- Email: [email protected]
Nucleation, growth and aggregation kinetics of monosodium aluminate hydrate from unseeded sodium aluminate solution
Journal of Crystal Growth 525 (2019) 125210
Contents lists available at ScienceDirect
Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro
Nucleation, growth and aggregation kinetics of monosodium aluminate hydrate from unseeded sodium aluminate solution ⁎
T
⁎
Bingxin Zhoua,c, Shaotao Caoa, , Shaowei Youa, , Fangfang Chena, Fangfang Zhanga, Bo Lib, Yi Zhanga a Key Laboratory of Green Process and Engineering, and National Engineering Laboratory for Hydrometallurgical Cleaner Production Technology, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China b Coalmine Alumina Co. Ltd, Sanmenxia 472100, Henan Province, China c School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China
A R T I C LE I N FO
A B S T R A C T
Communicated by Gen Sazaki
The crystallization of monosodium aluminate hydrate (MAH) from sodium aluminate solution is the key step in the hydro-chemical process for treating Bayer red mud. The nucleation, growth and aggregation kinetics of MAH from unseeded sodium aluminate solution with low supersaturation was studied. It was found that the increase of temperature or the decrease of initial αk (molar ratio of Na2O and Al2O3 in aluminate solution) could lead to the increase of average crystal size while the increase of agitation speed had an adverse effect. The growth rate, the nucleation rate and the aggregation kernel were determined using a volume-independent growth aggregation model. The calculation of aggregation kernel was divided into two parts in terms of crystal size: smaller than 10 μm and larger than 10 μm. Results implied that small crystals below 10 μm aggregated more significantly than large crystals. The aggregation dominated the enlargement of small crystals, but the enlargement of large crystals mainly stemmed from the growth rather than the aggregation.
Keywords: A1. Nucleation A1. Growth A1. Aggregation A1. Alumina production B1. Monosodium aluminate hydrate
1. Introduction The crystallization of monosodium aluminate hydrate (MAH) from the leaching liquor of Bayer red mud, a median step in the hydrochemical process for alumina production, is the key technology to recover aluminum and sodium from Bayer red mud [1,2]. Previous studies on MAH crystallization have been focused on the precipitation, nucleation, morphology and crystallization kinetics of MAH from concentrated sodium aluminate solution with high supersaturation [1,3–8]. However, the study on MAH crystallization from sodium aluminate solution with low supersaturation has rarely been reported. Sodium aluminate solution with low supersaturation is generally encountered in the hydro-chemical process when Bayer red mud is treated. The study is of great significance to the recovery of aluminum and sodium from Bayer red mud in the hydro-chemical process. The study of nucleation, growth and aggregation kinetics is important to control the crystal size distribution (CSD), as well as to improve the efficiency of liquid-solid separation in the industrial production [9–11]. The crystallization kinetics is usually investigated either with a continuous crystallizer or with a batch crystallizer. A continuous process, such as the mixed suspension and mixed product
⁎
removal (MSMPR) process, needs the achievement of steady state that demands long experimental time, large amount of raw materials and complex operation. In contrast, the batch crystallizers are simple, flexible, require less investment and involve less process development, and they are especially suitable for the crystallization systems which demand long residence time [12,13]. As the crystallization of MAH from low supersaturated solution requires long residence time during the industrial production in the hydro-chemical process, a batch system is a better match to the industrial process of MAH crystallization. Moreover, the kinetics of MAH crystallization in a batch crystallizer has not yet been reported in literatures, although the kinetics of MAH crystallization in the MSMPR crystallizer has been investigated. This research focused on the nucleation, growth and aggregation kinetics of MAH from the low supersaturated sodium aluminate solution in a batch crystallizer. Effects of crystallization parameters on CSD, crystallization yield and crystal morphology were discussed in detail. Kinetic parameters including the nucleation rate, growth rate and aggregation kernel were calculated according to the population balance equation. The study will have fundamental significance in hydro-chemical process for alumina production when Bayer red mud is treated.
Corresponding authors. E-mail addresses: [email protected] (S. Cao), [email protected] (S. You).
https://doi.org/10.1016/j.jcrysgro.2019.125210 Received 16 May 2019; Received in revised form 8 August 2019; Accepted 26 August 2019 Available online 26 August 2019 0022-0248/ © 2019 Elsevier B.V. All rights reserved.
Journal of Crystal Growth 525 (2019) 125210
B. Zhou, et al.
Nomenclature B B0 C C0 D G Gv k ka kV L MT MTotal n Ni
the moment Q inflow rate, m3/s R gas constant, 8.314 J∙mol−1∙K−1 R2 correlation index S supersaturation T crystallization temperature, K t crystallization time, s V suspension volume, m3 V0 slurry volume of the initial solution, m3 w i% mass percentage ka, kb, Ka rate coefficients
birth function, no. m−3∙m−1∙s−1 nucleation rate, no. m−3∙s−1 solute concentration, g∙L−1 solute concentration of the initial solution, g∙L−1 death function, no. m−3∙m−1∙s−1 linear particle growth rate, m∙s−1 volume growth rate, m−3∙s−1 kth stream aggregation kernel, s−1 volumetric shape factor crystal size, μm suspension density, g∙L−1 total mass of the initial solution, g population density, no. m−3∙m−3 the number of crystals corresponding to v¯i at the time of
Greek Letters αk molar ratio of Na2O and Al2O3 solution density, g∙L−1 ρs α, β, γ, δ, ε, θ, μ, σ kinetic orders
2. Materials and methods
radiation. The CAl2O3 and CNa2O in sodium aluminate solutions were determined by the titration method. The crystallization yield of MAH from the supersaturated solution was calculated based on the mass conversion as follows:
2.1. Materials Sodium hydroxide (NaOH) and aluminum hydroxide (Al(OH)3) were of analytical grade (AR) and purchased from Beijing Chemical Industry Co Ltd.. The ultrapure water with the resistivity of 18.2 MΩ∙cm−1 was used in all experiments.
