This article was downloaded by: [Stony Brook University]On: 28 October 2014, At: 16:28Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: MortimerHouse, 37-41 Mortimer Street, London W1T 3JH, UK

Journal of Nuclear Science and TechnologyPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/tnst20

Uranium Isotope Exchange between Gaseous UF6

and Solid UF5Yumio YATO aa Power Reactor and Nuclear Fuel Development Corp. , Akasaka, Minato-ku, Tokyo ,107 Phone: +81-3-3586-3311(ext.2652) Fax: +81-3-3586-3311(ext.2652) E-mail:Published online: 15 Mar 2012.

To cite this article: Yumio YATO (1996) Uranium Isotope Exchange between Gaseous UF6 and Solid UF5 , Journal ofNuclear Science and Technology, 33:10, 758-766, DOI: 10.1080/18811248.1996.9732000

To link to this article: http://dx.doi.org/10.1080/18811248.1996.9732000

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”)contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensorsmake no representations or warranties whatsoever as to the accuracy, completeness, or suitabilityfor any purpose of the Content. Any opinions and views expressed in this publication are the opinionsand views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy ofthe Content should not be relied upon and should be independently verified with primary sources ofinformation. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands,costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly orindirectly in connection with, in relation to or arising out of the use of the Content.

This article may be used for research, teaching, and private study purposes. Any substantial orsystematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution inany form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions

Journal of NUCLEAR SCIENCE and TECHNOLOGY, Vol. 33, No. 10, p. 758-766 (October 1996)

Uranium Isotope Exchange between Gaseous UF6 and Solid UF5

Yumio YATO

Power Reactor and Nuclear Fuel Development Cop.*

(Received July 4, 1995)

A new rate equation is derived for uranium isotope exchange reaction between gaseous UF, and solid UF, by assuming the total number of UF, molecules on the particle surfaces to depend on time. The reaction parameters included in the equation are determined from the experimental results, and are compared with the previous ones. The rate equation given in this work satisfies the related isotopic mass balance, and includes explicitly the terms related to the UF, density and the mean size of UF, particles, both of which cause an important effect on the reaction. Since the rate equation derived in this work facilitates the simulation of the reaction under various conditions, the long term behavior of a simulated exchange reaction is studied under the condition considered to be close to that in a recovery zone of the MLIS process.

KEYWORDS: isotopic ezchange, umnium, transfer reactions, umnium 235, umnium 238, umnium hexajluoride, uranium pentajluoride, laser isotope separation, nzte equation, non- linear parameter, least squares fitting, simulation, time dependence

I. INTRODUCTION In the atomic vapor laser isotope separation (AVLIS)

process, the photoselectivity has been reported to be very high but final selectivity is largely influenced by bulk effects such as ion scrambling in a photoionization zone and nonselective pickup onto an In contrast to this, the selectivity in the molecular laser isotope separation (MLIS**) process is not much influ- enced by molecular collision^(^)(^), because the selective infrared irradiation excites mostly the energy states of vibrational and rotational motions of nuclei and causes little effects on the electronic stated,). However, in the MLIS process, it is not in the irradiation zone but in the recovery zone that we should locate the problem of iso- tope scrambling. In this process, a significant amount of depleted uranium hexafluoride (UF6) gas will flow over the enriched uranium pentafluoride (UF5) particles trapped in an appropriate recovery device and the en- riched UF5 produced by selective photo-dissociation may be degraded by the uranium isotope exchange between gaseous UF6 and solid UF5:

235UF5 (s) +238UF6 (g) H 238UF5 (s) +235UF,5 (g). (1) This uranium isotope exchange reaction has been

