FUEL DESIGN AND CORE LAYOUT FOR A GAS-COOLED FAST …

FISSION REACTORS

KEYWORDS: gas-cooled fast re-actor, sustainable nuclear powersystem, integral fuel cycle

FUEL DESIGN AND CORE LAYOUT FORA GAS-COOLED FAST REACTORW. F. G. VAN ROOIJEN,* J. L. KLOOSTERMAN,T. H. J. J. VAN DER HAGEN, and H. VAN DAM Delft University of TechnologyInterfacultair Reactor Instituut, Mekelweg 15, 2629 JB Delft, The Netherlands

Received August 27, 2004Accepted for Publication January 13, 2005

The gas-cooled fast reactor (GCFR) is regarded asthe primary candidate for a future sustainable nuclearpower system. In this paper a general core layout ispresented for a 2400-MW(thermal) GCFR. Two fuel ele-ments are discussed: a TRISO-based coated particle andthe innovative hollow sphere concept. Sustainability callsfor recycling of all minor actinides (MAs) in the core anda breeding gain close to unity. A fuel cycle is designedallowing operation over a long period, requiring re-fueling with 238U only. The evolution of nuclides in theGCFR core is calculated using the SCALE system (one-dimensional and three-dimensional). Calculations weredone over multiple irradiation cycles including repro-cessing. The result is that it is possible to design a fueland GCFR core with a breeding gain around unity, withrecycling of all MAs from cycle to cycle. The burnupreactivity swing is small, improving safety. After severalfuel batches an equilibrium core is reached. MA loadingin the core remains limited, and the fuel temperaturecoefficient is always negative.

I. HISTORIC BACKGROUND AND RENEWED INTEREST

The gas-cooled fast reactor ~GCFR! is one of the sixGeneration IV nuclear reactor concepts that is attractingan increasing amount of attention worldwide. Within thisframework we investigated a GCFR core layout and fueldesign, focusing on high-temperature operation withcoated particle ~CP! fuel and sustainability. The GCFRconcept was already investigated in the 1960s and 1970sin the United States, Japan, the former Soviet Union, andEurope. Early GCFR designs were based on the pin-typeliquid metal fast breeder reactor ~LMFBR!, with a gas-

eous coolant replacing the liquid metal. One of the prin-cipal interests was the reduction of parasitic absorptionand moderation by the coolant, resulting in a harder neu-tron spectrum, improving the breeding gain. All designsused a gas coolant under high pressure ~5 to 12 MPa! anda prestressed concrete reactor vessel.

General Atomics ~United States!1,2 presented a de-tailed design for a GCFR with helium coolant and pin-type fuel with stainless steel cladding. The core consistsof a driver fuel zone containing highly enriched fissilematerial with radial and axial blankets. Mochizuki et al.3

prepared a design for a GCFR with fuel pins with stain-less steel cladding and helium coolant. This design alsohas a driver core and blankets. In the former Soviet Union,a GCFR was developed using dissociative cooling1,4,5: Aliquid ~N2O4! dissociates in the core and recombines toN2O4 in the cold leg, releasing heat. Special Cr-baseddispersion fuel pins were developed for use with the cor-rosive coolant.6 In Europe an international association~Gas Breeder Reactor Association! prepared four designsfor a GCFR, aptly named Gas Breeder Reactor ~GBR!-1through GBR-4 ~Refs. 7 and 8!. These designs featuredboth helium and CO2 coolant, and pin-type fuel as wellas CP fuel. The GBR-2 and GBR-3 reactors had elevatedoutlet temperatures ~7008C for GBR-2 and 6508C forGBR-3! for improved system efficiency. To accommo-date these temperatures CP fuel was required. GBR-2used helium, and GBR-3 used CO2 gas. Several prob-lems, including fabrication problems of the required ce-ramic parts, led to the development of GBR-4, which wasa less ambitious design with pin-type fuel, stainless steelcladding, helium coolant, and conventional coolant exittemperature. The temperature reduction allowed the useof steel in the core, while the loss in efficiency was offsetby a larger power output of the core. All GBR designsfeatured a U0Pu driver core and uranium blankets.

The main advantages of the GCFR were thought tobe reduced parasitic absorption by the coolant, betterchemical compatibility between coolant and cladding,and the impossibility of violent chemical reactions be-tween the coolant and air and water under accidental*E-mail: [email protected]

NUCLEAR TECHNOLOGY VOL. 151 SEP. 2005 221

conditions ~e.g., sodium reacts violently with both air andwater!. Fuel economy called for high power density. This,together with the absence of thermal inertia in the core,required a decay heat removal ~DHR! strategy with manyactive backup pumps and pressure holders to ensure ade-quate cooling under accidental conditions. The worst ac-cident for a GCFR is a depressurization, when all coolantis lost from the primary system. Even with active safetysystems, the safety case of GCFRs remained problematic,especially for depressurization accidents.9 It seems thatthe problematic DHR behavior and the lack of market de-mand for the GCFR led to an abandonment of the GCFRconcept from the early 1980s on.

Nowadays, the economic and societal circumstancesare changing: Fear of depletion of fossil fuel is replacedby a growing concern about CO2 pollution, and a replace-ment for fossil fuels is required. The reserves of uraniumare larger, and the consumption rate is lower than pre-dicted, allowing a shift from breeder reactors with a highbreeding gain and short doubling time to a design focus-ing on sustainability, with the goal of a self-sustainingcore, i.e., a core that breeds just enough new fissile ma-terial that refueling with a fertile material only is suffi-cient. Within the Generation IV framework,10 the designchoices for GCFR differ from the previous GCFR con-cepts, with the main focus now being on sustainability,and as such, the GCFR is the first nuclear reactor conceptto explicitly select sustainability as a primary design goal.The GCFR concept contributes to sustainable develop-ment in several ways: by reducing stockpiles of depleteduranium, by optimizing fuel efficiency, and by transmu-tation of transuranic ~TRU! material. The GCFR canproduce electricity at high efficiency, or it can be used forCO2-free hydrogen production.

This paper addresses some basic design choices inSecs. II and III. In Secs. IV and V, the fuel elements andfuel assemblies are presented, and in Sec. VI, the coredesign is given. The calculation scheme is presented inSec. VII, followed by the results in Secs. VIII and IX.

II. DESIGN CHOICES FOR THE GCFR

The goal of sustainability is achieved through sev-eral design choices. The GCFR uses a closed fuel cycle inwhich all TRUs are recycled, requiring refueling with238U or some other fertile material only. Cometto et al.11

have shown that such a fuel cycle scenario improves theutilization of uranium by a factor of 160 compared to astrategy using only thermal light water reactor ~LWR!systems. Hoffman and Stacey12 show that depleted ura-nium ~the tails of the enrichment process! will becomethe dominant contribution to the overall radiotoxicity ofall materials discharged to the repository from today’snuclear fuel cycle ~timescale: 105 yr!. By converting238U to 239Pu and subsequent fission, one is left with

fission products, most of which have much shorter half-lives than the radioisotopes in the 238U decay chain,thereby reducing the long-term footprint of today’s useof nuclear energy. For the GCFR a reprocessing strategyis envisaged with separation of the spent fuel into a streamof fission products and a stream of all actinides. Only thefission products, which have relatively short half-lives,are discharged from the fuel cycle into the repository.Proliferation resistance is increased because there is noseparation of Pu in reprocessing. Fertile blankets areavoided, enhancing the proliferation resistance of theGCFR fuel.

