REACTOR PHYSICS AND FUEL.CYCLE ANALYSES A. M. PERRY and H. F. BAUMAN Oak Rid,ge National Laboratory Oak Ridge, Tennessee J7gJ0 Received August 4, 1969 Revised October 9, 1969 ':i!:::::::::::::::::::::i::::::;:;i;l;i;i;:;:;:;:;:;11 !aaaallillllaaaaaaaa:.laaaaal As ?resently conceiued at oah Ri.dge National Laboratory and described in this i.ssue, the single- fluid^^llolten-salt Breeder Reactffi , operqting on the 23272-83u fuel cycle and based on a refeience design , has a breeding ratio of - r.06, specific fissile inuentory of r.s hs/uw(e), a fuel doubli.ng time of -20 years, and fuel cycle costs of ,-0.2 mill/kwh(d. start-up may be accomptished with either enriched uranium or plutonium, with titfle effect on fuel cost; the breeding ratio, aueraged oaer reactor life, is reduced 0.0r to 0.02 relatiae to the equilibrium cycle. operated as a conaerter, with limi.ted chemical processing, the reactor may haue a conaersion ratio in the range 0.8 to 0.9 with fuel cycle cosfs of 0.7 to 0.9 mill/hwh(e). INTRODUCTION One of the most important aspects of the Molten-Sa1t Reactor (usn) ,concept is that it is well suited for breeding with low fuel-cycle costs, and it does so in a thermal reactor operating on the "'Th-233U fuel cycle. This is true not primar- ily because of any unique nuclear characteristics, for the reactor is similar to other thermal reac- tors in terms of attainable fuel-moderator ratios, the unavoidable presence of certain parasitic neu- tron absorbers, and reliance on a fertile blanket to reduce neutron losses by leakage to an accept- ably low level for breeding. Indeed, th€ concept might be thought to have some a priori disadvan- tage, because a substantial fraction of the fissile material is invested in the heat transfer circuit and elsewhere outside the reactor core. The pe- culiar suitability of the molten-salt reactor for K EY WO RDS: mo lten-solr re- ocfors, fuels, economics, op- eroti on, bree d in g, thor i um -23'2, ylg?ium-233, pe r(o rm on c e, M SBR, f u el cy c le, cos f, breed.- ing rotio economical thermal breeding stems rather from the practical possibility of continuous removal of fission*produat wastes and "tP", and virfually ar- bitrary additions of uranium or thorium, without ot]rerwise disfurbing the fuel. This fundamental aspect of the molten-salt reactor, details of which are discussed in other papers of this series, has a profound effect on the relationship between neu - tron economy and fuel-cycle cost. The coinci- dence of good neutron economy with low fuel-cycle cost which characterizes the molten-salt reactor appears to be unique among thermal reactors and will be described more fuIly in this paper. GENERAL NUCLEAR CHARACTERISTICS The LiF /BeFz carrier salt used in the MSR concept is not by itself a very good moderator. Its moderating power is about half to two-thirds that of graphite (ttre exact value depending on the pro- portions of Li and Be in the salt), while its macro- scopic absorption cross section is an order of magnifude greater than that of graphite, even with the feed lithium enriched to 99.99570 in the tl,i isotope. (Wittr this composition, <L070 of the neu- tron absorptions in the salt occur in ul,i; nearly half are in fluorine, and about a third in tl,i.) It is evident, therefore, that an additional moderator is needed, and graphite is selected for this purpose because of its compatibility with the salt. There is only a weak connection between the fissile fuel concentration in the caruier salt and the heat transfer characteristics of the salt (aris- ing primarily from the influence of the thorium concentration on the physical properties of the salt), and as a consequence one has considerable latifude in selecting the uranium (and thorium) concentrations in the salt. Because the carrier salt itself constifutes a significant neutron poisoor the fuel concentration in the salt must not be set 208 NUCLEAR APPLICATIONS & TECHNOIOGY VOL. 8 FEBRUARY 19?O
Transcript
REACTOR PHYSICS ANDFUEL.CYCLE ANALYSESA. M. PERRY and H. F. BAUMANOak Rid,ge National LaboratoryOak Ridge, Tennessee J7gJ0
As ?resently conceiued at oah Ri.dge NationalLaboratory and described in this i.ssue, the single-fluid^^llolten-salt Breeder Reactffi , operqting onthe 23272-83u fuel cycle and based on a refeiencedesign , has a breeding ratio of - r.06, specificfissile inuentory of r.s hs/uw(e), a fuel doubli.ngtime of -20 years, and fuel cycle costs of ,-0.2mill/kwh(d. start-up may be accomptished witheither enriched uranium or plutonium, with titfleeffect on fuel cost; the breeding ratio, aueragedoaer reactor life, is reduced 0.0r to 0.02 relatiaeto the equilibrium cycle.
operated as a conaerter, with limi.ted chemicalprocessing, the reactor may haue a conaersionratio in the range 0.8 to 0.9 with fuel cycle cosfsof 0.7 to 0.9 mill/hwh(e).