first observed by Grigor'ev et ~ l . ( ~ ) , who have pointed out that the reaction expressed by Eq.(l) may easily occur through the intermolecular transfer of a fluorine atom

~~~

* Akasaka, Minato-ku, Tokyo 107. Tel. +81-3-3586-3311(ext.2652), Fax. +81-3-3505-5618, Email: yato@pnc.go.jp

**The process is often called RIMLIS instead of MLIS, by PNC and IPCR, after the name of RIKEN.

from a gaseous UF6 molecule to a solid UF5 molecule. They have suggested also that the reaction includes two processes: one is a rather rapid process due to the ex- change reaction on the surface layer of the particles and the other a relatively slow process due to a secondary reaction participated by underlying UF5 molecules ex- posed by successive fluorine transfer reactions, and have discussed a rate equation including these two processes. Several works(*)-(1o) have been done to confirm this in experimental and analytical ways.

In these works(7)-('o) the uranium isotope exchange reaction between UF6 and UF5 has been discussed within a framework that the number of available UF5 molecules on the particle surface that enter into the reaction would remain unchanged. The assumption of constant number of surface UF5 molecules reduces the rate equation into a second order differential equation with constant coef- ficients which has an analytical solution to be used as a conventional tool in analyzing experimental r e~u l t s (~ ) ( '~ ) . However, this treatment has some difficulty in satisfying isotopic mass balance, unless the total number of UF5 molecules is much greater than that of UF6 molecules. Although there has been an empirical approach by Yato et al.(9)("') to meet the isotopic mass balance, it is not enough sufficient on a theoretical basis and thus pro- vides unreasonable results in the estimate of a long term behavior of the reaction as discussed later.

The inconsistency of this assumption that the num- ber of UF5 molecules on the particle surface will remain constant may be understandable when we consider the nature of this reaction as illustrated in Fig. 1. In this figure, the reaction between natural UF6 gas and an en- riched UF5 particle is taken as an example. Natural UF6

758

Dow

nloa

ded

by [

Ston

y B

rook

Uni

vers

ity]

at 1

6:28

28

Oct

ober

201

4

Uranium Isotope Exchange between Gaseous UF, and Solid UF, 759

Fig. 1 Uranium isotope exchange reaction between UF, and UF,: (a) Gaseous UF, molecules collide with UF, molecules on the surface of enriched UF, particles. (b) Some of these collisions lead to the reaction and the isotopic concentration of the gas phase increases by this reaction. (c) The surface of the particle will be gradually replaced by natural UF, molecules. (d) There will be another collisions on the particle surface. (e) The collision leads to the intermolecular transfer of a fluorine atom from UF, to UF,. (f) By this reaction the UF, molecule converted from UF, migrates in the gas phase and exposes the UF, molecule just under it. On the other hand, the UF, molecule converted from UF, deposits on the particle surface. As a consequence, the number of UF, molecules on the particle surface increases gradually.

molecules having certain thermal velocities will collide with the surface of the enriched UF5 particle. Some of these collisions will lead to the reaction and the isotopic mole fraction in the gas phase will increase by this reac- tion. On the other hand, the surface of the particle will be gradually replaced by natural UF5 molecules as shown from (a) to (c) of Fig. 1. There will be further molecular collisions on the particle surface, some of which will lead to the fluorine transfer reaction from UF6 to UF5. The UF5 converted from gaseous UF6 will deposit somewhere on the particle surface. On the other hand, the UF6 con- verted from UF5 will go into the gas phase and this will expose some of the underlying UF5 molecules, that will now have the possibility to enter into further reactions, as shown from (d) to (f) of Fig. 1. As a consequence of successive reactions, the number of UF5 molecules on the particle surfaces will change gradually. However, this effect was not included in the previous works(’)-(’”).

The present work is done to derive and discuss a new rate equation for uranium isotope exchange reaction be- tween UF6 and UF5 which can satisfy the related iso- topic mass balance and include the time dependence in the number of UF5 molecules on the particle surface.