⎧ MAl2O3 − mAl2O3 = CAl2O3 × V1 209 ⎨ MTotal − 102 ×mAl2O3 = ρ1 × V1 ⎩
where the MAl2O3 was the initial total mass of Al2O3 in the solution (g), mAl2O3 was the quantity of the crystallized alumina (g), CAl2O3 was the concentration of alumina left in the filtrate after crystallization (g/L), V1, MTotal and ρ1were the volume (L), the total mass of the initial solution (g) and the density of the filtrate after crystallization (g/L), respectively. The crystallization yield could be expressed as follows:
2.2. Experimental methods The sodium aluminate solutions were made by the dissolution of aluminum hydroxide in sodium hydroxide solution to simulate the composition of leaching solution in the hydro-chemical process for treating red mud. NaOH, Al(OH)3 and pure water with a certain proportion were added to a nickel tank. The tank was heated by an electric furnace to solution boiling until solution was visually clear. The prepared solutions were filtered to obtain optically clear solutions. Experiments were carried out in a 300 mL jacketed stainless-steel crystallizer with Teflon lining, along with a Teflon impeller driven by a dynamoelectric agitator. The crystallizer was covered with a transparent plexiglass lid, and the temperature of the solution was controlled within ± 0.5 K by the circulating water heated by a thermo-stated bath to the crystallizer jacket. The time was recorded when the first visible crystals appeared [14]. Slurry samples were withdrawn from the crystallizer at different times, filtered immediately and washed with anhydrous ethanol. The crystals were dried for further analysis, and the filtrate was analyzed to determine the concentrations of Na2O and Al2O3. The operating experimental conditions of MAH crystallization are listed in Table 1. Repeated experiments were carried out to ensure the reproducibility at the same experimental conditions. The αk was the molar ratio of Na2O and Al2O3 in the sodium aluminate solution, expressed as:
αk =
CNa2O 102 × CAl2O3 62
(2)
Crystallization yield =
mAl2O3 × 100% MAl2O3
(3)
3. Results and discussion 3.1. Crystal characterization As shown in Fig. 1, results from XRD indicate that the crystals obtained under different experimental conditions are all identified as Na2O∙Al2O3·2.5H2O and the intensity differences in the reference and experimental patterns can be attributed to preferred orientation of the samples [3]. All population density distribution curves of MAH crystals exhibit the same trend. A typical population density distribution of MAH crystals is shown in Fig. 2. It can be seen from Fig. 2 that the population density curve exhibits two parts: an upward curve and a downward curve, and the boundary can be set as 10 μm according to the summary of experimental data. The behavior of small crystals presenting lower populations has also been discovered in other researches. Some researchers took this behavior as the result of the limitations of image analysis and neglected it because of the low percentage of crystals in the small size range [15]. However, it is apparently
(1)
Table 1 Conditions of MAH crystallization in a batch crystallizer.
2.3. Analytical methods The CSDs of crystals were measured with a Malvern Mastersizer 2000MU (instrument error, ± 3%) after dispersed in anhydrous ethanol, and the obtained CSD data was the average value of three measurements. The morphology of samples was analyzed by scanning electron microscopy (SEM, JSM-7001F, JEOL, Japan) and the solids were identified by X-ray diffraction patterns (XRD, X’pert MPD Pro, PanAnalytical, Netherlands) recorded with Cu Kα (λ = 0.15408 nm) 2
Parameters
Value (s)
Crystallization volume (mL) Agitation speed (rpm) Temperature (K) Na2O concentration (CNa2O, g/L) Al2O3 concentration (CAl2O3, g/L) Initial αk
200 200–500 319–353 540 55.52–111.04 8–16
Journal of Crystal Growth 525 (2019) 125210
B. Zhou, et al.
Fig. 4. CSDs of MAH crystals obtained at different agitation speeds (αk = 13, 323 K, t = 15 h).
This behavior is proved by Fig. 3 and it is discussed in Section 3.3.3. As is shown in Fig. 3, MAH crystals are truncated quadrangular orthopyramid crystals and small aggregated crystals. The resultant crystals have a different morphology from crystals obtained in a continuous process that are mainly spherical agglomerate crystals [5].
Fig. 1. XRD pattern of crystals crystallized from sodium aluminate solutions.
3.2. Effect of parameters
Fig. 2. Typical population density distribution of MAH crystals.
3.2.1. Effect of agitation The crystal size decreases with increasing agitation speed, as shown in Fig. 4. The volume average size of crystals decreases from 58.728 μm to 34.259 μm when the agitation speed increases from 200 rpm to 500 rpm. With the increase of agitation speed, particle collisions, including crystal-crystal contacts and crystal-agitator contacts, become more frequently. Particle collisions are important contributors to the formation of a large number of small crystalline fragments. Secondary nuclei are crystalline fragments that are the result of breakage and attrition caused by particle collisions. The second nucleation is promoted with the increase of agitation speed. Therefore, the average size of crystals is reduced.
unsuitable for this study because the crystals are large enough to be counted clearly. Some researchers took this behavior as the result of aggregation of small crystals but no further investigations were conducted [16]. Here, the decreasing population density in the small size range is attributed to the intense aggregation behavior of small crystals.
3.2.2. Effect of temperature As shown in Fig. 5, the crystal size increases as the temperature rises from 319 K to 353 K. It can be explained that the increase of temperature leads to the decrease of supersaturation, reducing the nucleation rate of particles and increasing the growth rate [17,18]. Moreover,
Fig. 3. Typical SEM images of MAH crystals (T = 323 K, 350 rpm, t = 15 h). 3
Journal of Crystal Growth 525 (2019) 125210
B. Zhou, et al.
crystallizer: (1) the solution is fully mixed; (2) there is no stratification at withdrawal [24]. Therefore, the population balance equation can be simplified as follows [19,25]:
∂n ∂ (Gn) dln V + +n =B−D ∂t ∂t dt
(8)
In a batch crystallizer, the mass balance equation can be shown as follows: (9)
(C (t) + MT (t)) × V (t) = V0 × C0
where C is the solute concentration (g∙L−1), MT is the suspension density (g∙L−1). Both sides are differentiated with respect to time, and then the equation can be changed into:
−
{
dC dln V + (C + MT ) × dt dt
}
=
dMT (t) dt
(10)
The growth rate models for the crystallization systems include the size-independent growth rate models, size-dependent growth rate models, aggregation models and growth rate dispersion models et al. [26]. It can be seen from Fig. 2 that the size-independent growth rate models and size-dependent growth rate models are inappropriate for this study due to the small upward curve of small crystals. It can be assumed that the aggregation models are more appropriate than the growth rate dispersion models according to the aggregation behavior of small crystals as shown in Fig. 3. Therefore, expressions of effective growth rate and nucleation rate are obtained using a volume-independent growth aggregation model based on the moment transformation method [19,27,28]:
Fig. 5. CSDs of MAH crystals obtained at different temperatures (αk = 13, 350 rpm, t = 15 h).