The coolant is helium at an inlet temperature of 4508C,a mixed outlet temperature of 8508C, and a pressure be-tween 7 and 10 MPa. Higher system pressure improveseconomy but worsens the effects of a depressurizationaccident. Direct cycle electricity production at high effi-ciency is the primary target with high-temperature heatapplications such as thermochemical hydrogen produc-tion as a secondary target. The thermal power of theGCFR has not yet been determined, but research focuseson a small unit with a thermal output of 600 MW~ther-mal! and a large-scale system with an output of 2400MW~thermal! ~Ref. 10!. The power density of the systemis determined by safety constraints, in particular, DHR incase of depressurization accidents; economic factors ~min-imization of fuel inventory and compactness of primarysystem!; and sustainability ~minimization of fuel needsfor long-term deployment!. Safety calls for low powerdensity, while the other factors improve with higher powerdensity. The tentative range set by the Generation IVInternational Forum in Ref. 10 is a power density be-tween 50 and 100 MW0m3, requiring a minimal coolantfraction in the core of 40%. GCFR power density is lowerthan in LWRs0pressurized water reactors ~PWRs! andmuch lower than in conventional LMFBRs ~300 to 400MW0m3!. However, it is much higher than with othergas-cooled reactors, such as the High-Temperature Re-actor ~HTR! or Pebble Bed Modular Reactor ~PBMR! ~3to 10 MW0m3!. The total amount of Pu in the fuel cycleis limited to 15 tonnes Pu0GW~electric! ~Ref. 10!.

III. FUEL AND CORE DESIGN

The temperatures in the GCFR core require a fullyceramic core. To obtain adequate breeding behavior with-out the use of fertile blankets, the fissile enrichment shouldbe rather low. This leads to a constraint on the minimumvolume fraction of fuel in the core to obtain a criticalsystem. Together with the required minimum volume frac-tion of coolant, the tentative volume fractions in the GCFRcore are 40 to 50% coolant; 10% structural materials;25% fuel; and 25% other materials, such as matrix ma-terial or cladding. The specific power ~power per unitmass of fissile material! is kept low because of the

van Rooijen et al. FUEL AND CORE DESIGN OF A GCFR

222 NUCLEAR TECHNOLOGY VOL. 151 SEP. 2005

combination of low volumetric power density and largefuel volume fraction. Some typical numbers are HTR,1.2 kW0g fissile; PWR, 1 kW0g fissile; and GCFR, 0.1 to0.3 kW0g fissile.

There are basically three possibilities for the GCFRbasic core type:

1. CP fuel, with or without a binding matrix

2. pin-type fuel with ceramic cladding

3. dispersion fuels based on ceramics ~small parti-cles of UPuC or UPuN embedded in SiC, TiC orTiN, or a comparable material!.

The fuel volume fraction in the core of a GCFR isrelatively low compared to an LMFBR. To obtain anadequate density of heavy metal ~HM! in the core, car-bide or nitride fuels are used. For the research presentedin this paper, nitride fuel has been used because of ease ofreprocessing and superior thermal behavior. To avoid 14Cproduction through the 14N~n, p! 14C reaction, enrich-ment to 99.9% 15N is required ~natural abundance 0.37%!.The economic feasibility of such enrichment is still amatter of debate.13

TRISO CP fuel has been used very successfully inthermal HTRs, and it is currently the reference fuelform for operating HTRs @High Temperature Engineer-ing Test Reactor ~HTTR! and HTR-10# and HTRs understudy @PBMR, Gas Turbine Modular Helium Reactor~GT-MHR!, Gas Turbine HTR ~GTHTR!, and Next Gen-eration Nuclear Plant ~NGNP!# , whereas the other twofuel concepts are completely new. Therefore, it was de-cided to use TRISO CP fuel as the basis for the GCFRfuel design presented in this paper, although a redesign ofthe TRISO particle is necessary to adapt the HTR-typefuel particle for GCFR application. Two redesigned coatedfuel particles are presented in this paper: a small particle~typical diameter: 1 mm!, similar to TRISO CPs, and ahollow fuel sphere @hollow sphere ~HS!# , an innovativedesign featuring a hollow shell of fuel surrounded bycladding, with a typical diameter of 3 cm.

IV. FUEL DESIGN

A TRISO CP is made of a spherical fuel kernel ~typ-ical diameter: 500 mm!, surrounded by a buffer of porousgraphite, a layer of pyrolytic carbon @inner pyrolytic car-bon ~IPyC!# , a dense SiC sealing layer, and an outer layerof pyrolytic carbon ~OPyC!. The buffer provides voidageto accommodate kernel swelling and fission gas releaseduring irradiation and protects the cladding layers fromrecoiling fission fragments. The SiC layer is the mainfission product release barrier and acts as a pressure ves-sel. The stress induced by a pressure difference DP overa thin shell of radius R and thickness d can be approxi-mated if d �� R ~thin shell approximation!:

sxx � syy �R

2d{DP . ~1!

This stresssxx should not exceed the maximum stresssmax of the shell material to avoid failure. An estimate ofthe pressure in the buffer Pbuf can be made using the idealgas law as a first approximation:

Pbuf �FIMA{n0{z{k{Tbuf

Vbuf, ~2!

where

FIMA � fissions per initial metal atom

n0 � number of HM atoms in the fuel kernelat beginning of cycle ~BOC!

z � number of gas atoms released into thebuffer per fissioned metal atom

k � Boltzmann’s constant

Tbuf ,Vbuf � temperature and open volume of thebuffer layer, respectively.

Note that Vbuf is a decreasing function of burnup. Thepressure difference over the cladding layer should notexceed the limits of the sealing layer. It can be readilyinferred from Eqs. ~1! and ~2! that a CP with a smallbuffer and a thin sealing layer cannot be used to highburnups.

The IPyC and OPyC layers contract under irradia-tion, thereby partly relieving the stress on the SiC layerinduced by the increasing pressure of fission gasses andkernel swelling during irradiation. The contraction rateof the pyrolytic carbon layers is roughly proportional tothe average neutron energy. In a fast neutron spectrum,the layers will contract too quickly and debond from theSiC layer, which leads to failure of the entire particle.Therefore, the IPyc and OPyC layers are removed fromthe design, and the material of the sealing layer is re-placed by ZrC, which is more easily soluble than SiC andchemically more stable at high temperature. The Zr nu-clei are more massive than Si nuclei, so damage ~atomdisplacement! induced by collisions with high-energy neu-trons will be less severe. A large volume fraction of fuelis required in the particle for GCFR application.

All these considerations together lead to a reviseddesign of the TRISO particle. The GCFR coated fuelparticle has a large fuel kernel, a small buffer of porousgraphite, and one thin sealing layer of ZrC. Some typicalfigures for contemporary HTR TRISO design and an en-visaged GCFR particle are given in Table I. The ratio ofbuffer volume to kernel volume of the particles reflectsthe burnup targets. Values presented in Table I are takenfrom Verfondern et al.14 for HTTR, Tang et al.15 forHTR-10, and from the HTR-N burnup benchmark analy-sis.16 The GCFR CP has a small buffer and relatively thinsealing layer ~no IPyC0OPyC available to support the



sealing layer!, so the maximum burnup will be limited toseveral percent. The temperature limits for the CPs arethe same as for HTR TRISOs, i.e., maximum operatingtemperature 12008C and fission product retention up to16008C.

In pebble bed reactors many TRISOs are combinedwith graphite to make large fuel pebbles. This configu-ration leads to a temperature difference DTp between thecenter and the surface of the pebble proportional to thepower produced:

DTp �Qp

8plrfz, ~3!

where

Qp � power produced by the pebble ~uniform powerdistribution within the pebble is assumed!

l � heat conductivity of the graphite mixture

rfz � radius of the fuel zone.

