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Crystal Growth Kinetics of the Uranium Peroxide
Available online at www.sciencedirect.com
Procedia Chemistry 7 (2012) 725 – 730
ATALANTE 2012 International Conference on Nuclear Chemistry for Sustainable Fuel Cycles
Crystal growth kinetics of the uranium peroxide Séverine Planteura*, M. Bertranda, E. Plasarib, B. Courtaudc, J.P. Gaillarda a
CEA, DEN, RadioChemistry & Processes Department, B.P. 17171,30207 Bagnols-sur-Cèze, France b Laboratoire Réactions et Génie des Procédés-ENSIC, 54100 Nancy, France c Areva Mines/SEPA ,87250 Bessines-sur-gartempe, France
Abstract The uranium peroxide precipitation is involved in the processing of uranium ores [1]. In order to determine the crystal growth kinetic parameters, an experimental study is performed in a stirred batch reactor over a wide range of experimental conditions. The experimental method adapted to the uranium peroxide crystal growth study consists in the following of hydrogen ion. This article gives the results obtained for the uranium peroxide crystal growth kinetic law. The treatment of the experimental data shows that the crystal growth rate corresponds to a birth and spread mechanism. 2012Elsevier The Authors. Publishedand/or by Elsevier B.V. under responsibility of the Chairman of the ATALANTE 2012 ©©2012 B.V...Selection peer-review SelectionCommittee and/or peer-review under responsibility of the Chairman of the ATALANTE 2012 Program Program Keywords: Uranium peroxide, precipitation, crystal growth
1. Introduction In the processing of uranium ores, the uranium is recovered from mill leach solutions by precipitation as yellow cake concentrates. Among the different existing processes, the continuous precipitation with hydrogen peroxide in fluidized bed leads to a high-quality solid particles [2]. The uranium peroxide precipitation is performed by mixing hydrogen peroxide and uranyl sulfate solutions according to the following reaction: HO (1) UO2 SO4 H 2O2 o UO4 .4 H 2O H 2 SO4 2
The objective of this article is to study the crystal growth kinetics of the uranium peroxide. Different methods are described in the literature for the determination of crystal growth rate [3]. Among them, the method developed by Bertrand-Andrieu et al. [4] for the uranium oxalate U(C2O4)2.6H2O presents the advantage to be
1876-6196 © 2012 Elsevier B.V...Selection and/or peer-review under responsibility of the Chairman of the ATALANTE 2012 Program Committee doi:10.1016/j.proche.2012.10.110
726
Séverine Planteur et al. / Procedia Chemistry 7 (2012) 725 – 730
experimentally flexible. This method is based on a high seed charge and the spectrophotometric measurement of the decrease of the uranium ion [U4+] concentration in solution. Experiments are performed in a stirred batch reactor. From the recorded data it is possible to determine the crystal growth mechanism and the kinetic constants as will be shown below. We have adapted this method to the uranium peroxide in order to determine the kinetic constants by recording the increase of hydrogen ion concentration [H+] versus time (see equation 1).
