ORNL-1810.txt

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CENTRAL RESFARCH LIBRARY

' DOCUMENT COLLECTICN

AEC RESEARCH AND DEVELOPMENT REPORT  ori-1s10

Reactors-Research and Power

 

R

3 4456 0349790 1

     
 
   
   
     
    
   
     

SOME ECONOMIC ASPECTS OF
THORIUM BREEDER REACTORS

H. C. Claiborne
M. Tobias

OAK TRIOGE NATIOCNAL LARCRATORY
CENTRAL RESEARCH LIBRARY

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OAK RIDGE NATIONAL LABORATORY
OPERATED BY ;

UNION CARBIDE NUCLEAR COMPANY

A Division of Union Carbide and Carbon Corporation

POST OFFICE BOX P - OAK RIDGE, TENNESSEE
ORNL-‘f 0

 

 

Copy No. é‘

REACTOR EXPERIMENTAL ENGINEERING DIVISION

J. A. Lane
Director

SOME ECONCMIC ASPECTS
OF THORIUM BREEDER REACTORS

by

H. C. Claiborne and M. Tobias

. 0cT 121959

Date Issued

Contract No. W-7405-eng-26

DECLASSIFIED

Y PEHORITY Ue ---I/p ~J/j.-—-.-— — i
:nAfi_-Z{’?mf.aq—.n_-J.,é_‘lé >

OAK RIDGE NATIONAL LABCRATORY
Operated by
~  UNION CARBIDE NUCLEAR COMPANY
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Reactors-Research and Power

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TABLE OF CONTENTS

List of Tables and Figures

Acknowledgement
SUMMARY
INTRODUCTION
TWO-REGION REACTORS
Methods and Ccnditions
Processing Cycle Times and Uranium Isotopes
Nuclear Calculations
Cost Estimation
 Reactor and Turbogenerator Plant Investment f
Efficiency ¢
Operation and Maintenance ¢
Inventories
Chemlcal Processing
Feed Costs
Results
Major Process Variables
Effect of Group-3 Poison Cross $é;tion.Variations
Effect of External Power Density Variations

Accuracy of the Two-Group Model and the Calculation of
Breeding Ratio

Accuracy of Cost Estimate
ONE -REGION REACTORS

Methods and Conditions

i‘.i;fi SOV ,fiwfi&fiz‘

 

1k

15
15
15
16
17
17
18
20

20

23
ol
4o
43

 

 
 

TABLE OF CONTENTS (Contd.)

 

Fission Product Poisgns
Isotope Conéentrations and Critical Equation
Cost Estimation
Results 
NOMENCLATURE

LIST OF REFERENCES

APPENDIX I - Constants Used in the Nuclear Calculations

Page

"
46
47
51
53

54

 
 

 

 

. -

LIST OF TABLES

Title Page
I. Nuclear Power Plant Efficiencies 15

II. Typical Cost Brcakio.m znd Heutron Balances for Two-Region
Reactors 27-28

I1T. Effect of Substantial Changes in the Nuclear Constants 29-30
Iv. Cost Breakdown and Neutron Balances for Several One-Region

Reactors Near Optimum Conditions 49-50

LIST OF FIGURES

 

1. Schematic Flowsheet for a Two-Region Thorium Breeder Reactor 31
2. Effect of Power on Cost of Two-Region Reactor Plant 32
5. Effect of Steam Conditions on Turbogénerator Plant Efficiency 33

L, Effect of Steam Conditions on Power Plant Cost for a 300 Mw

Plant | h
5 Effect of Blanket Thickness on Unlt Cost 55
6 Effect of Thorium Concentration on Breeding 36
T Effect of Group-3 Poisons on Unit Cost Breeding Ratio 5T
8 Effect of Blanket Uranium Concentration on Unit Cost 38
9 Effect of Group-3 Poison Cross Section on Unit Cost 359
10. Effect of Temperature on Unit Cost 4o
11. Effect of External Power Densities on Unit Cost 41
12. Effect of Process Cycle Time on Unit Cost 51
13. Effect of Process Cycle Time on Unit Cost 52
14.  Effect of Process Cycle Time on Unit Cost 23
15. Effect of Thorium Concentration on Unit Cost 54

16. Effect of Reactor Size on Unit Cost and Breeding Ratio 55

 

 
 

ACKNOWLEDGEMENT

The authors wish to express their appreciation for the veluable
advice givén in the ‘course of this work by M. C. Edlund, under whose
supervision this study was performed, R. B. Briggs, and D. E. Ferguson.
Grateful acknowledgément ig made to T. B. Fowler for his able and extensive

efforts in coding and supervising the ORACLE calculations.

 
 

SUMMARY

A study of the effects of geometrical and some operational variables
on the economics and characteristics of thorium breeder-power reactors has
been made as an aid in the selection of design criteria for the TBR program.

No original effort was made to estimate plant investmefit costs or
to introduce new concepts of reactbr technology. Plant investment was assumed
constant for all systems studied under equal power and temfierature conditions.
The state of technology and cost factors assumed were those‘reported by
-Briggs(3) and Arnold et al(l). The effect on power cost of core radius,
blanket thickness, blanket uranium and thorium concentrations, chemical pro-
cessing cycle times, poisons and external power density have been investigated
using a consistent method of calculation with a standardized set of nuclear
constants and cost factors. All results are for a 3-reactor power.station
delivering 375 Mw of electricity to a power grid.

For both one- and two-region reactors, the unit cost of power is

- rather insensitive to fairly large changes in nuclear parameters and process
variables. This is a direct consequence of plant investment and other fi;ed
charges representing nearly 80% of the power cogt.

The results, based on opergting and maintenance costs for conventional
power and chemical plants, indicate that a two-region reactor station could
produce power for 6.2 mills/kwh with a fuel cost of 1.8 mills/kwh. Applying
error limits to the items comprising the total cost, a cost range of 5.5 to
8.0 mills/kwh is obtained. |

The cost of power from a one-reglon reactor station was about 0.9
mills/kfih (2.6 mills/kWh fuel cost) higher than for a comparable two-region

system if the plant investment and other fixed charges are considered equal

 
 

 

 

—— >

for the two types. It is believed that the fixed charges will be somewhat
smaller for the one-region reactor because of simpler comstruction and
operation.

The spproximate characteristics of the reactors required for pro-

ducing power for the above costs are:

Two-Region | One-Region
Core diameter, ft 5 12
Blanket thickness, ft 2-1/4 | --
Core power, Mw 390 fi81
Blanket powver, Mw 91 -
Core povwer density, Mw 210 19
Thorium conc:, gm/kiter - . . 1000 260
Blanket uranium conc., gm/kg Th 3 . ae-
Core uranium conc., gm/kg D0 8.3 4.5
Core U-235 + U-233 conc., gm/kg D0 2.8 6.7
Core Thorex cycle, days 336 450
Blanket Thorex cycle, days 140 -
Hydraulic separator cycle, days 1 -
Average reactor temperature, °C 280 280

A comparison of the cost items in mills/kwh for near optimum one-

end two-region reactors (assumes equal fixed costs) is shown below.

Two-Region One-Region
Plant investment (less chem. proc.) 3.7k 3.74
Fuel inventory 0.4k 0.84

D0 inventory ' 0.52 0.66

 
— "

 

Two-Region One-Region
Fixed chemical processing 0.76 | 0.76
Variable chemlcal processing 0.32 0.18
Operation and maintenance 0.75 | 0.75
Feed (DEO and Th) - 0.20 0.25
Uranium (233 and 235) credit 0.49 0.05
Net unit cost of power 6.2 7.1

From these results, it is apparent that the net unit cost of pover
from the two-reglon reactor 1s nearly independent of the value of uranium
since the fuel inventory charge and the breeding credit are approximately
equal. This is not true for the one-region reactor, however. 1In that case,
the breeding credit is small compared to the fuel inventory charge, so that
any variation in the latter due to a change in the value of uranium will cause
a corresponding change in the cost of power which is virtually uncompensated

by the breeding credit.

 

 
 

 

I -5-

INTRODUCTION

 

The feasibility and the technology of aqueous homogeneous reactors
have been discussed elsewhere, most recently by Briggs(j). The presgnfi
work is concerned with the results of detailed calculations of the effect
of the major process variables on the power cost and characteristics of
thorium breeder reactors in order to help gelect design criteria for the
TBR. In addition, it was desirable to estimate the possible effect of
errors in the nuclear parameters on the cost of power.*

The different reactor systems were coupared on the basis of a
_fixed amount of electrical power (125 Mw per reactor) delivered to a power
grid since power is the main product. If power output were not constant,
the effect of the process variables would be masked by the effect of power
level, the most important factor in unit cost calculatioms.

An electrical power output of 125 Mw was chosen as standard for
one reactor or 375 Mw for a 3-reactor station. This is equivalént to
480.8 Mw of heat for a net station efficiency of 26%. The parameter
studies, other than temperature, were made for an average reactor
temperature of 280°¢.

| At the present time, it is impossible to estimate the cost of
electricity from nuclear power stations without a fairly large uncertainty.
Nevertheless, a study such as this, based as it is upon stated cost factors
and & consistent method of calculations, can be used to determine what is,
and what is not, of relative economic importance and further provides a

rational basis for the selection of most design criterisa.

 

¥ The ORACIE was used to perform the large number of required reactor
calculations.

 
 

', v Trooeat meph R

. - u.‘-’.’.‘;fi?’_l

by e T fiéf‘ Lo
") - S e ey Tk el

This report consisgts of two principal parts. The first part is
concerned with the two-region thorium breeder reactor and the second with
the one-region type. Cowmparison is made on a common basis insofar as

possible.

 

 
 

TWO-REGION REACTORS

 

 
 

A 5.

