7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
Reactive Mlultiphase Flow Simulation of Uranium Hexafluoride Conversion Reactor
N. A. Konan*', H. Neau*', O. Simonin*i, M. Dupoizat' and T. Le Goaziou~
University de Toulouse : INPT, UPS: IMFT: AllCe Camille Soula, 31400 Toulouse, France
SCNRS: Institut de M~canique des Fluides de Toulouse: 31400 Toulouse, France
i:AREVA NC BUChimie: BP 44, 26701 Pierrelatte, France
konand imft.fr, neaud imft.fr, simonind imft.fr and marc. dupoizat0 areva. com
Keywords: Fluidized bed, particle size distribution, uranium fluorination, shrinking core model, heat transfer
Abstract
Full threedimensional simulations of the fluorination process within a gassolid fluidized bed batch reactor is
challenged. NFluid MultiClass Eulerian approach to account for the distribution of the size of the tetrafluorure
particles of uranium is successfully used to describe the hydrodynamics of the bed and the heat and mass transfer
mechanisms due to the fluorination reaction. The chemical gasparticle reaction modeling integrates the external
diffusion mechanism of the reactant gas within the boundary layer of the uranium particles. Radiative heat transfer
between particles and convection/diffusion gasparticles heat exchange models are proposed. The simulation results
show that the amount and the regimes of the production of the uranium hexafluoride and the leak of the fluorine in
this batch reactor are consistent with the observations.
Nomenclature
Introduction
The perfect mixing of the bed and subsequently the ex
cellent rates of the heat and the mass transfers between
the gas and the solid particles, which make the control of
the reactions easier, are responsible of the widespread of
the gassolid fluidized reactor in nuclear industry. How
ever in accordance with the Geldart fluidizing particles
classification, cunning processes are mostly required for
the fluidization. For example in the uranium hexafluo
ride conversion, nonreactive particles mainly character
ized by a relatively easier fluidization and satisfactory
heat transfer properties (i.e. absorption, diffusion and
reflection) are typically added to the uranium particles
(Geldart Atype particles). The simulation of such a sys
tem is complex because of the multiscale mechanisms
taking place due to:
polvdispersion of the solid particles (size, type, ...),
heat exchange mechanisms,
Roman symbol
UF4 tetrafluorure uranium particle
Fo fluorine
UF4 uranium hexafluoride
Kp interparticle radiative diffusivity coefficient
(m's1)
X, mole fraction of the gaseous species q ()
X, mole fraction of the gaseous species q at the
surface of reactive particle ()
FD cumulative distribution function of the particle
size ()
Greek symbol
Pre density of phase k (kg.m )
rEx mass transfer rate of phase k (kg.m's1)
K empirical particle/vall heat transfer constant
(W.mn2.K1)
Subscripty
Y
p
Superscipty
in
*chemical reactions, ..
gas
particle
class of the reactive particle
The first two points gave rise to extensive works with
special attention to the interactions between the parti
cles and the gas, between the particles and the parti
cles with the walls: Derevich & Zaichik (1988), Reeks
(1991), Simonin et al. (1993), Boelle et al. (1995), Sakiz
& Simonin (1999), Marchisio et al. (2003), Fan et al.
(I II [}, Yamada et al. (1995), Patil et al. (2006), ... Ki
netics of the reactions are im estimated on the basis of
the diffusion of the reactant gas through the gas film
surrounding the particle (see e.g. Braun et al. (2000)).
For the fluorination, although it consists of twostep
chemical reactions that firstly creates porous intermedi
ate solid and secondly fields to uranium hexafluoride
gas, only the latter reaction is commonly accounted for
as it successfully represents the whole mechanism dur
ing the fluorination. Further discussions can be found in
Homma et al. (2005), Zhao & Chen (2008).
The recent works of Khani et al. (2008a) and
Khani et al. (2008b) integrate such mechanisms for the
reaction kinetics. However, the hydrodynamics of the
bed that ensures the mixing of the bed (and subsequently
allows controlled reactions) and the heat exchanges are
poorly im estimated within their gassolid fluidized two
phase models used for the uranium hexafluoride com er
sion.
