ac

ert

Article history:Received 14 November 2011Accepted 3 September 2013Available online 20 October 2013

Keywords:Molten SaltFast ReactorThorium cycleNeutronicsReprocessing inuence

Molten Salt Reactors (MSRs) are liquid-fuel reactors, in which the fuel is also the coolant and ows

is done in situ: a very small proportion of the fuel salt is ex-tracted and reprocessed regularly. Consequently, the couplingbetween the reprocessing and the core behavior has to be takeninto account in order to have a representative simulation of thereactor evolution.

of this paper is toSFR core p

nuclide ption evolution during the reactor operation is needed. Twnumerical tools were involved for that purpose: MCNPmeister, 1997) (which calculates the neutron population at a gi-ven time) and a homemade code: REM which solves theevolution equations. An interface between this evolution codeand MCNP has been developed, which take into account thereprocessing and the chemistry. This numerical scheme (detailedin Section 3) was previously used and qualied for previousstudy of MSR in thermal and epithermal neutron spectrum(Nuttin et al., 2005).

Corresponding author. Address: 15 rue Georges Clmenceau, 91406 OrsayCedex, France. Tel.: +33 169154494; fax: +33 169154507.

Annals of Nuclear Energy 64 (2014) 430440

Contents lists availab

Annals of Nuc

elsE-mail addresses: doligez@ipno.in2p3.fr, xavier.doligez@gmail.com (X. Doligez).Molten Salt Fast Reactor (MSFR) called Thorium Molten SaltReactor Nonmoderated (TMSR-NM) in previous works. Thiskind of reactor should be studied in a different way than solidfuel reactors. Indeed as shown in this paper, the reprocessing

by the uranium III over uranium IV ratio. The aimpresent a newway to make coupled study of the Mand its associated reprocessing unit.

To achieve that goal the calculation of each0306-4549/$ - see front matter 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.anucene.2013.09.009hysics

ropor-o main(Bries-1. Introduction

Previous studies have shown that a particular conguration ofMolten Salt Reactors (MSRs) could be very promising with a fastneutron spectrum (Mathieu et al., 2009; Merle-Lucotte et al.,2008). This conguration has been leading to the concept of

The salt chemistry is a key issue: the salt should be homoge-nous at any time in any place of the core in order to avoid risksof clogging heat exchangers with insoluble elements. Chemistryproperties change during the reactor operation because the ele-ment proportions are evolving in the salt. Corrosion in particular,depends exclusively on the red-ox potential, which could be xedthrough the core. A particular conguration presented in this paper called the Molten Salt Fast Reactorconsists in a Molten Salt Reactor with no moderator inside the core and a salt composition that leadsto a fast neutron spectrum. Previous studies showed that this concept (previously called Thorium MoltenSalt Reactor Nonmoderated) has very promising characteristics. The liquid fuel implies a special repro-cessing. Each day a small amount of the fuel salt is extracted from the core for on-site reprocessing.To study such a reactor, the materials evolution within the core has to be coupled to the reprocessing

unit, since the latter cleans the salt quasi continuously and feeds the reactor. This paper details the issuesassociated to the numerical coupling of the core and the reprocessing. It presents how the chemistry isintroduced inside the classical Bateman equation (evolution of nuclei within a neutron ux) in orderto carry a numerical coupled study. To achieve this goal, the chemistry has to be modeled numericallyand integrated to the equations of evolution. This paper presents how is it possible to describe the wholeconcept (reactor + reprocessing unit) by a system of equations that can be numerically solved.Our program is a connection between MCNP and a homemade evolution code called REM. Thanks to

this tool; constraints on the fuel reprocessing were identied. Limits are specied to preserve the goodneutronics properties of the MSFR. In this paper, we show that the limit rate for the reprocessing is2.5 l of fuel salt a day, which means that the fuel should be reprocessed within 7000 days approximatelyif there is a specic way to control the redox potential of the salt. Finally, a last part of this paper analyzesthe impact of chemical parameter uncertainties on the reprocessing performance.

2013 Elsevier Ltd. All rights reserved.a r t i c l e i n f o a b s t r a c tCoupled study of the Molten Salt Fast Reassociated reprocessing unit

X. Doligez a,, D. Heuer b, E. Merle-Lucotte b, M. Alliba IPNO-IN2P3-CNRS, Universit Paris Sud 11, Franceb LPSC-IN2P3-CNRS, Universit Joseph Fourier, Grenoble-INP, France

journal homepage: www.tor core physics and its

b, V. Ghetta b

le at ScienceDirect

lear Energy

evier .com/locate /anucene

The rst part of this paper will describe the MSFR concept asso-ciated to its reprocessing unit. This unit was designed in order tohave a viable model which takes into account all different elementspresent in the fuel salt (the quasi totality of the Mendeliev table)(Delpech et al., 2009a,b). In a second part the simulation code willbe described and special care will be taken with the coupling be-tween neutronics and chemistry. This part explains how the evolu-tion of quantities in each step of the reprocessing unit at any timeis calculated, taking into account the core evolution and the chem-istry of the reprocessing. The third part of this paper is dedicated tothe inuence of the reprocessing unit on the core. The impact ofthe reprocessing parameters on the core behavior is evaluated.

The last part deals with the characterization of the reprocessingunit in terms of heat transfer and risks of criticality. These resultsare necessary to the viability demonstration and to the assessmentof the concept. Finally an uncertainty analysis, focused on chemicaldata used for the reprocessing, is briey presented.

2. The MSFR and its associated reprocessing unit

lithium uoride salt with 22.5% of heavy nuclei (mostly thoriumand ssile material) (Merle-Lucotte et al., 2008).