For graphite pebbles in HTRs, DTp can reach values of3008C. The GCFR requires a larger power density andthus larger Qp than an HTR, and this, together with therequired maximum coolant temperatures, leads to an un-acceptably high centerline temperature of the fuel element.

Application of a fuel compact of a different design isalso problematic: The random close packing of spheresis ;63%, and the volume fraction of fuel inside a CP is~rk0rt !3, with rk the radius of the fuel kernel and rt theradius of the entire TRISO particle. To make a fuel com-pact with CPs and a matrix that satisfies the requirementof containing .45% of fuel by volume requires a CPwith a very large kernel and almost no buffer and clad-ding. When using CP fuel, direct cooling, i.e., a bed ofparticles with the coolant flowing between the particles,seems to be the most viable solution. An extra advantageis that the temperature differences between the fuel andthe coolant remain small.

The amount of voidage available in a CP is deter-mined by the porosity of the buffer layer, which is usu-

ally;50% for TRISO CPs. Removing all material in thebuffer layer creates more empty space to accommodatekernel swelling and fission gas storage. This observationhas led to the design of the HS innovative fuel particle.The HS is a hollow shell of fuel material with ceramiccladding around it ~Fig. 1!. It is comparable to the fuelelement proposed by Ryu and Sekimoto17 for GCFRapplications.

Recoiling fission fragments will penetrate the clad-ding, but this should be no problem as long as the clad-ding thickness is much larger than the penetration depthof the fission fragments ~typically several micrometers!.An HS could be manufactured by pressing a mixture offuel powder with a gelating agent to form hollow hemi-spheres. Two hemispheres are attached to each other andthen sintered to form a full sphere, onto which a thickceramic cladding layer is deposited. The sintering steptakes place at high temperature. The amount of gas withinthe void should be controlled during sintering. Doing so,the HS will be under compressive stress at room temper-ature ~gas contracted!, while at operating temperature theoverpressure inside the void remains limited. In a hollow

TABLE I

Geometry of Contemporary TRISO Designs

Reactor HTTR HTR-10 HTR-N GCFR

Design FIMA 3% 8% 80% —Kernel radius, rk ~mm! 300 249 120 350 to 380Buffer thickness, tb ~mm! 60 95 95 100 to 70IPyC thickness, tIPyC ~mm! 30 42 40 n0aSiC thickness, tSiC ~mm! 25 37 35 50OPyC thickness, tOPyC ~mm! 45 42 40 n0aTotal radius, rt ~mm! 460 465 330 500Relative buffer volume, Vbuf 0Vkernel 0.73 1.63 4.75 0.66 to 1.13

Fig. 1. A cross-sectional view of the HS fuel element. Theentire central void is available to accommodate fuelswelling and fission gas release.



fuel sphere, the inner void is completely empty, provid-ing more voidage than a TRISO CP with the same vol-ume fraction of fuel and cladding. An HS with the samevolume fractions of fuel and cladding as a TRISO CP hasmore space to store fission products and contains lessmoderating material, reducing parasitic absorption andyielding a harder neutron spectrum.

Both fuel elements presented in this paper offer manyparameters that can be tuned to optimize the fuel design.For instance, the volume fractions of fuel, buffer, andcladding can be varied.

V. PRESSURE DROP OVER PACKED BEDS OF SPHERES

In our design the fuel elements are cooled directly byhelium. The coolant flow through the packed bed causesa pressure dropDPpb, which drop should not exceed;2%of the system pressure in order to limit the requiredpumping power.18 It is necessary to find an expressionto estimate the largest allowable height of the packedbed of fuel spheres. DPpb can be estimated using theErgun-relation19:

DPpb

L� 150

~1 � e!2

e3

m f

dp2 u � 1.75

1 � e

e3

rf

dpu2 , ~4!

where

L � bed height

e � porosity of the bed

m f � viscosity of the fluid

dp � diameter of the spherical particles

u � superficial fluid velocity

rf � density of the fluid.

The superficial velocity is proportional to the mass flowrate _m:

_m � rf Au , ~5!

where A is the cross-sectional flow area. The mass flowrate required to remove the heat from a packed bed ofpower-producing spheres is proportional to the volumeof the bed multiplied by the average power density of thebed OQ:

_m �OQLA

cpDT, ~6!

where

DT � temperature rise over the bed of spheres

cp � isobaric heat capacity of the fluid.

It is assumed that the pressure drop over the bed is smallcompared to the system pressure, so that cp can be taken

as a constant. Combining the Eqs. ~4!, ~5!, and ~6! leadsto a revised expression for the Ergun relation:

DPpb � 150~1 � e!2

e3

m f

rf dp2

OQL2

DTcp

� 1.751 � e

e3

1

rf dp

OQ2L3

DT 2cp2 . ~7!

This alternative version of the Ergun relation can be usedto estimate the pressure drop over a bed of power pro-ducing spheres with a given volumetric power densityusing a given coolant at given temperature and pressure.For a core with OQ � 50 MW0m3, L � 7.5 cm, e� 0.37,DT � 4008C, Tout � 8508C, and a particle diameter of1 mm, Eq. ~7! gives DPpb � 0.04 bar, while for a particlediameter of 3 cm and a bed height of 50 cm, Eq. ~7! gives0.15 bar.

VI. OVERALL CORE LAYOUT

Using the results of Secs. IV and V, a core design canbe made:

1. With DT fixed, the pressure drop increases withincreasing power density, favoring a low power density~with the additional advantage of reduced pumping powerand DHR by natural circulation!.

2. The relatively low volume fraction of fuel in thespherical fuel elements with the constraint of a low fissileenrichment favors a large core to reduce leakage.

It was decided to prepare a core layout for a GCFRwith 2400-MW~thermal! output, an average power den-sity of 50 MW0m3, a height hc of 3 m, and a radius rc of2.25 m, with stainless steel reflectors. The fuel is made of238U and recycled LWR Pu. The Pu vector is taken fromthe HTR-N burnup benchmark16 and given by

238Pu0239Pu0240Pu0241Pu0242Pu � 10620240805% .

There are three enrichment zones in the core, chosento give a reasonably flat power profile at start-up. Thespecific power ~W0g fissile! is rather low for the GCFR,leading to long irradiation periods. For the simulationspresented here, one cycle takes 1900 days, resulting in aburnup of ;4 to 5% FIMA, depending on initial fuelloading. The temperature of the inlet and the outlet are450 and 8508C, respectively, and the system pressure is 7MPa. Using OQ � 50 MW0m3 and using the properties ofhelium rf , m f at an average temperature of 6508C, andcp � 5.2 J0g{K�1 ~Ref. 18!, the pressure drop can becalculated for a given geometry of the fuel bed and thefuel particles. For CPs with a diameter of 1 mm, themaximum allowable bed height is only several centi-meters, and for HSs with a diameter of 3 cm, the maxi-mum bed height is just several tens of centimeters.



The maximum allowable bed height for both types offuel spheres precludes the use of a pebble bed configu-ration as used in the PBMR or Thorium HTR ~THTR!.Instead, an approach with annular cylinders is taken: Thefuel spheres are located in annular cylinders, with thecoolant flowing radially through the beds of fuel spheres.

VI.A. Core with CP fuel

For CPs a fuel cylinder is made up of two perforatedconcentric annuli, with the CPs sandwiched between theperforated annuli ~Fig. 2!.

