we
use integral terms for the hot and cold zones. Again we averaged the
values for both zones because of uncertainties in the "hand calcula-
tlons. - Table 6 lists all quantltles needed except values of C and C’.
Using Egs. (32) and (33) we find

 
 

 

62

. : : - ORNL—-DWG 69-10096
0927 T 1 | !

 

0925
0.923 |-
0.921 |-
0.919 |-
S oo |-
0915 |-
0.913
0.9 -

0909 -

 

 

 

 

0.907 . 1 ‘
8.5 9.0 95 100 105 1.0 1.5 2.0
Fig. 14. Values of B(u,) over an Intermediate Range of u. Values.

This lower projection of F:l.g'j 7 was required by values ofcx/g jthat
occur in all molten-salt examples ' _

¢ = (4)(0.0741)(8.878)(0.6915) (3.1420 x 0.607 x 10~4)1/2 = 2,519 x 10-2
and |
= (2.519 x 1072)(6.0815 X 10-10) - 1.532 x 1011 |
For the cold zone, using Eq. (7¢);
aM(t)/2t1/2 = 2,519 x 1072(2.810 - 1.015) x 103

— 1.532 X 10~11(1.360 — 0.6102) x 107 = —6.96 X 107> g/secl/z\ .
 

 

8

o«

63

For the hot zone
CAM(t)/26%/2 = 2.519 x 1072(7.444 — 2.81) x 1073
-~ 1.532 x 10711(3.032 — 6.102) X 105 = +6.97 X 107 g/secl/? .

The negative sign indicates that the salt loses chromium in the cold

(x

;%(AM/{.JT) {gem™ sec'vz)

zone {by deposition on meteal) and gains in chromium in the hot zone
(by metal dissolution). After 1000 hr 2t1/2 = 3,80 x 10*3 gecl/?, so

AM(t=1000 hr) = 3.80 x 107%(6.96 X 107°) = 0.264 g Cr .

Figure 15 gives the chromium corrosion profiles for the actual and

prototype loops.

ORNL~-DWG 69-9931

 

 

  
  
 
  

 

 

   

     
 

     

 

 

-6 ) i ) : ) :
O T T T T T T T 1 "“020’ T 1 1 1 T
| ' ' 1140 - : 0. L — 1140
. ‘ : Cf +UF4
20— :
—~ 10 —
{100 < - — H00
1.0 — 05 '§
o -
: 1
g § 1060
w060 g o
0 ] E ~
' —
+ 5 &
. ~J
l: 10203 1020
- <
1.0. I’ | £ 2
/ : sl
p) 280 980
-2.0 :
Pt o1 040 040

 

 

 

 

 

0 Ot 02 03 04 05 06 07 08 09 10

O 0f 02 03 04 05 06 OF 0.8 09 {0
/, FRACTION OF WALL AREA AND/OR LOOP LENGTH

f FRACTION OF WALL AREA AND/OR LOOP LENGTH -

Fig. 15. Computed Chromium Corrosion Profiles Resulting from the
UF3/UF4 Redox Reaction. The salt is a modified LiF-BeF, mixture con-
taining no Fng. Proflles assume wall temperatures given by dashed
lines.

“In example III a balance point exists, and computer calculations

‘were carried out using the equilibrium constants given in Table 5. It

1is noted that AH is negative, and Fig. 16 shows that the mass transfer
occurs in the opposite direction, material is deposited in the hot zone

and removed in the cold zone.

WALL TEMPERATURE (°K)

 
 

 

 

  

 

   

 

 

x10"%) T T T l
' Cro+ 2HF .7
__———"”“\\ /h\ ///’/—\\
& \
's O F ." hN
- + +
_ i \
o -} /1 . N et
- I, : | \\
s /| LN
5 [ I \‘ _
3 f ! ! \
- I 1 fip’) \
s f(
Is 3 ’/ I L
-7 I . : \
4 | 1] Lt
o 0.2 0.4 0.6 0.8 1.0

40

1100

1020

980

940

f, FRACTION OF WALL AREA AND/OR LOOP LENGTH

Fig. 16.

Hz/HF Redox Reaction Carried out Under Hypothetical Conditions.
files are based on wall temperatures given by dashed lines.
case, chromium moves from cold to hot region.