In this paper Nfluid Eulerian approach derived from
Boltzmanntype equation (see Gourdel et al. (1999),
Simonin (2000)) is used to investigate the full three
dimensional behavior of the cloud of particles moving
within the reactive turbulent gas flow. The distribution
of the size of the reactive particles is accounted for using
the Method Of Class. The main chemical reaction con
sidered here is the reaction of the tetrafluorure particles
(UF4) with the fluorine (F2):
UF4+F, UFs, with AH, = 234.4kJ7.mol
(1)
The Eulerian modeling of the reaction rate is based on
the skrinking particle model including the external dif
fusion of the fluorine within the boundary layer of the
reactive particles. Both the radiative interparticle and
heat exchanges at the wall are accounted for.
MlultiClass EulerEuler Reactive Flow
Modeling
Hydrodynamics of the bed
Mass balance equation
Considering the chemical reactions giving rise to the
phase changes within the reactor, the mass transfers be
tween phases require that the mass balance satisfies:
in which pa and as denote the density and the volume
fraction of the kth phase, respectively. Us,; represents
the ith component of the mean velocity of the phase k.
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
Ex accounts for the interphase mass transfer rate and sat
isfies:
rex = 0 (3)
The alumina particles used as fluidizing agent are in
ert and do not react. Their mass transfer rate is null:
rA/1oz 0.O The reaction between the fluorine and each
class of the uranium particulate phase continuously gen
erates uranium hexafluoride towards the gas. Accord
ingly, the mass transfer rate r, of the gas stands for:
r,= C
U" tg
_gUF
N is the number of the reactive uranium particle classes.
~F4"9 represents the mass transfer rate occurring from
the mth uranium particle class towards the gas and rfew
refers to as the total mass transfer rate of the uranium
phase.
Momentum balance equation
Assuming the gravity as the only external force acting on
each phase k, the mean momentum equation is written:
i3L, itr ,
 i)P a u
9)r
S[LT,; LT<,;] Ex [ax Pl Rlc;4 + 8
itrj
+ Cmj Sntrc,;
(5)
in which P, is the mean pressure of the gas phase while
y; denotes the ith component of gravity.
The interfacial momentum transfer rate between the gas
and the particles is accounted for in the last term through
the drag force model:
V
5,, ,; 5, ,,, = a p,
V ,,;i LT,,, LT,,; 1 Vdp,, represents the ith component
of the mean relative velocity between the particles and
the surrounding gas, while the fluidparticle drift veloc
ity 11;;,, accounts for the dispersion effects due to the
particles transport by turbulent fluid motion and, follow
ing Simonin et al. (1993), is approximated by:
Vdpi = Dgpij1 a,,ar~j
where the fluidparticle turbulent dispersion tensor
reads:1
Duz>.id = 39917gpf6;y (8)
Qg1 dQgdZj
where q,, and T,,, are the fluidparticle velocity covari
ance and the eddyparticle interaction time. The fluid
particle turbulent dispersion tensor is closed by solving
a transport equation of the fluidparticle velocity covari
ance Vermorel et al. (2003).
The characteristic time 7,F, in (5) of the particle entrain
ment by the fluid motion is approximated by:
13 p, Dh (: yp
gp 4 pp dp , ()
with the local drag coefficient modeled by:
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
details of the closure assumptions for the Nfluid mod
eling can be found in Boelle et al. (1995), Gourdel et al.
(1999) and Ciais et al. (2007).
Thermal exchange in the bed
The reactor model contains two particle phases that ex
perience heat transfers with the surrounding gas and also
between the particles. With the assumption that the heat
exchanged by contact during the interparticle collisions
is negligible, the main heat exchange modes focused
within the bed as the chemical reactions proceed are:
I(I,,( itil (C'D,1Yen & \Tu, D,Ergun) Otherwise
(10)
The drag correlation of Wen & Yu (1966) and Ergun
(1952) are, respectively:
C'D,Ergun = + 200~ (11)
24[1 + 0.15Re 8] a '. if Rep < 1000
~Re, a
CD,1Yen &Yu
0. I1.. '7 otherwise
(12)
'U, and Re, = as ( v, ) dp/Vg refer to the relative ve
locity vector and the mean particle Reynolds number'
respectively.
RA,;y in (5) represents the gas turbulent Reynolds
stresses for k y and the particle kinetic stresses
for k = p, respectively, and is modeled according to
Boussinesqlike approximation. Closure of these mod
eling is achieved by solving the k =, transport equa
tions for gas phase, modified by additional terms ac
counting for the particle influence on the fluid turbu
lence, while transport equations are solved for the par
ticle agitation kinetic energy q~ (granular temperature)
and for the fluidparticle velocity fluctuation covariance
q,, for each particulate phase (see Simonin et al. (1993)
and Gobin et al. (2003)).
