ML19345E322

Effect of Pu Buildup on Temp Coefficient. Filed as Part of Amend 7 to Application for CP & Ol.Prepared for Util

ML19345E322
Person / Time
Site:	Yankee Rowe
Issue date:	04/01/1958
From:	Brooks W, Soodak H NUCLEAR DEVELOPMENT CO.
To:
References
NDA-2072-1, NUDOCS 8101060863
Download: ML19345E322 (30)

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W. L. Brooks

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H. Soodak

1. v April 1,1958 vag N 8)hg\\%

l work performed for gt The rankee Atomic Electric Company 3

4 UET0RY DOCKET R.!COM NDk t

j NUCLEARgEVELOPMENT CORPORATION OF AMERICA 2/O/Of W

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t NDA 2072-1 EFFECT OF PLUTONIUM BUILDUP ON TEMPERATURE COEFFICIENT 4

W. L. Brooks H. Soodak k

l April 1,1958 Work Performed for The Yankee Atomic Electric Company by The Nuclear Development Corporation of America NUCLEAR DEVELOPMENT CORPORATION OF AMERICA White Plains, New York Tz^ 0lu"lrsAi

s CONTENTS

1. Introduction and Summary 4

1.1 Conclusions...

4 1.2 Recommendations for Further Work...

6 1.2.1 Further Work on nf 6

1.2.2 Check on Calculation of p.

7 1.2.3 Effect of Control Rods..

7 1.2.4 Miscellaneous Items.

7

2. Reactivity Formula and Temperature Effects.

8 2.1 The Formula for k.....................

8 2.2 Temperature Effects 10

3. The Temperature Dependence of r/

13 3.1 The Cross Sections 14 3.2 The Beginning of Life Reactor 14 3.3 The End of Life Reactor.

17

4. The Temperature Dependence of p..

19

5. The Temperature Dependence of e 21

6. Temperature Dependence of Leakage Terms.

22

7. Work at Other Installations.

23 7.1 The Hanford Work...

23 7.2 E. I. DuPont (Savannah River) Work.............

23 7.3 Work Done at MTR 24 7.4 Work Done at NRX (Chalk River) 25 7.5 Work at Atomics International (North American Aviation) 27 7.6 Work at Brookhaven.

27

8. Bibliography 29 2

TABLES 1.1 Core Parameters of the Yankee Power Reactor at 68*F.

5 2.1 Reactivity Parameters for Yankee Power Reactor Temperature Coefficients at Beginning and End of Life.

9 2.2 Summary Table of Temperature Coefficients in Beginning of Life Reactor..

11 2.3 Summary Table of Temperature Coefficients in the End of Life Reactor.

12 3.1 Effective Cross Sections for Reactor Material and Logarithmic Derivatives 15 3.2 The Temperature Dependence of yf in the Yankee Reactor -

Cold Beginning of Life Case.

17 3.3 The Temperature Deper.dence of nf in the Yankee Reactor -

Cold End of Life Case...

18

~ ~

23 7.1 Departure from 1/v Behavior of U s and Puras Cross Sections in Water and Heavy Water.

24 o

3

1. INTRODUCTION AND

SUMMARY

This study was undertaken at the request of Yankee Atomic Electric Company. Its purpose was to review briefly the effect of plutonium buildup on the temperature coefficient of the Yankee Power Reactor. Some relevant core parameters are listed in Table 1.1. The study was divided into three parts:

1. A review of the calculations on the temperature coefficient done by Westaghouse. This phase of the work is described in Sections 2 through 6.

2. A brief look at work at other locations concerning the effect of plutonium buildup on temperature coefficient of reactivity. This is reported in Section 7.

3. Conclusions based on the results of 1 and 2, and recommendations for further work. These conclusions and recommendations are presented below.

1.1 CONCLUSION

S We believe, on the basis of the work reported in Sections 3 through 6, that 1

the calculations made at Westinghouse are essentially correct. We made order of magnitude calculations on the temperature coefficient of c and p by assuming that only the water density changed. For both e and p our results were close f

enough to those of Westinghouse so that the difference could be explained by our assumption. Some calculations to check the age, r, of the reactor were also

~

made. These calculations also checked the Westinghouse results quite closely.

The calculations of p, e and T were made using the same formulas as were used by Westinghouse. The calculation of nf was completely independent since the l

Westinghouse calculation was done by a machine code. Calculations were done i

i for two different temperature ranges - the cold" reactor from 50 to 86 F*

and the " hot" reactor from 498 to 534 F. Agreement is again satisfactory.

• Actually nf calculations were made for the temperature range' 77 T to 176 *F because the effective cross section values available to us were for these j

temperatures.

'4

Table 1.1 - Core Parameters of the Yankee Power Reactor at 68 F Fuel Rod:

Material uranium oxide (UO )

2 Diameter 0.290 in.

3 Density 10.07 g/cm Clad:

Material 304 SS Thickness 0.021 in.

