ORNL-TM-4804.txt

e ~1729 %
ORNL-TM-4804

 

 

A Method for Calculating the
Steady-State Distribution of Tritium
in a Molten-Salt Breeder Reactor Plant

R. B. Briggs
C. W. Nestor

 

 

 

OPERATED BY UNION CARBIDE CORPORATION = FOR THE U.S. ATOMIC ENERGY COMMISSION

 
 

Printed in the United States of America. Available from
National Technical Information Service
U.S. Department of Commerce
5285 Port Royal Road, Springfield, Virginia 22161
Price: Printed Copy $5.45; Microfiche $2.25

 

 

 

This report was prepared as an account of werk sponsored by the United States
Government. Neither the United States nor the Energy Research and Development
Administration, 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, completeness or
usefulness of any information, apparatus, product or process disclosed, or represents
that its use would neot infringe privately owned rights.

 

 
ORNL-TM-4804
UC-76 — Molten Salt
Reactor Technology

Contract No. W-7405-eng-26

Reactor Division

A METHOD FOR CALCULATING THE STEADY-STATE DISTRIBUTION
OF TRITIUM IN A MOLTEN~-SALT BREEDER REACTOR PLANT

R. B. Briggs
Central Management Office
C. W. Nestor
Computer Sciences Division

NOTICE
This report was prepared as an account of work
sponsored by the United States Government. Neither
the United States nor the United States Energy
Research and Development Administration, nor any of
theit employees, nor any of their c¢ontractors,
APR‘ L ]975 subcontractors, or tpeir ) employees, makes any
warranty, express or implied, or assumes any legal
liability or responsibility for the accuracy, completeness
or usefulness of any information, apparatus, product or
process disclosed, or represents that its use would not
infringe privately owned rights,

 

 

 

OAK RIDGE NATIONAL LABORATORY :$

Oak Ridge, Tennessee 37830
operated by
UNION CARBIDE CORPORATION
for the
U.S. ENERGY RESEARCH AND DEVELOPMENT ADMINISTRATION

 prare mAanUAENT UNLIMITE
DISTRIBUTION OF THIS DOCUMERS 7 1}[
i !
iii

CONTENTS

Abs tract * s . . . . L4 . L * - * - * * . - *

I. Introduction . L] ° . *® . e . - * . - - *

IT. Derivation of Equations and Computational Procedures

ITI. Solution of Equations . .« « &« « « o &
IV. Nomenclature . « « ¢ o o« o s o o o o o
V. Computer Program, Input Instructions and

Appendix — Program Listing . ¢« o« ¢« ¢ o ¢ o &

o * * * - . .

23

35

49

65
LIST OF FIGURES

Fig. 1. Molten-Salt Breeder Reactor System. . . . . .
Fig. 2. Sketch Of F(CK) VS CK . o - L ] L ] . . * . L * *
Fig. 3. Sketch of G(C,) VS8 C, « « & o« « s s o o o o &
K K
Fig. 4. Sample Problem Input .« « o o ¢ ¢ « o o o o &
Fig. 5A. List of Parameter Values Used in Calculation
Fig. 5B. Output from Iterative Calculations . . . . .
Figo SC. Output Sumary e & ® e+ & * % ® & 5 & & s s @

Fig. 5D. Output Produced by "CHANGE" Command. . . . &

Fig. 5E. List of Parameter Values Used in Calculation
"CHANGE" Command. « o « o o o o -6 o ¢ ¢ o o o o s o

Fig. 5F. Output from Iterative Calculations With New Parameters
Fig. 5G. Output Summary (New Parameters). « o« o « o« o s o o o o

Fig. 5H. Response to Unrecognized Command Card. « « « ¢« ¢« « « o

Fig. 5I. Normal Ending Message. . « « ¢ s o ¢ ¢ & o &

After

27
28
52
33
55
56

57

58
60
61
62

63
A METHOD FOR CALCULATING THE STEADY-STATE DISTRIBUTION

OF TRITIUM IN A MOLTEN-SALT BREEDER REACTOR PLANT
R. B. Briggs and C. W. Nestor, Jr.
ABSTRACT

Tritium is produced in molten salt reactors primarily by fissioning
of uranium and absorption of neutrons by the constituents of the fuel
carrier salt. At the operating temperature of a large power reactor,
tritium is expected to diffuse from the primary system through pipe and
vessel walls to the surroundings and through heat exchanger tubes into
the secondary system which contains a coolant salt. Some tritium will
pass from thé secondary system into the steam power system. This report
describes a method for calculating the steady state distribution of
tritium in a molten salt reactor plant and a computer program for making
the calculations. The method takes into account the effects of various
processes for removing tritium, the addition of hydrogen or hydrogenous
compounds to the primary and secondary systems, and the chemistry of
uranium in the fuel salt. Sample calculations indicate that 30 percent
or more of the tritium might reach the steam system in a large power

reactor unless special measures are taken to confine the tritium.
I. INTRODUCTION

Conceptual designs of Molten Salt Breeder Reactor (MSBR) power
plants usually can be represented by the diagram shown in Fig. 1. The
fissioning of uranium in the fuel salt heats the salt as it is pumped
through the reactor vessel in the primary system. The heat is trans-
ferred to a coolant salt that circulates in the secondary system and,
thence, to water, producing steam to drive a turbine-generator in the
steam system.

Fission products and other radiocactive materials are produced in
large amounts in the fuel salt. Much smaller amounts are produced in
the coolant salt by the flux of delayed neutrons in the primary heat
exchangers. The radioactivity is normally confined by the 'walls of
the piping and vessels. However, tritium is produced in the salts,
partly as a fission product, but mostly by absorption of neutrons by
lithium in the fuel salt. At the high temperature of an MSBR, tritium
diffuses through metals and might escape to the environs in amounts
thgt would be cause for concern.

The purpose of this report is to describe a method for calculating
the distribution of tritium in and its escape from an MSBR plant. We
assume that the tritium, born as tritium ions, is present in the fuel
salt primarily as tritium molecules® and tritium fluoride molecules. ¥

The ions are estimated to be produced at a rate of 2.6 X lOlh/MWsec***

 

*Tritium molecules are intended to include HT and H, molecules
when hydrogen is present.

*%Tritium fluoride molecules are intended to include tritium (and
hydrogen) ions associated with fluoride ions in the salt.

**%2420 Ci/day in a 2250 MW(t), 1000 MW(e) plant.
ORNL-DWG 68~1185EB

 

 

 

 

 

 

 

 

PURGE STREAM PURGE STREAM
FOR REMOVAL OF TRITIUM FOR REMOVAL OF TRITIUM
—~ FROM FUEL SALT FROM COOLANT SALT
) A
PRIMARY SECONDARY
SALT PUMP NaBFy—NaF SALT PUMP

 

 

1

COOLANT SALT

 

 

 

 

 

   

 

 
  
     

11150 °F

   

 

{300°F wp

 

 

 

 

  
  

 

 

 

 

GRAPHITE
MODERATOR
REACTOR
HEAT _
EXCHANGER Hi
1050 °F €W
TLiF -BeF,-ThFy-UF, STEAM GENERATOR
FUEL SALY SUPERHEATER, AND
—-— A T
1000 °F '
——
TURBO-
GENERATOR | L—==
STEAM

Fig. 1. Molten Salt Breeder Reactor System.
in a typical fuel salt. The relative concentrations of tritium and
tritium fluoride in the fuel salt are expected to be governed by the
equilibrium relationship for the reaction,

UF, + 1/2 T, 2 UF3 + TF ,
with uranium in the salt. The absolute concentrations are governed
by removal processes.

Three types of processes are provided for removing tritium from
the primary system: permeation through the metal of the walls of
piping and vessels, sorption on materials in contact with the salt,
and purging. We assume that tritium molecules that reach a metal
surface can sorb on the surface, dissociate into tritium atoms and
diffuse through the metal. Tritium in tritium fluoride and other
compounds is assumed to be chemically bound and unable to pass through
the metal.

Experience with the Molten Salt Reactor Experiment indicated that
tritium sorbs on and is tightly bound to graphite. We provide for
sorption of tritium and tritium fluoride on the graphite in the reactor
core.

Provision is made for purging tritium from the primary system by
circulating a stream of salt through an apparatus which extracts gaseous
tritium and tritium compounds. A contactor in which tritium and tritium
fluoride are transferred to a gas phase by virtue of their wvapor
pressures would be such an apparatus. Current designs for MSBR's
provide for sparging c¢f the fuel salt with helium bubbles in the
primary system to remove krypton and Xenon. Tritium and tritium
fluoride would be removed also. The sparging process can be treated

as an equivalent purging process in the calculatioms.
Tritium will reach the secondary system by diffusion from the primary
system through the walls of the tubes in the primary heat exchangers
and by neutron capture in the coolant salt. We provide for removal of
tritium from the secondary system by diffusion through the metal walls,
sorption, and purging. The secondary system would not normally contain
a sorber or have an elaborate purging system. Such processes, if
incorporated into the plant, would be designed specifically for removing
tritium.

The coolant salts do not normally contain constituents that are
reducible by tritium and, thereby, able to convert tritium into tritium
fluoride and make it unavailable to diffuse through the metal walls.
We, therefore, have provided for addition of hydrogen fluoride or other
hydrogenous compounds to the secondary system. We assume that tritium
will exchange with the hydrogen in the added compound and that the
compound will be extracted by the sorption and/or purge process.

The steam system and the cells around the reactor primary and
secondary systems are considered to be sinks for tritium. Tritium
reaching the steam system is assumed to exchange with hydrogen in the
water, and thdat reaching the cells is assumed to be oxidized to water.
The partial pressure of tritium is effectively zero.

In the calculations we assume that tritium and hydrogen behave
identically. The equation used for calculating the diffusion of
hydrogen through a metal wall states that the rate of transport per
unit of surface area is proportional to the product of a permeability
coefficient and the difference between the square roots of the partial

pressures of hydrogen at the inner and outer surfaces of the metal.
In this circumstance, addition of hydrogen can reduce the transport

of tritium through the metal. Suppose, for example, the partial
pressures of tritium and hydrogen at the outer surface of a pipe are
zero and the partial pressure of tritium at the inner surface is held
constant. If hydrogen were added to increase the total hydrogen partial
pressure at the inner surface by a factor of 100, the flow of hydrogen
plus tritium through the metal wall would increase by a factor of 10.
But the flow of tritium would decrease by a factor of 10 because of the
100-fold dilution of hydrogen. Because of other factors, the effect of
adding hydrogen may not be so dramatic, but the calculational method
provides for addition of hydrogen to the primary and secondary systems
and for hydrogen to be present at a specified concentration in the
steam system so that the effects can be studied.*

The calculational model describes the behavior of tritium in an
MSBR plant to the extent that it is known or has been inferred at the
present time. The removal processes can be included in or eliminated
from the calculations by careful choice of the values assigned to co-
efficients in the equations. The model probably does not include all

the chemical reactions and physical processes that will ultimately be

 

*The calculational procedure might have been developed to treat hydrogen
and tritium as separate species. Separate values then could be assigned
to important parameters, such as solubility and diffusion coefficients,
for each species. Interaction between hydrogen and tritium would be
taken into account by the equilibrium relationship

péT/pHQ *Pp, = kp for the reaction H, + T, ¥ HT .

However, kp has a value near 4 at temperatures of interest, which signi-
fies that hydrogen and tritium interact as though they are the same
species. Also, there are substantial uncertainties in the values for
most of the parameters. Complicating the procedure to treat hydrogen
and tritium separately would not, for the present, improve the accuracy
of the results.
shown to affect the distribution of tritium in an MSBR. In some
instances these effects can be included, when recognized, simply by
adjusting the coefficients in equations for processes presently in-
cluded. Others may require incorporation of additional processes.

Two assumptions in the calculational procedure should be recognized
for their potential for leading to major differences between the cal-
culated distribution of tritium and what would actually occur in a
reactor plant. Tritium, present in the salt as tritium fluoride, can
react with metal to yield tritium atoms that would dissolve in and
diffuse through the metal. Neglect of this reaction could cause the
calculations to be greatly in error under circumstances where most of
the tritium is present in the salt as tritium fluoride.

Oxide films (and possibly others) that form on metal surfaces
reduce the permeability of a metal wall to the passage of hydrogen.
They may also cause the transport to vary with pressure to a power
in the range of 1/2 to 1. The reduced permeability appears as a
coefficient in the transport equations of the model, but we make
no provision for changing the exponent on the pressure terms from
1/2. The calculated transport of tritium through the metal walls
and the effect of the addition of hydrogen in reducing the transport
would both be greater than would actually occur if the actual trans-
port were proportional to the pressure to a power in the range 1/2
to 1. The calculations would not underestimate the transport unless
the total pressure of tritium and hydrogen exceeded the reference

pressure for the permeability coefficient, which is usually 1 atm.
II. DERIVATION OF EQUATIONS AND COMPUTATIONAL PROCEDURES

In making the calculations, we first calculate the distribution of
hydrogen plus tritium in order to establish flows and concentrations of
the combined isotopes throughout the plant. Then we calculate the distri-
bution of tritium throughout the plant.

For calculating the distribution, the fluids in the primary and
secondary systems and the various parts of the steam system are assumed
to be well mixed and to contain uniform bulk concentrations of all
constituents, The calculations are for steady-state conditions, and
only hydrogen and tritium molecules are assumed to be able to sorb on
the metal surfaces, dissociate, and diffuse through the metal walls.
The various paths are defined and the distribution is calculated by the

use of the following set of equations.*

A. In the primary system:

1. Transport of hydrogen through the salt film to the wall
of the piping in the hot leg from the reactor vessel to

the heat exchanger:
Q1 = h1A1(CF — C1) (1a)

Transport through the pipe wall to the surroundings where

the hydrogen pressure is assumed to be negligible:

- p1A1 [(kl_cl)? _— 0] - RJLAI (klcl).r . (1b)

Qi ty t,

2. Transport of hydrogen to and through the walls of the cold-

leg piping from the heat exchanger to the reactor vessel:

 

*Symbols are defined in Section IV, Nomenclature.
10

Q2 = thz(CF - C3z) (2a)
1
5

- EzAziszz) . (2b)

Transport of hydrogen to and through the walls of the
reactor vessel and the shells of the heat exchangers in

the primary system:

Qs = hsAs(Cp — Ca) (3a)
z
- EaA:(kSCB) (3b)
3

Transport of hydrogen to and through the walls of the

tubes in the primary heat exchangers into the secondary

system:
Qe = haAa(CF'“ Ca) (4a)
Puhs + z
= . [(kacu) = (k12C12) ] . (4b)

Transport of hydrogen to the surfaces of the graphite

in the reactor vessel or to other sorber:

Q5 = h5A5(CF - Cs) . (Sa)
Sorption by the graphite or other sorber assuming that
the sorbing surface is replaced continuously and that
the concentration of sorbed gas is proportional to the
square root of the partial pressure:
+
Qs = B;W,As (ksCs) . (5b)

Removal of hydrogen by purge:

Qe = F1E1CF . (6)
11

7. Transport of hydrogen fluoride to and removal by sorber:
Q; = h7A7(CFF'“ Cs) (7a)

1
B,W.A, (k,Cy)~ . (7b)

8. Removal of hydrogen fluoride by purge:

Qs = FLE;C . (8)

FF

Because the molecular species involved may contain different numbers
of hydrogen atoms, all the calculations are done in terms of atoms of
hydrogen. This does not mean that the hydrogen necessarily diffuses as
single atoms, but only that a transport unit is one hydrogen atom and
the parameters are expressed in terms of single hydrogen atoms. A
Q value of 1 then represents the transport of one-half molecule of H,,
one molecule of HF, or one-fourth molecule of a compound 1like CH,, all per
unit time. Likewise, a C value of 1 represents a concentration of one-
half molecule of H,, one molecule of HF, or one-~fourth molecule of CH,,
all per unit volume.

