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How to improve the crystal size distribution (CSD) in crystallizers with the inner suspension circulation
Chemical Engineering and Processing 41 (2002) 585– 593 www.elsevier.com/locate/cep
How to improve the crystal size distribution (CSD) in crystallizers with the inner suspension circulation Piotr Synowiec * Department of Chemical and Process Engineering, Silesian Institute of Inorganic Chemistry, Gliwice, Poland Received 4 April 2001; received in revised form 3 October 2001; accepted 4 October 2001
Abstract An analysis of limited crystal growth in the crystallizer with inner suspension circulation has been studied. The new exhaustively theoretical analysis of crystal attrition sources, pumping effect and power input requirements, as well as the experimental investigations in concentrated suspensions have been done, respectively. In the light of collected theoretical and experimental evidence, in the Draft Tube Magma (DTM) crystallizers there are no significant possibilities for improvement of crystal size. The new constructional modification of DTM crystallizer was proposed for achieving better crystal quality. The new apparatus, with two coaxial draft tubes and partially hydraulic magma classification, makes possible to increase the mean crystal size up to 33%. The product efficiency from unit volume in this case is comparable with a DTM vessel. Moreover, the favorable conditions of crystal growth in a new crystallizer enable one to extend the residence time to 8 h, and because of that, to produce the crystals of the average size up to 1000 mm. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Crystallization; DTM crystallizer; Attrition; CSD
1. Introduction In industrial practice, the maximum mean size of crystals produced in the Draft Tube Magma (DTM) Crystallizers (Fig. 1), are limited to more or less 400 mm, and the maximum time of crystals growth does not exceed 3.5 h. Those practical parameters are determined by intensive solid phase attrition taking place during the inner suspension circulation created by means of the propeller located in the draft tube. Intensity of the circulation (pumping capacity) in the DTM apparatus for crystallization from solution is determinated by settled product capacity and supersaturation of solution, respectively. The mean source of crystal destruction, as it was admitted, has been generated mainly during crystal –impeller blade impacts. For the probability limitation of this kind of collision, the crystallizers with the low number of revolutions of the propeller or crystallizers with reduced power input have been proposed. Those innovations should have been favorable for the increase * Tel.: + 48-604-928-955; fax: + 48-32-237-1461. E-mail address: [email protected] (P. Synowiec).
of the mean crystal size. Although, the increase of particle size has been continually limited, the power-input reduction was significant. For better understanding the reasons of crystal destruction, the deeper analysis has been developed. In the light of this analysis another independent reason — turbulent attrition caused by liquid motion was predicted [1]. Considering the presence of the second destruction reason, it has enabled one to explain why only reduction of power input is not enough for the increasing of product quality.
2. Theory
2.1. The main sources of crystal attrition It is assumed in this work that the crystal attrition is caused by both independent sources, namely, the mechanical breaking forces (i.e. crystal –crystal, crystal – propeller, crystal –wall) and turbulent inducted breaking (i.e. shear stresses, drag stresses, pressure stresses).
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P. Synowiec / Chemical Engineering and Processing 41 (2002) 585–593
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However, the crystal– crystal and crystal– wall impacts have negligible effect on destruction [2,3]. For parent crystals larger than 200 mm the fluid-inducted stresses, by shear and pressure forces may also by negligible [1]. Thus, the total rate of secondary nucleation in the DTM crystallizer can by expressed by general form as follows: Bo,tot =Bo,im + Bo,turb
(1)
where Bo,im describes the rate of fine particle generation by means of crystal– impeller impact; and Bo,turb, the rate of fine fragments generation by turbulent drag forces. The components of each of these terms are described as follows: the effective intensity of stress, f %; the impact energy per unit energy needed to produce one fragment from crystal surface, E/e; the total number of parent particles in the crystallizer, nc. Thus
E Bo,im,turb =f % i nc ei
(2)
For crystal– impeller collisions, the effective intensity of stress is given by the relation: f %=
V: Q 1 L2 pT 8 o 2 4 m V Po s d m
(3)
The intensity of circulation, V: /V has been described by Parker [4] and the target efficiency, pT by Mersmann [5]. The maximum impact energy can by determined as kinetic energy of parent particles moving with velocity equal to tip speed, ut: 1 Eim = krL 3zcu 2t 2
(4)
The number of crystals in a unit volume of suspension is given by: nc =
k rL 3
(5)
Thus, the crystal– impeller secondary nucleation rate may be expressed by the following relation: Bo,im 8krL 5zc
Qo nc m Po eim
(6)
In the case of turbulent attrition, intensity of stress is equal to eddies fluctuation frequency, fe, described by Levich [6]: f %= fe = 0.258
m w
1/2
m w
1.4
(8)
where Zpd is the pressure drop caused by the difference between local motion of the fluid relative to that of the crystal [7].Whence
B0,turb 8 krL 6.6
m w
1.9
p − 0.8Dz 1.4z 0.4 l
nc eturb
(9)
Describing the effect of turbulent motion of the liquid on particle surface, the Kolmogorov theory of turbulence has been taken into consideration. The theoretical relation Eqs. (6) and (9) implies the stronger effect of particle size (5 or 6.6 exponent) on secondary nucleation rate than the unit power input (1 or 1.9 exponent). This relation explains why the reduction of power input is not a sufficient factor for the improvement of crystal size distribution. Analysing the theoretical and experimental effect of scale up on the secondary nucleation rate for geometrically similar vessels at constant power input, the following relation may be written [8]:
Bo,tot dm : 0.77 Bo,tot,lab dm,lab
−2
+ 0.23
(10)
It means that about 77% of the total destruction is generated by mechanical impacts, where the rest, i.e. 23% is caused by drag forces. The Eq. (10) implies additionally that the turbulent attrition rate is predicted to be independent from the vessel scale, when the mechanical component is rapidly decreasing in case of the increase of the crystallizer volume.
