- Email: [email protected]
Three-zone approach for precipitation of barium sulphate
,. . . . . . . . C R Y S T A L
GROWTH
ELSEVIER
Journal of Crystal Growth 166 (1996) 1004-1008
Three-zone approach for precipitation of barium sulphate M.L.J. van L e e u w e n , O.S.L. Bruinsma, G.M. van R o s m a l e n * Laboratory for Process Equipment, Delft Universib' of Technology, Leeghwaterstraat 44, Delft 2628 CA, The Netherlands
Abstract
The three-zone approach, introduced by GiSsele and Kind [1] [Chem. Ing. Tech. 63 (1991) 59], has been used to investigate B a S t 4 precipitation. Experimental relations for the growth and nucleation of B a S t 4 are found that show good agreement with those of Angerhder [2] [Thesis, TU Miinchen, 1994] and Van der Leeden [3] [Thesis, TU Delft, 1991]. The parameters studied in the three-zone approach are the feed concentration, circulation time and volume of the zones. Preliminary results show that the model used correctly predicts the influence of the above-mentioned parameters on the mean particle size and the conversion. Experiments conducted at various mixing conditions in the 3 zones show that the influence of the parameters becomes stronger when the mixing in the 3 zones becomes less intensive. This influence cannot be explained by the present model, which assumes that the zones are ideally mixed.
1. I n t r o d u c t i o n
Precipitation, also called reactive crystallization, often exhibits very fast reaction kinetics and so the final product characteristics can be greatly influenced by the way the reactants are mixed. Several authors have shown that by varying the intensity of mixing and consequently the supersaturation profile in the reactor, precipitates with different particle sizes a n d / o r morphologies can be produced [4,5]. Scaling up of precipitation processes, while maintaining a constant product quality, is therefore a difficult task. Precipitation reactions are mostly carried out in a stirred vessel. A simple process scheme is shown in Fig. 1. In order to react, the chemical species have to be mixed on a molecular scale. The process variables that affect product characteristics, such as the crystal size distribution (CSD), are the stirrer speed N and
* Corresponding author. E-mail: [email protected].
the concentration of the feed streams C O. In order to study whether the mixing will affect the product and in particular its CSD, a model is needed that describes both the mixing and the precipitation kinetics on a local scale in the reactor. For this purpose the reactor can be divided into a number of zones, each with its own species concentration, supersaturation, flow velocity, etc. The number of zones can be as high as in computational fluid dynamics (CFD) calculations or as low as in the three-zone model introduced by GiSsele and Kind [1]. Barium sulphate is selected as a model compound because its precipitation kinetics are well studied and it shows no tendency towards agglomeration under the conditions used in the experiments [2,5].
2. M i x i n g in a s t i r r e d v e s s e l
Mixing in a stirred vessel occurs on different length and time scales. Macro-mixing in the reactor is driven by the pumping of the stirrer. It causes circulation but no intimate mixing of the species, and
0022-0248/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved PII S0022-0248(96)00137-6
M.LJ. van Leeuwen et al. / Journal of Crystal Growth 166 (1996) 1004-1008
1005
For the three-zone model of Fig. 2 the mass balance for a zone i, at steady state, is given by
stirrer s p e e d d conc.
~.(~C)i n - ~((J~C)out-
3 K v G i m 2 Vi pi = O, Mw
i = 1...3. Product - CSD - Conversion
(3)
Eq. (3) is solved for both the cations and anions of the precipitated product, Ba 2+ and SO 2-. For the moments of the CSD the equations, as derived by Randolph and Larson [6], are used:
Omj Ot = OjJ +jGmj_, + E(&mj)i, - E(thmj)ou t
g e o m e t r y o f reactor Fig. 1. A schematic view of precipitation in a stirred tank reactor, the most important parameters are indicated.