The height of the cylinder is hc, while the particlebed thickness is;2.5 cm. The overall diameter of such afuel cylinder would be;10 to 15 cm. The coolant entersthe cylinder at the bottom and exits at the top. The cool-ant flows inward to keep a compressive stress on theperforated cylinders. All parts are ceramics. The highestfluid velocities will occur at the outlet and the inlet. Themaximum allowable fluid velocity determines the mini-mum areas of the inlet and the outlet, and this also puts amaximum on the volume fraction that the fuel beds can

occupy in the cylinder. The fuel beds occupy 75% of thecylinder volume. The fuel cylinders are arranged in ahexagonal lattice in the core. The overall core volumefraction of the coolant equals 57%, the volume fractionof the fuel spheres is 43%, and the fuel volume fractionis ~rk0rt !3 � 0.43. If annular hexagons are used instead ofannular cylinders, the overall coolant volume fractiondecreases, and the fuel fraction may increase. The pre-sented fuel cylinder concept is comparable to that pre-sented by Chermanne in Ref. 7. With a lower hc thevolume of the fuel cylinder is reduced, allowing for alarger fraction of CPs with the same power density, or alarger power density with the same fraction of CPs. Anexample of a GCFR core with low hc and high powerdensity is presented by Konomura et al. in Ref. 20.

VI.B. Core with Hollow Fuel Spheres

The HS concept allows a larger bed height. The re-actor core is divided into three concentric rings of fuelspheres, with the coolant entering between the beds. Thecoolant then flows through the beds and exits the reactor~Fig. 3!. The height of the beds in the axial direction is hc;in the radial direction it is;50 cm.Again, the highest fluidvelocities occur at the inlet and the exit. The maximumcoolant velocity determines the minimum dimensions of

Fig. 2. Annular fuel cylinder. The coolant enters at the bottom,flows inward through the packed bed of fuel particles~gray area!, and exits at the top. The inward flow as-sures a compressive stress on the inner cylinder. Thefuel bed is conical.

Fig. 3. An illustration of the core with hollow fuel spheres.From the inside out the white, light-gray and dark-grayareas are the three fuel beds, each with a different ini-tial enrichment. The outer light-gray area is the radialreflector. The top and bottom reflectors are not shown.The empty spaces are for the coolant flow. The coolantflow is indicated by the arrows.



the nonfuel areas, and thus, the overall maximum volumefraction of HSs is limited.

VII. CALCULATIONS

One-dimensional ~1-D! calculations were done toroughly estimate reactor parameters ~keff and fuel vectorevolution! and to make a fuel design. Three-dimensional~3-D! calculations were done to give more accurate re-sults for keff and fuel evolution and to have the possibilityof including axial reflectors and a more realistic temper-ature profile. Simulations where done using various mod-ules of the SCALE 4.4a code system,21 interconnectedby a Perl script and some in-house Fortran codes. A JEF-2.2 172-group AMPX library was used for cross-sectionprocessing.22 For the CPs the simulation assumes a hex-agonal lattice of fuel particles. Each CP is surrounded bycoolant, such that the volume fractions of fuel, cladding,and coolant in the unit cell correspond to the core averagevalues. This lattice does not correspond to the actual~stochastic! lattice, but the errors will be small as themean free path of a neutron in the GCFR is large com-pared to the size of a unit cell. For the HS fuel the reactoris subdivided into fueled and nonfueled regions. In thefueled parts the fuel is simulated as a hexagonal lattice offuel spheres. The volume fractions in the unit cell are theaverage values of the fuel bed ~i.e., 37% coolant!.

With regard to 1-D calculations, for each individualfuel region, CSAS1X ~BONAMI–NITAWL–XSDRNPM!is used to determine cell-weighted cross sections, andan extra XSDRNPM calculation is done to obtain thezone-weighted ~i.e., nonhomogenized! cross sections.The homogenized cross sections are then used in a 1-DXSDRNPM calculation over the entire reactor, with anaxial buckling to account for the finite height of the re-actor. The keff and the flux profile in the entire reactor aredetermined. The power profile is calculated from the fluxprofile and the mixture cross sections, including the re-flectors ~energy release from inelastic scattering is takeninto account!. The power profile and zone-weighted crosssections are used to calculate the fuel depletion ~COUPLE–ORIGEN-S! in each fuel region. Because of the 1-D cal-culation, only concentric fuel zones can be used, andthere is no axial dependence of the fuel depletion.

With regard to 3-D calculations, CSASIX ~BONAMI–NITAWL–XSDRNPM–ICE! is used to obtain homog-enized cross sections for each mixture defined in thereactor. Nonfuel mixtures are treated as well. An extraXSDRNPM calculation is used to obtain nonhomoge-nized cross sections for each mixture containing fuel.KENOV is used to determine keff and the flux profile ofthe entire reactor. The power profile is calculated usingthe flux profile and mixture cross sections. The powerprofile and nonhomogenized cross sections are used tocalculate the fuel depletion ~COUPLE–ORIGEN-S!. The

simulations done for this paper are essentially R-Z–typecalculations, but a full 3-D geometry can be simulated.

The fuel temperature coefficient ~FTC! was calcu-lated by performing a spectrum calculation at T0 � DT0,followed by a determination of keff ~T0 � DT0!. The FTCis calculated using

FTC �k~T0 � DT0 !� k~T0 !

k~T0 !{

1

DT0

and expressed in pcm08C, with DT0 � 1008C for 1-Dcalculations. For the 3-D caseDT0�2008C because KENOgives a confidence interval for keff and these intervalsshould not overlap for an accurate FTC. Simulations in-clude reprocessing, where it is assumed that all minoractinides ~MAs! are recycled and only 238U is added togive the same amount of fuel as the first core. The dif-ferences in Pu content per zone are maintained. One ir-radiation cycle takes 1900 days, and the fuel is allowed tocool down and decay for another 1900 days after irradi-ation ~ORIGEN-S is used to calculate the resulting fuelvector!. The new fuel composition is then calculated andirradiated for a new period.

VIII. RESULTS

For both the CP and HS concepts, two fuel compo-sitions were made using 1-D calculations: one fuel com-position with low and one with high Pu fraction. The fuelcomposition is such that the initial HM loading is roughlythe same for the CP and the HS cores, and such that thekeff ’s of the cores are roughly the same at fresh start-up.In the design with low Pu fraction, the HS core becomescritical with a slightly lower initial enrichment than theCP core ~13.4% for the CP and 12.5% for the HS core!.This is attributed to the fact that the CP core has morenonfuel material in the core ~the buffer material! givingslightly more absorption and a softer spectrum. Underthe assumption of a 50% efficient power conversion sys-tem, the GCFR will have 1200-MW~electric! output. Thelow Pu cores contain 15.7 tonnes Pu ~CPs! and 14.3 ton-nes Pu ~HS!, so they are close to but within the tentativemaximum of 15 tonnes Pu0GW~electric!. Both cores havea keff just above 1 at start-up.