TWO-REGION REACTORS
Methods and Conditions

The program for the study of the two-region reacto:‘has been pre-
viously outlined by Briggs and Edlund(h). The data that were used to get
cost_factors and process characteristics are,givén in other publications(5’lo),
and are discussed in a later section of this report.

A schematic flow diagram of the system studied is shown in Figure 1.
The core material will be chemically procesbed by two methods. The core
material is treated in a liguid-solids separation plant utilizing hydraulic
separators to.remove the precipitated poisons. This érocedure is capable
of removing 75% of the so-called group-3 poisons (fission product poisons
affected by chemical processing). A more complete discussion of -this

(1)

poison removal method is given by Arnold et al Complete poison
removal from the solution carrying the precipitated poisons is effected

in the Thorex plant at a rate considerably less than that used for liquid-
solid separation. Since the blanket materiasl is a slurry, poisons must be
removed from it by the Thorex process only.

In order to produce uranium of high enrichment (about 95% U-233)
the blanket stream will have to be partially processed for removal of the
excess U-233 (represented by breeding gain) before any mixing of the core
and blanket streams in the chemical pfocessing plant. The core enrichment
will be only 25-30% U-233. Byyprocessing to remove protactinium, uranium
composed of nearly 100% U-233 could be produced. For these calculations,
however, it was assumed that the uranium product would be that derived from

the blanket with all protactinium decayed to U-233 and mixed with the

uranium isotopes.

 

 
 

S 5-

The calculation procedure, which is successively described in the

 

following sections, consists of four main parts:

1) calculation of chemical processing cycle‘times apd uranium
isotope concentrations in the blanket and the core by isotope
balance equations for the particular blanket power selected
.(for any set of parameters, calculations were mfide for three
reactor powers); |

2) two-group nuclear calculations to determine the critical con-

) centration and the neutron balance which yields in turn the
core power and the ratio of resonance to thermal capture in
the thorium; o

3) unit cost calcfilations ;

4) plot of unit costs versus total reactor power so that the costs
at a particular total power can be used for comparison of the
systems.

The parameters studied were core diameter, blanket thickness,

blanket U-235 concentration, thorium concentration, core poisoms, tempefature
and power density of the system outside the reactor (piping and heat

exchangers).

Processing Cycle Times and Uranium Isotopes
For purposes of chemical process calculations, the fission product
poisons are considered to be composed of three groups(j). The first group
consists of the noble gases, the second of the high cross-section isotopes

and the third of the low cross-section isotopes which transmute by decay

or neutron capture into other nuclides of approximately the same low cross

 
 

section. The first two groups are virtually unaffected by chemical pro-
cessing rates required for agueous homogeneous reactors and their macro-
scopic cross section is approximated as 1.3% of the fission cross section
(0.8% high cross section isotopes and 0.5% residual noble gases). The
noble gases are continuously stripped during operation; the high cross
section isotopes are rapidly destroyed by neutron capture since their
cross section is around 40,000 b; The third group is, however, a function
of the chemical processing cycle.

For cofe processing, two modes of poison removal are employed --
poison precipitation with subsequent liquid-solid separation, followed by
Thorex. The precipitation step is capable of removing only some of the
atomic species comprising group-? poisons which will be called subgroup A;
the remainder, subgroup B, is not removed by precipitation. Both subgroups
are removed by the Thorex process. This is represented by the following

equations for equilibrium conditions.

 

 

- N
gy [Ef(es) + Ef(ea)] e - N(A)Tlcn(o) - ,f_,:(): =0 (1)
N(B) ) |
(-a)y [By(25) + Bye)] o, - 22 -0 (2)
and by definition
_In(a) + N(B)] o (3)
t; - B NI ES) | 2
o (3) N(o) | | | (4)

f03 = TL(E5) + £(23)

Solving for T

 

20’

2c ~ 2ya (3) ¢C \1-g)

_ \ 5| (5)
(£5-£5z) - yo~ (3) B T ¢

1l + 1l +

 

T

 

 
T—W

N -11- CEER

This equation actually defines an overall processing cycle for the core.
The optimum Thorex cycle time is, of course, that determined by a balance
between value of fuel recovered and inventory and chemical processing costs.
Another relationship between Tlc and T2c for minimum core processing cost
could be obtained by utilizing the processing cost equations. For this
study, however, the precipitation cycle (T,.) was set constant at one day
since the estimated cost(lo) of the precipitation process is practically
independent of the processing rate for reasonable flow rates. In addition
the core processing cost is very small (around 0.08 mills/kwh).

Under the present state of chemical process development, only the
Thorex process can be used to treat the blanket material because it is a
slurry. The equation for the blanket cyclé time is simply

“38 (6)

T = ——
B y o(3) fiB

For use in the nuclear calculations, determination of the concen-
trations of the wvarious isotopes in both coreiand blanket was necessary.
Both core and blanket contain U-233, U-234, U-235 and U-236. In a&dition,
the blanket contains Pa-233 and Th-232. Other isotopes that could be present
are neglected since even very small processing losses will prevent the build-
up of higher isotopes and the half-lives of Th-233 and Pa-234 are too short
to permit significant concentrations to occur.

For the blanket at equilibrium conditions, the following isotope

balance equations apply:

2N02)(1 + B) By - A(13)N(13) - 3A13) Iy - %%”—) - 0 (7)

 

N(13)8(13) - 5, (23) ¢ - “éf) -0 o (8

 

 
 

 

 

 

 

 

 

 

 

 

 

 

T(23) gy + 2013) gy - Do) g - 2 < o (9)
S (2b) g -3, (25) ¢ - M2 Lo (10)
"B
T..(25) g - T(26) ¢, - Né;‘” - 0 (11)
F——f,‘;) - 3(02) (14p) iy = (12)
K Py
¢B = Var [ff(25) +Zf(25)] 2
and p_ x 100
Ver = Vg +~-—§-‘-T——-- (14)
B
vy = &%r[fifi - (a + t)%] | - (15)
Similarly, for the core (neglecting chemical processing losses),
VBr Ffi(ea) + N(13) |
- 2. (23) =0 (16)
4 VCT | T s Zzaa. Q’C
v T I |
a7 E(S—“)- - Z(24) By + 24,(23) = O (17)
CT I JB
v [ ]
a7 ML - S(25) #y + B@) 4 =0 (18)
v |
a E[M—%@{IB - Y(26) 8, +53,(25) ¢, = O (19)
6
0° P
VCT=%E8'§+1JCC | (20)

These equations hold only for a breeding ratio of one or greater,

For breeding ratios slightly less than one the isotope ratios obtained are

 

 
 

— -13- : NS
. P SR o T R
Oy LTI e,

still approximately correct. Actually, except for one isolated case, the

 

,breedipg ratios were all greater than one.

- The method and eese of solution for the set of equations (Eq. 7
_through 20) depend on the selection of the independent variables and the
availability of automatic computing machinery.

In the present study, the dimensions (R, a and t); blanket power,
P,; blanket U-253 concentration, N(23); poison frattion in the core, f(3C);
the thorium concentration, N(OE)} the external power density'and the o
.average reactor temperature were gselected as the independent variables.

The ratio resonance to thermal.cepture in thorium, B, can only
be obtained from the nuclear calculation since ‘the fast flux is required to
determine it. It was necessary to estimate a value for B, compute the isotppe
concentrations, compute f from nuclear calculations and then compare the
value so obtained with the initial guess. After a little experience, it was

possible to estimate an initial wvalue of B'that required only two or three

iterations.

Nuclear Calculations¥*
The customary two-group method was employed for obtaining the

critical mass and neutron balance for the spherical two-region geometry.

(6, 14)

The major details of this procedure have been described elsewhere
(12)

The only novelty introduced was the use of a "thin shell"” approximation
to account more adequately for the effect of the zirconium core tank. The
nuclear constants used in the work are shown in Appendix I. These values

(2, 7, 13}

are based on or taken from several publications

 

* The ORACLE was used for the large number of calculations required. That
part dealing with the nu%lear calculations was based on an ORACLE code devised
by Willoughby and Fowler 2) for two-region spherical reactors. Calculation,
‘tape handling and punch-out time averaged only 8 minutes for the two-region
reactors and 30 seconds for the one-region reactors. If desk computers were
used, about 4 to 5 men-days would be required for each case.

 
 

 

 

 

 

— 2

Cost Estimation

Selection of proper cost factors is the most difficult part of the
evaluation of nuclear power stations. since no full-scale plant experience
is available. However, reasonable values based on laboratory and pilot
plant experience, coupled with normal industrial methods and practice, should
produce results with at least sufficient relative accuracy to aid in the
selection of design criteria and operating conditions.

No new effort was made to estimate the investment cost for a réactor,

(3)

turbogenerator plant or chemical processing plant; the estimates by Briggs
were used.,
Reactor and Turbogenerator Plant Investment

The basis for computing the cost of the reactor with associatéd
equipment and structures was $ll.65(5) per kilowatt of heat for a L50-Mw
reactor considered as an integral part of a B-reactor'power station. For
power levels different from 450 Mw per reactor, the unit investment cost
was corrected by use of Figure 2 (reproduced from ORNL-1642).

The unit investment cost for the turbogeneratorrplant, which 1s
dependent on the throttle temperature, was obtained from Figure 4 (repro-
duced from ORNL-164k2). The cost of boilers and coal and ash handling
equipment is excluded since the reactor plant replaces these items. Since
the total reactor power could not be predetermined, a quadratic equation
was fitted to the points shown in Figure 2, for purposes of calculation by
the ORACIE. Using a plant factor of 80% and a 15% amortization charge,

the result is

T .2

Investment (mills/kwh) ='%— (0.3387 - 2.828 x 10'LL P+1.873x10 ' P

n
+0.02140 C E,) | (21)

 

 
 

SRR 15-

 

where P = reactor power, Mw of heat
-E, = net station efficiency
E; = gross station efficiency
C = turbogenerator plant cost, $/electrical kw
Efficiency

The efficilency of the plant is shown as a function of throttle
temperature in Figure 3 (reproduced from ORNL-1642). Estimates were made
for the temperature drop from the reactor to throttle. Table I below‘lists

the estimates of the efficiencies used.