INTRODUCTION
One of the most important aspects of theMolten-Sa1t Reactor (usn) ,concept is that it iswell suited for breeding with low fuel-cycle costs,and it does so in a thermal reactor operating onthe "'Th-233U fuel cycle. This is true not primar-ily because of any unique nuclear characteristics,for the reactor is similar to other thermal reac-tors in terms of attainable fuel-moderator ratios,the unavoidable presence of certain parasitic neu-tron absorbers, and reliance on a fertile blanketto reduce neutron losses by leakage to an accept-ably low level for breeding. Indeed, th€ conceptmight be thought to have some a priori disadvan-tage, because a substantial fraction of the fissilematerial is invested in the heat transfer circuitand elsewhere outside the reactor core. The pe-culiar suitability of the molten-salt reactor for
K EY WO RDS: mo lten-solr re-ocfors, fuels, economics, op-eroti on, bree d in g, thor i um -23'2,ylg?ium-233, pe r(o rm on c e,M SBR, f u el cy c le, cos f, breed.-ing rotio
economical thermal breeding stems rather fromthe practical possibility of continuous removal offission*produat wastes and "tP", and virfually ar-bitrary additions of uranium or thorium, withoutot]rerwise disfurbing the fuel. This fundamentalaspect of the molten-salt reactor, details of whichare discussed in other papers of this series, has aprofound effect on the relationship between neu -tron economy and fuel-cycle cost. The coinci-dence of good neutron economy with low fuel-cyclecost which characterizes the molten-salt reactorappears to be unique among thermal reactors andwill be described more fuIly in this paper.
GENERAL NUCLEAR CHARACTERISTICS
The LiF /BeFz carrier salt used in the MSRconcept is not by itself a very good moderator. Itsmoderating power is about half to two-thirds thatof graphite (ttre exact value depending on the pro-portions of Li and Be in the salt), while its macro-scopic absorption cross section is an order ofmagnifude greater than that of graphite, even withthe feed lithium enriched to 99.99570 in the tl,iisotope. (Wittr this composition, <L070 of the neu-tron absorptions in the salt occur in ul,i; nearlyhalf are in fluorine, and about a third in tl,i.) It isevident, therefore, that an additional moderator isneeded, and graphite is selected for this purposebecause of its compatibility with the salt.
There is only a weak connection between thefissile fuel concentration in the caruier salt andthe heat transfer characteristics of the salt (aris-ing primarily from the influence of the thoriumconcentration on the physical properties of thesalt), and as a consequence one has considerablelatifude in selecting the uranium (and thorium)concentrations in the salt. Because the carriersalt itself constifutes a significant neutron poisoorthe fuel concentration in the salt must not be set
208 NUCLEAR APPLICATIONS & TECHNOIOGY VOL. 8 FEBRUARY 19?O
at too low a level, but rnust be high enough for thefuel to compete favorably (tor neutrons) with theIithium and the fluorine in the salt. On the otherhand, it must not be too high, Iest the inventory offuel outside the reactor core become excessive.The optimum fuel concentration, typically -0.2mo\eflo of UFe in the salt, or'-1 kg of uranium percubic foot of salt, is interrelated with the neutronspectrum in the reactor, which is a function of therelative proportions of fuel salt and graphite mod-erator in the core. Too large a proportion of saltIeads to an excessive fuel inventory and to a
poorly thermalized neutron spectrum, with a re-duced neutron yield, n; too large a proportion ofgraphite leads to excessive neutron-absorptionIosses in the graphite. An optimum salt volumefraction is typically found to be -13 to L\Vo.
The proper balance of the above factors does,
of course, depend in part on the power density inthe reactor core, which may be selected almostindependently of the power density in the remain-ing parts of the primary salt circuit. The muri-mum power density in the core is limited by fastneutron damage to the graphite moderator, whilethe removal power density in the external powerrecovery circuit is limited primarily by heat
transfer and pressure-drop considerations and by
requirements for pipe flexibility in the piping runsbetween the reactor vessel and the heat exchang-ers.
The necessity for maintaining a sufficientlyhigh fueI concentration to suppress neutron lossesin the carrier salt and in the moderator, togetherwith the requirement for appreciable core sizesimply to generate the requisite amount of pow€f,
leads to the conclusion that thorium must be pres-ent in the core, not merely in a surrounding blan-ket. However, the question of how the thorium isto be incorporated in the core is crucial to the
MSBR concept. one quickly recognizes severaldistinct possibilities, some much more desirablein principle than others, but full of implicationswith respect to reactor design and chemical pro-cessing.
we have previously given serious considerationto a two-f1uid reactor in which the fissile and
f ertile materials are carried in separate saltstreams, the bred uranium being continuoqslystripped from the fertile stream by the fluoridevotatility process. Blanket regions contain only
the fertile sa1t, while the core contains both fis-sile and fertile streams; these streams must be
kept separate by a material with a low-neutroncross section, that is, by the graphite moderatoritself. This approach appears to yield the best
nuclear performanc€, Owing primarily to a eombi-
nation of mu<imum blanket effectiveness and min-imum fueI inventory. It also exhibits attractive
Perry and Bauman FUEL-CYCLE ANALYSES
safety characteristics because expansion of the
fuel salt, upon heating, removes fissile materialfrom the core while leaving the thorium concen-
tration unchanged. The concept does, however,involve important questions regarding the reli-ability of the graphite "plumbingt' in the core, th9adequate proof of which may require a good dealof time and testing.
The present approach employs a single saltstream which contains both the fissile and the fer-tile materials. This concept represents a modestextrapolation of the technology already demon-strated in the MSRE. A central feafure of the
concept is the manner in which the single saltcomposition can be made to function adequatelyboth in the core and in the blanket (or outer core)regions. This is done by the simple expedient ofaltering the salt volume fractioil, making it con-siderably larger in the blanket than in the core.This undermoderation results in enhanced reso-nance capfure of neutrons by thorium in the outerregion, gives rise to a negative material bucklingin the outer region, and should in principle cause
a fairty rapid decrease in power density in the
blanket as a function of distance from the coreboundary. In practice, the distinction between the
core and blanket regions is not aS clear cut aS
this argument may suggest, but the idea worksreasonably welI. FigUre 1 illustrates the powerdensity distribution for our present reference de-sign based on the single-fluid concept. The en-
hancement of resonance neutron capfure in the
blanket (or outer core) region is indicated by the
ratio of neutron absorptions in 232Th to those in
"tU; this ratio is about 1.0 in the corer and 1.3
in the blanket. The salt annulus, which is requiredto allow the periodic replacement of the modera-tor, functions as a part of the outer core region.