WALL TEMPERATURE (°K)

(x10°€)

o

_27

(AM/LAT) (g em™! sec™"2)

<
Jdrf

-4

ORNL-DWG 69 - 9930

 

 

 

   

WALL TEMPERATURE (°K)

 

 

 

| | ! i
— ceP+2HF | M0
: N
7\
7 \
/_\ ; \ /\
— A _ 1100
|
it +
2 |
4 PN
- 7/ b\ — 1060
s SN
/ Y
/ ' \
/ ' “\ ,
— ,/ : \—» "] 1020
i \
| \
' flp") \\ ‘
[ " Flp) | v—f 980
7 | I \
h : : \
R L 040
o 0.2 0.4 0.6 0.8 1.0

f, FRACTION OF WALL AREA AND/OR LOOP LENGTH

Computed Chromium Corrosion Profiles Resulting from a

Pro-
In this
The salt considered is

a modified LiF-BeF, mixture containing no dissolved uranium or iron.

DISCUSSION OF MOLTEN-SALT RESULTS

In the past, the mass transfer equation was integrated graphically,

and areas under the curves were determined by planimeters.

However, by

introducing the prototype loop, we can perform a relatively simple

exact integration of all the equations as detailed in an earlier sec-

 tion. A computer was used to generate several of the mass transfer

curves, since this allows integration over many smaller segments then is

otherwise practical.

Table 7 gives the total amount

of chromium removed in 1000 hr for

each reaction. For examples II and III, whefe balance points exist,

AM(t = 1000 hr) also corresponds to the amount of material deposited.

Also included is the AM value for example I with balance points and no

excess Fels.

This calculation is given as an example of what could hap-

pen in a coolant circuit where FeFz is the only impurity that would

cause corrosion.

The balance points would result when only a small

amount of FeF; is present; weight losses would result at higher.temper-

atures and weight gains at lower temperatures in the system. Areas
 

 

i

: 65

 Table 7. Integrated Mass Transfer Flux (AM) for
- Molten-Salt Loops After 1000 hr

 

Chromium Transferred, g

" Integrated Planimeter Integrated Planimeter

 

Example Reaction Computer on Computer Formula on "Hand"
Results  Curve by Hand  Curve
, . Actual Loop
I  Cr(s) + FeFp(d)(xs)  0.595 0.5904
IT  cr(s) + Urs(a) L © 0.263  0.258
S IIT Cr(s) + H:F(g)  0.1684 0.1683
ox(s) + Fng(d) 0.062

: ': Prototype Loop
I Cr(s) + FeFo(d)(xs) - 0.6122  -0.6551

I - cr(s) + UF(d) | o 0.264 0.259
11T cr(s) +HR(g) = 0.1751  0.1760
cr(s) +=Fer(d)a" f 0.059

 

Assuming a balance po:l.nt with AH = +10, 370 cal/mole and
K, = 1.0 x 10710,

under the plots of AM against distance were also determined with a
planimeter, and the results are given in Table 7.

- It is first noted that graphical and numerical Aintegration gave
values quite close to one another. This is gratifyihg_becduse in the
past much dependence had been placed on graphiéal ihtegration -methods,
and now we see that the numerical calculations a.gree'quit'e well.
Although the agreement is not quite as good as in the liquid metal

case, again the AM's are ebout ‘the :same for the actua.i and prototype

profiles, so that good estima.tes of AOM may be made using the simple

yrototype. The disagreement is proportional to the dlfference in the

areas under the temperature prof:.le curves. Also, it makes no differ-

- ence in the final result ‘whether the profile is like that of the proto-

type or is a sawtooth. In Fig. 15 (example II) , the balance points
were f(p) ='0.34 and 0.90 and Tp ‘= 1036°K for the actual loop and

 
 

 

66

f(p) = 0.23 and 0.77 and Tp = 1042°K for the prototype. In Fig. 16
(example III), the balance points were f(p) = 0.43 and 0.71 and

Tp = 1083°K for the actual loop and £(p) = 0.36 and 0.64 and TP = 1083°K
for the prototype. Again, although the shapes of the profile obviously
affect the location of the balance points, the balance points and
balance témperatures are quite close in all cases. We also point out
that although maximums of weight loés and gain do occur at the maximum
temperature point in examples II and IIT, other ‘maximums (ggin or loss)
may occur at positions other than that of the minimum temperature.

This is illustrated in Fig. 16, where the maximumnweight loss occurred
at the intermediate value of 1030°K. The worst possible condition with
respect to the total amount of material removed was illustrated in
example I, where corrosion occurred on all portions of the loop. A ten-
fold difference in the value of AM corresponding to material removal

and deposition obtained in the same reaction without excess FeF; is

- shown in Table 7 for both the prototype and actual loops.