Table 1

Nuclear Power Plant Efficiencies

 

 

 

Av. Reactor Throttle Temp.
Temp., °C O Gross Efficiency Net Efficiency
320 (608°F) 1490 0.315 X .0.281
300 (572°F) 470 0.304 0.271
280  (536°F) 450 0.292  0.260
250  (482°F) 410 0.274 ok
200 (392°%F) 340 0.240 o.211

Operation and Maintenance

Operating and meintenance charges for the reactor and turbogenerator

plants were taken as 3% of the total investment.

Inventories
A 12% charge was assessed against all non-depreciating materials.
A1l fissionable materials were valued at 20/gram. Protactinium was con-

sidered a fissionable material only when outside the reactor.

 

 
I -16-

 

Heavy water was valued at $40/lb. To cover the slight holdup in
chemical processing and makeup invéhtory, the inventory of heavy water was
taken as that required to fill the reactor system at room temperature, an
amount sbout 25% greater than necessary at operating temperatures.

Thorium was valued at $5/lb with no appreciable charge for making the
Th0,-D0 slurry.

The feed stream inventory charges were based on the following holdup
times |

Spent core fuel 95 days
Spent blanket fuel

Th + U + 75% of Pa 55 days
25% of Pa 205 days

Thorium feed ' 30 days
The holdup time assoclated with the poison removal by the hydraulic

separator plant was considered negligible.

Chemical Processing

The estimated cost of the poison precipitation process and the hydraulic
separator plant was $210 per day(lo) or $70 pér day per reactor. This cost
was considered independent of the throughput for flow rates of the order of
25,000 liters/day per reactor.

A fixed charge of § 5,500 per day(3) or $1830 per day per reactor was
used for the Thorex plant. The cost includes chemical plant amortization
and fixed operating costs. The estimated cost of processing thorium was
$3.00 /kg and $0.50 /gram for fissionable material (U-233, U-235 and Pa con-
verted to U-233). In previous studies(3) $1.00/gram was the estimate for
| (10)

processing fissionable uranium; the lower wvalue represents a later estimate

by the Chemical Technology Division. Uranium losses were assumed to be 0.1%

 

 
 

 

Y -17-

of the amount processed through the Thorex plant.

Prior to procéssing in the Thorex plant, heavy water must be evaporated
from the feed streams. A charge of'$0.55/litef was used for the recovery
of heavy watef.(lo) |
Feed Costs

For breeder reactors (all reactors were breeders, with one exception),

only thorium is required and D2O,makéup. As is usual, 5% of D20 inventory

of the reactor 'system was estimated as the annual makeup requirement.

\Results

The results shown in the following tables and graphs are for two-region
thorifim‘reéctors delivering 125 electrical megawatts to a power grid. The
power stat;on is composed of three reaétors, three turbogenerators and one
chemical procéssing plant along with some accessory equipment common to the
three reactors.

| The major results of the study are shown in Figure 5. Results for five

typiqal cases are shown in Table II. It is immedigtely apparent that the
net unit cost is véry insensitive to the parameters investigated;-bnly\O,}
mills/kwh separates the highest and lowest cost reactors shotm. This is
a direct conseguence of piant investment aqdflother fixed éharges represent -
ing n;ar%y 86% of the power cost. |

The details of the effects of the individual process variables are
discussed bolow under the heading Major Process Variables. Effects of
external power density changes, er?ors in the group-5 poison$¢ross section
and errors in the two-group constants are reported in succeeding sectionms,
followed‘?y discussions of the accuracy of the two-group method and the

economics calculations.

 

 
 

 

E— 18-

 

Major Process Variables

 

1)

2)

3)

4)

Core Radius -- Variation of the core diameter from 4 to 7 feet
results in a power cost change of less than 0.3 mills/kwh. The
lowest cost is associated with 4-foot cores, but only a negli-
gible difference of 0.0l mill/kwh exists between L- and 5-foot
cores.
Blanket Thickness -- For the blanket concentrations used (500
to 1500 g Th/liter), the unit cost of power varies only about
0.1 mill/kwh for a range of blanket thickness between 1-1/2
and 3 ft. The optimum thickness is about 2 feet for a six-
foot core and 2-1/4 feet for a five-foot core.
Thorium Concentration -- Therlowest unit cost results from using
a thorium concentration of 1500 g/liter. However, the cost is
only 0.02 mills/kwh less than that for 1000 g/liter. Also, the
results indicate that if engineering considerations require the
use of thorium concentrations as!low as 500 g/liter, the slightly
increased unit coét would not preclude possible economic power
generation.

Fig. 6 shows the effect of thorium concentrationvon the

breeding ratio and net U-233 production and again indicates that

‘use of thorium concentrations greater than 1000 g/liter leads

to a rapidly diminishing improvement in the breeding ratio.

Ratio of U-233 Concentration to Thorifim Concentration -- About 3

g U-233/kg thorium (see Fig. 8) produces the lowest unit cost for
thorium concentrations of 1000 g Th/liter. Here aléo, only slight

changes in unit cost are produced by wide variations in the ratio

of U-233 to thorium.

 

 
 

 

5)

 

~19-

Poison Concentration -- The core poisons vhich are related
to the core processing cycle time have little effect on

the unit cost in the range 4 - 10% (se¢ Fig. 7). The gross
breeding ratio (processing losses neglected) increases
almost linearly with reduction in poisons. Below 3% poisons,
however, the net U-233 production and net breeding ratio
decrefiselsince the highly increased chemical processing

rate leads to significant uranium and protactinium losses.

In similar fashion, if the blanket U-233 concentration were
lowered to small values, the increased chemical procesgsing
rate required would likewise cause large fissionable material

losses, as well as high chemical processing costs.

6) Temperature -- Under conditions assumed, no optimum temper-

ature was found for the range of average reactor temperatures
congidered. Lower unit cost is obtained by increasing the
temperature, but Fig. 10 indicates that little 1is to be

gained by raising the average temperature appreciably over

. 280°%. An average reactor temperature of 280°¢ will probably

correspond to an exit temperature of about }OOOC.

If engineering considerations preclude core power densities appreci-

ably over 100

kw/liter, it would be necessary to increase: the core size or

operate with a larger portion of the total power in the blanket. The

former course

appears economically preferable. The reactors with five-

and six-foot cores shown in Table II where typical results for several condi-

tions are shown, have power densities of 210 and 122 kw/liter, respectively.

In order t6 reduce the power density of the five-foot core to 122 kw/liter,

 

 
 

A 20-

it would be necessary to operate with a U-233 concentration in the
blanket of about 12 g/kg of thorium. The cost of power would rise to
about 7 mills/kwh, the increase being due primarily to increased inven-
tory charges. The use of a 6-foot core, on the other hand, results in
a power cost of 6.45 mills/kwh.
Effect of Group-3 Poison Cross Section Variations

The results of reducing the group-3 poison cross section from
40 to 18 barns at 20°C are shown in Fig. 7. The higher value is a
conservative one that has been used in previous studies(5); the lower
value is the latest estimate(lo) for thorium-uranium reactors. In
general, reducing the poison cross section by over a factor of two
reduces the net unit cost by 0.1 mill/kwh and shifts the optimum
core poigons from'T to &. The core cycle time is the only result
appreciably affected (see Table II). A change greater than a factor
of two in the group-3 poison cross section (see Fig. 9) does not
appreciably affect the optimum U-233 concentration in the blanket
or the optimum blanket thickness of 2 and 2-1/L feet for the 6-foot
and 5-foot cores respectively.
Effect of External Power Density Variations

Other than plant investment the largest single cost is the
inventory charge -- nearly one wmill/kwh when using values of 20
and 14 kw/liter external power densities (previously used in
ORNL-1642 by Briggs) for the core and blanket systems respectively.
The effect of increasing these external power densities is shown in

Fig. 11. Doubling the core external power density of 20 kw/liter

reduces the cost 0.25 mill/kwh, but doubling the blanket external

 

 

 
 

S ;-

power demsity of 14 kw/liter saves only 0.07 mills/kwh. The saving
realized from further increases in power density rapidly decrease.
A recent design(9) of the TBR indicates that it 1s possible to
achieve external power densities as high as 61 and 55 kw/liter fqr
the core and blanket systems respectively. For this condition the
cost is 5.8 mills/kwh, only 0.11 mill/kwh lower than for 40 and 28
kw/liter. For these calculations, it was assumed that no change

in capital or operéting expense was necessary to achieve higher
power densities.

Effect of Errors in the Nuclear Constants

The two group nuclear constants which were estimated for use
in the nuclear calculations are probably accurate to within 10-20%.
The effect of such errors on the process characteristics and econ-
omics was uncertain. Consequently, a study of the effect of
substantial changes (* 50%) in the nuclear constants was made for
a typical case¥*,

Although the critical concentration and breeding ratio were
changed considerably, the changes in power costs were relatively
small being principally confined to altering the amount of credit
obtained from excess fuel production. The largest change observgd
was a difference of about 0.6 mill/kwh between two extreme cases.
Where only individual constants were altered, chqngesfin the net
cost were less than 0.1 mill/kwh.

Considerable changes in the core uranium concentration do nqt,

however, lead to proportionally large variation in fuel inventory

 

*The single exception to this procedure was the restriction offfl(E})
to the range 2.28 to 2.36, the approximate limits of accuracy in
this quantity cited in BNL 221.