II. DERIVATION OF RATE EQUATION Here we consider a reaction chamber with a vol-

ume V , which contains the total number N’ of UF6 molecules in the gas phase and the total number M, of UF5 molecules in the solid phase. In the initial state, the mole fraction 50 of 235UF6 in gaseous UF6 is assumed to be different from the mole fraction yo of 235UF5 in solid UF5. Minor isotopes such as 234U are neglected and thus the isotopes to be considered here are only 238U and 235U. While there may exist various sizes of UF5 particles in the chamber, the UF5 molecules which en-

ter into the reaction are considered to be those on the surface of the particle and thus we shall consider a pa- rameter M representing the total number of available UF5 molecules on the surfaces of all the UFS particles in the chamber. It is assumed that the gas phase is well stirred and thus immediately becomes isotopically ho- mogeneous. Although there may be a boundary layer of UF6 gas near the surface of UF5 particles as well as UFs molecules adsorbed on the particle surfaces, they were neglected in the present analysis.

1. Rate of Change in Number of 235UFg

For the exchange reaction to occur it is obvious that gaseous UF6 molecules with the thermal velocity v must collide with UF5 molecules on the solid surface. From the kinetic-molecular theory, the number of such colli- sions made in one second on a unit area, 2, is given

Molecules in Gas Phase

by(11)

(2) 1 4

2 = -E(N’/V).

Since the total surface area of the solid UF5 in the cham- ber can be expressed by MS2, the total number of col- lisions made in the chamber in one second, Z,, is given bY

(3) 1 4

2, = MS2Z = -MPV(N’ /V) ,

where 6 is the intermolecular distance of solid UF5. If some portion, wZ,, of these collisions are effective in leading to the reaction, the rate of change in the number of 235UF6 molecules in the gas phase can be expressed by

VOL. 33, NO. 10, OCTOBER 1996

Dow

nloa

ded

by [

Ston

y B

rook

Uni

vers

ity]

at 1

6:28

28

Oct

ober

201

4

760 Y. YATO

= ( I c O /MO) (NLM5 - NLM8) (4)

where w is the reaction probability and the subscripts 5 and 8 refer to 235U and 238U, respectively. In Eq.(4), the first term represents the intermolecular transfer of fluorine atoms from gaseous 238UF6 molecules to solid 235UF5 molecules, the second term the fluorine transfer from 235UF6 to 238UF5 molecules, and Ico, the constant for reaction rate at t=O, is defined in terms of Mo, the initial number of UF5 molecules on the particle surfaces, bY

Moli2V 4v

Ico = ~ W . ( 5 )

The derivation from Eq.(2) to Eq.(4) is quite similar to that of the previous analysis, where M5 and M8 were considered to depend on time but their sum, which must be equivalent to M , was assumed to be con~tant(~)-( l~) . It should be noted, however, that not only M5 and M8 but their sum, M:,+Ms=M, are considered to depend on time in the present analysis.

2. Rate of Change in Number of 235UF5

The successive fluorine transfer will result in a newly exposed surface of UF5 particles and thus some portion of the underlying UF5 molecules will participate in the reaction. Taking this effect into account, the rate of change in the number of 235UF5 molecules on the parti- cle surfaces is considered to be expressed by

Molecules on Particle Surfaces

(6) -=(%) dM5 +(%) ,

surface secondary dt

where (dM5/dt)sUrfac, is the contribution from the pri- mary surface reaction and (dM5/dt)secondary the contri- bution from the exposure of underlying UF5 molecules resulting from the increase of M by successive reactions. The first term in Eq.(6) can be formulated in a way sim- ilar to that for the gas phase and is given by

Prior to going to the derivation of the second term in Eq.(6), we will first consider the change in M with respect to time. As already stated above, the total num- ber of fluorine transfer reactions on the particle surfaces amounts to wZ, in every second. If we define a as the probability with which such reactions cause the increase in M and we assume the rate of change in M to decrease in proportion to (M,-M)/M, with the progress of the reaction, then the rate of this change can be expressed by

-- dM M s - M d t

N V = ako ( M,) (M, - M ) ,

where N is the number density of UF6 in the gas phase. When we assume a to be constant and thus indepen- dent of M , the integration of Eq.(8) yields the following expression:

