LA=9360

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An AffikrnativeActiorr/EqualOpporturdty Errtpfoyer

DISCLAIMER

This report was prepared as an account of work sponsored by an agency of the United States Government.Neither the United States Covernnrent nor arty agency thereof, nor aray of their employees, makes anywarranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness,or usefulness of any information, appamtua, product, or process disclosed, or represents that its use wouldnot infrirrge privately owned rights. Reference herein to any speciilc commercial produet, process, oraervfce by trade name, trademark, manufacturer, orotherwise, doea not neesssrily constitute or imply itsendomement, recommendation, or favoring by the United States Government or any agency thereof. Theviews arrd opirdom of authora expressed herein do not necessarily state or reflect those of the UnitedStates Government or any agency thereof.

LA-9360

UC-70Issued: October 1983

The Myth of Nuclear Explosions atWaste Disposal Sites

William R. Stratton

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CONTENTS

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...1

EXECUTIVESUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...1

I. INTRODUCTION:THEMYTH . . . . . . . . . . . . . . . . . . . . . . . . . . . ...2

II. PLUTONIUM PRODUCTION CONSIDERATIONS . . . . . . . . . . . . . . . . . . . 3

III. CRITICALMASS CONSIDERATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 4

IV. CRITICAL MASSOFAMIXTURE OF PLUTONIUM, SOIL,ANDWATER . . . . . 6

V. THEEFFECTOFTHERESONANCEAT 3200”C . . . . . . . . . . . . . . . . . . . 8

VI. CHARACTERISTICS OF APOSTULATED POWER EXCURSION . . . . . . . . . . 10

VII. THEORETICAL MODEL FOR POWER EXCURSIONS . . . . . . . . . . . . . . . . 12

VIII. APPLICATION TO A PLUTONIUM-WATER-SOIL MIXTURE . . . . . . . . . . . . 15

IX. CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...16

ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...17

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...17

vi

APOLOGIA

This study endeavors to show that an alleged event (postulated to be a nuclearexplosion in a waste disposal site) did not, in fact, happen. To show or prove thenegative is difllcult at best, and because the alleged event is said to have occurred in aquite inaccessible spot with nothing but hearsay testimony available, the task wouldseem to be nearly impossl%le. However, reasonable assumptions can be made, andphysically and mathematically rigorous analyses can be applied to conditions at thehypothetical site.

THE MYTH OF NUCLEAR EXPLOSIONS ATWASTE DISPOSAL SITES

by

William R. Stratton

ABSTRACT

Approximately 25 years ago, an event is said to have occurred in the plainsimmediately west of the southern Ural mountains of the Soviet Union that is beingdisputed to this very day. One person says it was an explosion of nuclear wastes buriedin a waste disposal site; other people say it was an above-ground test of an atomicweapon; still others suspect that an alleged contaminated area (of unknown size or evenexistence) is the result of a series of careless procedures.

Since the event, a number of articles about the disposal-site explosion hypothesiswritten by a Soviet exile living in the United Kingdom have been published. Althoughthe Soviet scientist’s training and background are in the biological sciences and hkknowledge of nuclear physics or chemistry is limited, people who oppose the use ofnuclear energy seem to want to believe what he says without question. The work of thkSoviet biologist has received wide exposure both in the United Kingdom and the UnitedStates.

This report presents arguments against the disposal-site explosion hypothesis.Included are discussions of the amounts of plutonium that would be in a disposal site,the amounts of plutonium that would be needed to reach criticality in a soil-water-plutonium mixture, and experiments and theoretical calculations on the behavior ofsuch mixtures. Our quantitative analyses show that the postulated nuclear explosion isso improbable that it is essentially impossible and can be found only in the never-neverland of an active imagination.

EXECUTIVE SUMMARY

The problems associated with producing a violentnuclear explosion in a disposal pit containing a mixtureof plutonium, soil, and water are examined. The postu-lated situation is that waste solutions from a chemicalprocessing plant contain some concentration of pluto-nium that is assumed to be discarded. The followingmatters are discussed.

The amounts of plutonium that are produced inreactors designed for that purpose are estimated for

“units” of 1000 megawatt years. Although the amountsof plutonium produced per reactor are relatively large,the amount that could have been discarded is relativelysmall if reasonably etllcient chemical processing tech-niques were used. It is most unlikely that hundreds ofkilograms could have been discarded.

The amount of plutonium required to produce acritical geometry in a mixture of soil and water and withwater reflection is estimated. Generally, depending onmoderation and reflection, either very large amounts ofplutonium or a large volume fraction of water is required.

1

I conclude that the amount of plutonium required forcriticality is more than could have accumulated in awaste stream; therefore, it is most unlikely that a criticalgeometry ever existed.

Nuclear power excursions* have been created insolutions both in the United States and France. Thesetransient experiments are analyzed by use of a rigorouslycorrect computer program. The quality of agreementbetween experiment and theory is examined and foundsatisfactory. Magnitudes of energy releases are presentedand discussed. The d~lculty (near impossibility) ofcreating an explosion in a solution reactor is illustratedby reference to experiments and also is analyzedtheoretically.

The same theory, with minimum modifications, is thenapplied to postulated critical mixtures of soil, water, andplutonium. Magnitudes of energy releases associatedwith reasonable and even unreasonable physical andchemical situations are derived and discussed. Theconclusion reached is that even if a critical situation werecreated and reactivity added at a most rapid rate, anexplosion of more than trivial magnitude (equivalent tothat of a few ounces of black powder) could not becreated.

I. INTRODUCTION: THE MYTH

The earliest references to an event or events nearKyshtym in the Soviet Union in 1958 suggested a“catastrophic accident” (Ref. 1) and an “atomic ex-

plosion” (Ref. 2), and several reports3 written by 6migr6sand released by the CIA** mention explosions of onesort or another. However, the first suggestion (to ourknowledge) that the event or events in question mighthave been a nuclear (not chemical) explosion associated

●A power excursion is the rise and subsequent fall of fissionpower that results from the addition of reactivity to a tissilesystem that is already close to the critical state. The reactivitycan be in the form of a control rod motion, addition of fissilematerial (U-235, Pu-239, U-233), change of neutron reflector,neutron moderator, etc.**In lg77, in response to the Freedom of Information Actrequests, the CIA-released censored reports of interviewsofpersons leaving the Soviet Union. Severalof those interviewedmentioned explosions in comection with an event or eventsnear Kyshtym in the late 1950s.All such reports are hearsay,as is Medvedev’sinformation on the same subject obtainedfrom different sources.

with nuclear wastes was made by Zhores Medvedev,4 aprofessional biologist. His colorful remarks included“nuclear reactions had led to overheating,” “anenormous explosion, like a violent volcano,” “radioactivedust and materials high up into the sky,” “strong windsblew the radioactive clouds hundreds of rniles~’ etc. InRefs. 5 and 6, the hypothesis of a nuclear explosion in achemical waste disposal site was asserted again.Medvedev’s strongest statements, however, were made inhis book,’ published in 1979, and in his own review8 ofhis book. He discusses, in a very qualitative fashion, theproduction of plutonium in a reactor designed for thatpurpose, the chemical dissolution of the fuel, separationof plutonium and uranium from the fission products, andthe final storage of those fission products. Withoutknowledge of actual practices (admitted to be the case),

he postulates practices, conditions, and events to fulfdlhis earlier adamant insistence that a nuclear explosionoccurred in a waste disposal site.

He mentions, as supporting evidence, the so-called Z-9trench in the Hanford, Washington, reservation area inthe U.S.9’10 He correctly states that low-level liquidwastes (“lean solutions”), containing very little pluto-nium and few fission products, were disposed of in thiscovered trench in the Hanford reservation soil. Heincorrectly asserts that (1) the trench contained approx-imately 100 kg of plutonium, (2) a near-disaster wasbarely averted, and (3) this amount of plutonium issufficient for nearly a hundred atomic bombs. Hisallegations relative to these points result either frominadequate review of the matter (the complete fde isreadily available) or from failure to understand thephysics and chemistry involved because of his special-ized biological training and background. The facts of thecase show that the original analysis of the criticality ofthe trench was in error; the upper limit of plutonium inthe ground was about 25 kg and may have been verymuch less.9’10His reference to 100 atomic bombs is

deemed by this author to be a clear exaggeration tosupport his earlier dogmatic assumption of nuclearexplosions in a Soviet waste disposal site.