The principal shortcoming of the single-fluidconcept, of course, is the substantial investmentof fissile material in the blanket region. This re-sults in a rather different compromise betweenbreeding gain and specific inventory than in the
two-fluid concePt, leading both to reduced effec-tiveness of the blanket region and to an apprecia-ble increase in fuel inventory. Forhrnately, thisfeafure of the single-fluid reactor is partly offsetby a reduction in neutron capfures in the carriersalt, owing to the fact that a single carrier saltcontains both fissile and fertile materials.
The preceding qualitative discussion is in-tended to provide a general understanding of the
interplay of factors aff ecting the selection of
MSBR design parameters. These factors are of
course quite numerous. They include core size,radial and urial blanket thickness, reflector thick-Ress, salt volume fractions in the core and blan-ket regions, thorium and uranium concentrationst
NUCLEAR APPLICATIONS & TECHNOLOGY VOL. B FEBRUARY 1970209
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Perry and Bauman FUEL-CYCLE ANALYSES
70
O'- ' ' I-0 50 100 150 200 2s0 300
CENTERLINE (cm)RADIAL DISTANCE FROM CORE
Fig. 1. Radial power density and fast flux distribu-tions-single-fluid MSBR.
chemical processing rates, and reactor powerIevel. Because the interaction of all these factorsis rather compl€xr and because of the need toidentify optimum values of the design variablesrather closelyr we have found it convenient tomake use of a comprehensive, automatic reactoroptimizatron procedure for arriving at that combi-nation of design parameters that will produc€, insome sense, the best attainable performance. TheReactor Optimization and Design code (nOOl isbased on a gradient projection method for locatingthe extreme value of a specified figure of merit,which may be any desired function of the breedingratio, the specific fuel inventoryr various ele-ments of the fueI cycle and capital costs, or anyother factors important to the designer. Thecomputational procedure comprises multigroup(synthetic), two-dimensional diffusion-theory cal-culations of the neutron fluxr &tr equilibrium fuel-cycle calculation which determines the criticalfueI concentration and nuclide composition consis-tent with processing rates and other variables,and the gradient projection calculation for movingthe cluster of independent variables in the direc -tion that most rapidly improves the figure ofmerit. Ttre optimization may be constrained bylimiting the allowed range of the independent vari-ablesr or by selecting in advance the desired value
(or a limiting value) of certain derived quantities,such as the ma:<imum power density.
The figure of merit used here in determiningreactor design specifications is related to the ca-pability of a reactor type to conserve fuel supplyin an expanding nuclear economy. For the specialcase of a linear increase in power generation, thetotal amount of nafural uranium that must bemined up to the point when the system becomesself-sufficient (i.e., independent of any externalsupply of fissionable material) is proportional tothe product of the doubling time and the specificfuel inventory. We have chosen to optim Lze ourMSBR design primarily on the basis of a quantitywhich we caII the fuel "conservation coefficientr"defined as the breeding gain times the square ofthe specific power, which is equivalent to the in-verse of the product of the doubling time and thefuel specific inventory. Therefore, a murimumvalue of the conservation coefficient is sought inthe optim i.zation procedure.
EOUILIBRIUII'I FUEL-CVCLE RESULTS
The result of a reactor optim tzation calculationis a set of specifications for the optimum reactorcordiguration, subject to any imposed constraints,together with a complete description of its equi-Iibrium fuel cycle. This description includes themultigroup neutron flux distributions, the result-ing power distribution, and the consistent set ofconcentrations of all nuclides present in the reac-tor. we have imposed constraints on mu<imumpower density (i. e., minimum graphite life), otroverall reactor vessel dimensions, and on chem-ical processing rates which we believe wiII resultin near-minimum power cost. Although we lackspecific irdormation as to the cost of chemicalprocessing as a function of fuel processing ratefor the liquid-metal extraction process, it appearsthat processing equipment sizes and operatingcosts wiII be comparable with those for thefluoride-volatiltty /uranium -distillation p r o c e s sconsidered for the two-fluid reactor. We havetherefore fixed the processing rates, listed inTable I, at values found to be essentiatly optimumin studies of the two-f1uid reactor, with minor ad-justments appropriate to the extraction process.While subsequent improvements in processingcost estimates may suggest some change in opti-mum processing rate and some change in fuel costestimates, we do not expect that these will resultin any major revision in performance estimatesfor the reactor.
The reference reactor configuration whrch re-sults from these and other (engineering) consider-ations is described by Bettis.l A summary of itsnuclear design characteristics is given in Table I.
210 NUCLEAR APPLICATIONS & TECHNOLOGY VOL. 8 FEBRUARY 1970
aAccording to our present flow sheet, Zt, Cd, In, and Sn
will be removed on a 200-day cycle, and Br and I on a
50-day cycle. The additional poisonitg, however, isnegligible.
A neutron balance for this case is given in Tableil, in which the normalization is to one neutronabsorbed in t3tI plus '*U.
Uncertainties in Neutron Gross Sections
We have estirnated the effect of uncertainties inneutron cross sections on the calculated perfor-
Perry and Bauman FUEL-CYCLE ANALYSES
TABLE I
Characteristics of the One-Fluid MSBR Reference Design
actor exhibits unusually low fuel-cycle costs incombination with good breeding performance. Thisresults primarily from the low specific fuel in-ventory and from a small but non-negligible ex-cess production of fuel, which results from theability to process the fuel rapidly at what appearsto be a very low unit cost.