its time scale is of the order of the circulation time in the reactor. The reacting species are each introduced at a feed point, where the feed is mixed with the passing bulk solution by turbulent motion. This process is referred to as meso-mixing. In the stirrer region the turbulent mixing is at its most intense and mixing occurs on the scale of the smallest eddies, where molecular diffusion takes over. This is referred to as micro-mixing. By investigating these mixing steps, the simple stirred vessel of Fig. 1 can be divided into three zones as shown in Fig. 2: two zones in which the feed streams are mixed with the bulk (the meso-mixing zones) and a main zone in which the bulk is mixed. The exchange rate between the zones corresponds to the macro-mixing in the vessel. This model of the stirred tank allows independent changes in the macro- and meso-mixing, whereas in one tank both simultaneously change when for instance the stirrer speed is changed.
=0,
j=0...3.
(4)
4. Experimental setup The experimental setup for the three-zone approach is schematically shown in Fig. 2. All 3 reactors are baffled and air tight, so that the streams of the inlet zones A and B towards the main zone are forced rather then pumped, which guarantees a constant volume of the inlet zones. The flow rates are controlled by the change in weight of the storage vessels with time. Solutions of BaC12 and N a z S O 4 are used as feedstocks. The chemicals employed are analytically pure, demineralized water being used in
I
3. Precipitation kinetics For the precipitation of BaSO 4 only nucleation and growth are important. For these two processes the following relations are used: G = K~S.~ and KjS m, (1)
~)
~C
where S, is an activity-based supersaturation ratio, defined as ([Ba2+ 1 [ S 0 2 - 1 ) '/2 y+_
Sa =
~Product
(2) (Ks(BaS04))
1/2 Y+*
Fig. 2. A schematic view of the three-zone approach.
1006
M.L.J. van Leeuwen et al. / Journal of Crystal Growth 166 (1996) 1004-1008
all experiments. Rushton-type stirrers were used for mixing (main zone six-bladed, D = 5.5 cm; inlet zones: four-bladed, D = 4 cm). The volumes could be varied from 0.4 to 1.2 litre for the main zone and from 0.1 to 0.6 litre for the inlet zones. Experiments have been carried out in a single baffled vessel of 1.2 litre. For these experiments the same reactor is used as for the main zone in the three-zone approach. The particle size distribution is measured by a Malvern 2605 forward laser diffraction device, using a Mie model. This device gives the most reliable results when measuring the area distribution. Solid samples of the product flow were taken by filtration over a 0.22 /xm millipore filter. The solid samples were washed with demineralized water (demi-water) and dried in air at 40°C. The samples were analyzed by scanning electron microscopy (SEM). Solution samples were taken by filtration over a 0.22 /xm filter. The samples were diluted at sampling and were analyzed by inductively coupled plasma spectrometry (ICP) for barium ions in order to determine the degree of conversion.
5. Results and discussion
=
5.5
~ ii
II
100
•
5
75
~ 4.5
tO ......
5o
(11 > c
o
o 3,
0
0.1
0.3
0.5
0.7
P Fig. 4. The influence of circulation parameter P on the surface mean particle size X32 (/zm) (series 1: C o = 1 m m o l / l and 2: CO= 2 mmol/1) and the % conversion (series 3: CO= 2 mmol/l) for BaSO 4 precipitation in the three-zone system. Volumes of 0.6 litre for the main zone and 0.1 litre for the inlet zones are used. The solid lines represent the modelling results, and the symbols, the experimental data.
particle size by the three-zone approach. To do this, three parameters can be independently varied in the three-zone experiments, namely the circulation flow rate ~brec, the inlet concentration C O and the volume of the three zones VL2,3. The circulation flow rate will be further given as the ratio thin
In Fig. 3, the influence of the stirrer speed N on the mean particle size X32 is shown for a single vessel. An explanation will be attempted of the observed influence of the stirrer speed on the mean
/ 4.5 m
E 2t'Xl ¢0
e
(~in
+
~)rec
,
0
(5)
The first experiments were carried out to study the influence of P on the mean particle size and the conversion, at feed concentrations of 1 and 2 mmol/1. The results are shown in Fig. 4. The lines in Fig. 4 are simulated with the three-zone model with the values n = 3 and m = 3 in Eq. (l). The values for Kj and Kg are fitted to the experimental data:
1
4
-4-
•
•
•
•
Kj = (9.70 ___3.07) ×
J
x
l0 6
( # / 1 . s)
and
3. t i 3 i 0
,
I
"1 I
Kg = (3.29 + 1.63) × 10 -]2 ( m / s ) .