However, because of the number of reports (Refs. 1-3)that mention an explosion (or explosions) and because ofMedvedev’s adamant insistence that there was an ex-plosion, we think that something of this sort could haveoccurred and may have been a part of whatever didoccur in 1958 near Kysht ym. We do not attempt toprove what kind of explosion might have occurred or

2

even that one did happen. In this report, the requirementsthat must be imposed on a ground disposal site to causeit to explode “like a violent volcano” are presented anddiscussed. The plausibility of Medvedev’s postulates willbe discussed as may be appropriate, and implications, if

any, to the environment will be addressed. We note inpassing that there is no firsthand evidence of an “ex-plosion.”

To clarify the problem and define the issues to beaddressed, we paraphrase Medevdev’s assumptions andpostulates and add comments as may be appropriate.

1.

2.

3.

4.

5.

The discarded solutions contained significant concen-trations of plutonium (this is an implicit assumption,not explicitly stated, but necessary for his thesis).Comment: the objective of the industrial activity wasproduction and extraction of plutonium metal; theproduct is too expensive to handle carelessly.

The liquid wastes from a Soviet chemical processingplant were discharged into a pit in the ground, instead

of into storage tanks. Comment: the use of tanks isaccepted practice for storage of high-level wastethroughout the world. I know of no reason what-soever for a different practice in the Soviet Union.

The plutonium precipitated on soil particles in a thinlayer of soil near the surface. Comment: this behaviorof plutonium is in accord with existing data; pluto-nium will precipitate from solution in a near-insolubleform close to the surface of the ground.

A great many kilograms of plutonium accumulated inthe disposal pit. Comment: because of his admittedlack of nuclear expertise, his estimates are veryqualitative. The amount that could be produced andthe mass actually required for criticality are calcu-lated in this report for various conditions.

Given a large mass of plutonium in the postulateddisposal pit, he hypothesized a supercritical conditionwas created by inflow of water. Comment: again,because of his lack of knowledge of criticality physics,the matter is not discussed quantitatively. Criticalityis one of the major topics of this report (see Sees. IIIand IV).

6. The supercritical condition caused by the plutoniumwater moderation and reflection created “an

enormous explosion, like a violent volcano.” Com-ment: the possibility of this condition occurring isexamined quantitatively below.

The plan of this report is to examine the severalrequirements needed to produce a near-critical systemand set the stage for a nuclear reaction in a water-moderated mixture of soil and plutonium. Realisticconditions and assumptions will be taken; wherepossible, reference will be made to known practice andhistory in the United States, France, or the UnitedKingdom. Reasonableness and/or probability will bejudged as data are developed. The analysis of conceptualnuclear power excursions in a waste solution storage sitein the ground will be examined in three stages. First, anestimate will be made as to the possible plutoniumproduction rate and the fraction that might have beendiscarded; second, the criticality characteristics of pluto-nium, plutonium solutions, and, in particular,characteristics of plutonium solutions in a rectangularbasin in soil will be examined; and third, the nuclearpower characteristics of a supercritical, soil-water-pluto-nium mixture will be studied and the possibility ofexplosions evaluated.

II. PLUTONIUM PRODUCTION CONSIDER-ATIONS

The amount of plutonium potentially available to haveaccumulated in a disposal pit is basic to this analysis, ofcourse. This amount is not available, but its order ofmagnitude can be estimated fairly readily. The thermalpower of the early World War II plutonium productionreactors (using natural uranium metal as fuel) in theUnited States was a few hundred megawatts, but later,with the availability of slightly enriched uranium and theadvantage of operating experience, the power level wasincreased over a period of years to several thousandmegawatts. It is reasonable to assume a comparablehistory in the Soviet Union. Thus, a “unit” of 1000 MWfor a year (300 days, to allow for refueling anddowntime) is convenient, and independent assumptionscan be made in regard to how many units per reactorand how many reactors for how many years at one siteneed be considered.

Given the assumptions of 1000 MW for 300 days,0.67 plutonium atom created per tission,ll’lz and the

3

equivalence of 1 W and 3 x 1010fissions/s, the plutoniumproduction rate would be 205 kg/year. The plutonium iscreated within the uranium fuel, and this fuel must bedissolved in acids (usually nitric). Separation of thefission products, uranium, and plutonium is ac-complished by wet chemistry techniques. Depending onthe process and management philosophy, less than 100’%of the theoretically available plutonium is generallyrecovered. Losses occur, fwst because the cladding hullsare not fuly dissolved, and second because the wetchemistry separation process itself creates losses. Thus,if the hull dissolution and wet chemistry were 99V0effective (reasonable), the amount lost would be about 2kg/year. If the recovery were only 959+0effective (verypoor), about 10 kg might not be recovered, Someoperations in the United States recover as much as99.9% of the plutonium available in solution.

Thus, if an average of several thousands of megawattswere available for several years (we note that in the1950s the Soviet Union must have been increasing theirplutonium production capacity both in numbers ofreactors and in fission power of each reactor), it isconceivable that several tens of kilograms could havebeen discarded in solutions containing fission products.It is safe to conclude that hundreds of kilograms wouldbe an unreasonably large amount to have been dis-carded. As will be developed later, tens of kilograms isnot sufficient plutonium to create the postulated criticalsystem.

111.CRITICAL MASS CONSIDERATIONS

The mass of a fissile material (Pu-239, U-233, U-235)needed to form a criticai* system or critical assembly isknown accurately for a very large number of differentmaterial densities, geometrical arrangements, diluents,poisons, and structural materials by virtue of hundredsof experiments:3-f5 performed during the past 37 years.These experiments are correlated and tied together by

use of rigorously correct neutron transport computerprograms*6 that have been used in many laboratoriesthroughout the world. The agreement between ex-————*A critical mass of fissile material is that amount of U-235,U-233, or Pu-239 along with diluents, poisons, and reflectorsin a defined geometry that will just sustain a constant fissionrate (any power level) or neutron population. An experimentalarrangement of materials is often called a “critical assembly”and is brought to the critical state by remote control andoperated at a very low, near-zero, power.

perimental and theoretical results is extraordinary, andfor reasonably definable geometrical situations, the re-sults of theory are regarded nearly as well as those of anexperiment. For poorly defined mixtures or geometries,bounding assumptions can be (and are) made to assure aconservative resul~ that is, overestimate criticality.

Calculations of this sort make use of tabular sets ofneutron cross sections. For a given material, say Pu-239,the neutron cross sectionsl’ must reflect the knownexperimental phenomena such as neutron capture withfusion, capture without fission (as caused by a poison),and scattering with a reduction in energy of the neutron.Because neutrons are born with high energy followingfission, the various interactions must be modeled fromseveral million electron volts down to thermal energy(about 1/40 eV). The cross sections used in the computa-tions for this study are from the Hansen-Roach 16-groupset,*8that is, a compilation that divides the energy regionfrom multimillion electron volts to thermal energy into16 regions. Each isotope of each chemical elementassumed to be in a computational model must have theappropriate cross sections defined. The excellence of thecombined use of these cross sections and (numerical)neutron transport equations is tested by results of studiesthat compute a wide variety of critical conditions. In theapplications of the functions used, as mentioned above,the comparison of theoretical critical radius or mass tothe experimental value is surprisingly good.1’

The neutron cross sections for capture, fission, andscatter for many elements in and near the thermal energy(room temperature) region are characterized by aproportionality to the reciprocal of the neutron velocity,such as

1cross section IX — .

v(1)

Because the neutron kinetic energy is proportional tothe square of the velocity, the cross section is thenproportional to the reciprocal of the square root of theenergy, such as

cross section cc —h’

(2)

and this is the functional form commonly found ingraphical presentations of cross sections.1’

A noteworthy exception to this general rule [Eq. (2)] isthe near-thermal fission cross section of Pu-239. Theexceptional character of this isotope is caused by a

4

resonance*” in the fission cross section at 0.3 eV or atabout 3200”C. The magnitude of the cross section atthis effective temperature is larger than at thermaltemperatures. This resonance seriously perturbs the I/vcharacter of the neutron cross section; at thermalenergies, the fission cross section is decreasing as theneutron energy is increasing but less rapidly than I/v.The general character of the cross section of plutoniumfor these energies is shown in Fig. 1.