Our simulations are based on a 3 GW thermal power, which cor-responds to 1.5 GW electric power with a mean temperature of700 C (thermodynamic efciency of 50%). As shown in reference(Merle-Lucotte et al., 2011) such a MSFR can be started either withuranium 233 or with the transuranic elements produced in pres-

sent to the waste and the quasi-totality of the gas is sent back intothe core. Only the production of gas due to ssion has to be ex-

X. Doligez et al. / Annals of Nuclear Energy 64 (2014) 430440 4312.1. Description of the core

A Molten Salt Fast Reactor is a Molten Salt Reactor where fuel isa uoride salt (mix of lithium uoride, thorium uoride and ura-nium uoride). Consequently the salt is the fuel but also thecoolant.

Previous works from CNRS have highlighted a particular cong-uration of the core which is really a step forward in the Molten SaltReactor concept (Merle-Lucotte et al., 2009; Heuer et al., 2010). Thesalt plays three roles simultaneously: fuel, coolant and moderator.A schematic view is shown in Fig. 1: the core comprises a singlecylinder whose internal diameter is approximately equal to itsheight and where the nuclear reactions occur within the owinguoride salt. Consequently, in order to maintain three connementbarriers, the vessel should contain all the primary coolant circuit(core, heat exchangers and pumps).

As there is no solid moderator material inside the core, the neu-tron ux depends only on the proportion of heavy nuclei present inthe fuel salt. Previous systematic studies have led us to choose aFig. 1. Molten reactor scheme.tracted around 2.9 mol per day of krypton, and 3.2 mol of xenon.Consequently, a small proportion (0.017%) of the gas ow injectedin the core is extracted from the system and sent to a 3 month stor-age (which is assumed to be bottle shaped). This storage allows thedecay of the xenon isotopes, some of which have decay constant ofseveral days. At the end of this storage, there are only mostly stableisotopes of rare gas and a fraction of Kr-85 (decay constant of3917 days). Daughter nuclei from radioactive gaseous elementsare supposed to be deposited on the storage wall.

Table 1MSFR characteristics.

Initial salt LiF(77.5%)ThF4(20%)233UF4(2.5%)Operating temperature 700850 CPower 3 GW (th)1.5 GW (elec)Initial blanket salt LiF-77.5%; ThF4-22.5%Blanket thickness 50 cmsurized water reactors. Because the results presented in this papercorrespond to reactor steadys state, they are independent of theinitial ssionable material (the stabilization is not presented hereand its study in the reprocessing unit needs further studies). In or-der to increase breeding ratio, there is a 50 cm thick radial blanketmade of lithium uoride and thorium uoride. This fertile salt is lo-cated in containers made with a nickel based alloy, so this salt isseparated from the fuel salt. Table 1 sums-up the principal proper-ties of the MSFR.

2.2. The reprocessing unit

The main goal of the reprocessing unit is to extract all the s-sion products while keeping all the actinides in the salt as the hea-vy nuclei are valuable. The reprocessing unit is divided in twodifferent parts: on one hand, there is a bubbling unit dedicatedto the extraction of insoluble elements as metal and rare gases.On the other hand, a pyrochemical unit performs the lanthanide/actinide separation and extracts the soluble ssion products. Thisis done in situ, on a small amount of the total fuel salt which is ex-tracted regularly from the reactor. The whole process is presentedin Fig. 2 and studied in reference (Delpech et al., 2009a,b). The fol-lowing presents the highlights of this study.

For the insoluble ssion products, a bubble injection is foreseenjust before the salt injector, and bubbles will be collected just afterthe core as shown in Fig. 1 (salt-bubbles separator). The gas usedfor extraction is a mix of helium, krypton and xenon from the coreproduction. The amount of gas injected is around 0.1% of the corevolume (7 l of gas per second injected in the fuel salt), hence thecore is saturated in gas and the extraction of gaseous ssion prod-ucts is optimized. Those elements are transferred in the injectedbubbles. The collected aerosol (containing also metallic particles),very radioactive, is rst stocked into a tank during a certain time.At this step, there is a mix of rare gas, noble metals and all daugh-ter nuclei (iodine, bromine, alkali and earth-alkaline elements) be-cause of radioactive decays. After ltration, metallic residues areFeedback coefcient From 5.3 to 4.8 pcm/KUranium 233 production 95 kg per year

clea432 X. Doligez et al. / Annals of NuConsidering the soluble elements such as lanthanides, the pro-cess is more complicated and slower. A fraction of the fuel salt isextracted each day for control and uorinated. The goal of this rststep is to extract elements that are gaseous when they are at a highoxidation state. Uranium, Plutonium, Neptunium and Protactiniumare rst concerned but the process extracts also some ssion prod-ucts as niobium, ruthenium, molybdenum or technetium. Iodinecould also be concerned. The idea is to inject gaseous uorine inthe salt to force the reaction describe in Eq. (1) when possible (Mstands for the considered element):

MFyx x=2F2 g MFy g 1This operation extracts 99% of uranium and neptunium and 90% ofplutonium (Mailen and Cather, 1968). After this step, the fuel salt(LiFThF4) contains minor actinides, and most of the soluble ssionproducts as the lanthanides.

As it is impossible to remove ssion products without removingactinides, a second step is foreseen to extract all the remindingminor actinides in order to inject them back into the fuel salt atthe end of the process. This is a reductive extraction, performedby a contact of the fuel salt with a bismuth pool saturated of tho-rium (as the thorium solubility is quite low, the saturation impliesthe best transfer from the salt to the bismuth pool). This reductionis done twice is order to avoid the rejection of actinides.