Density

7.8 Moderator

Material water (H O) 2 Density 1

Miscellaneous:

Lattice Spacing 0.425 in.

V2H 0/yCell 0.506

/y ell 0.129 VSS C

UO /V ell 0.365 C

V 2

Core Height 90.0 in.

We believe that the hot" temperature coefficient is large and negative

(~30x10-5/T) and is independent of the plutonium buildup. The main reason for this large negative coefficient is the effect of water expansion on the res-onance escape probability, p. The higher the temperature the less water there is and thus there is more resonance absorption. Further, the " cold" tempera-ture coefficient in the beginning of life reactor is most probably negative and again largely due to the effect of water expansion on p.

In the cold end of life reactor, however, the sign of the temperature coef-ficient cannot be ascertained with certainty. In this case, described in Table 2.3, the overall temperature coefficient in the range 50-86 F is -0.15x10-s/ F, as obtained directly from Westinghouse calculated values of the various components of k(nf, e,p, etc.) at 50 F and 86 F.*

• As described in Section 2, it was obtained by calculating the separate contribu-tions to k-1dk/dT and summing.

5

In addition to the directly calculated value of ni, Westinghouse also lists a

" graphical" value, which is obtained by them from a smooth curve

• drawn through the points of a plot of nf versus temperature. Their graphical values of nf lead to a " graphical" temperature coefficient of -2.11x10-s/ F in contrast to the directly calculated value of -0.15x10-8/ F. Because of the possibility of drawing various curycs as fits to the point data, we believe that strong con-clusions should not be based on the value of -2.11x10-8/ F.

The value of -0.15x10-s/T for the temperature coefficient of the cold, end of life reactor comes about from a cancellation of larger positive and negative terms. Its value and sign are thus clearly open to question. The main negative contribution is -2.64x10-8/T due to the effect of water expansion on resonance absorption. The main positive contribution is due to the temperature variation of nf, and is +3.42x10-8/ F.t In the beginning of life reactor this contribution is only +0.34x10-8/T. Thus the presence of plutonium in the end of life reactor contributes +3.1x10-8/T to the temperature coefficient due to its non-1/v behavior.

The work done at other locations on the effect of plutonium buildup is in agreement with our results in those cases where the available datp were suf-ficient to make comparisons. In the cases where data were insufficient, and direct comparisons impossible to make, there were no inconsistencies found.

1.2 RECOMMENDATIONS FOR FURTHER WORK In view of the uncertainty expressed above about the cold, end of life reactor, it appears to us that some further work is indicated. The best answer to the question of the temperature coefficient in the cold, end of life reactor would be obtained by actual measurement in the going reactor at various times through-out the reactor life. It would be considerably difficult to obtain trustworthy results on the basis of critical experiments which attempt to mock up either the whole reactor or part of it (e.g., a single box) at various stages of the reactor life.

Bad $i is a list of several suggestions for further theoretical work.

1.2.1 Further Work on af The results of the calculation of the effect of the non-1/v cross sectionr on nf are strongly dependent on the particular spectrum employed. (See Section 7.6 below.) Thus, close attention should be given to the problem of the correct

• The reason for this smoothing is given in Section 2.

t In aontrast to the " raw" value mentioned above, the Westinghouse " graphical" value is +1.5x10-8/ F and our independently calculated value is +2.2x10'8/ F.

6 i

spectrum. A possibility in this direction is to use different spectra in the fuel and moderator as is done by Westcott at Chalk River.1 Another possibility is to make use of the rod " blackness" concept as is done at Hanford.2 The effect of flux flattening across the cell might also be investigated more closely. A possibility is to use a P calculation for o75, rather than diffusion 3

theory.

1.2.2 Check on Calculation of p l

Since one of the two large terms that cancel to give the small temperature coefficient for the cold, end of life case is the variation of p, it would perhaps be worthwhile to seek a different method of calculating this term as a check.

A Monte-Carlo calculation of this term is one possible method.

1.2.3 Effect of Control Rods When the reactor is cold the control rods (and also some extra poison in the moderator) will be present in the reactor. The control rods will increase the effect of the leakage terms on the temperature coefficient and should thus tend to make the coefficient more negative. We, therefore, feel that studies should be made with the control rods in the reactor.

1.2.4 Miscellaneous Items A further source of error is uncertainty in the cross sections, particularly in the plutonium cross sections. Some investigation is indicated as to the likely magnitude of such uncertainties and their effect on the calculated value of the temperature coefficient.

Another area in which the calculations might be refined is in the calculation of r.

Westinghouse apparently did not include the effect of the thermal base change in their calculation. Since this is a positive reactivity effect (see Section 6) it should be investigated.

