ML19211A496

Critical Parameters of Pu Sys.Part 1:Analysis of Experiments

ML19211A496
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Site:	07106581
Issue date:	12/20/1968
From:	Clayton E, Hansen L, Lloyd R Battelle Memorial Institute, PACIFIC NORTHWEST NATION
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14897, NUDOCS 7912200015
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CRITICAL PARAMETERS OF PLUTONIUM Enzi 7 w

SYSTEMS.

PART 1: ANALYSIS fiEE M J

• • • k ^'

OF EXPERIMENTS K EYWORD$: criticolity, mass, uth L. E. HANSEN, E. D. C LAYTON, R. C. LLOYD, S. R. BIE R'.LA N, and p,ogrom >e g e r o r s, R.D. JOHNSON Battelle MemorialInstitute, Richland, Wuslan; ton 9?Jy nium, e n r i e le m e n t, s a fe ty, reproc e s sing, plutonium.240, fuels, plutonium nitrofes, re.

II' C ' '.' "* **d#*'

Received November 4,1963 P utonsu'm ossdes, polystyrene',

l Revised December 20, 1965 plutonnum.239 a basis for extending the existing criticality pre-dictions to higher 2* Pu contents and to other To predict the critical parameters of plutonium moderation ratios.

fueled systems one must establish the accuracy of In order to correct, and extend, the existing the computational methods to be employed and the widely used criticality data, theoretical calcula-accuracy and applicability of the available critical tions are required to predict the critical param-cxperiment data with which the calculations are to eters of systems for which no experimental data be compared. The accuracy of a multigroup diffu-are available. The reliability of these predictions sion theory code, HF.V, and a multigroup transport must be determined from the consistency with theory code, DTF-IV, was examined by analyzing which the computational methods reproduce the recent plutonium critical cxperiments. The ex-widest possible variety of experimental criticality periments cover the entire range of possible mod-data. The purpose of this paper is to analyze some cration ratios, and the plutomum fuels contain as of the calculational tecl...iques in use at our crit-M much as 23.2 isotopic percent Pu. All three ical mass laboratory by comparing computed basic geometries are represented by the experi-critical parameters with values measured, or mental data examined.

H ere necessary, the derived, for clean, homogeneous, plutonium-fueled criticality data were corrected, by means of addi-

systems, tional experiments aml/or calculations, to con-form to one-dimensional, cle a n, homcgeneous COMPUTATICNAL METHODS AND critical assemblies which could be adequately CROSS SECTIONS defined and used as a basis for establishing nu Icar criticality safety guidelines.

Two one-dimensional multigroup c o mp u t e r codes were employed in analyzing the available experimental data. These were HFN, a diffusion theory code,* and the transport theory code' DTF-IV. In calculations with the latter code, the trans-port equation was solved in the S approximation INTRCDUCTION with anisotropic scattering defined through the first Legendre moment of the scattering kernel.

A number of clean critical experiments have Both codes utilized multigroup constants (18 en-been performed in recent years on homogeneous, ergy groups) obtained from the GAMTEC-II code.'

plutonium-fueled systems. These experiments in-The HFN calculations were made using 50 spatial dicate the need for revising much of the data that mesh pomts in the core region with an additional have been used as a guide for establishing nuclear 20 mesh points, when applicable, in the reflector criticality safety specifications.' In particular, region. The DTF-IV code used 50 spatial mesh recent experimental data show that the values pomts total for all systems. For reflected sys.

given for critical dimensions and masses are quite tems. 30 mesh points were specified in the core conservative, especially for systems in the inter-regica and 20 points were included in the reflec-mediate neutron energy range (1 < H/Pu < 250).

or region. Both codes were converged in all These more recent data likewise can provide cases to within 0.1 mk.

1631 227 Nt' CLEAR APPLICAT!oNS v0L 6 APRIL 1963 371 79122000l5 4,1 C O P f

t' j

Itansen et al.

CItrrICAL PLUTONIU51 SYSTEAIS-PART I h>

Constants for the 17 fast groups (E > 0.683 eV) the HFN diffusion theory code will reproduce to a I

were averaged over a 66-group slowing down good degree of accuracy the experimentally deter-i spectrum computed using the Bi approximatica mined critical parameters of spherical, well mod-I to the Boltzmann equation. The source was erated Pu(NO ), solutions with '"Pu contents of f

defined by the 2"Pu fission spectrum. Resonance

< 5 wtQ. Indeed, the mean value of herr obtained 3

}

absorption by **Pu was computed using resonance from the multitude of spherical systems examined

[

parameters obtained from the GAM-I library was 1.000

• 0.004."

l using both the narrow resonance and narrow res-It should be noted that Richey also examined onance infinite mast approximations.

the accuracy of the DTF code for these same One thermal group was assumed (E < 0.683 systems. These calculations, however, did not eV), for which group constants were averaged reproduce the experimental data as well as did i

over a Wigner-Wilkins spectrum. A preliminary the diffusion theory calculations. The effects of I

investigation indicated that the most accurate re-using higher order Ss approximations and a j

suits would be obtained using thermal "Pu cross-higher order allowance for the anisotropic scat-2 O

section data normalized to the 0.0253 eV values tering by hydrogen were examined as a possible I

obtained from a 1962 least-squares analysis by cause of the errors associated with the DTF Sher.'