 

 

 
 

charges since the latter contain contributions of similar magnitude from
the blanket system. Thus, for two cases where the uranium concentration
differed by a factor of over 4, the fuel inventory charge differed by a
factor of 1.4. The effects upon breeding gain are, on the other hand,
almost directly converted into changes in credit received for excess fuel
production.

It seems reasonable therefore to conclude that errors in the two-
group constants are of secondary economic importance since 85% of fhe
power cost is tied up in factors unaffected by such errors.

A summary of the results and constants used is presented in Table III.
The most important cost increases were those produced by increases in the
quantities TB’ 0-3‘13’ Py and decreases in ’}]23. Increasing ’I'B produces
a rise in fast leakage at the expense of resonance capture in thbrium,
while all other neutron losses remain practically unaffected. Raising
cra.l3 causes protactinium absorpfion to rise at the expense of thorium
capture, as well as a change in core isotope ratios leading to higher
capture rates in U-234, 235 and 236. An increase in resonance escape
probability raises blanket power, increases leakage, depresses resonance
capture, and increases thermal capture. A decrease in both resonance
and thermal capture in thorium is the principal result of a fall in 9{23)
of 0.0k (1.T7%).

The critical concentration was most strongly affected by ‘1;, D2c’
and, naturally, %) . A 50% rise in the first two produced a critical
concentration increase of about 30%, while the 1.T% rise in 7(23)
caused a 4.4% decrease in concentration. The breeding ratio was not

significantly affected by changing either T; or Deé.

 

 
 

| -23-

None of the quantities investigated had a significant effect upon
blanket processing except py, for which a decrease of 504 led to a 12%
decrease in cycle time. The core thorex cycie was affected maifily by
the diffusion constants and ’T;; the greatest effect obéerved, produced
by lowering D2c’ was a decrease of cycle time by'about 134 days out.of
337. However, no significant changes were noted in either core or
blanket chemical procéssing‘costs. |
Accuracy of the Two Group Model and the Calculation of Breeding Ratio

For the large reactors studied, the two group procedure Qhould
provide an adequate estimate of the critical mass. The breeding ratio
is, however, far more sensitive to inadequacies in the mgthod.' For
example, difficulty arises in selecting a mefhod of treaping thorium
resonance captures. In this fiork, fést neutrons wefe assumed to
slow down without absorption, and captures due to resonance absorption
were computed by multiplying the number slbwed into the thermal group
by (1-p). This treatment overestimates the fast leakage by about
a factor of 3. Consequentlj; the bréeding ratio as.reported in
Table Ikaor a typical case may be low by about 0.02.
| A wuch wmore serioué source of iné.ccuracy results from uncertainties
in 'q. Errors in thé thermal value of‘q may produce an uncertainty of
+ 0.03 in the breeding ratio. Resonance captures in uranium may reduce
the breeding ratio by 0.08 if the resonance integral of U-233 ié 1500
b and‘resonance a is as high as unitj. | |

New datfi concerning the resondnde intégral bf.protactinium
(650 b) and the thermal cross section (63 b) reported by R. R. Smith(ll)
have only a slight effect on the breeding gain for the case of a |

1000 g Th/liter slurry; the absorptions in protactinium decrease by

 

 
 

 

A -2h-

only 0.002 absorptions per absorption in U-233.

 

Uncertainties in the poison cross section may be expected to have
little effect since it has been shown in a previous section that poison
levels may be varied over a range of 4-10% without appreciable cost
variation.

To sum up, the decrease in the breeding ratio produced by the factors
discussed above may be expectéd to be no greater than 0.13. While this
number represents an impbrtant unce?tainty in estimated production of new

material, its overall economic significance is slight.

Accuracy of Cost Estimate

The net unit cost of pover as determined for two-region reactors near
optimum cost (6.2 mills/kwh) is a result that is based on the limited
experience available. Obviously, the uncertaint& of this result is large
enough to span the competitive cost range for a nuclear power industry.
An estimate as to the overall accuracy is best made by assessing the
accuracy of the individual cost items that comprise the net unit cost of
pover. |

The largest single item is the reactor and turbogenerator plant‘
investment which represents 60% of the total unit cost. Of this cost, T5%
is for the turbogenerator plant and 25% is for the reactor and associated
equipment. Other cost ifiems are relatively small portions of the total;
the largest of these, the inventory charge, is 15% of the net unit cost.

Some of the individual costs comprising the net cost of power have
a fairly firm basis and error limits based on experience can be assigned
with a fair degree of confidencé. These items are capital investument,
maintenance and operation for'the turbogenerator plant; capital invest-

ment for the reactor plant and associated equipment; inventory and

 

 
 

 

 

L -25-

feed costs. Other charges which cannot be assigned error limits with any
degree of certainty are maintenance and operation of the reactor plant
and chemical processing. Fortunately, the individual costs that rest on
a falrly firm basis comprise approximately 80% (based on the total cost
without breeding credit) of the cost of power.

The accuracy of the turbogenerator plant investment cost 1is estimated
at +15%. For such a plant, based on vast industrial experience, the error
limit could be narrowed with a definite site selection and the establish-
ment of detailed design criteria (for example, nearly &% cost reduction could

(3)

be achieved by installing the turbogenerators outdoors). Briggs sets an
error range of O to +30% on the estimated cost of the reactor plant since
the figures used do not allow for construction contingencies. For mainten-
ance and operation of the turbogenerator plant, a fairly well known quantity,
a +15% assessment of the accuracy should be adequate.

It is difficult to estimate an error limit for the maintenance and
operating cost assumed for the reactor plant since a design in which these
costs are under control has not yet been visualized. Ultimately, they
might be expected to approach the costs for modern, conventional plants.

An error of O to +100% is assumed because of the unknown factors involved.

The error limits for the fixed chemical processing costs (investment,
operation and maintenance) also are difficult to estimate. A wvalue of
+25% is assumed here. Based on various designs and limited data, arguments
could be advanced for either raising or lowering the cost used. It is
felt that the part of the process{ng cost that is a function of the through-

put is as low as can be expected in the near future; consequently, a

0 to +100% limit is assumed.

 
 

A _26-

The nuclear and isotope calculations are probably accurate to within

 

+15%. Consequently, cost items (uranium inventory, thorium feed, breeding
gains, and, to some extent, prdcessing rates) based on these results have
about the. same degree of uncertainty if the external power density 1is
assigned approximately the same error range.

- Applying the estimated limits of accuracy to the cost items comprising
the 6.2 mills/kwh for a near optimum reactor, a cost range of 5.3 to 8.0
mills/kvh is obtained.

The cost of D,0 and the inventory charge (12% and $40/1b used in
this study) for non-depreciating items is Subjeét to government control
and at present it is difficult to predict the changes in the future.

The latest proposed pricing policy by the Atomic Energy Commission lists
the cost of D0 as $28/1b and requires only a 4% inventory or rental
charge for non-depreciating items. Applying these proposed costs, the

unit cost of power will be in the range of 4.6 to 7.2 mills/kwh.

 

 
 

-27-

Table II1

Typical Cost Breakdown and Neutron Balances

 

For Two-Region Reactors

 

Process Characteristics and Costs

r
Core diameter, ft 5
Thorium concentration,

g thorium/liter 1000
U235 concentration in

in blanket,.g/liter 3
Blanket thickness, ft 2-1/k4
Core external power density,

kw/liter 20
Blanket external power

density, kw/liter 14
Group-3 poison cross section

at 200C, b 40
Core poisons, % 7.0
Blanket poisons, % 4.33
Blanket power, Mw 89
Core power, Mw 202
Net unit cost of power,

mills/kwh 6.32
Plant investment (less chemi-

cal processing) mills/kwh 3.7k
Fuel inventory, mills/kwh 0.48
D20 inventory, mills/kwh 0.52
Fixed chemical processing

mills/kwh 0.76
Blanket processing, mills/kwh 0.26
Core processing, mills/kwh 0.09
Operation and maintenance,

mills/lcwh 0.75
Feed cost (DoO and thorium),

mills/kwh 0.20
Uranium (233 & 235) credit,

mills/kwh S 0.Lh
Gross breeding ratio 1.110
Net breeding ratio 1.109
Net U233 produced, g/day 59
U235 in product, wt. fraction 0.001k4
U233 in product, wt. fraction 0.959
Core system volume, liters 21,400
Blanket system volume,liters 17,100
Core concentration, g u233/

kg D20 2.55
Core. concentratlon, g U255/ \

kg D20 0.34

Core concentration, g uranium/

kg D20

9.21

>

1000

3
2-1/h4
20

1k

18
6.0
2.67
91
590

6.22

3. Th
O.Lh
0.52

0.76
0.25
0.07

0.75
0.20
0.49
1.121

1.119
65

- 0.0013

0.961
21,400
17,200
2 .48
0.30

8.30

 

 

2

1000

Z-l/h
Lo
28
18

6.0
2.7k

.~90

591
5.91

3. Th
0.35
0.3

0.76
0.24
0.06

0.75
0.13

0.46
1.115
1.11k
61
0.C01l4
0.958
11,600
14,000

2.49
0.31

8.49

500

20
14
40
7.0
5.50
392
6.53
3.74
0.37
0.49
0.76

0.20
0.09

0.75
0.19
0.050
1.013
1.012
0.0026
0.937
21,400
15,200
2.44
0.38

9.90

 

1000

20
1h
18
6.0
2.72
92
38
6.32

3.Th

0.40

0.5k

0.76
0.24
0.07

0.75
0.20

0.%8
1.096
1.095
51
0.001k4
0.960
22,600
18,100

1.59
0.19

5.3k

 
— 26-

Table II (Contd)