The importance of this resonance is the effect it mighthave on the criticality or reactivity of a water-moderatedplutonium system should it become critical and increasein temperature. If all neutrons were at exactly thethermal energy corresponding to the temperature of thematerial and if all fissions were caused by these neutrons,the system could become more reactive as the tempera-ture increased and could be at a maximum when thetemperature reached 3200° C. This behavior of neutronsis not the case, of course, but if the other materials (forexample, hydrogen) have cross sections strictly propor-tional to I/v, the effect of the resonance can beenchanced somewhat.19 That this resonance might in-fluence significantly the supercriticality characteristics ofthe postulated mixture of soil, water, and plutonium wasfwst brought to my attention by Freeman Dyson in1980.20

We have examined this matter carefully and foundthat at least two factors diminish the effect of theresonance in creating, as postulated by Dyson in Ref. 20,

——

*A resonance in a neutron capture (or fission) cross sectionmay be compared to a person pushing and adding energy to asecond person sitting on a swing. For ease in visualization, weimagine a swing from a high support so its period is longrelative to the pusher’s agihty. If the person pushing does so ator nearly at the obvious time, she is “in resonance” with theswing. If she pushes too frequently (too agile), or tooinfrequently (too lazy), or if in a direction di!Terent from theplane defined by the motion of the swing (intoxicated), she is“out of resonance.” If she attempts to “stick,” that is, to jointhe Person on the swing, it is much easier and with muchhigher probability of success if she is “in resonance” andacting in the same plane as the motion of the swing. If theswing is the plutonium atom and the pusher is the neutron, it isreasonable that the probability of sticking is greatest if thecontact is made at the resonance frequency. In the neutron andthe plutonium atom interaction, “frequency” and “angle” are“just right” at 3200”C. The combined properties of the twonuclei, as they join to become (momentarily) Pu-240 in anexcited state, determine the characteristics of the resonance.The capture cross section at this energy is very large butdecreases sharply at lower energies but especially rapidly athigher energies.

‘“”””~’”’

‘Oj__J0.1 1

NEUTRON ENERGY {eV)

Fig. 1. Absorption cross section (fission plus capture) of Pu-239 as afunction of incident neutron energy. Room temperature, about 68°For 20”C, is equivalent to 1/40 eV, whereas the Pu-239 resonance at0.3 eV is equivalent to about 3200”C.

an autocatalytic power excursion, that is, one duringwhich the reactivity increases as the power increases.These are as follows: (1) not all fissions are caused byneutrons at exact equilibrium with the thermal energy ofthe material. The equilibrium character of neutrons at agiven temperature is described by what is known as aMaxwellian distribution with some neutrons at what areeffectively higher and lower temperatures. As an exam-ple, if the peak of the neutron energy distribution is at 0.3eV but if a quarter of the neutrons are at a higher energy,where the cross section is lower by a factor of 100, theeffect of the resonance is decreased. Thus, the distribu-tion of neutrons can lessen the effect of the resonance.And (2) to moderate the neutrons, water must occupy alarge fraction of the volume, more in fact than may be

“ 21If water is present, the characteravailable in sandy sod.of the postulated power excursion will be dominated bythe response of water to the deposited fission energy, andthe very high temperatures will never be achieved as longas water is present in any quantity. The reactivitychanges in this case would be dominated by thermalexpansion, bubble formation, and boiling, all of whichwill be discussed in more detail below.

5

IV. CRITICAL MASS OF A MIXTURE OF PLUTO-NIUM, SOIL, AND WATER

To understand and appreciate the magnitudes of fissilematerial that are involved in dilute systems, a shortdiscussion of critical masses of tissile materials is ap-propriate. For example, if the critical mass(MI) of somearrangement of plutonium at a density of PI is known,

the critical mass (MJ at a different density (pJ is givenby

() 2

M2=Ml 3 .P2

(3)

To illustrate, the critical mass of an unreflected sphereof plutonium metal at a density of 19 g/cm3 is about 15kg; if the density of this material should be reducedprogressively to 0.1 g/cm3, the mass required for criti-cality would be an astounding 541,500 kg. The criticalmasses of more complicated mixtures generally are not

predictable by such simple relationships, and moresophisticated neutron transport theory techniqueslc’zzmust be used. As an example, Fig. 2 illustrates thecritical mass of homogeneous, spherical, unreflectedmixtures of highly enriched uranium (93.5% U-235,

6.5V0 U-238), water, and graphite.1’ The complicatedbalancing between dilution, neutron moderation, neutroncapture in water and graphite, and fission (and non-fission capture) of uranium cannot be predicted by thesimple relationship illustrated above, but the referencedcomputational method in conjunction with proven crosssection sets (for example, those in Ref. 18) producesrigorously correct results.23

Estimating the mass of plutonium that could con-stitute a critical mass in a mixture of soil and waterrequires a number of assumptions. These are listed withcomments and references as appropriate.

1. The area assumed for the disposal site was 9 m x 18m with a depth of 0.5 m. This is arbitrary butreasonable.

CRI

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Fig. 2 Unreflected, spherical critical masses of the three-phase, Sraphhe-water-emiched uranium mixtures are plotted versus theU-235 density. The uranium is 93.5% U-235 and 6.5% U-238. The atom ratios H/U-235 and C/U-235 are indicated on thecurves. The complexities of such data cannot be understood without the use of mmputational tools discussed in the text.

6

2.

3.

4.

5.

6.

7.

The composition of the soil was simplified to consistof SiOz (89Yo), A1Z03 (6.6%), and FeO (4.4VO).Thefull density is 2.43 g/cm3 (Ref. 10).

The plutonium in the soil was concentrated near thesurface as has been observed. 10The plutonium den-

sity distribution function is given in Table I. Thisdistribution is in reasonable accord with actual ob-servations of plutonium concentrations in soil thathas absorbed solutions containing very low levels ofplutonium. Apparently, soil particles selectively ab-

sorb and hold plutonium very tightly on their surf-aces, an interesting property per se.

Plutonium was assumed to be mixed in as a metalpowder or an oxide powder at several dfierentconcentrations. Each of these concentrations wasassigned to the position of the density function 1.0 forthe top layer with concentrations dropping off asspecified in assumption 3 above.

The isotopic concentration was 95?40Pu-239 and 5%Pu-240, again arbitrary but reasonable.

No neutron poisons were assumed to be present. Thisassumption is very conservative and maximizes thecalculated reactivity and minimizes the mass requiredto achieve criticality. Any real solution would haveneutron absorbers in at least the acids and some ofthe fission products.

Two water volume fractions were assumed as given inTable II. The amount of water for Case I is notunreasonable,zl but that for Case 11is extraordinaryand is quite unrealistically high. It would be muchmore like a thick liquid than wet sand.

TABLE I. Relative Density of Plutonium in Soil as aFunction of Depth

Soil Depth Relative Density(cm) of P Iutonium

o-2 1.02-8 0.458-15 0.15

15-23 0.0423-30 0.01530-50 0.0

TABLE IL Volume Fractions of Soil and Water As-sumed for This Study

Volume Fraction

Material Case I Case II

soil 0.7 0.4Water 0.3 0.6

8. The computation of reactivity used a transport code,0NEDANTZ4 with Hansen-Roach 16-group crosssections. 18 ONEDANT was used in planar (slab)geometry with a buckling corrections to simulate thefinite size of the disposal pit. The vflldity of thismethod of computation has been discussed above.