(6)
i
I
100
r-
~
k~-
~
i
200 300 400 stirrer speed [rpm]
~
i
500
600
Fig. 3. The influence of the stirrer speed N (rpm) on the surface mean particle size X32 ( # m ) for BaSO4 precipitation in a single vessel with a volume of 0.8 litre, a residence time of 8 min and a feed concentration of 1 mmol/l.
In Fig. 5 these experimentally found relations for nucleation and growth are compared to the relations found by AngerhiSfer [2] and Van der Leeden [3], showing reasonable agreement. The influence of P on X32 (series 1 and 2 in Fig. 4) is somewhat stronger than predicted by the model. To test what happens when the stirrer speed in the
M.L.J. van Leeuwen et al. / Journal of Crystal Growth 166 (1996) 1004-1008 1E-07
1007
5
.................................. - ~E+12 I ::::::::::::::::::::::::::::::::::::::::: .......... ::::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::: '? iii ii~iil/Tii: "
~,E08
4.9
~::::! !! !!!::!:!!!!? !
E
==iii!!!! E4.8 '-1
t"q
o') r~ IE-10
~
1
•i
..........= i:i i : :i
1E-11
× 4.7
"7 .........
4.6
=
i
1E+08 10
15
20
10
supersaturation Sa
15
20
supersaturation Sa
Fig. 5. Relations for growth and nucleation of BaSO 4 from our work ( - - ) , Angerhrfer [2] (. • • ) and Van der Leeden [3] ( - - - ) .
different zones is varied, an experiment has been carried out with N = 250 in all the zones. This experiment is compared to the (standard) situation of N = 450. The result given in Fig. 6 shows that with increasing stirrer speed, the experimental results are in better agreement with the model. In Fig. 7, the influence of the ratio (VJV2, 3) on X32 is shown. The total volume of the system is 1.6 litre and is kept constant. Both the simulation (line) and the experimental results show little influence of the ratio (V1/V2.~) on the particle size. From Figs. 4 and 7, it can be concluded that of the three parameters studied, the feed concentration has the strongest influence on the particle size, although all influences are rather small. 5.5
4.5 E
4.5
~--I
0
i
2
L _kq
4
I
6
~-
I
8
i
10
ratio (V1 / V2,3) Fig. 7. The influence of the ratio of Vm,i, / Vi,let in the three-zone approach on the mean particle size X32 ( / z m ) at a constant total volume of 1.6 litre. A feed concentration of 2 m m o l / l is used at a feed rate of 6 1 / h and a circulation ratio P = 0.33.
The combined results of the experiments of the three-zone approach should provide a tool to describe the behaviour of the single vessel from Fig, 3 in which the total volume of the three-zones is equal to the volume of the single vessel. Fig. 4 shows the influence of the circulation parameter and Fig. 7 that of the volume ratio of the 3 zones. A simple estimation of the circulation parameter in the single vessel unfortunately demonstrates that its P value is < 0.1 and thus is far below the range of P values in the three-zone experiments. Therefore, although the total volumes are the same, the results of the three-zone approach can not be used to describe the single vessel. The measured circulation ratio in the threezone approach indicates that such an approach is more appropriate to the study of a larger reactor, e.g. an industrial scale reactor.
4 6. Conclusions
2-5 i 2
i i
0.1
I
~
0.3
I
0.5
0.7
P
Fig. 6. Results of changing stirrer speed in the 3 zones, with CO= 1 mmol/1 and a total feed rate of 6 l/h. The stirrer speeds used are N = 450 (.) and N = 250 ( •); the solid line represents the modelling results.