Nomenclature
Mc ns S t texp tcalc Vs Vl Į ȕ
-1
crystal molar mass (kg.mol-1) solid particle quantity (mol) supersaturation ratio time(s) experimental time (s) calculated time (s) solid volume (m3) volume of solution (m3) crystal growth kinetic parameter (m.s-1) crystal growth kinetic parameter volume shape factor
a activity (mol.L ) solid concentration (mol.L-1) Cs g(L) mass particle size distribution (m-1) g kinetic order of growth G(t) linear crystal growth rate (m.s-1) I integral kg growth rate constant (m.s-1) Ka constant dissociation of hydrogen peroxide (mol².L-2) Iv Ks solubility product (mol².L-2) L particle size (m-1) crystal density (kg.m-3) Uc mk k order moment of the population density \ ( L, t ) number particle size distribution (m-4) distribution (mk-3) 2. Theoretical background 2.1. Determination of the crystal growth rate relation
In a stirred batch reactor, without nucleation, breakage and agglomeration, for a growth rate independent of the crystal size, the population balance is as follows: w\ ( L, t ) w\ ( L, t ) (2) G (t ) 0 wt
wL
The k-order moment of the population density is defined by : f
mk (t )
³ L \ ( L, t )dL k
(3)
0
Multiplying each term of the population balance by Lk, and after integration: dmk (t ) kG (t )mk 1 (t ) d (t ) The solid phase concentration is related to the size distribution by the following balance: Iv U c 3 Iv U c C s (t ) ³ L \ ( L, t )dL M m3 (t ) Mc c Derivating equation (5) and using equation (4), it comes:
(4)
(5)
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Séverine Planteur et al. / Procedia Chemistry 7 (2012) 725 – 730
dC s (t ) dt
3
Iv U c Mc
(6)
G (t )m2 (t )
dC s (t ) d [U ] 1 d [ H ] dt dt 2 dt so the hydrogen concentration and the crystal growth rate are linked by the following equation:
The molar balances give:
d[ H ] dt
6
(7)
Vs I v U c m2 (t )G (t ) VL M c
(8)
A seed charge is introduced into the liquid phase so that the total mass precipitating is less than 5% of the initial mass. Under these conditions, the total crystal surface area varies so a little that the second order moment can be considered constant during the experiments: (9) m2(t)§m2(0). Thus equation (8) becomes: d[H ] dt
6
Vs I v U c m 2 (0)G (t ) VL M c
(10)
The population density \ ( L, t ) is calculated from the volume size distribution g(L,t) : \ ( L, t )
C s (t ) M c g ( L, t ) Iv U c L3
(11)
and the second order moment can be written as: m2 (t )
f
2
³ L \ ( L, t )dL
C s (t ) M c
Iv U c
0
with : I (t )
f
I0
³ 0
(12)
I (t )
g ( L,0) dL L
The m2(t=0) substitution in the equation (10), leads to the final expression linking the hydrogen concentration evolution and the crystal growth rate : d[H ] dt
6
ns0 I 0 G (t ) VL
(13)
with ns0= VsCs0 : the crystal charge quantity initially introduced. To solve the system and obtain the kinetic law, it is necessary to replace G(t) by its expression as a function of supersaturation which depends on the growth mechanism. 2.2. Uranium peroxide crystal growth rate It has been experimentally observed for the uranium peroxide system that the crystal growth rate does not depend on the impeller speed. Therefore, the crystal growth is surface integration controlled and the global rate of crystal growth is related to the supersaturation ratio by an expression depending on the growth mechanism [3]: x
for the birth and spread mechanism: G S D 1 S 1 5 6 exp§¨ E 1 ·¸
(12)
x
for the screw dislocation mechanism: G S D 2 S 1 2 tanh§¨ E 2 ·¸
(13)
© S 1¹ © S 1¹
where the supersaturation ratio S=S(t) is calculated by the formula:
728
Séverine Planteur et al. / Procedia Chemistry 7 (2012) 725 – 730 aUO K a >H 2 O2 @ 2 2
S
where: aUO
2 2
>
10 2 pH Ks
@
(14)
J UO UO22 . The uranyl concentration is determined as a function of hydrogen ion 2 2
concentration, (see equation 1), so S=S([H+]). The activity coefficients are taken into account in the solubility model and are calculated with the Specific Interaction Theory (SIT) [5]. As it is seen by formula (14), the supersaturation ratio can be expressed only as a function of hydrogen ion concentration leading to the following equation: d[H ] G(S )
6
ns0 I 0 dt VL
(15)
By integrating this equation, we can obtain: t
VL 6n s 0 I 0
[H ]
³
[ H ]0
d[H ] G(S )
(16)
and the crystal growth parameters can be determined by a nonlinear regression method minimizing the function: F D , E
¦ t exp,i t calc,i 2
(17)
i 1,n