Given these assumptions and conditions, the criticalconcentration of plutonium was computed for severalareas (within the postulated disposal site conditions) andthicknesses of water reflection. The relative distributionof plutonium, as a function of depth as shown in Table I,was held constant. These criticality data are assembled inTable HI.

The major characteristic of these postulated, criticaImixtures of sand, water, and plutonium is the thin, slab-IiIce layer of plutonium near the surface. For thisgeometry, the required mass for criticality increases veryrapidly with a very slight diminution of the concentrationand increase in area to compensate. This effect is evident,for example, for the four critical masses in Case II with a10-cm water reflection. The concentration decreases onlyby 20%, but the mass required for criticality increases bya factor of 130, from 4.7 to 610 kg.

The critical amounts of plutonium for the full 9-m x18-m slab are extraordinary, ranging from 600 to 4000kg. These are very large amounts, and to assume thatthis quantity would be discarded suggests either extremenaivet6 or a determination to confuse and befog atechnical matter.

The whole area of the postulated disposal site need notbe used to create a critical system, however. Smallerareas can be made critical with increased water reflec-tion, water volume fraction, and plutonium concentra-tion (note that some plutonium densities are ex-traordinarily large in Table 111).We comment that CaseH, 60?40water by volume, is sufilciently unrealistic that itcan be discarded on this basis alone but, nevertheless, isdiscussed further below to complete our argument. The ‘

7

TABLE III. Computed Critical Concentrations andMasses for Two Volume Fractions ofWater, Various Areas, and Amounts ofWater Reflection

Water Plutonium Critical

Area Reflection Concentration Mass

(m’) (cm) (~~) (kg)

Case I: 30% Water

4 0 565 140

10 0 530 325

10 1 400 245

10 5 194 120

10 10 150 93

162 0 430 4300

162 1 340 3400

162 5 143 1430

162 10 114 1140

Case II: 6070 Water

1 104 10

10 010 110 510 10

162 0162 1162 5162 10

7665

1551217764

1361147161

4.716.196754840

13601140710610

critical masses for the smaller areas of Case I range from93 to 325 kg. Thus, a critical system for a fraction of thearea of the pit can be postulated, but the mass ofplutonium required is still very large, and it is unlikelythat such large, expensive, and precious amounts wouldknowingly or accidentally be discarded.

The conclusion of this section is that to create acritical system of plutonium in soil would be mostexpensive in the mass of plutonium, requiring highconcentrations or unrealistic amounts of water. Ex-istence of such a critical system is very unlikely.

V. THE EFFECT OF THE RESONANCE AT 3200”C

The importance of this resonance was mentionedabove. Briefly, if all neutrons causing fissions were in

exact equilibrium with the material temperature, thereactivity could rise (after some initial heating) to amaximum at the resonance. The resonance is illustratedin Fig. 1 for more energetic neutrons.

This effect could create what is called an autocatalyticpower excursion, because as temperature rises, thereactivity rises, the reactor period shortens, and thepower increases more rapidly. Such a self-feedingprocess could increase until the resonance temperaturewas reached.

However, as mentioned above, the neutrons are bornas fast neutrons with energies in the million-electron-voltrange. The amount of moderation (as with hydrogen) isimportant in calculating the reactivity because fissioncross sections are larger at thermal or near-thermaltemperatures. Hence, the reactivity at each temperaturemust reflect the neutron energy distribution at thattemperature. Some neutrons would cause fissions at highenergies and some while being reduced in energy, but thedominant effect on reactivity would derive both from thedistribution in energy of the thermal neutron populationand from the existence of absorbers such as hydrogen.

One can visualize the effect of the distribution ofneutrons by imagining, for example, the temperature

(energy) to be 460”C (O.1 eV). The peak of thedistribution would be at this point: neutrons at lowertemperatures would have a higher cross section, andneutrons at higher temperatures (closer to the resonance)also would have a higher cross section. For this con-dition, the effect of the neutron distribution is to raise theeffective cross section (see footnote on p. 5). However, ifthe equilibrium temperature were just at the maximum ofthe resonance, neutrons at both higher and lowertemperatures would see lower cross sections. Thus, theeffect of the distribution would be to wash out theinfhzence of the resonance to some extent. The modifiedcross section, with allowance for a Maxwellian distribu-tion in neutron energy, is illustrated in Fig. 3. Theeffective maximum is shifted to a lower energy, becausethe cross section (Fig. 1) decreases very sharply abovethe resonance at 3200”C.

A convenient way to characterize the moderation andthe distribution is to express the moderation (and absorp-tion) by the ratio of hydrogen to plutonium atoms

(H/Pu). An appropriate reactivity parameter is thereproduction factor for the infinite, unbounded (indimension) system, the so-called km. This parameterdepends only on neutron temperature and H/Pu ratioand not on the assembly size or density or boundary

8

TEMPERATURE (+.2

Fig. 3. Absorption (uJ and total (uJ cross sections for plutonium withallowance for a Maxwellian distribution of neutrons about energy E.These curves can be compared with that in Fig. 1, in which theneutrons are monoenergetic.

conditions. The result of these computations is presentedin Table IV and illustrated in Fig. 4.*

Table IV or Fig. 4 shows that, to have a positivetemperature coefficient (that is, reactivity at room tem-perature increasing as temperature increases), the ratioof hydrogen atoms to plutonium atoms (H/Pu) must begreater than 1000. For H/Pu = 800, the assembly—.———*These data were contributed by Gordon Hansen, Los A1amosNational Laboratory, 1981.

(mixture of materials) must get to about 300”C beforethe coefficient becomes mildly positive, whereas, forH/Pu less than 500, there is no region for which thereactivity increases with temperature.

To relate these data to the imaginary assembly athand, the H/Pu atom ratios can be calculated for theplutonium and water densities bounding or close to thosepresented in Table HI and for the soil depths and densityfunctions presented in Table I. These data are given inTable V.

2.0-HIPU -

km:005008001000

2000

1.4- 3000 -

1.2-r

l.o~0 500 1000 1500 2000 2500 3000 3500

TEMPERATURE (“C)

Fig. 4. The neutron reproduction factor (km) for an unboundedsystem (size not limited in any direction) consisting of Pu-239 andwater versus the equilibrium temperature of the mixture. Variousamounts of water are defined by the hydrogen atorrdplutonium atomratio, and cross sections are taken from Figs. 1 and 3. The apparentdominant effect of the Pu-239 resonanee in Fig. 1 is diminished by theneutron energy distrl%ution and the effeet of hydrogen absorption. Seetdso comments in Ref. 19.

TABLE IV. Infinite Reproduction Factors (kJ for Mixtures of Plutonium and Water

H/Pu 17 130 300 540 890 1470 2050 2630 3210

0 2.060 2.015 1.922 1.840 1.795 1.781 1.778 1.776 1.778200 1.945 1.912 1.847 1.792 1.763 1.756 1.753 1.750 1.750

500 1.795 1.776 1.745 1.726 1.718 1.720 1.717 1.713 1.711

800 1.667 1.658 1.653 1.664 1.675 1.685 1.682 1.678 1.673

1000 1.591 1.588 1.597 1.625 1.648 1.663 1.660 1.655 1.648

2000 1.296 1.310 1.366 1.455 1.523 1.559 1.556 1.550 1.536

3000 1.093 1.115 1.193 1.317 1.416 1.468 1.465 1.458 1.438

9

TABLE V. Hydrogen-to-Plutonium Atom Ratios for Two Volume Fractions of Water, for FourPlutonium Concentrations, and as a Function of Depth in Soil

soil Density H/Pu for Given Plutonium Densities

Depth Function Case I: 30% Water Case II: 60’%0Water

100 g/i 200 dk? 500 g/~ 20 dl 100 g/.4 200 dl

o-2 1 76 38 155 760 50 762-8 0.45 173 86 344 1730 115 1738-15 0.15 530 265 103 5310 354 530

15-23 0.04 1990 990 387 19900 1320 530023-30 0.015 5300 2650 1033 53000 3530 5300

From this table and Table IV, it can be seen that theinfluence of the resonance at 3200”C will be small atmost. The H/Pu ratio rises sharply with increasing depthof soil, but the temperature rise of tliese regions of suchan imaginary fissioning system would drop off rapidlywith depth simply because the relative plutonium atomdensity and hence fissions decreases rapidly.