M = M, - (M, - Mo) exp -aka - { (Z)t}. (9)

Equation (9) means that the total number of UF:, molecules on the particle surfaces changes exponentially from its initial value MO to the equilibrium value M,, the total number of UF5 molecules in the chamber.

The increase in M will lead to the exposure of under- lying UF5 molecules. It may be worth to mention that in this sense the present definition of a is equivalent to that in the pioneer work of Grigor'ev et u Z . ( ~ ) , where it is defined as the efficiency of the secondary process. If we assume that the underlying UF5 emerges with the ini- tial isotopic mole fraction yo, the contribution from this exposure to the rate of change in the number of 235UF5 molecules on the surface can be given by

f dMs 1 /dM\ = (dt)yo ( I secondary

N V = d o (%) (M, - M)Yo. (10)

From Eqs.(7) and ( l o ) , we have the following equation for the rate of change in the number of 235UF5 molecules on the particle surfaces:

3. Rate Equation in Terms of Isotopic Mole Fractions and Related Isotopic Mass Balance

To obtain the rate equation expressed in terms of isotopic mole fractions, we shall use the relationships Nl=xNV, N;=(l-x)NV, M5=yM and M8=(1-y)M in Eqs.(4) and (11). Noting that dM:,=Mdy+ydM, we now have the following rate equation:

dx dt Mo

d t

- = Ico ("> ( y - x )

_ -

+a (g) (Msi " ) (YO - Y ) } , (13)

where ~t: is the mole fraction of 235UF6 in the gas phase and y the mole fraction of 235UF5 on the particle surfaces

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

Dow

nloa

ded

by [

Ston

y B

rook

Uni

vers

ity]

at 1

6:28

28

Oct

ober

201

4

Uranium Isotope Exchange between Gaseous UF, and Solid UF, 761

averaged over all the particles in the chamber. We must mention that all the coefficients included in Eqs.(lZ) and (13) depend on time, because they include the time- dependent parameter M .

In an extreme limit M,>>NV, Eq.(9) gives M=Mo. When one more condition M,>>Mo is assumed, Eqs.(lZ) and (13) are reduced into the following expressions:

dx d t - = ko(Y - x )

(15)

which are equivalent to the ones derived by Grigor’ev et u Z . ( ~ ) This indicates that the previous rate equation is applicable under the conditions of an infinite amount of solid UF5(MS>>NV) and extemely large-sized UF5 par- ticles (M,>>Mo).

From Eq.(9) we can obtain the relationship 1

which is important to show that the rate equation de- rived here satisfies the related mass balance. Since there exists Mo of UF5 molecules on the initial particle sur- faces, the total number IU(t) of UF5 molecules to be exposed during the reaction time from 0 to t must be M(t)-Mo. This can be easily shown by the integration of Eq.(8) with the use of Eq.(16):

= ako(NV/M,) [Ms - M(t)]d t I” = M ( t ) - Mo.

Similarly, the total number I235 ( t ) of 235UF5 molecules to be exposed in the same duration must be [M(t)-Mo]yo and it can be easily confirmed by the in- tegration of Eq.(lO) as follows:

t

= ako(NV/M,)yo 1 [Ms - M(t)ldt 0

= [ M ( t ) - MO]YO. In the equilibrium state, these mass balance equa- tions are naturally reduced to I~(oo)=M,-Mo and 1235 (oo)=( M, -Mo)yo, respectively.

m. ANALYTICAL RESULTS AND DISCUSSION

1. Determination of Parameters

To determine the reaction parameters characterizing the exchange reaction, we shall use the experimental re- sults obtained by Yato et ~ l . ( ~ ) , which are summarized in Table 1 along with the experimental conditions neces- sary to the present analysis. As is obvious from Table 1, the 235UF6 concentration in the gas phase shows a rapid increase in the first several minutes, followed by a subse- quent gradual increase. This experimentally observed trend is quite similar to those observed by Grigor’ev et al.“) and thus suggests such a two-process reaction as discussed in the preceding sections. The experiment was made in a reaction chamber with a stirrer and the gas phase was considered to become isotopically homo- geneous during the sampling interval greater than 0.1 h. However, both of a boundary layer of UF6 near the pax- tide surface and a layer of adsorbed UF6 are neglected in the present analysis, and thus the reaction parameters determined here may include these effects.

Since the values of V, N , M, and yo are given from the experimental condition, the constants unknown in Eqs.(l2) and (13) are the reaction parameters ko, a and Mo. These parameters can be determined from the ob- served values of ~ ( t ) by an algorithm as described by Marquardt(13) for least-squares determination of non- linear parameters. To take account of the influence by intermittent samplings for the measurements of x ( t ) , the