calculations. It was concluded that for well mod-This investigation consisted of comparing the erated spheres the DTF calculations were ade-effective multiplication factors computed using quately converged (within 3 mk) using the S.

various thermal and epithermal "Pu cross-sec-approximation with anisotropic scattering defined 2

tion data for two measured critical systems:

through the P approximation.

i PuOrpolystyrene' (2.2 wt% 2ePu, H/Pu = 15) and To determine if critical parameters can be i

a spherical Pu(NO3), solution system' (4.6 wt?c accurately predicted for semi-infinite cylinders

'"Pu, 32.2 g Pu/ liter). The additional data con-and for higher 8"Pu coatents in well-moderated j

sidered in this survey were those reported by systems, values of herr were computed, using the Westcott,' Drake and Dyos,' Leonard, and Sher" HFN code, for the Pu(NO ), solution critical ex-3 (the last in 1965). The effective multiplication periments reported by Smith. These solutions factors computed using these data were found to contained 13.51 wt% 2"Pu and had plutonium con-be in error by 1 to 5.4% more than were the centrations ranging c216 g Pu/ liter. The cylinders values obtained using the data which were nor-were unreflected, with diameters of 13.4 and 17.9 malized to the Sher 1962 values.

in. Computed values of k,rr ranged from 0.986 to 1.002, and were examined as a function of the CORREL. ATION OF THEORY AND axial buckling of the cylinder.

EXPERIMENT This evaluation of the data is based on the assumption that the DB' leakage correction, nec-Theoretical calculations are required to pre-essary in the one-dimensional HFN code, intro-dict the critical parameters of systems for which duces an error in the calculations. It would seem no experimental data are available. The results of appropriate, therefore, to examine the variation of these calculations will be reliable only if a wide k,rt not only as a function of the magnitude of the variety of experimental data can be reproduced DB correction, but also as a function of the frac-2 with consistency. Since computational methods are tion of the total leakage which this correction applicable primarily to idealized systems, and represents.

since criticality safety specifications are based Figure 1 shows the dependence of computed primarily on idealized systems, it is necessary to multiplication factors on the ratia of axial to total correct the experimental data so that the cleanest buckling for both these systems and those re-possible systems are represented. The theoretical ported by Bruna** (1.5 wtQ '"Pu), which have been results can be compared with these corrected analyzed by Richey.** The assumed linear nature experimental data to provide an unambiguous of the variation is most valid for small values of judgement on the validity of the computational the ratio and departs frorn linearity as the ratio techniques. If the result of these comparisons is increases. If one uses only the data for which the favorable, the calculations may be used to provide' linear relationship is apparent (B '/Bx 4 0.4, 2

4 guidance in establishing nuclear criticality safety see Fig. 1), then extrapolation, by means of a specifications.

least-squares fit, to Ba* = 0.0 yields a here of 1.0041 for the 13.51 wt% 2"Pu data, and 1.0044 Well Moderated Systems for the 1.5 wtfc '"Pu data. Each data point shown in Fir 1 represents a different Pu(NO ) solution 3

it can be seen from an examination of the re-critical experiment.

suits obtained by Richey** and by Lloyd et al.' that The values of k,tr that would be computed for 372 NUCLEAR APPLICATIONS VOL.6 APRIL 1969 1631 228 t

Hansen et al.

CRITICAL PLUTONIUM SYSTEMS-PArtT I the additional thickness of steel increases the flux

,,. r. a s

- UNatFitCitD 13.4-tN.- olau CYttNote. D.31% 240pg depression in the steel and thereby reduces the g

o y

a unstritCito u.9

=.-olaM CYtthDen.H.51% 240 u effect such that it is not representative of the P

a wann atrttCtro

.e-in.-o rau Cvtinota.t.55 28 "

l i,

thickness added.

p watte errttCito 12.s-in.-otAM CTLlhorn. t.5s 240Pu Nperiments to re-evaluate the effect of mate-5

' a 8 '"

rials extraneous to these Pu(NO ) solution sys-3 E

- x'" 5 " ""d, s,' g tems were recently performed with another j

Pu(NOA solution containing ~241 g Pu/ liter (18.4 wt9 *Pui with a free acid molarity of -4.14.

a 2 l.oo88

=

g.o,oi The e experiments utilized a water reflected slab I enuu ',

b

- trast savan'r s rir that was 5.80 in. thick and an unreflected slab j

8 8.35 in. thick. When stainless-steel plates were l

l added, they were placed diagonally across the l

5

• " "o

s. :

o. :

o. 3

o. 4

o. 5 square matrix of the support structure as shown in Fig. 2(b). The effect of these additional plates AXl At luCKLING TO TOTAL BuCKilNC n Afl0 should be more representative of the effect of the Fig. 1 Comparison of computed multiplication factors steel contained in the support structure matrix.

for cylindrical systems.