2.2. Pumping effect and power input reduction possibilities The pumping capacity required in the crystallizer is expressed by the following equation: V: =
G: c Dc
(11)
The propeller number of revolution indispensable for the required pumping capacity can be calculated from: V: =Qosd 3m
(12)
The unit power input necessary for obtaining the required number of revolution are given by: m=
P Pos 3d 5m = 8 Pos 3d 2m V Ms
(13)
assuming that V8d 3m and Ms = Vzs. Combining Eqs. (13) and (12) gives:
(7)
The respective energy of drag forces is described as:
Ed = VcDpd 8 krL 6.6p − 0.8Dz 1.4z 0.4 l
m8
1 2 Po V: s Qo dm
(14)
P. Synowiec / Chemical Engineering and Processing 41 (2002) 585–593
Relation Eq. (14) predicts that for obtaining the required pumping effect with simultaneously low power input the constructional solution of the system should be found (i.e. propeller– draft tube) in which the circulation is generated by means of a low rotating stirrer with a maximum acceptable diameter. Additionally the system should be characterized by a low value of the power number and a high value of the volumetric flow number. The practical aspects of these remarks have been discussed in details elsewhere [8– 10].
587
The last equation implies a very limited effect of reduction of the unit power input on the increase of mean crystal size. However, for example, a 40% reduction of m theoretically caused only the 12% increase of the mean particle size, but a significant m reduction gives notable savings of the production costs.
3. Investigations
3.1. Identification of attrition sources 2.3. Restricted increase of the mean particle size In light of the presented theoretical analysis concerning the sources of secondary nucleation rate in the DTM crystallizers, it has been clearly shown that reduction of the power input only is not a sufficient factor for the considerable improvement of the size of crystals produced. The point is how the power input reduction affects the increase of a mean crystal size. The theoretical dependencies Eqs. (6) and (9) can by simplified to the formula: Bo 8m 1 + 1.9L 5 + 6.6
The experiments concerning the sources of destruction have been carried out in the agitated vessel geometrically similar to the typical DTM crystallizer. Two vessels of volume 1.5×10 − 3 and 24×10 − 3 m3 have been investigated. The apparatus was equipped with the draft tube and the six-blade turbine. The geometrical relations of experimental setup, similar to that in use at present, has been shown in the paper [1]. The investigation principles have been described in the same work.
(15)
The experimental data, shown on the next pages, enables one to determinate the average value of exponents. Thus: Bo 8m 1.2L 5.25
(16)
A dependence between change of the unit power input, secondary nucleation rate and crystal size may be expressed as follows:
Bo,2 m : 2 Bo,1 m1
1.2
5.25
L2 L1
(17)
where m1 \m2. The formula Eq. (17) clearly shows that the reduction of the unit power input from m1 to m2 enables one to decrease the rate of secondary nucleation and increase the crystal size. Secondly, this limited increase of crystal size again influences the rise of the secondary nucleation rate (because the particle size is in the exponent of 5.25). Assuming that particle growth can last to the moment when the secondary nucleation rate reaches its previous level, a new condition may be written as: Bo,2 =1 Bo,1
(18)
what means that the maximum theoretical increase of crystal size in the DTM crystallizer caused by the power input reduction is equal to:
L2 L1
:
max
n
1 (m2/m1)1.2
0.19
=
m1 m2
0.23
(19) Fig. 1. Draft Tube Magma Crystallizer.
588
P. Synowiec / Chemical Engineering and Processing 41 (2002) 585–593
Fig. 2. Dependence of secondary nucleation rate on unit power input generated in laboratory scale vessel.
Fig. 3. Dependence of secondary nucleation rate on crystal size generated in laboratory scale vessel.
Crystals of potassium sulfate K2SO4 and potash alum KAl(SO4)2 · 12H2O were used during the tests, respectively. The volumetric solid phase concentration in the range of 0.03–0.17, unit power input 0.4– 1.5 W kg − 1 and parent crystal size of 100– 900 mm have been studied. The crystal attrition sources interact and complete with each other. For that reason two assumptions have been made: (i) the turbulent secondary nucleation rate is achieved by means of the rubber coated stirrer; (ii) the minimum crystal–impeller impact secondary nucleation
rate is a difference between total secondary nucleation rate caused by the steel turbine and the rubber coated stirrer. The majority of fines produced in each run were observed to be in the size range 3–25 mm, with no significant changes of the mean parent particle size after a 2-h test. The ratio between the initial and final particle size after each run was in the range 0.99–0.95, what indicates that crystal destruction has mainly a surface character.