Characterizing the Exchange Reaction

Table 1 Experimental conditions and resultst1 along with analytical results

t 1 0 - l 7 ~ ( t ) ~ O - ~ O M ~ y ( t ) z ( t ) ~ ( t ) X ( t ) c a l t Z At3 0.0 2.98 1.69 0.03268 0.03268 0.007194 0.007194 0.000000 0.1 2.89 - - - 0.007326 0.007328 -0.000002

0.2 2.86 - 0.007366 0.007361 0.000005 0.5 2.82 - 0.007373 0.007377 -0.000004 1.0 2.79 - - - 0.007393 0.007392 0.000001

3.0 2.76 - 0.007449 0.007449 0.000000

- -

- -

- -

t* Ref.(9) by Yato et al.: Solid UF, was prepared from slightly enriched UF, by photolysis with a XeCl laser. Reaction experiment was done between 93 m g of enriched UF5 and natural UF, under pressure of 8.05 Torr in a chamber with a stirrer whose volume was 1 . 6 0 ~ 1 0 ~ cm3. Note that t is in hour, N in molecules/cm3, M , in molecules and 5, y and z in mole fraction.

t z Values calculated by using best fitted parameters. t3 A=z(t) - z(t)cai.

VOL. 33, NO. 10, OCTOBER 1996

Dow

nloa

ded

by [

Ston

y B

rook

Uni

vers

ity]

at 1

6:28

28

Oct

ober

201

4

762 Y. YATO

id

t * I 0.0076

(b)

i

I 1

Table 2 Parameters characterizing uranium isotope exchange between gaseous UF, and solid UF,, and comparison with parameters determined by pre- vious works

Previous works (a)t' (b) t2

Description This work

Parameterst3 ko 0.111 0.111 0.01 - 0.40 a 0.0134 0.0104 0.6 - 0.8

3.10 3.15 -

Derived Parameterst3 1ogWt4 0.968 0.947 l . l f 0 . 3 1 0 - ~ n 3.50 3.33 -

d 0.0230 0.0225 - -

t1 Ref.(lO) by Yato et al. t z Ref.(7) by Grigor'ev et al. t3 ICo is in h-', Mo in molecules, u in collision-', ?i

t 4 Derived by assuming 6=7A and T=300K. in molecules/particle, and 2 in pm.

The present analysis provides not only z ( t ) but also the change in the mole fraction of 235UF5 on the particle surfaces y(t). As shown in Fig. 2(b), the surface layer of solid UF5 reaches rapidly its equilibrium mole frac- tion with the gas phase. However, what matters in the MLIS process is the change in the isotopic mole fraction of solid UF5 as a whole. This can be evaluated from

4 t ) = {M(t)Y(t) + [Ms - M(t)lYO)/MS (18) and the result is shown also in Fig. 2(b). The depletion of isotopic mole fraction averaged over the whole solid UF5 is very slow and small because of a small reaction probability of underlying UF5 molecules.

i

'1

1 2 3 4 0.00700 LA- 1 2 3 I- 4 O O t,

t(h) t (h)

Fig. 2 Observed and calculated isotopic mole fractions in gaseous UF, and solid UF,: The solid lines are produced by the numerical way to take into account of the influence of gas sam- plings with the parameters ko=O.l l l h-', a=0.0134 and M0=3.10x1019 molecules. (a) Mole fraction of 235UF6 in gas phase. The lines with different a values are produced by assuming the same ko and Mo as the best fitted line. (b) Mole fraction of 235UF5 on the particle surface and in the whole solid.

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

Dow

nloa

ded

by [

Ston

y B

rook

Uni

vers

ity]

at 1

6:28

28

Oct

ober

201

4

Uranium Isotope Exchange between Gaseous UF, and Solid UF, 763

are compared with those given by the previous works in Table 2. Since the parameters by Yato et uZ.('O) are based on the same experimental data, the comparison will clarify the difference of both rate equations. As is obvious from Table 2, the parameters derived from both equations are very similar to each other. However, the experimental result studied here was obtained under the condition NV/Ms=26.5, where the time dependence of M can not be ignored as discussed above. And there is a distinctive difference, as discussed later, in the long term reaction behaviors predicted from both rate equa- tions even if the same parameters are given. This will be obvious when we consider that the constant parameters ko and a of the previous rate equation are replaced by ko(M/Mo) and u(Mo/Ms)(Ms-M)/Ms, respectively, in the present equation.

The parameter appropriate to make a comparison among experiments made under different conditions is the reaction probability w which can be obtained by

(19)

As shown in Table 2, the value w determined from the present analysis is 0.968xlO-' collision-' and is fairly in good agreement with (l.lf0.3) x lo-' collision-l ob- tained by Grigor'ev et ~ 1 . ( ~ ) in spite that the different expressions are taken for the rate equation.

