Chapter V

CRITICALITY SAFETY INPROCESSING PLANTS

A. Plant Features with Criticality Potential

Processing plants contain a multiplicity of work stations, and areas for both long-term andshort-term storage. Criticality safety considerations go beyond the analysis of each of thesein terms of subcritical individual units or storage arrays. The progression of fissile materialthrough a plant involves transfers and special handling during which unusual conditionsmay be encountered. It is important that these operations be governed by procedures andbe carried out by well-trained personnel.

Consider a plant for processing highly enriched uranium as solids, such as fabrication ofweapon components or fuel elements for reactors. It is essential to avoid the effect ofmassive fissile units falling together or encountering other units as the result of an accidentwith transfer equipment. Minimum spacing between units can be maintained by the use ofbirdcages, provided there are appropriate procedures for loading and unloading them.

In a plant for scrap recovery or processing irradiated fuel, the operations involving fissilesolutions must be carefully planned. It is noteworthy that all criticality accidents thathave occurred in processing plants have involved solutions. Mishaps that have led to theseaccidents include solution leakage, precipitation, dissolution of solids, instrument failure,and transfer among vessels. Avoidance of these mishaps calls for continued cooperation ofcriticality safety and operating personnel.

In general, both physical and administrative criticality safety practices must be tailoredto specific plant conditions. This requirement inevitably will require judgment. Specialevaluation also may be required because there is no “standard” plant for which universalcriticality safety recipes can be defined.

97

B. Administration

Provisions of Standard ANSI/ANS-8.19, Administrative Practices for Nuclear CriticalitySafeiy, are of major significance in processing plants. This Standard recognizes thatcriticality safety requirements must contribute to the physical and economic functions of aplant in a balanced manner. Accordingly, it places no requirement on the form of plantorganization. Instead, requirements of the Standard are expressed in terms of management,operational supervisors, and a criticality safety staff provided by management.

The Standard emphasizes that effective criticality control, like other branches of safety,requires the positive support of management and implementation by supemisors withassistance of the criticality safety staff. It identifies associated respcmsibilities, calls foreffective training of personnel and concise operating procedures, and has sections on processevaluation, material control, and planned response to criticality accidents.

c. Training

The training program for persons involved in operations with fissile material should maliesafety considerations, including criticality safety, an integral part of a program that providesnecessary job skills. Standard ANS1\ANS-8.20, NucZearCriticality Safety Training,appliesto personnel associated with operations where there is the potential for a criticality accident.Provisions of the Standard are consistent with the precept that safety education will bemost meaningful and readily assimilated if it is clearly relevant to operations. It followsthat local supervision should participate in criticality safety training, or conduct it withthe support of criticality safety specialists. Appropriate training of supervisory personnel isimplied.

The Standard calls for training in the recognition of criticality alarms and the properresponse to them. Training should be supported by discussion of selected criticalityaccidents. Stratton)s history of nuclear accidents30 describes each in sufficient detail to behelpful for this purpose. Accounts of real accident experience in training talks can helpkeep the audience awake.

D. Criticality Alarms and Response

Criticality alarms have twice initiated lifesaving evacuation of areas in which accidentsoccurred.30 The value of such systems is therefore clear in areas for processing significantamounts of fissile material. Guidance for the design, installation, and maintenance ofsuch systems may be obtained from Standard ANSI\ANS-8.3, Criticality Accident AlarmSystem. This document directs that an accident alarm system must be considered for any

98

DI

area containing more than a threshold quantity of fissile material. The Standard calls foran easily recognized signal for immediate evacuation in case of an alarm. It recommendsthat the response of the alarm system to radiation be tested at least monthly, each signalgenerator be tested at least once every three months, and an evacuation drill be performedat least annually.

The existence of an alarm system carries with it certain responsibilities. The system mustbe maintained to provide confidence that it will function if needed, and to minimize thefrequency of false alarms. False alarms can have a negative impact on safety by creating apotential for injury as a result of precipitous response. False alarms also tend to destroyconfidence in the system. Unannounced drills are not endorsed.

The response to an alarm is to be governed by an emergency plan with elements given inthe administrative Standard ANS1\ANS-8.19. Further features of an emergency plan arebeing considered.