The inventory of fissile material in the reactorand chemical processing plant amounts to some1480 kg, includittg - 100 kg each of 235u
?^1d "tP";when valued at $f g .00/g for "t and 233Pa and
$11 .20/g for "uU, this material is wortJr $19 mil-Iion. With an effective annual inventory chargerate of tTfto/year and a 0.8 plant factor, the fuelinventory thus contributes 0.2'l mill/kWh( e) to the
211
A. Description B. Performance
IdentificationPower, MW(e)
Mw(th)Plant factorDimensions, ft
Core zone L
HeightDiameter
Region thiclmesses
Axial: Core zone 2PlenumReflector
Radial: Core zoneAnnulusReflector
Salt fractions
Core zone L
Core zone 2PIenaAnnulusReflector
Salt composition, moleTo
UF+ThF+BeFzLiF
Processing cycle times for removalpoisonsa
and Xe; secNb, Mo, Tc, Ru, Rh,Te, Zt; sec
; Cd, In, Sn; daysLa, Ce, Pr, Nd, Pfir,; daysRb, Cs, Ba; Year
, I; days
Pd, Ag,
Sm, Eu,
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Peak damage flux, E >50 keV , nf ("*'Core zone 1
ReflectorVesseI
Power density, flcm3AveragePeakRatio
Fission power fractions bY zone
Core zone L
Core zone 2
Annulus and plenaReflector
14.3L.0623.18
L478L.52
22
sec)
3.2 x1014
4.2xLoL33. ? x1011
22.265.22.94
0. 7650.1670.0560.0L 2
mance of the MSBR. By far the most importanteffect is the uncertainty in the average value of rlof 23sU in the MSBR spectrum, which leads to an
uncertainty in the breeding ratio of t0.012. Un-certainties in the cross sections of other impor-tant MSR nuclides (such as F) make a relativelysmall contribution to the overall uncertainty in thebreeding ratio, which is estimated to be 1O.016. Adetailed discussion of cross-section uncertaintiesis given in a report bY PerrY.t
Equi librium Fuel-Cycle Costs
As stated before, the molten-salt breeder re-actor exhibits unusually low fuel-cycle costs in
ts^A tTrlia
NUCLEAR APPLICATIONS & TECHNOLOGY VOL. 8 FEBRUARY 1970
fuel-cycle cost. The fuel salt, with a compositionLIF /BeFz/ThF+ = 72/ L6/ L2 moLe7o, respectively,is estimated to be worth $3 million, including thethorium. At t07o/year, this contributes 0.04 mrLL/kwh(e) to the fuel cycle cost. For a conversionratio of 1.062, fuel production results in a reduc-tion of 0.09 milI/kwh(e) in the fuel cycle cost.The cost of thorium burnup, in contrast, is negli-gible [-0.002 mill/kWtr( e)].
The chemical process for removal of fissionproducts, which is under development for use withthe single-fluid MSBR, involves the accumulationof rare-earth fission products in a portion of thesalt stream in the liquid bismuth extraction tower.The concentration of rare-earth trifluorides inthis salt is limited by solubility to -0.7 moLe%o; itis presently planned to limit this concentration bydiscarding -0.5 fts /day of carrier salt having-100 times as high a concentration of rare earthsas the salt circulating in the reactor. The makeupof carrier salt (including ThF+) required to com-pensate for this discard thus contributes -0.5 x$f A+O /ttt = $932/day to the fuel cost, i.e., 0.0bmil/kWh(e) at 0.8 plant factor.
The cost of processing the fuel for removal offission products and for isolation of "tPa from thecirculating salt stream is difficult to assess pre-cisely. Otrr tentative estimate of these costs, in-cluding both capital and operating expens€, is -0.3mil/kWh(e), based on the rapid processing ratesindicated in Table I"3 h summ a;ty t therefore, weestimate that the equilibrium fuel-cycle cost willbe -0.? mil/kWh(e)r &s shown in Table m, for asingle-fluid MSBR of the reference design"
EFFECT OF CHANGES IN REACTORDESIGN PARAIIIIETERS
Although our computational procedure is de-signed to lead directly to the optimum combinationof reactor parameters, it is nonetheless a matterof some interest to see how deviations of theseparameters from their optimum values will affectthe performance of the reactor. The influence ofthese parameters on reactor performance may beinvestigated by assigning specific perfurbed val-ues to each parameter in furn, the others retain-ing their reference values, and performing theflux and equilibrium fuel-cycle calculations forthe perfurbed cases. b:r some instances, a se-lected subset of the unperfurbed variables may beallowed to be reoptimized, using ROD, if there isreason to suppose that such reoptimrzation willpartially compensate for any adverse effect of theperfurbation. The effect of several specific de-parfures from the reference 1000 nnw(e) designgiven in Table I is discussed in the followingparagraphs.
Reactor Plant Size
The effectiveness of the blanket (outer core)region depends very much on its thickness. Nor-mally, the blanket will contain a larger fraction ofthe salt inventory for a small than for a largerreactor. Thus, both the fuel specific power andthe breeding gain, for an optim rzed reactor, in-crease as the reactor plant size is increased, asshown in Fig. 2. This is true when the reactorsare compared at equal core life (ttre solid curves)or at equal average core power density (ttre dashedcurves). A brief listing of dimensions and otherparameters for 500, 1000, 2000, and 4000 MW(e)reactors is given in Table fV.
212 NUCLEAR APPLICATIONS & TECHNOLOGY VOL. B FEBRUARY 19?O
01234REACToR PoWER [ 1 0' MW(e)]
Fig. 2, Effect of power level on MSBR performance.