From the preliminary results presented here, it can be concluded that the three-zone approach provides, in principle, a tool to study the precipitation of BaSO 4. The model predicts the influence of the circulation rate, the feed concentration and the volume of the zones on the mean particle size and the conversion correctly. Experimental relations for growth and nucleation of BaSO 4 have been found, which show good agreement with the work of
1008
M.LJ. van Leeuwen et aL / Journal of Crystal Growth 166 (1996) 1004-1008
Angerh~Sfer [2] and Van der Leeden [3]. From experiments with varying mixing conditions in the 3 zones, it is found that the influence of the circulation parameter P becomes stronger with decreasing mixing intensity. This influence cannot be explained by the model used, because this model assumes that all the zones are ideally mixed. It is proposed that improvements in the model will be investigated in future work.
Symbols ~b C A p Mw
Flow rate (l/s) Concentration (mol/l) Total area of crystals (m2/1) Density of crystals ( k g / m 3) Mol. weight of crystals (kg/mol)
Kv, a
y+ kg kj
Volume and area shape factor Activity Growth constant (m/s) Nucleation constant ( # / 1 - s)
References [1] W. GiSsele and M. Kind, Chem. Ing. Tech. 63 (1991) 59. [2] M. Angerhtifer, Untersuchungen zur kinetik der fdllungskristallisation von bariumsulfat, Thesis, TU Miinchen, 1994. [3] M.C. van der Leeden, The role of polyelectrolytes in barium sulphate precipitation, Thesis, TU Delft, 1991. [4] D.E. Fitchett and J.M. Tarbell, AIChE J. 36 (1990) 511. [5] S.T. Liu, G.H. Nancollas and E.A. Gasiecki, J. Crystal Growth 33 (1976) 11. [6] A.D. Randolph and M.A. Larson, Theory of Particulate Processes, 2nd ed. (Academic Press, San Diego, CA, 1988).
GROWTH
ELSEVIER
Journal of Crystal Growth 166 (1996) 1004-1008
Three-zone approach for precipitation of barium sulphate M.L.J. van L e e u w e n , O.S.L. Bruinsma, G.M. van R o s m a l e n * Laboratory for Process Equipment, Delft Universib' of Technology, Leeghwaterstraat 44, Delft 2628 CA, The Netherlands
Abstract
The three-zone approach, introduced by GiSsele and Kind [1] [Chem. Ing. Tech. 63 (1991) 59], has been used to investigate B a S t 4 precipitation. Experimental relations for the growth and nucleation of B a S t 4 are found that show good agreement with those of Angerhder [2] [Thesis, TU Miinchen, 1994] and Van der Leeden [3] [Thesis, TU Delft, 1991]. The parameters studied in the three-zone approach are the feed concentration, circulation time and volume of the zones. Preliminary results show that the model used correctly predicts the influence of the above-mentioned parameters on the mean particle size and the conversion. Experiments conducted at various mixing conditions in the 3 zones show that the influence of the parameters becomes stronger when the mixing in the 3 zones becomes less intensive. This influence cannot be explained by the present model, which assumes that the zones are ideally mixed.
1. I n t r o d u c t i o n
Precipitation, also called reactive crystallization, often exhibits very fast reaction kinetics and so the final product characteristics can be greatly influenced by the way the reactants are mixed. Several authors have shown that by varying the intensity of mixing and consequently the supersaturation profile in the reactor, precipitates with different particle sizes a n d / o r morphologies can be produced [4,5]. Scaling up of precipitation processes, while maintaining a constant product quality, is therefore a difficult task. Precipitation reactions are mostly carried out in a stirred vessel. A simple process scheme is shown in Fig. 1. In order to react, the chemical species have to be mixed on a molecular scale. The process variables that affect product characteristics, such as the crystal size distribution (CSD), are the stirrer speed N and
* Corresponding author. E-mail: [email protected].