3. Experimental The uranyl sulphate solution is prepared by dissolution of pure uranium trioxide in a sulphuric acid solution heated at about 80°C. The uranium peroxide is precipitated at room temperature by mixing a uranyl sulphate solution with a 30% hydrogen peroxide solution. The experimental set-up (Fig. 1b) consists of a glass baffled batch reactor equipped with a marine propeller. The precipitation is initiated by the rapid injection of a controlled volume of hydrogen peroxide to a uranium sulphate solution charged with a known amount of uranium peroxide crystals. To follow the crystal growth, a pH electrode and a homemade program record pH value as a function of time. In these experiments we used the FU 20 Yokogawa pH-meter with accuracy to within 0.001 pH value. The pH decrease during a crystal growth test is not higher than 0.1 unity pH, so for each experiment the pH can be considered constant. Particle size measurements (Fig. 1a), before and after experimental runs, confirm that there are effectively no agglomeration, no breakage and no nucleation. The recorded pH values are used in the formula (16) to calculate time by integration. The calculated time and experimental time values are used in the equation (17) in order to obtain Į and ȕ best values. (a)
(b)
Grnnulometric graphs before and after the growth test
6
Volume distribution %vol
5 4 3 2 1 0 0,1
1
10
100
1000
particules size (µm)
Fig. 1. (a) Particle size distribution before and after growth test; (b) crystal growth set-up
729
Séverine Planteur et al. / Procedia Chemistry 7 (2012) 725 – 730
4. Results and discussion To determine the crystal growth mechanism, the kinetic parameters are optimized for each mechanism by evaluation of the crystal growth test time. The Figures (1, 2, 3) compare the calculated time using the kinetic parameters optimized and the experimental time for different experimental conditions. The experiments are carried out with pH equal to 2.5 and 3 and with sulphate concentration included between 0.001 and 0.1 mol.L-1. (a)
(b)
Birth and spread [SO4]=0,001 pH=3
100
100,0
80 t_calc
80,0 t_calc
Screw dislocation [SO4]=0,001 pH=3
120
120,0
60,0
60
40,0
40
20,0
20
0,0 0
20
40
60
80
100
0
120
0
t_exp
20
40
60
80
100
120
t_exp
Fig. 2. comparison between calculated and experimental time values (pH=3, [SO42-]=10-3mol.L-1 and S from 60 to 14): (a) birth and spread mechanism; (b) screw dislocation mechanism (a)
(b)
Birth and spread [SO4]=0,001 pH=2,5
Screw dislocation [SO4]=0,001mol/L pH=2,5
35,0
35,0 30,0
30,0 25,0
25,0 t_calc
t_calc
20,0 15,0
20,0 15,0 10,0
10,0
5,0
5,0 0,0
0,0
0
5
10
15
20
25
30
35
0
5
10
15
t_exp
20
25
30
35
t_exp
Fig. 3. comparison between calculated time and experimental time (pH=2.5, [SO42-]=10-3mol.L-1 and S from 18 to 10): (a) birth and spread mechanism; (b) screw dislocation mechanism (a)
(b)
Birth and spread pH=3 SO4=0,1mol/L
90,0
90,0
80,0
80,0
70,0
70,0
60,0
60,0
50,0
50,0
t_calc
t_calc
Screw dislocation pH=3 SO4=0,1mol/L
40,0
40,0 30,0
30,0
20,0
20,0
10,0
10,0
0,0
0,0 0
10
20
30
40
50 t_exp
60
70
80
90
0
10
20
30
40
50
60
70
80
t_exp
Fig. 4. comparison between calculated time and experimental time (pH=3, [SO42-]=0.1mol.L-1 and S from 44 to 5): (a) birth and spread mechanism; (b) screw dislocation mechanism
90
730
Séverine Planteur et al. / Procedia Chemistry 7 (2012) 725 – 730 Table 1. Kinetic parameters and correlation index calculated for each experiment (room temperature) Birth and spread mechanism
Screw dislocation mechanism
ȕ1
Į2 (m.s-1)
ȕ2
[SO4 ]=0.001, pH=3
4.8.10
-10
54.7
3.9.10-6
4.9.10-6
[SO42-]=0.001, pH=2.5
4.3.10-10
33.1
1.3.10-7
1.8.10-4
Experimental parameters 2-
2-
[SO4 ]=0.1, pH=3
-1
Į1 (m.s )
2.2.10
-11
3.1
-12
1.5.10
4.7
The mathematical treatment of the experimental data, presented on Table 1, shows that the growth rate corresponds to a birth and spread mechanism. Sulphate and hydrogen ions influence the crystals surface state so the crystal growth depends on these experimental parameters, especially on sulphate ion concentration. 5. Conclusion According to the reaction, hydrogen ions are produced during the reaction (1), so an experimental method is developed to determine the mechanisms and calculate the kinetic parameters of the linear crystal growth rate by recording hydrogen concentration versus time. The treatment of the experimental data shows that the mechanism which governs the uranium peroxide growth is the birth and spread mechanism. The experiments also show that kinetics parameters depend slightly on pH and sensibly on sulphate ions. The research is on process to find kinetic parameter expressions as a function of hydrogen and sulphate ions.