Elements of the emergency plan include procedures for evacuation to specified assemblystations, actions after assembly, and treatment of injured and exposed persons in accordancewith advance arrangements.

Personnel must be trained in their proper response to the alarm including the use of.evacuation routes and designated assembly points. Emergency plans must be kept current;evolution of a plant can influence the procedures to be followed in the event of an alarm.

E. Material Control

One criticality accident occurred because a concentrated fissile solution in a polyethylenecylinder was mistaken for a dilute solution.30 This occurrence emphasizes the value oflabeling or other positive identification of fissil-ematerial in helping to avoid routing errorswithin a plant. Also of value are posted limits at work stations and storage areas. Ifobserved, for example, in the transfer of material along a glove-box line, posted limits canprevent inadvertent overloading of a box.

Labeling and posted limits cannot take the place of up-to-date procedures used by well-trained personnel, but should make errors less likely. Computerized accounting procedures,such as proposed for safeguards, should contribute further to the reduction of transfererrors.

Provisions for handling fissile material during inventories must be as carefully planned asfor regular plant operation. This need is emphasized by the three criticality accidents thatresulted from misdirection of solutions during inventory.30

99

An occasional requirement that should be anticipated is the emergency storage of fissilematerial that can accumulate as the result of interruptions of normal operations. Mishapssuch as faulty processing or equipment failure may interrupt the flow of solutions, andaccidents or other disruptions may prevent material from leaving the plant.

In a plant layout, the convenience of proper operations should be considered. To be avoided,for example, is transfer of material through a working area when another convenient route isavailable, and unnecessary processing of different fissionable materials in the same area. Toillustrate, use of the same furnace for casting enriched and natural uranium, except duringindependent campaigns, could contribute to the confusion of feed items. An example ofmaking mishaps inconvenient is to transfer fissile material on a single plane, as with specialcarts. Transfer by crane over other fissile material would be objectionable.

F. Process Startup

Before initial operation of a plant, or of a module that is new or revised, confirmationof the proper condition of its components is mandatory. Confirmation includes testingof instrumentation, valves, seals, transfer devices, and ventilation and fire-protectionequipment. At this point, adequacy of training should be established.26

It is also important to reassess criticality safety before startup. The initial assessment canbe influenced by evolutionary changes during construction. Even though the effect .of eachchange has been considered, the as-constructed configuration should be examined.

At this stage, it is appropriate to reconsider matters of judgment about the adequacyof the experimental basis for evaluating the criticality safety of operation. Judgment isinvolved in decisions concerning the appropriateness of directly applicable experiments,of experiments used for va~dating calculations, or of additional safety margins-appliedwhen validation is questionable. Any doubt usually can be resolved by means of neutron-multiplication measurements as outlined in Standard ANS1\ANi9-8.6~Safety in Co’’~ducting

,,,,

Subcritical Neutron-Multiplication Measurements in Situ. These measurements, conductedduring stepwise introduction of fissile material, would identify safely subcritical conditions.In general, they would simply provide reassurance that normal operation is acceptable.They must not cause personnel to relax concerning accident potential.

100

9

I

9

G. Maintaining Safety Provisions

During plant operation, continuous observation and periodic surveys are means of guardingagainst adverse effects of evolutionary change in conditions or practices. Has a vessel thatcould contain more than a critical volume been brought into a process..area? Has equipmentfor fissile material been used for other material? Should features of fire protection bereviewed because of changed plant content? Have precautions against the consequences ofnatural disasters such as earthquake, flood, or tornado been relaxed over time? The list ofquestions does not stop here. In fact, it depends on detailed plant features, regulations, andthe policy of plant management. Thus, the wish for a universal check list would be futile.

H. Examples of Plant Application

1. Dissolver for Water-Reactor Fuel

The safe geometry of a 100-liter dissolver for chopped U(3.2)OZ fuel elements is to beexplored. The shape of the dissolver should be simple and it is to be surrounded by a steamjacket. Full water reflection should be assumed to allow for water in the steam jacket andfor incidental reflection.