P. Synowiec / Chemical Engineering and Processing 41 (2002) 585–593 Table 1 Predicted and observed dependence on secondary nucleation rate simplified to the formula Bo 8 L am b a
b
Impact (crystal–turbine) Exponent Eq. (6) 5 Slope of regression line 4.99–5.01 (Fig. 2)
1 1.06–1.10 (Fig. 1)
Turbulence (drag stress) Exponent Eq. (9) 6.6 Slope of regression line 6.11–6.26 (Fig. 2)
1.9 1.82–1.98 (Fig. 1)
In order to determine the main reason for crystal attrition, after specially prepared tests, the regression line, based on experimental data, have been plotted. The slope of each regression line has been compared with adequate theoretical exponents in Eqs. (6) and (9), (Figs. 2 and 3). Replacing, at a constant power input, the stainless steel turbine with the rubber coated stirrer, the secondary nucleation has been reduced by about 77% in case of K2SO4 and KAl(SO4)2 · 12H2O.
589
Additionally, an increase in the dependence of a number of attrition fines on the unit power input was observed using the rubber coated turbine (exponents 1.98 and 1.82) in place of the steel impeller (exponents 1.18 and 1.21), Fig. 3, thus confirming the increased proportion of the turbulent drag attrition contribution. Successive confirmation of the presence of two independent destruction sources, are focused the investigations on the effect of crystal size on the attrition rate. The secondary nucleation rate, Bo, has been recalculated as the average number of fine particles generated in unit time per parent crystal, B %o, because for constant the number of parent particles in the vessel decreased proportionally as the parent crystal size, L increased. The result of comparison between theoretically, as well as experimentally determined exponents of the particular variables are collected in the Table 1. The theoretical relation Eq. (10) describing the effect of scale-up on secondary nucleation changes has been tested in two additional vessels, i.e. 24 l and 9 m3, respectively. The results are shown in Fig. 4. The difference between theoretical curves and experimental data are less than 6%.
Fig. 4. Effect of scale-up factor (dm/dm,lab) on secondary nucleation rate for constant power input. Table 2 Comparison of experimental and calculated values of the effect of the unit power input on a mean crystal size and secondary nucleation rate
KAl(SO4)2 · 12H2O KAl(SO4)2 · 12H2O KAl(SO4)2 · 12H2O KAl(SO4)2 · 12H2O KNO3 KCl (NH4)2SO4
m2/m1
Lmi2/Lmi1
Bo,2/Bo,1 Experimental
Bo,2/Bo,1 Calculated
D (%)
Reference
0.333 0.667 0.50 0.575 0.315 0.143 0.255
1.172 1.077 1.088 1.104 1.194 1.185 1.262
0.653 0.920 0.706 0.748 0.717 0.269 0.740
0.615 0.908 0.678 0.864 0.634 0.236 0.658
−5.8 −1.3 −4.0 15.5 −11.5 −12.2 −11.0
[5] [11] [12,13]
590
P. Synowiec / Chemical Engineering and Processing 41 (2002) 585–593
Fig. 5. Double Draft Tube Crystallizer.
3.2. Effect of reduction of the unit power input on the mean crystal size The experimental verification of relation Eq. (19) has been performed in the MSMPR crystallizer. Some data published by Mersmann [5,11– 13] has been also employed. Only the data obtained for the same value of the supersaturation of solution and the same residence time but for the different unit power input has been taken into consideration. The results are presented in Table 2 The calculated values of the ratio Bo,2/Bo,1 are very close to the measured ones. The maximum error between these compared results amounts only to 15.5%. The collected experimental material testifies to a very weak effect of the reduction of the unit power input on a crystal size increase in the crystallizers with inner suspension circulation. The strong destruction during magma circulation in the DTM crystallizers are caused by crystal– impeller impacts in small scale, and by turbulent drag stresses in
large scale, respectively. The second source of destruction is particularly effective in the area of a rotating stirrer located in the draft tube, as unit power input distribution is not homogeneous in the whole vessel volume. In the light of Mersmann’s work [14], in this place of apparatus the local unit power input is about ten times higher than the average value, admitted in the discussed equations. The second independent source of destruction-liquid turbulence, existing next to the mechanical one, explains why in the case of scaling-up, when the target efficiency of impacts is rapidly decreasing, the secondary nucleation rate does not decline simultaneously so quickly. Independence of the turbulent drag forces from the apparatus volume and the inhomogeneous power input distribution keep the secondary nucleation rate still on a relatively high level, particularly when magma circulation is kept going through the draft tube. All of the listed premises exclude the possibilities of a prominent increase of the crystal size without constructional changes of the apparatus, usually modifying a circulation of suspension. Taking into consideration the high level of crystals destruction and a limited CSD improvement in the DTM apparatus, the new constructional modification named the Double Draft Tube (DDT) crystallizer has been worked out [15] (Fig. 5). The DDT solution includes two coaxial draft tubes and the opposite direction of suspension flow in relation to the DTM. The hydraulic classification of suspension takes place in the upper part of the vessel. Small amount of slurry hits to the central draft tube while remaining part of particles is aimed to a space between the central and exterior draft tube, respectively. The comparative experiments were carried out in the continuously working plant of total volume equal to 0.2 m3. When about 30 –40% of crystals circulated through the central draft tube and other part of grains were held in the zone between the central draft tube and vessel jacket the satisfying mean crystal size increase has been observed. Such conditions of flow have given the comparable product efficiency from cubic meter of apparatus in the DDT, as well as in the DTM crystallizer and made possible to protect the majority of growing crystals against increased level of attrition located in the space surrounding the stirrer. The results of investigations focused on sodium chloride as well as ammonium sulfate crystallization are presented in Fig. 6a and b, respectively. During experiments the supersaturation of solution and the residence time in both apparatus have been kept on the constant level as well. On the average mean crystal size obtained in the DDT crystallizer has been bigger than 33– 36% in comparison to that produced in the DTM, when the proportion of magma hydraulic separation was the same as mentioned above.