The conclusion of this section of the study is that theresonance in the fission cross section of plutonium at3200”C would have little, if any, significant influence onthe characteristics of a postulated power excursion in theassembly of materials as postulated. This conclusionmakes the proposition that a severe nuclear powerexcursion could occur on a waste disposal site in soileven more improbable, if not practically impossible.Nevertheless, for completeness, the characteristics ofpower excursions will be reviewed and applied as ap-propriate to the imaginary plutonium-sand-water system.

VI. CHARACTERISTICS OF A POSTULATEDPOWER EXCURSION

The preceding discussion developed characteristicsthat would be required for a critical mixture of pluto-nium, soil, and water. The dominant characteristics arethe large amounts of water needed (volume fractions of0.3 and 0.6 water were used as examples) and the verylarge mass of plutonium required.* The large amount ofwater immediately suggests that the fissioningcharacteristics of the mixture will be comparable to thefissioning characteristics of water solutions of uranium

—— .—

*A critical slab can be created with lesser amounts of water,but the amount of plutonium required increasesastronomical.

or plutonium. To provide background for an analysis ofpostulated nuclear power excursions in the plutonium-water-soil mixture, we will examine briefly the

characteristics of solutions.The importance of understanding solution criticality

and power excursion behavior in water reactions arisesfrom the use of solutions in spent-fuel chemical process-ing plants. Generally, spent fuel is dissolved in strongacids (primarily nitric), and the separation of plutonium,uranium, and fission products is completed by solutionchemistry techniques. The importance of control ofcriticality to the safety of operating personnel and tointegrity of equipment is obvious. Indeed, in the historyof nuclear criticality accidents and incidents,23 about adozen have occurred with solutions in processing plantsor during the performance of solution experiments. Twoof these accidents resulted in fatalities, but thecharacteristics of all were such that no physical damageto equipment resulted. Personnel safety requirementsmake the need for experiments and precise calculationsobvious.

As mentioned above, a very large number of criticalityexperiments with solutions have been completed. Theseserve to provide validation points for theory, and, indeed,the correspondence between theory and experiment isextraordinary, suggesting that the various parameters arewell understood. Safety in processing plants is controlledin part by assuring that solutions of a given concentra-tion are allowed to be only in containers of a “safe” sizeor in a container that has fixed poisons. However, severalof the solution accidents occurred because a solutionreached a container of the wrong size or one withinsufllcient poison, the solution became supercritical, anda power excursion developed.

10

Because of this history and because of expectations oflarge-scale chemical processing, the French Com-missariats a l’Energie Atomique (CEA) authorized a

series of experiments in the late 1960s to investigatepower excursions in uranium solutions. The objectivewas to establish the level of risk in order to designadditional protection if needed. The experimentsperformed were straightforward and applicable to theproblems for which they were designed and, uninten-tionally, also applicable to the plutonium-soil-water rrtix-ture postulated by Zhores Medvedev. The series ofexperiments was designated “Consequences Radiologi-ques d’un Accident de Criticite” (CRAC) (Ref. 26).

The CRAC experiments followed a series of experi-ments in the United States known as the KineticsExperiments in Water Boilers (KEWB) (Ref. 27). Thislatter program was started in the mid- 1950s and ex-tended into the early 1960s. In this case, the solution wasin the form of a small reactor, fully equipped withcooling coils and control rods. The KEWB reactors wereused both for various steady-state experiments and fortransient or excursion experiments. The transient orexcursion experiments were initiated by control rodmotion and were contained, as opposed to the CRACexperiments, which were initiated by pouring uranylnitrate solution into an open tank already containing anear-critical volume of solution. In spite of the dif-ferences of geometry, containmen~ and mode of initia-tion, the early stages and most significant part of thepower excursion were comparable in behavior. The samestatement could be made for a sudden change ofreactivity from a different cause, say by addition of areflector.

If a subcritical volume of solution is made super-critical, the response of the system can be describedeasily, at least qualitatively. Upon becoming super-critical, the system fission power begins to rise, the ratedepending on the amount of reactivity added; this ratecan be very slow or very fast, for example, equal to adoubling of power once or twice per millisecond inextreme cases. This rate is many, many times faster thanwould occur by action of natural processes. This powerrise would continue until solution expansion mechanismswould allow increased leakage of neutrons, consequentreduction of reactivity, and reduction of power to a lowlevel. This first rise and fall is often called the powerspike or the transient. The peak power attained duringthis spike is higher than the power during any followingfluctuation and is proportional to a measure of the rateof adding reactivity or to the amount added. Typical

CRAC experimental fission rate traces are reproduced inFigs. 5 and 6. The oscillatory behavior following the fwst

power spike is supported by the rate of pouring solutionand by the existence of delayed neutrons, whoseprecursor nuclei were created during the spike. Figure 7illustrates the solution temperature measured during oneof the experiments; the time at which boiling occurs isseveral hundred seconds after the start of the experiment,long after the quenching of the power spike.

The mechanisms that limit the rise of power in the fustspike and control the subsequent power level are three innumber and are naturally occurring in any solutionreactor. Thermal expansion is fmt to be evident; as the

‘NS18! 1 1 7

\

\End of Solutlon Addition

I I I.S400 8s.00 10200

TIME (S)

Fw. 5. Relative fission rate versus time for CRAC experiment number04. The CRAC program,26 “Consequences Radiologiques d’unAccident de Criticite~ consisted of experiments during which asolution of enriched uranium nitrate was poured into a large diametercylinder to heights well in excess of the critical height. The result wasa fission power excursion, an example of which is illustrated in thisfigure.

FISSIONWS, , , 1 1 I ,

I

1 on -

1 on

10“

I@

30=

10“

1 Om , ,

0 126 250 S76 600 626 760 876

TIME (S)

Fig. 6. Relative fission rate versus time for CRAC experiment number12.

110[ 8 I I 1 I 1 I I -1

‘:~125 292 375 625 760 875

TIME Is)

F%. 7. Temperature of the solution versus time for CRAC experimentnumber 12. The upper curve was near the center, while the lower wasat the boundary of the container. Note that boiling temperatures werenot achieved for 725 s afler the start of the experiment.

temperature rises, the solution expands and even a smallamount is signflcant for increasing neutron leakage. Thesecond is bubble formation resulting from fissionproducts passing through water and creating hydrogen,oxygen, and steam. These tiny bubbles also cause thesolution to expand in volume and increase neutronleakage. Finally, and much later, boiling temperaturesare reached, and, usually, the onset of boiling reducesreactivity and power substantially more.

The CRAC experimental programzb consisted of alarge number of power excursions (about 40) in twocylindrical vessels of diameters 30 and 80 cm. Theuranium in the water-umnyl nitrate solutions was highlyenriched, about 93 LYO U-235, and solutions of variousconcentrations were used. Generally, at least threeimportant conclusions can be derived from these experi-ments that are significant to the study at hand. First, thereactivity quenching mechanisms, thermal expansion,bubble formation, and (later) boiling are invariablypresent; the fust two limit the magnitude of the fwstpower spike. Second, the power excursions are notdestructive; some splashing of solution occurred innearly every experiment, but the most violent of thesesplashes was only a bit more than two meters high. Themost violent experiment created a hydrostatic pressure*.—— ——

*The hydrostatic pressure is a liquid-phase pressure, thecharacteristics of which are a very steep pressure-volumerelationship. That is, a very small increase in volume (ordecrease of density) reduces pressure dramatically. This isdifferent from a pneumatic (compressed gas) pressure, which,for the same magnitude, stores much more energy. Thehydrostatic pressure generally will create Iittie motion ordamage.

high enough to bend the aluminum supports of the tank.These measured (and computed below) hydrostaticpressures are strictly proportional to the peak power inthe fwst spike raised to the two-thirds power as isillustrated in Fig. 8. And third, for the more severetransients, the first power spike invariably dominates theexperiment in terms of power, pressure, splashing, etc.Boiling of solution never occurred until long after thefirst power excursion, and boiling did not contribute tothe early splashing of any of the experiments. A generalconclusion is that to create a highly destructive powerexcursion in a solution system with a free (air) surface ismost diflicult if not impossible.