If the rates of inflow of tritium and hydrogen atoms (R; and R,,
respectively) to the primary system are given, a material balance over
the primary system gives

8
R; + R = I Q. (9)
i=1 *
In our calculations, all flow rates in the sum on the right-hand side

of Eq. 9 are positive or zero except for Q,, the transport through the
12

heat exchanger tubes to the secondary system. Q, can be positive,

negative or zero, depending on the conditions in the various systems.

Hydrogen is present in and is removed from the primary system as hydrogen

fluoride, but we provide no input of HF. It is produced by the reaction
UF, + +H, < UF, + HF ,

which has an equilibrium quotient

X(UFs)  _BPAER)

XUR) [P (Ha) ]

or

X(UFy) | “7“rF 1

Corrosion and other chemical considerations make it desirable to maintain
the ratio X(UF5)/X(UF,) = 1/U at a constant value,* so the concentration
of HF in the bulk of the salt can be related to the hydrogen concentration
by

2
Cop = -11\-{{-{71 (ksCp)? . (10)

We replace CFF by the equivalent function of C_, in Eqs. 7a and 8 to obtain

F
expressions for @, and Qg in terms of CF'
B. Secondary System:
1. Hot-leg piping:
Qio0 = thAlO(CC — C10) (11a)
1
- Piohio (kloclo)f . (11b)

Cio

 

#This might require that hydrogen be added to the primary systems as
a mixture of hydrogen and hydrogen fluoride.
13

Cold-leg piping:

Q11 = hy1An, (CC - C11)

= EA%ALL (k110111%
11

Transport through the primary heat exchanger tubes into the
primary system:
Qrz = hi24y (C. - Ci2)

| 1
= %‘?‘u‘[(kmczz)f - (kuCu)T] .

Transport through the steam generator tubes into the
Steam system:

Qi3 = hi3A;; (CC - C13)

A 1 1
= P‘%?—Bl—i [(k13€13)7 - (RZICZI)TJ .

Transport through the superheater tubes into the steam

system:

Qiy = hitAqy (CC - C1y)

A 1
= R‘l—‘l&i [(kmcm)%" (kzzczz)r] .

Transport through the reheater tubes into the steam system:

Q15 = hisA;s (CC - C15)

1
P‘uti\—;i [(kzsCls)% ~ (k23C2 3)7] .

Removal by sorber as hydrogen:

Q16 = higAis (CC - Cig)

1
B3WsA16(k16C1g)° .

(12a)

(12b)

(13a)

(13b)

(14a)

(14b)

(15a)

(15b)

(16a)

(16b)

(17a)

(17b)
14

8. Removal by purge as hydrogen:

Qir = FSEBCC . (18)

9. Removal by sorber as HF:

Qis = h1eA1a(CCF — C1s) (19a)

1
BuWuhia(kisCia) > - (19b)

10, Removal by purge as HF:

ng = FqEqC . (20)

CF

Since we assume that the hydrogen fluoride does not release hydrogen
to diffuse through the metal walls, and that there are no chemical reac-
tions in the secondary system that make the concentrations of hydrogen and
hydrogen fluoride interdependent, we write separate material balances for

the two species for the distribution of total tritium and hydrogen:

17

Rs + Ry = I Q (21a)
i=10

Rs = Q18 + Q1o -« (21b)

In these equations all the R's and all the Q's have positive or
zero values except for Qi2, Qi3, Q14 and Q;s5, which can have negative

values.

C. Steam generator system:

1. Transport through the steam generator tubes into the secondary

system:
Q1 = h21A13(CSG -~ Cz1) (22a)
A 1 1
= E'l—ta‘*z—s‘[(kzlcz D7 - (&, 3C13)7] . (22b)
13

2. Transport through superheater tubes into the secondary system:

Qz2 = hzzAlu(CSS - Cz2) (23a)
15

A 1 1
= E‘l'i';:i [(kzzczz)z_ - (klucw)?] . (23b)
3. Transport through the reheater tubes into the secondary system:
Q23 = hz3A15(Cop = C23) (24a)
A 1 1
= PJ‘f:—lji [(kzaczs)r - (kzscls)y] . (24b)

and C_._ will be given.

I
n the steam system the values for CSG’ CSS SR

The steam flows will be so large that the diffusion of hydrogen through
the metals should not have much effect on the concentration of hydrogen
in the steam. Under these assumptions, we do not require a material
balance over the steam system. If hydrogen is added to the feed water
as hydrazine or in some other manner to give a specified ratio of
hydrogen to H,0, then this ratio, coupled with the steam tables, can be
used to calculate the hydrogen concentrations in the water and steam in
the steam-raising equipment. Without addition of hydrogen the
concentrations are established by the dissociation of water.

We now need to solve the above equations to obtain values for all
the flow rates and concentrations. We carry this out in the following
sequence, discussed in more detail in Sec. IIIL.

1. Calculate C Cis, Q18 and Q;9 from equations 19a, 19b, 20

and 21b.

CF’

2. Assume a value for CC.

3. Calculate Qip5, Q115 Qi15, Q17 and C;¢ from equations 1lla, 11b,
12a, 12b, 17a, 17b and 18.

4. Calculate Qi13, Qis, Qis, Ci13, Ciy and Ci1s from equations léa,
14b, 15a, 15b, 16a, 1l6b, 22a, 22b, 23a, 23b, 24a and 24b,
noting that the steam system and the secondary system are

coupled by the relationships Qi3 = -Q21, Q14 = -Qz22 and
Qis = —Q23.
16

5. Calculate Q;, from the material balance, Eq. 2la.

6. Calculate CF’ Ci12 and Cy from Eqs. 4a, 4b, 13a, 13b, the
relationship Q4 = -Q;» and the value of Qi» obtained in step 5.
These concentrations should all be positive. If any one of them
is negative, steps 3 through 6 must be repeated with a larger

value of CC.

7. When positive values have been found for CF’ Ci2 and Cy4,

calculate Qi, Q2, Q3,5 Qs Q65 Q7,5 Qss Cs, Cpp and Cy.

8. Calculate RF from

8

Rp = iil Qi - (R; + Rp) &
If RF is positive, hydrogen must be added to the primary system
in order to maintain a balance. This means that CF is too large,
which in turn means that CC is too large, and steps 3 through 8§
must be repeated with a smaller value of CC. If RF is negative,
CC is too small and steps 3 through 8 must be repeated with a
larger value of CC.

When this process has been repeated until the ratio is

 

R, + R,

 

sufficiently small, the flows and concentrations of hydrogen plus tritium
and of hydrogen fluoride plus tritium fluoride have been established
throughout the plant and we can proceed with the calculation of the
tritium distribution. We ignore the difference in the properties of

the two isotopes and assume that they behave identically. Thus,

hydrogen and tritium compounds have the same solubilities and
diffusivities, and if a hydrogenous compound, such as HF, is added

to a mixture of hydrogen and tritium, exchange will occur to give a

ratio of tritium to hydrogen that is the same in hydrogen* and the

added compound.

 

*H,, HT and T,.
17
We now proceed with the calculation of the tritium distribution.

D. Primary system:
1. Transport through walls of hot-leg piping:

Qs1 = UFT Q; . (25)

“r

2. Transport through walls of cold-leg piping:

Q32 = EEI Q2 . (26)

“r

3. Transport through wall of reactor vessel and shells of heat

exchangers in primary system:
Q33 = _FT Q3 . (27)

4, Transport through walls of primary heat-exchanger tubes

into the secondary system:

Qay = hyA,y (CFT - Cay) (28a)

il

B [decsr ~ osery| - (260)
Equations 25 through 27 are straightforward, simply indicating that
the amount of tritium flowing with hydrogen is proportional to the fraction
of the concentration that is tritium when the flow of both is into a sink
with a zero concentration of both. Equation 28a is straightforward,
indicating that the flow of tritium from the bulk salt to the wall is
proportional to the difference between the concentrations of tritium in
the bulk fluid and the wall. Equation 28b, however, requires some

additional explanation.
18

The rate of transport of hydrogen through a metal wall can be

expressed as

I) .

_DA v _
Q= t (CI Co

where D is the diffusivity of hydrogen atoms in the metal, the C's are
the concentrations of hydrogen atoms dissolved in the metal at the inner
(I) and outer (0) surfaces, t is the metal thickness and A is the surface
area. Assuming no interaction of tritium and hydrogen atoms as they
diffuse through the metal, the rate of transport of tritium is

_DA

QT t

¥ t
- C .
(o 0
The concentration of hydrogen + tritium atoms in the metal at the
surface is

1
¢ = s = so)?

where S is a solubility coefficient and P is the partial pressure of
hydrogen + tritium and is equal to the product of Henry's law coefficient
and the concentration of hydrogen + tritium in the salt at the surface.
Assuming that the ratio of tritium to hydrogen + tritium in the metal

at the surface is the same as that in the salt at the surface, we can

write
v — CTI — %-CTI kICTI
C —C————S(kC) _.._._.=S_..._.._.1.
TI T C I'T” C | s
I 1 (kICI)

and a similar expression for the outer surface. Then,

kiCr kqCro
1 = 1

(kICI)f- (kOCOy?

 

_ DSA
U = 7%
19

and by substituting the permeability coefficient, p, for the product,
DS, we obtain Eq. 28b. This treatment is necessary here because

the net flows of hydrogen and tritium may be in opposite directionms.
The equations provide a means for taking into account the effect of the
mass action laws on the concentrations of tritium in the metal and its
transport through the metal.

5. Removal by graphite or other sorber:

C
FT
Q35 = T Qs » (29)
F
6. Removal by purge:
C
FT
Q3 = Rl Qg (30)
F

7. Removal by graphite or other sorber as tritium fluoride:

CFT

Q37 = = Q7 , (31)
Cr

8. Removal by purge as tritium fluoride:

C
Qag = EEE'QB . (32)
7 :

The tritium balance over the primary system is:

38
Rl = 2 Qi . (33)
i=31
E. Secondary system:
1. Hot-leg piping:
C
CT
Quo = ¢ Qo - (34)
20

2. Cold-leg piping:
C
CT
Qui =5 Q1 (35)
C

3. Transport through primary heat exchanger tube walls into

primary system:

Quz = R128u(Cop = Cuz) (36a)
= -E-li-l}-ii _klz_C"f_z__' - kquq v .
ty [(klzclz)’f (kaCoa)i | (36b)

4. Transport through steam generator tube walls into the steam

system:

Qus = h13A13(CCT ~ Cy3) (37a)

_ P13Ais klgcual
tiy (ki13Ci3f2

. (37b)

Calculations of the tritium distribution are based on the assumption
that tritium will exchange so rapidly with the hydrogen in the steam to
form tritiated water that the tritium concentration will be effectively
Zero.

5. Transport through the superheater tubes into the steam system:

Quy = hluAlu(CCT - Cuy) (38a)

_ PauAyy _kiuCuy
= 1 . 8b
tiv  (ki14C1y)7 (38b)

6. Transport through the reheater tubes into the steam system:

Qus = h1sA15(Cop = Cus) © (39a)
- Pisfis  _kisCus | (39b)

ti1s (k15C15)7
21

7. Removal by sorber as tritium:

C
Qus = == Qe « (40)

“c

8. Removal by purge as tritium:

C
Quz = 7§I'Q17 . (41)

C

9. Removal by sorber as tritium fluoride:

C
Quo = == Qis - | (42)
C

10. Removal by purge as tritium fluoride:

C
Quo ='?§2 Qio o (43)
C

The balance over the secondary system is:

49
R.3 = z Qi . (44)
i=40

Since the tritium concentration in the steam system is assumed to
be negligible, no equations are needed for the steam system.

To calculate the distribution of tritium, we solve Eqs. 2544 in
the following sequence, discussed in more detail in Section III.

1. Assume a tritium concentration, C T° in the secondary system

C
and calculate Qso0, Q415 Qus through Q,s from Eqs. 34, 35, 37a,

37b, 38a, 38b, 39a, 39b, 40, 41, 42 and 43.
2. Calculate Q42 from the material balance, Eq. 44.

3. Calculate CFT from Eqs. 28a, 28b, 36a and 36b, the relation-
ship Qs34 = -Q42 and the value of Q4. from step 2., If the value

of CFT is negative, increase the estimate for C,, and repeat

CT

steps 1 through 3. When we have found a positive C Ts We

F
proceed to step 4.
22

Calculate Q3;, Q32, Qs33, Q3ss, Qse, Qs> and Qse from Egs. 25-32.

Calculate RF’ where

38

= I Q, — R,
Tl

is the term that must be added to the left side of Eq. 33 in

order for the equation to balance. If R, is positive, tritium

F
must be added to the primary system, so CFT and CCT are too
large; if RF is negative, CFT and CCT are too small. Adjust
the value of CCT and repeat steps 1 through 5. When IRF/R1|

is sufficiently small, the calculations are finished.
23
ITTI. SOLUTION OF EQUATIONS

In the procedure discussed above, we begin with the calculation of

CCF’ Cisy Qie and Q,s with Eqs. 19a, 19b and 20, and the material balance,

Eq. 21b:
Qis = hlBAla(CCF — Cia) (19a)
3
= Bu,WsA;15(k18C1s)” (19b)
Qio = FhEhch s (20)
Rs = Qis + Q15 - (21b)

Eq. 19b requires that Q,s > 0 and Eq. 20 requires that Qi > 0, so if
Rs = 0, 21b requires that Qs = Q;9 = 0. If Rs > 0, we combine 21b, 20

and 19a to obtain

Rs - Q8 = FLE,C_ = Rs — h1aA15(CCF = Ci1s8) »

CF

or

c . = RsthiahA1eCis
CF Fqu‘i‘hlaAla (]_QC)

Substituting 19c into 19a, setting the result equal to 19b and collecting
terms we obtain

1
o — Cis = BCig » (194d)

where we have defined

Rs
F,E, °’

_ F‘.E¢.+hleAla} [Bhw‘.} 4
P = [ FLE, His [kls] ’

 

u:

and

 
24

Squaring both sides of 19d results in a quadratic equation for C;s}
since the right-hand side of 19d is positive, we want the root of this

quadratic which is less than a. We have

Cfa —'(2a+32)cle +0* =0 >

_2a+B2 + V(2a+B>) 2 ~4a

C
18 5

To obtain the root less than o, we want the root with the negative sign.
To avoid possible loss of significant figures, we note that the product

of the roots is &2, so that we can write the solution in the form

2

 

o
ClB = 2 . (lge)
a+-B— 1+ \/l+—ng-
2 B
Then we have
1
Qis = BhwhAls(klecls)T-, (19b)
_— R5 + hlBAIBC].B
CCF = TF.E. + DioAss (19¢)
and
Qo = F&Euch . (20)

With some value for CC we proceed to the calculation of Qio, Qi:,

Q165 Q17 and Cis. Egs. 1la, 11b, 12a and 12b read

Qio = h1oA10(CC — C10) » (11a)
A 1

Qio = Ei%:LQ (kIOCIO)E., (11b)

Qi1 = hllAll(CC — C11) > (12a)
25

A 1
Qi = P—;—l—l (k1:1C11)2 (12b)

These equations (11 and 12) are identical in structure, as aive Egs. 1,

2, 3, 5, 7, 17 and 19. For Egs. 11 and 12 we define

 

C1=C Ol=ki

c’ t.h

ii

and Eqs. 11 and 12 then can be written in the form of quadratics in the

concentration Ci:

2 2 _
Ci (2C1+a)Ci + C]_ 0o .