The idea to extract lanthanides is to transfer these elementsfrom the fuel salt to a chloride salt via a bismuth pool. As lantha-nides are more stable in the chloride salt than in the uoride salt,

Fig. 2. Schematic view ofr Energy 64 (2014) 430440those elements, initially present in the fuel salt, will ow throughthe bismuth pool to go into the chloride salt. A contact between theuoride fuel salt with the second bismuth pool loads a small pro-portion of the lanthanides into the metallic phase. A second contactof this phase with a chloride salt extracts back the lanthanidesfrom the bismuth to the chloride salt. As this operation is not veryefcient, this step has to be done several times (around 20 times)in order to have acceptable extraction efciencies (Delpech et al.,2009a,b).

The last lanthanide extraction from the chloride salt is per-formed by a hydrolysis with water in order to precipitate lantha-nides oxides.

After this step, the fuel salt is clean, a last anodic oxidation willreloaded actinides from the rst bismuth pool into the fuel salt inorder to send back heavy nuclei in the core.

The fertile blanket is reprocessed the same way, but simpler: auorination extracts uranium, neptunium and plutonium, and thena reductive extraction removes all impurities. Fuel salt and fertilesalt are not reprocessed together but the unit developed for thefuel salt is able to treat the fertile salt.

Radioactive decays and chemical extraction compete with eachother in the reprocessing unit and the goal of the simulation is tocalculate the concentration of each isotope at each step of the fuelcycle, taking both processes into account.

Because the conguration leads to a fast neutron spectrum theprotactinium does not need any special treatment. Indeed, in ther-mal Molten Salt Reactors, the protactinium has to be separated

the reprocessing unit.

cleafrom the fuel salt in order to decay in 233U. This step is necessarybecause of the high capture cross section of the 233Pa in a thermalneutron spectrum but it is not needed in fast conguration of Mol-ten Salt Reactors. Indeed, the capture cross section is much lower.Calculations presented in this paper do not consider any specicstep for the protactinium.

2.3. Chemical form of each element

Each element is in equilibrium between an oxidant (ox) and areductant (red) form as shown in the following equation:

ox ne red 2The Nernst equation set the equilibrium and links the bath potentialE to the activities of each species involved in that particular equilib-rium. The Nernst relation is reminded in the following equation:

E E0 RTnF

lnaoxared

3

In that equation, R, T, n, F stand for the ideal gas constant, the tem-perature, the number of electrons exchanged per reaction, and theFaraday constant. E0 represents the standard potential of the redoxcouple while aox and ared the activities of the oxidant and the reduc-tant. In our condition, we can assume that all the chemical species(except lithium, uorine and thorium) are at innite dilution; con-sequently, activity coefcient does not vary with the concentration.In those conditions Nernst relation can be written as in the follow-ing equation:

E E0 RTnF

lnoxred

4

where [ox] and [red] represents the molar concentration of the oxi-dant and the reductant and E0 stands for the apparent standardred-ox potential.

We assume that the ratio of activity coefcient is close to 1,consequently the apparent standard potential can be approxi-mated by the standard potential of each redox couple. Knowingit and E, the salt potential, it is possible to predict, for each chem-ical species the major oxidation state of each element. The HSCsoftware (Outokomopu, 2002) and its associated database wereused to build a predominance diagram for each species functionof the potential. The salt temperature is chosen at 650 C. The ref-erence used for calculations were the F2(g)/F couple. Hence, it ispossible to write an equilibrium as: ox nF red n2 F2. Thanksto the free Gibbs energy values for each species tabulated in thedatabase, HSC is able to calculate the standard potential in refer-ence to the uorine couple.

Uranium plays a particular role among the elements present asit is the redox buffer. Indeed, the salt potential is xed with theUF3/UF4 ratio. This ratio has to be chosen between 1 and 1/100;it should not be larger than 1 to avoid equilibrium with metallicuranium and it should not be too small to ensure that uranium isa valid redox buffer. In the following, the ratio is set to 1/100. Thisratio control the salt potential to a given value E (equal to 3.53 Vin reference to the F2(g)/F couple). Once E is calculated, the ratiooxred is deduced for each element and the major oxidation state isfound. The results are presented in Fig. 3: black elements are eithermetallic or rare gas elements (oxidation state equal to 0), blue ele-ments are tetrauoride elements (oxidation state equal to 4), redelements are triuoride elements (oxidation state equal to 3), thealkaline earth elements (oxidation state equal to 2) are displayedin green and yellow elements are alkali (oxidation state equal to

X. Doligez et al. / Annals of Nu1). Finally, violet ones are bromine and iodine whose oxidationstate is assumed to be equal to 1. The behavior of these elementsremains uncertain and may evolve during reactor operation as thefuel salt composition evolves. In order to perform our study, we as-sumed that those elements are partially extracted by the uorina-tion step of the reprocessing so they cannot accumulate in the fuelsalt. Consequently, their inuence on the complexation of otherspecies remains negligible.

3. Calculation mean

3.1. Evolution equation

Inside the core the population of each nucleus is given by amaterial balance equation. Variations are due to neutron capturesand radioactive decays, so that the nuclei concentrations varyaccording to Eq. (5) known as the Bateman equation.

@Ni@t

Xji

kj!iNj hrj!i/iNj kiNi hri/iNi 5

In this equation Ni represent the number of nuclei of isotope i, attime t, ki, its decay constant, /, the neutron ux and ri the neutronabsorption cross section (so hri /i represents total reaction rate ofthe considerate reaction rate). With the same notation, ki?j repre-sents the product of the decay constant of the nucleus j by thebranching ratio of the decay considered, and rj?i the cross sectionof the production of nucleus i thanks to a neutron capture by nu-cleus j.