The high Pu cores have a lower HM loading than thelow Pu cores; otherwise, keff would become very largebecause of high fissile content. The high Pu cores in factcontain a smaller total mass of Pu than the low Pu cores~;13.5 tonnes Pu!. The difference in keff at BOC of thelow Pu CP core and the high Pu CP core is negligible, butfor the HS core, there is some difference in keff betweenthe high and low Pu versions. The different HM loading~see Table II! is achieved for the CP core by using asmaller fuel kernel. The outer radii of the buffer and thecladding are kept constant, so the volume of the buffer islarger for the CPs with a smaller kernel. The larger buffer



TABLE II

Results of the Burnup Study for the CP Core*

Results for CP Core

Low Pu Content High Pu Content

Batch 1

HM total ~kg! 117 379 917 25Percentage of which is Pu ~kg! 15 733013.4% 13 830015.1%

238Pu0239Pu 1%062% 1%062%240Pu0241Pu0242Pu 24%08%05% 24%08%05%DPu0DPufissile �2.2%0�0.7% �0.7%0�6.1%EOC MA mass ~kg! 514 592kmax 0kmin 1.065101.0491 1.065801.0116FTC

max0FTCmin ~pcm0K! �2.070�1.42 �2.60�1.5

Batch 2

HM total ~kg! 117387 91731Percentage of which is Pu ~kg! 16083013.8% 13728015%

238Pu0239Pu 0.85%063.7% 0.87%061.7%240Pu0241Pu0242Pu 26.3%04.3%04.9% 27.9%04.4%05.1%DPu0DPufissile �3.7%0�1.3% �2.0%0�2.1%EOC MA mass ~kg! 734 850kmax0kmin

1.044901.0333 1.004500.9941FTCmax0FTCmin ~pcm0K! �1.790�1.48 �2.50�1.3

Batch 3

HM total ~kg! 117392 91736Percentage of which is Pu ~kg! 16672014.3% 14002015.4%

238Pu0239Pu 1.1%063.4% 1.2%060.0%240Pu0241Pu0242Pu 27.9%03.1%04.6% 30.4%03.5%04.8%DPu0DPufissile �3.3%0�1.3% �2.3%0�0.7%EOC MA mass ~kg! 851 994kmax 0kmin 1.052101.0360 0.991000.9959FTCmax0FTCmin ~pcm0K! �1.880�1.33 �3.00�0.96

Batch 4



Geometry of the Fuel Element

Kernel radius, rk ~mm! 380 350Buffer radius, rb ~mm! 450 450Cladding radius, rc ~mm! 500 500

*All MAs are recycled; 238U is added after each batch.



volume also means that some of the extra reactivity ofthe high Pu fuel is lost by extra absorption in the buffermaterial. For the HS core the thickness of the fuel shellis varied. A smaller fuel shell means a larger centralvoid.

The 1-D calculations show that both cores have anegative FTC and that the magnitude of the FTC de-creases slightly during irradiation. The decrease is causedby the hardening of the spectrum due to fission productbuildup during irradiation. In Fig. 4 the flux per unitlethargy is given at 0 and 1900 days of irradiation, to-gether with the resonances of sa of 238U. Note the de-creased flux in the resonance region after 1900 days ofirradiation.

The 1-D calculations show that the high Pu coreshave a net consumption of fissile Pu over the first irradi-ation cycle. The low Pu cores have a net increase infissile mass during irradiation, but during the subsequentdecay period, some of the 241Pu decays. The HS corewith low Pu loading has a net increase of fissile mass,and the CP core has a slight decrease in fissile mass afterdecay. Overall, the low Pu cores have more conversion,which is as expected ~more 238U nuclei to absorb neu-trons!. Comparing the evolution of the nuclide densitiesin the cores, there is not much difference between the CPand HS cores. This applies for Pu as well as for the MAs.Apparently, the influence of the buffer material is not bigenough to cause large spectral changes. In all cores thereis a noticeable consumption of 241Pu, offset by a net

production of 239Pu in the low Pu cores. In the high Pucores, there is a net consumption of 239Pu.

A 3-D calculation including reprocessing was done.An irradiation and subsequent decay period are desig-nated as one batch. A total of four batches was simulatedfor all core designs. Each batch includes 1900 days ofirradiation and 1900 days of decay, so four batches equala period of 15 200 days ~� 41.6 yr!. The 3-D calculationsinclude a top and a bottom reflector of stainless steel. Acomparison between 1-D and 3-D results of the first batchshow that the nuclide evolution is nearly the same, butkeff is consistently higher for the 3-D calculations. Ap-parently, the top and bottom reflectors have no greatspectral influence, but they do reduce leakage and im-prove keff . As an example the 1-D and 3-D keff and FTCof the low Pu CP core are given in Fig. 5, with the cor-responding evolution of the Pu density in Fig. 6. Fig-ures 7 and 8 show the same for the HS core with high Puloading. The 3-D FTC graph is not as smooth as the 1-DFTC, due to the statistical nature of the KENO calcula-tions. The results could be improved, but the requiredCPU time would increase drastically.

The reprocessing strategy involves recycling of allactinides in the GCFR. This means that the fuel at thebeginning of a new batch will contain all MAs that havenot decayed during the decay period. In practice, onlysome isotopes of Am ~241Am, 242mAm, 243Am! and Cm~243Cm, 244Cm, 245Cm! are stable enough to be present inthe new fuel in appreciable amounts. In Tables II and III,the sum of the masses of Np, Am, and Cm is given at endof cycle ~EOC! ~one cycle comprises 1900 days of ir-radiation and 1900 days of decay!. Americium-241 is the

Fig. 4. The flux per unit lethargy as a function of energy after0 and 1900 days of irradiation in the HS core. Theresonances ofsa of 238U are also shown.After 1900 daysthe spectrum has hardened, giving a lower flux in the238U resonances, leading to lower absorption and adecrease in the magnitude of the FTC. The BOC spec-trum of the CP core is indicated by dots. This spectrumis softer than the HS spectrum.

Fig. 5. ~a! The keff of the CP low Pu core as calculated using1-D and 3-D calculations. ~b! The FTC of the CP lowPu core.



decay product of 241Pu. It is the most abundant of theMAs, and it is the only MA whose mass increases duringthe decay period. During irradiation a net consumption of241Am occurs, but this is offset by production from 241Pudecay during the decay period. In the first few fuel batches,241Am production from 241Pu decay is much more thanthe consumption during irradiation, but this situationchanges in the later fuel batches because the higher amountof 241Am in the fuel leads to higher consumption of 241Am.

VIII.A. Results for CPs

The results of the burnup simulation for the CP coresover four fuel batches are summarized in Table II, whichgives the initial HM and Pu mass for each fuel batch, aswell as the Pu vector at BOC of each batch. The changeof the total amount of Pu ~238Pu through 242Pu! is giventogether with the change of fissile Pu ~239Pu and 241Pu!.The total mass of MA in the core, which is the sum of themasses of 237Np, 241Am, 242mAm, 243Am, 243Cm, 244Cm,and 245Cm at EOC is indicated in Table II. Because of theapplied calculation scheme, the MA mass at BOC is equalto the EOC mass of the previous cycle, except for the firstbatch. Also given are the minimum and maximum valuesof keff and FTC. The keff is not necessarily a monotoni-cally decreasing function of irradiation time, and it seemsbetter to give the minimum and the maximum values ofkeff and FTC per batch. After 1900 days of irradiation, thelow Pu core reaches a burnup of 3.8% FIMA, and thehigh Pu core, which has a lower initial HM loading,reaches a burnup of 4.9% FIMA. Using Eq. ~2! with z �0.8, the pressure in the buffer at these burnups is esti-mated between 2 and 4 MPa, so the CPs are still undercompression in the reactor.

VIII.A.1. Plutonium Evolution

Note the large increase of 240Pu in both cores and thedecrease of 241Pu. The low Pu core has a good conver-sion of 238U to 239Pu, resulting in a fuel vector with ahigh amount of 239Pu and 240Pu at the beginning of thelast batch. The high Pu core has lower conversion, so theloss of 239Pu and 241Pu is not made up by conversion of

Fig. 6. Evolution of 239Pu, 240Pu, and 241Pu during batch 1 forthe CP low Pu core. Lines indicate 3-D results; dotsare the 1-D results. The differences between the 1-Dand the 3-D results are very small.