4 7

2. REACTIVITY FORMULA AND TEMPERATURE EFFECTS The formulas, with one exception, used in this analysis are those used by CAPA, Westinghouse, and supplied to us by Howard Arncid. The one exception to this statement concerns rf. Westinghouse uses a machine code, SOFOCATE, to obtain (vE )th and (Z la th, and divides the first by the second to obtain nf.

f 2.1 THE FORMULA FOR k The formula used for the effective multiplication, k, of the reactor is the standard four-factor" formula, N'W k = (1+1B2)(1+L2B2)

The various terms have the standard meaning.3 Their values as calculated by Westinghouse are given in Table 2.1 at a few temperatures and for the beginning of life and end of life conditions.

It will be observed that two values of nf are given in the table, a raw" value and a " graphical" value. The " raw" values are calculated directly from SOFOCATE printouts while the graphical value is obtained by drawing a smooth curve through plotted points of nf versus temperature. Inputs to SOFOCATE are limited to four significant figures and thus some " scatter" is obtained in the results. It was felt by Westinghouse that the curve more nearly represented the correct values of ni than the calculated points.

We felt that our calculated values corresponded more closely to the " raw" values calculated from given number densities and cross sections as read from BNL-325. Therefore, the comparisons made between our calculated results and those of Westinghouse make use of the " raw" data from Westinghouse.

8

+

=

l Table 2.1 - Reactivity Parameters for Yankee Power Reactor Temperaturc Coefficients at Beginning and End of Life

• Number Densities - atoms (molecules)/cm x10'8'- Homogentred Core 8

8 8

Temp yf nf L

r B

U*"

3U" U"

Pu'"

Pu '8 Pu '

Li HO SS 8

8 8

8 8

• 8

,]/e7 x10' wl08 w1os wl08 x108 x10 x10' x108 x10

'F raw graphical e

p cm cm m

8 50 1.48678 1.48670 1.03849 0.76953 2.73223 49.450 7.1301 1.05469 2.48096 7.96699 1.70246 1.00944 g 68 1.48667 1.48657 1.03851 0.76921 2.76167 49.534 7.1282 1.05326 2.48016 7.96444 1.70055 1.00911 y 86 1.48696 1.48685 1.03856 0.76800 2.79815 49.702 7.1263 1.05180 2.47937 7.96191 1.69651 1.00879 E 498 1.49754 1.49803 1.04360 0.72836 4.30139 66.521 7.0832 1.02262 2.46143 7.90430 1.35827 1.00149 5 534 1.49957 1.49957 1.04450 0.72011 4.54681 70.042 7.0794 1.02130 2.45987 7.89926 1.30339 1.00086 5

50 1.41221 1.41257 1.03849 0.76953 2.52044 49.450 7.1301 1.06781 1.86229 9.27899 7.91055 3.38255 3.67826 2.84319 1.11650 1.70248 1.00944 3 68 1.41308 1.41295 1.03851 0.76921 2.54167 49.534 7.1282 1.06628 1.86170 9.27601 7.90801 3.38147 3.67707 2.84228 1.11615 1.70055 1.00911 y 86 1.41395 1.41334 1.03856 0.76880 2.57643 49.702 7.1263 1.06470 1.86111 9.27307 7.90550 3.38040 3.67591 2.84138 1.11579 1.69651 1.00879 m 498 1.43026 1.43026 1.04360 0.72836 3.76636 66.521 7.0832 1.03120 1.84764 9.20598 7.84830 3.35594 3.64931 2.82082 1.10772 1.35827 1.00149

'E 534 1.43241 1.43223 1.04450 0.72011 3.95639 70.042 7.0794 1.02896 1.94647 9.20010 7.84329 3.35379 3.64698 2.81892 1.10701 1.30339 1.00086

• The data in this table were extracted from tabulations made by H. C. Hecker of CAPA, Westinghouse.

O

2.2 TEMPERATURE EFFECTS The temperature coefficient, k-1 dk/dT, may be expressed as:

1 dk I dtzf I de 1 dp 1

d 1

d k H 6 f dT + i W + p dT 1+L2B2 dT (

1+7B R O 2

In this study independent estimates were made of the first three terms in this equation, and some checking done on the fifth term. Results are given in suc-ceeding sections below.

A breakdown of the various effects as calculated from the numbers in Table 2.1 is given in Table 2.2 for the beginning of life reactor and in Table 2.3 for the end of life reactor. The various coefficients were calculated by using the relation 1 dX _ X +aT - X - AT T

T X dT XT 2AT It is interesting to note in these tables that for the hot (516 F) reactor almost the total negative temperature effect is in the variation of the resonance escape probability, p. The other effects are much smaller and just about cancel each other out. This is also the case for the cold (68*F) beginning of life reactor but is not the case for the cold end of life reactor.

9 10

I Table 2.2 - Summary Table of Temperature Coefficients in Beginning of Life Reactor

• Contribution to k-idk/dT at:

Variable Factor 50-86 F 498-534 "F nf(raw)

+0.34x10-5

+3.76x10-5 e

+0.19x10-5

+2.4 x10- 5 P

-2.64x10-5

-32x10-5 kk

- 2.10x10-5

-26.8x10-5 2

7B

-0.3 8x10-5

-6.50x10- 5 2 2 LB

- 0.05x10-5

- 0.48x10- 5 Leakage.