For the reflected system, the additional steel increased the critical height by 4.419

• 0.035 in.

infinite length cylinders (B4 = 0.0) are in good The critical height of the unreflected system de-agreement despite the large difference in Pu creased by 6.059 e 0.032 in. These changes in concentration. They also agree well with the critical height are equivalent to changing the crit-average k,rr (1.00

• 0.004) computed for the 4.6 ical thicknesses by +0.11510.005 in. and -0.230 wtQ

• • 'Pu, spherical, Pu(NO3) solution data. It 20.005 in. for the reflected and unreflected sys-appears, therefore, that the critical parameters tems, respectively (see Fig. 3).

of well moderated, plutonium fueled systems can An at:empt us also made to gompute the effect be accurately predicted in spherical and semi-of the additional steel by uniformly distributing infinite cylindrical geometries for systems con-the stainless steel, on a volume basis, through taining up to -20 wt% ***Pu.

the region enclosed by the support structure. The Critical parameters of semi-infinite stabs have steel support structure occupied 5.90% of the total been estimated by extrapolation from critical ex-volume contained in the 4.5-in.-thick region adja-periments performed in slab geometry using cent to the slab walls. Upon insertion of the C

Pu(NO ). solutions containing 4.6 and 23.2 wt '

additional steel, 9.759 of this volume was occu-3 o

• • Pu."'" For the reported, cican, water reflected pied. The change in critical thickness due to this slabs of Pu(NO3) solution, the HFN code computed

-65~c increase in steel us computed to be 0.104 effective multiplication factors which were high by in. for the reflected case, which compares favor-as much as 2.7%. The multiplication factors com-ably to the measured change of 0.115 in. For the puted for the reported, clean, unreflected slabs unreflected system, the change was computed to were low by -79. These results indicate that the be 0.350 in as compared to the measured change effects of the stainless steel which contains and of 0.230 in. This large error in the computed supports the Pu(NO3) solution, and the effects of effect for the unreflected system arises from the room return neutrons, have been either experi-fact that this system can not be represented as a mentally or analytically underestimated.

diffusing medium, thereby introducing a large An experimental determination of the effects of error i.nto the multigroup diffusion theory calcu-the steel tank walls and support structure has lations. The effect of the support structure for been previously reported. These results were I

used to correct the measured, critical, infinite slab thicknesses to the clean, critical. infinite aoostrosat slab thicknesses reported by Lloyd et al."'"

sta mit s s 5" " "-

The effect of the support structure was deter-Aconicsat mined by adding steel adjacent to the steel con-y{^1yt,5,5yl,

tained in the support structure (see Fig. 2(a)).

Since the addition of stainless steel in this manner does not significantly increase the probability that l's n. sf ashttss sitti surecer a neutron that escapes from the solution will im, sinuCrunt nost unn er scuant Maram pinge on the stainless steel, the effect of the added ia)

(b) thickness of steel is greatly underestimated. Also, particularly in the case of the reflected systems, Fig. 2.

Support structure matrix with additional steel.

NL' CLEAN APPLICATIONS VOL 6 APn!L 1969 373 1631 229

Ilansen et al.

CRITICAL PLUTONIU51 SYSTE3tS-PART !

room return is between -10 and 151 The average "c.n. orja.

a wait" 8tFLEcfED stA85 albedo obtained from these measurements is i,

o umstrtictro stass 0.1293 i 0.0022, or 12.93" room return. Since 36

c ~o. rm"1 these measurements do not conclusively yield a l a n "* 86'a-system-averaged value for the room return,

,",c,,,

c I

i multiplication factors were computed for the three g

I unreflected systems reported by Lloyd et al."

as a function of the percent of neutrons returned E

a.n. roia.

n re.ssia.

c y

i

/c to the exterior surface of the support structure.

c'

\\

The systems considered did not include any cor-

• * ~ " " " *

[

rections for materials extraneous to the solutions.

e These calculations yield an average room return

{

of 13% as the value necessary to obtain criticality.

5 This result agrees very well with the average 3

E measured room return of 12.93% The critical O

slab thicknesses were, therefore, computed as a function of the room return for these systems to

\\

determine the change in the critical slab thickness 23 associated with a room return of 13%

The effect of the stainless-steel tank ulls on N

the critical thickness of Pu(NO )4 solutions has 3

a been computed and measured experimentally.

5*

• 8 Good agreement has been obtained previously' etsitetto camCAL sLas THICxhtss between the Computed and measured Corrections necessary for both reflected and unreflected

s. :

a. s

s. 4

s. s

s..

a.

e. o,. i spherical systems. It ras, therefore, expected unntrtierto camcat sta: inicxhtss that these calculations would yield equally accu-Fig. 3 Stainless steel effects on Pu(NO ), slab exper-cpe ons for h slab sysums. Measure-3 ments show this to be true for the unreflected iments.

slabs, but large differences are observed for the reflected slabs. The computed effects of the tank each of the previously measured slab systems was walls for these systems are considered to be determined by computing the change in critical valid, however, since not only has agreement with thickness for that slab due to the support struc-measured values been obtained for other geome-ture, a T,ss,

This value us then converted to tries, but the critical thickness of the reflected i

the change in the critical thickness which would slabs including the surrounding materials, as well be measured for the support structure, ATHp, by as the individual effect of the support structure, assuming that the effects of the support structure have also been computed accurately. If the mea-could be computed with equal accuracy for all of sured corrections had been utilized, a maximum the critical infinite slab systems. Thus, in a change of -3% in the critical thickness of the reflected slab a THp =(0.115/0.104)a THic, while clean, infinite slabs would result.