Fig. 7. ~a! The keff of the high Pu HS core calculated using 1-Dand 3-D calculations. ~b! The FTC of the same core.

Fig. 8. Evolution of 239Pu, 240Pu, and 241Pu during batch 1 forthe HS high Pu core. Lines indicate 3-D results; dotsare 1-D. The differences between the 1-D and the 3-Dresults are small.



TABLE III

Results of the Burnup Study for the HS Core*

Results for Hollow Fuel Sphere Core

Low Pu Content High Pu Content

Batch 1


238Pu0239Pu 1%062% 1%062%240Pu0241Pu0242Pu 24%08%05% 24%08%05%DPu0DPufissile �4.4%0�2.7% �1.8%0�6.3%EOC MA mass ~kg! 458 427kmax 0kmin 1.029401.0331 1.084401.0307FTCmax0FTCmin ~pcm0K! �2.30�1.2 �1.840�1.41

Batch 2



Batch 3


238Pu0239Pu 1%065% 1.2%061.3%240Pu0241Pu0242Pu 26.7%02.8%04.4% 29.4%03.2%04.8%DPu0DPufissile �3.9%0�2.4% �1.6%0�0.7%EOC MA mass ~kg! 742 688kmax 0kmin 1.051601.0310 1.014101.0100FTCmax0FTCmin ~pcm0K! �2.00�0.7 �1.730�1.48

Batch 4


238Pu0239Pu 1.3%064.3% 1.5%060%240Pu0241Pu0242Pu 27.8%02.5%04.1% 30.9%03.0%04.6%DPu0DPufissile �3.0%0�1.5% �1.5%0�0.3%EOC MA mass ~kg! 806 746kmax 0kmin 1.062501.0451 1.015301.0087FTCmax0FTCmin ~pcm0K! �1.80�0.8 �1.880�1.28

Geometry of the Fuel Element

Sphere diameter ~cm! 3 3Cladding thickness ~cm! 0.2 0.2Fuel thickness ~cm! 0.325 0.225

*All MAs are recycled; 238U is added after every batch.



238U. The total Pu mass in both the low and high Pu coresgrows from batch to batch. Conversion of 241Pu to 242Puis low and decreases in later batches because of a de-creasing 241Pu content.

VIII.A.2. keff

The high Pu core has quite a big loss of fissile massduring the first and second batches, resulting in a sub-critical system in the third and fourth batches. However,an increase of the HM loading would improve the situ-ation, and because the spectrum and geometry of the CPwould not change much, the evolution of the nuclideswould not be highly affected. This means that the calcu-lations presented here still give valuable results. For theCP fuel the buffer volume is larger for a smaller fuelkernel. Because the buffer contains graphite, moderationand absorption increase with decreasing kernel size. Asofter spectrum leads to increased resonance absorptionby nonfuel materials in the core, reducing keff .

VIII.A.3. FTC

The FTC is always negative and shows a decreasingmagnitude during burnup.

VIII.A.4. Minor Actinides

The high Pu core produces more MAs than the lowPu core, which is as expected ~more Pu available forconversion and a slightly softer spectrum favoring ab-sorption over fission of actinides!. Notice that the in-crease in MA mass gets smaller from batch to batch; e.g.,in the first batch of the low Pu CP core, 514 kg of MAsare formed, and in the fourth batch, the EOC amount isonly 79 kg more than the EOC mass of batch 3.

VIII.B. Results for HSs

For the HS core the same burnup simulation overfour fuel batches was performed. The results are summa-rized in Table III, which gives for each fuel batch theinitial HM and Pu mass, the Pu vector at BOC, the changein Pu mass over the irradiation period, and the change infissile mass. Also given is the EOC MA mass. The min-imum and the maximum values of keff and FTC are alsogiven. The burnup reached after 1900 days of irradiationequals 4% FIMA for the low Pu HS core and 5.3% FIMAfor the high Pu version.

VIII.B.1. Plutonium Evolution and keff

The HS fuel element has a lower volume fraction ofnonfuel material than the CPs because the HS lacks thebuffer material. A reduction of the thickness of the fuelshell does not increase the amount of nonfuel materials inthe core. This means that the neutron spectrum and ab-sorption are almost unaffected by a change in fuel load-ing of an individual fuel element. The initial enrichment

of the low Pu HS core is almost 1% lower than the low PuCP core, and keff is slightly lower than the low Pu CPdesign. The low Pu content causes a large conversionfrom 238U to 239Pu. The low Pu HS design shows anincrease of the fissile mass for all four fuel batches. Sincethe total Pu mass also increases from batch to batch,conversion from 238U to 239Pu decreases in the later fuelbatches, and although the Pu mass grows quickly ini-tially, the Pu content in the fourth batch is still lower thanthe initial enrichment of the high Pu core.

The high Pu HS core has a lower HM loading thanthe high Pu CP core, offset by a higher initial enrichmentof the fuel. The magnitude of keff is comparable for bothcores, as is the evolution of Pu in the core during the fourbatches. The high Pu HS fuel shows a considerable lossof fissile material in the first two fuel batches but remainscritical during four batches. At the start of the last batch,the amount of 241Pu has decreased drastically in bothcores, while the loss of fissile mass per batch is reducedfrom 6.3% in the first batch to only 0.3% in the last batch.The high Pu core has a lower production of 239Pu, result-ing in a Pu vector that is rich in 240Pu. Conversion of241Pu to 242Pu is low and decreases in later batches be-cause of a decreasing 241Pu content.

The total Pu mass in the high Pu HS core changesby 0.9% from the first to the fourth batch. In the sameperiod the Pu mass of the high Pu CP core increases by3.6%. The Pu in the CP core contains more 240Pu thanthe HS Pu. This is attributed to different initial Pu con-tents, and the softer spectrum in the CP core; i.e., reso-nance absorption by 239Pu is enhanced, reducing the fissilemass and keff while at the same time producing 240Pu.Plutonium-241 ~converted from 240Pu! is also slightlyhigher in the CP core.

VIII.B.2. FTC

FTC is always negative with a decreasing magnitudein the course of the irradiation.

VIII.B.3. Minor Actinides

In comparison to the CP core, the HS core producesa smaller amount of MAs. This can be attributed to lessabsorption by and more fission of MAs because of theharder neutron spectrum in the HS core ~see Fig. 4!.

We can draw the conclusion that it is possible toobtain a breeding close to unity. The low Pu CP and highPu HS core concepts look the most promising becausethey maintain criticality without too much increase offissile material.

IX. EXTENDED TIME CALCULATIONS

To examine the long-term evolution of the fuel, acalculation was done over eight fuel batches. Two reactor



configurations were simulated: the CP core with low Pucontent and the HS core with high Pu content. In Table IVa short summary of the results is given: the initial Pucontent of every batch at BOC, and DPu and DPufissile

per batch from BOC to EOC ~which includes reprocess-ing!. Also given is the EOC MA mass for each fuelbatch.

