-
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: [email protected],
[email protected] (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