Reactor (internal & external)

 

inventories, kg

Thorium 17,100 17,200 14,000
U233 97.1 96.2 66.3
y23> 6.3 5.5 3.2
Pa22> 18.6 19.0 18.2
Feed stream inventories, kg
Thorium 6,500 6,800 6,400
U235(includes Pa23d) 5%,1 45,4 45.9 .
U255 3.0 1.5 1.6
Core thorex cycle, days 198 336 182
Blanket thorex cycle, days 146 140 120

Net thorium feed, g/day
Flux at core wall, n/cm® sec

Absorptions in fuel

 

557 625
1.06x1015 1.10x1015 1.08x1015

621

Neutron Balance

U233 (core) 0.7957 0.7941 0.7950
U253 (blanket) 0.2043 0.2059 0.2050
U255 (core) 0.1164 0.103%5 0.1066
U222 (blanket) 0.0004 0.000L 0.0005
Neutron losses (other than
fuel)
Core
Poisons 0.0576 0.0486 0.0487
y23h 0.1153 0.1024 0.1054
U236 0.018%4 0.0163 0.0168
Sulfur 0.002k 0.0021 0.0022
Core tank 0.0%05 0.0309 0.0308
D20 0.0169 0.0172 0.0172
Blanket
Thorium (thermal) 0.8114 0.8171 0.8143
Thorium (resonance) 0.3297 0.3351 0.3351
Protactinium 0.0188 0.0192 0.0226
Poisons 0.0080 0.0050 0.0051
y23h 0.0018 0.0017 0.0019
y236 3%10-T 35x10-T bx10-T
D20 0.0027 0.0028 0.0027
Fast leakage 0.0265 0.0264 0.0264
Slow leakage 0.0075 0.0075 0.007h
Total absorptions and losses 2.56U43 2.5362 2.5437
Neutrons produced from U223  2.3200 2.3200 2,%200
Neutrons produced from U235  0.24hl 0.2172 0.2238
Total neutrons 2.5641 2.5372 2.5438

 

0.7928
0.2072
0.1350
0.0010

0.0584
0.1328
0.0214
0.0026

0.0396
0.017k4

0.8230
0.2264
0.0358
0.0104
0.00%2
8x10-7
0.0059
0.0508
0.0423

2.6040
2.3200
0.28L2
2.6042

5
1.36x1015

18,100
84.3
3.8
18.8

6,600
L4 .0
1.5

208
150
610

0.84x1015

L7508
.2102

.1039
.000k

O OO0

OO OO0
Q
|_I
()
\N

 

 
 

Extrapolation

distance, in.

15.24

 

of U235
vé.}e

 

(13)

K

!OD

TB
212.4

 

 

 

 

Effect of Substantial Changes

T.62
15.24¢
22.86

2.28
2.36

h8.4
145.2

106.2
191 .2

233.6
318.6

109.0
196.2
239.8
327.0

0.T745
2.24

0.5865

1.76

0.835
2.505

0.6152

1.8L46

0028
0.84

Comblnation case 1

(D's, T's, p high;
extrapolation dis-

tance low)

Combination case 2
(D's, T's, p low;
extrapolation dis-

tance high)

6.257
6.229
6.219

6.354
6.109

6.158
6.299

6.136
6.210
6.248
6.324

6€.217
6.227
6.2354
6.259

6.223
6.238

6.224
6.256

6.224
6.2%6

6.214
6.255

6.181
6.308

6.692

6 .080L

~29-

Table III

0.3879
0.4173
0.429k

0.2896
0.5546

0.4965
0.3262

0.5288
0.4400
0.3943
0.3062

0.3956
0.4130
0.4210
0.435h

0.4048
0.4235

0.42k4kg

0.3952

0.4332
0.4097

0.3797
0.4300

0.4913%
0.3262

0.0102

0.5131

 

in the Nuclear Constantsa

097
.10k
107

073
1355

1.124
1.086

HFHEFHH RFHEPPF

o

151
.110
.098
077

-099
.103
.105
.109

.101
.106

.101
-099

.107
10k

-095
107

122
.082

.00k

.128

B(G) G(U)
51.7 8.4
55.5 8.4
59.0 8.4
38.6 8.8
T2.6 8.1
66.3 7.8
L5.7 9.0
70.5 8.8
58.6 8.5
52.6 8.4
40.8 8.2
52.8 6.7
55.1 8.0
56.1 8.8
58.0 10.8
54.0 7.5
56.4 9.0
5T7.0 7.5
52.7 8.9
57.1 9.5
50.2 7.8
50.6 5.1
57.4 10.8
65.4 8.3
43.5 8.6
1.2 15.4
68.42 3.5

o

 
 

 

— -30- ?" ?(‘y-,‘ *zi‘*w-{l

Table III (contd)

& The following properties were common to all the calculations performed:

Temperature L LI I B "« % v 0 & 8 0 & s a8 &S 88 s 28000

Grams of U233 per kilogram of thorium. 3

Grams of thorium per llter...........,... 1000

Poison fraction in core.....ceceoeseceees 0.06

REBCEOT POWET +eravevearenerronaspeaccasss U480.8 Mw (125 Mw elect.

output )

Core aiametertl..t!‘._...lIC.I.OU“I.IOCD. Sft

Pressure vessel diametereceecersssesnsssas 9 TL

External power densities, kw/liter

Core Systemil..i..tl..'....l........ 20
Blanket SYSteM.eeceesssacecasassesss 1h
The symbolg in column headings are defined as follows:

Cp = total power cost, mills/kilowatt-hour

CX = credit for excess fissionable material produced,
mills/kilowatt-hour

BR = breeding ratio, atoms of fissionable material produced
per atom of fuel burned

B(G) = net grams of fissionable material produced per day
G¢(U) = uranium concentration in core, grams of uranium per
kilogram of heavy water
c

This row gives results for standard case. Underlined numbers are values
chosen for parameters in standard case.

 

 
 

 

 

 

CORE

_3]_

ORNL-LR-DWG 4084A

ThO, SLURRY
MAKEUP

 

 

 

 

LIQUIDS —SOLIDS
SEPARATION

 

 

 

 

ThO, RECYCLE

 

 

Y

 

 

 

EXTRA U2

 

THOREX PLANT et~

 

 

BLANKET

 

 

 

 

 

 

FISSION PRODUCTS

Fig. 1. Schematic Flow Sheet for a Two Region Thorium Breeder Reactor.

 
 

 

REACTOR PLANT COST PER Mw OF HEAT RELATIVE TO

THAT OF 1350 Mw-1000 psia STATION

3.0

1.0

 

 

 

 

 

 

O

300° C-2000 psia PLANT
° o

 

 

 

. ! ] T
250° C-1000 psia PLANT AND

300° C—1600 psia PLANT WITH
HOMOGENEQUS CATALYSTS

 

 

 

 

 

400 800 1200 1600 2000 2400 2800 3200
PLANT POWER (Mw heat)

Fig. 2. Effect of Power on Cost of Two—Région
Reactor Plant.

 

 
 

THERMAL EFFICIENCY (%)

40

38

36

34

32

30

28

26

24

22

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

e S
DWG. 23095
| |
THERMAL EFFICIENCIES BASED UPON:
1. SATURATED STEAM REHEATED TO LIMIT |
MOISTURE IN EXHAUST TO 12% AT t%in. Hg
2. THREE STAGES OF FEEDWATER HEATING
_ 3.125-Mw, 1800-rpm TURBOGENERATORS —
600 psia
P ~
, X "
4OODSIO\ ??\GV
350 400 450 500

THROTTLE TEMPERATURE (°F)

Fig. 3. Effect of Steam Conditions on Turbogenerator

Plant Efficiency.

 

 
 

INVESTMENT COSTS (DOLLARS PER kw CAPABILITY)

90

80

70

60

50

40

30

20

 

_34_

DWG. 23096

 

DATA FOR SATURATED-VAPOR PLANT BASED UPON THREE STAGES OF
FEEDWATER HEATING, 1%, in. Hg EXHAUST PRESSURE, STEAM REHEATING
TO LIMIT MOISTURE IN EXHAUST TO 12%

DATA FOR SUPERHEATED-VAPOR PLANT BASED UPON THREE STAGES OF
FEEDWATER HEATING, 1V, in. Hg EXHAUST PRESSURE, SUPERHEATING TO

LIMIT MOISTURE IN EXHAUST TO 12 %

 

TOTAL

 

=3
w
&
B
m

—— 400
—— 600
— 850

S op

SATURAT

140

 

- 100 psia —f—— 215 psia

 

-
.
]

0

 

 

FPC ACCOUNT No. 314

TURBOGENER
CONDENSERS

ATORS,
, etc

“ 30

o
R

46

[
T
m
L
I
m
5
m
o
=
T

 

 

66
960

1465

120

100

80

 

/

 

 

No. 311 BUILDI

NGS AND GRO

UNDS

\

 

 

No. 312 FEEDWATER EQUIPMENT

| Nos.

 

342

 

TRANSMISSION PLANT

 

 

343
Na. 315

 

MISC. |

No. 316

ACCESSORY ELECTRICAL EQUIPMENT

 

 

 

No. 340

 

 

 

T

 

 

200

400

600

800

THROTTLE TEMPERATURE (°F)

1000

1200

Fig. 4. Effect of Steam Conditions on Power—Plant Cost for 300 ~Mw Plant.