Table 9 shows a limiting value of 26.4 cm for the subcritical diameter of a long cylinder ofheterogeneous oxide.86 This value is essentially the inside diameter of 10-inch Schedule-5Spipe. The diameter limit for solution is significantly greater. Because a cylinder of thisdiameter has a capacity of 55 liters per meter of length, the height of a 100-liter dissolverwould be about 1.8 m. A design study will show whether this height meets functionalrequirements.

Should this long, small diameter prove to be undesirable, an alternative would be anannular tank surrounding a neutron-absorbing material to reduce neutron exchange withinthe configuration. If the absorbing material is water and the inside diameter is at least30 cm, the annular thickness can be approximated by a reflected infinite slab specified inTable 9 to be 12.6-cm thick. If additional conservatism is desired, a thickness of 10 cmand an inside diameter of 40 cm may be assumed for the design study, the capacity ofwhich is about 157 liters per meter. Accordingly, a vessel of 100-liter capacity would havenear-equilateral external dimensions. Before adoption, the acceptability of the final designshould be confirmed either by a validated calculation or by in situ neutron-multiplicationmeaimrements.2g

9

Of course, this dissolver encompasses more than the simple container. In the first place, toaccommodate irradiated fuel, it must be one component of a shielded fuel-handling system.The container must be modified for introduction of the chopped fuel, draining solution,and withdrawal of residual solids. Sparging to facilitate uniform dissolution also may prove

101

desirable. The ultimate criticality safety evaluation must take into account auxiliaries andinteraction with other components.

Further, there may be special requirements for campaigning fuels from different sources,for instance, the fuel up to 4 wt% ZS5Uin tile following example of plant application. If

the possibility of handling fuel at somewhat more than 3.2 wt% 235Ucan be foreseen, itshould be more effective to plan for it at this stage than to adapt to it later. Actually, the“conservative” annular thickness of 10 cm may prove to be suitable for fuel enrichments ofnearly 5 wt$lo235U. ..-

2. Storage of Low-Enriched Uranium Solution

Consider vessels for storing a variety of uranium solutions in which the 235Uenrichment willnot exceed 4 wt?loand the uranium density will remain below 750 g/L. A total capacity of1890 liters (500 gal) is desired, and, because of the possibility of long-term storage and thedifficulty of internal inspection, a single vessel packed with Raschig rings is not selected.The preferred arrangement is a planar bank of cylinders near a 12-m-long, 5-m-high concretewall, with a narrow walkway between the cylinders and wall.

According to Table 8, the subcritical limit on cylinder diameter for U(4) solution is 30 cm;the next smaller commercial pipe size is 10-inch Schedule-5S (26.6-cm-i.d.). At a usableheight of 4.6 m, the capacity per cylinder is 250 liters and 8 cylinders would be required.Construction and operational convenience would be met by a one-meter center spacing ofcylinders and would result in additional space at the ends of the bank of cylinders.

A walkway of 0.7 m separates the cylinders from the concrete wall and reduces the effect ofthe wall to that of incidental reflection on each vessel. Because the 30-cm diameter limitis based on full water reflection, which is much more effective than incidental reflection,it is necessary to show that the effect of interaction among the cylinders is acceptable.According to validated KENO calculations,147k.ff = 0.725 for a single cylinder having only2.5-cm-thick water reflection, and k,ff = 0.785 for the linear array spaced from the concretewall, showing that interaction is adequately small. Thus, it is appropriate to proceed withthe design of this arrangement and with detailed exploration of contingencies:

The low values of k,ff suggest the reasonableness of further investigation of a storagebank with significantly increased capacity. For example, a one-dimensional calculation ofa 12-inch Schedule-5S pipe (31.5-cm-i. d.) instead of the 26.6-cm pipe resulted in a keffof 0.9. The capacity of 8 cylinders at the 4.6 m height would be increased to 750 gallons.Of course, a careful computational study and analysis of contingencies would be requiredbefore adopting this approach.

102

3. Solution in Tanks Packed with Boron-Containing RaschigRings

In certain cases, as noted before, an alternative to geometrically subcritical tanks forsolution storage is the use of large capacity tanks packed with borosilicate-glass Raschigrings. Typically, although one-quarter to one-third of the tank volume is sacrificed to theglass absorber, the tank may still accommodate large volumes of solution more efficientlythan long, limited-diameter cylinders or thin slab-like containers. Other than for primarycriticality control, Raschig rings in auxiliary tanks may protect against accidental criticalityresulting from inadvertent diversion of fissile solution to those tanks.