crystal growth tends to be diffusion controlled at high temperature and integration controlled at low temperature [19]. High temperature can also reduce the viscosity of the aluminate solution. The decrease of the viscosity increases the rate of diffusion at high temperature, which promotes the growth of MAH crystal. Therefore, the crystal size is increased at high temperature. 3.2.3. Effect of initial αk As shown in Fig. 6, the crystallization yield decreases with the increase of initial αk (see Eq. (1)) and remains unchanged after 15 h of crystallization, except for the crystallization with initial αk of 16. The increase of initial αk shows that the concentration of Al2O3 decreases and the initial supersaturation of the aluminate solution is reduced [20]. Thus, the crystallization yield of MAH is decreased when the initial αk increases. As shown in Fig. 7 and Table 2, the CSD narrows with the decrease of initial αk, together with the decrease of volume average crystal size and span. The range of the initial supersaturation is from 1.7 to 3.4. Although this range of the initial supersaturation is low for the Na2O-Al2O3-H2O system, the increase of the initial supersaturation still promotes the nucleation. This results in the formation of large number of small crystals, which finally decreases the average crystal size. The d0.1 is 23.777 μm at supersaturation 3.4, greater than 18.680 μm at supersaturation 1.7. The increase of d0.1 is probably caused by the aggregation of large number of small crystals at high supersaturation.
− Gv (t) =
=
ρs kV ∗
{
dC dt
k ∑i = 1
{
dC dt
+ (C + MT ) ∗
ρs kV ×
}
(vi ∗ n i (v¯i, t ) − (vi + 1 − vi ) ∗ n i (v¯i, t ))
+ (C + MT ) × k ∑i = 1
dlnV dt
dlnV dt
}
(vi + 1 × (v¯i, t ))
(11)
B0 = n 0 × Gv ≈ n (v¯min, t ) × Gv
(12) −3 −1
where Gv is the volume growth rate (m ∙s ), ρs is the solution density (g∙L−1), k v is the volumetric shape factor. It is assumed that the volumetric shape factor is constant in order to simplify the calculation. The population densities of minimal crystals obtained in the measurements are treated as that of crystal nucleus [19]. The Eq. (8) is integrated in the range of particle volume from zero to infinity, and gives
3.3. Crystallization kinetics According to the crystal size distribution of the obtained crystals, kinetic parameters including the growth rate, nucleation rate and aggregation kernel are calculated and regressed using the population balance equation. The general population balance equation proposed by Randolph and Larson can be expressed as follows [9]:
d (logV ) ∂n ∂ (Gn) + +n =B−D− dt ∂t ∂L
∑ k
nk Q k V
(7)
where V is the suspension volume (L), L is the crystal size (μm), n and nk are population density and slurry population density of outflow at size L (no. m−3∙m−1) respectively, Q is the volumetric flow rate (m3∙s−1), k is the kth stream, G is the linear particle growth rate (m∙s−1), B and D represent birth and death functions (no. m−3∙m−1∙s−1), and t is crystallization time (s). As the experiments are conducted in a batch crystallizer, Qk can be set equal to zero. There are some general assumptions for a batch
Fig. 6. Crystallization yields of MAH at different initial αk (T = 323 K, 350 rpm, t = 15 h). 4
Journal of Crystal Growth 525 (2019) 125210
B. Zhou, et al. vi + 1
∫ vi
∂ (Gv n) ΔNi dv ≈ Gv × ∂t vi + 1 − vi
(16)
vi + 1
Ni (t) =
∫ n (v, t )dv ≈ n (v¯i, t ) × (vi+1 − vi)
(17)
vi
(Ni (t) represents the number of particles corresponding to v¯i ). The right side of Eq. (13) can be changed into [26,27,29,30]: vi + 1
∫ vi
{
ka 2
vi
∫0
n (v − u) n (u) du − ka n (v )
∫0
v max
}
n (u) du dv (18)
Then the formula of the aggregation kernel ka can be expressed as follows: i=n
ka = Fig. 7. CSDs of MAH crystals obtained at various initial αk (323 K, 350 rpm, t = 15 h).
S1
8 10 13 16 1
S=
3.41 2.73 2.10 1.70
S
is
CAl2o3 C∗ Al2O3
d0.1
d0.5
23.777 18.951 19.784 18.680
36.147 34.209 36.994 37.587
d0.9 54.015 54.641 64.561 68.194
D[4,3]2 37.773 38.692 39.804 40.807
0.84 1.04 1.21 1.31
the initial supersaturation of the solution, expressed as: (4). In which the calculation of the C*Al2O3 is based on the solu-
B 0 = kb ×
MTγ
∑ di4 ∑ di3
ka = K a ×
S∊
θ
× Gv × B0
Span is used to reflect the width or the spread of crystal size distribution,
(19)
(20) (21)
μ
(22)
3.3.1. Growth rate The regressed correlation of growth rate is expressed as
Gv = 5.1346 × 10−25exp ⎛ ⎝
3
+ Ni ∑ Nj)
× Sδ
bility data of aluminum hydroxide in the Na2O-Al2O3-H2O system [21–23]. D[4,3] is the volume mean size, expressed as: D4,3 =
ΔNi ) vi + 1 − vi
−E ⎞ × MTα × S β Gv = k g × exp ⎛ ⎝ RT ⎠
Span3
2
Gv ×
The calculated kinetic parameters including the growth rate, nucleation rate and aggregation kernel under different crystallization conditions are fitted according to the empirical power-law expressions [26,30–33].