Several "rules" for mass transfer follow from these results. The
common areas among the three examples are temperature, flow conditions,
and selective chromium removal from the Hastelloy N. Since dissolution
is endothermic for examples I and II, the mass transfer is from higher
to lower temperatures. More material is removed and deposited in
example II, which has the largest energy of solution. ‘In example IIT,
where dissolution is exothermic, the mass transfer occurs from low to
high temperature. Because temperature enters the mass-transfer func-
tion as an exponential term, an increase in the maximum temperature
greatly increases AM. For example, an increase of 50°K would about
double the AM.

Table 8 shows the constants A and B used to calculate egquilibrium
constants from log KT = A + B(103/T); also shown is the sign of the
energy function for various reduction-oxidation reactions in LiF-BeF,-
base fluoride salts. Example I calculations discussed earlier were for
an NaF-ZrF,; salt. From the values given in the'table, we will discuss
the mass-transfer aspects of the various reactions. | |

As mentione@ earlier and shown in the calculations, one of the .

requirements that must be met for mass transfer in the direction of
 

&

 

67

Table 8. Equilibrium Constant Parameters®™ for Reactions
with HF and With Salt Constituents and Tmpurities
in LiF-BeFp-Base Molten Fluorides

 

 

A o . 0 Sign
Reaction . A" . B K1075°K of
Cr(s) + 2HF(g) ==CrFp(d) + Ho(g)  -5.12 9.06 2.03 x10® -~
Fe(s) + 2HF(g) == FeFo(d) + Ha(g)  -5.20 5.31 1.83 x 100 -
Ni(s) + 2HF(g) == NiFp(d) + Hp(g)  -8.37  3.60 9.52 x 106 -
RUF,(a) + Ha(g) - 2Ur;(d) + 2HF(g)  8.14 -18.66" 6.06 x 10710
BeF(d) + Ha(g) == Be(s) + 2HF(g) 7.21 —21.56 1.43 x 10713
cr(s) + 2UF4(d)== 2UF3(d) + CrFp(d) 3.02 -9.6 1.23 X 107®  +
cr(s) + BeFa(d) == CrFz(4) + Be(s) 2.09 —12.51 2.84 x 10~10
Cr(s) + FeFp(d) = CrFp(d) + Fe(s)  0.08 +3.94 5.56 X 10° —
Cr(s) + NiFa(d) == CrFo(d) + Ni(s) = 3.25 +5.46 2.14 x 108 -
Fe(s) + 2UF;(d) == FeFp(d) + 2UF3(d) 2.94 -13.35 3.32 X 10-10
Fe(s) + BeFp(d) = FeFp(d) + Be(s) = 2.01 -16.25 7.77 x 10-14
" Fe(s) + NiFo(d) = FeFa(d) + Ni(s)  3.17 +1.71 8.8 x 10% -
Mi(s) + 2uF,(d) = NiFp(d) + 2UFs(d) -0.23 -15.06 5.76 x 10-15
Ni(s) + BeFa2(d) = NiFy(d) + Be(s) =~ -1.16 -17.96 1.35 x 10~18

 

®constants of equation log KT = A+ B(103/T).

decreasing temperature is arpositive energy of solution.- In this |
respect, the reactions,ofmthealloy:constituents_with UF, and BeF, and
the reduction of UF, and_Bng by_hydrogen meet this criterion. It is
noted that in all these.cases,with the exception of the oxidation of
ehromiun by UF,, the calculated talue of K is quite small, so these

_reactions would be nnfa#orable and the yields would'be quite small. 1In

reference to mass transfer 1n the opposite direction, as favored by the
other reactlons, most of the equilibrium constants are quite large. The
relative ease of chromium.movement followed by iron and then nickel, is
pointed out by the relative values of the equilibrium constants. For
example, for reactions with UFs, Kygs0 ox = = 1076, lO'lo,rand 10~15, respec-
tively. _Reactions of molybdenum are not included because equilibrium

 

 
 

 

68

constants are not available. However, because the free energies of
formation of molybdenum and nickel.fluorides aré nearly equal, we would
~ expect the equilibrium constants to be about the same.

With respect to the UF, corrosion feaction, methods are now being
considered to measure the U(III)/U(IV) ratio and thus determine the
oxidizing or reducing potential of the UF,-containing molten salt.
Additions of beryllium are being used to adjust this potential and con-
trol the corrosion rate. Investigations are also under way for the
possible application of 2°Nb deposition as the redox indicator.48

We also wish to consider if loop conditions are actually the -same
as those under which the equilibrium quotients were determined. Actually
we beg the question: can mass transfer occur in & loop in the direction
of low to high temperature as is theoretically shown from the FeF, and
HF reactions with balance points in LiF-BeF, salts? Recent experimental
work#® in salt systems containing UF;, FeF,, and HF show evidence of
mass transfer only from high to low temperature. However, nothing is
known about the effects of the ccmbihations of the reactants or what
effect removal of elements other than chromium fTOm_the_alloy'might have
on.the overall process. It would be interesting to speculate what ratio
of CrFz; to FeF; would be needed in a UF4¢containing sdlt.to stop the |
mass-transfer (and the cbrrosion) process altogéther. A promising future
goal would be to carefully isolate the above components and to run the
verifying experimental tests in 1oops |