From Egs. 1lb and 12b, the flow rates Q;o and Q,; must be positive, so

that the root desired in each case is the smaller one. We have

 

 

C Cy i 10, 11
. = s 1 % ’ ’
* c1+9‘-(1+ 1+Cl)

2 o
and

P.A, 1

_ i = . _
i
By putting
Cl = CC ’

BsWs
=(§12)k16 ’
Cis can be calculated in the same fashion (Eqs. 17a and 17b) and the

flow rates Q.6 and Q,, are

1
Qi = BawsAls(k1sc1s)7-s

Qi7 = FsEscC .
26

We continue with step 4, the calculation of the flow rates Q,s,
Q14 and Q;s, and the corresponding concentrations C;s, C;, and C,s,
using Eqs. l4a, 14b, 15a, 15b, 16a, 16b, 22a, 22b, 23a, 23b, 24a and
24b. Note that the secondary system and the steam system are coupled

by the equations

Qis = =Q21, Qia = Q22 and Q15 = -Q23 .

The three equations 14, 15 and 16 all have the same structure and can

be written in the form

 

P 1 1
— = K T _ T
=G oo - aep?] (2)
h, (C; —Cz) = h (C:—Cp) , (b)
where K = 13, 14 and 15, C, = CC’ L =21, 22 and 23, and we identify
C. as CSG’ CSS and CSR for K = 13, 14 and 15, respectively. We can
solve Eq. b for CL:
ht(cl-C) +hC2 h
c =X K L - K,-c)+c, . (c)
L hL hL K

Since C, must be non-negative, there is a maximum permissible value

L
Cémax)’ which is the value such that
h
K (c1 c(max)) +Co =0,
h K
L
or
h
clmax) C, + 2 Cs . (d)
K hK

If we substitute (c) into (a) and rearrange, we have
27

k + | * %‘l
Ce = Co v gk & (G0 * G _[kKCK] ’ (e)
KK L
or, more concisely,
CK = F(CK) .

To locate the solutions (if any) of this equation, we need to

(max)

examine the behavior of F(CK) for 0 < C 5_CK . We find that

K

F(0) >0
and

F'(CK) < 0, F'(O) = =®
F"(CK) _>_ 0.

The graph of F(CK) then looks like the curve in Fig. 2.

“k

F(CK).

 

 

0 CK
Fig. 2. Sketch of F(CK) vs CK.

(max)

For there to be a solution between zero and CK

, we must have

(max)

“k

> F(Cémax)) and upon substitution of our expression (d) into
F(CK), we find that this condition is satisfied. We will now examine

the function

G(CK) = C_ — F(CK) .

K
28

We note that

G(0) = =F(0) <0

(max)

G(CK

) >0

and

G'(CK) =1 —-F'(CK) > 0 [since F'(CK) < 0] .

This insures that G(CK) has one and only one zero in the range

(max)

< : " = " " <
0<CcC E-CK . Since G (CK) F (CK), G (CK) < 0, and the graph

K
of G(CK) looks like the curve shown in Fig. 3.

(max)

' c(c"))

 

 

 

G(0)

Fig. 3. Sketch of G(CK) vs CK

With a suitable Cél) we can compute G, = G(Cél)) < 0 (for example,
starting with Céi) = () and with a suitable Céz), G, = G(Céz)) >0
(Céz) = Cémax), to start). An approximation to the solution CéT), is

derived from the inverse linear interpolation:

(1) _ (2)
(D) _ G2Cy G1Cy
K G2 - G]_ >

as shown in Fig. 2. A better approximation can be derived with inverse

quadratic interpolation:

(X) (O-GT) (O_G2) (1)

(O_Gl) (O—GT) (2) (O_Gl) (O"Gz)
= e————————— (O
K~ (6:-6) (G:~62) K

+ e c{D

C t .
(Gz*G1)(G2-GT) K (GT—Gl)(GTQGI) K
29

With G"(CK)_i 0 as shown and G'(CK) >0, GT = G(CéT)) will be positive
T

and CéT) should be larger than the root. If Céx) is larger than Cé ),

we replace Céz) by CéT), G2 by GT’ and repeat the inverse linear inter-

i (x) , (T)

polation. If, however, CK is smaller than CK , we calculate

GX = G(Cé%)); and if this value is negative, we replace Cél) by Cé#),

G, by Gx’ Céz) by CéT) and G, by GT’ and repeat the inverse linear

interpolation., If GX is positive, we replace Céz) by Céx) and G, by GX

and repeat the inverse linear interpolation. We terminate this process

when
(T)
&
(%)
CK

1 <C

TOL °

or when we have done 50 iterations. The tolerance CTOL is defined in a
DATA statement in our program. We have found that the procedure converges
in about four iterations for CTOL = 10™° and in about six iterations for

_ -7
CTOL 1077,

The required flow rates Q;s;, Q215 Qias Qz22, Q15 and Q23 can now be

computed from
Q; = hiAi(CC-— ci)

Qg = ~Q» 1 =13, 14, 15 .

The flow rate of hydrogen and tritium through heat exchanger tube

walls from the secondary to the primary system, Q,,, is
Qiz = Rs + Ry — (Qio + Q1 + Qis + Qus + Qs + Q16 + Qy7) ’

and from Eq. 13a,

C12=C_££_.
C hi.A,
30

If the value for C,. is negative, we have used too small a value for
CC’ so we double our previous guess and start over at step 3. ' If the
computed value is positive, we proceed to calculate (Eq. 13b)

1 3 t,]?
Cy = E:’[(klzc1z)]-—'%ii;f]

’

and finally,

- _9;2
CF Cu hyAg

If the computed value for C_ is negative, we need a larger value for

F
CC’ so we double our previous guess and return to step 3. If positive,
we proceed to step 7, the computation of the remaining flow rates Q,,
Q2, Q3, Qs, Qg, Q7 and Qs and the concentrations Cs, Cop and Cy.

We can write Egqs. 1, 2 and 3 in the form

P.A, 1
= - _ 11 z s =
Qi = hiAi (CF Ci) . (kici) , 1 1, 2, 3,

and with

 

the resulting quadratic equations can be solved in the same way as

those for C;, and Cy;. Egs. 5 can be manipulated into the same form

with

_{Bw; }?
o = hs k5

so that we can calculate Cs, and from it

1
Qs = B1WiAs (ksCs)Z . (5b)
31

Again, Eqs. 7a and 7b can be written as a quadratic for C; with

BoWo |2
o "_—‘]:2172 k7
s0 that we can calculate
1
Q7 = BoWpAy (k7Cy)7
Qg = FzEchF
and
8
R.= 2, Q -Ri-Re
; i
i=1
where CFF is
1
. MU T
o 6(50}_,) : (10)

This is the end of the first part of the procedure if RF is small

enough. We test the condition

Rp

Ri+R,

 

 

 

TTOL

(where the quantity TTOL is defined in a DATA statement in our

program) and if it is satisfied, we proceed to the second part. If

not, we adjust C, in a variety of ways, depending on what information

C

we have accumulated so far. We carry out a preliminary search for

two values of CC which bracket the root, i.e., one for which RF is

negative and the other for which RF is positive. If this is the

first iteration or if both our present and previous values of RF

have the same sign, we multiply CC by a factor m such that

-R_/(R1+R3)
m = 10 RF
32

but limited to the range
.01 <m <100

When we have bracketed the root, we combine inverse linear and
inverse quadratic interpolation in much the same way as we did for
the solution of the equations for C;3, Ci;n and Ci15, keeping the root
bracketed and attempting to reduce the length of the interval con-
taining the root. When this process has converged, we proceed to
the tritium calculation.

With a value for CCT’ the concentration of tritium in the

secondary salt, we compute

C
Qu 0 ='EEI Q1o (34)
C
C
Qyy = EEE Qi1 (35)
C

and from Egs. 37a, 37b, 38a, 38b, 39a and 39b we obtain

]
h1st13(C13/k13)%/pyy
Cus = 1 C 37
“* 7 1+hyst13(Crs/k13)% /prs CT (37¢)

_ pP13A13
Qus t13(C13/ky3)? Cus (370)

1
h14t14(614/k14yT/P1u (38¢c)

C = C
T 1hyet1s (Cru/kys)E /piy  CT

PisAqy
=-—-—-————-——_—.—_—.‘
Qus t1u(Cry/kyy)? Cu (38b)

1
h15t15(C15/k15)77P15 (39¢)

C =
"3 7 1+h;st15(Cys5/kys)% /p1s CT

Qus = __pisAis  Cus (39b)
t15(C1s5/ky5)?
33

CCT
Qysp = EE_ Qs 1= 16, 17, 18, 19 (40-43)
Qu2 = R3=Qu0-Q41-Qu3-Qus=Qus5-Que~Qu 7~Qu=Qu o (44)
and finally
= _ Qua
Gz = Cop = §,A0 .

If this value is negative, we have used too small a value for

C in the same way as before, we double C and try'again, starting

cT’ CT
at Eq. 34. When we have found a positive C,2, we compute

3
- [ Cu Cyo _ tuQuo
Cau (ku) (C1z/k12)¥ PuAy

Again, if C3, is negative, we need to double C_, and try again.

CT

When we have found a positive Cj3,, we compute

= _ _Quo
CFT Css hyAy

and continué with the doubling scheme until Cy2, C3y and CFT are all

positive. We can now compute the flow rates

CFT
Q30+i =“C_~Qi’ i=1, 2, 3, 5, 6, 7, 8
F

and

§?
= Q. -~ Ry .
¥ i=31

OQur test is now on |RF/R1|’ and we use the same adjustment and

interpolation procedures as for CC.
35

Iv, NOMENCLATURE

A = surface area, cm®

A1

hot leg of primary system (piping and
pumps)

cold leg of primary system (piping)
reactor vessel and heat exchanger shells
tubes of primary heat exchanger

core graphite for sorption of hydrogen

core graphite for sorption of hydrogen
fluoride

hot leg of secondary system (piping, pumps,
half of shells on steam-raising equipment)

cold leg of secondary system (piping, half
of shells on steam-raising equipment)

A

4

tubes of steam generators
tubes of superheaters

tubes of reheaters

sorber of hydrogen

sorber of hydrogen fluoride

 

Reference

Value® Name*#*

 

A

6 X lO5

5X lO5

3.5 X 106

4.9 X 107

5.2 X 107

5.2 X lO7

1.1 X 107

8.8 X 106

4.9 X 107

3.1 X lO7

2.7 X 107

1.8 X lO7

*The reference values are based on the design of a 1000 MWe molten salt
breeder reactor plant described in ORNL-4541.
**Acronym used in FORTRAN computer program; if no entry appears, the
parameter is not used in the program.
36

 

Reference
Value Name
B = sorption factor, atoms/cmaatml/2 B
21
Bl = hydrogen + tritium on core graphite 3 X10
21
B2 = hydrogen fluoride on core graphite 3 X 10
B = hydrogen + tritium on sorber in secondary
3 18
system 1 X 10
B = hydrogen fluoride on sorber in secondary
4 18
system 1X10
C = concentration, atoms/cm®
CF = hydrogen + tritium in bulk of primary salt CF
CFF = hydrogen + tritium as hydrogen fluoride in
bulk of primary salt CFF
CFT = tritium in bulk of primary salt CFT
CC = hydrogen + tritium in bulk of secondary salt CC
CCF = hydrogen + tritium as hydrogen fluoride in
bulk of secondary salt CCF
CCT = tritium in bulk of secondary salt CCT
CSG = hydrogen in bulk of water in steam generator 10
(672°K) 2 X 10 CSG
CSS = hydrogen in bulk of steam in superheater 11
(783°K) 9 X 10 CSS
CSR = hydrogen in bulk of steam in reheater 11
(755°K) 1 X 10 CSR
Cl = hydrogen + tritium in salt at surface of hot
leg of primary system C
C2 = hydrogen + tritium in salt at surface of
cold leg of primary system
C3 = hydrogen + tritium in salt at surface of

reactor vessel and heat exchanger shells
37

Reference
___Value =~ Name

hydrogen + tritium in salt at surfaces
of heat exchanger tubes in primary
system

hydrogen + tritium in salt at surfaces
of core graphite in primary system

hydrogen fluoride in salt at surfaces
of core graphite in primary system

hydrogen + tritium in salt at surface
of hot leg in secondary system

hydrogen + tritium in salt at surface
of cold leg in secondary system

hydrogen + tritium in salt at surfaces
of heat exchanger tubes in secondary
system

hydrogen + tritium in salt at surfaces
of steam generator tubes in secondary
system

hydrogen + tritium in salt at surfaces
of superheater tubes in secondary system

hydrogen + tritium in salt at surfaces
of reheater tubes in secondary system

hydrogen + tritium in salt at surfaces
of sorber in secondary system

hydrogen fluoride in salt at surfaces
of sorber in secondary system
38

Reference
__Value = Name
€0 7 7
C21 = hydrogen in steam at surfaces of steam
generator tubes in steam system
022 = hydrogen in steam at surfaces of super-
heater tubes in steam system
C23 = hydrogen in steam surfaces of reheater
tubes in steam system
C — = ——
24 C33
C34 = tritium in salt at surfaces of heat
exchanger tubes in primary system
C357C41 = 7
C42 = tritium in salt at surfaces of heat
exchanger tubes in secondary system
C43 = tritium in salt at surfaces of steam
generator tubes in secondary system
C = tritium in salt at surfaces of super-
A .
heater tubes in secondary system
045 = tritium in salt at surfaces of reheater
tubes in secondary system
E = efficiency E
El = removal of hydrogen + tritium from purge _1
stream in primary system 5 X 10
E2 = removal of hydrogen fluoride from purge _>
stream in primary system 1.7 X 10
E = removal of hydrogen + tritium from purge
3 . : -1
stream in secondary system 1.8 X 10
E4 = removal of hydrogen fluoride from purge 3

stream in secondary system 1.8 X 10~
39

F = flow rate, cm®/sec

B

purge stream for removal of hydrogen +
tritium from primary system

purge stream for removal of hydrogen
fluoride from primary system

purge stream for removal of hydrogen +
tritium from secondary system

purge stream for removal of hydrogen
fluoride from secondary system

h = mass transfer coefficient, cm/sec

By

hydrogen through primary salt to surfaces
of hot leg in primary system

hydrogen through primary salt to surfaces
of cold leg in primary system

hydrogen through primary salt to surfaces
of reactor vessel and heat exchanger shells
in primary system

hydrogen through primary salt to surfaces
of heat exchanger tubes in primary system

hydrogen through primary salt to surfaces
of core graphite in primary system

hydrogen fluoride through primary salt to
surfaces of core graphite in primary system

hydrogen through secondary salt to surfaces
of hot leg in secondary system

Reference
Value Name

3.6 X 10

3.6 X 10

5.0 X 10

5.0 X 10

1.6 X 10

6.0 X 10

9.0 X 10

1.9 X 10

3.0 X 10>

3.0 X 10>

7.4 X 1072
11

12

13

14

15

16

17

18

19

20

21

22

23

Henry's law coefficient,

0.83 x 10 %% [k'

hydrogen

40

through secondary salt to surfaces

of cold leg in secondary system

hydrogen
of tubes
system

hydrogen
of tubes
system

hydrogen
of tubes

system

hydrogen
of tubes

hydrogen

through secondary salt to surfaces
in heat exchangers in secondary

through secondary salt to surfaces
of steam generators in secondary

through secondary salt to surfaces
in superheaters in secondary

through secondary salt to surfaces
in reheaters in secondary system

through secondary salt to surfaces

of sorber in secondary system

hydrogen

fluoride through secondary salt

to surfaces of sorber in secondary system

hydrogen
of steam

hydrogen
of steam

hydrogen

through water
generators in steam system
through steam
generators in steam system

through steam to surfaces of tubes

of reheaters in steam system

(cm’melt) (atm.)
atom H

moles H, -1
(cm® melt) (atm.)