IX.A. Plutonium Evolution

The low Pu CP core reaches a Pu fraction equal to theinitial Pu fraction of the high Pu HS core at the beginningof batch 6, but where the CP core shows a positive DPuand DPufissile in batch 6, the high Pu HS core shows aconsiderable loss of fissile material in the first batch.This difference is attributed to small spectral differencesbetween the CP and HS core and to differences of the Puvector, which contains more 240Pu in batch 6. In batch 6the CP core has a better conversion from 240Pu to 241Puand a net increase of 241Pu during the irradiation periodwhile 239Pu is almost constant. In the first batch of thehigh Pu HS core, there is a rapid increase in 240Pu, 239Pushows a gradual decrease, and 241Pu shows a rapid de-crease. In Fig. 9 the Pu densities are given for the low PuCP core in batch 6, and Fig. 10 gives the Pu density of thehigh Pu HS core in batch 1. Especially, the evolution of241Pu is different.

In batch 8 the Pu content of the low Pu CP corereaches the same value as the high Pu HS core in batch 5.Again, the CP core has an increase in fissile mass, and theHS core has a slight decrease from BOC to EOC, but inthis case the differences are small. The differences areattributed to the difference in Pu vector, which is slightly

TABLE IV

Results of the Burnup Study over Eight Batches

Long-Term Burnup

CP Core0Low Pu

HS Core0High Pu

Batch 1

Pu initial 13.4% 15.5%DPu0DPufissile �2.2%0�0.7% �1.8%0�6.3%EOC MA mass ~kg! 514 427

Batch 2


Batch 3


Batch 4


Batch 5


Batch 6


Batch 7


Batch 8


Fig. 9. Evolution of 239Pu, 240Pu, and 241Pu in batch 6 for thelow Pu CP core. The density of 239Pu is almost constantduring irradiation, and 241Pu increases. The increase of241Pu is the cause of the overall increase of fissile ma-terial during irradiation. During the decay period 22%of the 241Pu nuclei will decay, and batch 7 will startwith roughly the same 241Pu density as batch 6.



more 240Pu rich in batch 8, leading to better conversionof 240Pu to 241Pu. Figures 11 and 12 give the Pu densityin the low Pu CP core in batch 8 and in the high Pu HScore in batch 5, respectively.

In the later fuel batches,DPu decreases for both cores:The total amount of Pu becomes almost constant. This isdue to an equilibrium setting between 240Pu productionon one side and conversion of 240Pu to 241Pu on the otherside. It seems that the equilibrium core would have;16.5% Pu, with a large amount of 240Pu.

The high Pu HS core has an almost constant densityof 239Pu during all batches except the first two ~decreasein the first batches!. During all fuel batches except thefirst two, the amount of 241Pu increases during irradia-tion. During subsequent decay ;22% of 241Pu decays,leading to the negative DPufissile from batch to batch.However, the higher density of 240Pu in the later batchesleads to more 241Pu production during irradiation, im-proving DPufissile. In the low Pu CP core, the 239Pu den-sity stabilizes after batch 5. The high 240Pu content in thelater batches leads to higher 241Pu production. In the laterbatches DPufissile decreases for the low Pu CP core, indi-cating that an equilibrium is reached.

IX.B. keff and FTC

For the first batch, keff of the low Pu CP core is adecreasing function, but in all subsequent batches, keff

increases during irradiation. This is attributed to the in-crease of fissile mass after the first batch. For the high PuHS core, keff decreases during irradiation in the first twobatches, but in all subsequent batches, keff increases from

Fig. 10. Evolution of 239Pu, 240Pu, and 241Pu in batch 1 for thehigh Pu HS core. The overall Pu enrichment in thiscase is the same as in Fig. 9, but the different Puvector causes a different evolution. Plutonium-239shows a decrease, and 241Pu shows a rapid decreaseduring irradiation, with 240Pu increasing rapidly. Thetotal fissile mass decreases. During the decay period22% of the 241Pu will decay, so batch 2 starts with aneven smaller amount of fissile material than indicatedin this graph.

Fig. 11. Evolution of 239Pu, 240Pu, and 241Pu in batch 8 for thelow Pu CP core. The overall Pu enrichment in thiscase is the same as in Fig. 14. The 239Pu is almostconstant, as is 241Pu. Also, 240Pu shows a less rapidincrease as in earlier batches. This seems an indica-tion that an equilibrium is being reached.

Fig. 12. Evolution of 239Pu, 240Pu, and 241Pu in batch 5 for thehigh Pu HS core. The overall Pu enrichment in thiscase is the same as in Fig. 13. The fuel vector for thisperiod does not differ very much from the vector inFig. 13, and the evolution of the nuclide densities isalmost the same. The 239Pu is almost constant, as are241Pu and 240Pu. The decay of 241Pu during repro-cessing still causes a smaller fissile mass at the be-ginning of batch 6.



BOC, reaches a maximum sometime between 1200 and1400 days, and then decreases again. At EOC keff is largerthan at BOC and only slightly larger than 1 for the HScore. By increasing the total HM loading of the core, onecan increase keff . For both cores keff at the beginning of abatch is not equal to keff at the end of the previous irradi-ation period because of the loss of fissile material due todecay of 241Pu and because the fissile material has adifferent spatial distribution in the new core.

In all cases the FTC is negative. An illustration isgiven in Figs. 13 and 14, where keff is given for the lowPu CP core and the high Pu HS core in batch 6. Themagnitude of the FTC is somewhat smaller than in thefirst batch, an effect caused by the presence of MAs inthe fuel ~see Figs. 5 and 7 for keff and FTC in the firstbatch!.

IX.C. Minor Actinides

Upon inspection of Figs. 9, 11, and 12, it is clear thatthe densities of the various Pu nuclides are almost con-stant in the later fuel batches. This is also true for theMAs: The masses of MAs in both cores grow from batchto batch, but in the later batches, the increase per cycle ismuch smaller than in the first batches.

The evolutions of the Pu nuclide density in the lowPu CP core and low Pu HS core do not differ fundamen-tally, so it is expected that the low Pu HS core will havelong-term performance similar to the low Pu CP core,with the most important difference that keff will be anincreasing function for the first batch as well. The highPu CP core has a keff below 1 for the third and fourthbatches, but this can be improved by increasing the HM

loading of the core. This core should have long-termperformance similar to the high Pu HS core. The perfor-mance of the cores regarding MAs is also expected to notdiffer fundamentally between the CP design and the HScores.

X. CONCLUSION

The specific demands of the GCFR core with, for agas cooled reactor, a relatively high power density, a highvolume fraction of fuel, and the impossibility of using steel,requires a totally new fuel and core concept. TRISO CPfuel can be used, but a redesign of the CP is necessary toadapt it to the GCFR environment. It is difficult to apply afuel compact of CPs embedded in a matrix because thevolume fraction of fuel in the fuel compact would be ~too!low and because of thermal limitations in the high-power-density GCFR core. Therefore, a core concept is chosenwith direct cooling of the coated particles, with the extraadvantage that the fuel temperatures will be only margin-ally higher than the temperature of the coolant. The appli-cation of more or less proven TRISO technology reducesresearch and development needs for the GCFR.

A burnup simulation was done for a 2400-MW~thermal! GCFR core, with a power density of 50MW0m3. The core has no blankets and uses a mix ofLWR discharge Pu and 238U for the first fuel loading. Inthe reprocessing step all TRU material is recycled in thecore. The goal of a self-sustaining core, i.e., a core thatproduces enough new fissile material such that refuelingwith only a fertile material ~238U in this case! is suffi-cient, is met. Two core designs with two Pu loadings ~lowand high! were simulated, with an initial Pu content of

Fig. 13. The keff and FTC in batch 6, low Pu CP core. Thesmaller magnitude of the FTC ~compare Fig. 5! iscaused by the MAs in the fuel in batch 6.