LT,,; represents the ith component of the mean veloc
ity of the mass crossing the interface between gas and the
reactive particle phase, as the reaction proceeds. This
velocity is assumed to be equal to the reactive particle
velocity, i.e. LT,,; =Utry,;.
Tensor OA~ij in (5) represents the laminar viscous
stress for the gas (k y ) and the collisional stress for
the dispersed phases (k p). SA ,;~ represents the col
lision transfer term between k and p particle species in
the momentum balance equation modeled on the basis
of their locally relative velocity and their kinetic energy
as the main mechanisms driving their collisions. Further
*the convection/diffusion heat transfer (II, p) from
the gaseous phase towards the particles is modeled
according to:
Iptg = lyp = ppla (T,
T
T,) (13)
such that the characteristic time scale T" of this
COnvection/diffusion heat transfer (within the heat
transfer coefficient correlation) is given by:
1_6X, (NU)~
Tp p pI> di
(14)
in which A, is the thermal conductivity of the
gaseous phase. (NuL)y + 0.55Re Pr t/s3
represents the Nusselt number of the particle phase
while Pr pg vg C'pg / denotes the Prandtl num
ber. L',, is the specific heat of the kth phase in the
reactor.
* the enthalpy exchanged (H,) from reactive parti
cles towards the gas due to the mass flux crossing
the particle surfaces because of the mass transfer
induced by the chemical reactions. With assump
tion that the reaction enthalpy is directly released in
the surrounding gas, the mean enthalpy of the mat
ter crossing the interface due to reaction is set to the
enthalpy of the reactive particles (H, HUF4).
* the radiative heat transfer between particles of the
dense phases. Assuming that the radiation between
the particles in the bed takes place in the frame of
the Rosseland approximation through a diffusion
mechanism, Konan et al. (2009a) write the radia
tive flux in the alumina particle enthalpy equation
as proportional to the temperature gradient with a
radiative thermal diffusion coefficient given by:
32a dpTp
Kz' = 
P0 9Qr ppp
(15)
in which a is denotes the StefanBoltzmann con
stant and T, the temperature of the particles.
Then in the absence of external heat sources, the distri
bution of the enthalpy of each phase in the bed satisfies
the transport equation
i)z (as 'a Ke dHA )
as Prc + ag pr UIs,
Oft itry
+ [H, HI,] Ex, + C II/na
(16)
In the last term, II,, = O for both particle phases p
and q since the heat exchanged during the interparticle
collisions is assumed to be negligible. The first term
on the righthand side is a transport term written in the
frame of the gradient approximation with an effective
phase diffusivity coefficient K^
*for the particle phase:
KI, = KI + Kz', (17)
KI and Kz' are the contributions due to the trans
port of the enthalpy by the velocity fluctuations and
the radiative heat transfer between the particles, re
spectively.
(18)
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
(W.m2.K1) must be modeled in terms of many fac
tors, such as the particle properties, the wall emissivity
or the bed void fraction. However it may also be as
sessed using experimental data (see e.g. Yamada et al.
(1995)) or the "wallfunction model". In a first approxi
mation, the heat transfer coefficient at the wall hpu, in
(19) is simply assumed to be proportional to the volume
fraction az, of the considered dispersed phase such that:
hp7@ = /Cal, (21)
/c is an arbitrary constant coefficient. Consistently with
the measurement of the heat transfer coefficients in the
experimental fluidized bed by Yamada et al. (1995)
about 2 6 x 103 If.m2.K1, the constant /c is set
to 104 W.m2.K1
Evolution of the sizes of reactive particles and
gaseous species
Size of the reactive particles
The proceeding of the chemical reaction within the reac
tor of course gives rise to another reactive particle size
distribution. As the phenomena inside the reactor are
sizedependent, the determination of this instantaneous
size distribution is crucial. Introducing, for a given ura
nium particle class or, the mean number of particles per
unit mass XyF4' then the locally instantaneous mean di
ameter reads:
*for the gas:
K, = K~ + K
where K' and K are the contributions to the trans
port of the enthalpy due to the gas turbulence and
the laminar diffusivity, respectively.