Because of these experiments with solutions of fissile

materials and because of the required conditions forcriticality for the postulated soil-water-plutonium mix-ture (almost a thick or dense solution), a reasonableconclusion is that not only is a critical system mostunlikely, but that a severely violent (that is, highlyexplosive) excursion is nearly impossible. Nevertheless, atheoretical model will be applied to the problem forcompleteness.

WI. THEORETICAL MODEL FOR POWER EX-CURSIONS*

The theoretical model used to analyze the CRAC and

KEWB experiments is part of a computer programdesigned to integrate the neutron kinetics equations with

the addition of a linear response to energy deposition,rise in temperature, or appearance of pressure. Manysuch programs exist for applications in the field ofreactor physics, dynamics, and kinetics. One of theearliest such programs was the Los Alamos RTS code,28which was used in the late 1950s and early 1960s toelucidate questions in regard to delayed neutrons, criti-cality accidents, and reactor dynamics. The particularformulation used in this study is the “Mackin Program”(Ref. 25) created for the specitic purpose of studying theextensive KEWB and CRAC series of experimentsmentioned earlier. Discussion herein will be brief becaus;complete descriptions of the code, testing, and applica-tions can be found in Ref. 25.

In all such computations, a basic assumption made isthat the rate of change of reactor power (rate of change.——. —*The theoretical model used for analyses in this study and thecomputer calculations performed to illustrate the physicaleffects are the work of Harry M. Forehand, Los AlamosNational Laboratory.

12

107 ;I I I

0 ExPadlllwItU Data KEWB

PRESSURE :

(Pa)O Experltial Data cRAC

/~v

i - Lamt %uara. Flt/.

t

‘O”!’’””:/I104 ~ , ,(, , , , I , ,s, I , a I I 1 ),,

103 10’ 10s 106

POWER (Wlcm3)

Fig.8. Hydrostatic pressure developed in the initial power spikeversus the peak specific fission ~wer. The experimental data show arelationship: pressure proportional to (specific power)v3. The theoryveriiies this relationship but also shows tb.at, for more extremecondhions, the pressure increases even less rapidly as peak powerincreases.

of neutron flux) is proportional to the existing reactorpower (neutron flux). The proportionability factor is thereactivity in excess of the critical condition or state. Forstudies of the solution experiments, the complete set ofdelayed neutrons is incorporated as an integraI part ofthe program. The feedback from deposited fission energyis associated with the reactivity proportionality factor;that is, the reactivity is a function of temperature,density, and state of solution (microbubbles, boiling,etc.). In abbreviated form, if

E@) =

n(t) =

‘r .

fission energy deposited (a function of time),dEldt = reactor power, a rate of change of

energy (also a function of time), andl/(o = reactor period or rate of change of

reactor power,

then the following functional relationship holds:*

j n(t) = am(t) = 6.) ~ .

If

(4)

*If additional investigations are pursued, it is important to notethat nomenclature is not universally the same. In this dis-cussion, that chosen is taken to be the same as in Ref. 25 forconvenience to the reader. Other references may have adfierent notation. I apologize for the double use of p(t) bothfor density and for reactivity.

p(t) =

p=

k?=

Ci(t) =

~=

reactivity as a function of time,the fraction of neutrons that are delayed in

time,the neutron generation time or the time forthe neutron density or fission power to rise by afactor of e = 2.718,concentration of delayed neutron precursors,anddecay constant,

+ Cl(t) = (+n(t) - kiCi(t) ,

(5)

(6)

and the reactivity p(t) can be expressed by

p(t) = aOT(t)+ alT~t) + ~V(t) , (7)

in which T(t) is temperature, V(t) is volume, aOand al arethe linear and quadratic components of the temperaturecoetllcient of reactivity, and $ is the void coefficient ofreactivity.

The temperature (or temperature rise) is computeddirectly from the deposition of fission energy and knownheat capacities. The microbubble volume VJt) is givenby the functional relationship

{

o for E < ECVm(t) =

~ vl(E~t) - E~] for E(t) > EC(8)

in which,

v=

EC=

constant relating energy density to radiolyticbubble volume,* andthreshold energy for production of micro-bubbles.

———*A comparable modelhas been used that relates fissionenergydensity to pressure resulting from the radiolytic gases createdby fissionparticles. This is also describedin Ref. 25.

13

This set of differential equations has been pro-grammed for a fast digital computer and tested againstexperimental data such as those from the CRAC andKEWB series of experiments. Pertinent parameters are

the density of U-235 in the solution (this tiects theneutron lifetime), the reactivity insertion rate (for exam-ple, addition of solution or motion of control rods), pasthistory of operation (affects delayed neutrons), and avolume of solution large enough that container walls are,at most, a minor perturbation. Observable that shouldbe matched (for example, from Figs. 5, 6, and 7) are thereactor period, the peak specific power, the energyrelease and temperature rise for the ftrst spike, andprediction of the hydrostatic pressures created, if any.Prediction of the onset of boiling should follow withoutdiftlculty.

The specific fission power, as a function of time, is aprimary output of the Mackin Code; from this powerdensity and the derived energy density, the temperaturerise, bubble volume, expansion, etc., are computed.Examples of this output are illustrated in Fig. 9. At zerotime, reactivity insertion rates of 10, 5, 1.05, 0.5, or 0.1

$/s” were imposed on the computational model, and thecomputed specific power rose exponentially until thereactivity quenching mechanisms were strong enough tostop the rise. The internal pressure was a maximum atthis time, as can be deduced from Figs. 8 and 9. Thetraces on Fig. 9 can be compared, qualitatively, to theshape of the early portion of the power traces in Figs. 5and 6.

A quantitative comparison of Mackin computations toKEWB and CRAC experimental data is shown in Figs.10 through 13. Figures 10 and 12 compare the calcu-lated and experimental peak specific power for bothseries, whereas Figs. 11 and 13 illustrate the fissionenergy density deposited in the power spike to the time ofpeak specific power. Generally, the theoretical predictionof peak specific power is very good and not significantlydifferent from the apparent fluctuations in the experimen-tal data. The integrated specific power, or energy densitydeposited in the power spike to the time of peak specificpower or for the complete spike, is less precise forrelatively long period transients but becomes moreprecise for the short period experiments. These latter

*The dollar ($) was proposed as a unit of reactivit y in 1945. It

is the interval of reactivity between delayed critical, where allneutrons are needed including those delayed in time, andprompt critical, where only prompt neutrons are needed tomaintain a constant fission rate. A rate of 0.1 $/s is a veryrapid rate of change of reactivity for a reactor.

102

POWER

(W/cm3) il

110-2

10-’

3

100

!

//IITIME (s)

Pig. 9. Specific fission power versus time as computed by the MackinCode. The reactivity insertion rates were 10,5, 1.05,0.5, and 0.1 $/s.

106I

J

106 . EmwbnOnt.1 0.1.

_ Cakuktbn

104PoWER

~ / ~

o

(Wlcm3) o103 0

00

102 0

0

10’

100

10-’

10-2 10-’ 10° 10’ 102 103 104

MAXIMUM INVERSE PERIOO (S-’)

Fig. 10. Comparison of the results of the Mackin Code~ with KEWBprogram experimental data. Peak speeitic power is plotted against theinverse peciod. The inverse period is proportional to the rate at whichreactivity is added.

experiments are much more important if prediction ofviolent effects is the objective of the study.