In salts proposed for use in a breeder reactor system, ThF, is
includ=d. The ThF, will not oxidize chromium, so its presence will not
affect the corrosion process.
| It must be again emphasized that there is a parallel betwesn the
results,ln Report I and here. The mass-transfer equations of Report I
were derived as analogs of heat flow equations. Rate equations of this
type consist of driving forces and resistances. The resistances in ’

Report I were based on the first-order reaction rate constant and the

 

“8R. E. Thoma,, ORNL, personal communication.

49J. W. Koger and A. P. Litman, MSR Program Semiann. Progr Rept.
Feb. 28, 1969, ORNI~4396, pp. 243-253. | |
 

9

 

69

film coefficient. The driving forces are differences ‘that are involved
in both mechanisms. For example, when solution rate is controlling,

the important difference is that between the'equilibrium:corrosion
product solute concentrations at the high and low temperatures of the
system, while, when diffusion controls, the difference is that between
the bulk alloy concentration and the surface alloy concentration of the
active alloying element. The results do not depend on the shape of the
profile in the mechanism of Réporf I and only sometimes in the mechanism
given here. The corrosion product concentration differed with tempera-
ture (position) in Report I, while here we assume constant concentration
of the corrosion product throughout the loop. This is quite important,

because the use of the equilibrium constant allows us to change only one

variable with temperature. ' This was not possible in Report I.

As we mentioned earlier, liquid Velésities in pump loops are
orders of magnitude greater than those in thérmal‘convectionrloops.
Throughout this report we have assumed that conclusions about pump loop
corrosion behavior are good for thermal convection loops’and XiEE.XEEfiE-
Of course, if the process is truly controlled by solid-state diffusion
in the alloy, then velocity will not affect the mass transfer.

© SUMMARY

We have elected to summarize the molten—Salt results since we wish
to illustrate several cogent points. 1In this portion of the report our
main purpose was to discuss the molten-salt corrosion (mass transfer of
chromium) of Hastelloy N in pdlythermal loops for cases where solid-
state diffusion controls throughout the system. We have demonstrated
the versatility of the methodrby showing three different examples:

removal of chromium from all'portions of the loop, hot-to-cold leg

~ transfer, and cold-to-hot leg transfer.

‘Calculations for both transient and quasi-steady-state conditions

were based on a mathematical development of the idealized diffusion

- process, wherein corrosion rates depefid directly on the rate at which

constituents of alloys diffuse into, or out of, container walls as influ-

enced by the condition of wall surfaces exposed to a high-temperature

 
 

 

70

liquid. The transient effects (the effects of mass transfer across the

liquid films on corrosion) were negligible because of their short dura-

tion. The quasi-steady-state condition assumed a pre-equilibration of

the salt with CrF»> such that the concentration of CrF; did not change.

‘The balance points and the amount of material entering or leaving
the various zones of the loops for the vérious sysfiems were determined
for the quasi steady state. The calculation was adaptable for both the
prototype "tent-shaped" and actual loop temperature profiles. The
results obtained from the prototype, which were quite simple to calcu~
late, agreed very well with the results from the actual profile. Tmpor-
tant variables discussed in this treatment with respect to the mass
transfer process were the energy of solution of the corrosion reaction,
the energy of activation for diffusion, the equilibrium constant of the
corrosion reaction, and its temperature dependence.

In conclusion, the practical importance of the calculations lies

in the fact that, if the proper experimentel data are available, one

may determine, before running a loop test, the magnitude and manner in
which the mass transfer will occur. One may also predict the“changes
expected in a completed experiment if the temperature conditions are |
varied with the developed equations. Of perhaps even greater importance

is the fact that a priori calculations of this type are required to

predict the concentration that will give a pre-equilibration condition

at the beginning of an experiment. This is necessary for one td run a

systematic well-developed test.
 

¥

s

My nONIRaOEDED DO

 

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A. M. Weinberg ¥
J. R. Weir

M. E. Whatley

J. C. White

R. P. Wichner

L. V. Wilson

Gale Young

H. C. Young

J. P. Young _

E. L. Youngblood

F. C. Zapp

C. M. Adams, Jr. (Consultant)
Leo Brewer (Consultant)
Jan Korringe (Consultant)

Sidney Siegel (Consultant)

EXTERNAL DISTRIBUTION

" R. E. Anderson, SNS, AEC, Washington, DC 20545

W. Brehm, WADCO, P. O. Box 1970, Richland, WA 99352

E. G. Case, D1v151on of Reactor Standards, RDT, AEC,
Washington, DC 20545
- 214.
215.
216.
217.

218.