-0.43x10-5

-7.03x10-5 Dopplert

-0.63x10-s

-0.79x10-5 1(~ !dk/dT

-3.16x10- 5

-34.62x10-5

• The numbers in this table were calculated from values of the parameters at different temperatures (see text). These values were supplied by Westinghouse.

t The Doppler coefficients were supplied to us by Westinghouse as part of a table in which the total reactivity coefficient was obtained by addition of the listed Doppler coefficient to the other coefficients.

This implies that the listed Doppler coefficient is normalized to a degree rise of moderator temperature.

D s

11

Table 2.3 - Summary Table of Temperature Coefficients in the End of Life Reactor

• Contribution to k-8dk/dT at:

Variable Factor 50-86 F 498-534 F 7;f (raw)

+3.42x10-5

+4.18x10-5

(

+0.19x10-5

+2.40x10-5 P

-2.64x10-5

-31.7x10- 5 k

+0.97x10-5

-25.12x10-5 2

TB

- 0.3 8x10-5

- 6.55x10- 5 2 2 LB

-0.11x10-5

-0.37x10-5 Leakage

-0.49x10-5

-6.92x10-5 Dopplert

-0.63x10 5

-0.79x10-5 k-2dk/dT

-0.15x10-5

-3 2.83x10-5

• The numbers in this table were calculated from values of the parameters at the different temperatures (see text). These values were supplied by Westinghouse.

t The Doppler coefficients were supplied to us by Westinghouse as part of a table in which the total reactivity coefficient was obtained by addition of the listed Doppler coefficient to the other coefficients. This implies that the listed Doppler co-efficient is normalized to a degree rise of moderator temp-erature.

i

)

12

3. THE TEMPERATURE DEPENDENCE OF r;f An expression for af may be written in the form:

A r/ = BER where A=

vNof ggg 1

(i refers to fuel rod)

B=

Ng4 1

N oy (j refers to moderator and clad)

C=

j J

and R=eI/o]= ratio of average flux in moderator to that in fuel.

The logarithmic derivative of 7;f may then be written in the following form:

!dB

\\

1d 1 dA 1

dC dR 1 dA B

1 dB U

yf dT X W ~ B+CR R 5

Hj X R B+CR B W-I

\\

CR l dC 1 dR CdT+iiHj

~

B+CR Contributions to this derivative may be divided into three groups:

1. that due to the non-1/v character of the cross sections,.

2. that due to the flattening of the flux at higher temperatures, and

3. that due to density changes.

-To calculate these three effects we expand the factors in the expression for nf and take derivatives.

13

T 3.1 THE CROSS SECTIONS The values of the effective cross sections used in this analysis were cal-culated at Savannah River by H. D. Brown.' He tabulates 7_ [o(E)o(E)dE o(E)dE where cp(E) is the flux spectrum due to a fission source in a homogeneous mix-ture of water moderator and pure absorber. The shape of the spectrum depends on the amount of absorber in the mixture and effective cross sections are given 3

for a numi'er of values of the absorption cross section per cm of the reactor.

For a(E) he reads the curves in BNL-325 up to 2.87 ev. o(E) is assumed to vary as 1/v above this value.

Resonances above the change-over energy are to be accounted for in the resonance integral of the absorber.

As is stated above,the effective values of the cross sections are evaluated for several values of absorption of the reactor. We chose the set that was close to the reactor parameters, i.e., E =0.1040_cm-1 The cross sections are given a

in Table 3.1 below at two energies - 0.0257 ev (=77 F) and 0.0304 ev (=176 F).

The logarithmic temperature derivative is obtained by forming U176 ~ Uff g=

99 X ff6YUff U

2 and the difference, c, between this and the logarithmic derivative for a 1/v absorter is calculated. Both the temperature derivative and e are tabulated.

3.2 THE BEGINNING OF LIFE REACTOR For the reactor at beginning of life the factors in the expression for 7;f are:

f A = v2sN s 2s>

0 2

B=N0 s + N 0*s, = B s + B s 25 28 2

2 ss $s + N C=N H0HO= Css + CHO U

0 2

2 2

r 14

Table 3.1 - Effective Cross Sections for Reactor Material and Logarithmic Derivatives Ea = 0.1040 cm'1 F(KT)

Material 0.0257 0.0304 6

e B (1/v) 300.09 290.76

-3.20 0

Li (1/v)

• 28.2 27.3

-3.20 0

SS (1/v)

• 1.003

-3.20 0

H O (1/v)

• 0.264

-3.20 0

2 U as (abs) 262.77 252.09

-4.20

-1.00 2

23 U s (fiss) 219.63 210.72

-4.17

-0.97 23 Ue 1.091

-3.20 0

Pu23s (abs) 495.21 499.29

+0.83

+4.03 Pu238 (fiss) 338.68 339.13

+0.13

+3.33 Pu240 (abs) 932.04 901.71

-3.34

-0.14 Pu1 (abs)t 585

+0.83

+4.03 Pu241 (fiss)t 436

+0.13

+3.33

• These cross section values were obtained by multiplying the 2200 m/sec values by the same factor as for boron.