To take into account the reprocessing, it is necessary to add anextraction term when considering the nuclei present inside thecore. The reprocessing capacity is characterized by the time neededto reprocess the whole core, when considering the extraction of thesolubilized elements. Supposing that the species in the fuel salt arehomogeneously partitioned, the probability to extract a nucleusfrom the core to the reprocessing unit is given by 1TLanthanides where

TLanthanides is the time needed to reprocess the whole core. If TLantha-nides is expressed in days, 1TLanthanides of the fuel salt is extracted each

day to the reprocessing unit. Hence, the chemical decay constantcan be expressed as kChemi 1TLanthanides.

Concerning the extraction thanks to the bubbling, we denedTBubbling as the time needed to decrease by a factor 2 the populationof one isotope in the fuel salt. For the non-solubilized elements it ispossible to write the following equation: Nt TBubbling Nt2where N(t) stands for the number of nuclei present in the fuel saltat time t. This TBubbling time can easily be assimilated to a bubbling

decay through the relation: kBubblingi ln2TBubbling where TBubbling is thecharacteristic bubbling time. The calculation of those chemicalextractions term is discussed in the next paragraph.

Materials are added continuously during operation thanks tothe feeding of the reprocessing unit. Consequently, for MSRs, Eq.(4) becomes the following equation:

@Ni@t

Xji

fkj!iNj hrj!i/iNjg kiNi hri/iNi kChemi Ni

kBubblingi Ni Ai 6As the production of 233U inside the core is not sufcient to com-pensate its disappearance (the core itself is not breeder), adding s-sionable material is necessary to maintain the reactivity. Inoperation, this ssionable material comes from the blanket.

The neutron ux and reaction rates are calculated thanks toMCNP (Briesmeister, 1997), and the integration of Eq. (5) is donethanks to a Runge and Kutta fourth order method using a home-made code called REM (Heuer et al., 2010). This materials evolution

r Energy 64 (2014) 430440 433is constrained by several parameters such as constant power, con-stant amount of heavy nuclei and the criticality of the system overtime.

orm

434 X. Doligez et al. / Annals of Nuclear Energy 64 (2014) 430440Eq. (3) does not allow the tracking of isotopes inside the repro-cessing unit. To implement a complete coupling with the chemis-try, we assumed that each chemical step can be represented by arst order kinetic process, so that there is a rst order transferfunction that links each consecutive step. Fluorination, reductiveextraction in bismuth, back-extraction are different steps of theprocess. Section 3.2 justies the rst order kinetic assumption.Moreover, such an hypothesis is necessary to maintain Eq. (6) asa linear differential equation that can be easily solved numerically.

By this way, each isotope is no longer characterized by 5 dimen-sions (atomic number, mass number and isomeric state), but by 4dimensions. Indeed its localization in the system is added and adisappearance term in each localization which is different for eachelement. Fig. 4 illustrates the coupling scheme.

In the reprocessing unit, there is no neutron ux, the evolution

Fig. 3. Chemical fof each isotope satises Eq. (7). In this equation, P represents thelocation of nucleus i, and kChem;Pi the total disappearance by chem-istry of nucleus i from location P. kChem;p!Pi (resp. k

Bubbling;p!Pi ) is the

constant associated to the step in the chemical unit (resp. in thebubbling unit) that would imply the transfer of nucleus i fromthe location p to location P. The other notations are consistent withnotations in Eq. (6).

@Ni@t

Xji

kj!iNj kiNi kChem;Pi Ni XpP

kChem;p!Pi Ni XpP

kBubbling;p!Pi Ni

7

Fig. 4. Core evolution to chemical processing coupling scheme.3.2.1. Bubbling unitAs mentioned in the Section 2.2, the gaseous ssion products

are quickly extracted from the core by trapping on gas bubbles,and stored a certain time (long as compared to the time spent inthe core). In order to simplify the bubbling unit, the gas used forthe extraction is a mix of krypton and xenon from the core produc-tion. It is basically a simple loop where the gas ows from the core3.2. Reprocessing modeling

If Eq. (7) shows how the simulation of the coupling is possible,the problem is now in the calculation of the chemical extractionconstants. This paragraph presents the discussion of the modelingof each step in the process and the way the chemical extractionconstants are calculated.

of each element.to the bubbling unit and from the bubbling unit to the core. It isjust needed to extract the daily production in order to maintainthe total amount of gaz. The process is efcient if the gaseous s-sion products do not decay into the fuel salt but rather in the bub-bling unit. Indeed, their decays lead to the formation of alkali andearth-alkaline which are delicate to extract. The following explainsthe evaluation of the performance of the bubbling unit which isillustrated in Fig. 5.

Considering an isotope i (and k its decay constant), Si is the totalamount of that isotope in the salt and S0i , the amount dissolved inthe fuel salt. The disappearance term that applies to isotope ithanks to bubbling will affect only Si S0i (the amount over the sol-ubility limit). This disappearance can be written as

Fig. 5. Bubbling unit scheme.

kbubbling Si S0i . Let Ri be the amount of isotope i in the storage.The gas in the storage is used for the bubbling, so that there is afeeding term for the amount inside the core (Si): it is writtenkrgRi (with g the proportion that goes into the core the rest goesto the bottle used for the 3 month storage and kr the constantassociated to the kinetic of the transfer). The production term ofisotope i is written sSi in the salt (produced by ssion or radioactivedecay) and sRi in the storage (in that case produced only by radio-active decay). Finally the amount present in the bottle is written Bi.Eq. (8) give the evolution of isotope i in each step of the bubbling.

dSidt sSi kSi kbubblingSi S0i krgRidRidt sRi kbubblingSi S0i kRi krRidBidt 1 gkrRi kBi

8>>>:

8

3.2.2. Extraction of the lanthanidesThe uorination process is a well-known industrial process: it is

used for solid fuel fabrication. Even if the environment will be dif-ferent (more radioactivity, use of uoride salt), this step does notrepresent a key issue in the process study. ORNL have demon-strated the extraction of uranium (99.9%) and plutonium (99%)with a fall drop process (Mailen and Cather, 1968). In our studywe assume a 1 h process that extracts 99% of the uranium and nep-tunium, and 90% of the plutonium.