P. Synowiec / Chemical Engineering and Processing 41 (2002) 585–593
The better conditions of crystal growth in the crystallizer discussed enable one to extend the residence time up to 8 h and the production of crystals in the range of 600–1000 mm, Fig. 6a. Additionally, the mass distribution versus particle size, Fig. 6b, shows the practical absence of particles below 60 mm in the slurry withdrawn from the DDT crystallizer. Comparing the shape of sodium chloride crystals from the DTM and DDT crystallizer, the intensity of attrition in the first case may be easily estimated, Fig. 7.
4. Conclusion In the light of theoretical, as well as experimental evidence, in the crystallizers with an inner suspension
591
circulation there are no significant possibilities for improvement of a crystal size only by means of the power input reduction. The presented analysis clearly shows two independent sources of the crystal attrition, i.e. crystal-stirrer impacts and turbulent drug forces. In small scale, the first reason of destruction has got a significant effect on crystal destruction. When a volume of crystallizer increases, the importance of mechanical impact declines, and turbulence acting on a particle surface is mainly responsible for crystal attrition. The experimental results are consistent with theoretical relations. The area of exceptional intensive particle breakage, for both sources, is located inside the draft tube, in the area when the propeller is rotating, or the local values of unit power input distribution are the highest. This
Fig. 6. Comparison of: (a) median crystal size Lmi vs. residence time t; (b) particle density distribution q3 in the DTM and DDT crystallizers. (The experiments have been curried out in the 0.2 m3 continuously working pilot plant).
P. Synowiec / Chemical Engineering and Processing 41 (2002) 585–593
592
kv L M nc Po Qo s t ut = ^dms V: V q3 = mi /(mtotDL) m p pT z Dz = zc−zd Dc D= ([cal]−[exp]) /[exp]100
Fig. 7. Sodium chloride crystals withdrawn from: (a) DTM and (b) DDT apparatus.
reason makes impossible a significant improvement of CSD without changes of the way of a forced magma circulation. The DDT crystallizer proposed allows to protect mean stream of the circulated crystals against the zone with the highest destruction intensity, simultaneously keeping the simplicity of construction. That is why the significant increases of mean particle size were observed. Moreover, the effective reduction of stress intensity permits the application of the DDT for production of crystals in the range of 600– 1000 mm with the residence time up to 8 h, respectively.
Appendix A. Nomenclature Bo dm e, E G: f%
secondary nucleation rate (m−3·s−1) impeller diameter (m) energy (J) mass flow (kg s−1) effective intensity of stress (s−1)
Indices c mi cal o f rub im s exp st lab tot m turb
volumetric shape factor crystal size (m) mass (kg) number of particles (m−3) power number volumetric flow number impeller speed of rotation (s−1) residence time (s) tip speed (m s−1) pumping capacity (m3 s−1) volume (m3) mass fraction (kg kg−1·m−1) unit power input (W kg−1) dynamic viscosity (Pa s) target efficiency density (kg m3) zl (kg m−3) solution supersaturation (kg m−3) volumetric solid phase concentration in suspension error (%)
Crystal Mean Calculated Initial Fluid Rubber Impact Suspension Experimental Steel Laboratory Total Stirrer turbulent
References [1] W. Wu¨ hlk, G. Hofmann, Types of crystallizers, Int. Chem. Eng. 27 (2) (1985) 197 – 204. [2] B.C. Shah, W.Z. McCabe, R.W. Rousseau, Polyethylene vs. stainless steel impellers for crystallization processes, Am. Inst. Chem. Eng. J. 19 (1973) 194. [3] P. Synowiec, A.G. Jones, P. Ayazi Shamlou, crystal break-up in dilute turbulently agitated suspensions, Chem. Eng. Sci. 48 (20) (1993) 3485 – 3495. [4] N. Harnby, M.F. Edwards, A.W. Nienow, Mixing in the Process Industries, second ed., Butterworth – Heinemann, London, 1992. [5] J. Pohlisch, A. Mersmann, The influence of stress and attrition on crystals size distribution, Chem. Eng. Tech. 11 (1988) 40 – 49. [6] V.G. Levich, Physicochemical Hydrodynamics, McGaw Hill, New York, 1962. [7] D. Parker, S. Kaufman, D. Jenkins, Flock break-up in turbulent floculation process, J. Sanit. Eng. Div. ASCE, February, vol. 98, No. SA1 (1972) 79 – 99.
P. Synowiec / Chemical Engineering and Processing 41 (2002) 585–593 [8] P. Synowiec, Taking a new look at crystals attrition phenomenon in crystallizers with suspension circulation, Wrocław Tech. Univ., Press 66/41, Wrocław 1998. [9] P. Synowiec, R. Sangl, Selected Problems of the Hydrodynamics in a Draft Tube Crystallizer, In: A. Mersmann (Ed.), Proceedings of the 11th Symp. on Ind. Crystallization, Germany Garmisch-Partnerkirchen, 1990, pp. 65 –70. [10] P. Synowiec, Hydraulic Operating Condition of the DTM Crystallizer, In: Z. Rojkowski (Ed.), Proceedings of the 12th Symp. on Ind. Crystallization, Poland Warsaw, 1993, 5/121– 126.