the concentration of the feed streams C O. In order to study whether the mixing will affect the product and in particular its CSD, a model is needed that describes both the mixing and the precipitation kinetics on a local scale in the reactor. For this purpose the reactor can be divided into a number of zones, each with its own species concentration, supersaturation, flow velocity, etc. The number of zones can be as high as in computational fluid dynamics (CFD) calculations or as low as in the three-zone model introduced by GiSsele and Kind [1]. Barium sulphate is selected as a model compound because its precipitation kinetics are well studied and it shows no tendency towards agglomeration under the conditions used in the experiments [2,5].
2. M i x i n g in a s t i r r e d v e s s e l
Mixing in a stirred vessel occurs on different length and time scales. Macro-mixing in the reactor is driven by the pumping of the stirrer. It causes circulation but no intimate mixing of the species, and
0022-0248/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved PII S0022-0248(96)00137-6
M.LJ. van Leeuwen et al. / Journal of Crystal Growth 166 (1996) 1004-1008
1005
For the three-zone model of Fig. 2 the mass balance for a zone i, at steady state, is given by
stirrer s p e e d d conc.
~.(~C)i n - ~((J~C)out-
3 K v G i m 2 Vi pi = O, Mw
i = 1...3. Product - CSD - Conversion
(3)
Eq. (3) is solved for both the cations and anions of the precipitated product, Ba 2+ and SO 2-. For the moments of the CSD the equations, as derived by Randolph and Larson [6], are used:
Omj Ot = OjJ +jGmj_, + E(&mj)i, - E(thmj)ou t
g e o m e t r y o f reactor Fig. 1. A schematic view of precipitation in a stirred tank reactor, the most important parameters are indicated.
its time scale is of the order of the circulation time in the reactor. The reacting species are each introduced at a feed point, where the feed is mixed with the passing bulk solution by turbulent motion. This process is referred to as meso-mixing. In the stirrer region the turbulent mixing is at its most intense and mixing occurs on the scale of the smallest eddies, where molecular diffusion takes over. This is referred to as micro-mixing. By investigating these mixing steps, the simple stirred vessel of Fig. 1 can be divided into three zones as shown in Fig. 2: two zones in which the feed streams are mixed with the bulk (the meso-mixing zones) and a main zone in which the bulk is mixed. The exchange rate between the zones corresponds to the macro-mixing in the vessel. This model of the stirred tank allows independent changes in the macro- and meso-mixing, whereas in one tank both simultaneously change when for instance the stirrer speed is changed.
=0,
j=0...3.
(4)
4. Experimental setup The experimental setup for the three-zone approach is schematically shown in Fig. 2. All 3 reactors are baffled and air tight, so that the streams of the inlet zones A and B towards the main zone are forced rather then pumped, which guarantees a constant volume of the inlet zones. The flow rates are controlled by the change in weight of the storage vessels with time. Solutions of BaC12 and N a z S O 4 are used as feedstocks. The chemicals employed are analytically pure, demineralized water being used in
I
3. Precipitation kinetics For the precipitation of BaSO 4 only nucleation and growth are important. For these two processes the following relations are used: G = K~S.~ and KjS m, (1)
~)
~C
where S, is an activity-based supersaturation ratio, defined as ([Ba2+ 1 [ S 0 2 - 1 ) '/2 y+_
Sa =
~Product
(2) (Ks(BaS04))
1/2 Y+*
Fig. 2. A schematic view of the three-zone approach.