Graphite Moderator Life
The useful lif e of the graphite moderator isIimited by radiation damage effects, caused by
fast neutrolrs. As discussed by Eatherlyrn we have
for the present adopted a limiting fast-neutronfluence (ngraphite volume change at the end of exposure.Since the fast-neutron flux is almost entirely de-termined by the local power density (per unit vol-
Perry and Bauman FUEL-CYCLE ANALYSES
ume of salt-plus-moderator), there is a nearlyunique relationship between maximum core power
density, plant utilization factor, and useful core
Iife, for a specified manimum fluence. While one
expects a higher power density to be accompanied
by a reduced fuel inventorYr there is in fact apower density above which increased neutronIeakage losses and other associated losses inbreeding gain more than offset the reduced inven-tory, and the fuel yield and the conservation coef-ficient then decrease. These trends are exhibitedin Fig. 3, which shows breeding gain, specific in-ventory, fuel yield, and conservation coefficient as
a function of core life. In this comparison, blan-ket, reflector, and plenum thicknesses were held
constant, and the core size was specified. OnIy
the salt volume fraction was reoptimized, and itchanged very little.
Thorium Concentration
The thorium concentration in the fuel salt pri-marily influences the uranium inventory and the
breeding ratio. For a reactor configUration verysimilar to our present reference design (nut
having a slightly lower estimate of the requiredexternal salt volume) we have examined the irdlu-ence of thorium concentration on reactor perfor-mance over the range 10 to L4 moleflo ThF+. Crosssections were carefully computed for each regionin each case and iteratively adjusted to allow forresultant changes in reactor configUration. Inthese calculations, core suze, radial and urialblanket thickness€s, and core salt volume fractionwere all subj ect to reoptimization.
t0 rr-- CSNSTANT CgRE L I FE I
- - -- CONSTANT RATIO OF REACTOR
POWER T0 C0RE VOI-UME I
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TABLE IV
Performance of Single-Fluid MSBR's as
a Function of Plant Size
0;
GRA'HITE CgRE LIFE (yeor)
Fig. 3. Performance of 1000 MW(e) MSBRtion of core life (at 0.8 plant factor).
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Reactor Power, nAW(e)
500 1000 2000 4000
Core height, ft
Core diameter, ftSal! specific volume,
ftTMw(e)
Fuel specific inventorYtksl Mw(e)
Peak power densitY, W / cm3
Peak flux ( > 50 keV),!}ta n/ (c*' sec)
Core life, Years at 0.8 PF
Leakage,n/fissite absorption x 1000
Breeding ratio
Annual fuel yield, Vo/ Year
Conservation coefficient
9.44
L0.42
1.75
1.65
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NUCLEAR APPLICATIONS & TECHNOLOGY VOL. B FEBRUARY 1970 213
Perry and Bauman FUEL-cycLE ANALYSES
The basic interpLay, of course, is between ris-ing breeding gain and rising inventoryr as thoriumand uranium concentrations are increased. Boththe annual fuel yield (y) and the conservation co-efficient (cc1 should exhibit a peak, when plottedas a function of thorium concentration, but thepeaks will occur at different places because of thedifference in weight assigned to the specificpower. These trends are shown in Fig. 4. It maybe seen that there is quite a broad murimum inthe conservation coefficient in the vicinity of LzmoLe%o ThFa.
Salt Volume Fractions
core. In aII of our calculations, the optimum saltvolume fraction in the core has fallen in the range12 to 15 voL%o, with a carbon/fissile-uranium atomratio close to 9000. As indicated earlier, the vol-ume fraction is rather closely determined by abalance between fuel inventoryr degree of neutronmoderation, and neutron absorptions in the mod-eratoq for the reference design, the optimum saltfraction was 0.132.
Blanhet. The volume fraction of salt in the blan-ket (outer core) is central to the whole concept ofa single-fluid, L000 nrrw(e) molten-salt breederreactor. We have tested the effect of variations insalt fraction (in ttre radial blanket) under the spe-cial assumptions of constant overall salt volumeand constant outer diameter of the blanket region.Results of these calculations show that a broadoptimum exists in the range of 0.85 to 0.6 for thesalt fraction. The choice of 0 .97 for the referencereactor was initially selected to permit, if de-sired, the use of a randomly packed baII bed in theblanket.
cc
G (x 100)
I(xv
l0)
REFERENCE DESIGNII
I
aPa Removal Rate
Rapid and inexpensive isoration of tt'pa fromthe circulating fuel stream is essential for eco-nomic breeder operation of the single-fluidmolten-salt reactor concept. The necessity forremoving the Pa and allowing it to decay outsidethe neutron flux may be seen from Fig. b, in whichwe show the approximate loss in breeding ratioassociated with Pa absorptions as a function ofspecific power and of the processing cycle timefor continuous isolation of pa from the circulatingsalt stream. (This 1oss incrudes both the neutronIosses in the "tpa and the destruction of latent"tu") As one would expect, the pa removal cyclemust be short compared to the 40 -day mean decayIife, if significant losses are to be avoided. Theeffect of the Pa removal rate (along with certainfission products) on the breeding performance ofMSRts is shown in Figo 6. Note that for no pa re-moval, the reactors considered are high perfor-mance converters rather than breeders.
Removal of Fission Products
The fission products may be divided into sev-eral groups, according to their chemical behaviorin molten salt systems" The main groups, roughlyin order of importance as neutron poisons, are thenoble gases, the rare earths, ilr€ noble and semi-noble metals, the volatile fluorides, and the stablefluorides not readily separable from the carriersalt.
0.J0
0.08
0. 06
0. 04
0.02
0l0 100 1000
PR0CESSINc CYCLE TIME FOR pa REM0VAL (days)
2,6(5
ooa4
bs
ou.l
1B
t6
l4
l2
oH
C)Fu- &,
E= c5H<u z'll :z F{:i= n
=< E=_? a(J r-t z,u->u-dL! I ./,E=2
lrJ YZ'> doz,
<J> lrld=lrl tr-tt',z,o(J
ot l0ll 12 13 14
THORIUM C0NCENTRATION (mole%)
Influence of thorium concentrationformance of a single-fluid MSBR.
l5
Fig.on the per-
5, Approximate loss in breeding ratio associatedwith neutron absorptions itr 233pa for a single-fluid MSBR.