219,

220.

221.
222.

223.

224 .
225.

226.
227 .

228.
229.
230.
231.
232.

233.
234~235.
236.

237-239.
240,

241.
2.

243,

244, .
245,
246
247 .

248 .
249,

250.
251.
252.

 

 

73

. Coats, Sandia Corp., P. O. Box 5800 Albuquerque, NM 87115
. Cohen, General Electric, BRDO, Sunnyvale, CA 94086
. Cope, RDT, SSR, AEC, Osk Ridge National Laboratory
. deBoisblanc, Ebasco Service, Inc., 2 Rector St.,
New York, NY 10006
C. B. Deering, Black and Veatch, P. 0. Box 8405
Kansas City, MO 64114
A. R. DeGrazia, RDT, AEC, Washington, DC 20545
L. F. Epstein, LMFBR Program Office, Argonne National Laboratory,
9700 South Cass Ave., Argonne, IL 60439 |

OO R
= g

'J. E. Fox, RDT, AEC, Washington, DC 20545

K. Goldman, United Nuclear Corp., Grasslands Rd.,

Elmsford, NY 10523

D. H. Gurinsky, "Brookhaven National Laboratory, Upton, Long
Island, NY 11973

Norton Haberman,‘RDT, AEC, Washington, DC 20545

E. E. Hoffman, General Electric, Nuclear Systems Program,

P. 0. Box 15132, Cincinnati, OH 45215

K. E. Horton, RDT, AEC, Washington, DC 20545

T. F. Kassner, Argonne National Laboratory, 9700 South Cass
Ave., Argonne, IL 60439

E. C. Kovacic, RDT, AEC, Washington, DC 20545

Kermit ILaughon, RDT, OSR, AEC, Oak Ridge National Laboratory

A. P. Litman, SNS, AEC, Washington, DC 20545

G. Long, UKAEA, Harwell, Englend

H. G. MacPherson, Nuclear ‘Engineering Department, University
of Tennessee, Knoxville, TN 37916

C. L. Matthews, RDT, OSR, AEC, Oak Ridge National Laboratory
T. W. McIntosh, RDT, AEC, Washlngton, DC 20545

J. M. McKee, Argonne National Laboratory, 9700 South Cass Ave.,
Argonne, IL 60439

P. A. Morris, Division of Reactor Licensing, RDT, AEC,
Washington, DC 20545 :

P. Murray, Westlnghouse, ARD, Waltz Mill Site, P. 0. Box 158,
Madison, PA 15663 .

J. Neff, RDT, AEC, Washington, DC 20545

H. Pearlman, Atomics. International P. 0. Box 309, Canoga. Park,
CA 91305

T. K. Roche, Stellite Division Cabot Corp., 1020 W. Park Ave.,

Kokomo, IN 46901

H. M. Roth, AEC, Oak Ridge Operations

D. W. Shannon, WADCO, P. O. Box 1970, Richland WA 99352

M. Shaw, RDT, AEC, Washington, DC. 20545

A. A, Shoudy,.Atomlc Power Development Associates, Inc.,
1911 First Street, Detroit, MI 48226

J. M. Simmons, RDT, AEC, waahlngton, DC 20545 _

E. M. Simons, Battelle Memorial Institute, 505 King Ave.,
Columbus, OH 43201 -

B. Singer, RDT, AEC, Washington, DC 20545

W. L. Smalley, AEC, Oak Ridge Operations

Earl O. Smith, Black and Veatch, P. O. Box 8405, Kansas
City, MO 641L4

 
 

7%

" 253. J. A. Swartout, Union Carbide Corp., 270 Park Ave., New York, NY
- 10017 '
254, A. Taboada, RDT, AEC, Washington, DC 20545
255. C. Tyzack, UKAEA, Culcheth, England
256. J. R. Weeks, Brookhaven National Laboratory, Upton, Long Island,
NY 131973
257. G. A. Whitlow, Westlnghouse, ARD, Waltz Mill Site, P. O. Box 158,
Madison, PA 15663
258. Laboratory and University Division, AEC, Oak Rldge Operations
259. Patent Office, AEC, Oak Ridge Operations .
260-454. Given distribution as shown in TID-4500 under Metals, Ceramics
and Materials category (25 copies — NTIS)

e