 

Reference

Value

Name

 

to surfaces of tubes

to surfaces of tubes

3.4 X 10
9.7 X 10
4.3 X 10~

4.7 X 10
4.0 X 10~

8.0 X 10

8.0 X 10

5.8

12

30

2

2

2

2

2

1

1
41

-1

 

10-24 [k' moles HF ]

(cm® melt) (atm.)
hydrogen in primary salt in hot leg in
primary system (973°K)

hydrogen in primary salt in cold leg in
primary system (838°K)

hydrogen in primary salt in reactor
vessel and heat exchanger shells in
primary system (908°K)

hydrogen in primary salt in heat
exchangers in primary system (908°K)

hydrogen in primary salt in reactor core
in primary system (923°K)

— —

hydrogen fluoride in primary salt in
reactor core in primary system (923°K)

hydrogen in secondary salt in hot leg in
secondary system (894°K)

hydrogen in secondary salt in cold leg in
secondary system (723°K)

hydrogen in secondary salt in heat
exchangers in secondary system (809°K)

hydrogen in secondary salt in steam
generators in secondary system (783°K)

hydrogen in secondary salt in superheaters
in secondary system (866 °K)

hydrogen in secondary salt in reheaters in
secondary system (810°K)

Reference
Value

1.2 x 10°%

2.0 X 1071

1.5 X 107+

1.5 X 1071

1.4 x 1071

3.4 X 10+

5.0 X 1071

4.0 X 1074

4.5 X 10+

3.5 X 10+

4.0 X 1071

7

7

7

7

7

8

8

8

8

8

8

Name
16

17

18

19

20

21

22

23

42

hydrogen in secondary salt in contact
with sorber in secondary system (773°K)

hydrogen fluoride in secondary salt in
contact with sorber in secondary system
(773°K)

hydrogen in steam in steam generators in
steam system (660 °K)

hydrogen in steam in superheaters in the
steam system (755°K)

hydrogen in steam in reheaters in steam
system (714 °K)

equilibrium quotient for reduction of UF4 by
hydrogen, atnfi/fi (923°K)

permeability coefficient for hydrogen in metal

(atoms H) (mm)

16 , (cm® H, STP) (mm)

 

 

(sec) (cm?) (atm) 2/2

~—— = 1.5 X 10

at average temperature of metal in hot leg
in primary system (973°K)

at average temperature of metal in cold
leg in primary system (838°K)

at average temperature of metal in reactor
vessel and heat exchanger shells in
primary system (873°K)

at average temperature of metal in tubes
in heat exchangers in primary system
(873 °K)

Reference
Value

4.4 X 10718

4.5 X 10”29

5.1 X 10720

4.8 X 10'20

1.12 X 107°

(hr) (cm?) (atm) /2

2.1 X 1015

6.7 X 1014

9.0 X 1014

9.0 X 1014

Name

M
43

ps_pg = -

Pig at average temperature of metal in hot leg
in secondary system (893°K)

pll = at average temperature of metal in cold
leg in secondary system (723°K)

Pi2 = Py

p13 = at average temperature of tubes in steam
generators in secondary system (723°K)

P14 = at average temperature of tubes in super-
heaters in secondary system (838°K)

Pys = at average temperature of tubes in

reheaters in secondary system (773°K)
= pressure, atm, or other appropriate units

= rate of transport, atoms of hydrogen and/or
tritium per second

Q1 = hydrogen + tritium through walls of hot
leg in primary system '

Q2 = hydrogen + tritium through walls of cold
leg in primary system

QB = hydrogen + tritium through wall of reactor
vessel and shells of heat exchangers in
primary system

Q4 = hydrogen + tritium through walls of tubes
in heat exchangers from primary system to
secondary system

Q5 = hydrogen + tritium to core graphite in
primary system

Q6 = hydrogen + tritium to purge in primary
system

Reference
Value

15

1.1 X 10

1.8 X lOl4

9.0 x 10%*

1.8 X 1014

6.7 X 1002

3.5 X 1014

Name
44

Reference
Value Name

 

hydrogen fluoride to core graphite in
primary system

hydrogen fluoride to purge in primary
system

hydrogen + tritium through walls of hot
leg in secondary system

hydrogen + tritium through walls of
cold leg in secondary system

hydrogen + tritium through walls of
tubes in heat exchangers from secondary
system to primary system = —Q4

hydrogen + tritium through walls of the
steam generator tubes from the secondary
system into the steam system

hydrogen + tritium through walls of the
superheater tubes from the secondary
system into the steam system

hydrogen + tritium through walls of the
reheater tubes from the secondary system
into the steam system

hydrogen + tritium to sorber in secondary
system

hydrogen + tritium to purge in secondary
system

hydrogen fluoride to sorber in secondary
system

hydrogen fluoride to purge in secondary
system

hydrogen through walls of steam generator
tubes from steam system into secondary

system = -Ql3
45

Reference
Value Name

hydrogen through walls of superheater
tubes from steam system into secondary

system = —Q14

hydrogen through walls of reheater tubes
from steam system into secondary system =
Qs

tritium through walls of hot leg in
primary system

tritium through walls of cold leg in
primary system

tritium through wall of reactor vessel
and shells of heat exchangers in primary
system

tritium through walls of heat exchanger
tubes from primary system into secondary
system

tritium to core graphite in primary
system

tritium to purge in primary system

tritium fluoride to core graphite in
primary system

tritium fluoride to purge in primary
system

tritium through walls of hot leg in
secondary system

tritium through walls of cold leg in
secondary system

tritium through walls of heat exchanger
tubes from secondary system into primary

system = -Q34
46

 

Reference
Value Name
Q = tritium through walls of steam generator
43 .
tubes from secondary system into steam
system
Q44 = tritium through walls of superheater tubes
from secondary system into steam system
Q45 = tritium through walls of reheater tubes
from secondary system into steam system
Q46 = tritium to sorber in secondary system
Q47 = tritium to purge in secondary system
Q48 = tritium fluoride to sorber in secondary
system
Q49 = tritium fluoride to purge in secondary
system
rate of production or addition, atoms/sec R
Rl = tritium in primary system 5.8 X lO17
R2 = hydrogen to primary system 0
R3 = tritium in secondary system 0
R4 = hydrogen to secondary system 0
R5 = hydrogen fluoride to secondary system 0
RF = hydrogen or tritium to primary system
in order to obtain overall material
balance -
temperature, °K
wall thickness, mm T
tl = hot leg in primary system 13
t = cold leg in primary system 13

2
47

 

Reference
Value Name
t3 = reactor vessel and heat exchanger shells
in primary system 50
t4 = tubes in heat exchangers in primary
system 1
t.._ = e
5 %9
t10 = hot leg in secondary system 13
t1l = cold leg in secondary system 13
f12 7 %
t13 = tubes in steam generators 2
t14 = tubes in superheaters 2
t15 = tubes in reheaters 1
= i U
U = ratio XUF /XUF 100
4 3
W = replacement rate, fraction/sec W
wl = core graphite or other sorber of hydrogen
in primary system 1
W2 = core graphite or other sorber of hydrogen
fluoride in primary system 1
W3 = sorber of hydrogen in secondary system 1
W4 = gorber of hydrogen fluoride in secondary
system 1

X = mole fraction
49

V. COMPUTER PROGRAM, INPUT INSTRUCTIONS AND SAMPLE PROBLEM

The FORTRAN-IV program listed in the Appendix was written to pro-
vide a flexible and easily used tool for parameter studies. Many of the
system parameters listed in Sec. IV have standard or reference values,
and we have written the program to allow the user to specify a new value
for any parameter, to use the reference value, or to reset a parameter
to its reference value. Instructions to the program are in the form of
simple commands, followed by numerical values as required.

Output from the program consists of the summary of concentrations,
flow rates and fractions shown in Fig. 2, any input commands, and various
messages from the program to display the progress of the iterative parts
of the calculation.

The three options currently available to the user are

(a) OUTPUT

(b) OUTPUT__ALL“CRBE* all commands begin in column 1; (the

underline indicates a blank space)

(c) OUTPUT __ALL PRINTER
With choice (a), the summary output is sent to logical unit 20 and all
ofihef output is sent to logical unit 6 (the line printer); with choice
(b), all output is sent to logical unit 20; and with choice (c¢), all
output is sent to logical unit 6, For choices (a) and (b), appropriate

data definition (DD) statements for unit 20 must appear in the user's

job control language.

 

*The program was designed to be used from a remote terminal with the
‘Conversational Remote Batch Entry system; hence the use of "CRBE" as
a keyword. However, the program in no way depends upon the availability
of the CRBE system.
50

To change various system parameters, the command is

CHANGE__XXX

where XXX is replaced by the appropriate variable name as listed in

Sec, IV,

(CF 2 CFF’

parameter value in cols. 1~10.

If the variable name refers to one of the named concentrations
csns CSR)’ the next line of input must contain the new

If the variable name refers to any of

the subscripted variables in Sec. IV, the next line must contain a

starting index, n;, a stopping index n

variables specified by the subscripts n

2

1

through n,-

and the new values for the

A maximum of

seven consecutive values is allowed; if there are more than seven, put

the subsequent values on subsequent lines,

starting index of zero.

CARD COLUMN

End with a 1

ine with a

The following example illustrates the format.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 72 E3 E4 ?5}6; 7 8910 11{12 13114|15|16|17{18 |19 {20 21!22523524%25 26|27 12829 |30 |31 3:?33%34 35136137
CHANGE A
1 3] 1., 2 +6;f 1.0 +6| 7.0 + 6
13 6 2 . + 6
0
This will insert new values for Al, A2, A3 and A13 of 1.2 X 106,

1.0 X 106, 7.0 X 10

6

and 62 X 106, respectively.

to be changed, the second subscript need not appear.

The user can supply starting estimates for CC

and C

If only one value is

o’ the concen-

trations of hydrogen plus tritium and tritium in the bulk of the

secondary salt, with the "CHANGE'" command.

11

the program will use 1 X 10

for C

C and

If no values

10

1 X10 for C

CT

are supplied

 
51

To perform a calculation when all the necessary changes have been
made, the command is
RUN

A calculation will then be done with the parameters specified.
For subsequent cases, all parameters will have the values present at
the end of the preceding calculation; to change the parameters, the
user can supply additional "CHANGE" commands. To reset parameters to
their reference values, the command is
RESET XXX
If "XXX" is left blank, all parameters will be reset; if "XXX" is the
name of a subscripted variable, all entries with the given name will
be reset; and if "XXX'" is the name of one of the named concentrations

(C., C oo CSR) then just that concentration will be reset. If,

F’> “FF’
for example, after running the case specified by the '"CHANGE" command
in the example, a user put
RESET___A
then all the A's would be reset to their reference values.
The program will stop when an end-of-file condition is detected
on the standard input unit, i.e., when it runs out of data.
The input and output for a sample problem are shown in Figs. 4
and 5. Reference values from Section IV were used in the sample calcula-
tion. The results indicate that 30 percent or more of the tritium might

reach the steam system in a large power reactor unless special measures

are taken to confine the tritium.
52

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4516 (718910 11!1213 14115|16 |17 |18 |19 |20)21|22|23 |24 |25|26 127 {28]29 |30 |31|32(33|34|35(36/37}38

 

cd QO B 8 ~ -~ ~— Y
m Qg o~ »
H =2 0O w2 H4d 0

~ ~ M
~ ¥* H d

/ X

XX1 J¢B (nnonnnonn), "ADDRESS ', CLASS=A
EXEC FHRTHLG,GHSIZE=62K
KED.SYSIN DD *
HEX DECEK
@ . FTO5F001 DD *
PUT ALL PRINTER
N GE A
2 +6 1.0 +6 7.0 + 6
+ 7
CH

Fig. 4. Sample Problem Input
VALUES IN

ARRAY

MAME A  DIMENSION 20 USED

1

6.,00000D0 05
-1.000000 00

— . 8.80000D 06 = 4900000 07

 

e - 5200000001

NAME F
1

3.60000D 05
 NAME H
1

1.600000~02
-1.C0000D 00
_3.40000C-02

8.00000D-01

$.800000 00

Fig. DA.

DIMENSICA

DIMENSTION

v

2

5.000000 05
5200000 07

C.0 -1.00000D0 CO
NAME B DIMENSION 5 USEED
1 2
_ 3.000000 21  3.C0000D0 21
NANME C DIMENSION 50 USED
| 2
0.0 0.0
0.0 0.0 _
0.0 0.0
0.0 040
0.0 0.0
0.0 0.0
0.0 0.0
e 00 060
0.0 0.0
NAME CN DIMENSION 10 USED
1 2
. ~1l2000000 00 -1.C00000 00
1.00000D 10 2.000000 10
NAME £ CIMENSION 5 USED
1 2

1.70000D0-02

S USED
2

3.600000 05

25 USEL
2

6.000000-03
3.000000-03
9.70000D~02
-1.00000D0 00
1.20000D0 0Ol

S STARTS

53

18 STARTS
3

AT

3.500000
-1.0C000D
3.100000
0.0

06
0o
a1

4 STARTS
3

AT

. 1000000 18

45 STARTS
3

AT

DO0O00D0O0O0O00O0
¢
CO0OO0O0DOOO

AT
3

9.00000D

00
i1
4 STARTS AT
3

1.8C000D-01

4 STARTS AT
3

5.0C000D 05

23 STARTS AT
3

9.0C0000~-05
-1.000000 00
4.3C0000-02
8.000000-01
3.000000 01

4

4.900C00 07
-l 000CCC 0O
2. 700CCC 07

21
4

1.000CCD 18

26
4

0.0
0,0
0.0
0.0
0.0
0.0
0.0
0.0
0.0

16
4

1. 000CCD 11
1.000C0CD 11

86
4

1. 800CCC-C3

91
4

5.00CCCC G5

96
4

1« 90GCCC~-02
-1 COCCCD 00
4.700CCC-02
-1.000CCD ©C

5

5.2CC00D 07
1.100000 07
1.80000D0 07

LI
ODOOOCOHODOO

OO0 OOO0O0
s 0 8 8

5
-1.CC000D 00

5

3.000000—-03
1.400000—02
4.CC0000-02
-1.€0000D OC

List of Parameter Values Used in Calculation .
VALUES IN ARRAY V

NAME K DIMENSION 25 USED
1 2

1.200000-17 2.00000D0-17

-1.00000C 00 1.500000-19

—  _5400000D0-18 _ 4.00000D-18_

4.400000-18 -~1.000000 QO
4.500000-20 5.10000D0-20
NAME P DIFMENSION 20 USED

1 2

2.10000D0 15 6.70000D0 14

 

 

1.80000D0 14 9.00000D 14
NAME R CIMENSION 10 USED
1 ~ - S
5,800000 17 0.0
NAMF ¥ DIMENSION 20 USED
1 2
© 1.300000 01  1.300000 Ol
-1.000000 00 -1.000000 QO
1.30000D0 01 1.00000D0 00
NAMF W DIMENSIONM 5 USED
e ML 2

1.000000 00 1.00000D0 00

NAME M CIMENSION 1 USEC
1 2
 1.120000-06
NAME U  DIMENSION 1 USED
1 2

~ ... 12000000 02

54

23 STARTS
3

AT

1.500000-17

-1.0C000D

00

_4+500000-18
1.,100000-20
4.800000-20

15 STARTS
3

9.000000D
-1.000000
1.8C000D

S STARTS
3.