Fig. 4.
214
I
S=3
I
I
0
I
vl
llw
tl
,2 ./a
lllr,l-+
llfr
,/7:.5
l-rJ
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//
7-/,
z 0'I U.]J
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CYCL
I
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/7/
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//
I-.|.0
I
ll(D.
tl-.--
7//-.J
/al
0.5
I
NUCLEAR APPLICATIONS & TECHNOLOGY VOL. 8 FEBRUARY 19?O
syeorSALT DtsCAN(NOT INCLUDING 7r)
_I 3o-day Pa
3-day Pa CYCLE
-SALT DISCARD( INCLUDES 7r)
4yeor\Ov"Ot\
NO Pa REM0VAL
O
d.
=3 1.00a/,d.u.J
=o(J
1.10
I .05
0.95
0 .900 100 200
RARE EARTH REM0VAL CYCLE (days)
Perry and Bauman FUEL-CYCLE ANALYSES
whose potential poisoning effect is of real con-cern. The chemical behavior of this group of fis-sion products is discussed in detail by Grimes:For the present purpos€r it is sufficient to notethat we believe -|Wo of these nuclides will remainin the core regions of the MSBR. On this basis,the poison fractiotr, P (t ), of all nuclides in thegronp and the time-averaged poisoning, V(t ), uP
to time t after start-up with clean graphite, areshown in Fig. 7. Since we anticipate replacementof the graphite aftervQ years, w€ may see fromFig. 7 that the average reduction in breeding ratioattributable to the accumulation of these nuclidesis 0.004. This effect is more than compensated bythe burnout of toB in the graphite, and these ef-fects are assumed to cancel, in our calculations.
The "semi-noble metalsr" including Zt, Cd,In, and Sn, are assumed to be removed in an ad-junct to the Pa removal process. The poison ef-fect of this group is small and they could also beremov€d, if necessary, by a gradual discard offuel salt (from which the uranium would be recov-ered by fluorination).
The volatile fluorides of Br and I are relativelyunimportant and are removed in the fluorination
300
Fig.6. Conversion ratio vs processing cycle times-single-fluid MSBR.
An outstanding characteristic of the molten saltreactor is the relative ease with which the noblegases --notably 135 Xe- can be removed from thesalt stream" This aspect is discussed in detail byScotta; suffice it to say here that we estimate aresidual poisoning eff ect ( reduction in breedingratio), due to 135 Xe together with other noble gas
fission products and their daughters, of not morethan 0.005.
The effect of the rare earth rernoval cycle onthe breeding performance of single-fluid MSR's(at various Pa removal rates) is shown in Fig. 6.The abitity to process the fuel rapidly for rareearth removal is one of the most important char-acteristics of the molten salt reactors. Whilerapid rare earth and Pa removal are required forgood breeding performance, there is considerableflexibility to trade off nuclear performance fordecreased processing rate (and processing cost)at the discretion of the designer.
The "noble metalsr" which do not form stablefluorides and do not remain in the fuel salt, wouldhave a serious adverse eff ect on the breedingratio if they simply attached thernselves to thegraphite moderator in the core. The nuclides inthis group, which includes Nb, Mo, Tc, Ru, Rhtand several others of less importance, have acombined yield of 0.35 and, if they accumulated inthe reactor core over a long enough period oftime, would eliminate any chance of breeding.Most of the nuclides in this group, however, have
small neutron-absorption cross sections and saht-rate very slowly, or else they have very- lo*yields. It is primarily nuMo, nnT", totR*, and rosRl
2 4 6 8 toTIME (calendar years)
Fig. 7 . Change in breeding ratio due to noble-metalfission products in MSBR.
0.0.|4
0.0.|2
0.010o
d.
2 o.oo8olrllr I
E.co
= o. 006lrl(5=(-)
0.004
0. 002
,/
/1,u
/
/
-/
/
.aP(t)
,/rNUCLEAR APPLICATIONS & TECHNOLOGY VOL. 8 FEBRUARY 1970 215
Perry and Bauman FUEL-CYCLE ANALYSES
step of the Pa removal process. The stable fluo-rides of Rb, Sr, Cs, and Ba are removed by thediscard of salt from the rare earth process on aIong cycle, typically eight years.
REACTOR START.UP AND APPROACHTO EOUILIBRIUM
The preceding discussion has dealt only withthe equilibrium fuel cycle, in which aII nuclideconcentrations-and particularly those of the ura-nium isotopes -are time-independent and havetheir asymptotic values. This condition is in factapproached rather rapidly in an MSBR, because ofits relatively high specific power. Nonetheless, itis of interest to examine the transient fuel-cyclecharacteristics of the reactor when it is initiallyfueled with enriched uranium (t*U) or with plu-tonium.
There is considerable latifude in specifying theinitial fuel loading for the reactor, even when theequilibrium fuel cycle is well defined, since theinitial thorium concentration rr&yr at the discre-tion of the operator, be quite different from theequilibrium value. We have, in fact, tried dif-ferent initial thorium concentrations, and find noadvantage in choosing a value different from theequilibrium one. In the following discussion,therefore, it will be understood that the thoriumconcentration is held constant at L2 mole%.
2.0
.|.6
2 3 3g
-_
/\2 3 +g
z 2 3 5g
2 3 sg
235u Start-up
Start-up of the reactor on enriched uranium(gS7o zssg; results in an initial conversion ratiosubstantially less than unity. However, because233U is much more reactive than 235U in the MSBRspectrum, the export of fissile material from thereactor plant may begin quite soon after start-uprand indeed well before the conversion ratio acfu-ally exceeds unity.