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[11] A. Mersmann, Hochschulkurs Kristallization aus Lo¨ sungen, Tech Univ, Munich, 1988. [12] J. Ploß, T. Tengler, A. Mersmann, Chem. Ing. Tech. 57 (6) (1985) 536 – 537. [13] A. Mersmann, R. Sangl, M. Kind, J. Pohlisch, Attrition and secondary nucleation in crystallizers, Chem. Eng. Technol. 11 (1988) 80. [14] H. Laufhu¨ tte, A. Mersmann, Local energy dissipation in agitated turbulent fluids and its significance for the design of stirring equipment, Chem. Eng. Tech. 10 (1987) 56 – 63. [15] Patent RP no. 166510, 1995.
How to improve the crystal size distribution (CSD) in crystallizers with the inner suspension circulation Piotr Synowiec * Department of Chemical and Process Engineering, Silesian Institute of Inorganic Chemistry, Gliwice, Poland Received 4 April 2001; received in revised form 3 October 2001; accepted 4 October 2001
Abstract An analysis of limited crystal growth in the crystallizer with inner suspension circulation has been studied. The new exhaustively theoretical analysis of crystal attrition sources, pumping effect and power input requirements, as well as the experimental investigations in concentrated suspensions have been done, respectively. In the light of collected theoretical and experimental evidence, in the Draft Tube Magma (DTM) crystallizers there are no significant possibilities for improvement of crystal size. The new constructional modification of DTM crystallizer was proposed for achieving better crystal quality. The new apparatus, with two coaxial draft tubes and partially hydraulic magma classification, makes possible to increase the mean crystal size up to 33%. The product efficiency from unit volume in this case is comparable with a DTM vessel. Moreover, the favorable conditions of crystal growth in a new crystallizer enable one to extend the residence time to 8 h, and because of that, to produce the crystals of the average size up to 1000 mm. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Crystallization; DTM crystallizer; Attrition; CSD
1. Introduction In industrial practice, the maximum mean size of crystals produced in the Draft Tube Magma (DTM) Crystallizers (Fig. 1), are limited to more or less 400 mm, and the maximum time of crystals growth does not exceed 3.5 h. Those practical parameters are determined by intensive solid phase attrition taking place during the inner suspension circulation created by means of the propeller located in the draft tube. Intensity of the circulation (pumping capacity) in the DTM apparatus for crystallization from solution is determinated by settled product capacity and supersaturation of solution, respectively. The mean source of crystal destruction, as it was admitted, has been generated mainly during crystal –impeller blade impacts. For the probability limitation of this kind of collision, the crystallizers with the low number of revolutions of the propeller or crystallizers with reduced power input have been proposed. Those innovations should have been favorable for the increase * Tel.: + 48-604-928-955; fax: + 48-32-237-1461. E-mail address: [email protected] (P. Synowiec).
of the mean crystal size. Although, the increase of particle size has been continually limited, the power-input reduction was significant. For better understanding the reasons of crystal destruction, the deeper analysis has been developed. In the light of this analysis another independent reason — turbulent attrition caused by liquid motion was predicted [1]. Considering the presence of the second destruction reason, it has enabled one to explain why only reduction of power input is not enough for the increasing of product quality.
2. Theory
2.1. The main sources of crystal attrition It is assumed in this work that the crystal attrition is caused by both independent sources, namely, the mechanical breaking forces (i.e. crystal –crystal, crystal – propeller, crystal –wall) and turbulent inducted breaking (i.e. shear stresses, drag stresses, pressure stresses).
0255-2701/02/$ - see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 2 5 5 - 2 7 0 1 ( 0 1 ) 0 0 1 7 8 - 7
P. Synowiec / Chemical Engineering and Processing 41 (2002) 585–593
586
However, the crystal– crystal and crystal– wall impacts have negligible effect on destruction [2,3]. For parent crystals larger than 200 mm the fluid-inducted stresses, by shear and pressure forces may also by negligible [1]. Thus, the total rate of secondary nucleation in the DTM crystallizer can by expressed by general form as follows: Bo,tot =Bo,im + Bo,turb
(1)
where Bo,im describes the rate of fine particle generation by means of crystal– impeller impact; and Bo,turb, the rate of fine fragments generation by turbulent drag forces. The components of each of these terms are described as follows: the effective intensity of stress, f %; the impact energy per unit energy needed to produce one fragment from crystal surface, E/e; the total number of parent particles in the crystallizer, nc. Thus
E Bo,im,turb =f % i nc ei
(2)
For crystal– impeller collisions, the effective intensity of stress is given by the relation: f %=
V: Q 1 L2 pT 8 o 2 4 m V Po s d m
(3)
The intensity of circulation, V: /V has been described by Parker [4] and the target efficiency, pT by Mersmann [5]. The maximum impact energy can by determined as kinetic energy of parent particles moving with velocity equal to tip speed, ut: 1 Eim = krL 3zcu 2t 2
(4)
The number of crystals in a unit volume of suspension is given by: nc =
k rL 3
(5)
Thus, the crystal– impeller secondary nucleation rate may be expressed by the following relation: Bo,im 8krL 5zc
Qo nc m Po eim
(6)
In the case of turbulent attrition, intensity of stress is equal to eddies fluctuation frequency, fe, described by Levich [6]: f %= fe = 0.258
m w
1/2
m w
1.4
(8)
where Zpd is the pressure drop caused by the difference between local motion of the fluid relative to that of the crystal [7].Whence
B0,turb 8 krL 6.6
m w
1.9
p − 0.8Dz 1.4z 0.4 l
nc eturb
(9)
Describing the effect of turbulent motion of the liquid on particle surface, the Kolmogorov theory of turbulence has been taken into consideration. The theoretical relation Eqs. (6) and (9) implies the stronger effect of particle size (5 or 6.6 exponent) on secondary nucleation rate than the unit power input (1 or 1.9 exponent). This relation explains why the reduction of power input is not a sufficient factor for the improvement of crystal size distribution. Analysing the theoretical and experimental effect of scale up on the secondary nucleation rate for geometrically similar vessels at constant power input, the following relation may be written [8]:
Bo,tot dm : 0.77 Bo,tot,lab dm,lab
−2
+ 0.23
(10)
It means that about 77% of the total destruction is generated by mechanical impacts, where the rest, i.e. 23% is caused by drag forces. The Eq. (10) implies additionally that the turbulent attrition rate is predicted to be independent from the vessel scale, when the mechanical component is rapidly decreasing in case of the increase of the crystallizer volume.