Table 2 CSDs of MAH crystals obtained at different initial αk (T = 323 K, 350 rpm, t = 15 h). Initial αk
ΔNi dlnV + Ni × dt + Δt i=n ∑i = 1 (0.5 × ∑ (Nm Nj)
∑i = 1 (
(5)
−3493.483 ⎞ × MT0.698 × S 0.498 RT ⎠
R2 = 0.949 (23)
The calculated growth rates range from 9.27 × 10−23 to 5.29 × 10−22 (m−3∙s−1) Fig. 8, and they are lower than the growth rates of MAH in an MSMPR crystallizer which have the order of magnitude of 10−20–10−19 (m−3∙s−1) [6]. The low growth rate can be attributed to the small driving force for crystallization at low supersaturations. The exponent of supersaturation is 0.498, while that of suspension density is 0.698, indicating that the growth rate depends more on the change of suspension density than that of supersaturation. 3.3.2. Nucleation rate The nucleation rates are correlated as a function of suspension density MT and supersaturation S by means of nonlinear regression, as shown in Fig. 9. MT and S is related to the secondary nucleation and primary nucleation, respectively. Therefore, B0 represents the apparent nucleation rate. The regressed result is expressed by Eq. (24):
B0 = 6.482 × MT0.4 × S 0.895
Fig. 8. Growth rate correlation. ∞
∞
∞
∞
0
0
0
0
∂ (Gv n) dv + ∫ dv = ∫ (Ba − Da ) dv ∫ ∂∂nt dv + ∫ n dlnV dt ∂t
∫ vi
∂n dNi ΔNi dv = ≈ ∂t dt Δt
(13)
(14) 3.3.3. Aggregation kernel The population density curve shows a sharp upward trend in the range of smaller than 10 μm (Fig. 2), and it is speculated that this behavior is derived from the intense aggregation of small crystals. Therefore, the calculation of aggregation kernel is divided into two
vi + 1
∫ n dlndtV dv = Ni dlndtV vi
(24)
The exponent of suspension density in nucleation rate expression is 0.4, and that of supersaturation is 0.895. The order of supersaturation is greater than that of suspension density, implying that the primary nucleation is dominant in this system. It is because the solutions are of relative low supersaturations and no seeds are added during the crystallization process. In the early stage of the crystallization, primary particles are formed. These primary particles collide with each other to form aggregates during their growth.
The left side of Eq. (13) is simplified as follows: vi + 1
R2 = 0.998
(15) 5
Journal of Crystal Growth 525 (2019) 125210
B. Zhou, et al.
ka = 9.948 × 10 41 × S 2.9353 × Gv 2.8167 × B0 0.00045
R2 = 0.960
(25)
For crystals larger than 10 μm, the experimental aggregation kernel has the order of magnitude of 10−28–10−26, and the value is much lower than the value of growth rate. The result implies that the crystal growth is more important for the enlargement of large crystals than the aggregation, and the aggregation of large crystals is negligible. The enhancement of the crystal size of MAH in this work is different from the MAH crystals obtained in the MSMPR crystallizer where crystal enlargement is mainly derived from crystal growth, rather than aggregation [6]. 4. Conclusions Nucleation, growth and aggregation kinetics of MAH from unseeded highly caustic aluminate solution with low supersaturation in a batch crystallizer was studied using a volume-independent growth aggregation model. Effects of parameters were also analyzed in detail. Temperature and initial αk had a positive effect on the growth of MAH crystal, but the agitation speed had an adverse effect. MAH had a slow growth rate due to the low supersaturation. The calculation of aggregation kernel was divided into two parts with crystal size of 10 μm as the boundary. It was found that small crystals below 10 μm aggregated more significantly than large crystals. The aggregation dominated the enhancement of the size of small crystals, but the growth was responsible for the enlargement of large crystals.
Fig. 9. Nucleation rate correlation.
Declaration of Competing Interest The authors declared that there is no conflict of interest. Acknowledgements This research was funded by the National Natural Science Foundation of China (No. 51674233), the Henan Transfer Project of CAS Scientific and Technological Achievements (No. 2019103), the Guangxi Natural Science Foundation (No. 2016GXNSFEA380002), the Shanxi Province Coal Based Low-carbon Technology Major Projects (No. MC2016-05), and Major Science and Technology Program for Water Pollution Control and Treatment (2018ZX07402005).
Fig. 10. Aggregation kernel correlation of crystals smaller than 10 μm.
References [1] S.T. Cao, Y.F. Zhang, Y. Zhang, Preparation of sodium aluminate from the leach liquor of diasporic bauxite in concentrated NaOH solution, Hydrometallurgy 98 (2009) 298–303. [2] L. Zhong, Y.F. Zhang, Y. Zhang, Extraction of alumina and sodium oxide from red mud by a mild hydro-chemical process, J. Hazard. Mater. 172 (2009) 1629–1634. [3] S.T. Cao, Y.F. Zhang, Y. Zhang, Nucleation and morphology of monosodium aluminate hydrate from concentrated sodium aluminate solutions, Cryst. Growth Des. 10 (2010) 1605–1610. [4] S.W. You, Y.F. Zhang, S.T. Cao, F.F. Chen, Y. Zhang, Crystallization of monosodium aluminate hydrate from a concentrated aluminate solution containing silica, Hydrometallurgy 115–116 (2012) 104–107. [5] S.W. You, T. Guo, P.F. Liu, X. Mao, Y.F. Zhang, Precipitation of monosodium aluminate hydrate from concentrated sodium aluminate solution, Hydrometallurgy 183 (2019) 125–129. [6] S.W. You, Y.F. Zhang, S.T. Cao, F.F. Chen, Y. Zhang, Crystallization kinetics of monosodium aluminate hydrate in concentrated sodium aluminate solutions, Ind. Eng. Chem. Res. 51 (2012) 7736–7741. [7] V.S. Sazhin, The crystallization of sodium aluminate, China Industry Press, Beijing, 1964. [8] V. Rayzman, I. Filipovich, L. Nisse, Y. Vlasenko, Sodium aluminate from aluminabearing intermediates and wastes, JOM 50 (1998) 32–37. [9] A.D. Randolph, M.A. Larson, Theory of particulate processes, analysis and techniques of continuous crystallization, New York, 1971. [10] A. Vancleef, S. Seurs, J. Jordens, T. Van Gerven, L.C.J. Thomassen, L. Braeken, Reducing the induction time using ultrasound and high-shear mixing in a continuous crystallization process, Crystals 8 (2018) 326. [11] J. Jordens, E. Canini, B. Gielen, T. Van Gerven, L. Braeken, Ultrasound assisted particle size control by continuous seed generation and batch growth, Crystals 7 (2017) 195. [12] J.B. Rawlings, S.M. Miller, W.R. Witkowski, Model identification and control of
Fig. 11. Aggregation kernel correlation of crystals larger than 10 μm.