The heat exchange at the wall is due to the laminar
heat gas conduction effect and to the radiation exchange
between the particles and the wall. Furthermore, Ko
nan et al. (2009b) assumed that the main contribution of
the heat exchanged by the nearwall computing cell with
the thermal boundary layer is dominated by the parti
cle heat transfer. Relying on such analysis, the thermal
wallfunction approach proposed to avoid the detailed
computation of the thermal boundary layer, leads to the
following practical boundary conditions for the gas and
the particle phases:
("H, \ T, \
+a~p~l ~ KI ily } = appC K"p iy } n
T, and T, are the temperatures of the gas and the wall,
respectively. The sub script Y refers to the first grid point
from the wall.
The heat transfer coefficient at the wall hp,
XhO v n 4,
'c ~ ma = ,
(22)
where d n4, and X~F, are the initial mean diameter
and the corresponding number of particles per unit mass.
Considering that the reactor operates in batch mode
and with the assumption that attrition and breakup
events do not happen despite the friction between par
ticles and the reaction that might occur inside the reac
tive particles, the timeevolution of the mean number of
particles per unit mass XyF, of the class n in the bed
writes:
dzid mtdXvF,3
X~F4 r~F4~g
(23)
in which D ",j denotes the diffusivity coefficient due to
the transport by the particle velocity fluctuations (Ab
bas et al. 2009).
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
Ta,,2 Ea/RS refers to the activation temperature of
the fluorine reaction and E, is the activation energy. f,
is the kinetic constant of the reaction. Xi represents
the mole fraction of fluorine at the surface of the parti
cle. Following Konan et al. (2009a), the mole fraction of
fluorine at the surface of the reactive particle (Xs2), ac
counting for the diffusion of fluorine within the bound
ary layer of the reactive particles, is given by:
Balance of species of the gaseous mixture
With the assumption of a mixture of ideal gases within
the reactor, the density of the gaseous mixture (p,) and
the mass fractions (Y,) of the oth specie of the gas are
governed by
PefW,
p, =
R,T,
R,T,P, WN2 N
2 2 1 V~ + 2 4
8, 8xy
(30)
(25)
v~ and a, are the viscosity and the Schmidt turbulent
number of the gaseous mixture, respectively. W, and
R, are the gas molar mass and constant, while Pev is
pressure reference inside the reactor.
Wy2 accounts for the vanishing rate of the fluorine
whereas Weye represents the apparition rate of uranium
hexafluoride. In accordance with the chemical reaction
equation (1) these reaction rates satisfy:
DF2 represents the diffusion coefficient of fluorine in ni
trogen while Sh is the Sherwood number given by the
empirical relation of Ranz and Marshall (1952)
Sh=2+055e S 4 with Sc= (31)
The effect of the fluorine external diffusion within the
boundary layer of the uranium particles has been much
investigated in our previous works (Konan et al. (2009a),
Konan et al. (2009b)) for several initial monosized fully
3D simulations of the hexafluoride conversion. It ap
peared in such conditions that the chemical reaction lim
itation by the fluorine external diffusion around UF4
particles was not measurable, even with the largest parti
cle size initial monodisperse distributions. Furthermore,
an a priori analysis of the characteristic time scale of
the chemical reaction with respect to the size of the par
ticles demonstrated that this time significantly increases
at higher temperature with the particle diameter. Ac
cordingly for a given control volume with the reactive
particle size distribution, the external effect of the fluo
nine nught most probably significantly affect the Eule
rian reaction rate.
Computation conditions overview
The threedimensional unsteady simulation of the reac
tive fluidized bed is performed with NEPTUNE_CFD
software using the Eulerian Nfluid modeling ap
proach for fluidparticle turbulent polydispersed reac
tive flows proposed in this paper and implemented
in NEPTUNE_CFD V1.08 aTlse version by IMFT
(IHStitut de M~canique des Fluides de Toulouse).
NEPTUNE_CFD is a computational multiphase flow
Software developed in the framework of the NEPTUNE
project, financially supported by CEA (Commissariat g
l'Energie Atomique), EDF (Electricit6 de France), IRSN
(Institut de Radioprotection et de Stiret6 Nucl~aire) and
AREVANP. To account for the requirement imposed
by the characteristic transfer time scales that strongly
W2 Wy26
Wev4, UF
WeU'Fua (26)
WeV4
W, (with a = N,, F2, UF6 and UF4) in (24) and (26)
are the molar mass of the gaseous species and the ura
nium particles. Note that the reaction rate of nitrogen is
null (W y2 0).