Acknowledgement The authors gratefully acknowledge the Metallographic and Chemical Analysis Laboratory for the analyses of uranium peroxide solubility and the Process Integration Laboratory for their help for the pH regulator development. The authors are also thankful to AREVA for sponsoring this PhD study.
References [1] B. Courtaud, J. Thiry, F. Auger, Procédé de préparation de concentrés d’uranium par précipitation en lit fluidisé, et préparation d’UO3 et d’U3O8 par séchage/calcination des dits concentrés, WO 2010/051855, France, 2010. [2] B. Courtaud, F. Auger, J. Thiry, A new process for uranium precipitation-increasing bulk yellowcake density: Uranium 2010, Saskatoon, Canada, 2010, pp. 39. [3] J. Garside, A. Mersmann, J. Nyvlt, Measurement of crystal growth and nucleation rates: IChemE, Rugby, 2002. [4] M. Bertrand-Andrieu, E. Plasari, P. Baron, Determination of nucleation and crystal growth kinetics in hostile environment - Application to the tetravalent uranium oxalate U(C2O4)2.6H2O: The Canadian Journal of Chemical Engineering, 2004, pp. 930-937. [5] E.Giffaut, P.Vitorge, H.Capdevila., Adjustment of Activity Coefficients as a Function of Changes in Temperature, using the Specific Interaction Theory, J. Alloys Compounds, 213/214, 1994, 278-285.
Procedia Chemistry 7 (2012) 725 – 730
ATALANTE 2012 International Conference on Nuclear Chemistry for Sustainable Fuel Cycles
Crystal growth kinetics of the uranium peroxide Séverine Planteura*, M. Bertranda, E. Plasarib, B. Courtaudc, J.P. Gaillarda a
CEA, DEN, RadioChemistry & Processes Department, B.P. 17171,30207 Bagnols-sur-Cèze, France b Laboratoire Réactions et Génie des Procédés-ENSIC, 54100 Nancy, France c Areva Mines/SEPA ,87250 Bessines-sur-gartempe, France
Abstract The uranium peroxide precipitation is involved in the processing of uranium ores [1]. In order to determine the crystal growth kinetic parameters, an experimental study is performed in a stirred batch reactor over a wide range of experimental conditions. The experimental method adapted to the uranium peroxide crystal growth study consists in the following of hydrogen ion. This article gives the results obtained for the uranium peroxide crystal growth kinetic law. The treatment of the experimental data shows that the crystal growth rate corresponds to a birth and spread mechanism. 2012Elsevier The Authors. Publishedand/or by Elsevier B.V. under responsibility of the Chairman of the ATALANTE 2012 ©©2012 B.V...Selection peer-review SelectionCommittee and/or peer-review under responsibility of the Chairman of the ATALANTE 2012 Program Program Keywords: Uranium peroxide, precipitation, crystal growth
1. Introduction In the processing of uranium ores, the uranium is recovered from mill leach solutions by precipitation as yellow cake concentrates. Among the different existing processes, the continuous precipitation with hydrogen peroxide in fluidized bed leads to a high-quality solid particles [2]. The uranium peroxide precipitation is performed by mixing hydrogen peroxide and uranyl sulfate solutions according to the following reaction: HO (1) UO2 SO4 H 2O2 o UO4 .4 H 2O H 2 SO4 2
The objective of this article is to study the crystal growth kinetics of the uranium peroxide. Different methods are described in the literature for the determination of crystal growth rate [3]. Among them, the method developed by Bertrand-Andrieu et al. [4] for the uranium oxalate U(C2O4)2.6H2O presents the advantage to be
1876-6196 © 2012 Elsevier B.V...Selection and/or peer-review under responsibility of the Chairman of the ATALANTE 2012 Program Committee doi:10.1016/j.proche.2012.10.110
726
Séverine Planteur et al. / Procedia Chemistry 7 (2012) 725 – 730
experimentally flexible. This method is based on a high seed charge and the spectrophotometric measurement of the decrease of the uranium ion [U4+] concentration in solution. Experiments are performed in a stirred batch reactor. From the recorded data it is possible to determine the crystal growth mechanism and the kinetic constants as will be shown below. We have adapted this method to the uranium peroxide in order to determine the kinetic constants by recording the increase of hydrogen ion concentration [H+] versus time (see equation 1).