parts: aggregation kernel in the range of smaller than 10 μm and that of larger than 10 μm. As shown in Figs. 10 and 11, the experimental aggregation kernels in the range of smaller than 10 μm have the order of magnitude of 10−18–10−20 that are much higher than the order of magnitude of 10−28–10−26 of crystals larger than 10 μm. The value of aggregation kernel below 10 μm is greater than the value of growth rate which has the order of magnitude of 10−23–10−22. It can be concluded that small crystals aggregate more significantly than large crystals and the aggregation is responsible for the enlargement of small crystals. The correlated expression aggregation kernel of crystals smaller than 10 μm is shown as follows:
6
Journal of Crystal Growth 525 (2019) 125210
B. Zhou, et al.
[13]
[14] [15]
[16]
[17]
[18]
[19] [20] [21] [22]
[23] S.T. Cao, Applied and fundamental research for crystallization of monosodium aluminate hydrate. Beijing, 2010. [24] T. Guo, S.W. You, B. Yang, S.T. Cao, Y. Zhang, Crystallization kinetics of Na2CO3 in Bayer aluminate solutions during the evaporation process, CrystEngComm 20 (2018) 3722–3727. [25] X. Zhang, G. Qian, X. Zhou, Kinetic modeling on batch-cooling crystallization of zinc lactate: The influence of malic acid, J. Cryst. Growth 463 (2017) 162–167. [26] H.M. Omar, S. Rohani, Crystal population balance formulation and solution methods: a review, Cryst. Growth Des. 17 (2017) 4028–4041. [27] J.A. Wojcik, A.G. Jones, Particle disruption of precipitated CaCO3 crystal agglomerates in turbulently agitated suspensions, Chem. Eng. Sci. 53 (1998) 1097–1101. [28] D.M. Ginter, S.K. Loyalka, Apparent size-dependent growth in aggregating crystallizers, Chem. Eng. Sci. 51 (1996) 3685–3695. [29] J.A. Wójcik, A.G. Jones, Experimental investigation into dynamics and stability of continuous MSMPR agglomerative precipitation of CaCO3 crystals, Chem. Eng. Res. Des. 75 (1997) 113–118. [30] N.S. Tavare, A.V. Patwardhan, Agglomeration in a continuous MSMPR crystallizer, AlChE J. 38 (1992) 377–384. [31] A.G. Jones, J. Hostomsky, S. Wachi, Modelling and analysis of particle formation during agglomerative crystal precipitation processes, Chem. Eng. Commun. 146 (1996) 105–130. [32] J.F. Wang, Z.B. Li, Crystallization and agglomeration kinetics of hydromagnesite in the reactive system MgCl2-Na2CO3-NaOH-H2O, Ind. Eng. Chem. Res. 51 (2012) 7874–7883. [33] J.S. Wey, J.P. Terwilliger, Effect of temperature on suspension crystallization process, Chem. Eng. Sci. 2–3 (1980) 297–305.
solution crystallization processes: a review, Ind. Eng. Chem. Res. 32 (1993) 1275–1296. F. Castro, A. Ferreira, J.A. Teixeira, F. Rocha, Influence of mixing intensity on lysozyme crystallization in a meso oscillatory flow reactor, Cryst. Growth Des. 18 (2018) 5940–5946. Z. Amjad, Mineral scales in biological and industrial systems, CRC Press, Boca Raton, 2013. G. Capellades, P.U. Joshi, K. Dam-Johansen, M.J. Mealy, T.V. Christensen, S. Kiil, Characterization of a multistage continuous MSMPR crystallization process assisted by image analysis of elongated crystals, Cryst. Growth Des. 18 (2018) 6455–6469. S.W. You, Y. Li, Y.F. Zhang, C. Yang, Y. Zhang, Synthesis of uniformly spherical bayerite from a sodium aluminate solution reacted with sodium bicarbonate, Ind. Eng. Chem. Res. 52 (2013) 12710–12716. R.Q. Liu, M. Huang, X.L. Yao, S. Chen, S. Wang, Z.R. Suo, Gas-liquid reactive crystallization kinetics of 2,4,6-triamino-1,3,5-trinitrobenzene in the semi-batch procedure, J. Cryst. Growth 491 (2018) 6–15. S. Shayanfar, V. Aghazadeh, A. Saravari, P. Hasanpour, Aluminum hydroxide crystallization from aluminate solution using carbon dioxide gas: effect of temperature and time, J. Cryst. Growth 496–497 (2018) 1–9. J.W. Mullin, Crystallization, fourth ed., Butterworth-Heinemann, Oxford, 2001. H. Peng, J. Vaughan, Aluminate effect on desilication product phase transformation, J. Cryst. Growth 492 (2018) 84–91. Α.Α. Aгpaнoвcкий, Alumina Production Handbook, Metallurgical Industry Press, Beijing, 1974. Y.F. Zhang, Y.H. Li, Y. Zhang, Phase diagram for the system Na2O-Al2O3-H2O at high alkali concentration, J. Chem. Eng. Data 48 (2003) 617–620.
7
Contents lists available at ScienceDirect
Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro
Nucleation, growth and aggregation kinetics of monosodium aluminate hydrate from unseeded sodium aluminate solution ⁎
T
⁎
Bingxin Zhoua,c, Shaotao Caoa, , Shaowei Youa, , Fangfang Chena, Fangfang Zhanga, Bo Lib, Yi Zhanga a Key Laboratory of Green Process and Engineering, and National Engineering Laboratory for Hydrometallurgical Cleaner Production Technology, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China b Coalmine Alumina Co. Ltd, Sanmenxia 472100, Henan Province, China c School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China
A R T I C LE I N FO
A B S T R A C T
Communicated by Gen Sazaki
The crystallization of monosodium aluminate hydrate (MAH) from sodium aluminate solution is the key step in the hydro-chemical process for treating Bayer red mud. The nucleation, growth and aggregation kinetics of MAH from unseeded sodium aluminate solution with low supersaturation was studied. It was found that the increase of temperature or the decrease of initial αk (molar ratio of Na2O and Al2O3 in aluminate solution) could lead to the increase of average crystal size while the increase of agitation speed had an adverse effect. The growth rate, the nucleation rate and the aggregation kernel were determined using a volume-independent growth aggregation model. The calculation of aggregation kernel was divided into two parts in terms of crystal size: smaller than 10 μm and larger than 10 μm. Results implied that small crystals below 10 μm aggregated more significantly than large crystals. The aggregation dominated the enlargement of small crystals, but the enlargement of large crystals mainly stemmed from the growth rather than the aggregation.