2.2. Pumping effect and power input reduction possibilities The pumping capacity required in the crystallizer is expressed by the following equation: V: =
G: c Dc
(11)
The propeller number of revolution indispensable for the required pumping capacity can be calculated from: V: =Qosd 3m
(12)
The unit power input necessary for obtaining the required number of revolution are given by: m=
P Pos 3d 5m = 8 Pos 3d 2m V Ms
(13)
assuming that V8d 3m and Ms = Vzs. Combining Eqs. (13) and (12) gives:
(7)
The respective energy of drag forces is described as:
Ed = VcDpd 8 krL 6.6p − 0.8Dz 1.4z 0.4 l
m8
1 2 Po V: s Qo dm
(14)
P. Synowiec / Chemical Engineering and Processing 41 (2002) 585–593
Relation Eq. (14) predicts that for obtaining the required pumping effect with simultaneously low power input the constructional solution of the system should be found (i.e. propeller– draft tube) in which the circulation is generated by means of a low rotating stirrer with a maximum acceptable diameter. Additionally the system should be characterized by a low value of the power number and a high value of the volumetric flow number. The practical aspects of these remarks have been discussed in details elsewhere [8– 10].
587
The last equation implies a very limited effect of reduction of the unit power input on the increase of mean crystal size. However, for example, a 40% reduction of m theoretically caused only the 12% increase of the mean particle size, but a significant m reduction gives notable savings of the production costs.
3. Investigations
3.1. Identification of attrition sources 2.3. Restricted increase of the mean particle size In light of the presented theoretical analysis concerning the sources of secondary nucleation rate in the DTM crystallizers, it has been clearly shown that reduction of the power input only is not a sufficient factor for the considerable improvement of the size of crystals produced. The point is how the power input reduction affects the increase of a mean crystal size. The theoretical dependencies Eqs. (6) and (9) can by simplified to the formula: Bo 8m 1 + 1.9L 5 + 6.6
The experiments concerning the sources of destruction have been carried out in the agitated vessel geometrically similar to the typical DTM crystallizer. Two vessels of volume 1.5×10 − 3 and 24×10 − 3 m3 have been investigated. The apparatus was equipped with the draft tube and the six-blade turbine. The geometrical relations of experimental setup, similar to that in use at present, has been shown in the paper [1]. The investigation principles have been described in the same work.
(15)
The experimental data, shown on the next pages, enables one to determinate the average value of exponents. Thus: Bo 8m 1.2L 5.25
(16)
A dependence between change of the unit power input, secondary nucleation rate and crystal size may be expressed as follows:
Bo,2 m : 2 Bo,1 m1
1.2
5.25
L2 L1
(17)
where m1 \m2. The formula Eq. (17) clearly shows that the reduction of the unit power input from m1 to m2 enables one to decrease the rate of secondary nucleation and increase the crystal size. Secondly, this limited increase of crystal size again influences the rise of the secondary nucleation rate (because the particle size is in the exponent of 5.25). Assuming that particle growth can last to the moment when the secondary nucleation rate reaches its previous level, a new condition may be written as: Bo,2 =1 Bo,1
(18)
what means that the maximum theoretical increase of crystal size in the DTM crystallizer caused by the power input reduction is equal to:
L2 L1
:
max
n
1 (m2/m1)1.2
0.19
=
m1 m2
0.23
(19) Fig. 1. Draft Tube Magma Crystallizer.
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P. Synowiec / Chemical Engineering and Processing 41 (2002) 585–593
Fig. 2. Dependence of secondary nucleation rate on unit power input generated in laboratory scale vessel.
Fig. 3. Dependence of secondary nucleation rate on crystal size generated in laboratory scale vessel.
Crystals of potassium sulfate K2SO4 and potash alum KAl(SO4)2 · 12H2O were used during the tests, respectively. The volumetric solid phase concentration in the range of 0.03–0.17, unit power input 0.4– 1.5 W kg − 1 and parent crystal size of 100– 900 mm have been studied. The crystal attrition sources interact and complete with each other. For that reason two assumptions have been made: (i) the turbulent secondary nucleation rate is achieved by means of the rubber coated stirrer; (ii) the minimum crystal–impeller impact secondary nucleation
rate is a difference between total secondary nucleation rate caused by the steel turbine and the rubber coated stirrer. The majority of fines produced in each run were observed to be in the size range 3–25 mm, with no significant changes of the mean parent particle size after a 2-h test. The ratio between the initial and final particle size after each run was in the range 0.99–0.95, what indicates that crystal destruction has mainly a surface character.