Time-dependent inventories of the uraniumisotopes are shown, for the reference single-fluid1000 Mw(e) MSBR, in Fig. I, while the conversionratio and the cumulative net feed of fissile mate-rial to the circulating fuel salt are shown in Fig.9. It may be noted that very little additional fuelis supplied to the reactor in excess of the initialcritical mass required for start-up. There is, ofcourse, some loss in performance, averaged overthe life of the reactor, associated with this initialphase of the fuel cycle. The average reduction inbreeding ratio, over the lif e of the plant, is'-0.018, while the increase in the present value ofthe 30-year fuel-cycle cost is +0.02 mi11/kWh(e).
Pu Start-Up
A useful attribute of the molten-salt reactor isthe capacity of the LIF /BeFz/ThF+ carrier salt tocontain plutonium in the form of PuF3, with a sol-ubility in excess of 1 mole?o at the operating tem-peratures of the MSBR. We have considered thestart-up of the MSBR on plutonium whose compo-sition is typical of the material discharged from a
Conversion ratio and cumulative fissile feed-enriched uranium start-up.
\\
/ \t \\ \
I\
NUCLEAR APPLICATIONS & TECHNOLOGY VOL. B FEBRUARY 1970
PWR or BWR with a fuel exposure in the neigh-borhood of 20 000 MWd/T, specifically, 59 .770
"nPr, 24.LVo zaoPu, L2.2Vo 'ntPt, and 4.0Y0'*Pu. A
notable difference between the plutonium and ura-nium start-up cases is the much lower initial in-ventory of plutonium, which is due to the veryIarge effective cross sections of the plutoniumisotopes in the MSBR spectrum. These isotopesburn out very rapidly, howev€fr and additionalplutonium must be supplied for a time until nearlyenough "tJ is produced to sustain the chain re-action by itself. Thereafter, the concentrations of
"nP*, 2a0Pu, and 'ntPu decrease rather sharply,while that of 'aPu decreases more slowly until theplutonium ceases to make a net positive contribu-tion to the reactivity. At this point, the plutonium(now mainly z+zps) is isolated from the circulatingfuel salt and discarded. If this is done, the resultis a seU-sustaining "t-fueled reactor in whichthe 235U and '*U concentrations are temporarilybelow their equilibrium values, and the asymptoticbreeding ratio is approached from the high side.
NUCLEAR APPLICATIONS & TECHNOI'OGY VOL. 8 FEBRUARY 1970
Perry and Bauman FUEL-CYCLE ANALYSES
These features of the plutonium start- up areexhibited in Figs. 10, 11, and 12.
The average breeding ratio, over a 30-yearplant tife at 0.8 plant factor, is reduced by '-,0.008relative to the equilibrium cycle. The presentvalue of the fuel-cycle cost is acfually decreasedby ,-0.04 mill/kW4(e) if one assigns to the fissileplutonium a value i that of enriched "uU.
OPERATION UIITH LIMITED FUEL PROCESSING
The combination of good breeding performancewith low fuel-cycle cost, which is associated witheconomical processes for the rapid removal offission products and protactinium, is an impor-tant feafure of the molten-salt reactor concept.Nevertheless, quite satisfactory fuel costs can be
achieved in the absence of fuel processing for re-moval of protactinium or fission products, eI-though the reactor will of course not breed whenoperated in this fashion.
In examining this alternate mode of operation,we posfuIate the occasional batch discard and re-placement of the entire inventory of carrier salt,including the thorium, but not including the ura-nium; the latter is to be recovered by fluoridevolatility (as was done with the MSRE tueI salt)and recycled to the reactor. The removal of
noble-gas fission products from the salt by gas
sparging and of noble-meta1 fission products by
OPERAT I NG T IME _ EQU IVALENT FULL-POI'IER YEARS
Inventories of uranium isotopes and total plu-tonium for plutonium start-up of MSBR.
2.0G4J
No
alrld. ,lOJ
=U.J
==u.J
9za
^ .|.6
g)iz
(Y!
o
a 1.2u.J
d.OF=u,J
= o.BElrJFV'v,
0.4
20l612
Y 242
^
241
\ \
\239
\
/
233
/\" ?34
235
??6
217
Perry and Bauman FUEL-CYCLE ANALYSES
2.0 fuel-cycle costs for the converter reactor, with asalt discard cycle, to be 0.7 to 0.8 mill/kWh(e).compared with the MSBR, the principal cost dif-ferences are a saving of -0.2 mill/kwh(e) in fuelprocessing, an increase of 0.2 to 0.3 mil/kWh(e)for fuel burnup, and possibly some reduction offuel and salt inventory charges (0. 1 mil/kWtr(e)].Thus, the fuel-cycle cost for the converter re-actor, without chemical processing for removal ofprotactinium or of fission productsr appears to bewithin 0.1 mill/kWh(e) of the cost for the breederreactor.
TEI'IPERATURE COEFFICIENTS OF REACTIVITY
Expansion of the single fissile-fertile salt inthe one-fluid reactor reduces the density of mostof the absorbing materials in the same proportion,so that one might expect a very small prompttemperature coefficient of reactivity. The densitycoefficient of the salt is in fact very small. b:r
addition to this, however, there is both a positivecontribution to the salt-temperature coefficientassociated with the shift in thermal-neutron spec-trum with increasing salt temperature, and a neg-ative contribution associated with the Dopplerbroadening of resonance capfure lines in thoriurn"The latter predominat€sr resulting in a promptnegative coefficient of -2.4 x 10-5 0 h/ h/ "C.
The graphite moderator contributes a positivecomponent to the overall temperafure coefficient,attributable to an increase in the relative crosssection of "uU with increasing neutron tempera-fure. This results in an overall coefficient whichis very small, though apparently negativ€r i.e.,-0.5 x 1o-5 /"c.