1 These cross section values were obtained by multiplying the 2200 m/sec values by the same factors as for Pu23 s, e

i 15.

The logarithmic temperature derivatives of these expressions are (it is assumed that the only density change is in the water):

1 dA _ 1 dof3 A dT ol3 dT a

1 dB _ B s 1 do a

Bs 1 do,

2 3

2 f dT B dT B og dT B

do$,o CHO 1

dPH O 1 dC _ Css 1 dois + CH,0 1

2 2

C dT C

ds dT C

a dT C

pH O dT g

2 lt is now possible to write for all the o's 1 do 1 do\\

3Y i

1/v Then all the 1/v contributions cancel when the temperature derivative is cal-culated. We therefore need to consider only the values of e in this calculation.

In this case the expression for the temperature derivative reduces to

[ Css 1 d(n c) _ f Bs a

Bs a

CR CHO 2

2 2

ss +

af dT 8

B+CR 25 B+CR 28 B+CR C

C HO 2

CHO 1

dPH O 1 dR\\

2 2

+

C PH O dT R dTj 2

The last two terms in this expression are the water expansion and flux leveling effects, respectively. The rest of the terms make up the non-1/v contribution to the derivative. The results of the calculation for the cold case are given in Table 3.2. The water expansion effect is calculated in the range from 77 to 176T as are the cross section terms. Density data were obtained from the Handbook of Chemistry and Physics. The flux-leveling effect was calculated for the range from 50 to 86T from data supplied to us by Westinghouse.

(Table 2.1 above.)

Table 3.2 shows the relative importance of the non-1/v cross sections and the other effects, and shows good agreement between our calculation and that of Westinghouse.

16

Table 3.2 - The Temperature Dependence of nf in the Yankee Reactor -

Cold Beginning of Life Case Temperature Range: 77-176*F Variable Factor Contributions to 1 x10' ni dT non-1/v cross section

-0.239 water expansion

+0.131 flux leveling

+0.13 5 total

+0.027 4

results from Table 2.2

+0.034 (from 50 to 86'F only)

It should be noted that the U 35 cross sections fall off more rapidly than 1/v. This accounts for the large negative contribution due to non-1/v cross sections. The buildup of plutonium should thus affect this term in the nf variations much more greatly than the flux-leveling and water expausion terms.

No effective cross section values for the hot reactor are included in the Brown tabulation. However, estimates of the flux-leveling and water expansion effects may be made. These turn out to be +0.06x10"' and +0.45x10-' respec-tively.

It is interesting to note that we calculated a value of 1.502 for nf as com-pared to a value of 1.487 as calculated by Westinghouse. The agreement is within 1%.

3.3 THE END OF LIFE REACTOR Calculations for the end of life reactor are made in the same manner as those for the beginning of life reactor except that plutonium and fission product buildup is included. It should be noted that all calculaticas are made with no ns in the core (those made by Westinghouse also do not include Xenon). The Xe results are given in Table 3.3.

These results show that there is a positive contribution to the temperature coefficient of nf due to the non-1/v charader of the plutonium cross sections.

The effect of the Pu241 buildup is probably underestimated in this calculation since the resonance is at a slightly lower energy than that of Pu23s. However, even if the very conservative assumption is made that the PP fission cross section does not vary with temperature and the corresponding absorption cross section varies as 1/v, the temperature coefficient of nf only riset to 0.305x10-4 17

i Table 3.3 - The Temperature Dependence of nf in the Yankee Reactor -

Cold End of Life Case Temperature Range 77-176 7 Variable Factor Contributions tol (U'9 x104 af ~dT non-1/v cross sections

-0.037 water expansion

+0.127 flux leveling

+0.129 total

+0.219

^

results from Table 2.3

+0.342 (50-86 F only)

The total positive effect of the plutonium buildup as calculated from cross sections in Table 3.1 is seen to be less than the negative contribution due to the UM.

It should be noted that the comparison made in Table 3.3 is between our calculation and the " raw" calculation made by Westinghouse. Their " graphical" fit gives a smaller temperature coefficient of nf (0.15 as compared to 0.34).

w l

r 18 c

l

I i

4'>++;,,

ph 4'A#

s

-eE Ev <e 1.