0.0

15 STARTS
3

5000000
-1.000000
2.00000D

4 STARTS
3

1.000000

1 STARTS
3

1 STARTS
3

AT

14
00
14

AT

AT

01
00
00

AT

00

AT

AT

121
4

le 500CCD~-17

-l.000CCL

00

3.500CC0-18

-1sCOCCCD
146
4
9.000CCD
-1.000CCD
6. 700CCD

166
4

0.0

176
4

1.000CCD
-l.000CCC
2.000CCOD

196
4

1.000CCD

201
4

202

Fig. 5A. (Continued) .

co

14
00
14

co
0o
]¢)

00

S

1.4C0000-117
3.4C€0000~-18
4,C€00000-18

-1.€00000

5
-1.C0000D
1.100000D
3.500000
5

C.0

5

-1.€00000D
1.30000D

- 1.€0000D

co

oc
15
14

00

cC
55

I TERATIVE SOLUTION FOR CC

NCC CCl1 CCL CcCX RFX cc2
0 3.47462D 17 1.00000D 11
1 2.52116D 10 ~2.91224D 17
2 2.52116D 10 5.93131D 10 1.62379D 16 1.00000D0 11
5.742380 10 1.92741D 14
4 2.52116D 1C 5.,740250 10 1.13535D 13 5.742380 10

5.74012D 10 1.02747D 08
ITERATIVE SOLUTION FOR CCT

NCC CCl cCL CCX RFEX Cc2
0 1.000000 10 -4.71400D 17
1 4.,33784D 16 5.74012D0 10

Fig., 5B, Output from Iterative Calculations.
56

OUTPUT SUMMARY

STEAM SYSTEM
FLOW OF H + T INTO STEAM SYSTEM
FLOW OF T INTO STEAM SYSTEM
FLOW OF H INTO STEAM SYSTEM
FRACTION OF T INTO STEAM SYSTEM

SECONDARY SYSTEM
FLOWS
H + T INTO SECONDARY FROM PRIMARY
T INTO SECONDARY FROM PRIMARY
H « T THRU PIPE WALLS INTO CELLS
T THRU PIPE WALLS INTQO CELLS
SORPTION BY SINK
H + T
T
HF
TF
REMOVAL BY PURGE
H+ 7T
T
HF
TF
FRACTION OF T
PASSING THRU PIPE WALLS
SORBED BY SINK AS T
- SORBED BY SINK AS TF
REMOVED BY PURGE AS T
REMOVED BY PURGF AS TF
CONCENTRATIONS IN SECONDARY SALT
H + T (CC)
T (CCT)
HF {(CCF)

PRIMARY SYSTEM
FLOWS
H + T THRU WALLS INTO CELL
T THRU wWALLS INTO CELL
SORPTION BY SINK
H+ T
T
HF
TF
REMOVAL BY PURGE
H+ T
Y
HF
TF
FRACTION OF T
PASSING THRU WALLS INTQO CELL
SORBED BY SINK AS T
SURBEE BY SINK AS TF
REMOVED BY PURGE AS T
REMCVED BY PURGE AS TF
CONCENYRATIONS IN PRIMARY SALT
H ¢« T (CF)
T(CFT)
HF (CFF)

Fig, 5C. Output Summary.

1.710720 17
1.76310D0 17
-5.,238000 15
3.03983D-01

2.385010 17
2.39047D 17
6.226260D 16
5. 793000 16

0.0
0‘0
0.0
0.0

5.16611D 15
4.80662D 15
0.0
0.0

0.0
0.0
8.287270-03
g.0

5.740120 10
5340690 10
0.0

3.6B84360 15
2.67847D 15

4.45130D 16
4.44419D 16
2.328070 17
2.32435D 17

5.136120 16
5.127910D 16
9.13321D 15
9,11861D 15

6.34219D-03
1.66239D-02
4., 007500~-01
8.84122D-02
1.572170-02

2.85340D0 11
2.84884D 11
1.49235D 12
57

A t 1. 3)
——..— 1e20000C 06 _1.000000 Q6 7.00CCOD Q6
A (13.13)
6.20000D 07

Fig. 5D. Output Produced by '"CHANGE" Command.
58

VALUES IN ARRAY V
" DIMENSTON 20 USED 18 STARTS AT
1 2 3

AANE A

1.20000D 06 1.000000 06 1.000000 06

-1.€00000 0O 5.200000 07 -1.0000G0 00

—— 82800000 06 = 4900000 07 = 6.20Q000 Q7
0.0 ~1.000000 QO 0.0

hAME B DIMENSION 5 USEC 4 STARTS AT
1l 2 3

—  3.000000 21  3.000000 21 1.0C000D 18
MNAME C DIMENSION 50 USED 45 STARTS AT

 

1 2 3

7944140 07 6.585480 07 1.620350 05
0.0 -—-1e622450-05. C.0 = .. .
2.996290 09 2.873180 11 6.7T74C8D 08
4,061480 02 0.0 0.0

2.03867D 10 9.00153D0 11 1.0006%9 11
0.0 0.0 0.0

0.0 0.0 0.0

e QaQ Q0 . Qa0 .
0.0 1.055700 11 3.167720 08

NAPE CN DIMENSION 10 USEL S STARTS AT
1 2 3

3118030 11  1.56002D0 12 . 2.901430 11
5.43552D 10 2.000000 10 9.0C0000 11

NAME E DIMENSION 5 USEC 4 STARTS AT
1 S 2 3

—_— 5.000000-0) 1.70000D-Q2  1.800000-01

NAKE F OIMENSION 5 USEC 4 STARTS AT
1 2 3

 3.600000 05 3.600000 05 5.000000 05

 

MAME H DIMENSION 25 USED 23 STARTS AT
1 o 2 3

1.600000-02 6.000000~-03 9.00000D-05
-1.000000 0O 3.,000000~-03 -1.0C000D0 GO

3,40€000-02 9,70000D-02_ 4.300000—-02 .

8.,000000-01 -1.0000C0 CC 8.000000-01
5800000 00 1.200000 01 3.000000 01

Fig. 5E. List of Parameter Values Used
"CHANGE" Command.

4

4.900CCC 07
-1.000CC0 0O

- 2«T700CCD 07

21
4

1.000CCD 18

26
4

T.732730 10
0.0
1.3795EC 10
0.0
0«0
0.0
2.86783D 10
0.0
4«745617C 08

76
4

. 542842CD 1Q
L. 000CCC 11

86
4

- 1. 800€CE-03

91
4

5.000C00 05

%6

4

1.500CCD~-02
-1« 000CCLC 00

4.700CCE~-02

-1.COCCCD CO

5

5200000 07
1.100000 07
1.800000 07

S

€.544380~-09
6.13618D 08
1«41313D 0S
0.0
C.0
C.C
0.0
0.0
1.165100 08

5

3.000000-03
1. 40000002
4.C0000D-02
-1.C0000D0 0C

in Calculation After
VALUES IN ARRAY V

 

 

 

59

MAME K DIMENSIOM 25 USED 23 STARTS AT 121
1 2 3 4
1.200000-17 2.00000D-17 1.5C0000-17 1.500CC0-17
-1.000000 00 1.500000-19 -1.000000 00 =1.C00CCD OC
. _5.00000D0-18 . 4.000000=18 4.500000-18 3.5000CC~18
4.40000C-18 -1.000000 00 1.100000-20 =-1.000€CD GO
4.500000-20 5.10000D-20 4.800000-20
NAME F DIMENSION 20 USED 15 STARTS AT 146
1 2 3 4
© 2.100000 15 6.700000 14 9.000000 14 $.000000 14
-1.000000 00 ~1.000000 00 =-1.000000 00 =-1.C0CCCD 0O
1.800000 14 9.00000D0 14 1.800000 14 6.700CCD 14
NAME R DIMENSION 10 USEC 5 STARTS AT 166
e X2 3 4
5.800000 17 0.0 0.0 0.0
NANE T OIMENSION 20 USED 15 STARTS AT 176
1 2 3 4
© 1.300000 01 1.300000 01 5.000000 01l 1.000CCD GO
~1.€00000 00 ~1.000000 00 —-1.000000 00 —1.000CCC GO
1.300000 01 1.0000CD OC 2.000000 00 2.000CCC 0O
NAME W DIMENSICN 5 USED 4 STARTS AT 196
] Y2 3 4
1.C00000 00 1.00000D 00  1.000000 00 1.000CCC 00
NAME M CIMENSION 1 USEC 1 STARTS AT 201
1 2 3 4
e o e e
NAME U DIMENSION 1 USEC 1 STARTS AT 202
1 2 3 4
1.00000D 02
Fig. 5E. (Continued).

5

1.400000—17
3.40000D~18
4.CC000D~18

-1.€C0000D

5
~1.C0000D
1.100000
3.500000
5

C.C

5

~1.€00000D
1.300000
1.C00000

oC

acC

14

00

0¢
60

ITERATIVE SOLUTION FOR CC
NCC CCl1 CCL CCX

0
1 3.24168D 10
2 3.24168D 10 4.44522D0 10
4.41906D 10
4 3.241680 10 4.41900D 10
ITERATIVE SCLUTION FOR CCT

NCC CCl CCL CCX

0
1 2.6727T70 10

RF X

1.44089D
-1.339230
2.914080
6.331820
1.41909D

RFX

1.74565D
-2.02375D

17

15
12
11

17
17

ccz
5.740120 10
5.74012D 10

4.41906D 10

CcCc2?

5340690 10

Fig. 5F. Output from Iterative Calculations With New Parameters.
61

QUTPUT SUMMARY

STEAM SYSTEM
FLOW OF H @ T INTO STEAM SYSTEM
FLOW OF T INTO STEAM SYSTEM
FLOW OF H INYO STEAM SYSTEM
FRACTION OF T INTO STEAM SYSTEM

SECONDARY SYSTEM
FLOWS
H + T INTO SECONDARY FROM PRIMARY
T INTO SECONDARY FROM PR IMARY
H + T THRU PIPE WALLS INTO CELLS
T THRU PIPE WALLS INTO CELLS
SURPTION BY SINK
H+T
T
HF
TF
REMOVAL BY PURGE
H+T
T
HF
TF
FRACTION OF T
PASSING THRU PIPE WALLS
SORBED BY SINK AS 7
SORBED BY SINK AS TF
REMOVED BY PURGF AS T
REMOVED BY PURGE AS TF
CONCENTRATIONS IN SECONDARY SALT
H e7T (CC)
T (CCT)
HF (CCF)

PRIMARY SYSTEM
FLOWS
H + T THRU WALLS INTO CELL
T THRU WALLS INTO CELL
SURPTION BY SINK
H + T
T
HF
TF
REMOVAL BY PURGE
H+ X
T
HF
TF
FRACTION QF T
PASSING THRU WALLS INTO CELL
SORBED BY SINK AS T
SORBED BY SINK AS TF
REMOVED BY PURGF AS T
REMOVED BY PURGE AS TF
CUNCENTRATIONS IN PRIMARY SALT
H + T (CF)
T(CFT)
HF (CFF)

Fig. 5G.

1.85851D 17
1.89989D 17

-4.13811D0 15

3.275680-01

2.38032D 17
2.384640 17
4, 82035D 16
4.47799D 16

0.0
0.0
0.0
0.0
3.97710D 15
3.69463D 15

0.0
0.0

7.720670-02
0.0
0.0
6.37006D-03
0.0

4.419000 10
4.105150 10
0.0

7.26328D 15
7.25410D 15

4.38759D 16
4.38205D 16
2.31135D 17
2.30843D 17

5.06261D 16
5.05621D 16
9.06761D 15
9.05616D 15

1.25071 0-02
T.555260-02
3.98006D-01
8.71760D-02
1.561410-02

2.81256D 11
2.809010 11
l.48164D 12

Qutput Summary (New Parameters).
ERRCR -

UNRECNGNTZEC INPLT

.. CARD IMAGE 1S5 1 2 3 4

17345673901 2345€678501234567890123456765C12345678
ZILCH

5 6
901234567890123456789

Fig. 5H. Response to Unrecognized Command Card.

7 8
01234567850

29
63

" NGRMAL STOP ~ ALL CATA PRCCESSED

IHCO021 STOP 0

Fig., 5I. Normal Ending Message.
65

APPENDIX

PROGRAM LISTING
tFVFI

1SN
1SN
TSN
I SN

TSN
1SN

TSN

TSN
iSN
TSN

TSN

TSN
I SN

¥ SN

iSN
TSN
TSN

TSN
TSN
ESN
TSN
15N
SN
TSN
TSN
ISh
I SN

1SN
TSN
[ SN
TSN
I SN
¥ SN
TSN
{SN

ESN
I SN
TSN
TSN
TSN
TSN
I5N
1SN
TSN
FSk
TSN
1SN
15N
TSN
TSN
I SN
TSN
ISN
TSN
fSN
F SN
15N
TSN
TSN
I SN
SN
TSN
TSN
TSN
1SN

1.6

66

nEc 12} 087260 FORTRAN H DATE
COMPIIFR CPTIOANS = KNAMF=  MAINLUPT=UZ2¢L INECNT=G5.SI2E=0000K,
SGLRCFEBLDICeNUL ISToACCECK.LEACNDOMAPMCEDIT,NOICNOXREF

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EMPLICTT REALSD (A~He 0-4)

RFAL*A K,V

REAL*4 HALL+HCUToHLRRVHPRT ¢ HCFALFRES. FRUNHALK FTEELCARD
DIMENSECN AL200 BU%)e CU50)s CNELOs E(S)e FUS)s H{25),

1 Kt{25ke FL20). RELODe TH20G) s WlS)e CARCE20). VALULT)
NIMEASITN CLS0)

FOUIVALENCE {ALLIoVIAb)e (AULIavIE210). (CELIeVIZEM),
1 (CRELYaVIT6) e (ECLIaVIBG) e (FLEDaVIGL)IaiHIL) VLSO ),
2 (KALYov{L21))e (PLLIGvILab) e (RODFeVILE6I)e [ T(LbaVi1TE)),
3 fWik v (1563 ). IMeViZOLdde (LeVIZ2C2}H)

FQUIVALFNCE (CN(L)oCFIy TCNI2D4CFFIe [CNE3DLCFT)e (CN(4)CCH,
1 (CM{5)eCCFYe (iN{OodoeCLTHs (CALTILCSGYe (CN(B)CSS)s (CNES).CSRI
COMNONZRLK2/ The 10UTe IPR4 KCLTe KPR

CCMMCN /BLKL/ ¥iE250)

COMMCN/RLKY/ 1UIMIZ0). TUSE(ZC)y NM{2C)s [BEG(2C)s NMCA{1GC),

1 AVARJACN
DATA +ALL/4HALL /o HUUT /4HUUTP /o FCREZAFCRAE/ JHPRT/Z4HPRIN /Y
1 HCHA/4HCHANS HRES/SHRFSE/ s FRUN/GHRUN / +HBLK/&H /

NATA XTLCG/2 3607 +HIEE/ 4KT /
DAYA CTICL/1.C~7/s TTUL/LWD-T/

CTOL ANC TTGL ARE THE CONVERCENCE TOLERANCES FOR C SCLVE
ANL TF RESFPECLTIVELY.