These fairly good agreements are mainly due to the unique facet that ko and Mo, and hence w, can be deter- mined virtually by the initial rapid increase and the sub- sequent saturation of ~ ( t ) which are primarily ascribed to the initial surface reaction as pointed out above.

However, the a value determined in the present anal- ysis is 0.0134 and is much smaller than those obtained by Grigor'ev et al., who have reported a=0.6 to 0.8. Since they prepared the solid UF5 from UF6 by using a mer- cury lamp, this disagreement is considered to be proba- bly due to the difference in the surface conditions of UF5 particles or the particle sizes. Furthermore, there may be

the possibility that the difference comes from the effect neglected in the present study such as a boundary layer of the gas around the particles. Further experimental works are necessary to eliminate these ambiguities.

3. Long Term Behavior of Simulated

Shown in Fig. 3 are the long term behaviors of the uranium isotope exchange reaction calculated from the previous rate equations. In these calculations, the same reaction conditions and parameters as studied in the present analysis are assumed. As seen from Fig. 3(a), under the condition studied here, NV/Ms=25.6, the rate equation by Grigor'ev et u Z . ( ~ ) is not consistent with the isotopic mass balance, and all three isotopic mole frac- tions, x, y and z , increase until they reach yo=0.03268, the initial isotopic mole fraction of solid UF5. This in- consistency is due to their assumption of M,>>NV and M,>>Mo, which are equivalent to the assumption of an infinite amount of solid UFF, and large-sized particles, re- spectively. Yato et al.(*') proposed a method to modify this. However, it is only at both limits, t=O and t=m, that their empirical method satisfies the isotopic mass balance as shown in Fig. 3(b). As shown in Fig. 4, the result calculated by the rate equation proposed in this work seems very reasonable. Both of the mole fractions in the gas phase and on the particle surfaces, 3: and y, almost overlap each other in the time scale of this figure, because they reach rapidly their equilibrium mole frac- tion as shown in Fig. 2(b). The calculation also shows that the average mole fraction of the whole solid UF5, z, decreases gradually and it is around 140 h that these three become very close to their equilibrium mole frac- tion: 0.8124 mol%. It may be worth to mention that this consistency with the mass balance is due to such a the- oretical basis of the rate equation proposed in this work as described in Sec.11-3.

One more distinctive feature to be mentioned is that it includes explicitly the terms related to the UF6 den-

Exchange Reactions

t I I I / l

1000 2000 3000 4000 5000 1000 2000 3000 4000 5000 0 ' 0

t (h) t (h)

Fig. 3 Long-term behavior of exchange reaction simulated by the previous methods: The reaction conditions and parameters are the same as those of Fig. 2. (a) Based on the rate equation by Grigor'ev et a1.(7) (b) Based on the method by Yato et al.(")

VOL. 33, NO. 10, OCTOBER 1996

Dow

nloa

ded

by [

Ston

y B

rook

Uni

vers

ity]

at 1

6:28

28

Oct

ober

201

4

764

.. yo, Zo -

Y. YATO

'X, Y

0.04 1

Fig. 4 Simulated exchange reaction between high den- sity UF, gas and fine UF, particles: The re- action conditions and parameters are the - same as those of Fig. 2. ( N = 2 . 8 ~ 1 0 ~ ~ c r n - ~ , d=0.023 Pm)

sity and the mean size of UF5 particles, both of which are considered to cause the most dominated effects on the reaction. This can be easily understood from the second term of Eq.(13):

It is not fully confirmed yet whether the parameter a is constant for a long time or is independent of particle sizes. However, it may be of interest to study a long term behavior of the reaction under various conditions even with the assumption of constant a, because there has been no way to study this by the previous rate equations that assume an infinite amount of solid UF5(Ms>>NV) and extremely large-sized UF5 particles (MS>>Mo).