TEST TARGET (MT-3) 1.0 5 m t2A y,T EE I.l

[55 lilM l.8 I.25 1.4 1.6 r

=

1. 4 k+ d 4%

Y>,,

kv

4. THE TEMPERATURE DEPENDENCE OF p Westinghouse uses a standard formula, which includes a correction for cell interactions, to calculate the resonance escape probability p. This formula is N

S p = exp{ -

[9.7 + 26.3 g (1 - 6C)]}

We assumed that only the water density changed and that this change affects only (E. It will affect the correction factor C but this factor contributes only s

about 5% to p.5 With this assumption the logarithmic derivative is 1 dp 1

d&E3, p g=-(in p) - ( I dT The slowing down power (E is mainly due to the presence of water. As a s

result, 1

d(Es _1 dp (Es dT

~ pH Using values of p from Table 2.1 and standard values for water density we get

~2.96x10-'/T as the average value of 1 dp pN in the range from 77-176'F. This compares with the Westinghouse value

(

- 2.64x10-5 given in Table 2.2 for the cold reactor. For the hot reactor we obtain -4.68x10-'/'F for our calculation as compared to -3.2x10-'/ F for the -

calculation as made by Westinghouse. The fractional density variation of water that we used was for variation at a constant pressure of 2000 psi in the range 19 h

m

from 500-600T and was 1 dp

- 1.45x10' J/ F p dT

~

This number was calculated from data found in Keenan and Keyes.s The differ-ence between our values and Westinghouse values could be due to our neglect of 1

the variation of C with temperature.

Westinghouse argues that the buildup of plutonium hardly affects the reson-ance escape probability. This is most probably true since the fraction of pluton-lum present in the rod is small(< 0.5% of the amount of U238) and the amount of 23 Us changes only slightly.

a 4

)

f 20

5. THE TEMPERATURE DEPENDENCE OF e The formula used by Westinghouse to calculate e is an empirical one derived from work done at Bettis. It is 0.1672 c-1 =

HO N

2 + 0.3205 x

1 +1.238 N NU U

where the subscript x in the above formula refers to reactor materials other than water or uranium. Upon taking the temperature derivative of this expres-s'on one obtains, assuming that the water density is the only variable:

N 1 de _

(e-1)2 1.238 H O 1 dp 2

c dT e

0.1672 NU kN Substituting numbers for the temperature range 50-86 F the calculated result is +2.4x10-s/ F as compared to +1.88x10~8/ F as calculated from Westinghouse results (Table 2.1).

At the high temperature the result calculated on the above assumption is

+3.30x10-8/ F as compared to the Westinghouse value +2.4x10~5/#F in Table 2.2 above.

The assumption that only the water density changes (and not also NU and Nx) tends to overestimate the temperature coefficient contribution due to a change in c.

e 21

6. TEMPERATURE DEPENDENCE OF LEAKAGE TERMS Work on this aspect of the problem was restricted to checking the " age" calculations using the quasi-empirical formula supplied by Westinghouse:

1 r=3E E sl tr where o t and otr are derived from fits to experimental data.' Their values s

may therefore be poor for mixtures that are very different from those to which they were fitted. However, the mixtures in the Yankee Reactor appear to be close enough to those fitted.

The one question remaining as regards the age calculations is the variation of age with the change in thermal base. This is a positive reactivity effect (i.e!,

age decreases as neutron temperature is raised) and is given by

!\\

dr _

1 1,

7 ETh T7 (Eoj dT 3(E Est If one takes E = 2 Mev then the value of dr/dT is -5.21x10-3 cm / F at the cold 2

n temperature and -4.05x10-3 cm / F at the hot temperat9re.

2 The corresponding positive changes in age (which do not contain the effect of the thermal base change) as calculated by Westinghouse are 7.00x10-8 cm/op 2

at the cold temperatum and 9.79x10-1 cm / F at the hot temperature.

2 The effect of the thermal base change thus nearly cancels the effect of density changes at the cold temperature but has negligible effect at the hot temp-erature.

22 i

7. WORK AT OTHER INSTALLATIONS During the course of the investigation we looked at results obtained at other installations on this or similar problems. In order to make quantitative comparisons with these results, wherever practical, we calculated the de-23 23s parture, e, of the U s and Pu cross sections from 1/v behavior for various temperature ranges and absorption. These data are listed in Table 7.1.

The results of the investigations on work at other places are given below.

7.1 THE HANFORD WORK 2

G. W. Stuart has made some calculations on the effect of exposure and consequent buildup of plutonium on the neutron temperature coefficient of a graphite-moderated, natural uranium reactor. He obtained curves of the 2

2 temperature dependence of n, f, and M =7+t for the reactcr. The results are classified and appear in the Hanford report.

The significant thing about this work is that only neutron temperatura effects were considered and thus no credit could be taken for density effects.

7.2 E. L DUPONT (SAVANNAH RIVER) WORK Telephone calls were made to H. D. Brown at Savannah River and E. Hones at Wilmington. Mr. Brown stated that calculations of n for plutonium bearing l

rods are beset with many pitfalls. Whether the temperature coefficient is negative or positive can depend on the way the cross section curves are read.