The experimental peak hydrostatic pressuresmeasured in these experiments are shown in Fig. 8.These momentary hydrostatic pressures are proportionalto the specific power raised to the two-thirds power, aswas mentioned earlier. The Mackin Code does notcompute pressures from basic principles, but this hasbeen done (in an independent study) by application of aversion of a dynamics program,25129which can computethe production of hydrostatic pressures and the action ofthese pressures to expand the system and hence reduce

14

lo~ $ I I I I I

ENERGY

(Jlcm3)o Exp.rlmental Data

_ Calcutatlm

; J ;

o

1020

0

.0

00

10’ 00 0

0

100 I10-2

MAXIMUM INVERSE PERIOD (S-l)

Fig. 11. Comparison of results of theory with experimental data.Specitic energy density generated to the time of peak specific power isplotted against the inverse period. Experiments are from the KEWBprogram.

10=I

ENERGY

(Jtct+)o E~D.*s

_ Calctitbn

,.2-0

0

~ -O

10’ z

,oo-,, I&(, ,,,,,, ,,,,,1 I I In –

10-2

I

10-’ 10° 10’ 102 103 104

MAXIMUM INVERSE PERIOD (S-l)

Pig. 13. Comparison of theory and experiment. Specitic energydensity at the time of peak power is plotted against the inverse period.Data sre from the CRACseries of experiments.

VIII. APPLICATION TO A PLUTONIUM-WATER-SOIL MIXTURE

106 I

106 0 Eqxdm.ntti Data

- Csk.lmt(on

104>POWER(Wlcm9

1037 G

102

10’a

10’J? ~

10-’e%l,,, ,11[ I,,,,,,, ,11181,, 11!81, rm10-2 10-’ 100 10’ 1o* 103 104

MAXIMUM INVERSE PERlOO (S-’)

Fig.12.Comparison of theory and experiment.Peak specificpowerfor CRAC experimentsis plotted against the inverse period.

pressures. The significance of this latter program is todemonstrate the correspondence between peak specificpower and peak pressures. Specific power is predictedaccurately by the Mackin Code and, therefore, pressuresare known well.

The computer program generally overpredicts theenergy release for the comp[ete power spike (not il-lustrated); this result can be regarded as a conservatismin the case of predictions of dfierent systems in which“magnitude and/or violence” of the excursion is animportant factor.

To apply the Mackin Code to the plutonium-water-soilmixture requires a few more assumptions. The mostimportant of these are listed below.

1.

2.

3.

4.

5.

The specific heat of the water-soil-plutonium mixturewas adjusted for the volume fraction of water andthe presence of soil and plutonium.

The reacting zone was assumed (arbitrarily) to be a75-cm radius, 50-cm plug in the (also assumed)larger rectangular disposal site. An assumption ofsize was necessary to relate change of temperatureand volume to reactivity.

The expansion was constrained to be only in theupward direction. This would overemphasize theupward motion, if any.

The reactivity insertion rate was related to the forcedflow of water through a 4-in. pipe. This flow wouldbe 0.155 m3/s and result in an increase of reactivityfor the whole pit of 1.05 $/s. Fractions and multiplesof this rate were taken arbitrarily. A realistic rate ofchange of reactivity from water flooding might be afew cents per second.

The effect of the resonance in the plutonium crosssection at 3200° C (as shown in Figs. 1 and 3) was

15

—

6.

imposed upon the computation in addition to what-ever reactivity insertion rate was chosen. That is,given an assumed value of H/Pu and some calcu-lated change of temperature, the change implied byFig. 4 was imposed upon the computation ofreactivity as the calculation proceeded. In fact,exaggerated values of H/Pu were chosen toemphasize the influence of resonance.

The Mackin Code is a “point” kinetics computation.This, in essence, means that the properties of thecritical system are assumed to be uniform through-out. This is very conservative for this problem as aspace-dependent model would reflect the existence ofthe much higher plutonium concentrations near thesurface. A high surface concentration would lead toeasy and quick expansion of this layer; hence, noexplosion whatsoever. A space-dependent modelexists, but this was deemed to be unnecessary for thestudy.

Given the modifications listed above, the MackinCode was applied to imaginary power excursions in theplutonium-soil-water system. Three ratios of hydrogen toplutonium were chosen, 1,000, 2,000, and 3,000, eventhough these are unrealistically conservative in relationto the amount of water required. Reactivity insertionrates up to 10 $/s (equivalent to ten 4-in. pipes ejectingwater at the maximum rate) were assumed. The mostsignificant results of these calculations are illustrated inFig. 14, in which the peak specific power (watts per cubiccentimeter) is plotted against the maximum reciprocalperiod attained during the power excursion. Data for thethree H/Pu ratios are plotted along with a collection ofexperimental data for both the KEWB and CRAC seriesof experiments. The only change from the experimentaldata is to increase the peak specific power as the H/Puratio increases. These calculated peak power densitiesshould then be transferred to Fig. 8, which shows thismomentary hydrostatic pressure as a function of peakspecific power. The peak hydrostatic pressures calcu-lated this way are only smaU multiples of an atmosphereand quite incapable of causing a disturbance moreviolent than a moderate splash. Because the momentarypressure increases only as the peak specific fission powerraised to the two-thirds power, it is apparent that aphysically violent excursion is improbable to the point ofbeing impossible. Even the exaggerated cases neversuggest “an enormous explosion, like a violent volcano.”

108I ,1 , , ,,,,,1 , ! , 111111 , , I 01!,11 , , ,tn##! I

E?.Pmlme”tml Data

1060 CRACA KEWB /

Ce.k.l.tlon /10’?

PoWER v HIPu .1000

(W/cm9

.Qlf0 HIPu -2000

10=>● H/Pu .3000

/

~ fA

w“ ‘A0“ c.

102 ~PA

.O ~

10’ ~ ‘i.

J

10°2 a

10-’ #[10-2

MAXIMUM INVERSE PERIOD (S-’)

Fig. 14. Comparison of theory and experiment with the effect of thePu-239 resonance included. Peak specific power is plotted against theinverse period. Data for both the KEWB and CRAC experiments areilhsstrat~ whereas the solid lines show results for excursionscalculated to occur in the postulated soiI-water-plutonium mixtures.The effect of the resonance is to raise the peak power by a factor of10 or 20. From tie data in Fig. 8, the hydrostatic pressure will beraised by only a factor of 4 to 7 for impossibly large amounts of water(high H/Pu). Pressures are at most a couple of atmospheres, far toolow to cause a violent eruption.

A somewhat hidden conservatism in this last step of

the investigation should be emphasized. This is the effectof the experimentally observed density gradient of pluto-nium in soil that follows when a solution is disposed of inthe ground. The plutonium is selectively deposited at andnear the surface; very little penetrates more than a fewcentimeters. This effect means that fission densitiescreated during an excursion would be largest near thesurface, and hence, pressures would be dissipated easilyand quickly. Any inertial confinement and subsequentexplosion would be negligible.

IX. CONCLUSIONS

The physical problems associated with a postulatedfission-product acid-uranium-plutonium disposal site insoil have been examined. The materials have beensimplified to include only SiOz, FeO, Alz03, water, andplutonium. Any neutron-capturing (poison) material hasbeen ignored. This is a conservatism that may be largebut that cannot be made quantitative.

This imaginary solution was assumed to be depositedin a 30-cm-thick layer of soil in a concentration gradient

16

similar to that actually observed in experiments, which ispreferentially near the surface. Critical masses in apostulated soil pit 9 m x 18 m with about 50’%0water byvolume and with water reflection were in the hundredsand thousands of kilograms. Smaller volumes could havesmaller critical masses but with large volume fractions ofwater or extraordinarily high concentrations of pluto-nium. Critical masses with substantially less water

moderation are possible only with very much greatermasses of plutonium. To postulate these masses to bediscarded is most unlikely and uneconomic, given thatthe object of the activity is to create and chemicallypurify plutonium.