MALN PRCGRAM FUR CALLULATICN OF MSER TRITIUM FLOW

SET LP REFERENLE VALUES TN WORKING ARRAY V
CALl SETREF(HELK)
RFAD A CARD AND CHELX FOR INSTRLCTIONS
100 RFACHIM I ENC=94T) CARD

FCRMATLIZ0AG)
[F{CARDEL) JNFLHUUTY GU TD 12¢C

-

SET CUTFUT UNIT NUMBERS

TFICARD(3) JNFuBALL) GO TO 11€%
EFICARDLA) .NEoHLKY) O TO 105

1C4 XOUT=TCLT
KPR=TCUT
G 70 100

1C5 [FICARDIG) JFCHPRTY GO TO 1IC
WRITE(K{LT.2)

2 FORMATUY CLTFUT NUT SPeCIFIEC CORRECTLY')

WRITFIKCUT 20} (Bel=1+8)e CARL

20 FORMATHY CARC IMAGE IS',1Xe8(SXIL)/1SX48{10HL23456T8901/15X420A4/

1 1x)

WRITEIK{UT .21

FORMAT(* ALL CUTPUT TU SUMMARY LNIT')

GC TC 1C4

110 KCUT=[FF

L14 KPR=IPR

?

—

GG 1C 160
LIS KCUT=ICLTY
GO 1L 114
CHECK FCR CHANGFS IN WURKIMG VALUES
120 TFICARDIL) JNELHCHAD GU TG 135
CALL MAYCH{CARULI) eNMsNVARyNK)
TF{AKLMELD) GE TU 49
CALL MATCHICARUD(I )« NHCNoNCNLANC)
IF{ANC.AFLO GO TO 121
WRITE LKCUT 44 )
4 FORMATLY ERRCR IN CHANGE SPECIFICATICNS?)

1C6 WRITFIKEUT20) (i+i=1e8)s CARL
G0 10 100

121 RFAC{IN.T} VALUILL)

FCRWATIEID.O)

JEIREGI4)+NC-1

Vidi=vaLu(l}

WRITE{KCUT<12) CARD{S).vALULL)

FCRWAT(1XoAGe1PELG.S)

GO TC 1G0

125 RFACUTING2) N1l N2s.VALU

FURMAT{2E3,TF U0)

IFIMN.FC0) GC TU 100

J=TREGIAK)I~1+N1

IF(N2.FL.0) N2aN1

L=i

00 130 h=h],N2

ViJizvatulL)

I=L+1

J=Jd+1

CONTIALF

Ny=A2=-h1+¢1

WRETEAKLLY o13} CARDE3 ) oNLoN2,AVALULL ) sL=LsNV)

FORMATIIN B o432+ k24" 1/ (1X1PSFL4.5)])

-

—
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GC TC 125
CHECK FCR RESET — PUT REFERENCE VALUES BACK INTO ¥

[FECARDIL}NELHRES) GU TO 15C
IFLCARDI3}.NELHBLK) GU TO 137
CALL SETREF(CARDIN)

GG TC 100

NAME NOT PLANK — TEST AGAIMNST NV ARRAY

CALL MATCHICARDI(3 )} JNN+NVAR,NK)
TFUAKLNELD) GC TO L36

A0 MATCH FOUND IN NM = TRY MMCN

CALL MATCHICARD(3 )+ NMCNoNCNs AC)
IFIM.NELO) GC TO L1306

WRITE{ KUY ,5)

FORPAT(' ERRCR In RESET SPECIFICATIONS?)
6C TIC 1¢é

CHECK FCR PRINT

IF{CARDIL).NELHPRE) GO TO 155
IF{CARCU3) NELHBLK)Y GU TO 152
CALL LCCK{CARDI3})

60 10 160

MAME NCT ELANK — TEST AGAINST NV ARRAY

CALL MATCHACARDII) cNMeNVARSNK)
IFIAKL.AELOQ) GC TO 151

AC MATCH FCUND IN NM - TRY AMCN

CALL MATCH{CARDE3) +NMCNNCNWAC)

TF{AM .NELO) GC TO 151

WR] TE(KCUT.8)

FORMATI® ERRCR IN PRINT SPECTFICATIONSY)
G0 1C 1Cs

TFICARC (1) EC.HKUNY GO TO 160
WRITE(KLUT «6)

FORMATI® ERRCR ~ UNRECOGNIZEC INPLT')
60 1C 106

KTRY=1

[SW=}

NCC =0

cC2=0,D0

CHFCK FCR FAILURE TO SET CC MNC CCT

I#1(C.LEL0.00) CC=1.D11
IFICCT.LELO.CO} CLT=LaD10

FRIAT WCRKING ARRAY V UN LINE PRINTER

KSAV=KCLT
KOUT=[FR

CALL MFWPG
CALL LCCKR{HBLK)
CALL NEWPG
KOUT=KS AV

GG 1C 200

GET C(18)+ CCF. QU183 AND ¢(19)
ECS. 194,84 20, 218

Cl18)=0.00

CCF=0.00

ci{1a)r=0.c0

Q(19)=0.CO

CALL MEWFG

TFERIS) JECL.0.D0) GO TU 205
FE=F (4 )%E(4)

HA=H{1A}*A(18)

FEPH=HA+FE

BW=PR{&4)*nid)
AFSCxIBWSFEPH/IFE®HILB)))e*29K(]18)
ALFA=R{S)/FE

CUlB)=ALFASR2 /L ALFA+.5DUSBESC* {1.DC+DSCRTIL.D0¢4,COSALFA/BESQ)))
CULB)=Ph*A (&) ¥DSORTI(C{LB)*K{18))
CCF=({R(S5)*+rASC (LG )/FEPH

QU 15)=CCFoFE

CONTINLE

AEGIM CALCULATION GF QUANTITIES CEPENCENT ON CC
GET CUEC)s CULL)s QLAO)s €M1}
FOS. 11A.Ry 12448

NCC=NCC+]
IFINCCLLELSO) GO TD 301
WRITEIKILT 35} HALK

PAGE 002
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35 FORMATL® FAILURE IN SULUTION FOR CC'.81)
G 10 1C0

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15
30

Do 305% I1=1G,11

ALF A=REL)I(PRID/LTLLIOHEL)) )¥*2
CALL COLACECCALFALC(LY)
OQIT)=PUEY®*ALL)*DSARTIKIII*CLLIINTILIY
CONTINLE

GET Cl{lel, Cliad — EuS. 174.8

Bw=R{3)%n(2)
ALFAaK(16)%{PH/H{Lb) }*%2

CALL CCLADICC,ALFALCLLE))
0{Ll6)=BweA{16)0USURTIK (L6 IEC{16))

GET Ci17) - EQ. 18
QILTAI=FLII*ELI)*LL

GEY C(13)« 0(13}s Cll4)se Cl14), CL15), O(15)
ELS. 14A8.BFs 22As LD9AsB. 234, L6A.Be 244

IGOCF=Q

CALL CSCLVEICCSCSGePIl3)aTE13)sF (130 (21)eK{130.K121)4CTCL
1 IGLCCF.CL13),CL21))

TFLIGCCFaLELO) GU TU 320

K1=13

K2=21

€2=C56G

WRITFUKCUT«301 KiekZ

FCRFATLE® FAILURE IN SULUTION FCR C{",12+*) AND CU*s12.:"}7}
IGO{F==1

CALL CSCLVE{CCAC2eP UKL e TUKLIoF{KL o (K2IoKIKL) (KEK2)CTOL S
1 IGLCF.ClK1).CIKZ))

GO 0 160

320 CALL CSOLVFICCCSSePllaloTlladatihaber[22)oKI14YaKE22).CTCL,

I IGCCF«Col4FCL2211
[FUIGCCFLLELC) GU TO 425
Kl=14
K2=22
C2=C8S
G0 10 315

325 CALL CSCLVEECCCSRePLLOI T UL e r L Sda b {220 RKL15)4KE23).CICL,

3130

33

8

33

34

B

5(

5

o

&

0

1

O

1 {GOCFeCHII5)CiZ3))
TFITGOCFLLELO) GO FO 330
Kl=15
K2=23
C2=CSK
GO TO 318

Cl13) Q21 )ewiladsQt224.Q1151.012231}

nao 3% (=12,15
QUIN=HUE® AL )*(CC-CHL})
QiB+11=-C(1)

CONTIALEF

GET COlZ). Clwl Anl C{22) - EQS. 214, 13A.R

CLLI2)=RI3)D4R14-C{1GI~0IL II=C 01 2)=C (R4 3-0(15)-Q116)-0117)
Qle=-C(12}

CeL20=C0-C{l2)/(HIl21 %A (4} )

TF{Ci12}3.6Y,0.00) GO TU 340

1c=12

WRT TE(KCLT+80) MCCoHBLKeCCe ECeCICH

FORMATIIXa13,7 CLOSALeY =%, JPEL4.5," CL'0124*) =*4E]4.5)

TF C112) 1S NEGATIVE. ADJULST CC ANC TRY AGATA
CO=C0e0C

SFE IF AN UPPER LIMIT (LCZ2§ wAS FCLNE.
IF SC. CC MOT FXCEED 1T

IF{CC2.EC.CaCO} GU TO 300
TA{CC.ALY.CC2) GU TU 300
CC=C0.50C*(CC24u.5D0%LC)
6C 1€ 300

GET Cd4) AND Cr — EQS. 13248 &£.8

Clar={DSCRTI(KIL2I®ECELZII-ULLZI*TLA)/IPL4bvAL4)) h*e2/K(4)
CF=C(4)-Cl12)/(Hl4)®A(%))
IFICF.GTLO.CC) GO TO 500

IF CF IS NEGATIVE. AUJUST CC ANC TRY AGAIN

WRETE(KCLT 811 NCCoHBLKCCoHELKSCF

FORMATULXeT3 " LC%eALl,y? =4, JFEL4.5.% (F',4Ls" =*,€l4.51)
G TC 316

IF{KTRY.AELL) GO TO 501

RF1=0.CC

RF2=0.1C

PAGE 0063
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KTRY=2

NCC =0

WRITE(KCLTSCIHALK

FORMAT(® ITERATIVE SOLUTIGN FCR CCY'oAL/EX/
i % ACC'o6Xe"CCL e kLXotCOLYs L1Xe®COX 21X "RFX 411X, *CC 271X}

BEGIN CALCULATION OF QUANTITIES CEPENCENT ON CF
GET Cilde Ci20s CU3). GlL)s Ct2)e CLI)
FQS. tdeBe 2heBe 3A:B

DC 505 I=l.3
ALFA=zR(TI*(PALI/CTCLI*HiTl)ine2

CALL CCUADICF, ALFALCILY)

(T N=PLI)*ALT)®OSURTLKLII*CAIII/TLT)
CONTIMLE

CET CES)s CI%) ~ EQS. 5.8
Ru=P{l)*wi1}
AtFA=K[5)® (BN/HI5) ) 682
CALL CCLADICF ALFALCLIS))
DIS)=ARAIS)EDSCRTIK{SI®C(5))

GFY Cia) - EQ. &
Ql6)=F{1)*E(1)%CF

GET CFF ~ EC. 10
CFFxNMeLODSCRTIKISI*LFI/KLTY

CET C€(The CITY — EQS. TA.P
AR=P{209u{Z}
ALFA=K(TI*(Bu/HITI)*%2
CALL CCLADICFF.ALFALCLT)I
QU7 I=EwsALTI*OSCRTIKLTI®C{TH)

CET CI{B) -~ FGe 8
CUAI=F{2)%EL2)¢CFF

CALLLLATE RF FOR EQ. 9
RSUM=RILI+RI2])
RFEECILISCA2I4CEII+Q {4 40{5)4CLI6 )40 LT 10Q(EB)-RSUM
TEx=RF /RSLM

TEST CCMVERGENCE
IFLOABSITE).LT.TTOL) GO TG 7CC

ACT CONVERGED ~ CHECK KTRY 7O SEE whAT NEXT
EFUKTRY . AFL2) GU TO 540

KTRY=2 FEANS PRELIMINAWY SEAACKH FOR CC1 AND CC2
WHTC+ BRACKET THE ANSWER

IF (RF.CT.0.[0) GU TO 510
ccl=CC

/F1 =RF

WRTITEIKCUT +5%5) NCL+LCLWRF
FORMATILINGI3.1PEL 9B ectiXo EL14aE)
GC 10 515%

ccz2=cC

RF2 =RF

WRITE(KCUT «56) MC.RFZ.CL2
FORMATLLIX 13,4244 1P2F14.5)
IFIRFI*RF2) 530.520e5186

RFEL1®RF2 PCSITIVE SHOULD NEVER FAFPEN ~ SOMETHING WRCNG
WRITE(KCUT 51} HBLK
FCRMATIY RFIPRF? POSITIVE = SCVMETHIMG FCULED UP IN CC*,AL)
GO TC iCO

STILL LCCKIANG FUR ONE LIMIT = ALJUST CC AND TRY AGAIN
KEEP AQJUSTMENT FACTOR LESS THAN 1C0 AND GREATER THAN .01

TFXCLG=TE*XCLEG
TFICABSITEXCLG) oGl o426D0) TEXCLE=OSIGNI4.6D0,TENCLG)
ADJ=DLCGICCH-TEXCLG
CCxCEXPUALY)
G0 10 300
RF1*AF2 NFGATIVE — ANSWER ERACKETEL
KTRY=3
IAVERSE LINEAR INTERPOLATICA

CCL=tRF1*CC2 -.RFZ¢CC1II(RF1-FF2)

PAGE 004
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KTRY=z4

EF{ISw.ECa2) GG TU 537
Ci=CCL

60 1C 3Co

CCT=CCL

GC 1C 7C5

IFIRTRY.ECL3) GU TO 535
IFIKTRYJNELG) GG TU 555

KTRY=4 MEAMS INVERSE LINFAR INTERPCLATION HAS BEEN
CCPFLETED AND RFECCL) CALCLLATED

WRITE(K{LT452) NLCoLCLl.CLC.RF,(C2
FORMATI{1XsI3,1P2E1445¢14X+2E14.5)
RFT=RF

INVEFSE CLAURATIC INTERPCLATICN

D1=kF1-RFT

N2=kF2=-PFT

D3=C2-N1

COX=CCLORF I®FF2/ (DL*0DZ)-CCLoRFT*RFZ/{C1*D3)+CC2%RFL2*RFT/{D2%D3)
TRICCXLLTLCCL) GU TU 545
TFICCXLCTLCC2) G TO 545
KTRY=5

TF{ISwaECa2) GO TU 544
CC=CCX

GC 1C 3Co

COT=C0X

GO 1C 71Cs

IFIRFTLLTLCL.CC) 6O TO 550
€cz=CcCL

RFZzRFT

GO 10 520

cCl1=CCt

RF1=RF1T

GC TC S20

KYRY=5 PEANS INVERSE QUALCRATIC INTERPOLATION HAS BEEN
COCMPLETED AN RFLCCX) CALCLLATEL

TFIKTAYNELSY GU TO 585
RFX=RF

WRITE(KCUT +52) CCX+RFX
FCRMAT(IZ2X«1FZE14.51)