Mr. Hone said that they had made calculations on a particular (unspecified) lattice of D O and natural uranium. In the beginning of life case the contributions 2

to the temperature coefficients due to n, p, and leakage were all negative. The terms due to p and to leakage were about equal and were about twice as great as that due to n. At high (unspecified) exposure the n term became slightly positive but was greatly outweighed by the still negative p and leakage terms.

The work done by DuPont is, of course, classified. Therefore, more specific details could not be given on the telephone.

33

Table 7.1 - D parture from 1/v Behavior of U235 and Pu23s Cross Sections in Water and Heavy Water Cross Temperature Abdorption e

-1 4

Section Moderator Panges em x10 Remarks U235 (abs) 25-80 'C 0

-1.24 23 U s (fiss) 25-80"C 0

-1.20 Cold Pu23s (abs)25-80t 0

+4.82 Clean Pu233 (fiss) 25-80 t 0

+3.9 5 23 U s (abs) 131-191 C 0

-0.78 Hot U235 (fiss) 131-191 t 0

-0.85 Clean Pu233 (abs) 131-191*C 0

+7.76 Pu233 (fiss) 131-191 t 0

+6. 91 U235 (abs)

DO 25-80 t 0.0167

-0.9 Cold 2

U235 (fiss)

DzO 25-80 t 0.016'?

- 1.1 Poisoned Puras (abs)

DO 25-80'C 0.0167

+3.8 DO 2

2 Pu23s (fiss)

DO 25-80 t 0.0167

+3.0 2

23 U s (abs)

HO 25-80'C 0.1040

-1.00 Cold 2

U235 (fiss)

HO 25-80 t 0.1040

-0.97 Poisoned 2

Pu2ss (abs)

HO 25-80t 0.1040

+4.03 HO 2

2 Pu233 (f ss)

HO 2.5-80 t 0.1040

+3.33 2

7.3 WORK DONE AT MTR 8

a report by B. W. Johnson and H. L. McMurry at MTR presents results of 4

calculations concerning replacement of U s by Pu23s in the MTR. They came to 23 23 the conclusion that equally reactive cores of U s and Pu239 have about the same temperature coefficient. The value of the coefficient is given as -5x10-5/ F of which the water expansion is said to be the largest part. It is further noted by Johnson and McMurry that the measured temperature coefficient is -10x10~5/ F 23 for the U s reactor.

It is interesting to estimate the contribution to 1 dk li H due to the non-1/v cross section behavior in the U s loaded MTR and Pu23s 23 loaded MTR. According to Section 3, these contributions are given by i

24 4

f c -fga f

where c and ca measure the departures of the fission and absorption cross sections from 1/v behavior, and f is the fraction of neutrons absorbed in the fissionable material (thermal utilization). In the r mctors calculated by Johnson and McMurry, the f was 0.85 in the U s case and 0.' in the Pu233 Using the 23

cold poisoned" H O values for e, as listed in Tabh. 7.1, the non-1/v contribu-2 tions are

-1.2x10-5/ F for the U s loading 23

-3.0x10-5/*F for the Pu239 loading In this case, therefore, the non-1/v Pu239 effect is more negative by -1.8x10-5/ F 23 than the non-1/v U s effect. The reason for this is the high value of the fraction 233 f

of neutrons absorbed in Pu coupled with the fact that da is larger than e for Pu239 (due to the increased importance of absorption in the Pu resonance).

tas 7.4 WORK DONE AT NRX (CHALK RIVER) 8 D. G. Hurst reports that calculations are currently in progress at Chalk River to check into the effect of exposure on the temperature coefficient of NPD (a heavy-water moderated and cooled power reactor now under design).

The method of calculating temperature coefficients is to use calculated effective cross sections (Maxwellian spectra plus dE/E tails) at two different tempera-tures to calculate the reactivity parameters. As an example (the only one supplied) they find for a reactor representative of NPD that a 40t drop in neutron temperature in the fuel assembly has the following effect on the buckling:

Average Irradiation 2

of the Fuel (integrated flux);

AB neutrons per kilobarn (Meters-2) 0 0.091 0.25 0.039 0.50 0.001 0.75

-0.034 1.00

-0.060 By way of orientation one neutron per kilobarn corresponds approximately to 3000 megawatt days per ton of natural uranium. The negative values of AB2 in the above example correspond to positive temperature coefficients according to the approximate relation:

25

2 2

1 dk ~ M AB

-1 2

2 pg=

40 l

This temperature coefficient is that due to changes in af due to non-1/v cross sections behavior. The change in neutron temperature was taken equal to the change in moderator tempernture. The above coefficient, assuming an 2

2 M =300 cm varies from -3.8x10-5/ F for no burnup to +2.5x10-5/ F for full (3000 mwd / ton) burnup.

These coefficients may be estimated by the methods of Section 3. Thus, for the beginning of life reactor (zero irradiation), the non-1/v effectis e23sf f235 23sa e

wheref235 is the fraction of " thermal" absorptions that occur in 635, and is 0.58 for a natural uranium rod. Using cold poison D O values for c from 2

Table 7.1 results in a coefficient of

-4.2x10-5/ F 4

For the large irradiation (~3000 mwd / ton) case, the non-1/v effect due to U236 and Pu239 is 23sf 23sf 23s _ c23saf239) c g235 _ c2ssa f235 + [ c g

where the f's are the fractions of thermal" absorptions occurring in the in-dicated element and the g's a re the fractions of " thermal" fissions that occur in the indicated element. We estimate that g23s ~ 0.54 23 f s ~ 0.30 g239 ~ 0.46 f238 - 0.3 2 238 at the high burnup. (The absorption fraction f of the U238 is about 0.31.)