The actinide/lanthanide separation is more questionable. Theprocess is dened and quantied from a thermochemical point ofview in reference (Delpech et al., 2009a,b). However, this workdoes not present any kinetic values. For a complete coupling study,the disappearance term of one isotope in one region by nuclear de-cay has to be compared to its disappearance by chemical extrac-tion. As shown in Section 2, the elementary process is a contactbetween the fuel salt and a bismuth pool. This contact is assumedto be done with a counter ow exchanger. Moriyama et al. (1991)

X. Doligez et al. / Annals of Nuclear Energy 64 (2014) 430440 435The two extraction constants in this equation (kbubbling and kr) can bepreselected. They determine the physical properties of the bubblingunit (size of the storage, gas composition, etc.). As the system is atsteady state, the amount of gas extracted by the reprocessingshould be equal to the amount of gas produced. Hence g is xed.

Supposing the time spent in the intermediate storage very long,kr is consequently very small and the amount of gas in the storagewill be large. The efciency of the bubbling extraction is deter-mined by those two constants: kbubbling determines the time spentin the core for all insoluble elements and the ratio kr over kbubbling

determines the fraction of gaseous radioactive elements that de-cays outside the core. This ratio should be as small as possible, be-cause if a gaseous element decays outside the core, the daughternuclei will be metallic and will not go back into the core.

The constant associated to the extraction from the core can becalculated from different bubbling characteristics such as thequantity of gas inside the core, the performance of the bubble/saltseparation, etc. The analysis of the MSRE (experiment performed atLANL in the 1960s) gives a typical time of 30 s. This value was keptand the inuence of the constant associated to the storage wasstudied. Fig. 6 shows the fraction of decays from gaseous elementslost in the fuel salt versus the duration of storage. 1000 s storageseems a good compromise: the storage volume is 6.5 m3 whichseems to be small enough to be located inside the reactor vesseland the loss of decays in the fuel salt remains small. 10,000 s wouldimply an decrease of 2% of this loss for krypton and 0.5% for xenononly while increasing the storage volume by a factor 10.Fig. 6. Bubbling unit performance.shows that with an agitated interface, the reaction is limited by dif-fusion in the salt or in the liquid metal. Without any agitation,some solid metallic complex could be formed and those couldblock the transfer at the metal/salt interface. Knowing that themechanism is really complex the assumption that the metallicphase is more agitated is made. Consequently, the mass transferin the metallic phase is accelerated and the limiting process wouldbe the mass transfer inside the fuel salt. This last is not supposed tobe directly agitated, thats why we assume that the limiting step inthe mass transfer is the diffusion inside the fuel salt. The followingshows how the transfer could be modeled with such a stronghypothesis. However, the reduction kinetics is dependent on thetechnology chosen for the process and this choice is not settledown. Consequently, further studies have to be made on thosereductions kinetics in order to be better taken into account in thistype of coupled calculation.

Fig. 7 presents a scheme of the physics involved in the reductionand of the hypothesis made for the extraction modeling. The mate-rial ux (/) is given by the following equation (9).

/ k Csalt Cinterfacesalt

9

Csalt is the concentration inside the salt (Cinterfacesalt is the concentration

at the interface), k a transfer coefcient, function of the diffusioncoefcient of the considerate species inside the fuel salt. Introduc-ing the partition coefcient given by Eq. (10) (Cmetal stands for theconcentration inside the metal),Fig. 7. Schematic view of a counter-ow exchanger.

D1 CmetalCinterfacesalt

10

Eq. (9) becomes:

/ k Csalt k CmetalD1 11

Finally those uxes are written as a function of the number of atomsinside the salt (Nsalt) using Eqs. (12) and (13), where a is the ex-change surface, to obtain Eq. (14).

@Nsalt@t

/ a 12

Nsalt

Fig. 9. Partition coefcient for a chloride loop.

436 X. Doligez et al. / Annals of Nuclear Energy 64 (2014) 430440Csalt Vsalt 13

dNsaltdt

kD1Vmetal=a

Nmetal kVsalt=aNsalt 14

Writing equation 14 as dNsaltdt kmetal!saltNmetal ksalt!metalNmetal, thechemical decay constants corresponds to the transition metalthrough salt (resp. salt through metal) by Eq. (15) (resp. Eq. (16)).

kmetal!salt kD1Vmetal=a 15

ksalt!metal kVsalt=a 16

In the case where the assumption of one limiting phase is not valid,a second transfer coefcient is introduced in Eqs. (13) and (14).

Partition coefcient of one element is function of the thoriumpartition coefcient because of the equilibrium between thoriumand the other elements. Partition coefcients are plotted in Fig. 8for a uoride salt and in Fig. 9 for a chloride salt. Those were calcu-lated thanks to the HSC software and its associated database anddo not rely on any experiment. As partition coefcients dependson the melt composition (Delpech, 2013), the values we calculatedare not very reliable consequently, the last section of this paperpresents a sensitivity study of the whole reprocessing to those par-tition coefcients.