The reaction conditions which must be given in such simulation studies are 20, yo N, V, Ms and the mean diameter d of UF5 particles. In the present analysis, a is assumed to be constant and it is considered to be obvious from its definition that w may depend on tem- perature but is independent of these reaction conditions. The remaining parameters ko and Mo can be estimated by using Eqs.(5) and (17), respectively. In the follow- ing simulation studies, the values of xo, yo, N, V, M,, d, w and a are the same as those given in Table 1 and determined in this work, unless specified.

The calculation of Fig. 4 is made under the condition of high UF6 density, N=2.8x 1017 cmP3, far beyond the one assumed in the MLIS process. Its maximum number density has been reported to be less than 1015 cmP3 as a target possible to obtain the required ~e lec t iv i ty(~) (~) , or to be 5-6x 1014 cmP3 to avoid condensation at low tem- perature in an expansion nozz1e(14). Figure 5 is the re- sult calculated under N=5.3x 1014 cmP3 with other con- ditions unchanged. Under low UF6 density, the surface

-

0.04

, z

g c e 0.0211:, al - = 0.01 F

t I I

40 80 120 160 200

f (h)

Fig. 5 Simulated exchange reaction between low density UF, gas 2 n d fine UF, particles (N=5.3x1014 cmP3, d=0.023pm)

reaction becomes slow mainly because of the decrease of UF6 bombardment on the solid surface, and the time required for its equilibrium is about 40 h. Furthermore, the depletion in the isotopic mole fraction of the whole solid UF5 is quite slow and small, and the reaction time of 200 h seems to be still far from the equilibrium even for such submicron particles, d=0.023 pm, of UF5 as as- sumed in the calculation.

The solid UF5 produced by photoselective dissocia- tion is considered to become large-sized particles in a relatively short time by collisions in a recovery device. Figure 6 is the result calculated by assuming a to be constant and the mean diameter of UF5 particles to be 1 pm, far smaller than those observed(14)(15) in the MLIS process. The isotopic mole fraction on the particle sur- face is rapidly equilibrated with that of the gas phase be- cause of the high UF6 density assumed, while the deple- tion in the concentration of the whole solid UF5 is slow due to the small number of surface molecules compared to the total number in the large-sized UF5 particles. Shown in Fig. 7 is the result calculated by assuming the condition of N=5.3x101* cmP3, d=l pm and z0=0.0025,

$ e 0.021 - d[ 0.01

40 80 120 160 200 0

0

t (h)

Fig. 6 Simulated exchange reaction between high den- sity UF, gas and large-sized UF, particles (N=2.8x1017 ~ m - ~ , d=l pm)

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

Dow

nloa

ded

by [

Ston

y B

rook

Uni

vers

ity]

at 1

6:28

28

Oct

ober

201

4

Uranium Isotope Exchange between Gaseous UF, and Solid UF, 765

~ s *' 0.03 0*04*

J 40 80 120 160 200

Fig. 7 Simulated exchange reaction between UF, and UF, under the condition close to that of the recovery - zone of MLIS process (N=5.3x1Ol4 cmP3, d=l pm, z0=0.0025, y0=0.03268)

f (h)

somewhat close to that in a recovery zone of the MLIS process. In this condition the depletion of 235UF5 con- centration averaged over the whole UF5 particles is not significant even after 200h of the exchange reac- tion, because the depletion is virtually limited to the particle surface. If Eq.(9) is rewritten in the form of M=M, - (Ms -Mo)exp( -at*), the non-dimensional time t* can be expressed by t *=(vwa~ ,S3 /4 ) (N/d ) t . Since this gives t*=12 for t=4 h under the experimental condi- tion given in Table 1, it can be said that the assumption of constant a is a good approximation under the condi- tion t*<12 as shown in Fig. 2. The values oft* are 1.1, 13 and 0.03 at t = 200 h in Figs. 4, 5 and 6, respec- tively. However, this does not eliminate the ambiguity of the dependence of a on the particle size.

w. CONCLUSION Based mainly on the molecular-kinetic theory, a new

rate equation for the uranium isotope exchange reac- tion between gaseous UF6 and solid UF5 is derived by considering the total number M of UF5 molecules on the particle surfaces to increase with the reaction time. The previous rate equation based on the assumption of constant M is shown to be the one derived from this new rate equation under the condition of an in- finite amount of solid UF5 and extremely large-sized UF5 particles. From the analysis made on the exper- imental data of this exchange reaction, a comparison is made among the reaction parameters determined by the newly proposed equation as well as by the previ- ous ones. The previous methods fail to satisfy the re- lated isotopic mass balance in the study of a long term reaction behavior and their application should be lim- ited to the study of the exchange reaction within a short period of time from the initial state. The rate equa- tion given in this work meets this mass balance and furthermore includes explicitly the terms related to the UF6 density and the mean size of UF5 particles, both