Nomenclature
Mc ns S t texp tcalc Vs Vl Į ȕ
-1
crystal molar mass (kg.mol-1) solid particle quantity (mol) supersaturation ratio time(s) experimental time (s) calculated time (s) solid volume (m3) volume of solution (m3) crystal growth kinetic parameter (m.s-1) crystal growth kinetic parameter volume shape factor
a activity (mol.L ) solid concentration (mol.L-1) Cs g(L) mass particle size distribution (m-1) g kinetic order of growth G(t) linear crystal growth rate (m.s-1) I integral kg growth rate constant (m.s-1) Ka constant dissociation of hydrogen peroxide (mol².L-2) Iv Ks solubility product (mol².L-2) L particle size (m-1) crystal density (kg.m-3) Uc mk k order moment of the population density \ ( L, t ) number particle size distribution (m-4) distribution (mk-3) 2. Theoretical background 2.1. Determination of the crystal growth rate relation
In a stirred batch reactor, without nucleation, breakage and agglomeration, for a growth rate independent of the crystal size, the population balance is as follows: w\ ( L, t ) w\ ( L, t ) (2) G (t ) 0 wt
wL
The k-order moment of the population density is defined by : f
mk (t )
³ L \ ( L, t )dL k
(3)
0
Multiplying each term of the population balance by Lk, and after integration: dmk (t ) kG (t )mk 1 (t ) d (t ) The solid phase concentration is related to the size distribution by the following balance: Iv U c 3 Iv U c C s (t ) ³ L \ ( L, t )dL M m3 (t ) Mc c Derivating equation (5) and using equation (4), it comes:
(4)
(5)
727
Séverine Planteur et al. / Procedia Chemistry 7 (2012) 725 – 730
dC s (t ) dt
3
Iv U c Mc
(6)
G (t )m2 (t )
dC s (t ) d [U ] 1 d [ H ] dt dt 2 dt so the hydrogen concentration and the crystal growth rate are linked by the following equation:
The molar balances give:
d[ H ] dt
6
(7)
Vs I v U c m2 (t )G (t ) VL M c
(8)
A seed charge is introduced into the liquid phase so that the total mass precipitating is less than 5% of the initial mass. Under these conditions, the total crystal surface area varies so a little that the second order moment can be considered constant during the experiments: (9) m2(t)§m2(0). Thus equation (8) becomes: d[H ] dt
6
Vs I v U c m 2 (0)G (t ) VL M c
(10)
The population density \ ( L, t ) is calculated from the volume size distribution g(L,t) : \ ( L, t )
C s (t ) M c g ( L, t ) Iv U c L3
(11)
and the second order moment can be written as: m2 (t )
f
2
³ L \ ( L, t )dL
C s (t ) M c
Iv U c
0
with : I (t )
f
I0
³ 0
(12)
I (t )
g ( L,0) dL L
The m2(t=0) substitution in the equation (10), leads to the final expression linking the hydrogen concentration evolution and the crystal growth rate : d[H ] dt
6
ns0 I 0 G (t ) VL
(13)
with ns0= VsCs0 : the crystal charge quantity initially introduced. To solve the system and obtain the kinetic law, it is necessary to replace G(t) by its expression as a function of supersaturation which depends on the growth mechanism. 2.2. Uranium peroxide crystal growth rate It has been experimentally observed for the uranium peroxide system that the crystal growth rate does not depend on the impeller speed. Therefore, the crystal growth is surface integration controlled and the global rate of crystal growth is related to the supersaturation ratio by an expression depending on the growth mechanism [3]: x
for the birth and spread mechanism: G S D 1 S 1 5 6 exp§¨ E 1 ·¸
(12)
x
for the screw dislocation mechanism: G S D 2 S 1 2 tanh§¨ E 2 ·¸
(13)
© S 1¹ © S 1¹