TOTAL INVESTMENT (DOLLARS PER kw CAPABILITY)

 

 
 

NET UNIT COST (mills/kwhr)

7.0

6.9

6.8

6.7

6.6

6.5

6.4

6.3

6.2

 

O!!L- Ll-!l! ll!l\

 

 

3gOFU

 

TEMPERATURE, 280°C
233

 

 

PER kg OF Th

CORE POISONS, 7%
125 Mw OF ELECTRICITY
480.8 Mw OF HEAT
GROUP 3 POISON CROSS—-SECTION,
40 b AT 20°C

 

 

N\

/?ft', {000 g OF Th/liter

 

N\

\ 5-ft CORE DIA, 500 g OF Th/liter
-6 ft; {000 g OF Th/liter

 

 

 

/

=

_-6ft; 1500 g OF Th/liter

/

 

 

 

- 5ft; 750 g OF Th/liter
5 ft; 1000 g OF Th/liter

§</ /<it; 1000 g OF Th/liter
T-— —‘—

 

 

 

 

 

 

 

 

 

 

 

 

L = /
™ -y v e e [ ————————
\\4 ft. 1500 g OF Th/liter
\5ft; 1500 g OF Th/liter
1Yo 1¥/a 2 24 2V 2% 3 3Ya

BLANKET THICKNESS (ft)

Fig. 5. Effect of Blanket Thickness on Unit Cost.

 
 

NET UZ%°° PRODUCTION (g/day)

_36_

ORNL-LR-DWG 4088

 

 

 

 

 

 

 

 

 

 

 

70 145
62 / ] 113
54 // .11
46 /EMPERATURE, 280°C —1 1.09
CORE DIAMETER, 5 ft
3g OF U233 PER kg OF Th
OPTIMUM BLANKET THICKNESS
CORE POISONS, 7%
38 125 Mw OF ELECTRICITY o7
480.8 HEAT Mw
GROUP 3 POISON CROSS SECTION,
40b AT 20°C
30 | J | .05
500 700 900 1100 1300 1500

THORIUM CONCENTRATION (g/liter)

Fig. 6. Effect of Thorium Concentration

on Breeding.

GROSS BREEDING RATIO

 

 

 
 

 

NET UNIT COST (mills/kwh)

6.9

6.7

6.6

6.5

6.4

6.3

oL
M

_37_

ORNL-LR-DWG 8575

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1,24
149
TEMPERATURE: 280°C
CORE DIAMETER: 5 ft
3 g OF U%%%/kg OF Th I
| THORIUM CONC: 1000 g/liter
| BLANKET THICKNESS: 2 ft
| 125 Mw OF ELECTRICAL POWER
\\ 480.8 Mw OF HEAT
{ GROUP-3 POISON —— 445
CROSS SECTION
\ 18 b AT 20°C
- —— 40 b AT 20%C
\\ 143
144
1.09
1.07
0 2 4 6 8 10

CORE POISONS (%)

Fig. 7. Effect of Group-3 Poisons on Unit Cost and Breeding Ratio.

NET BREEDING RATIO

 
 

 

-38-

ORNL-LR-DWG 4086

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6.8 | [ '
TEMPERATURE, 280°C
CORE DIAMETER, 5ft
- BLANKET THICKNESS, 2 ft
S 6.6 CORE POISONS, 7%
= 125 Mw OF ELECTRICITY
g 480.8 HEAT Mw
Z 6.4 \\
QO '4j\\\\ . .
- % 1000g OF Th PER liter
= 15009 OF Th PER liter
S 6.2 d
l._
F|
<
6.0
0 1 2 3 4 5 6

BLANKET CONCENTRATION (g OF U%°® PER kg OF Th)

Fig. 8. Effect of Blanket Uranium Concentration on Unit Cost.

 

 
{mills /kwh)

NET UNIT COST (mills /kwh)

 

6.5

 
  

NET UNIT cOME

-39-

[

ORNL-LR—DWG 3832B

 

X

— — —

U%33 CONCENTRATION: 3g/kg OF Th

 

 

  
 

6—ft CORE

 

 

 

 

 

 

 

 

 

 

2%

 

\ 2—ft BLANKET
6.4 -

\\\ ",
6.3 A
5—f+ CORE
'\_
6.2
1% 1% 2 2Va oY,
BLANKET THICKNESS (ft)
TEMPERATURE: 280°C
THORIUM CONCENTRATION: 1000 g /liter
CORE POISONS: 6%
ELECTRICAL POWER: 125 Mw
HEAT: 480.8 Mw
GROUP-3 POISONS: 18 barns AT 20°C
———— GROUP-3 POISONS: 40 barns AT 20°C
6.5

 

 

CORE DIAMETER, 5ft

 

 

 

 

 

 

 

 

6.3
24—t BLANKET /(\ 4
\/ 2/ -ft BLANKET
6.2
1 3 5 7 9 10

BLANKET CONCENTRATION (g OF u233/kg OF Th)

Fig. 9. Effect of Group 3 Poison Cross Section on Unit Cost.

 
 

NET UNIT COST (mills/kwhr)

g

-40-

ORNL-LR-DWG 4089

 

7.0

6.8

|
t9,-ft BLANKET | ‘

CORE POISONS 6%

 

\ 1000 g OF Th PER liter
Y

 

6.6

39 OF U%32 PER kg OF Th

\ 125 Mw OF ELECTRICITY —

—

 

\,

 

6.4

\ 2-ft BLANKET

 

6.2

. 2'/4-ff BLANKET \

 

 

 

N

 

 

 

 

 

 

 

 

 

2, ft BLANKET—
|

S

 

 

6.0
200

220 240 260 280 300
AVERAGE REACTOR TEMPERATURE (°C)

Fig. {O. Effect of Temperature on Unit Cost.

320

 

 
 

NET UNIT COST (mills/kwh)

6.5

6.4

6.3 |

6.2

6.1

6.0

5.9

5.8

-4~

 

ORNL-LR-DWG 38348

 

]

TEMPERATURE: 280°C
CORE DIAMETER: 5ft
BLANKET THICKNESS: 2 Y4 ft
CORE POISONS: 6%
'ELECTRICAL POWER: 125 Mw
HEAT: 480.8 Mw

U233 CONCENTRATION: 3g/kg OF Th
Th CONCENTRATION: 1000 g/liter

 

 

 

 

 

 

 

 

= CORE EXT. POWER DENSITY,
\\20 kw/liter

\

 

 

 

 

 

 

 

\
\
T

 

 

 

 

 

 

 

 

\30 kw/liter
\\40 kw/liter
-\\;
12 16 20 24 28 32

EXTERNAL POWER DENSITY FOR BLANKET (kw/liter)

Fig. 11. Effect of External Power Densities on Unit Cost

 
 

ONE-REGION REACTORS

 

 
s— s-

 

 

ONE-REGION REACTCRS

Methods and Conditions

Use of slurry in the one-region reactor system precludes hydraulic
geparation as a method of poison removal. All pbison removal must
be done in the more expensive Thorex plant. It was assumed that the
fuel would be in the form of a UO}—ThO2 slurry in D20.

The calculations for the one-region reactor were considerably easier
than for the two-region reactors. No iteration is required to determine
the resonance to thermal absorption in the thorium. Therefore, it is
possible to write a set of equations covering the isotope concentrations
and the nuclear calculations which could be solved simultaneously by a
gimple iterative procedure.

The independent variables were reactor size, thorium concentration,
process cycle time and external power density.

It is to be noted that the basic configuration of a three-reactor
power station has been preserved here in order to provide as close a
comparison as possible of the two systems. It may be argued that such
a scheme places the one-region system at an initial disadvantage
because of the much lower power density which results. The underlying
philosophy of the three-reactor station was to limit the individual
power sources to the order of 100 Mw of electricity because of network
considerations. Possibly 375 Mw of electrical power from a two-reactor

station composed of one-region reactors would be more economical.

 
 

. s -,-",,,";"5:" O
Ll T T e
e X a0 T s

Fission Product Poisons

 

The fission product poisons were handled in the same fashion as the
two-region reactor. Since only the Thorex process is used, the equation

for the processing cycle time is similar to equation (6).

T = §—3§—¢ (22)

Isotope Concentrations and Critical Equation

As in the two-region calculation, the higher isotopes of thorium and
of uranium beyond U-236 need not be considered. In addition, the effect
~of the U-238 added with the enriched feed (9%.5% U-23%5, 2.0% U-234, and
4.5% U-238) for the non-breeders was neglected because of the small

quantity and small cross section. The critical equation is simply
. 2
o [125) B,(25) + m(23) B(23)] = (2 +T5%) (B + 02%) (23)

and the relationship for the resonance to thermal absorption can easily

be shown to be

2
(1 -p) (P2 + Tq)

 

 

 

 

 

Poe = % $5(02) (24)

For a one-region reactor under equilibrium conditions,
[1 + a(oe)]z(oe) g - A(3) W(13) -Z(13) ¢ - KB -~ 0 (25)
N13) 1(13) + o [M2 8@ 0 (a5 g - M) <o (26)
2(24) L5 (23) 4 -5(ek) #+5(15) § - (1-0) HEL g (27)

T .
B25) L m(oh) ¢ -5 (25) § - (1-9) B2 - g o (28)

T

 

 
 

a— s- —

T.(25) ¢ - £(26) ¢ - (1-q) HEL - 0 (29)

 

4 = _3.38 x 1016 PN (30)
2p(23) + 2p(25)

For breeder reactors the set of equations shown above (22 through 30) was
solved simultaneously by iterative methods with the feed of U-235 (F25) set
equal to zero. However, to handle the case of breeders and non-breeders
with the same general method, another equation is used that relates the
gross breeding ratio (no chemical losses), chemical processing losses
(0.1% used for all reactors) and the U-235 feed for the non-breeders.
Obviously Jjust enough U-235 must be added to make the‘net breeding ratio
equal to one. Therefore by a direct material balance (or by combining

equations 25, 26, and 28 and assigning a processing loss),

F(25) /¢ V 0.001[1\1(13) + N(23) + N(25)] ]
D)+ s o R O

In brief the calculation was performed in the following wmanner.