In order to maximize the actinide/lanthanide separation, wechoose a volume of metal equal to the volume of salt in the rstreductive extraction and a volume of metal 10 times bigger inthe second reductive extraction.

4. Reprocessing limit

The previous section has shown how it is possible to simulatenumerically the coupling between the reprocessing unit and theFig. 8. Partition coefcient for a uoride loop.core evolution. The rst task is to identify a limit for thereprocessing.

4.1. Inuence of the reprocessing on the physical properties of the core

4.1.1. Plutonium solubilityThe plutonium solubility in a lithium uoride, thorium uoride

mix was measured at the BARC laboratory (Sood et al., 1975). Fromthose data, we can assume that the plutonium solubility is close to5 at.% in our conguration. However, other elements (especiallylanthanides which are valence-3 elements) could impact and de-crease the plutonium solubility in the salt. The complete study ofthe plutonium solubility in the fuel salt is a huge study. In orderto simplify the problem, the assumption that the total concentra-tion of all valence-3 elements (plutonium and lanthanides) shouldnever be higher than 5 at.% is made. The reprocessing affects theamount of lanthanides in the core directly: a reduced reprocessingrate would imply a smaller disappearance term in Eq. (5) for lan-thanides. As a result the lanthanide concentration in the salt wouldincrease and the 5% limit for plutonium and lanthanides might bereached. Fig. 10 shows the amount of valence-3 elements in thesalt as a function of the global reprocessing time. To maintain thisvalence-3 proportion below 5 at.%, the reprocessing time has to beless than 10,000 days or so.

4.1.2. Breeding ratioThe breeding ratio expresses the balance between the creation

of 233U through neutron capture on 232Th and the destructionof 233U through ssion or neutron capture. It is directly linkedFig. 10. Proportion of valence-3 elements.

to neutron capture rates. As the lanthanides are not extracted bythe bubbles and as they are the most capturing elements, the bub-bling efciency will not affect the breeding ratio signicantly. Thecapacity for the extraction of the lanthanides from the fuel saltdetermines their population in the core. Breeding ratio calculationspresented in Fig. 11 shows that the core itself is not over-breederbut the MSFR with the blanket is a breeder reactor if the timeneeded to reprocess the whole fuel salt and the blanket salt issmaller than 7000 days. One should remember that the neutronspectrum is rather fast so that the neutron capture cross sectionsof ssion products are small.

4.1.3. Feedback coefcientThe feedback coefcients are dened as the variation of reactiv-

ity in response to a variation of the core temperature. This coef-cient has to be negative to ensure the stability of the reactor. It

Thus any neutron reaction with an uranium IV will lead to the cre-ation of a single uorine atom that will shift the equilibrium thatdetermines the redox potential in the fuel salt as demonstratedby the following equation:

UF3 12 F2g ! UF4 18

Consequently, any reaction on uranium is in fact a disappearance ofuranium whose oxidation state is III. This statement has alreadybeen studied in (Delpech et al., 2009a,b) and (Delpech et al., 2010).

The reactor operation thus implies a shift in the redox potentialthat has to be compensate by a feeding of uranium III. This is pos-sible as some uranium is extracted from the fuel salt in the uori-nation step of the reprocessing. This uranium is then reduced toeither UF3 or UF4. Operators choose the chemical form of the ura-nium before injecting it back into the fuel salt, controlling by thisway the redox potential of the fuel salt.

As 16.2 mol of uranium disappear each day by neutron reac-tions, 16.2 mol of the 32,746 mol present in the core have to be ex-tracted from and reintroduced in the core as UF3. Consequently, theentire core should be reprocessed within 37,246/16.2 days orapproximately 2000 days. No compensation would imply a shiftof 4.3 mV per day due to UF3 disappearance.

References (Delpech et al., 2009a,b) and (Delpech et al., 2010)present other possible ways to control the redox potential. Oneof them consists to perform the reduction of UF4 to UF3 by addinga reducing agent in the salt as metallic thorium for instance. Those

Zr 0.318 +4 1.272Kr + Xe 0.606 0 0Noble metals

(Nb + Mo + Tc + Ru)0.4 0 0

Total 1.953 3.049

X. Doligez et al. / Annals of Nucleacomprises two terms: the density and the Doppler coefcients.The density coefcient reects the density variation due to a tem-perature variation and can be linked to a void coefcient, while theDoppler coefcient corresponds to the variation of neutronic crosssections with the temperature.

Because the reprocessing changes the salt composition, thosecoefcients will depend on the reprocessing time. However, thefast neutron spectrum does not vary much with the reprocessing,so that this dependence is not so obvious. The Doppler and densitycoefcients are plotted in Fig. 12, clearly showing no noticeablevariation with the reprocessing capacities provided the reprocess-ing is faster than 10,000 days.

4.2. Reprocessing needs

From the previous paragraph, we can conclude that the repro-cessing time does not impact the reactor physics so much. Themain goal of the reprocessing is to control the chemistry of the fuelsalt and avoid any solubility problem. As stated in Section 3.2, thepotential of the salt is determined by uranium, but uranium disap-pears from the salt by neutron capture or ssion. Neutron captureson uranium IV (oxidation state is 4), lead to the creation of Neptu-nium III (oxidation state is 3). Table 2 shows that ssions also leadto the formation of valence-3 elements. In that table, Y stands forthe probability of formation normalized to ssion of uranium233. Z represents the oxidation state of the considerate elementin the fuel salt. Consequently, the line TOTAL corresponds tothe mean oxidation state of the two ssion products.