Practically, the transport equation (25) of the gaseous
species is solved on the one hand for the fluorine (since
it is the only one which directly reacts with UF4 part 
cles) and on the other hand to the nitrogen because its
reaction rate is null. The mass fraction of the uranium
hexafluoride is computed according to:
Y, ye = 1 YF2 Y2
Mass transfer rate from the reactive particles
Considering that the chemical reaction uniformly arises
at the surface of any nonporous single particle with uni
form surface temperature Ts 4 TU4, Randriananiv
elo et al. (2007) show that the Eulerian reaction rate of
the mth uranium particle phase class writes:
6ayq WUF4PrefX(2
09,4 977 kF2 (TU4) (28)
"AF RSTUF4
where the chemical kinetic modeled in accordance with
an Arrheniustype law reads:
ky2 TK) =c O 4 (29)
(24)
8xy%(l~~ ag 8xy
7th International Conference on Multiphase Flow,
decrease as the reactions proceed, coupled solving of
the enthalpy and efficient implicit methods to accurately
control the drastic change in the source terms were im
plemented. The performances of NEPTUNE_CFD for
high parallel computing are highlighted in Neau et al.
(2010).
The pilot is typically a circular column surmounted
by a dome and topped by three smokestacks (see figure
1). The fluorination process starts with the prior pre
heating of the bed, during 10 seconds, at 45000 using
the nitrogen. The second stage of the process consists of
the injection of the gaseous mixture of the fluorine (I I' .
in mole fraction) and the nitrogen ! n'. ., within the in
let of the reactor at a lower temperature (about 10000)
than for the preheating stage. The measured size of the
uranium particles spans from 0.5 pm to 1600 pm whose
discretization is described below. Regarding the inert
particles, although the size distribution may modify hy
drodynamics of the bed, they are assumed to have the
same diameter dAl20s 150 pm. The measurements
show that a few seconds after the injection of the gaseous
mixture, UF6 iS Obtained at the outlet of the reactor and
rapidly reaches a constant value, corresponding to the
:I I' mole fraction of F2 introduced. After approxima
tively three minutes, the amount of UF6 seamlessly de
creases while the leak of the fluorine is observed at the
same time at the outlet.
Unstructured finite volume method is employed and
further details about the numerical resolution methods
can be found in M~chitoua et al. (2003). The mesh
of the domain (see figure 1) is comprised of around
195, 000. The time step during the preheating of the
bed as well as for the hexafluoride conversion is typi
cally about at 5 x 10ss. Hydrodynamics simu
lations not reported here were carried out using meshes
comprising two and three times more cells than the mesh
presented herein. The initial height of the bed is 0.6 m.
The inlet velocity of the gas is set to 0.38 m.sl and
0.2 m.sl for the preheating and the conversion stages,
respectively. The total initial mass of the particles inside
the reactor is composed of 1I' uranium tetrafluoride
and of course I I' is the alumina.
During the conversion, the gas/particle reaction does not
locally happens anymore when the size of the reactive
particles is smaller than a given diameter (taken about
1 pm).
Discretization technique of the uranium particle size.
Given the total initial volume fraction so 4 Of the ura
nium particle phase and the measured distribution of
the particle size, the accounting for the size distribution
in the simulations is carried out by discretizing (in the
diameter space) the normalized cumulative distribution
to loo looo
Figure 2: Illustration of the discretization of the cumu
lative distribution function of the measured
uranium particle size distribution.
function of the particle size defined by:
Sp (dl) (32)
dldUd
FD (dUF4) = P (D < dUF4)
where p is the particle size probability. Considering six
uranium classes, the discretization is shown in figure 2.
For each interval resulting from the discretization, a
particle mean diameter corresponding to the dso of the
given class is computed. Regarding the initial volume
fraction of each class, it is assessed on the basis of the
representativeness of the corresponding sampling. Then
for the given total volume fraction so F4 Of the uranium
particle phase, the initial volume fraction of each class
constitutes a fraction of a ,4 evaluated according to
the ratio of the area delimited by the class interval over
the total area under the cumulative distribution function.
With these arrangements, the initial mean diameters of
the six classes range from 14 pm to 1401 pm and the
initial volume fractions of the corresponding classes are
summarized in Table 1.