American National Standard Use of Borosilicaie-Glass Raschig Rings as a Neutron Absorberin Solutions of FissiZeMaterial, ANSI\ANS-8.5, definesappropriate conditions for criticalitycontrol. Restrictions exclude the use of alkaline solutions, HF, and hot, concentratedH3POq. Temperature and radiation fields also are limited. The Standard defines chemicaland physical properties that are typified by Pyrex type 7740 and Kimbal type KG-33 andlimits the ring size to 3.81-cm-o.d. It specifies packing conditions and gives requirementsfor inspection and maintenance. Finally, maximum densities of fissile material in vessels ofunlimited size are specified for three different volume percentages of glass. Typically, as theglass volume fraction ranges from 0.24 to 0.32~density limits range from 150 to 200 g/L for233U,from 270 to 4’00 g/L for 235U-enriched uranium, from 115 to 180 g Pu/L for 239Pu,and from 140 to 220 g Pu/L for plutonium containing more than 5 wt~o 240Pu.

Although it is unlikely that these reasonably generous limits would restrict a practicalprocess, there could be unusual circumstances that would require greater glass fractions.Because computational models cannot closely approximate randomly packed Raschigrings,148 the preferred guidance for increased limits would be experimental data nearthe desired conditions or computational results verified by in situ neutron multiplicationmeasuremerits.29 An example of an experimental system that is subcritical at a plutoniumdensity greater than that permitted by the Standard is reported by Lloyd, Bierman, andClayton.137 The subcritical density of plutonium (8.3 wt% 240Pu) in nitrate solution was391 g/L when a 61-cm-diameter tank was filled to a depth of 99.1 cm. Raschig ringscontaining 4.0 wt~o boron occupied 18.870 of the volume, and there was an effectivelyinfinite water reflector on the tank walls and base.

Nurrni149reports the use of borosilicate-glass rings with enriched uranium solutions thathave free fluoride-ion contents greatly exceeding the limit specified in the Standard. Becauseof this deviation, there is daily visual inspection and semiannual emptying of tanks fordetailed examination. This is a more stringent maintenance schedule than that required bythe Standard.

Another approach to environments that are hostile to borosilicate glass is suggested byexperiments at Battelle Pacific Northwest Laboratories137 with plutonium solutions ina tank packed with stainless steel Raschig rings containing 1.0 wtYo boron. A 45.7-cm-diameter tank, water reflected on sides and bottom, was packed with 1.27-cm-o.d.,

103

I

1.Z7-cm-long steel rings occupying 27.070of the volume. At a depth of 99.1 cm, plutonium(8.3 wt% XOPU)solutions at densities of 275 g Pu/L with 480 g No3/L and of 412 g Pu/Lwith 602 g N03/L were subcritical.

A further example includes data on plutonium-uranium nitrate mixtures in a 61-cm-diameter tank, water reflected on the sides and bottom and packed with glass Raschig ringscontaining 4 wt~o boron.137–138The rings, which were 3.81-cm-o.d. and 4.32 cm in length,displaced 18.8?loof the solution volume. At a depth of 90.4 cm, solution at a density of180 g U/L (0.66 wt% ZSSUin u) and 78.4 g Pu/L (5.7 wt% 240Puin Pu) containing 377 g

N03/L was subcritical.

4. Solution Holdup Design

A cell in a U(93.2) reprocessing facility has a concrete floor area of 9 m2 and analyses haveshown that the neutron interaction between the process vessels and between the vessels andthe floor is negligible. The floor with sidewalls will serve as a catch basin for solutions thatmay leak from the vessels. An overflow line is to be installed in the floor, draining to apoisoned catch tank, thereby limiting the thickness of solution. The maximum expected235u density in UOZ(N03)2 is 25o g/L. A permitted solution height over the floor is to

be determined. The configuration of the solution is conservatively approximated by anefl?ectivelyinfinite uniform slab with a thick concrete reflector on one side and incidentalreflection on the other side.