UF4 !fission2FPF3 12 F2g 17Fig. 11. Breeding ratio function of the reprocessing time.Fig. 12. Feedback coefcient, function of the reprocessing.

Table 2Fission products abundance and oxidation state.

Fission products Fission yield(Y)

Degree ofoxidation (Z)

ProductYZ

Br + I 0.015 1 0.015Rb + Cs 0.004 +1 0.004Sr + Ba 0.072 +2 0.144Lanthanides + Y 0.538 +3 1.644

r Energy 64 (2014) 430440 437options are not studied more in details in this paper but it shouldbe noticed that if such a choice is made, the 2000 days limit doesnot stand anymore. In that case, the core should be reprocessed

seems prohibitive. Table 4 shows the evolution of the heat produc-tion for 40 l of the fuel salt.

Waiting 1 day before doing any operation on the fuel salt wouldimply that the heat generated is divided by 2. Waiting an extra daydoes not really change the issue. Only after another 30 days isagain divided by 2. Each waiting day means the control of 40 l offuel salt. In view of those values, a cooling time of 1 day for the fuelsalt, before starting the uorination process is suggested.

Fig. 13. Evolution of the alkali and earth alkaline elements.

Fig. 14. Neutron capture rates of alkali and earth alkaline.

cleawithin 7000 days to keep the plutonium concentration beyond itssolubility limit.

4.3. Alkaline and earth-alkaline

The reprocessing, as it is outlined in Fig. 2, does not allow theextraction of alkali and earth alkaline elements. Their extractionseems very complicated as those elements behave like lithium ina uoride salt. However, it could be done using a stronger reducingagent. The process assumed that a step may be developed to ex-tract them together with the lanthanides. With this assumption,their neutron capture and production rates have been calculatedand presented in Table 3.

As shown in this table, the production of earth-alkaline and al-kali elements is rather small and their neutron capture rate is 100times lower than that of the lanthanides. This means that if theamount of those elements in the salt is 100 times larger than thatof the lanthanides their reaction rates will be equivalent to those oflanthanides.

As shown in the previous paragraph, neutronics does not con-straint the reprocessing rate, and an accumulation of alkali andearth alkaline in the fuel salt should not induce a strong degrada-tion of the good characteristics of the core. Figs. 13 and 14 showthe evolution of quantities and neutron capture rates of alkaliand earth alkaline elements during 200 years of salt irradiationwithout attempting to remove those elements. At the end of the200 years, the system is still over-breeder and the breeding ratiois not affected.

5. Reprocessing assessment

With Eq. (5), the calculation of the composition of each nucleusin each component of the entire reprocessing system is possible.Those compositions are useful to calculate heat production (dueto nuclear decay) and other back end cycle quantities such as crit-icality in order to identify any other constraint on the reprocessing.Those quantities are also entries for further studies such as designparameters, radiation protection or chemical process optimization.

5.1. Heat production

This part is dedicated to the calculation of the heat productiondue to nuclear decay. This heat production is fundamental for fur-ther studies (safety, design or even non-proliferation issues) anddepends clearly of the coupling between the reprocessing unitand the core. Heat produced by exothermic reactions is not calcu-lated here.

The nuclear decay data chosen are from the ENSDF data base.

Table 3Alkali and earth alkaline reaction rates.

Elements Ln

Neutron capture rate (normalized to one ssion neutron) 5.6 103Production (mol/days) 0.87

438 X. Doligez et al. / Annals of NuThe heat production in the reprocessing unit is a function of thetime of reactor operation; the calculations presented here aremade after a long time of operation (200 years) in order to be closeto the steady state conditions. We assume that all the energy dis-sipated thanks to nuclear decay lead to an increase of temperatureof the salt, structural material or biological protection. Results areshown in Fig. 15.

As shown in this gure, the maximum heat production is lo-cated in the rst compartment of the unit and reaches approxi-mately 80 kW which seems acceptable. There is no value thatCs Ba Rb Sr

2.2 105 2.3 105 1.6 106 1.9 1060.15 0.4 8.3 103 0.45

r Energy 64 (2014) 4304405.2. Criticality risks

Table 5 shows the neutron multiplication factor for the compo-sition of the fuel salt and for the uorination residues. This latestconcerns all the valuable elements that have been extracted thanksto the uorination process and then reduced into a usable form.We assume it is a mix of uranium uoride, protactinium uoride,neptunium uoride and plutonium uoride that have been ex-tracted from the uorination of 40 l of fuel salt.

X. Doligez et al. / Annals of Nuclear Energy 64 (2014) 430440 439Fuel salt and uorination residues are the only two composi-tions that contain ssionable material. In order to quantify the crit-icality risks various disturbances has been studied as follow:moderation with graphite (25 cm thick), and a doubling of thereprocessing rate.

Criticality calculations for Table 5 were made assuming asphere as geometry. Clearly, the handling of uorination residuesrequires special care in the choice of structural materials and thegeometry of the uorination reactor. In the case of double extrac-tion (80 l of fuel salt uorinated) and moderation with graphite aneutron multiplication factor of 1.68 is obtained which is obviouslyunacceptable. For that reason, a 40 l per day reprocessing rate is amaximum.

6. Chemical data uncertainty analysis

Some of the processing system data are not known withprecision. Among these, the most important are the partition

Fig. 15. Heat generated in

Table 4Evolution of the heat generated in 40 l of fuel salt.

Cooling time Heat (kW)

1 s 2621 h 821 day 492 days 4430 days 20

Table 5neutron multiplication factor in the reprocessing unit.