P. Synowiec / Chemical Engineering and Processing 41 (2002) 585–593 Table 1 Predicted and observed dependence on secondary nucleation rate simplified to the formula Bo 8 L am b a
b
Impact (crystal–turbine) Exponent Eq. (6) 5 Slope of regression line 4.99–5.01 (Fig. 2)
1 1.06–1.10 (Fig. 1)
Turbulence (drag stress) Exponent Eq. (9) 6.6 Slope of regression line 6.11–6.26 (Fig. 2)
1.9 1.82–1.98 (Fig. 1)
In order to determine the main reason for crystal attrition, after specially prepared tests, the regression line, based on experimental data, have been plotted. The slope of each regression line has been compared with adequate theoretical exponents in Eqs. (6) and (9), (Figs. 2 and 3). Replacing, at a constant power input, the stainless steel turbine with the rubber coated stirrer, the secondary nucleation has been reduced by about 77% in case of K2SO4 and KAl(SO4)2 · 12H2O.
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Additionally, an increase in the dependence of a number of attrition fines on the unit power input was observed using the rubber coated turbine (exponents 1.98 and 1.82) in place of the steel impeller (exponents 1.18 and 1.21), Fig. 3, thus confirming the increased proportion of the turbulent drag attrition contribution. Successive confirmation of the presence of two independent destruction sources, are focused the investigations on the effect of crystal size on the attrition rate. The secondary nucleation rate, Bo, has been recalculated as the average number of fine particles generated in unit time per parent crystal, B %o, because for constant the number of parent particles in the vessel decreased proportionally as the parent crystal size, L increased. The result of comparison between theoretically, as well as experimentally determined exponents of the particular variables are collected in the Table 1. The theoretical relation Eq. (10) describing the effect of scale-up on secondary nucleation changes has been tested in two additional vessels, i.e. 24 l and 9 m3, respectively. The results are shown in Fig. 4. The difference between theoretical curves and experimental data are less than 6%.
Fig. 4. Effect of scale-up factor (dm/dm,lab) on secondary nucleation rate for constant power input. Table 2 Comparison of experimental and calculated values of the effect of the unit power input on a mean crystal size and secondary nucleation rate
KAl(SO4)2 · 12H2O KAl(SO4)2 · 12H2O KAl(SO4)2 · 12H2O KAl(SO4)2 · 12H2O KNO3 KCl (NH4)2SO4
m2/m1
Lmi2/Lmi1
Bo,2/Bo,1 Experimental
Bo,2/Bo,1 Calculated
D (%)
Reference
0.333 0.667 0.50 0.575 0.315 0.143 0.255
1.172 1.077 1.088 1.104 1.194 1.185 1.262
0.653 0.920 0.706 0.748 0.717 0.269 0.740
0.615 0.908 0.678 0.864 0.634 0.236 0.658
−5.8 −1.3 −4.0 15.5 −11.5 −12.2 −11.0
[5] [11] [12,13]
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Fig. 5. Double Draft Tube Crystallizer.
3.2. Effect of reduction of the unit power input on the mean crystal size The experimental verification of relation Eq. (19) has been performed in the MSMPR crystallizer. Some data published by Mersmann [5,11– 13] has been also employed. Only the data obtained for the same value of the supersaturation of solution and the same residence time but for the different unit power input has been taken into consideration. The results are presented in Table 2 The calculated values of the ratio Bo,2/Bo,1 are very close to the measured ones. The maximum error between these compared results amounts only to 15.5%. The collected experimental material testifies to a very weak effect of the reduction of the unit power input on a crystal size increase in the crystallizers with inner suspension circulation. The strong destruction during magma circulation in the DTM crystallizers are caused by crystal– impeller impacts in small scale, and by turbulent drag stresses in
large scale, respectively. The second source of destruction is particularly effective in the area of a rotating stirrer located in the draft tube, as unit power input distribution is not homogeneous in the whole vessel volume. In the light of Mersmann’s work [14], in this place of apparatus the local unit power input is about ten times higher than the average value, admitted in the discussed equations. The second independent source of destruction-liquid turbulence, existing next to the mechanical one, explains why in the case of scaling-up, when the target efficiency of impacts is rapidly decreasing, the secondary nucleation rate does not decline simultaneously so quickly. Independence of the turbulent drag forces from the apparatus volume and the inhomogeneous power input distribution keep the secondary nucleation rate still on a relatively high level, particularly when magma circulation is kept going through the draft tube. All of the listed premises exclude the possibilities of a prominent increase of the crystal size without constructional changes of the apparatus, usually modifying a circulation of suspension. Taking into consideration the high level of crystals destruction and a limited CSD improvement in the DTM apparatus, the new constructional modification named the Double Draft Tube (DDT) crystallizer has been worked out [15] (Fig. 5). The DDT solution includes two coaxial draft tubes and the opposite direction of suspension flow in relation to the DTM. The hydraulic classification of suspension takes place in the upper part of the vessel. Small amount of slurry hits to the central draft tube while remaining part of particles is aimed to a space between the central and exterior draft tube, respectively. The comparative experiments were carried out in the continuously working plant of total volume equal to 0.2 m3. When about 30 –40% of crystals circulated through the central draft tube and other part of grains were held in the zone between the central draft tube and vessel jacket the satisfying mean crystal size increase has been observed. Such conditions of flow have given the comparable product efficiency from cubic meter of apparatus in the DDT, as well as in the DTM crystallizer and made possible to protect the majority of growing crystals against increased level of attrition located in the space surrounding the stirrer. The results of investigations focused on sodium chloride as well as ammonium sulfate crystallization are presented in Fig. 6a and b, respectively. During experiments the supersaturation of solution and the residence time in both apparatus have been kept on the constant level as well. On the average mean crystal size obtained in the DDT crystallizer has been bigger than 33– 36% in comparison to that produced in the DTM, when the proportion of magma hydraulic separation was the same as mentioned above.