From Table 1, the specified subcritical thickness of an infinite slab of U02(N03)2 reflectedby 30-cm-thick water is 4.9 cm. A thick water reflector on both surfaces is expected tobe more effective than concrete reflection on one and incidental reflection on the other.It follows that the specified height of the overflow pipe should not exceed 4.9 cm. Thechosen height should be measured from the lowest portion of the floor as established by anelevation survey.

104

APPENDIX

This Appendix provides a description of the calculational study leading to the curvespresented in Figures 2 through 13 of this document. The motivation for this study was toprovide quantitative examples illustrating the relationship between system reactivity (k,fi)and system geometry. Inferential in these curves are the partial derivatives of geometricalsize ($) versus k.ff. Figures from report LA-108t50-M5’, Critical Dimensions of Systemscontaining ’235u, 23~Pu,U-rid233””u,lg86 Revision;”were adapted to provide a basis for the

illustration. This adaptation appears directly in Figures 2 through 13. The adaptationbrings forward results from LA-1086o-MS for experimentally determined critical systems.These data provide a reference to interpret the curves. The three well-established fissileDuclides ZSSU,~ss~, and Zsgpuwere selected for the co-nstructionof the exam-pies.The 235U

was taken to be present as U(93.2). System compositions were taken to be metal-watermixtures and were selected to systematically span the entire range from limiting criticalfissile density (7 to ’13 grams per liter in water) to pure metal density (approximately20 ~ilograms per liter). For these systems, the neutron spectrum varies systematically froma thermalized distribution for dilute fissile densities to a slightly softened fission spectrumfor the pure metal systems. Three system geometries were selected to complete the setof examples: spherical, infinite circular cylinder, and infinite planar slab. In each case,the fissile-bearing region is surrounded by a tight-fitting pure.water reflector of effectivelyinfinite thickness. These are classic geometries which occur repeatedly in the literature ofcriticality safety. The first documented occurrence of these geometries and the associatedcharacteristic curves, known to the editors, is found in the report (2~-400,Chain Reactionof Pure Fissionable”Mat;rials in Solution.150

The metal-water systems used in the examples have no direct experimental analog. Uraniummetal and plutonium metal are not, in a chemical sense, soluble in water. However, themetal-water mixtures are neutronically approached in an asymptotic sense for dilute fissilesystems. 111such systems the atomic ratio of the hydrogen to the fissile atomic species isvery high (above 1000). In these systems, the other nuclear species needed for a chemicalsolution, such as nitrogen and fluorine, are also very dilute and have a minimum perturbingeffect. Hence, these dilute systems approach the idealized metal-water mixture. Overthe remaining range, however, the chemical constituents, such as nitrogen and fluorine,represent a serious perturbation from the idealized metal-water mixture. Hence, anycomparison between calculational and experimental results requires a careful and accuratedetermination of the impact of the presence of these other nuclear species.

Caution should be exercised in the application of the curves presented in Figures 2through 13. First, the reader should recognize that the curves represent calculationalresults. Second, the reader should note that these calculations do not conform tocurrent validation and verification criteria. No attempt has been made to document arigorous compliance with such criteria. That is, software and platform verification andthe comparison of calculational results with experimental results have not been carriedout as described in Chapter I, Section B-4 of this document, The Role of Calculational -

105

Validation. Instead,we complywiththe traditionalcriteriafor reportingscientificresultsby providingsufficientdetailto allowfor independentreproducibilityand confirmationofresults.

The valueof k,fiwascalculatedfora specificnuclidetype,density,andsystemdimension(r).The dimension x corresponds to a spherical diameter, an infinite cylinder diameter, or aninfinite slab thickness. For each nuclide type, density, and system geometry, four to fivevalues of r were selected which resulted in calculated k.ff’s in the range 0.5 to -1.2. Inaddition the value of km for an infinite metal-water mixture was calculated. To determinethe value of x for a particular value of k,ff, the appropriate set of calculational results werefitted to a continuous curve having the following algebraic form.