A TRp = (0.230/0.350) a THie for the unreflected Table I lists the corrections obtained using the

systems, above techniques that are necessary to determine Further experiments were performed to mea-the critical thicknesses for clean, infinite slabs sure the fraction of those neutrons escaping from of Pu(NO )4 solution from the infinite slab data 3

an unreflected slab that are subsequently returned reported by. Lloyd et al."

which include the to the slab from external reflectors such as the surrounding materials.

hood walls, floor, and the tamper tank framework.

Table II gives the critical thicknesses of the This effect was determined by measuring the reflected and unreflected infinite slabs of Pu(NO ).

3 albedo, 3, at the exterior boundary of the support solution, including the surrounding system,"'"as structure using the technique described by Wein-well as the corrected, clean, critical, infinite slab stock and Phelps. Since the albedo is a function thicknesses. The computed slab thicknesses are of position on each face of the slab due to the also shown. The maximum difference between a location of the slab relative to extraneous reflec-computed and experimental clean, infinite slab tors, the albedo was measured at positions that thickness is 3%. The average difference between should yield the approximate maximum and mini-the measured and calculated critical thickness for mum values on each face of the slab. These the seven clean slabs examined is 0.91 measurements indicate that the system-averaged IJsing the aforementioned data as a guide, it 374 NUCLEAR APPLICATIONS VOL.6 APRIL 1969 L

163 L 230

IIansen et al.

CRITICAL PLUTONIU11 SYSTEatS-PART I TABLE I Pu(NO ). Solution Slab Tank Corrections 3

Pu(NO3) Sol.,

Pu(NO ne Sol.,

Pu(NO3)a Sol.,

Pu(NO2) Sol.,

2.34Af HNO3, 5.00M HNO3, 1.60M HNO3, 2.23M HNO3, 53 g Pu/ liter, 53 g Pa liter, 202 g Pu!! iter, 234 g Pu/ liter, 4.6 % 24 Pu (cm) 4.61 *Pu acm) 23.2"c 24o Pu (cm) 23.2% "Pu (cm)

Tank Walls, Reflected

-0.732

-0.757

-0.534

-0.512 T. ink Walls, Unreflected

+ 0.326

+ 0.33 5

+ 0.359 Support Structure, Reflected

-0.335

-0.360

-0.476

-0.512 Support Stnicture Unreflected

+ 0.832

+0.566

+0.941 Itoom Return (13 ), Unreflected

+1.05

+1.09

+1.24 TABLE II Criticality of Infinite Pu(NO3)4 Solution Slabs Water-Reflected Clean Water-Unreflected Slab Clean-Unreflected Slab Plus Reflected Plus System (cm)

Slab (cm)

System fem)

Slab (cmJ Pu(NO )4 Solution 3

Description Exptl.

Calc Exptl. l Cale ExptL Cale Exptl.

Calc 2.34 M HNO,

14.7 14.27 16.91 16.9 1 10.2 10.26 9.13 9.22 3

240 59 g Pu/ liter,4.65 Pu 5.00 M HNO3, 15.7 15.44 17.99 15.19 10.9 11.16 9.78 10.0S 58 g Pu/ liter, 4.67 24 Pu 1.60MIf NO,

18.65 17.91 21.19 20.94 12.76 12.65 11.70 11.64 3

202 g Pu/ liter, 23.'% 24opu 2.233f HNO,

3 234 g Pu/ liter, 23.27 'Pu 22.05 13.45 13.39 12.43 12.41 appears that the HFN multigroup diffusion theory at an H 'Pu atomic ratio of 15, and having *Pu code, with multigroup constants obtained from the isotopic concentrations of 2.2 and 8.080'.* These c

GAMTEC-II code, will compute the critical pa-experimental data were acquired for bare and rameters quite accurately for all clean, one-Plexiglas reflected parallelepipeds and were ex-dimensional plutonium fueled systems containing trapolated by means of buckling conversion to up to the least 300 g Pu/ liter with as much as 25 easily defined one-dimensional systems. Critical wtfo** Pu.

parameters were computed for these one-dimen-

),

sional systems using the DTF-IV multigroup undermoderated Systems transport the.- code and were found to agree fairly well with the experimentally determined Until recently, with the exception of the plu-critical parameters. This calculational method I

tonium metal experiments, no homogeneous ex-appears to slightly underestimate the critical perimental criticality data that could provide a parameters of the 2.2 wt% Pu fuel and, to a firm basis for establishing criticality safety slightly greater extent, to overestimate the crit-guidelines have been available for undermoderated ical parameters of the 8.08 wt'o Pu fuel.

systems. The data presently available are ex-The 2.2 wt5 ** Pu data have been previously tremely limited, but there are a few that can be used as a basis for deriving critical parameters used as " bench marks" for establishing the accu-of "Pu(metal)-water mixtures for bare and water 2

racy of calculational models in the undermoder-reflected systems.' Using the same technique, ated range.

critical parameters for these systems were ob-One set of recent experimental data was accu-tained from the data accumulated on the 8.08 wt?c mulated using PuO -polystyrene plastic compacts

*Pu fuel. Table III presents a comparison of 2

NL.' CLEAR APPLICATIOs VOL.6 APRIL 1969 375 1631 231 o*go gW o

o Wd

Ilansen et al.