Keywords: A1. Nucleation A1. Growth A1. Aggregation A1. Alumina production B1. Monosodium aluminate hydrate
1. Introduction The crystallization of monosodium aluminate hydrate (MAH) from the leaching liquor of Bayer red mud, a median step in the hydrochemical process for alumina production, is the key technology to recover aluminum and sodium from Bayer red mud [1,2]. Previous studies on MAH crystallization have been focused on the precipitation, nucleation, morphology and crystallization kinetics of MAH from concentrated sodium aluminate solution with high supersaturation [1,3–8]. However, the study on MAH crystallization from sodium aluminate solution with low supersaturation has rarely been reported. Sodium aluminate solution with low supersaturation is generally encountered in the hydro-chemical process when Bayer red mud is treated. The study is of great significance to the recovery of aluminum and sodium from Bayer red mud in the hydro-chemical process. The study of nucleation, growth and aggregation kinetics is important to control the crystal size distribution (CSD), as well as to improve the efficiency of liquid-solid separation in the industrial production [9–11]. The crystallization kinetics is usually investigated either with a continuous crystallizer or with a batch crystallizer. A continuous process, such as the mixed suspension and mixed product
⁎
removal (MSMPR) process, needs the achievement of steady state that demands long experimental time, large amount of raw materials and complex operation. In contrast, the batch crystallizers are simple, flexible, require less investment and involve less process development, and they are especially suitable for the crystallization systems which demand long residence time [12,13]. As the crystallization of MAH from low supersaturated solution requires long residence time during the industrial production in the hydro-chemical process, a batch system is a better match to the industrial process of MAH crystallization. Moreover, the kinetics of MAH crystallization in a batch crystallizer has not yet been reported in literatures, although the kinetics of MAH crystallization in the MSMPR crystallizer has been investigated. This research focused on the nucleation, growth and aggregation kinetics of MAH from the low supersaturated sodium aluminate solution in a batch crystallizer. Effects of crystallization parameters on CSD, crystallization yield and crystal morphology were discussed in detail. Kinetic parameters including the nucleation rate, growth rate and aggregation kernel were calculated according to the population balance equation. The study will have fundamental significance in hydro-chemical process for alumina production when Bayer red mud is treated.
Corresponding authors. E-mail addresses: [email protected] (S. Cao), [email protected] (S. You).
https://doi.org/10.1016/j.jcrysgro.2019.125210 Received 16 May 2019; Received in revised form 8 August 2019; Accepted 26 August 2019 Available online 26 August 2019 0022-0248/ © 2019 Elsevier B.V. All rights reserved.
Journal of Crystal Growth 525 (2019) 125210
B. Zhou, et al.
Nomenclature B B0 C C0 D G Gv k ka kV L MT MTotal n Ni
the moment Q inflow rate, m3/s R gas constant, 8.314 J∙mol−1∙K−1 R2 correlation index S supersaturation T crystallization temperature, K t crystallization time, s V suspension volume, m3 V0 slurry volume of the initial solution, m3 w i% mass percentage ka, kb, Ka rate coefficients
birth function, no. m−3∙m−1∙s−1 nucleation rate, no. m−3∙s−1 solute concentration, g∙L−1 solute concentration of the initial solution, g∙L−1 death function, no. m−3∙m−1∙s−1 linear particle growth rate, m∙s−1 volume growth rate, m−3∙s−1 kth stream aggregation kernel, s−1 volumetric shape factor crystal size, μm suspension density, g∙L−1 total mass of the initial solution, g population density, no. m−3∙m−3 the number of crystals corresponding to v¯i at the time of
Greek Letters αk molar ratio of Na2O and Al2O3 solution density, g∙L−1 ρs α, β, γ, δ, ε, θ, μ, σ kinetic orders
2. Materials and methods
radiation. The CAl2O3 and CNa2O in sodium aluminate solutions were determined by the titration method. The crystallization yield of MAH from the supersaturated solution was calculated based on the mass conversion as follows:
2.1. Materials Sodium hydroxide (NaOH) and aluminum hydroxide (Al(OH)3) were of analytical grade (AR) and purchased from Beijing Chemical Industry Co Ltd.. The ultrapure water with the resistivity of 18.2 MΩ∙cm−1 was used in all experiments.
⎧ MAl2O3 − mAl2O3 = CAl2O3 × V1 209 ⎨ MTotal − 102 ×mAl2O3 = ρ1 × V1 ⎩
where the MAl2O3 was the initial total mass of Al2O3 in the solution (g), mAl2O3 was the quantity of the crystallized alumina (g), CAl2O3 was the concentration of alumina left in the filtrate after crystallization (g/L), V1, MTotal and ρ1were the volume (L), the total mass of the initial solution (g) and the density of the filtrate after crystallization (g/L), respectively. The crystallization yield could be expressed as follows:
2.2. Experimental methods The sodium aluminate solutions were made by the dissolution of aluminum hydroxide in sodium hydroxide solution to simulate the composition of leaching solution in the hydro-chemical process for treating red mud. NaOH, Al(OH)3 and pure water with a certain proportion were added to a nickel tank. The tank was heated by an electric furnace to solution boiling until solution was visually clear. The prepared solutions were filtered to obtain optically clear solutions. Experiments were carried out in a 300 mL jacketed stainless-steel crystallizer with Teflon lining, along with a Teflon impeller driven by a dynamoelectric agitator. The crystallizer was covered with a transparent plexiglass lid, and the temperature of the solution was controlled within ± 0.5 K by the circulating water heated by a thermo-stated bath to the crystallizer jacket. The time was recorded when the first visible crystals appeared [14]. Slurry samples were withdrawn from the crystallizer at different times, filtered immediately and washed with anhydrous ethanol. The crystals were dried for further analysis, and the filtrate was analyzed to determine the concentrations of Na2O and Al2O3. The operating experimental conditions of MAH crystallization are listed in Table 1. Repeated experiments were carried out to ensure the reproducibility at the same experimental conditions. The αk was the molar ratio of Na2O and Al2O3 in the sodium aluminate solution, expressed as:
αk =
CNa2O 102 × CAl2O3 62
(2)
Crystallization yield =
mAl2O3 × 100% MAl2O3
(3)
3. Results and discussion 3.1. Crystal characterization As shown in Fig. 1, results from XRD indicate that the crystals obtained under different experimental conditions are all identified as Na2O∙Al2O3·2.5H2O and the intensity differences in the reference and experimental patterns can be attributed to preferred orientation of the samples [3]. All population density distribution curves of MAH crystals exhibit the same trend. A typical population density distribution of MAH crystals is shown in Fig. 2. It can be seen from Fig. 2 that the population density curve exhibits two parts: an upward curve and a downward curve, and the boundary can be set as 10 μm according to the summary of experimental data. The behavior of small crystals presenting lower populations has also been discovered in other researches. Some researchers took this behavior as the result of the limitations of image analysis and neglected it because of the low percentage of crystals in the small size range [15]. However, it is apparently
(1)
Table 1 Conditions of MAH crystallization in a batch crystallizer.