In the above expression a, ~, and y are fitting parameters. This form provides amonotonically increasing k,ff versus r which asymptotically approaches km for large xThe curves shown in Figures 2 through 13 were generated by fitting a spline throughthe calculated values of x for each selected fissile density. The calculational results wereproduced using the MCNP Monte Carlo code (see Ref. 13). The cross-sections werebased on ENDF/B-V cross-section evaluations provided by the XTM group at Los Alamos.Specifically, the MCNP nucli.deidentifiers (ZAIDS) shown in Table 16 were used.

Table 16

Nuclides, Cross-Section Evaluations, and AtomicWeights Used for Calculational Results

106

Nuclide

IH

160

233u

235u

238u

239pu

Avogac

ZAID

1001.5OC

8016.50c

92233.50c

92235.50c

92238.50c

9~239.55c

)’s number(atoms/b-cm)

Atomic Weight

1.00782475

15.994914,80

233.03962900

235.04392497

238.05078549

23!3.05215781

0.602204345

9B The lwtr.Olt version of the S(a,fl) scattering model was used for the water in the

metal-water mixture and for the water in the reflector.

Table 17 gives values of the mass densities assumed for water and for the metal state of eachnuclide. Table 18 gives the number densities of hydrogen and oxygen used for the 15.2-cm

9water reflector. Tables 19 through 21 give the number densities calculated for 22 selectedfissile mass densities for the three fissile nuclides ZSSU,ZSSU,and 239PU.Finally, Tables 22

through 24 list the final calculated geometrical dimensions (x values) used to produce thecurves shown in Figures 2 through 13.

Table 17

Mass Densities Assumed forWater and Fissile Metal

Mass DensityMaterial (g/cm3)

Water 0.997801

233UMetal 18.05

235UMetal(93.2 Wt% 23’U) 18.76

II 239PuMetal I 19.74

Table 18

Calculated Number Densities forthe 15.2 cm Water Reflector

NumberDensityNuclide (atoms/b-cm)

IH 0.066725294

160 0.033362647

.

107

108

Table 19

Fissile Mass Densities and Calculated NumberDensities for 233UMetal-Water Mixtures

233u

MassDensity(kg/L)

0.0050.0060.0070.0080.0090.0100.0110.0120.0130.0140.0200.0300.0500.1000.2000.5001.0002.0005.000

10.00014.00018.050

Number Densitv (atoms

233u

.000012921

.000015505

.000018089

.000020673

.000023257

.000025841

.000028425

.000031010

.000033594

.000036178

.000051683

.000077524

.000129206

.000258413

.000516826

.001292064

.002584128

.005168257

.012920642

.025841285

.036177799

.046643517

“\

1~

.066706810

.066703114

.066699417

.066695720

.066692024

.066688327

.066684630

.066680934

.066677237

.066673540

.066651360

.066614393

.066540459

.066355625

.065985955

.064876948

.063028602

.059331909

.04.8241833

.029758372

.014971603

.000000004

160

.033353405

.033351557

.033349709

.033347860

.033346012

.033344163

.033342315

.033340467

.033338618

.033336770

.033325680

.033307197

.033270230

.033177812

.032992978

.032438474

.031514301

.029665955

.024120916

.014879186

.007485802

.000000002

Table 20

I?issileMass Densities and Calculated NumberDensities for U(93.2) Metal-Water Mixtures

235u

Mass Number Density (atoms/barn-cm)Density(l{g/L) 235u 238u IH 160

0.005 .000012810 .000000923 .066706212 .0333531060.006 .000015373 .000001107 .066702396 .0333511980.007 .000017935 .000001292 .066698580 .0333492900.008 .000020497 .000001477 .066694764 .0333473820.009 .000023059 .000001661 .066690947 .0333454740.010 .000025621 .000001846 .066687131 .0333435650.011 .000028183 .000002030 .066683315 .0333416570.012 .000030745 .000002215 .066679498. .03.33397490.013 .000033307 .000002399 .066675682 .0333378410.014 .000035869 .000002584 .066671866 .0333359330.020 .000051242’ .000003691 .066648968 .0333244840.030 .000076863 .000005537 .066610805 .0333054030.050 .000128105 .000009229 .066534479 .0332672400.100 .000256209 .000018457 .066343665 .0331718320.200 .000512419 .000036915 .065962035 .0329810180.500 .001281046 .000092286 .064817147 .0324085741.000 .002562093 .000184573 .062909001 .0314545002.000 .005124186 .000369145 .059092707 .0295463545.000 .012810464 .000922863 .047643827 .023821914