CRITICAL PLUTONIUlf SYSTEAIS-PART I TABLEIC Critical Parameters of "Pu(metal)-Water 311xtures 2

Predicted Using the 2.2 wtc 24oPu Predicted Using the 9.08 wt9 ***Pu PuO2-Polystyrene Data Reflector PuO2-Polystyrene Data (cm)

(cm)

Infinite Slab Thickness Dare 11.66

• 0.30 Radius of Sphere Bare 11.35

• 0.25 13.81

• 0.16 Radius of Cylinder Bare 13.41

• 0.13 10.04

• 0.155 Infinite Slab Thickness Water 9.77

• 0.13 4.33 = 0.07 Radius of Sphere Water 4.13

• 0.05

{

Radius of Cylinder Water 10.17

• 0.14 10.40 s 0.17 6.54

• 0.14 6.37

• 0.13 f

• Richey* reported a value of 10.52. which recalculation has shown to be incorrect.

i, these predicted critical parameters. The system-of the PuO particles, each particle was assumed atic error introduced by the presence of the addi-2 to be a sphere of the maximum radius, 0.0075 cm.

tional ** Pu is readily app 1 rent, even though the maximum difference is only 5$ These differences The density of the particles was taken to be the could be caused by 1) the assumption that the theoretical density of PuO, 11.46 g PuO /cm'.

2 2

experimental data were obtained for homogeneous These particles were assumed to be embedded in systems when in reality the system consisted of a spherical shell of polystyrene whose density is small PuO particles admixed with polystyrene, or 1.065 g/cm* and whose radius was such that the i

2

2) from the incorrect treatment of the resonance system-averaged H/Pu atomic ratio was pre-absorption by ** Pu in a homogeneous mixture of served. Since these assumptions do not predict PuO and polystyrene.

the system-averaged fuel and moderator concen-2

'e An attempt has been made to determine if the trations, a void region was assumed to be present adjacent to the moderator shell. The assumed effect of the particulate nature of the PuO2 is sufficient to account for the disagreement noted dimensions used in the computational model for between the measured and computed critical pa-each ***Pu content fuel are given in Table IV.

I rameters reported by Richey' for PuO -poly-2 styrene mixtures. The effect of having PuO T* *

• 2 particles embedded in polystyrene, as opposed to Assumed Dimensions Used in Computational Model having a truly homogeneous PuO2-polystyrene mixture, are twofold:

outer Radius outer Radius Radius or of Polystyrene et Fuel Puon Particle Shell Void Region

1) The depression of the thermal flux in the (wt% *Pu)

(cm)

(c m)

(em) fuel particle decreases the thermal utilization factor of the material. This effect tends to make a.03 7.5 x 10-'

1.5437 x 10-'

1.5970 x 10-'

the measured critical size of a system containing 2.2

't.5 x 10-8 1.5452 x 10-'

1.5613 x 10-8 PuO particles greater than the critical size of an 2

equivalent homogeneous fuel-moderator mixture.

There is (to our knowledge) no currently avail-

2) The self-shielding of the

• • • Pu resonance able computer code that can accurately evaluate decreases the resonance integral of the mixture, the energy spectrum and, thus, the broad-group and this effect tends to make the measured crit-material cross sections in a finite system con-ical size of a system containing PuO taining multiple, small, but finite heterogenieties.

2 particles smaller than the size of an equivalent homoge.

Therefore, the shift in the energy spectrum within the particulate system from that in the corres-neous fuel-moderator mixture.

ponding homogeneous mixture could not be evalu-The magnitude of these effects increases with ated. As a result, it was necessary to assume that tne small PuO particles did not cause a the size of the particles. Unfortunately, th' par-2 ticle size distribution was not measured for either spectral shift, and the multigroup cross sections used for these expenments; computed for the homogeneous mixtures by the of the two oxideJ however, an upper limit of 0.15 mm wr 3 placed GAMTEC-II code were, therefore, used tc com-pute the spatial effects.

on the diameter of those particles.

To examine the possible magnitude of tt.2 effect The thermal flux depression within the PuO particle for each ** Pu content fuel was evaluated 2

376 St* CLEAR APPLICATIONS VoL 6 APRIL 1969 1631 232

Ilansen et al.