 

For a particular value of power (P), reactor diameter (for a sphere
B = % ) process cycle time (T) and thorium concentration (N(Oé)), the
critical equation (eq. 22) was used to calculate the concentration of
U-233 with no poisons, Pa or higher isotopes of uranium. The other
isotopes were then calculated with F(25) = O for the first iteration.
Then equation (28) was used to compute F(25). If F(25) was minus,
the reactor was arbreeder and the iteration with F(25) = O wae con-
tinued until the desired accuracy (»0.01%) was attained. If the

reactor was a non-breeder, the percentage recycle, g, was set egual

to 0.999 (all recycled minus the 0.1% processing loss) and the value

 

 
 

E— 6-

 

of F(25) computed from equation (31) was used in each successive lter-
ation until sufficient convergence occurred. Hand calculations of this
nature would be gquite laborious, requiring several hours of computation
for each reactor. All the required instructions and equations, however,
were easily coded and the ORACLE averaged only around 15 seconds per

reactor calculaetion.

Cost Estimetion

 

No attempt was made to egtimate the-investment cost of the one-
region plant. For initial comparison purposes, it can be assumed that
this cost is comparable to that of the two-region plant.

All other cost factors are the same as used for the two-reg;on

study.

oot

All results are for 125 Mw of electrical power delivered to a
power grid for a ofie—region reactor operating at an average temperature
of 280°% (equivalent to 480.8 Mw of heat with a net station efficiency
of 26%); An external power density of 20 kw/liter was used in all
cases.

The unit cost of power is shown as a net partial cost in the
following table and graphs. ‘This cost is the sum of the inventory
charges, feed (thorium and for non-breeders U-235), D,0 makeup and
chemical processing charges that are a function of throughput minus
the credit for breeding gain, if any. Costs not included are the fixed
charges on the plant investment (reactor, turbogenerator and chemical

processing), fixed operating @osts for the chemical processing plant

 

 
o - e

and operating and maintenance which is usually taken as a percentage of
the plant investment (3% in the two-region study). The comparable fixed
cost for the two-regiofi reactors isv5.25 mills/kwh. Consequent;y, for
initial comparison, the total unit cost can be obtained by adding the
fixed cost of 5.25 mills/kwh to the net partial uhit costs shown.

The resulits for 5 reactor éizes of interest at near optimum conditions
are ppesented in Table IV. It is immediately apparent that for one-region
reactors near the optimum cost conditions large breeding gains cannot
"be obtained and high isotopic purity (~~95%) fi-235 cannot be produced
without a protactinium recovery prOcess; This would involve separation
of protactinium from the uranium isotope mixture as soon as practical
‘after discharge from the reactor. Such a procedure would not oédinarily
be required for the two-region reactor since a product of about‘95%
pufity is expected.

The effect of the chemical processing cycle (determines the fission
pbison level) is shown in Figures 12, 13, and 1k for the reactor diameters
from 10 to 16 ft. In general the optimum cycle time increases with
increase in thorium concentration and reactor diameter; the optimum cycle
time for the reactors near optimum cost appear to be about twice as large
as for a two-region machine. For non-breeders it was assumed that a
30-day supply of U-235 feed was on hand, but no reserve supply of fission-
able material was assumed for breeders. Thus the loss in credit from the
breeding gain and the additional inventory charge caused the abrupt
changes in slope that appear in the graphs at the point of change:
from breeder to non-breeder.

The net partial cost as a function of diameter and thorium concen-

tration at optimum cycle time (determined from Figures 12, 13, and 1h)

 

 

 
 

S -18-

is shown in Figure 15. It is apparent that, for the reactor sizes of

 

interest, the optimum thorium concentrations are between 200 and 300 g/liter.
The effect of reactor diameter (determined from Fiéure 15) on the
partial unit cost of power for optimum process cycle times and thorium con-
centrations is shown in Figure 16. The minimum partial unit cost of 1.88
mills/kwh occurs for a reactor size of 12 ft with a thorium concentration
of 260 g/liter. From a cost viewpoint there is little variation in the
range of reactor sizes from 10 to 1k ft, the maximum difference being only
0.12 mills/kwh,
The comparable minimum partial cost for the two-region reactor is
0.97 mills/kwh. Therefore, a cost differential of 0.9 mills/kwh seems to
exist in favor of the two-region reactor provided that the fixed costs for
the two reactor types are equal. This difference 1s, of course, uncertain
because of possible unforeseen engineering difficulties which may arise
in the course of construction and operation of either type reactor. It
is not unreasonable to suppose, for instance, that fixed costs may be
somewhat smaller for the one-region reactor because of simpler construction.
Clearly, questions such as these can be resolved only by comparison of the

performance of actual reactors.

 

 
 

Cost Breakdowns and Neutron Balances for Several
One-Region Reactors Near Optimum Conditions*

Reactor diauwmcter, ft

Thorium concentration,g/liter

Process cycle time, days
Net partial cost of power,
“mills/kwh

Uranium (U253 and U235)credit

mills/kwh
Chemical processing (less
fixed costs), mills/kwh
Feed costs (Th, D20, U)
mills/kwh
Do0O inventory, mills/kwh
Uranium inventory,mills/kwh
Total system volume, liters
Power density in reactor,
xw/liter
Gross breeding ratio
Net breeding ratio
Net breeding gain (U235 and
U235) g/day
Critical concentration,
g U255/kg D2O
Critical concentration,
g U235 /kg D20

Uranium concentration,
g U/kg DQO’

Reactor (internal & external)

inventories, kg
Thorium
U233
U235
Pa23>

Feed gtream inventories,kg
Thorium _
U233 (includes Pa)
U235

U235 in product, wt. fraction
U232 in product, wt. fraction

Thorium feed, g/day
U230 feed, g/day
Reector poisons,

-49-

Table IV

Process Characteristics afid Costs

10
300
450
2.00
0
0.17
0.40
0.52
0.92
38,900
32.4

0.957
0.956

7.99
1.18
26.08

11
300
400

1.92
0.0L
0.20
0.22
0.58
0.96
43,800

4.1

1,011

1.009
5.T9
7.62
0.71

17.60

13,100
270.9
25.%
19.8

1,800
41.8
345
0.433
0.038
560

4.93

12
250
400

1.88

0.057

'0.18

0.25
0.66
0.84

49,700

18.8

1.012

1.010
6.3
5.82
0.56
13.4k2

12,400
236.0
22.5
19.9

1,700

37.0
3.1

0.434
0.038
561

5.46

13
250
500
1.93
0.15
0.16
0.28
0.75
0.89
56,600
14.8
1.035
1.03L4
20.4
5.60
0.46

10.68

14,200
258.8
21,2
20.9

1,600
324
2.3
0.52k4
0.040
580

6.10

 

1L
200
450

2.01

- 0.11

0.16

0.52.
0.86
0.7T"

64,700

11.8
1.025
1.02%4

14 .3

4,15

0.37
8.50

12,900
220.4
19.7
20.4

 
Absorptions and losses

-50-

Table IV (Contd)

Neutron Balances

 

 

pa23>3 0.0191 0.0186 0.021L 0.0206 0.0235
~yadd 1.0000 1.0000 1.0000 1.0000 1.0000
y23h 0.1090 1.1019 0.1040 0.0910 0.0986
U255 0.1599 0.1009 0.1029 0..0883 0.0966
236 0.0235 0.0095 0.0095 0.00L4 0.0061
D0 0.0070 0.0073 0.0095 0.0099 0.0133
Poisons 0.0573 0.0491 0.0545 0.0601 0.0629
Th232 (thermal) 0.5516 0.5775 0.6269 0.6516 0.6998
Th222 (resonance) 0.4687 0.4520 0.4063 0.4043 0.3488
Fast leakage . .0.1873 0.1518 0.1309 0.1123 0.0993
Slow leakage 0.07081 0.062% 0.0694 0.0622 0.0730
Total neutrons absorbed
and lost 2.6541 2.5309 2.5351 2.5046 2.5218
Production
Neutrons from Ued2 2.3200 2.32000  2.3200 2.,3200 2.3200
Neutrons from U235 0.3341 0.2109 0.2151 0.1846 0.2018
Total neutrons produced 2.6541 2.5309 2.5351 2.5046 2.5218

* 125 Mw of electricity, 480.8 Mw of heat. Average temperature 280°C, external
power density, 20 kw/liter.

 

 
PARTIAL NET UNIT COST OF POWER (mills/kwh)

 

_5]..

 

ORNL-LR-DWG 8576

 

2.6

|

125 Mw OF EL!IECTRICITY

480.8 Mw OF HEAT

AVERAGE TEMPERATURE; 280°C

ONE REGION; ThO2—UO3z— D0 SLURRY

2.5 \ \ \\2509 OF Th/liter
N

 

 

2.4

200

 

 

150

REACTOR DIAMETER 46 ft | 175

[/

2.3

2.2 \

 

 

/

|

 

 

 

 

 

 

 

175
> REACTOR DIAIMETER 15 ft
A
2.2 \\
\ 300
150

 

/

 

 

 

 

 

 

 

2.4
[ ———
REACTOR DIAMETER {4 ff 200

2.0

 

100 200 300 400 500 600 700
CHEMICAL PROCESS CYCLE TIME (days)

Fig. 12. Effect of Process Cycle Time on Unit Cost.