10.000. .025620928 .001845726 .028562361 .01428118014.000 .035869299’ .002584017 .013297187 .00664859417.484 .044796448 .003227126 .000000004 .000000002

,,,

109

110

Table 21

Fissile Mass Densities and Calculated NumberDensities for 239PUMetal-Water Mixtures

239pu

hfassDensity(kg/L)

0.00.50.0060.0070.0080.0090.0100.0110.0120.0130.0140.0200.0300.0500.100().2()()0.5001.0002.0005.000

10.00014.00019.740

Number Densitv (atoms

239pu

.000012596

.000015115

.000017634

.000020153

.000022672

.0000251S1

.000027710

.000030230

.000032749

.000035268

.000050383

.000075574

.000125957

.000251913

.000503827

.001259567

.002519134

.005038267

.012595668

.025191337

.035267872

.049727697

U,

IH

.066708393

.066705013

.066701632

.066698252

.066694872

.066691492

.066688112

.066684731

.066681351

.066677971

.066657690

.066623888

.066556283

.066387273

.066049252

.065035190

.063345086

.059964879

.049824257

.032923220

.019402390

.000000003

160

.033354196

.033352506

.033350816

.033349126

.033347436

.033345746

.033344056

.033342366

.033340676

.033338985

.033328845

.033311944

.033278142

.033193637

.033024626

.032517.595

.031672543

.029982440

.024912128

.016461610

.009701195

.000000002

233uMass

Density(kg/L)

0.005

0.006

0.007

0.008

0.009

0.010

0.011

0.012

0.013

0.014

0.020

Iiefl

0.80.91.0

0.80.91.0

0.80.91.0

0,80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

Table 22

Calculated Dimensions for 233u Metal.water Mixtures

SphereDiameter

(cm)

———

——

——

317.12——

105.78——

76.12179.13

62.29104.73

54.1680.25

177.95

48.5567.26

112.46

44.7159.4488.23

32.9339.8849.50

InfiniteCylinderDiameter

(cm)

———

—

—

238.93

—

78.38

—

55.63135.31

—

45.2276.90

38.8558.24

135.68

34.7848.7183.69

31.6842.7264.94

22.7227.9335.19

InfiniteSlab

Thickness(cm)

———

—

—

——

149.53

—

47.43

—

32.51”84.71

—

25.5846.12

21.6734.2884.06

18.9228.0250.54

16.9624.0438.59

11.2014.4719.10

233u

MassDensity(kg/L)

0.030

0.050

0.100

0.200

0.500

1.000

2.000

5.000

10.000

14.000

18.050

k,ff

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

SphereDiameter

(cm)

26.1030.4035.65

21.2624.3027.85

17.7620.0822.71

15.7417.8020.09

14.2016.1118.19

13.2715.1117.12

12.3414.0715.99

10.7512.3214.04

9.0410.4011.88

7.949.19

10.52

7.008.119.31

InfiniteCylinder

Diameter(cm)

17.5020.7224.74

13.8216.0918.72

11.0712.7914.75

9.5011.0012.69

8.259.63

11.18

7.538.87

10.35

6.858.119.50

5.776.898.12

4.715.666.71

4.084.915.83

3.584.315.11

InfiniteSlab

Thickness(cm)

7.849.87

12.36

5.466.848.45

3.604.645.83

2.503.384.38

1.602.373.27

1.141.842.68

0.791.392.15

0.430.871.47

0.250.540.97

0.180.410.75

0.140.330.60

111

235u

Mass)ensity‘kg/L)-

0.005

0.006

0.007

0.008

0.009

0.010

0.011

0.012

0.013

0.014

0.020

112

Table 23

Calculated Dimensions for U(93.2) Metal-Water Mixtures

kefl

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

SphereDiameter

(cm)

—

——.——

——

—

130.68—

87.111273.95

69.41137.49

59.5195.99

—

53.1677.93

173.45

48.6467.72

115.37

35.5143.9456.68

InfiniteCylinderDiameter

(cIn)

—

———

——

—

98.23

63.90833.96

—

50.49103.27

—

42.8370.72

38.1057.02

129.51

34.6349.0485.54

24.6231.0340.69

InfiniteSlab

I’hickness(cm)

——

———.