P. Synowiec / Chemical Engineering and Processing 41 (2002) 585–593
The better conditions of crystal growth in the crystallizer discussed enable one to extend the residence time up to 8 h and the production of crystals in the range of 600–1000 mm, Fig. 6a. Additionally, the mass distribution versus particle size, Fig. 6b, shows the practical absence of particles below 60 mm in the slurry withdrawn from the DDT crystallizer. Comparing the shape of sodium chloride crystals from the DTM and DDT crystallizer, the intensity of attrition in the first case may be easily estimated, Fig. 7.
4. Conclusion In the light of theoretical, as well as experimental evidence, in the crystallizers with an inner suspension
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circulation there are no significant possibilities for improvement of a crystal size only by means of the power input reduction. The presented analysis clearly shows two independent sources of the crystal attrition, i.e. crystal-stirrer impacts and turbulent drug forces. In small scale, the first reason of destruction has got a significant effect on crystal destruction. When a volume of crystallizer increases, the importance of mechanical impact declines, and turbulence acting on a particle surface is mainly responsible for crystal attrition. The experimental results are consistent with theoretical relations. The area of exceptional intensive particle breakage, for both sources, is located inside the draft tube, in the area when the propeller is rotating, or the local values of unit power input distribution are the highest. This
Fig. 6. Comparison of: (a) median crystal size Lmi vs. residence time t; (b) particle density distribution q3 in the DTM and DDT crystallizers. (The experiments have been curried out in the 0.2 m3 continuously working pilot plant).
P. Synowiec / Chemical Engineering and Processing 41 (2002) 585–593
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kv L M nc Po Qo s t ut = ^dms V: V q3 = mi /(mtotDL) m p pT z Dz = zc−zd Dc D= ([cal]−[exp]) /[exp]100
Fig. 7. Sodium chloride crystals withdrawn from: (a) DTM and (b) DDT apparatus.
reason makes impossible a significant improvement of CSD without changes of the way of a forced magma circulation. The DDT crystallizer proposed allows to protect mean stream of the circulated crystals against the zone with the highest destruction intensity, simultaneously keeping the simplicity of construction. That is why the significant increases of mean particle size were observed. Moreover, the effective reduction of stress intensity permits the application of the DDT for production of crystals in the range of 600– 1000 mm with the residence time up to 8 h, respectively.
Appendix A. Nomenclature Bo dm e, E G: f%
secondary nucleation rate (m−3·s−1) impeller diameter (m) energy (J) mass flow (kg s−1) effective intensity of stress (s−1)
Indices c mi cal o f rub im s exp st lab tot m turb
volumetric shape factor crystal size (m) mass (kg) number of particles (m−3) power number volumetric flow number impeller speed of rotation (s−1) residence time (s) tip speed (m s−1) pumping capacity (m3 s−1) volume (m3) mass fraction (kg kg−1·m−1) unit power input (W kg−1) dynamic viscosity (Pa s) target efficiency density (kg m3) zl (kg m−3) solution supersaturation (kg m−3) volumetric solid phase concentration in suspension error (%)
Crystal Mean Calculated Initial Fluid Rubber Impact Suspension Experimental Steel Laboratory Total Stirrer turbulent
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P. Synowiec / Chemical Engineering and Processing 41 (2002) 585–593 [8] P. Synowiec, Taking a new look at crystals attrition phenomenon in crystallizers with suspension circulation, Wrocław Tech. Univ., Press 66/41, Wrocław 1998. [9] P. Synowiec, R. Sangl, Selected Problems of the Hydrodynamics in a Draft Tube Crystallizer, In: A. Mersmann (Ed.), Proceedings of the 11th Symp. on Ind. Crystallization, Germany Garmisch-Partnerkirchen, 1990, pp. 65 –70. [10] P. Synowiec, Hydraulic Operating Condition of the DTM Crystallizer, In: Z. Rojkowski (Ed.), Proceedings of the 12th Symp. on Ind. Crystallization, Poland Warsaw, 1993, 5/121– 126.
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[11] A. Mersmann, Hochschulkurs Kristallization aus Lo¨ sungen, Tech Univ, Munich, 1988. [12] J. Ploß, T. Tengler, A. Mersmann, Chem. Ing. Tech. 57 (6) (1985) 536 – 537. [13] A. Mersmann, R. Sangl, M. Kind, J. Pohlisch, Attrition and secondary nucleation in crystallizers, Chem. Eng. Technol. 11 (1988) 80. [14] H. Laufhu¨ tte, A. Mersmann, Local energy dissipation in agitated turbulent fluids and its significance for the design of stirring equipment, Chem. Eng. Tech. 10 (1987) 56 – 63. [15] Patent RP no. 166510, 1995.