CRITICAL PLUTONRIM SYSTEMS-PART I using the appropriate thermal-group cross sec-the fuel bearing particles. Since the particle size tions. The thermal disadvantage factor, 4 /p distribution is not known, however, and since the g,

was computed for each of the fuel-moderator-void primary purpose of these calculations was to cells. From these values new cell-averaged ther-define the maximum error limits associated with mal-group constants were derived for each PuO2-the determination of homogeneous critical param-polystyrene mixture. The adjusted thermal-group eters from the heterogeneous experimental data, constants were lower than the homogeneous values the largest possible effect was the one consid-obtained from the GAMTEC-II code by -3.0% for cred.}

the 2.2 wt% ** Pu fuel, and by -3.5% for the 8.08 The computed effect of the maximum particle wtQ 24oPu fuel.

size is small for the 2.2 wt% ***Pu systems, and To correct for the resonance self-shielding in the corrected critical dimensions of homogeneous the particles, Wigner's rational approximation and PuO -polystyrene systems are slightly smaller the narrow resonance infinite mass approximation than the values measured. This is due to the fact were assumed valid. The resulting expression for that the primary effect was the reduction of the the resonance integral of a particle containing an thermal utilization factor. The reflected slab did admixed moderator is not follow this trend due to the spectral shift throughout the thin slab caused by the Plexiglas reflector. In this system, the resonance self-(a, + o., ) ea dE I(NRIM) *

+a, +o.,'E shieldin; was predominant. The effect of the r

e adF resonance self-shielding was also predominant for all of the systems containing 8.08 wt% ***Pu. As where the notation is that used by Lamarsh.** The a result, the corrected critical parameters are cell-averaged cross sections computed for the 2.2 larger than the values for the measured assem-and 8.08 wt% ** Pu fuels based on the above reso-blies. Table V gives an estimate of the corrected nance integral decreased from the homogeneous homogeneous results obtained by assuming that values by about 3 and 5%, respectively. This cor-the average effect of the particle size is the rection was applied only to the interval 0.683 eV 4 average of the maximum and minimum possible E5 1.86 eV, since at higher energies the mean-effects (i.e., particle radii of 0.0075 and 0.0 cm).

free-path increased rapidly and, hence, the self-The error limits specified with the estimates of shielding became negligible. (It is important to the homogenecus critical parameters incorporate note that these cross section changes overesti-both the maximum and minimum possible effects.

mate the true changes by -1% because the The computed homogeneous critical param-resonance integral calculation does not account eters given in Table V agree with the corrected for the interaction (Dancoff correction) between measured homogeneous critical parameters within TABLE V Critical Parameters of PuO -Polystyrene Systems at H/Pu = 15 2

PuO -Polystyrene PuO -Polystyrene 2

2 2.2% 2'8Pu 9.0gg anoPu b

b Experimental

• Experimental Si Cale' Experimental

• Experimental S Cale' 4

(cm)

A

.)

(cm)

Icm)

(cm)

(cm) e Arrays Infinite Slab Thickness 16.09

• 0.41 15.96

• 0.54 15.94 13.45 = 0.41 18.74 2 0.67 19.77 Radius of Sphere 19.58

• 0.22 18.44

• 0.36 15.25 21.17

• 0.21 21.44

• 0.47 21.33 Radius of Infinite Cyl.

13.64

• 0.21 13.53

• 0.32 12.34 15.53 = 0.21 15.79

• 0.41 15.63 Plexiglas Reflected Arrays Infinite Slab Thickness 5.99

• 0.10 6.03

• 0.14 6.20 7.3520.09 7.53

• 0.29

9. N Radius of Sphere 13.54 = 1.22 13.52

• 0.24 13.47 15.64 e 0.21 15.39

• 0.45 15.90 Radius of Infinite Cyl.

8.59

• 0.19 9.59 0.19 5.53 10.04 z 0.21 10.22

• 0.39 10.24

' Values derived from experimental data.'

bValues derived from experimental data and corrected to homogeneous systems.

' Values calculated for homogeneous systems.

NUCLEAR APPLICATIONS VOL.6 APRIL 1969 377

Itansen et al.

CRITICAL PLUTONIUM SYSTEMS-PAftT I the true uncertainty of the presently available ex-gm perimental data. Using these corrected critical ;

parameters to predict the critical parameters of

=

3Pu(metal)-water mixtures (as was done using 5 the experimental data to obtain the values given ;

in Table III), the agreement between values ob-

• O tained from the 2.2 and 8.08 wt% '"Pu data is 5 l

l

'l significantly improved. Furthermore, the values obtained using these data agree with the values i

previously reported by Richey,' obtained using the s, l

j 2.2 wt% **Pu data, to within 0.06 cm.

i Critical experiments have also been performed I with PuO -polystyrene plastic compacts at an [ n 2

H/Pu atomic ratio of 5 and an isotopic '"Pu con-E centration of 11.46%. Critical dimensions for {

clean, one-dimensional systems derived from i

s to o

these data *' are shown in Table VI along with the corresponding multiplication factors computed by unstne os raerectes <= :nosisi the DTF-IV multigroup transport theory code.

Fig. 4 PuO particle size analysis.

TABLE VI puted as a function of the order of the Ss approxi-Critical Parameters of Puor. Polystyrene Systems at II/Pu = 5 mation to determine if the space-angle mesh assumed in the calculations was adequate to define Critical D ension S. Computed the thin, undermoderated, reflected infinite slab.

These calculations were also made fcr the re-inftatte stab Bare 16.83. o.31 1.0128 flected infinite slab data reported at an H/Pu ratio Thickness of 15. since this same error, to a lesser degree, Radius of Sphere Bare 19.68 a 0.23 1.0198 was also observed for those systems (Table V).