——

———

60.42

—

37.71562.43

—

29.0362.92

24.2042.25

—

21.0333.3580.40

18.7728.0952.14

12.3716.4722.63

235u

MassDensity(kg/L)

0.030

0.050

0.100

0.200

0.500

1.000

2.000

5.000

10.000

14.000

17.484

k,ff

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

SphereDiameter

(cm)

28.1733.3740.18

23.2026.8531.22

19.6022.5125.82

17.7820.3623.32

16.6319.1522.06

16.2018.8121.76

15.7218.4121.53

14.3016.7819.64

12.3114.3716.68

11.0812.9214.97

10.0811.7613.62

InfiniteCylinderDiameter

(cm)

19.0122.9427.98

15.2017.9621.28

12.4414.5617.02

10.9612.8815.06

9.9911.8313.98

9.5511.4713.72

9.1711.1413.41

8.159.98

12.10

6.908.39

10.09

6.12.7.448.92

5.52.6.728.05

InfiniteSlab

Thickness(cm)

8.7711.2014.42

6.287,969.99

4.375.687.19

3.304.455.79

2.473.584.88

2.063.194.52

1.712.834.19

1.242.223.45

0.851.602.56

0.671.282.07

0.561.091.77

239pu

MassDensity(kg/L)

0.005

0.006

0.007

0.008

0.009

0.010

0.011

0.012

0.013

0.014

0.020

Table 24

Calculated Dimensions for ZagpuMetal.Water Mixtures

k,ff

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

0.80.9”1.0

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

SphereDiameter

(cm)

235.44

84.59344.79

61.59100.75

50.9572.49

135.53

44.8459.5589.85

40.6552.2072.23

37.6547.2662.44

35.38.43.6956.03

33.5440.9651.55

32.0638.8148.15

26.9031.6737.68

InfiniteCylinderDiameter

(cm)

178.13——

61.77264.35

—

44.4674.83

36.3952.66

101.00

31.7042.9566.19

28.5337.3652.75

26.2433.5545.03

24.5130.7740.18

23.1228.7436.76

21.9927.1134.15

18.0521.6126.22

InfiniteSlab

Thickness(cm)

114.24.—

36.54171.68

—

25.0444.68

—

19.9530.466.1.68

16.8924.1639.16

14.8920.4930.27

13.3818.0225.40

12.2716.2822.32

11.3914.9120.01

10.6613.8718.34

8.1010.3313.16

239pu

MassDensity(kg/L)

0.030

0.050

0.100

0.200

0.500

1.000

2.000

5.000

10.000

14.000

19.740

k,fi

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

0.80.91.0

SphereDiameter

(cm)

23.3127.0431.52

20.6323.7427.37

18.6621.4624.68

17.6620.3723.48

16.7519.4022.44

15.8618.3821.26

14.5616.8419.42

11.9813.8015.82

9.2710,6512.14

7.768.91

10.13

6.237.138.08

InfiniteCylinderDiameter

(cm)

15.2918.0421.42

13.1615.4918.19

11.5813.6816.09

10.7312.7315.07

10.0011.9314.18

9.3311.2013.35

8.4510.1212.03

6.748.059.53

5.076.047.09

4.194.985.84

3.343.954.60

InfiniteSlab

Thickness(cm)

6.267.98

10.08

4.816.227.90

3.634.896.34

2.944.145.55

2.353.524.88

1.973.064.33

1.552.503.62

0.961.612.42

0.570.991.49

0.420.731.12

0.310.530.81

113

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CRITICALITY SAFETY IN PROCESSING PLANTSA. Plant Features with Criticality PotentialB. AdministrationC. TrainingD. Criticality Alarms and ResponseE. Material ControlF. Process StartupG. Maintaining Safety ProvisionsH. Examples of Plant Application

APPENDIXReferences