1006
M.L.J. van Leeuwen et al. / Journal of Crystal Growth 166 (1996) 1004-1008
all experiments. Rushton-type stirrers were used for mixing (main zone six-bladed, D = 5.5 cm; inlet zones: four-bladed, D = 4 cm). The volumes could be varied from 0.4 to 1.2 litre for the main zone and from 0.1 to 0.6 litre for the inlet zones. Experiments have been carried out in a single baffled vessel of 1.2 litre. For these experiments the same reactor is used as for the main zone in the three-zone approach. The particle size distribution is measured by a Malvern 2605 forward laser diffraction device, using a Mie model. This device gives the most reliable results when measuring the area distribution. Solid samples of the product flow were taken by filtration over a 0.22 /xm millipore filter. The solid samples were washed with demineralized water (demi-water) and dried in air at 40°C. The samples were analyzed by scanning electron microscopy (SEM). Solution samples were taken by filtration over a 0.22 /xm filter. The samples were diluted at sampling and were analyzed by inductively coupled plasma spectrometry (ICP) for barium ions in order to determine the degree of conversion.
5. Results and discussion
=
5.5
~ ii
II
100
•
5
75
~ 4.5
tO ......
5o
(11 > c
o
o 3,
0
0.1
0.3
0.5
0.7
P Fig. 4. The influence of circulation parameter P on the surface mean particle size X32 (/zm) (series 1: C o = 1 m m o l / l and 2: CO= 2 mmol/1) and the % conversion (series 3: CO= 2 mmol/l) for BaSO 4 precipitation in the three-zone system. Volumes of 0.6 litre for the main zone and 0.1 litre for the inlet zones are used. The solid lines represent the modelling results, and the symbols, the experimental data.
particle size by the three-zone approach. To do this, three parameters can be independently varied in the three-zone experiments, namely the circulation flow rate ~brec, the inlet concentration C O and the volume of the three zones VL2,3. The circulation flow rate will be further given as the ratio thin
In Fig. 3, the influence of the stirrer speed N on the mean particle size X32 is shown for a single vessel. An explanation will be attempted of the observed influence of the stirrer speed on the mean
/ 4.5 m
E 2t'Xl ¢0
e
(~in
+
~)rec
,
0
(5)
The first experiments were carried out to study the influence of P on the mean particle size and the conversion, at feed concentrations of 1 and 2 mmol/1. The results are shown in Fig. 4. The lines in Fig. 4 are simulated with the three-zone model with the values n = 3 and m = 3 in Eq. (l). The values for Kj and Kg are fitted to the experimental data:
1
4
-4-
•
•
•
•
Kj = (9.70 ___3.07) ×
J
x
l0 6
( # / 1 . s)
and
3. t i 3 i 0
,
I
"1 I
Kg = (3.29 + 1.63) × 10 -]2 ( m / s ) .
(6)
i
I
100
r-
~
k~-
~
i
200 300 400 stirrer speed [rpm]
~
i
500
600
Fig. 3. The influence of the stirrer speed N (rpm) on the surface mean particle size X32 ( # m ) for BaSO4 precipitation in a single vessel with a volume of 0.8 litre, a residence time of 8 min and a feed concentration of 1 mmol/l.
In Fig. 5 these experimentally found relations for nucleation and growth are compared to the relations found by AngerhiSfer [2] and Van der Leeden [3], showing reasonable agreement. The influence of P on X32 (series 1 and 2 in Fig. 4) is somewhat stronger than predicted by the model. To test what happens when the stirrer speed in the
M.L.J. van Leeuwen et al. / Journal of Crystal Growth 166 (1996) 1004-1008 1E-07
1007
5
.................................. - ~E+12 I ::::::::::::::::::::::::::::::::::::::::: .......... ::::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::: '? iii ii~iil/Tii: "
~,E08
4.9
~::::! !! !!!::!:!!!!? !
E
==iii!!!! E4.8 '-1
t"q
o') r~ IE-10
~
1
•i
..........= i:i i : :i
1E-11
× 4.7
"7 .........