Radius of Infinite Bare 14.40 a 0.22 1.0235 crunder The results of these calculations are given in Table VII. As can be seen, the Se approximation Infinite Stab Plexiglas 5.98 a 0.10 0.9635 is sufficiently accurate for most purposes. The Th """*

primary source of error, therefore, is probably Radius of Sphere Plexiglas 14.15 : 0.37 0.9997 the fact that the cross sections used for the Radius of Inflatte Plexiglas 8.93 a 0.36 0.9998 puO -polystyrene region were averaged over a C ""d" Y

2 spectrum characteristic of the PuO2-polystyrene mixture. The true spectrum, however, is signi-The particle size distribution was measured ficantly more thermal due to the moderation of for the PuO used for these experiments. The neutrons in the Plexiglas reflector. This would 2

average particle size was found to be 0.0089 mm, also account for the fact that the magnitude of the with 99% of the particles having a diameter of error introduced appears to be a function of the 2"Pu content of the fuel.

< 0.02 mm (see Fig. 4). This is much smaller than the maximum particle diameter of 0.15 mm i

found in the H/Pu = 15 systems. Furthermore, m

I the neutron enerEY spectrum in the H/Pu = 5 C mputed Muluphcanon Fadors for Plutglas Beneced assemblies is much harder than the one in the infinite Stabs as a Funetton of the H/Pu = 15 assemblies. These circumstances re-order of the S. Approximauon duce the probability of neutrons interacting with Ir the fuel particles. As a result, no corrections s.

si.

Thickness computed computed

{

were made for the effects of the PuO particles 2

Fuel (cm) 4.n 4.n in the H/Pu = 5 systems.

{

For the reflected infinite slab, the particle size puo, poiy,,yr,n, i

n/Pu = 15 2.2 wt% '"Pu 5.99*

0.9895 0.9873 I

effects may account in part for the observed 3.6%

puo,.poiystyrene discrepancy in the computed multiplication factor, if/Pu = 15. s.08.t% "'Pu 7.38*

0.9753 0.9732 since for this system some neutrons will be mod-P60s. Polystyrene erated in the reflector and returned to the fuel-H/Pu = 5.11.46 wt% "*Pu 5.98*

0.9635 0.9632 bearing region at resonance energies. Since these

' Thickness reported by Richey et al.'

effects would be small, values of k fr were com-

• Thickness reported by Bierman et al.

378 NL' CLEAR APPLICATIONS VoI-6 APRIL 1969

?

.D I

1631 234

Ilansen et at CRITICAL PLUTONIUM SYSTEMS-PART I The error in the computed multiplication fac-Tnis work was performed under Contract No. AT(15-tors for unreflected systems represents a dis-1)-1530 between the U.S. Atomic Energy Commission and Battelle Memorial Institute. Permission to publish crepancy of -2% between the measured critical dimensions and the values that would be computed.

is grata:uny acknawledged.

For example, in the unreflected sphere the differ-ence between the lower limit of the experimentally determined radius and the computed value is only REFERENCES

-0.15 cm. The reflected sphere and infinite cylin-der calculations are in excellent agreement.

g l

The critical mass of a water reflected *"Pu 1.

H. C. PAXTCN, J. T. THOMAS, A. D. CALLlHAN, i

sphere has been rec, ntly reevaluated." The me:'-

and E. B. JOHN 5ON, " Critical Dimensions of Systems

!l sured critical mass of 5.43 kg agrees quite well Comaining 22' t 2" Pu, and U," Technical Note No.

232 with the value cor.puted using the DTF-IV code, TID ~005, Div. of Tech. Info. Extens., U.S. Atomic Energy Commission (June 1964).

5.21 kg.

2. J. R. LILLEY, " Computer Code HFN-Multigroup, CONCLUSICNS Multiregion Neutron Diffuston Theory in One Space Dimensica," H W-71545, General Electric Company, Richland, Washington November 1961).

For well moderated plutonium-fueled systems there are sufficient experimental data to establish

3. K. D. LATHRCP, "DTF-IV-A FORTRAN-IV Pro-the accuracy of the HFN multigroup diffusion gram for Solt:ng the Multigroup Transport Equation theory code when utilizing multigroup constants with Anisotrop;c Scattering," LA-3373, Los Alamos obtained from the GAMTEC-H code. These calcu-Scientific Laboratory (July 1965).

lations are quite accurate for all geometries and for all systems whose isotopic 2"Pu ccattnt is 4.

L. L. CARTER, C. R. RICHEY, and C. E. HUGHEY, "GAMTEC-U: A Code for Generating Consistent Multi-s 25C'o Ze usi n an ansPort

"*""5 For undermoderated systems there are still Theory Calculat::ns,,, BN%L-3a, Pacific Northwest very few experimental data on clean, homogeneous Laboratory tMarch 1965).

systems. The available data, however, do indicate that the critical parameters of reflected homoge-

5. R. 5HER and J.

FELBERBAUM, "Least Squares neous systems with isotopic 2"Pu contents of Analysis cf 2200 nUsec Parameters of ssU,838U, and 2

c 12Tc can be computed reasonably well using the 2"Pu," BNL-722. Broo: haven National Laboratory (1962).