Because the postulated disposal system has verysignit3cant amounts of water, the characteristics offission power transients in solutions have been in-vestigated and are reported. Only with significant effortcan a solution be forced to cause damage or violence(splashing) during a power transient. From the experi-ments themselves, it is evident that creating an “explo-sive” excursion in a solution is most d~lcult, and itshappening by accident is essentially impossible.

A neutron-point kinetics computer program (MackinCode) was used to investigate the properties of asupercritical soil-water-plutonium mixture even thoughsuch a mixture is most unlikely. The code predicts thatfor even extraordinary flooding rates, the power ex-cursion would not produce a violent physical effect. Thisis the case even for exaggerated emphasis of the reso-nance at 3200° C in the fission cross section of Pu-239.

Finally, we would like to comment on Medvedev’s8postulate that spring floods caused a drastic increase inthe proportion of water in the water-soil-plutoniummixture. First, the earlier arguments about masses ofplutonium and the influence of the H/Pu ratio areunaltered as is the dkcussion about the experiments andcalculations of the solutions excursions. Only the addi-tion of water as moderator and reflector in the theoreticalstudy would change. In the calculations, the referencerate was O.155 m3/s from a 4-in. pipe; rates ten timesthis, or 15.5 m3/s, also were assumed. From theresults, it is apparent that a reactivity insertion rate tentimes this, or 155 m3/s, could be assumed without thecalculations showing pressures suftlcient to cause signitl-cant damage or violen~e c$uing the excursion. A rate of

%6$155 m3/s is equal to 1; ft3/s, an extraordinary rateand quite impossible to achieve short of a good-sizedriver.

Thus, it is shown that a violent nuclear explosion in asoil-based, chemical solution disposal site is so dmtcult to

achieve that it may be taken to be impossible. Earliercomments said to have originated with Sir John Hill in1977* in the United Kingdom relating to the impossi-bility of such an explosion were timely and correct.

ACKNOWLEDGMENTS

Gordon E. Hansen and Harry M. Forehand, Jr.,contributed a great deal to the technical content of thisreport. The discussion of the resonance in the plutoniumcross section was developed by Hansen, whereas theavailabdity of the Mackin Code, as created by Forehand,made the analysis of postulated power excursions fairlypainless. I thank both gentlemen for their contributions.

However, responsibility for the conclusion of thestudy, namely, the essential impossibility of a nuclearexplosion in a waste disposal site, as postulated, is mine.

Finally, I would also like to thank the following peoplefor their contributions to this report: Linda Randolph,Jane Sherwood, Jan Harris, Kyle Wheeler, and RichardMiller.

REFERENCES

1.

2.

3.

4.

5.

——

“soviet Catastrophe Reported/’ quoted in the New

York Times, April 14, 1958, p. 6, picked up from aUnited Press article in Berlingske Tidende News-paper, Copenhagen, Denmark, April 13, 1958.

“Serious Accident in Soviet Atomic Plant? ForeignTourist Trafilc Prohibited in Sverdlovsk Area,” DiePresse Newspaper, Vienna, Austria, March 18,1959.

Central Intelligence Agency reports released in 1977and available from the CIA. (These are also pub-lished in Ref. 7)

Z. Medvedev, “Two Decades of Dissidence,” NewSci, 72,264 (November 4, 1976).

Z. Medvedev, “Facts Behind the Soviet Nuclear

Disaster:’ New Sci. 74,761 (June 30, 1977).—

*Sir John Hill, United Kingdom Granada televisionprogram,1977, and United Kingdom Science NOWradio program,1977; also Interview with the Press Association, LondonTimes, November 8, 1976; and Letter to the Editor, LondonTimes, February 8, 1977.

17

6. Z. Medvedev, “Winged Messengers of Disaster,”New Sci. 76,352 (November 10, 1977).

7. Z. Medvedev, Nuclear Disaster in the Urals (W. W.Norton and Company, New York, 1979).

8. Z. Medvedev, “Nuclear Disaster in the Urals:’ NewSci. 84, 115 (October 11, 1979).

9. A. E. Smith, “Nuclear Reactor Evaluations of216-Z-9 Enclosed Trench;’ Atlantic llichiield HanfordCompany document ARH-2915 (1973).

10. L. L. Ames, “Characterization of Actinide BearingSoils: Top Sixty Centimeters of 216-Z-9 EnclosedTrench:’ Battelle Pacific Northwest Laboratoriesdocument BNWL-1812 (1974).

11. H. D. Smyth, Atomic Energy for MiIita~ Purposes:The Ofjcial Report on the Development of theAtomic Bomb Under the Auspices of the UnitedStates Government (Princeton University Press,

New Jersey, 1945).

12. R. L. Murray, Nuclear Reactor Physics (Prentice-

Hall, Inc., Englewood Clitl’s, New Jersey, 1957).

13. H. C. Paxton, “Critical Data for Nuclear SafetyGuidance,” Los Alamos Scientific Laboratory re-port LAMS-2415 (May 1960).

14, W. R. Stratton, “Criticality Data and FactorsAffecting Criticality of Single Homogeneous Units,”Los Alamos Scientific Laboratory report LA-3612(September 1967).

15. H. C. Paxton, “Critical Dimensions of Systems

Containing U-235, Pu-239, and U-233,” USAEC

Technical Information Service Document TID-7028

(1964).

16. B. G. Carlson, “The Numerical Theory of NeutronTransport,” in Methods in Computational Physics(Academic Press, New York, 1963), Vol. 1.

17. S. F. Mughabghab and D. 1. Garber, “Neutron

Cross Sections,” Brookhaven National Laboratoryreport BNL-325 (1973), 3rd ed.

18. G. E. Hansen and W. H. Roach, “Six and SixteenGroup Cross Sections for Fast and IntermediateCritical Assemblies,” Los A1amos Scientific Labora-tory report LAMS-2543 (November 1961).

19. W. R. Stratton, Reply to D yson letter, Science 208,652 (May 16, 1980).

20. F. J. Dyson, Letter to Science Magazine, Science208, 652 (May 16, 1980).

21. R. E. Collins, Flow of Fluids through PorousMaterials (Reinhold Book Corp, New York, 1961).

22. K. D. Lathrop, “DTF-IV, A Fortran-IV Programfor Solving the Multigroup Transport Equation withAnisotropic Scattering,” Los Alamos Scientific Lab-oratory report LA-3373 (November 1965).

23. W. R. Stratton, “A Review of Criticality Acci-dents,” Los Alamos Scientific Laboratory reportLA-36 11 (September 1967).

24. R. D. O’Dell, F. W. Brinkley, Jr., and D. R. Marr,“User’s Manual for ONEDANT: A Code Packagefor One-Dimensional, Qiiusion Accelerated ~eu-tron Particle ~ransport~’ Los Alamos NationalLaboratory report LA-9 184-M (February 1982).

25. H. M. Forehand, “Effects of Radiolytic Gas onNuclear Excursions in Aqueous Solutions,” doctoraldissertation, University of Arizona, 1981.

26. P. LeCorche and R. Scale, “A Review of the

Experiments Performed to Determine the Radio-

logical Consequences of a Criticality Accident,”

Oak Ridge Y-12 Plant report Y-CDC- 12 (Novem-

ber 1973).

27. M. S. Dunenfeld and R. K. Stitt, “A SummaryReview of the Kinetic Experiments on WaterBoilers,” North American Aviation documentNAA-SR-7087 (February 1963).

18

28. G. R. Keepin, “General Solution of the ReactorKinetics Equations,” Nucl. Sci. Eng. 8,670 (1960).

29. D. M. Peterson, W. R. Stratton, and T. P.McLaughlin, “PAD: A One-Dimensional, CoupledNeutronic-Thermodynamic-Hydrodynamic Com-

puter Code,” Los Alamos Scientific Laboratoryreport LA-6540-MS (December 1976).

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