TEST AFT AND RFX T0O SEE WHAT NEW LIMITS ARE

TFIRFX.CTLC.LO) GO TQ 570
IFIRFTLGT.0L.E0) GU TG 585
IFCDABS(RFX) .GT.DABS(RFTR) EC TC StQ
CC1=CCX

RF1=RFX

GO 10 530

ccz=CCL

RFZzRFT

GC TC 560

TFIRFTLLT.0.C0) GO T4 580
IFIRFX.CTLRFT) GO T 565
CL2=CCx

RFZ zRF X

G TC 530

CCl1=CCL

RFL=RFT

GO 1C 575

WRITECKCUT +54) KTRY

FORMATIL? KTRY =t,.]4/% FRRUR'*)
G6r 1C 100

CALCLLATICN OF TRITIUM DISTRIBUTICA - CCT SEY BY
CHAMAGE ENSTRUCTIUN

KTRY=]
I5SW=2
NCC T=0

GET CL4C) AND QU&l) ~ EQS. 34 AND 35

NCCTsNCCT+1
TF{MCCTLLELS0) GU TO 706
WRTTEIKCUT435) HTEE

GC 1C 100

RATIC=CCT/CC
ClaC)=RETI(®C{LO)
C{41)=RATIC*C L1}
QSUKF=C141)+40140)

GET CU431eCl44)eCl45)sC163)00(a4)s0145) = EQSs 3TA, B, 3B8A.B, 394,68

0OC 710 =43445

J=[-30
TE=T{JISLSCRYICIGI/KLIN)
HICCP=TC*H{JI/P L)

PAGE 005
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PAGE 006

CiLI=sCOTorICCP/LL . QUSHILOP)
FIEREL NI Y INELIAN G IS I
QSUM=CITI+ESUN

T10 CONTINLE

GET Cl46) THKU Wi49) — EQS. 40 THRU 43

0o 715 1246449
Ci1)=Q{ I=-3C)*RATIO
QSUM=C{TIeClSUM

715 CCNTINLUE

o

GET Ci42) ANU Ul34) — EC. 44 — MATERTAL BALAMCE

Cl{4?2bsFlA)=LSUM
Qi34)12-Cl42)

CFT Cl42) —EU. 36A - CHECK FCR POSITIVE

Cla2)=CLV=Cla2)/ il l2)nal4))
[F{C(42).GT.C.00 6O TU F25
1C=42
721 WRITEUKEUT 80) MLToniEE, CCTIC,CLIC)
T20 COT=CCT+CCT
GC 1C 105

Cle2) FCSITIVE = GET Ci34) - EQ. 288 - CHECK FCR POSITIVE

125 ({340 s {0{42) /CSURTIC LM/ REE2DI-TLAISCL42)/{PL4I*A14) ) )*DSORT{LLS)
s$/Kita))
FFIC134).GT.0.CO} GU TG 730
fC=34
GO 10 721

C(34) PCSITIVE - GET CFV - EC. 782 -~ CHECK F(R POSETIVE

730 CFT=CI34)}-Cl42i/inladxilad)
TF{CFTAGT.04) GO TO 73H
WRETEIKCUTs81) NLLT HTEE+CCTLFTEE.CFT
GC TC 12C

CFTe CL24) ANU Cil42) ALL FCSITIVE - CHECK KTRY
FOR MEXT S5TEP

T3S TFEKTRYLAELL) GU TN 750
KTRY=2
RF1z20.0C
RF2=0.C0
NCC 1=0
WRITE(KCLT+50) HTEE
750 RATIF=CFT/CF
QTS¥=0.L0
no 155 I1=31,38
TFET.ECa341 CC TO 755
O(1 )=RATIF*QI[-30}
755 QISM=CTISMeLL])
RF=CTSVM~R{1}
TF=RF/A(])
[FICARSITEN.LTTTUL) 6L TU 9CC
TFEXTRY AFL2) GO TO 790
TF{RFLETL0.00) GU 10O 760
cC1=CCT
RFL=2RF
WRETECKCLT «55) NCCT.CCLoRFL
GC L 7¢5%
760 CC2=CCT
RF2 zRF
WRITE(KCLT +56) NCCTRF2,L(2
765 LFE{RELI*RF2) 530,770, 764
766 WRITEULKEUT51) HIFE
60 7€ 100

STILL LCCKING FUR ONE LIMIT = ACJLST CCT AND TRY AGAIN
KEEF ADJUSTMENT FACTOR LESS THAM JCO AND GREATER THAN .01

770 TFXCLG=TE*XCLLG
IF(DARSITEXCLG) 6T o4a6D0) TEXCLEXCSICN(4460C, TEXCLG)
ADJ=CLOCHCCT )=TEXCLG

CCT=CEXFLACJI
Gr 10 7C5
750 {FUKTRYLEC.3) GU TO 35
IFIKTRY AEe4) GO FO 7495
WRTITEIRCUT 452 NCCT+CCEoCCToRFoLC2
G ¥C 542
195 IFIKTRYLAF.5) GG TO 545
GO T1C 556

CLTPLT SECTEON
SUMNARY QULTPUT TO UNIT KGOUT

900 CALL NERPG
WRTTE LKCUT 92}
G2 FCRMAT{® OLTPUT SUMMAKY'/1X)
72

ISN €427 OMTSS=CI13)eCI14)+0415)

TSN Q428 QISS=C {43040 4a)+Ui45)

TSN 0429 OHS $=ChTS5-0TSS

TSN 0430 RSUM=1.00/7{R{LI+R(3))

ISN 0431 FRTSSxzRSLM*CTSS

ISN 0432 WRITELKCUT 497) QHTSS OTS5S5CHSS,FRTSS

15N D433 S3 FORMATL* STERAM SYSTEM*/5X+*FLCR CF H ¢ T INTO STEAM SYSTEM!,

1 1PELG6.5/5Xe"FLOW UF T INTOD STEAM SYSTEM*,E20.5/5Xe*FLLCW CF H %,
2*INT0 STEAM SYSTEM®o£Z20.5/5X«*FRACTION OF T INYC STEAM SYSTEM®,
3 Flé.5/1x%)

TSN Q0414 QhTFu=CC10I¢CE11)

TSN 0435 OTPW=CL40)+CE41)

TSh 0416 FRTPR=CTPRORSUM

1SN 0637 FISSK=C {46 3RSUM

1SN 0438 FRYSF=CL4B)*RSUMN

1SN 0439 FRRFT=C{4TI*RSUM

TSN 0440 FRRPF=C{49)%RSUM

TSN 0441 WRITEAKLLT+94) Qlals0i34) s OHTFMoCTPRsCULE) ¢ Q(463,0(180,C148),
L CUL7)4CH4T) oClLT)eQ(eY)e FRTPReFTSSKsFRTSF«FRRP T, FRRPF

ISN 0442 WRITELKCUT«95) CC+CLTWCLF

1SN 0443 B4 FORFMAT(Y SECCNDARY SYSTEMS/® FLORS? /5X,*H ¢ T INTC SECONDARY ¢,

LYFRCF PRINMARY 'S IPEL1445/5K+'T INTO SECCNLCARY FROM PRIMARY?,E18.5/
7 S5Xe'H ¢ T THRU PIPE wALLS INTC CELLS®¢EL5a5/5Xe*T THRL PIPE '
FOWALLS INTC CELLSYWEL9.5/" SCRPTION BY SINK'/SXe'H ¢ T4,28X%.

G F L4aB/5Xe ' T o32A0ELaad /5K e "FF Py 3XeEL&.5/5XKe ' TF e 31 XsEL4.5/

51 REFMCVAL PY PURGE"/5Xe®H ¢ T 2EXE14a5/5Xe Tt 432X4Ei%.5/5K,
GFHF * 431X e E14.5/5XK+* TFY 431 XeEl4.5/" FRACTION CF T*/SXs"PASSING',
Tt THRU FTPE WALLS "o lO0xe kLl %.5/5X+*SCRPED BY SINK AS T'.14X.EL14.57
8 SXe*SCRREL PY SINK AS TF's 13X, ELl4.S5/5X+"REMOVELC BY PURGF AS T¢,
9 12XsFE14.5/5X "HEMUVED HY PURCE AS TF®,L1XeEk4.5)

ISN Q444 9% FORNAT(* COMNCENTRATIONS IN SECCNCARY SALT'/S5X,*H ¢ T (CCY*,23X.
1 IPFLl4u5/5Xe"T {CLT)}? 426X eEL145/5Xs'HF (CCF)'¢25XsELl%.5/1X/1X)

ISN D445 CrTaaCl1eC(2)¢C(3)

SN 0446 OTW=Cl311eC{32)+0(33}

TSN 0447 FRTY®C=CTho*RSUN

1SN D448 FISST=C (35 )%RSUM

TSN 0449 FISSTF=C(3T7)9%RSUM

ESN 0450 FTRPT=C(36)*RSUM

TSN 0451 FTRFTF=C{3E}*RSUM

TSN 0452 WRETE(KCUT 96} CHTW LT wew(5)CE35),C0T7).0(3T),0(62.0(3€&1,C18),
1 CI38)«FRTRCAFTISST,FTSSIF.FTRFYLFTRPTF

1SN 0453 WRITEIKTLY +97) LF+CFTWLFF

TSN Q454 96 FORMATUI® PRIMARY SYSTEM'/? FLCWS*/5%: 'K + T THRU wALLS INT) ¢,

VICELLY 4 1PE2145/5X+*T THRU WALLS INTO CELL'+11XeEl4eS/" SORPTION
2BY SENKI/SXe'H & T'o20XeEL4a5/5XKe T 222X E14a5/5Xs "HF* 31 XeEL4.5/
3 GX'TF*eIIXWEl4.5/" REMOVAL BY PLRGE*/SXe'H ¢ T?,28x,E14.5/5X,
LT 32 XeEL4aS/oKe *HF? e31XeE14.5/5X ' TF?,31XWEL4.5/" FRACTION OF
5T*/5Xs "PASSING THRU wALLS ENTC CELL',E19.5/5X.*SORBED BY SINK AS *
hotTP e 14XsE14.5/9K " SURBED BY SIAK AS TF® J3X,E14.5/5X. "REMOVED *,
T*RY PURGE AS T'.lZ2Xekl4a%/5X¢"REMOVEL BY PURGE AS TF*,11X.El4.5)

ILSN 0455 ST FCRMAT(® CONCENTRATEUNS IN PRIMARY SALT*/5X.*H + T {CF)*423X,
1 IPEL4.5/5Ke ' TULFT) * 42X EV4L5/5Xe "HF [CFF)'e25X,Fl4a5)
TSN 0456 CALL MEWFG
FSN 0457 Gr TC 160
C
C END €F FILE ODETECTEL uN INFLE UMIT
8
TSN 0458 $G7 CALL MFRFPG
ISN 0459 WRITEIKLLT.99)
TSN D46C $9 FNHEAT{® NCRMAL STOP — ALL CAYA PROCESSECY)
1SN 0461 STCF
ISN 0462 END
*NOPTINAS 1IN FFFECT® NAME= MATAGOPT=02.LINECNT=9E,STIZE=CTCOK,
®NPTICNS IN FFFFCTH STURCF+EBCCIC NOLISToNCDECKLCAC,NEMAPLNOEDT ToNOID+ MCXREF
®STATISTICS* SOURCF STATENEMIS = 48] +PHOGRAM SIZE = 10188

*STATISTICS* NN DIAGNOSTICS GENERATED

sesksd FND CF COMPILATION #9333 45K BYTES OF CORE NOTY USED
LEVFL

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DATA
DATA
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NAT A
DATA

ICGIM / 20056504 10+5¢5¢25¢25+2C+1Co20050Llels6%0/
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AM/4HA shHn + 4HC v4hFCN 4 4FF v 4HF +4HH .
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NFCN /7 4HGF o 4HUFF o 4hCFT o &4FCC G 4HCCF o 4HCCT o 4HCSG o
QHCSS o 4HCSR +4H /

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DAT &

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SCURCEvEBCLLCNOLIST o NODECKLCALNCHMAP,NOEDIToNDID . ACXREF

SCURCE STATENMENTS = Ll +PROGRAVM SIZE = 8

DIAGNOSTICS GEMERATED

125K BYTES OF CORE NCT USED

DATE 74.304/09.19.05
LEVEL

1SN

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COMPILER CPTIONS = MAMEx MAIN,OPT=Q2

0007

0003
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(DEC 72)

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oL INECAT =SS5, SIZExQ000K,
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SUBRCUTTNE SETREF (NAME])
SETS VARIABLES TD THEIR REFERENCE VALUES. IF NAME 1S BLANK.
AtL VARIAELES AS SPECIFIEC IN THE ARRAY NM wWILL BE SET.
IF NAME 1S PhNT, ALL VARIABLES IN THE ARRAY VREF
Wikl BE PRINTED.

IMPLICIT REAL®E {A~hs0-1)

REAL%4 VWRC+VWeWdRD

CCMPCA/RALKY/ TUIM{20)s IUSE(2C)s NMU20)e EBEGi..ss NMUMLCH,
i NVARLACN

DIMENSICMN VRFFIZ290). VOLE155). vQ2{15)

EQUIVALENCE IVEL{L).VREFI96))s (VO2LL).VREFEL1TE))

V01l ANC VC2 ARE OUMMY ARRAYS USEC IN THE INITIALIZATION OF
PARYS OF VREFs THE REFERENCE ARRAY .,

DATA [RLMK/4H £ o IPRT/4HPRAY/

DAT2 VRFRD/4HVREF/ o+ V/4HV /

CCMMCN/BLKZ/INe EOUTs IPRs KCLT. KPR

COMMCN /BLKL/ vi250)
THF COMPENT CARUS INTERSPERSED AMOMNC THE FOLLOWING
CCNTTALATION CARDS CAUSE MO TROULEBLE WIFTH THE GRNL CCMPILFR.
TH1S IS CCNTRARY TO THE RULE ON PG. 12, GC28-6515-8,
TRV SYSTEN/360 ANL SYSTEM/370 FCRTRAN IV LANGUAGE.