of which are considered to cause the most dominant effects on the reaction. This feature facilitates the simu- lation studies on this reaction under various conditions. While there is still some ambiguity in the dependence of the parameter a on the particle size as well as on the reaction time, a long term behavior of the exchange reaction is simulated under the condition somewhat close to that in a recovery zone of the MLIS process. The result indicates that the depletion of 235UF5 concentra- tion averaged over the whole UF5 particles is not signif- icant even after 200 h of the exchange reaction.

[NOMENCLATURE]

a : Probability of exchange reactions leading to increase of

d : Mean diameter of initial UF, particles (cm) ko: Constant for U-isotope exchange reaction rate at t=O

n : Mean size of initial UF, particles (molecules) v: Thermal velocity of gaseous UF, molecules (cm/s) t : Reaction time ( s ) t': Non-dimensional time defined by t*=(C~a4~6~/4)(N/2)t

z(t): Mole fraction of 235UF, in gas phase y(t): Mole fraction of 235UF, in surface layer of UF, particles .z(t): Mole fraction of 235UF5 averaged over whole solid UF,

M -

(s-l) - -

zo: Value of z ( t ) at t=O yo: Value of y(t) at t=O 6: Intermolecular distance in solid UF, (cm) w : Probability of intermolecular collisions leading to

M : Total number of UF, molecules on all the particle

Mo: Number of UF, molecules on initial particle surfaces

M,: Total number of UF, molecules in reaction chamber

M5: Number of 235UF, molecules on particle surfaces

M8: Number of 238UF, molecules on particle surfaces

N ' : Number of UF, molecules in gas phase (molecules) Ni : Number of 235UF6 molecules in gas phase (molecules) NL: Number of 238UF6 molecules in gas phase (molecules) N : Number density of UF, in gas phase (molecules/cm3)

N5: Number density of 235UF6 in gas phase (molecules/cm3) N8 : Number density of 238UF, in gas phase (molecules/cm3) V : Volume of reaction chamber (cm3) Z : Number of molecules striking unit surface of wall in unit

Z, : Total number of collisions on all the particle surfaces in

exchange reaction (collision-')

surfaces (molecules)

(molecules)

(molecules)

(molecules)

(molecules)

time (collisions/s~cm3)

one second (collisions/s)

ACKNOWLEDGMENT

The encouragement and support by Mr. H. Nakano and Mr. N. Sasao of Power Reactor and Nuclear Fuel De- velopment Corp. was vital to the completion of the work.

VOL. 33, NO. 10, OCTOBER 1996

Dow

nloa

ded

by [

Ston

y B

rook

Uni

vers

ity]

at 1

6:28

28

Oct

ober

201

4

766 Y. YATO

The authors wish t o thank Prof. Y. Fujii, Tokyo Insti- tute of Technology, for his suggestions and comments.

( 9 ) (10)

-REFERENCES- (11)

(12) Rapp, D., Francis, W.E.: J. Chem. Phys., 37, 2631 (1962). Solarz, R.W.: UCID-20343, (1985). Arisawa, T.: Proc. Int. Symp. on Isotope Separation and Chemical Exchange Uranium Enrichment, Tokyo, p.147 (1990). Meyer-Kretschmer, G., Schweizer, G.: ibid. p.123. Schweizer, G.: Proc. 2nd Workshop on Separation Phenomenon in Liquids and Gases, Versailles, France, p.653 (1989). Born, M., Oppenheimer, J.R.: Ann. Phys., 84, 457

Grigor’ev, G.Y., et al.: Sov. J. Chem. Phys., 3[10], 2275 (1986). Onoe, J., et al.: J. Nucl. Sci. Technol. 28[8], 777

(13) (14)

(15)

(1927). (16)

(1991).

Yato, Y., Funasaka, H.: ibid. , 29[3], 296 (1992). Yato, Y., Suto, O., Funasaka, H.: ibid., 32[5], 430 (1995). See, for example, Moelwyn-Hughes, E.A.: “Physical Chemistry”, Pergamon Press, Oxford, p.45 (1961). Onoe, J., et al.: Laser Sci. Res., IPCR, No.12, p.79

Marquardt, D.W.: J. SIAM, 11, 431 (1963). Yato, Y., Shimasaki, Y., Sasao, N.: Proc. Symp. and Panel Discussion on Forwarding to New Advancement of Fuel Cycle, At. Energy SOC. Jpn., p.77 (1991), [in Japanese]. Shimasaki, Y., et al.: Nihon-Genshiryoku-Gakkai Shi ( J . At . Energy SOC. Jpn.), 35[4], 280 (1993), [in Japanese]. See, for example, Perry, J.H.: “Chemical Engineer’s Handbook”, (4th ed.), Chap.8, p.6, McGraw-Hill, New York,(1963).

(1990).

JOURNALOFNUCLEARSCIENCEANDTECHNOLOGY

Dow

nloa

ded

by [

Ston

y B

rook

Uni

vers

ity]

at 1

6:28

28

Oct

ober

201

4