2.3. Analytical methods The CSDs of crystals were measured with a Malvern Mastersizer 2000MU (instrument error, ± 3%) after dispersed in anhydrous ethanol, and the obtained CSD data was the average value of three measurements. The morphology of samples was analyzed by scanning electron microscopy (SEM, JSM-7001F, JEOL, Japan) and the solids were identified by X-ray diffraction patterns (XRD, X’pert MPD Pro, PanAnalytical, Netherlands) recorded with Cu Kα (λ = 0.15408 nm) 2
Parameters
Value (s)
Crystallization volume (mL) Agitation speed (rpm) Temperature (K) Na2O concentration (CNa2O, g/L) Al2O3 concentration (CAl2O3, g/L) Initial αk
200 200–500 319–353 540 55.52–111.04 8–16
Journal of Crystal Growth 525 (2019) 125210
B. Zhou, et al.
Fig. 4. CSDs of MAH crystals obtained at different agitation speeds (αk = 13, 323 K, t = 15 h).
This behavior is proved by Fig. 3 and it is discussed in Section 3.3.3. As is shown in Fig. 3, MAH crystals are truncated quadrangular orthopyramid crystals and small aggregated crystals. The resultant crystals have a different morphology from crystals obtained in a continuous process that are mainly spherical agglomerate crystals [5].
Fig. 1. XRD pattern of crystals crystallized from sodium aluminate solutions.
3.2. Effect of parameters
Fig. 2. Typical population density distribution of MAH crystals.
3.2.1. Effect of agitation The crystal size decreases with increasing agitation speed, as shown in Fig. 4. The volume average size of crystals decreases from 58.728 μm to 34.259 μm when the agitation speed increases from 200 rpm to 500 rpm. With the increase of agitation speed, particle collisions, including crystal-crystal contacts and crystal-agitator contacts, become more frequently. Particle collisions are important contributors to the formation of a large number of small crystalline fragments. Secondary nuclei are crystalline fragments that are the result of breakage and attrition caused by particle collisions. The second nucleation is promoted with the increase of agitation speed. Therefore, the average size of crystals is reduced.
unsuitable for this study because the crystals are large enough to be counted clearly. Some researchers took this behavior as the result of aggregation of small crystals but no further investigations were conducted [16]. Here, the decreasing population density in the small size range is attributed to the intense aggregation behavior of small crystals.
3.2.2. Effect of temperature As shown in Fig. 5, the crystal size increases as the temperature rises from 319 K to 353 K. It can be explained that the increase of temperature leads to the decrease of supersaturation, reducing the nucleation rate of particles and increasing the growth rate [17,18]. Moreover,
Fig. 3. Typical SEM images of MAH crystals (T = 323 K, 350 rpm, t = 15 h). 3
Journal of Crystal Growth 525 (2019) 125210
B. Zhou, et al.
crystallizer: (1) the solution is fully mixed; (2) there is no stratification at withdrawal [24]. Therefore, the population balance equation can be simplified as follows [19,25]:
∂n ∂ (Gn) dln V + +n =B−D ∂t ∂t dt
(8)
In a batch crystallizer, the mass balance equation can be shown as follows: (9)
(C (t) + MT (t)) × V (t) = V0 × C0
where C is the solute concentration (g∙L−1), MT is the suspension density (g∙L−1). Both sides are differentiated with respect to time, and then the equation can be changed into:
−
{
dC dln V + (C + MT ) × dt dt
}
=
dMT (t) dt
(10)
The growth rate models for the crystallization systems include the size-independent growth rate models, size-dependent growth rate models, aggregation models and growth rate dispersion models et al. [26]. It can be seen from Fig. 2 that the size-independent growth rate models and size-dependent growth rate models are inappropriate for this study due to the small upward curve of small crystals. It can be assumed that the aggregation models are more appropriate than the growth rate dispersion models according to the aggregation behavior of small crystals as shown in Fig. 3. Therefore, expressions of effective growth rate and nucleation rate are obtained using a volume-independent growth aggregation model based on the moment transformation method [19,27,28]:
Fig. 5. CSDs of MAH crystals obtained at different temperatures (αk = 13, 350 rpm, t = 15 h).
crystal growth tends to be diffusion controlled at high temperature and integration controlled at low temperature [19]. High temperature can also reduce the viscosity of the aluminate solution. The decrease of the viscosity increases the rate of diffusion at high temperature, which promotes the growth of MAH crystal. Therefore, the crystal size is increased at high temperature. 3.2.3. Effect of initial αk As shown in Fig. 6, the crystallization yield decreases with the increase of initial αk (see Eq. (1)) and remains unchanged after 15 h of crystallization, except for the crystallization with initial αk of 16. The increase of initial αk shows that the concentration of Al2O3 decreases and the initial supersaturation of the aluminate solution is reduced [20]. Thus, the crystallization yield of MAH is decreased when the initial αk increases. As shown in Fig. 7 and Table 2, the CSD narrows with the decrease of initial αk, together with the decrease of volume average crystal size and span. The range of the initial supersaturation is from 1.7 to 3.4. Although this range of the initial supersaturation is low for the Na2O-Al2O3-H2O system, the increase of the initial supersaturation still promotes the nucleation. This results in the formation of large number of small crystals, which finally decreases the average crystal size. The d0.1 is 23.777 μm at supersaturation 3.4, greater than 18.680 μm at supersaturation 1.7. The increase of d0.1 is probably caused by the aggregation of large number of small crystals at high supersaturation.