 
 

24

2.0

N -
n w

PARTIAL NET UNIT COST OF POWER (mills/kwh)
N

2.0

1.9

1.8

ORNL-LR-DWG 8577

 

\

 

/4509

OF Th/liter

 

<"

175

 

 

 

REACTOR DIAMETER, 13 ft

 

 

- ¢]0)

 

 

 

- 250

 

 

 

 

125 Mw OF ELECTRICITY
480.8 Mw OF HEAT

AVERAGE TEMPE

RATURE: 280°C

ONE REGION; ThO,-U0O3-D,0 SLURRY

 

W

 

OF Th/liter

 

 

O~

300

 

 

 

REACTOR DIAMETER, 42 ft

 

 

 

 

 

 

 

 

{00 200 300

400

500

CHEMICAL PROCESS CYCLE TIME (days)

600

Fig. 43. Effect of Process Cycle Time on Unit Cost.

700

 

 
 

PARTIAL NET UNIT COST OF POWER (mills/kwh)

_53_

ORNL-LR-DWG 8578

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2.3 T T
125 Mw OF ELECTRICITY
480.8 Mw OF HEAT
150 g OF Th/ liter AVERAGE TEMPERATURE; 280°C
\ ONE REGION; ThO,—UO3z—D,0 SLURRY
2.2 ' '
175 \. /
200\ REACTOR DIAMETER {4 ft
21 ‘K
250\ /
300
_/
Xa
1.9
2.3 —
150
175
200
2.2 \
/
REACTOR DIAMETER 10 ft
21 \——._
300
250
2.0
100 200 300 400 500 600

 

 

 

 

700

CHEMICAL PROCESS CYCLE TIME (days)

Fig. 14. Effect of Process Cycle Time on Unit Cost.

 
 

PARTIAL NET UNIT COST OF POWER (mills /kwh)

-54-

ORNL-LR-DWG 8579

 

| |
125 Mw OF ELECTRICITY

480.8 Mw OF HEAT
AVERAGE TEMPERATURE; 280°C

ONE REGION; ThO,~UO3—D,0 SLURRY
2.5 OPTIMUM PROCESS CYCLE

 

 

 

 

REACTOR DIAMETER 16 ft

 

/

N
W

 

15 ft

/

 

14 ft

 

Z i\

7
N

 

2.0 \
{3 ft
11 ft
1.9 -

 

N

 

 

 

 

 

 

1.8

 

 

100 150 200 250 300 350
THORIUM CONGCENTRATION (g/ liter)

Fig. 15. Effect of Thorium Concentration on Unit Cost.

400

 
 

PARTIAL NET UNIT COST OF POWER (mills /kwh)

2.5

2.4

2.3

2.2

21

2.0

 

_55_

ORNL-LR-DWG 8!80

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

125 Mw OF ELECTRICITY 1
480.8 Mw OF HEAT
AVERAGE TEMPERATURE: 280°C |
ONE REGION; ThO,—U03—D,0 SLURRY 1.06
OPTIMUM PROCESS GYCLE AND Th CONCENTRATION
1.04
// —— ' .02
/ 1.00
——gl—
/ / 0.98
. 0.94
10 1 12 13 14 15 16

REACTOR DIAMETER (ft)

Fig. 16. Effect of Reactor Size on Unit Cost and Breeding Ratio.

GROSS BREEDING RATIO

 
 

-56-

NOMENCLATURE

Core radius, cm

Breeding gain, atoms of fissionable material produced per atom of
fuel burned

Reactor buckling, cmm2

Net grams of fissionable material produced per day
Turbogenerator plant investment, $/kw

Totél power cost, mills/kwh

Credit for excess fissionable material produced, mills/kwh

D, diffusion constant, cm-l, for fast and slow groups, respectively

2
Gross efficiency of power plant

Net efficiency of power plant

Poison fraction

Net feed to reactor, atoms/sec

Core uranium concentration grams of uranium per kg of heavy water
Fraction of group-3 poisons that can be precipitated

External power density, kw/liter

16

Power constant, 3.38 x 10 fissions/Mw sec

Concentration, atoms/cm3

Resonance escape probability

Reactor power, Mw

Fraction of material processedignd returned to reactor
Inside Radius of pressure véssel, cm

Thickness of core vessel, cm t=1.39R x lOfe
Chemical process cycle time, sec

Reactor or system volume, cm5

Yield of group-3 fission products, 1.31 atoms/fission

 

 
 

AR -57-

B Ratlc of resonance to thermal absorption
o liicroscopic cross section, cm2
I  Mecroscopic cross section, cm
¢ Average neutron flux of system, neutrons/cme-sec
A Decay constant, sec
T Fermi age, cu’
Subscripts:
a Total capture
B | Blanket
C | .Core
f Fission captfire
T Radiative capture
T Total system
1 Hydraulic separator processing
2 Thorex processing .
3 Group-3 poisons

Parenthetical Symbols (used to identify N, A, o=, andL):

A Group-5 poilson subgroup.A

B Group—finpoison subgroup B

0 Precipitated poisons not removed in hydraulic separators
5 Group-3 poisons

25 U-233

2k U-234

25 U-235

26  U-236

13 Pa-23%3%

02 Th-252

 

 
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REFERENCES

Arnold, E. D, Gresky, R. J., Klotzbach, R. J., and Irvine, A. R.,
"Preliminary Cost Estimation: Chemical Processing and Fuel Costs
for a Thermal Breeder Reactor Power Station", ORNL-1761, Jan. 27, 1955.

AEC Neutron Cross Section Advisory Group, Neutron Cross Sections, BNL-170,
-170A, -170B, -221, (1952-1953).

 

Briggs, R. B., "Aqueous Homogeneous Reactors for Producing Central-Station
Power", ORNL-1642, May 13, 195k.

Briggs, R. B., and Edlund, M. C., "A Preliminary Program for the Conceptual
Design of the TBR", ORNL-CI-54-8-89, August 13, 195k.

Fowler, T. B., and Willoughby, R. A., "ORACLE Code for the Two-Group, Two-
Region Homogeneous Reactor Calculation", ORNL-CF-54-7-38, July 7, 195k.

Glasstone, S., and Edlund, M. C., Elements of Nuclear Reactor Theory,
Chapter XIII, (1953).

 

Halperin, J., et al, "Capture Cross Sectlion of Pa-2335 for Thermal Reactor
Neutrons", Reactor Science and Technology, p. 108, Vol. 3, TID-2010,
(sept., 1953).

HRP Quarterly Progress Report, ORNL-181%, October 31, 195k.

 

HRP Quarterly Progress Report, ORNL-1853, January 3, 1955.

Klotzbach, R. J., "Comments on Proposed Power Breeder Design Calculations”,
ORNL-CF-54-8-78, August 10, 195L.

Smith, R. R., Letter to J. Halperin, RRS-14-55A, March 28, 1955.

Tobias, M., "A Thin Shell Approximation for Two-Group, Two-Region
Spherical Reactor Calculations", ORNL-CF-54-6-135, June 16, 195k.

Tobias, M., "Calculation of Fermi Ages for ThOo-Heavy Water Slurries”,
ORNL-CF-54-9-97, September 14, 195h4.

Visner, S., "Nuclear Calculations for Homogeneous Reactors Producing
U-233", ORNL-CF-51-10-110, October 22, 1951.

 

 
 

 

oy o -50-

APPENDIYX T

Constants Used in the Nuclear Calculations

1. Thermal Microscopic Cross Sections at 28000, barns. (Corrected for a
Maxwell Boltzmenn Distribution) '

 

 

Absorption Cross - Radiative Capture Fission Cross
Substance Section, og Cross Section, oF Section, 6Ff
Th-232 L.52 -- --
Pa-~233 96.8 | -- o --
U-233 | 380.7 B 3h.3 ‘ 346.4
U-23h 57.4 -- --
U-235 41k.0 65.1 348.9
U-236 5.81 - -
Dp0 1.76 x 1077 -= --
S L 0.316 \ - --
Group j poisons 13.1 - -~

. S T |
2. Macroscopic Absorption Cross Section of Zircalloy at 280°% = 5.897 x 10 > emt.

e s 0
5. Diffusion Constants, Ages, and Resonance Escape Probabilities at 280°C for
Various Thoria-Heavy Water Slurries.

Concefitration of Fast Diffusion Slow Diffusion Fermi Age Resonance Escape
Slurry, g Th/l Constant, D1B, cm Constant, D2B, cm Ty, cm@  Probability,ps

 

-

200 1.73 1.19 21k 0.728
750 1.53 1.18 212 0.638
1000 1.49 1.17 P12 0.560
1500 1.47 1.17 207 0.435

4. Diffusion Constants, Ages, and Resonance Escape Probabilitiles at Various
Temperatures for a Thoria-Heavy Water Slurry containing 1000 g‘Th/l.

 

 

Temp. Fast Diffusion Slow Diffusion Fermi Age Resonance Escape
°C Constant, DiB, ecm Constant, Dop, cm Tg, cm Probability
200 -1.34 0.998 168 0.590
250 1.42 1.09 190 0.575
280 1.49 1.17 212 0.560
300 1.56 1.24 23k 0.547

320 “1.62 1.34 260 0.530

 

 
 

el -60- ¥ et

5. Diffusion Constants and Ages for Uranyl Sulfate-Heavy Water Solutions at
Various Temperatures. Resonance Escape Probability Taken as Unity for

 

 

 

all Cases.

Temp. Fast Diffusion Slow Diffusion Fermi Age
oc Constant, Dic, cm Constant, Doc, cm T, em
200 1.46 1.05 167
250 1.57 1.1k 193
280 1.67 1.25 218
300 1.76 1.30 2LL
320 1.87 1.40 276

6. Density of Heavy Wéter; Zircalloy and Thoria at Various Temperature, g/cme.

 

 

 

Temp. Heavy Water, 99.8L¢ Do0
oC Thoria Zircalloy at 2000 psi
200 | 9.69 | 6.55 0.959k4
250 (a1l temperatures) (all temperatures) 0.8935
280 0.8395
300 i 0.7959

320 0.7480