DTF transport theory code for all geometric con-

6. C. R. RICHEY, J. D. WHITE, E. D. CLAYTON, and figurations except reflected slabs. The reflected R. C. LLOYD, " Criticality of Homogeneous Plutonium slabs cannot be computed accurately using this Oxide-F.astic Ccmpacts at H:Pu = 15," NucL Sci. Eng.,

technique due to the spectral shift which is not 23,150 October 1365),

t accounted for when averaging the energy-depen-dent cross sections by means of the GAMTEC-H 7

R. C. LLOYD C. R. RICHEY, E. D. CLAYTON, and code. For unreflected systems the critical dimen.

D. R. SKEEN, " Criticality 5tudies with Plutonium Solu-sions computed for all geometric configurations tions " Nucl. Sci. Eng., 25, 165 (1966).

deviate from the measured values by no more

8. C, H. %E5TCOTT and D. A, ROY, "Effectiva Cross than the established experimental uncertatntles Section Values. r Well-Moderated Thermal Reactor increased by I?c of the critical dimension. It is Spe:tra," CRFP-H2, Chalk River Nuclear Laboratories important to note, however, that larger differ-(1953).

I ences do exist between the computed critical parameters and those that were measured di-

9. M. K. DRAKE and M. W. DYOS, "A Compilation and rectly. These differences occur in the resonance Evaluaticn cf the Nuclear Data Available ice the Ma2or energy region, notably at H/Pu = 15. The cause Plutonium Isotcpes," GA-6576 General Atomic Divi-si n General Dpamics Corp. (1965).

of these differences can be defined precisely only through the accumulation and analysis of 10 B. R. LEONARD, Jr., " Survey of the Status of Low additional experimental data acquired under very Energc Cross secticas of Fissile Nuclides," Neutron carefully controlled conditions.

Phys. Proc. Sy n:p. held at Rennselaer Polytechnic In-stitute. May 1961 Academic Press, New York. N.Y.

(1962).

ACKNOWLEDGMENTS

11. R. SHER and J. FELBERBAUM, "Least Squares The authors wish to express their appreciation to Analysis of the 2200 m/see Parameters of U8 38, U23s, Mrs. Donna Andersen for her assistance in the ccm-and Pu239," BNL-316 Brcokhaven National Laboratory pilation of this manuscript.

(1965).

NUCLEAR APPLICATIONS Vol.6 APRIL 1969 379 1631 235

?& W, Ym 6

Hansen et al.

CRITICAL PLUTO)iU51 SYSTEMS-PART I

12. C. R. RICl!EY, " Theoretical Analyses of Ilomo-17 R. C. LLOYD, E. D. CLAYTON, and L. E. HANSEN, geneous Plutonium Critical Experiments," Nucl. Sci.

" Basic Criticality Experiments with Plutonium Nitrate Eng., 31, 32 (1968).

Solutions in Slab Geometry," BN%L-472, Pacific North-west Laboratory, p. 5.1 (Caober 1967).

13. J. C. SMITil, " Critical Parameters of Plutonium-R E. l' WEINSTOCK and J. P. PHELPS, "A Simple Hydrogen Systems-Some Experimental Measurements, Detector for the Lieast.rement of Room-Scattered Neu-H.S. R.C./C.S.C./ P.30 UKAEA-The Reactor G rou p, trons." Nucl. Sci. Eng., 18, 525 0 964).

Dounreay, Caithnesa (September 1964).

19. G. A. JARVIS, G. A. LINENBERGER, J. D. ORN-

14. J.

BRUNA J. P. BRUNET, R. CAISERGUES, C.

DOFP, a: d H. C. PAXTON, "Two Plutonium Metal CLOUET D'ORVAL. J. K. KREMSER, J. LECLERC, Critical Assemblies," Nucl. Sci. Eng., 8, 525 (1960),

and P. VERRIERE, " Criticality Experiments on Plu-tonium Solution, Experimental Results," CEA-2274,

20. J. R. LAMARSH, " Heterogeneous Reactors " In-Commissariat i l'Energie Atomique, Centre d' Etudes froduction to Nuclear Reactor Theory, p. 370, Addison-Nucleaires, Saclay (1963).

Wesley Publishing Company, Inc., Reading. 51assa-chusetts (1966).

15. R. C. LLOYD, E. D. CLAYTON, and L. E. HANSEN*

21. S. R. BIERMAN, L. E. HANSEN, R. C. LLOYD, and

" Criticality of Plutonium Nitrate Solutions in Slab E.

I'. CLAYTON, " Critical Experiments with Homo-Geometry," Trans. Am. Nucl. Soc., 11, 331 (196S).

PuO -Polystyrene at 5 H/Pu," Trans. Am.

g..eous 2

Nucl. Soc.,11, 350 i1968); Nucl. Appl., 6, 23 (1969).

16. R. C. LLOYD. E. D. CLAYTON, L. E. HANSEN, and C. A. ROGERS, " Basic Criticality Experiments with

22. M. U. GEER and D. R. SMIT!!, " Measurement of Plutonium Nitrate Solutions in Slab Geometry," BN%L-the Critical Mass of a Water-Reflected Plutonium 775, p. 5.1, Pacific Northwest Laboratory (July 1968).

Sphere," Trans. Am. Nucl. Soc., 11, 378 (1968).

1631 236 1

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380 Nt*CLEAll APPUCATIONS VO L. 6 APRIL 1969 i