where the supersaturation ratio S=S(t) is calculated by the formula:
728
Séverine Planteur et al. / Procedia Chemistry 7 (2012) 725 – 730 aUO K a >H 2 O2 @ 2 2
S
where: aUO
2 2
>
10 2 pH Ks
@
(14)
J UO UO22 . The uranyl concentration is determined as a function of hydrogen ion 2 2
concentration, (see equation 1), so S=S([H+]). The activity coefficients are taken into account in the solubility model and are calculated with the Specific Interaction Theory (SIT) [5]. As it is seen by formula (14), the supersaturation ratio can be expressed only as a function of hydrogen ion concentration leading to the following equation: d[H ] G(S )
6
ns0 I 0 dt VL
(15)
By integrating this equation, we can obtain: t
VL 6n s 0 I 0
[H ]
³
[ H ]0
d[H ] G(S )
(16)
and the crystal growth parameters can be determined by a nonlinear regression method minimizing the function: F D , E
¦ t exp,i t calc,i 2
(17)
i 1,n
3. Experimental The uranyl sulphate solution is prepared by dissolution of pure uranium trioxide in a sulphuric acid solution heated at about 80°C. The uranium peroxide is precipitated at room temperature by mixing a uranyl sulphate solution with a 30% hydrogen peroxide solution. The experimental set-up (Fig. 1b) consists of a glass baffled batch reactor equipped with a marine propeller. The precipitation is initiated by the rapid injection of a controlled volume of hydrogen peroxide to a uranium sulphate solution charged with a known amount of uranium peroxide crystals. To follow the crystal growth, a pH electrode and a homemade program record pH value as a function of time. In these experiments we used the FU 20 Yokogawa pH-meter with accuracy to within 0.001 pH value. The pH decrease during a crystal growth test is not higher than 0.1 unity pH, so for each experiment the pH can be considered constant. Particle size measurements (Fig. 1a), before and after experimental runs, confirm that there are effectively no agglomeration, no breakage and no nucleation. The recorded pH values are used in the formula (16) to calculate time by integration. The calculated time and experimental time values are used in the equation (17) in order to obtain Į and ȕ best values. (a)
(b)
Grnnulometric graphs before and after the growth test
6
Volume distribution %vol
5 4 3 2 1 0 0,1
1
10
100
1000
particules size (µm)
Fig. 1. (a) Particle size distribution before and after growth test; (b) crystal growth set-up
729
Séverine Planteur et al. / Procedia Chemistry 7 (2012) 725 – 730
4. Results and discussion To determine the crystal growth mechanism, the kinetic parameters are optimized for each mechanism by evaluation of the crystal growth test time. The Figures (1, 2, 3) compare the calculated time using the kinetic parameters optimized and the experimental time for different experimental conditions. The experiments are carried out with pH equal to 2.5 and 3 and with sulphate concentration included between 0.001 and 0.1 mol.L-1. (a)
(b)
Birth and spread [SO4]=0,001 pH=3
100
100,0
80 t_calc
80,0 t_calc
Screw dislocation [SO4]=0,001 pH=3
120
120,0
60,0
60
40,0
40
20,0
20
0,0 0
20
40
60
80
100
0
120
0
t_exp
20
40
60
80
100
120
t_exp
Fig. 2. comparison between calculated and experimental time values (pH=3, [SO42-]=10-3mol.L-1 and S from 60 to 14): (a) birth and spread mechanism; (b) screw dislocation mechanism (a)
(b)
Birth and spread [SO4]=0,001 pH=2,5
Screw dislocation [SO4]=0,001mol/L pH=2,5
35,0