4.6
=
i
1E+08 10
15
20
10
supersaturation Sa
15
20
supersaturation Sa
Fig. 5. Relations for growth and nucleation of BaSO 4 from our work ( - - ) , Angerhrfer [2] (. • • ) and Van der Leeden [3] ( - - - ) .
different zones is varied, an experiment has been carried out with N = 250 in all the zones. This experiment is compared to the (standard) situation of N = 450. The result given in Fig. 6 shows that with increasing stirrer speed, the experimental results are in better agreement with the model. In Fig. 7, the influence of the ratio (VJV2, 3) on X32 is shown. The total volume of the system is 1.6 litre and is kept constant. Both the simulation (line) and the experimental results show little influence of the ratio (V1/V2.~) on the particle size. From Figs. 4 and 7, it can be concluded that of the three parameters studied, the feed concentration has the strongest influence on the particle size, although all influences are rather small. 5.5
4.5 E
4.5
~--I
0
i
2
L _kq
4
I
6
~-
I
8
i
10
ratio (V1 / V2,3) Fig. 7. The influence of the ratio of Vm,i, / Vi,let in the three-zone approach on the mean particle size X32 ( / z m ) at a constant total volume of 1.6 litre. A feed concentration of 2 m m o l / l is used at a feed rate of 6 1 / h and a circulation ratio P = 0.33.
The combined results of the experiments of the three-zone approach should provide a tool to describe the behaviour of the single vessel from Fig, 3 in which the total volume of the three-zones is equal to the volume of the single vessel. Fig. 4 shows the influence of the circulation parameter and Fig. 7 that of the volume ratio of the 3 zones. A simple estimation of the circulation parameter in the single vessel unfortunately demonstrates that its P value is < 0.1 and thus is far below the range of P values in the three-zone experiments. Therefore, although the total volumes are the same, the results of the three-zone approach can not be used to describe the single vessel. The measured circulation ratio in the threezone approach indicates that such an approach is more appropriate to the study of a larger reactor, e.g. an industrial scale reactor.
4 6. Conclusions
2-5 i 2
i i
0.1
I
~
0.3
I
0.5
0.7
P
Fig. 6. Results of changing stirrer speed in the 3 zones, with CO= 1 mmol/1 and a total feed rate of 6 l/h. The stirrer speeds used are N = 450 (.) and N = 250 ( •); the solid line represents the modelling results.
From the preliminary results presented here, it can be concluded that the three-zone approach provides, in principle, a tool to study the precipitation of BaSO 4. The model predicts the influence of the circulation rate, the feed concentration and the volume of the zones on the mean particle size and the conversion correctly. Experimental relations for growth and nucleation of BaSO 4 have been found, which show good agreement with the work of
1008
M.LJ. van Leeuwen et aL / Journal of Crystal Growth 166 (1996) 1004-1008
Angerh~Sfer [2] and Van der Leeden [3]. From experiments with varying mixing conditions in the 3 zones, it is found that the influence of the circulation parameter P becomes stronger with decreasing mixing intensity. This influence cannot be explained by the model used, because this model assumes that all the zones are ideally mixed. It is proposed that improvements in the model will be investigated in future work.
Symbols ~b C A p Mw
Flow rate (l/s) Concentration (mol/l) Total area of crystals (m2/1) Density of crystals ( k g / m 3) Mol. weight of crystals (kg/mol)
Kv, a
y+ kg kj
Volume and area shape factor Activity Growth constant (m/s) Nucleation constant ( # / 1 - s)
References [1] W. GiSsele and M. Kind, Chem. Ing. Tech. 63 (1991) 59. [2] M. Angerhtifer, Untersuchungen zur kinetik der fdllungskristallisation von bariumsulfat, Thesis, TU Miinchen, 1994. [3] M.C. van der Leeden, The role of polyelectrolytes in barium sulphate precipitation, Thesis, TU Delft, 1991. [4] D.E. Fitchett and J.M. Tarbell, AIChE J. 36 (1990) 511. [5] S.T. Liu, G.H. Nancollas and E.A. Gasiecki, J. Crystal Growth 33 (1976) 11. [6] A.D. Randolph and M.A. Larson, Theory of Particulate Processes, 2nd ed. (Academic Press, San Diego, CA, 1988).