Case considered keff

Fuel salt (40 l) 0.198Fluorination residues 0.576Fuel salt + moderation 0.198Fluorination residues + moderation 0.968Fuel salt from a double extraction (80 l) 0.579coefcients. Indeed the data available in the bibliography (Ferriset al., 1970) do not deal with the same fuel salt composition. Theyconcern a lithium uoride, thorium uoride and beryllium uoride

the reprocessing unit.mix. Consequently, it is impossible to compare our partition coef-cient calculations to actual experiments even if the order of mag-nitude between our calculation and the data from (Ferris et al.,1970) should be the same.

The extraction efciency of a particular element is dened asthe ratio of the outgoing quantity, from the reprocessing unit tothe waste (the rest is sent back to the core), over the ingoing quan-tity into the reprocessing unit coming from the core. From this def-inition, a well-designed reprocessing unit should have very lowefciencies for actinides and efciencies close to one for ssionproducts (lanthanides). As ssion products evolve inside the repro-cessing unit due to nuclear decay, the global efciency for ssionproduct is a result of a coupled calculation of the core and thereprocessing unit evolution.

Fig. 16. Extraction efciencies for lanthanides.

cleaThis coupled calculation is based on our partition coefcientcalculated thanks to the HSC database. In order to study the uncer-tainties associated to the chemistry of reductive extractions, theextraction efciencies for different elements as a function of thevariation of the partition coefcients have been calculated. Parti-tion coefcient deviations from the supposed value are quantiedon a logarithmic scale, which means that a deviation of +1 impliesa 10 times increase in the partition coefcient. All the other param-eters (volume of salt, volume of metal, iterations, etc.) remain un-changed. The chemical decay constant dened in Eqs. (15) and (16)are calculated for different partition coefcient values. Then it ispossible to resolve Eq. (7) that describes the concentration of eachnucleus at each step of the reprocessing unit. Consequently, the ra-tio of the ingoing quantity over the outgoing quantity can be calcu-lated for different partition coefcient values.

Figs. 16 and 17 show the result of this study. The reference casepartition coefcients as calculated in the condition of therst reduc-tive extraction step are recalled for each element. Fig. 16 shows thatapartition coefcient 10 times larger thancalculated for lanthanideswould imply a strong decrease of the efciency from approximately80% to 60%. A 10 times lower partition coefcient for lanthanideswould imply efciencies smaller than 50% for lanthanides. Our cal-culations show that the process is sensitive to those partition coef-cients. Consequently, further studies on a lithium uoride, thoriumuoride salt are needed to conrm our hypothesis.

Fig. 17. Extraction efciencies for actinides.

440 X. Doligez et al. / Annals of Nu7. Conclusion

This paper presents the tool we developed to study the MSFRcoupled to its associated reprocessing system. Thanks to this tool,it is possible to fully take into account the inuence of the repro-cessing unit on the neutronics of the reactor. Moreover, thanks toa very simple description of the reprocessing unit, the evolutionof each isotope outside the core is followed. Taking into accountnuclear decays into the reprocessing unit is fundamental in a con-cept like the MSFR because some of the involved isotopes are shortlived nuclei; the efciency of the extraction clearly depends on thekinetic of each step of the process. Consequently, a simple geome-try and modeled the kinetics of the chemistry to perform a full cou-pled study is chosen.

This paper shows that no constraints on the reactor operationare due to the reprocessing. Rather this later is a way to controlthe salt chemistry and the redox potential. This lack of constraintis due to the fast neutron spectrum inside the core: ssion prod-ucts reaction rates are low and their extractions are not critical.Consequently, a good margin remains for the reactor operation.For instance, alkali and earth alkaline elements do not have to beextracted since their production is small as compared to that ofmetals and lanthanides. Consequently it is possible to let themaccumulate in the fuel salt during 200 years without observing alarge impact on the breeding ratio.

With this coupling, quantities in each part of the reprocessingsystem at any time during operation have been calculated. Withthose quantities relevant back end cycle properties such as the crit-icality or the heat production due to nuclear decay are evaluated.Criticality risks have to be taken into account especially in the fuelsalt uorination step. Indeed, the isotopic composition of the prot-actinium, uranium, neptunium and plutonium extracted is highlyenriched in uranium 233 and could be over critical in the presenceof moderation.

Finally an analysis of chemical uncertainties on reductiveextraction partition coefcients is presented. If those coefcientswere overestimated by a factor of 10 for lanthanides, the lantha-nide extraction efciency could be reduced to less than 20%. Con-sequently, knowing coefcient with precision for the exact MSFRfuel salt is necessary for further studies. Moreover, kinetic studiesof reductive extraction are required in order to be better modeledin our numerical tool and to conclude to the limitation of the pro-cess. Limitations can come from diffusion, interfaces limitations, orchemical mechanism.

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Coupled study of the Molten Salt Fast Reactor core physics and its associated reprocessing unit1 Introduction2 The MSFR and its associated reprocessing unit2.1 Description of the core2.2 The reprocessing unit2.3 Chemical form of each element

3 Calculation mean3.1 Evolution equation3.2 Reprocessing modeling3.2.1 Bubbling unit3.2.2 Extraction of the lanthanides

4 Reprocessing limit4.1 Influence of the reprocessing on the physical properties of the core4.1.1 Plutonium solubility4.1.2 Breeding ratio4.1.3 Feedback coefficient

4.2 Reprocessing needs4.3 Alkaline and earth-alkaline

5 Reprocessing assessment5.1 Heat production5.2 Criticality risks

6 Chemical data uncertainty analysis7 ConclusionReferences