The prompt negative salt coefficient wiII large-Iy govern the response of the reactor for tran-sients whose periods are several seconds or less.The small overall coefficient will provide littleinherent system response to impressed reactivitychang€s, and it will consequently be necessary toprovide control rods to compensate any reactivitychanges of intermediate duratiorl. Long-term re-activity effects, such as those associated with thefuel cycle, are compensated by adjustment of thefuel concentration in the salt.
SUTIMARY AND CONCLUSION
While a fuII economic optimization of thesingle-fluid molten-salt breeder reactor has notyet been undertaken, it is apparent that godbreeding performance can be achieved in conjunc-tion with unusually low fuel-cycle costs, subject tothe successful completion of chemical processingdevelopments now under way. That is, a breeding
/
PuPURCHASED 239 + 24 )
J-
CONVERSION RATIOlltltl
,/
,71*r^ rM soLD ( 233 + 235 )
I
I
1.3
1.6 1.2CD
J
.'to\., | ,2tt',Fz,=o=3 o.gl-a
F
J
===(J0.4
ol.l F
d,
=ol-{
v,d,
1.0 E=o(J
0.9
0.981? 16 20
OPERATING TIME - EQUIVALENT FULL-POWER YEARS
Fig. L2. cumulative purchases and sales of fissile ma-
l;t:l"li_* nversion ratio MSBR with pluroni-
deposition and by escape to the off-gas system, &sobserved in the MSRE, are assumed to occur.
An optimum salt discard rate exists, for whichthe cost of replacing the salt (and recovering ura-nium) is balanced against the fuel makeup cost,which depends on the conversion ratio and henceon the level of fission-product poisoning. In addi-tion, howev€r, there is a minimum discard raterequired to limit the concentration of rare-earthtrifluorides in the circulating fuel salt to an ac -ceptable level ((1 mole%). This consideration perse will place a limit of -10 years on the salt re-placement interval.
We have investigated the trend in fuel-cyclecostsr os a function of the salt replacement inter-val, for a molten-salt converter reactor which isdefined in terms of its general nuclear character-istics, such as neutron leakage and fuel inventoryrbut whose engineering design has not been speci-fied in detail. We found the fuel costs to be ratherinsensitive to the salt replacement interval from3 years to 8 or 10 years, with a broad minimum at5 to 6 years. The conversion ratios ranged from0.84 for a -year salt-replacement interval to0.78 for a lO-year interval.
We have not yet made any detailed estimates ofeosts for the fluorination plant and for the chem-ical treatment plant necessary to control the com-position of the salt over long periods of time.Allowing 0.1 mill/kWh(e) for this equipment andits operation, and 0.1 mil/kWh(e) for graphitereplacement in the reactor core, we estimate the
218 NUCLEAR APPLICATIONS & TECHNOLOGY VOL. 8 FEBRUARY 19?O
ratio of >1.06, together with a specific fuel inven-tory of <1.5 kg/IvIW(e), will be attainable withfuel-cycle costs of ,-0.? mill/kWh(e). The asso-ciated fuel doubling time is -20 years.
The MSBR fuel cycle may be initiated eitherwith enriched uranium or with plutonium dis -charged from light-water reactors. The reductionin breeding ratio, averaged over the life of the re-actor, is <0.02 and 0.01, respectively, for theuranium and plutonium start-up cases relative tothe equilibrium case. The present value of thefuel-cycle cost is increased, relative to that forthe equilibrium cycle, by "'0.02 milt/kWh(e) forthe uranium-start-up caserwhile for the plutonium-start-up case the cost appears to be0.04 miII/ kWh
Iess, based on a fissile plutonium value equal to
: that of 235 u.' Development of the technology for molten-saltreactors themselves and for the associated chem-ical processes for removal of protactinium and
fission products need not necessarily be carriedout on precisely the same time schedule, sincean economically attractive fuel cycle may be
achieved with a salt-discard cycle, resulting in aconversion ratio of 0.8 to 0.9. A given reactor,operated initially in this w&Yr could subsequentlybe operated as a breeder by the addition of ap-propriate processing equipment to the reactorplant.
ft is tfius apparent that there is considerablelatifude in the mode of operation of molten-saltreactofsr with only small variations in fuel-cyclecost. We believe that this can facilitate the devel-
Perry and Bauman FUEL-CYCLE ANALYSES
opment of the molten-sa1t reactor and of the asso-ciated chemical-processing technology on timeschedules appropriate to each, and will encouragean orderly progress toward the achievement of an
economical breeder reactor.
ACI(NOTLEDGTETUTS
The authors wish to acknowledge the contributionsmade by many of their colleagues to the work reportedhere, and in particular those made by R. S. Carlsmith,W. R. Cobb, E. H. Gift, and O. L. Smith. This researchwas sponsored by the U.S. Atomic Energy Commissionunder contract with the Union Carbide Corporation.
REFERENCES
1. E. S. BETTIS and R. C. ROBERTSON, "The Designand Performance of a Single-Fluid MSBR," Nucl. ApPl-Tech., 8, 190 (1970).
2. A. M. PERRY , "[rfluence of Neutron Data in the
Design of Other Types of Power Reactofs," ORNL-TM-2L57, Oak Ridge National Laboratory (March 8, 1968).
3. M. E. WHATLBY, L. E. McNEESE, W. L. CARTER,L. M. FERRIS, and E. L. NICHOLSON, "EngineeringDevelopment of the MSBR Fuel Recycle," Nttcl. APPI.Tech.,8, 170 (1970).
4. E. P. EATHERLY and D. scoTT, "Graphite and
Xenon Behavior and Influence on MSBR Design,tt Ntrcl.APPI. Tech., 8, t79 (1970).