Fig. 14. The keff and FTC in batch 6, high Pu HS core.



;13 and 15.5%. As expected, a lower Pu content im-proves Pu production from 238U. In all core concepts thetotal Pu mass increases during irradiation, and in the lowPu cores, the fissile mass also increases during irradia-tion. In the high Pu cores on the other hand, the fissilemass decreases during irradiation. It is possible by ad-justing the total HM loading and the Pu content to obtaina fuel composition that gives a slight increase in fissilemass during the first batches, with the increase of fissilemass becoming smaller in later batches. The resultingfuel vector will be rich in 239Pu and 240Pu and poor in241Pu. Calculations have shown that the Pu vector has animportant influence on the evolution of the fuel. A smalldifference in the Pu vector can make the difference be-tween a net consumption or production of fissile materialwith the same overall Pu content. All studied cores arecurrently below the limit of 15 tonnes Pu0GW~electric!,and there is some room for optimization.

The keff is an increasing function of irradiation timeor shows a maximum, especially in the later fuel batches.This means that the GCFR could be operated for a longtime with a limited amount of overreactivity at BOC. Thecalculated values of keff are sometimes barely larger thanunity, and for one core design, they are even smaller than1, but this can be improved by enlarging the HM loadingof the core. Under all circumstances the FTC is negative,with a decreasing magnitude during irradiation due tofission product buildup.

The goal of a self-sustaining core can be achievedwith the GCFR concept. The resulting Pu is quite rich in240Pu, improving proliferation resistance. Only 238U isadded to the core during its lifetime to make the new fuel.Because all TRUs are recycled in the core, only fissionproducts are put into the repository. Because of high-temperature output, high-efficiency power conversion ispossible. All these points together make the GCFR areactor concept that fits better into the picture of sustain-able development than present reactor concepts. The pre-sented core concepts remain within the tentative limitsset on the volume fractions of fuel, coolant, and struc-tural materials within the Generation IV roadmap.

The core layout and fuel design presented in thispaper still offer many opportunities for optimization. Forinstance, a relatively simple material ~stainless steel! hasbeen used for the reflectors. There are several com-pounds, e.g., ZrSi compounds, that have better neutronicperformance. The height0diameter ratio of the core canbe varied. A lower core allows for a higher volume frac-tion of fuel elements in the core, or a more “open” corecan be designed to improve natural circulation behavioror enable operation at a higher power density. The ge-ometry of the fuel elements has various free variables,offering many possibilities for optimization. For in-stance, the buffer volume may be reduced because burnupsbeyond 5 or 6% FIMA will not be reached. A highervolume fraction of fuel per fuel element enables a moreopen core or a reduction of core volume.

APPENDIX

A NOTE ON FUEL ASSEMBLY DESIGN

For the CP core the particle beds should not exceeda height of ;2 or 3 cm. In a first approximation, a fuelassembly is modeled as a simple cylinder with a radiusrcyl � 6 cm. Within this cylinder is the particle bed,modeled as a simple right annulus of inner radius ri andouter radius ro. The power produced within one grid cellis simply the product of the power density times thevolume of the outer cylinder and corrected for the hex-agonal pitch ~the fuel cylinder does not completely fill ahexagonal grid cell!, and for the power peaking. If DT isknown ~or chosen to be some value!, the mass flow ofcoolant through the fuel cylinder is known from the for-mula _m � Q0cpDT, with Q the power of the fuel cylinder.If the coolant enters the cylinder from below, and if itflows in the area between the outer cylinder and thefuel bed, the entrance area Ain of the coolant is known~Ain �p~rcyl

2 � ro2!!, as are the temperature and pressure

of the cold coolant. With these numbers the flow speed ofthe coolant at the entrance vin is given by

vin �_m

rf ~Pin , Tin !Ain

with Pin and Tin the pressure and temperature of the fluidat the entrance. The maximum speed needs to be selected~for this paper 125 m0s is assumed!, and now the corre-sponding Ain can be calculated, and this gives the valueof ro of the particle bed. Using the same reasoning, thevelocity of the hot gas leaving the cylinder can be calcu-lated, and using the same maximum v, ri of the particlebed is found using Aout � pri

2. Using the fact that theannulus is a simple straight annulus, the volume of theparticle bed can be calculated as a fraction of the entirefuel cylinder ~rcyl

2 0~ro2 � ri

2!!, and doing so the volumefractions of coolant and particles for the entire core areknown. This calculation is conservative as it is based onthe most highly rated fuel assembly requiring the largestmass flow of coolant. The same approach gives the di-mensions of the fuel beds of the HS core.

NOMENCLATURE

A � cross-sectional flow area

Ain � coolant entrance flow section

Aout � coolant exhaust flow section

cp � isobaric heat capacity of fluid

dp � diameter of spherical particle

FTCmax � maximum value of FTC

FTCmin � minimum value of FTC

hc � height of core



k � Boltzmann’s constant

keff � effective core multiplication factor

kmax � maximum value of keff

kmin � minimum value of keff

L � packed bed height

_m � mass flow rate

DMA � change in mass of MA isotopes

n0 � initial number of HM atoms in the fuel kernel

DP � pressure difference

Pbuf � buffer pressure

Pin � coolant pressure at inlet

DPpb � pressure drop over packed bed

DPu � change in mass of all Pu isotopes

DPufissile � change in mass of fissile Pu isotopes

Q � power produced by a fuel cylinder

OQ � average power density

Qp � power produced by a pebble

R � shell radius

rb � radius of TRISO buffer

rc � radius of core

rcyl � radius of fuel cylinder

rfz � radius of the fuel zone

ri � inner radius of fuel cylinder

rk � radius of TRISO fuel kernel

ro � outer radius of fuel cylinder

rt � radius of entire TRISO particle

DT � temperature rise over packed bed

Tbuf � temperature of the buffer

DTp � temperature difference between center andsurface of fuel pebble

Tin � coolant temperature at inlet

Tout � coolant temperature at outlet

T0 � nominal operating temperature

DT0 � temperature increase to calculate FTC

u � superficial fluid velocity

Vbuf � free volume of the buffer

vin � coolant flow speed at entrance

z � number of gas atoms released from fuel perfissioned metal atom

Greek

d � shell thickness

e � packed bed porosity

l � heat conductivity of graphite mixture

m f � fluid viscosity

rf � density of fluid

sii � tangential stress in shell

smax � maximum ~rupture! stress

REFERENCES

1. G. MELESE and R. KATZ, Thermal and Flow Design ofHelium-Cooled Reactors,American Nuclear Society, La GrangePark, Illinois ~1984!.

2. A. TORRI and D. R. BUTTEMER, “Gas-Cooled Fast Re-actor Safety—An Overview and Status of the U.S. Program,”Proc. Gas-Cooled Reactor Safety and Licensing Aspects(IWGCR-1), Lausanne, Switzerland, September 1–3, 1981, p. 51,International Atomic Energy Agency ~1981!.

3. H. MOCHIZUKI, T. IZAKI, K. TAKITANI, H. KOIKE,Y. KOBAYASHI, Y. MATSUKI, T. OOKA, R. TANAKA, T.WATANABE, and T. KOBAYASHI, “Design Study of a Gas-Cooled Fast Breeder Reactor,” Proc. Gas-Cooled Fast Reac-tors, Minsk, USSR, July 24–28, 1972, IAEA-TECDOC-154,International Atomic Energy Agency ~1972!.

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FUEL DESIGN AND CORE LAYOUT FOR A GAS-COOLED FAST …