Results and discussions
The figure 3 exhibiting the volume fractions of the
phases within the reactor shows an excellent mixing be
tween phases. Actually, both the uranium (phase in mi
nority within the reactor) and the alumina (particulate
phase in large majority and mainly driving the bed dy
namics) are thoroughly distributed almost everywhere in
the bed. One can observe the accumulation of the alu
mina in the nearwall region (see also figure 5) as well
as in the core of the reactor. The presence of gas bub
bles is also highlighted by the volume fraction of the gas,
Table 1: Initial particle size distribution of the uranium
particles resulting from the discretization of the
measured size distribution. The initial total
volume fraction of uranium phase is: a ,4~
4.68 x 10
UF4 ClRSs Diameter Volume fraction
# (p~ m) with respect to a ,4~
1 14.13 0.15~' .
2 98.09 I'.
4 459.33 17 I.' .
5 906.36 42.21%
6 1401 29.** 1' .
inside the bed, that sometimes reaches unit at some re
gions. Such a behavior is typical to fluidized bed operat
ing at the correct fluidization velocity. This furthermore
reveals that the hydrodynamic of the bed is reasonably
simulated by the mechanisms accounted for through the
modeling presented above.
As for the chemical reaction between uranium parti
cles and the fluorine, the mass transfer rate of the gas r,
[see equation (4)] presented in figure 4 shows that the
fluorination mainly happens within the lower region of
the reactor, from the inlet as soon as the fluorine is in
jected. This explains the "absence" of the fluorine at the
outlet, in accordance with the figure 4. The uranium hex
afluoride produced from the reaction is transported up
to the smokestacks, where the maximum value of _'s .
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
Figure 1: Sketch and mesh of the pilotplant. (a) Full reactor, (b) main column, (c) top of the reactor showing the
smokestacks for the gas recovery and (d) bottominlet.
ag9 aAl20s OUF4
1.00 0.62 0.08
0.52 015 1, 0.02
Figure 3: Snapshots of the volume fractions of the
phases within the reactor: slices operated at
y 0 m and t = :', . (T is the total time
to completely consume the uranium particles
within the reactor)
corresponding to the injected mole fraction of fluorine,
is furthermore reached. However, we can observe within
two of the gas recovery smokestacks that this maximum
value is not reached. This is due to the fact that these
smokestacks are closed, so that the UF6 trapped there
can not easily be renewed because of the gas flow sig
nificantly affected by the corners in these regions.
The figure 5 presents the alumina phase temperature
distribution at two locations within the bed: z = 0.1 m
(close to the inlet where the reaction occurs) and z =
0.5 m (almost at the top of the bed). The snapshots show
that the temperature is uniformly distributed in both the
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
gs XUFe XF,
7.4 20.0 15.1
5.6 16.2 11.3
3.7 12.4 7 6
1.9 8.7 3 8
0 0 4.9 0 0
Figure 4: Snapshots of the gas mass transfer rate r, (4)
and the mole fractions of the uranium hexaflu
oride (XUFG) and the fluorine (XF2): slices
operated at y = 0 m and t = .s', . (T is the
total time to completely consume the uranium
particles within the reactor)
transversal and the streamwise directions: the bed is
isothermal and the reactor operates as perfect mixer as
expected. That reveals furthermore the reasonable ac
counting for the heat exchange modes within the bed.
The figure 6(a) presents the time evolution of the to
tal mass of the uranium and those of each class inside
the bed. A total time T after the beginning of the con
version, we can observe that all the uranium is consumed
by the fluorine. This consumption appears to be linear
up to roughly I .' r, thus expressing that all the fluorine
injected (or at least almost all) reacts with the uranium
particles within this period (Konan et al. 2009a). In other
words, the leak of fluorine is weak (see figure 7). This
roughly happens after the consumption of about 7i .' of
the initial total mass.
Figure 6(b) shows that the smallestsize particles are the
first to be completely consumed.
The cumulative distributions of the mass of the uranium
particles with respect to the mean diameter of UF4 pa.
ticles are measured (with particle bin size about 1 pm)
during the simulation at different instants and plotted in
figure 8. The exhibited stairs indicate a uniform distri
bution of the diameter per class. This reveals that the
diameters of the reactive particles of each class may be
represented by only one diameter. Then although the
reaction typically occurs at the inlet (see figure 4), the
diameter of the uranium particles per class within the re
actor is quasiuniform. This confirms that the reactor is
perfectly mixed. The time evolution of the cumulative
distributions also unsurprisingly confirm that the total
mass of uranium is increasingly composed of smallsize
particles, as the reaction proceeds. Typically at t = T,
the reactive particles inside the reactor have a diameter
about 98 pm (see figure 8(d)).