35,0 30,0
30,0 25,0
25,0 t_calc
t_calc
20,0 15,0
20,0 15,0 10,0
10,0
5,0
5,0 0,0
0,0
0
5
10
15
20
25
30
35
0
5
10
15
t_exp
20
25
30
35
t_exp
Fig. 3. comparison between calculated time and experimental time (pH=2.5, [SO42-]=10-3mol.L-1 and S from 18 to 10): (a) birth and spread mechanism; (b) screw dislocation mechanism (a)
(b)
Birth and spread pH=3 SO4=0,1mol/L
90,0
90,0
80,0
80,0
70,0
70,0
60,0
60,0
50,0
50,0
t_calc
t_calc
Screw dislocation pH=3 SO4=0,1mol/L
40,0
40,0 30,0
30,0
20,0
20,0
10,0
10,0
0,0
0,0 0
10
20
30
40
50 t_exp
60
70
80
90
0
10
20
30
40
50
60
70
80
t_exp
Fig. 4. comparison between calculated time and experimental time (pH=3, [SO42-]=0.1mol.L-1 and S from 44 to 5): (a) birth and spread mechanism; (b) screw dislocation mechanism
90
730
Séverine Planteur et al. / Procedia Chemistry 7 (2012) 725 – 730 Table 1. Kinetic parameters and correlation index calculated for each experiment (room temperature) Birth and spread mechanism
Screw dislocation mechanism
ȕ1
Į2 (m.s-1)
ȕ2
[SO4 ]=0.001, pH=3
4.8.10
-10
54.7
3.9.10-6
4.9.10-6
[SO42-]=0.001, pH=2.5
4.3.10-10
33.1
1.3.10-7
1.8.10-4
Experimental parameters 2-
2-
[SO4 ]=0.1, pH=3
-1
Į1 (m.s )
2.2.10
-11
3.1
-12
1.5.10
4.7
The mathematical treatment of the experimental data, presented on Table 1, shows that the growth rate corresponds to a birth and spread mechanism. Sulphate and hydrogen ions influence the crystals surface state so the crystal growth depends on these experimental parameters, especially on sulphate ion concentration. 5. Conclusion According to the reaction, hydrogen ions are produced during the reaction (1), so an experimental method is developed to determine the mechanisms and calculate the kinetic parameters of the linear crystal growth rate by recording hydrogen concentration versus time. The treatment of the experimental data shows that the mechanism which governs the uranium peroxide growth is the birth and spread mechanism. The experiments also show that kinetics parameters depend slightly on pH and sensibly on sulphate ions. The research is on process to find kinetic parameter expressions as a function of hydrogen and sulphate ions.
Acknowledgement The authors gratefully acknowledge the Metallographic and Chemical Analysis Laboratory for the analyses of uranium peroxide solubility and the Process Integration Laboratory for their help for the pH regulator development. The authors are also thankful to AREVA for sponsoring this PhD study.
References [1] B. Courtaud, J. Thiry, F. Auger, Procédé de préparation de concentrés d’uranium par précipitation en lit fluidisé, et préparation d’UO3 et d’U3O8 par séchage/calcination des dits concentrés, WO 2010/051855, France, 2010. [2] B. Courtaud, F. Auger, J. Thiry, A new process for uranium precipitation-increasing bulk yellowcake density: Uranium 2010, Saskatoon, Canada, 2010, pp. 39. [3] J. Garside, A. Mersmann, J. Nyvlt, Measurement of crystal growth and nucleation rates: IChemE, Rugby, 2002. [4] M. Bertrand-Andrieu, E. Plasari, P. Baron, Determination of nucleation and crystal growth kinetics in hostile environment - Application to the tetravalent uranium oxalate U(C2O4)2.6H2O: The Canadian Journal of Chemical Engineering, 2004, pp. 930-937. [5] E.Giffaut, P.Vitorge, H.Capdevila., Adjustment of Activity Coefficients as a Function of Changes in Temperature, using the Specific Interaction Theory, J. Alloys Compounds, 213/214, 1994, 278-285.