DATA VREF
REFERENCE VALUES FOR ALL)}

17.6C60050603.%00049.1060224C060=1200052.0602%2~1.00 +11.0€48.,8D6¢
2 49.06031aC6¢27.06018.060U0aCCe=1.00:0.0042%~1.0C &

REFFRENCE VALUES FOR di1)

3e021e3e0élelalilbolallBe-1.CC,

~

REFERENCE VALUES FOR CL1) RRE ALL ZERC

W

45%0.0C +5%-1.00 o«
REFEREMCE VALUES FOR CNLI)
4 6%-1,LC +2.C10e%aDidedaiile=)aCCy

REFERENCE VvALUES FUR ELT)

WA

«500s. (1700, .1800,.0016D0+=1.C0,
REFFREMNCE VALUES FUR F(I1)
6 3o D5+ 2abC5+5.05¢%.5e=1.D0/
REFFRENCE VALUES FOR HIUE)
DATA vC1/
1 1.b60=206e0=20%e)=5a1a90~2e3,0-34=1.0Cs3.0-3,2%=1.0C
7 74402430840~ 249.TD=20%230-244,70~2+% 400~ 2+ o 8D0+~1.00+,8D0s
3 2%=-1.CC +5.8D0042400430.C042%-1.0C &
FEFERENCF ValuES FUR KIET1}
4 1u2D-17+2aD0-1701090~1T701e5C0-17¢1040-11e~1400s1+50~19,42%=1.00¢
53e40-18s5.0-18s4a0=1de4a50-1803450~1804a0-18.4.40-184~1.DC,
X 1410=2C02%=1e00e%e50~2009.1C~2C44+8L-2Co29=]1,0C,
REFERENCE VALUES FDR P{(I1)

62.1D15+62TC1449.0014¢9,0014,459~1.CCe1a1015 12801449200 1441.8014,
TO.TCl4e3a5C1445%-iaD00

REFERENCE ¥ALUES FUR RID)
B S.ED1T+4%C.CC oo®~f.00 /
REFFRENCE VALUES FUR T}

DATA v(C2/
L 2%13.C0 +50.0001a00e5%=31.00 +2%13.0C 1.0002%2.0C +1oCCo5%-1.00,

KEFEFENCE VALUES FOR Wik}
2 4%1.00C +-1.CCs

REFERFMCE VALUE FOR M
31t 20-¢¢

REFEREMCE VALUE FOR U

& laf2/
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CHECK NAME

TFERAPELEQLIBPLAKY GO TO A02
TFIMNAPELEC.IFRT) GU TO k15

LECK FCF vaTCH IN NM TABLE

CALL MATCHINAME oiMs NVAK. NKJ
TFiMK.hFLO) GO TO LUL

MO MATCF FCUND — PRINT MESSACE

CHECK ABME AGAINST O TABLE

CALL MATCHINAME JNMUNJNCNe KC)

TFIKCLECLO) GC TO 300

JIBEGI&IeXC-1]

VIiJI=VREFLJ)

RFTLRA

WRTTE{KCLT 1) NAME

FORMATUIX/®* AL MATCH FOR *4A4e* IN SETREF - NO CFANGE [N v'}
RETLRA

NAME = RAM{AK)

Ni=hK

N7 =hK

GC 1C 1C3
Nl=]

N2=hVER

BE 118 M=N1,A2
T1=1LSELM)
J=TREGIMN]

PO 105 I=141T7
VIJIsVREF{J}
J=d+l
CONTINLE
RETLRA

FRINT ALL REFERENCE VALUES

LINES=5C

WORCzVvWRE

DO 130 M=14NVAR

1T=TUSEIND /544
TFCLINES+#ITLLELSU) GO TO 120
CALL MEWFG

WRETEIKRCLT+2) wLROD

FORMATL® VALUES IN ARKAY *.A4}
LINES=C

WRTTECKCUT3) NMINI JOTMIND o TLSEINDSTREGIN) o e I=145)
FORNMATILIX/ Y NAME %4A4e? DIMENSICN® o I4,* USED's14," STARTS AT*I4/
1 7Xe4(11413X)1071X)2

J1=1BEG{N)

11=J1

J2=T14+TLSEIN)-1

N0 125 Jd=dled2.%
12=FING LT 144,020

WRITE{K(LY 4 ) (VREFIL)I=i1412)
FORMAT{IXs1PSEL%.5)

Il=12+1

CONTIMLE

LINFS=LENFSelT

CGNTIMLE

RETLRA

FNTFY LCCK

WORC=Vh

FRIMNTS VALUES IN V SELECTEL BY AAME. IF NAME
IS PLAKK. PKRINT ALL.

CHECK MNAME
IFIMAPELEC.TIRLNK} GO TO 132
LCCK FCF MATCH IN TABLE

CALL MATCHINANME JNMeNVARNK]
TFOAKLMNELD) GC TO 201

CHECK MEMF AGAINST CN TABLE

CALL FATCHINAME+NMUNoNCHe KC)

IF[#C.EC.0) GO TO 301

JaTBEG(4)ekC~1

WRITEIKCLT«6) NMCNIKCIe Jo VEJD

FORMATELX/1XoAdet =VI?oI34%)e VALUE =%+ 1PELG.5)

RFTLRN

WRITEIKCLUT«5) NAME

FORMATY{1X/® NC MATCH FOUND FCR *.A4,% [N LDOK — NO PRIAT®)
RETLRA

PAGE 002
76

1SN 0085 2C1 Nl=hK
1SN OOR& N7=hK
1SN CCR7 G0 TC 135
iSN 00AR 132 Ni=1
1SN 00R9 NZ2=AVAR
C
c FREMT SELECTED VALUES IN Vv
c
1SN €0S0 135 LINFS25C
1SN 0091 DG 150 M=Al,h2
1SN 0097 IT=LUSFIN /544
TSN 0093 TECLENESOITLIELS0) GO TO 140
1SN €095 CALL NFWPG
1SN 009¢ WRITE(KCLT .2} WORD
1SN 0097 L TNFS=0
ISN €098 140 WRITECKCUTL3) AMIN) o IDIMENI G TUSEIND, TEEGINDG (T, [ 1, 5)
1SN 0099 JE=IREGIN]
1SN c10¢ 11=J1
TSN 0101 J2= T1¢TLSEIN)-]
1SN 0107 PO 145 J=Jled2.45
1SN 0103 12=0ENQLI144,02)
TSN 0104 WRITE(KCUT 4) (VIEla1=11412)
1SN 6105 1=12+1
1SN 0106 145 CONTINLE
1SN 0107 LINFS=LTMES#IT
ISN 0108 150 CONTIMUE
1SN 0109 RETURM
1SN olla END
*OPTINAS IN FFFFCTS NAME=  PAINCUPT=02.LINECNT=S5,SIZF=0CO0K,
€NPTINNS IN EFFECT* SCURCE+ EBCCICo NOLISToNUCECK.LCAC.NCMAPSNOEDT TaNOID o NOXREF
*STATESTICS® SFLRCF STATERERTS = 109 +PROGRAM SIZE = 3996

*STATESTICS* NN CIAGNOSTICS CEMEFRATED

skekkk END (F COMPELATION #%wdsn 106K BYTES OF CORE NET USED

PAGE 003
77

LFVYFL  21.6 (DEC 72) 057280 FORTRAN H DATE  T4.3C4/09.19.44

COMPILER (PTINKRS — MAME= MAINSOPT=02.L FMECAT=95,512E=0000
SCLRCE-&HCUIC-NGLIST-ICEFCK.LCID.NDHAP.hDEDlT.kOID NOXREF

ISN 0002 SUBRCLYINE CSCLVEICLeC2ZePKe THKolrKoHLoKKoKL+EPS, ICOCF.CKWCL) CsaL 1co
ISN 0003 IMPLICIT REAL®*3 (A-HeO-1)
1SN G0C4 REAL®8 k¥, KL
1SN 00CS TEST=1CC.LO
1SN 0006 ASSIGK S5 TC K csoL Lie
ISN Q007 HKOFL=H k/HL csoL 115
ISN Q008 PCTH=PK/{TKEHK) csoL 122
1SN Q009 CKMAX=C14C2Z/FKCHL
c csoL 130
c CHECK F{R SCLUTION csoL 131
C CSOL 132
ISN 0010 CKZ2=CKFAX csoL L33
TSN OGL1 G2=CK2-C1+FUOTH®OSURTIKK®LK2Z)
15N 0O01Y2 IFLG2.GT.0.} GO TG &5 CsSoL 135
ISN 0014 ASSIGM 120 TC K csaL 136
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1SN 0016 4 FCRMATICING SCLUTIUN®) CSCL 138
15N Q0L7 167 (F=1 CsoL 139
TSN 0018 GC IC 90 CSCL 140
TSN QOI9 85 IF{IGITF.CF.0) LU TO 95 CSOL 1461
C csoL 142
C FEACING FCR DEBUG PRINTOUT CSCL 145
[ CSCL 150
1SN 0021 S0 PRIMF 15 Cls C2¢ PKRe THse hKe FlL¢ KKse KLso EPS CSCL 155
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2 LKLY alIXe?CRT o i Xe?CXY o L2X4"CK2 ICX"TEST*/IX) CsCL 162
1SN 0023 GC TC Ko (S5.1300 CsSCL 163
C csoL 165
C START iTERMIUONS FUK CK csoL 170
C csoL 175
ISN 0024 65 CKI=0. CS5CL 176
ISN Q00?25 CKCLO=CK]
TSN 0026 CLI=KL* [HK{HL*CL+C2)
ISN 0027 Gl=—{C1+PCTH*OSQRTICLL))
ISN 0028 nao11s 1T=1.50 CsOL 1BQ
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ISN CC29 CKT={CKLI*G2-CKR2*GLI/ LG2-G ] csoL 182
1SN 0030 IF{CARSICKCLLC/CKT~1.D0}LTLFPS) GO TO 120 CSOt 183
c
C IF NCT CCAVERGEDs TRY INVERSE OGUADRATIC INTERPTLATICN
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ISN 0033 FF=C14PCTHI[CSORT(CLT)~DSURTIKK*CKTH)
TSN 00%4 G=C kT-FF csoL 192
TSN 0035 DGL=6G~G1 cSoL 193
1SN 0036 062 =G6-G2 CS04L 194
ISN 0037 D€3=DG2-DG 1 csoL 195
ISN 0038 CA=~GHG2RCKL/{0GI®LG L) ¢GLPG29CKT/ICCI*CG2)+4G1*G*CK2/{DGA*DG2} CsSOL 196
I SN 0039 TFUIGCCF.GELC) GU TO 200 CSCL 240
C CSCL 245
c CEBLG FRINTOUT £soL 250
T csaL 255
I SN 0041 PRINT ZoIT+CKE«CRTSCXeCRZ2TEST
TSN 0042 2 FCRMATUIXT34EP5FLl4a5)
1SN 0043 200 IF{CX.LELCKLY GO TO 102 csoL 197
1SN 0045 IFICXCGELCKT) GO TO 102 €saL 198
1SN 0047 TEST#DABS{CKRCLUO/CX=La00)
TSN 0048 TF{ TESTLETLEFS) GO TG 20l
TSN DOSO CKT=CX
ISN 0051 GC TC 120
1SN G052 201 CLX=KLO{HKCHL*AC1-CX)+C2)
TSN 0053 FX=C1+PCTH® (DSURFICLXI-DSORTIKK®CX))
TSN 0054 GX=CX-FX CSCGL 201
1SN 0055 CKNLD=CX
TSN 00%6 IF{GXatTaCul GO TU 11Ul csoL 202
ISN 0058 CK?2=CX csoL 203
TSN 0099 G2=GX CE0L 204
TSN 00s0 6N T0 1S
ISN 0061 1€1 CKE=CX CSCL 206
1SN 0062 Gl=GX csoL 207
1SN 0063 GO0 10 105 csoL 208
15N 0064 1C2 TEST=DABS(CKCLD/CKT-1.D0) CsCcL 225
1SN D065 CKOLD = CKY CSCL 228
ISN 0066 IF(TESTLLELEFS) GU TN 120 csoL 227
ISN 00648 IF (G «<EC. 0.CO) GG TO L20 csoL 230
ISN Q070 IFIG.GT0.) GC TD 105 csoL 231
ISN 0072 Gl=6 CsaL 232
TSN ODT3 CK1=CKXT csoL 233
ISN 0074 Gr TC 115
1SN 0075 105 G2=G CSCL 235
ISN 0076 CK2=CKT csoL 236
ISN 0017 115 CONTIMLE
c csotL 27%
C FRINT NCN~CONVERGENLE ALARY¥ €S0t 280
C csOL 285
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TSN 0079 3 FCRMAT IO (SCLVE UNABLE TC FINC ROCT*) csoL 295
78

ISN 00AQ TGOUF=MAXO (1,4 IGUOF*L)

TSN 0081 RETURNM

TN 0082 120 Crk=CKY

ISk 00A3 CL=rMRCRLR(UL-CK)+C2

TSN 0084 130 RFTLRA

1SN 008RS END
*NPTIONS IN FFFECTe MAME=  MAINGPT=02 LINFONT=G5,STZE=CCCOK,
SOPYIONS IN FFFECT# SCURCE+EBCCIC,NOLESTe NGOECKsLCAL,NCHAP,NOEDIT+NO KD+ NOXREF
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sektds END (F COMPILATICN #esdsx

CSCL
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300
305
310

320
325

121K 8YTES OF CORE NCT USED

PAGE 002
79

LEVFL  21.6 (NFC 72 CS/360 FCRTIRAN M DATE
COMPILFR CPTIONS — NAKE= MAINGPT=02, | INECNT=65,5I2E=0000
SCLRCE.FBLDIC.NOL IST, RCCECK.LCAC.NOHAP.ADEDIT NOICeNOXREF
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c NEWP 105
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C EJECT TC & NEw PAGE. IF NCT, PRINT 5 BLANK L INES. NEWP 115
I NEWP 120
1SN 0003 CCMMCN /BLK2/ INe [UUTe IPRs KCUT, KPR NEWP 125
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TSN 0008 RETLRA NEWP 145
1SN 0009 100 WRITE(KLUT+2) NEWP 150
1SN 0010 7 FORFATLEHL) NEWP 155
1SN aolt RFETLRN NEWP 160
1SN 0012 END NEWP 165
*OPTIONS IN FFFFCT®# MAWEa PAIN,OPT=D24LINECNT*G5,SIZE=QCOOK,
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SSTAVISTICS® NO DIAGNOSTICS GENERATED
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LEVFL  21.6 IDFC 12} C5/260 FCRTRAN H DATE
COMPIIFR CPTIONS — MANEZ  MAINDPTZ02,L INECNT=$5,512E=0000K .
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¢ CCUA 105
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1SN 0008 END CCUA 160
*NPTIONS IN FFFFCTH MNAME=  MATNGLPT=024 LINECNT=S5,S12E=CCCAK,

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®STATISTIC S*

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SCLRCE STATEREMNTS = T «PROCRAM SIIE = 444

N0 DUAGNOSYICS CERNERATED

FND (F COMPILATION sossus 133K BYTES GF CORE NOT USED

21.6 (ODFC 72} C5/32€C FCRTRAN H DATF

NAVME= MaINUPT=02.L INECAT=65,.S1ZE=0000

COMPTIFR CPTIONS —
SCURCESEBCUICNUL IST . hCDiCK.LCAC.NGHAF‘hUEDiToNDID-NDKREF

0002 SUBRCUTINE MATCH (NAME. NTAB. Mo NMAT)
C
C SEARCHFFS THF ARRAY NTAB WITH NN ITEMS FOR THE FIRST
[# CCCLRRFMCE OF NAME. I+ NAME IS NCT FOUNG TN NTAB. NMAT
C IS RETUENEC wITH THE VALUE ZERO.
C

ocel DIMFASICN AT2P (10)

acoe NMAT = O

a00s NG 100 Axl.NA

0006 IF [ICCHMPAINAME., NTABIN). &) .AE. C) GO TO 100

o008 NMAT = M

cend RFTLRM

Qo1l4q 1G0 CONTINGE

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SCURCE«FRCCICNOLISToNUDECKLCACJNCMAPLNOEDIT¢NOID« NCXREF

SCURCF STATFMENTS = 11 +PROGRAM STZE = 398

ND  OTAGNCSTEICS GEMERATED
FND CF COMPILATION s#ess¢ 133K €YTES OF CORF NOT USED

NG CTAGNCSTICS THI1S STEP

74.3C4/09.20.10

74.304/09.20, 2%

T4.304/09,20,38
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