Figure 5: Alumina phase temperature distribution (left
hand pictures) and volume fraction (right
hand pictures): snapshots captured within the
bed at z = 0.1 m (top pictures) and z = 0.5 m
(bottom pictures).
Concerning the amount of the fluorine, at the mo
ment the total mass of uranium within the reactor is low
(about . .' with respect to the initial total amount), the
leak becomes increasingly significant (see figure 7). At
the same time, the conversion of uranium hexafluoride
which was maximum (almost I I' 1 starts decreasing up
to the end of the simulation (figure 7). Consistently with
the chemical reaction considered here, the conversion is
then in opposition with the leak of the fluorine, since
one mole of fluorine yields one mole of uranium hex
afluoride.
The temperature of the gas recovered at the
smokestack seamlessly and sensibly increases with re
spect to the preheating temperature of the bed at 4500 C
(see figure 9). At the end of the conversion, the
gas temperature approximatively reaches 5000C. De
spite the exothermic reaction of the fluorine (AH,
234.4 kl7mol ), the reactor warming reasonably
seems controlled by the cooling of the wall at 4000C.
Even though the thermal wall boundary conditions pro
posed in (19)(21) evidence an active control of the tem
perature within the reactor, these models must be scruti
nized enough.
ConclusionS
The full threedimensional simulations of the uranium
hexafluoride conversion within a fluidized bed reactor
has been carried out by using the multiclass method to
account for the reactive particle size distribution and the
471.6 472.0 472.4 472.8 473.2
471.9 472.0 472.1 472.2 472.3
5\
,
cc
0.00 0.15 0.3L 0.48 0.62
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
U.2 U.4 U.6 U.8
Figure 6: Evolution of the uranium mass inside the reactor. (a) Total mass. (b) Total mass per class c: () class #1,
(): class #2, (0): class #3, (0): class #4, (0): class #5 and (a): class #6. merry and my~,, refer
to the initial total mass of the total uranium and per class, respectively.
20
15
600
550
500
400
350
300
0.2 0.4 0.6 0.8
0.2 0.4 0.6 0.8
Figure 7: Evolution of the mole fraction of the gaseous
species at the smokestack: (0) uranium hex
afluoride and (H) fluorine. (T is the total time
to completely consume the uranium particles
within the reactor)
Nfluid Eulerian approach to predict the lwdrodynam
ics coupled with the chemical reaction. The radiative
interparticle heat transfer is modeled on the basis of a
diffusion mechanism and thermal wall boundary condi
tions account for the heat exchange at the wall. External
diffusion of the fluorine within the boundary laver of the
uranium particles is considered. The Eulerian reaction
rate is modeled assuming the shrinking particle model.
NFluid Eulerian Approach allowed to reasonably
simulate the threedimensional hydrodynamics of the
Figure 9: Time evolution of the temperature of the gas
at the smokestack. (T is the total time to com
pletely consume the uranium particles within
the reactor)
bed because of the typical behaviors of the bed exhib
ited by the calculations. The bed and the gas temper
atures appeared to be efficiently controlled around the
preheating bed temperature. Accordingly, the uranium
hexafluoride production regimes and the leak of the flu
orine for this batch reactor are in good agreement with
the measurements.
Future works will focus on the continuous feeding of
the uranium particles within the reactor. This will ne
cessitate strategies or alternative methods able to keep
the same level of the hydrodynamics description on the
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
5UU 1UUU
15UU U
1UUU
15UU
0.4
0.2
500 1000 1500 0 500 1000
Figure 8: Cumulative distribution of the total mass of the uranium particles inside the reactor with respect to the
particle size. (a) at the beginning of the reaction, (b) at t = Ill' r, (c) at t = 7i .' r and (d) at the end of
the simulation [L = T].
bed and which can easily integrate the chemical reac
tions. Further perspectives will be the investigation of
the influence of the small scales (below those resolved in
the current simulations) which might control some pro
cesses within the reactor such as the reaction rate, the
drag of the particles and the heat exchanges.
Acknowledgements
This work was granted access to the HPC resources of
CALMIP under the allocation P0111 (Calcul en Midi
Pyr~ndes).
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