Again using the cold poison D O values for the c's results in 2

-2.4x10-5/T due to U s 23

+5.0x10-5/'F due to Ph238 for a total of

+2.6x10-5/T at 3000 mwd / ton Our estimated values of -4.2x10-5 and +2.6x10-5 agree well with the values of -3.8x10-5 and +2.5x10-5 which are based on an M value of 300 cm,

2 2

26 t

s

7.5 WORK AT ATOMICS INTERNATIONAL (NORTH AMERICAN AVIATION)

A telephone call was made to E. R. Cohen at Atomics International. He stated that they had made calculations on the effect of plutonium buildup in Calder Hall type reactors. They carried the calculations far enough to see that their calculations would agree very closely with those made at Hanford by G. W. Stuart.2 They, therefore, use the Hanford Numbers in their work.

7.6 WORK AT BROOKHAVEN A call was made to J. M. Hendrie at Brookhaven National Laboratory. He stated that in the beginning of life condition the graphite " vacuum" temperature coefficient at normal operating temperature was -1.6 inhours/'C (approximately

- 2.3 x10-5 5k/k per T). During a shutdown for graphite annealing in November, 1955, when the average exposure was approximately 340 mwd / ton, the coefficient was measured to be -0.6 inhours/'C ( -0.9x10~5 6k/k/'F). This coefficient was approximately constant in the temperature range from 30-160'C. Above 160t the coefficient gets more positive and is positive above 200'C.

j The change in coefficient is attributed to the buildup of plutonium in the fuel, and is 1.4x10-5/ F.

We may estimate, by the method in Section 3, the non-1/v contributions to the temperature coefficient of the BNL Renctor. For the unexposed reactor this contribution is given by 2sf(1) _ c2saf c

where f is defined in Section 7.4 above. For the exposed reactor the formula is 2sf 2s,,2sa f s + e4sf

'8 4 a 49 2

g g

8

-E g

where the f's and g's are defined in Section 7.4 above. Using the various c's d

for the four cases of Table 1.1 the results are:

Non-1/v Contribution Cross Sections Used Unexposed Exposed Change x105 x105 5

x10 Cold, clean

- 5.1

-4.6

+0.5 Cold, poisoned. D O

-4.2

-3.8

+0.4 2

Hot, clean

-4.0

-3.0

+1.0 27 a

.~.

Values of the f's and g's were estimated at 340 mwd / ton burnup and were:

2 g= 0.94 and f = 0.54 for U ss, and g=0.06 and f =0.05 for Pu29, 2

For the beg:.nning of life reactor f s was estimated to be 0.58 for the natural uranium rod.

The above tabulated values of the change in temperature coefficient show that the calculated change depends significantly on the neutron spectrum used.

None of the spectra used is the cortect" one for a graphite lattice. Thus, although we cannot reproduce the measured change value, neither can we say that the methods used result in a contradiction with measurement.

s

"* w,,

4 j:l g

j *-

-J 9,A o k.);

28 s

1 2

= -

i

8. BIBLIOGRAPHY

1. C. H. Westcott, Effective Cross-Section Values for Well-Moderated Thermal Reactor Spectra, CRRP-680, Jan. 25,1957.

2. G. W. Stuart, HW-36825,1955. (Classified.)

3. S. Glasstone and M. C. Edlund, The Elements of Nuclear Reactor Theory,"

D. Van Nostrand Company, New York,1952,

4. H. D. Brown, Tables of Effective Neutron Cross Sections in Water Moder-ated Reactors, DP-194, Jan.1957.

5.

W. H. Graves, Determination of Reactivity Lifetime for Enrichment, Light Water Moderated Power Reactors, p.16, WIAP-NM-36, Oct.15,1954,

6. J. H. Keenan and F. G. Keyes, " Thermodynamic Properties of Steam,"

John Wiley and Sons, New York,1936.

7. Arnold, Calculation of Fast Group Constants, WCAP-649, Aug.1957.

8. B. W. Johnson and H. L. McMurry, Comparison of Flux and Power Dis-23 tribution, and Void and Temperature Coefficients of the MTR with U s and Pu23s Fuel, IDO-16384, July 26,1957.

9. Letter to W. Brooks, dated Dec. 12', 1957.

9 Y

0 29