− Gv (t) =
=
ρs kV ∗
{
dC dt
k ∑i = 1
{
dC dt
+ (C + MT ) ∗
ρs kV ×
}
(vi ∗ n i (v¯i, t ) − (vi + 1 − vi ) ∗ n i (v¯i, t ))
+ (C + MT ) × k ∑i = 1
dlnV dt
dlnV dt
}
(vi + 1 × (v¯i, t ))
(11)
B0 = n 0 × Gv ≈ n (v¯min, t ) × Gv
(12) −3 −1
where Gv is the volume growth rate (m ∙s ), ρs is the solution density (g∙L−1), k v is the volumetric shape factor. It is assumed that the volumetric shape factor is constant in order to simplify the calculation. The population densities of minimal crystals obtained in the measurements are treated as that of crystal nucleus [19]. The Eq. (8) is integrated in the range of particle volume from zero to infinity, and gives
3.3. Crystallization kinetics According to the crystal size distribution of the obtained crystals, kinetic parameters including the growth rate, nucleation rate and aggregation kernel are calculated and regressed using the population balance equation. The general population balance equation proposed by Randolph and Larson can be expressed as follows [9]:
d (logV ) ∂n ∂ (Gn) + +n =B−D− dt ∂t ∂L
∑ k
nk Q k V
(7)
where V is the suspension volume (L), L is the crystal size (μm), n and nk are population density and slurry population density of outflow at size L (no. m−3∙m−1) respectively, Q is the volumetric flow rate (m3∙s−1), k is the kth stream, G is the linear particle growth rate (m∙s−1), B and D represent birth and death functions (no. m−3∙m−1∙s−1), and t is crystallization time (s). As the experiments are conducted in a batch crystallizer, Qk can be set equal to zero. There are some general assumptions for a batch
Fig. 6. Crystallization yields of MAH at different initial αk (T = 323 K, 350 rpm, t = 15 h). 4
Journal of Crystal Growth 525 (2019) 125210
B. Zhou, et al. vi + 1
∫ vi
∂ (Gv n) ΔNi dv ≈ Gv × ∂t vi + 1 − vi
(16)
vi + 1
Ni (t) =
∫ n (v, t )dv ≈ n (v¯i, t ) × (vi+1 − vi)
(17)
vi
(Ni (t) represents the number of particles corresponding to v¯i ). The right side of Eq. (13) can be changed into [26,27,29,30]: vi + 1
∫ vi
{
ka 2
vi
∫0
n (v − u) n (u) du − ka n (v )
∫0
v max
}
n (u) du dv (18)
Then the formula of the aggregation kernel ka can be expressed as follows: i=n
ka = Fig. 7. CSDs of MAH crystals obtained at various initial αk (323 K, 350 rpm, t = 15 h).
S1
8 10 13 16 1
S=
3.41 2.73 2.10 1.70
S
is
CAl2o3 C∗ Al2O3
d0.1
d0.5
23.777 18.951 19.784 18.680
36.147 34.209 36.994 37.587
d0.9 54.015 54.641 64.561 68.194
D[4,3]2 37.773 38.692 39.804 40.807
0.84 1.04 1.21 1.31
the initial supersaturation of the solution, expressed as: (4). In which the calculation of the C*Al2O3 is based on the solu-
B 0 = kb ×
MTγ
∑ di4 ∑ di3
ka = K a ×
S∊
θ
× Gv × B0
Span is used to reflect the width or the spread of crystal size distribution,
(19)
(20) (21)
μ
(22)
3.3.1. Growth rate The regressed correlation of growth rate is expressed as
Gv = 5.1346 × 10−25exp ⎛ ⎝
3
+ Ni ∑ Nj)
× Sδ
bility data of aluminum hydroxide in the Na2O-Al2O3-H2O system [21–23]. D[4,3] is the volume mean size, expressed as: D4,3 =
ΔNi ) vi + 1 − vi
−E ⎞ × MTα × S β Gv = k g × exp ⎛ ⎝ RT ⎠
Span3
2
Gv ×
The calculated kinetic parameters including the growth rate, nucleation rate and aggregation kernel under different crystallization conditions are fitted according to the empirical power-law expressions [26,30–33].
Table 2 CSDs of MAH crystals obtained at different initial αk (T = 323 K, 350 rpm, t = 15 h). Initial αk
ΔNi dlnV + Ni × dt + Δt i=n ∑i = 1 (0.5 × ∑ (Nm Nj)
∑i = 1 (
(5)
−3493.483 ⎞ × MT0.698 × S 0.498 RT ⎠
R2 = 0.949 (23)
The calculated growth rates range from 9.27 × 10−23 to 5.29 × 10−22 (m−3∙s−1) Fig. 8, and they are lower than the growth rates of MAH in an MSMPR crystallizer which have the order of magnitude of 10−20–10−19 (m−3∙s−1) [6]. The low growth rate can be attributed to the small driving force for crystallization at low supersaturations. The exponent of supersaturation is 0.498, while that of suspension density is 0.698, indicating that the growth rate depends more on the change of suspension density than that of supersaturation. 3.3.2. Nucleation rate The nucleation rates are correlated as a function of suspension density MT and supersaturation S by means of nonlinear regression, as shown in Fig. 9. MT and S is related to the secondary nucleation and primary nucleation, respectively. Therefore, B0 represents the apparent nucleation rate. The regressed result is expressed by Eq. (24):
B0 = 6.482 × MT0.4 × S 0.895
Fig. 8. Growth rate correlation. ∞
∞
∞
∞
0
0
0
0
∂ (Gv n) dv + ∫ dv = ∫ (Ba − Da ) dv ∫ ∂∂nt dv + ∫ n dlnV dt ∂t
∫ vi
∂n dNi ΔNi dv = ≈ ∂t dt Δt
(13)
(14) 3.3.3. Aggregation kernel The population density curve shows a sharp upward trend in the range of smaller than 10 μm (Fig. 2), and it is speculated that this behavior is derived from the intense aggregation of small crystals. Therefore, the calculation of aggregation kernel is divided into two
vi + 1
∫ n dlndtV dv = Ni dlndtV vi
(24)
The exponent of suspension density in nucleation rate expression is 0.4, and that of supersaturation is 0.895. The order of supersaturation is greater than that of suspension density, implying that the primary nucleation is dominant in this system. It is because the solutions are of relative low supersaturations and no seeds are added during the crystallization process. In the early stage of the crystallization, primary particles are formed. These primary particles collide with each other to form aggregates during their growth.
The left side of Eq. (13) is simplified as follows: vi + 1
R2 = 0.998
(15) 5
Journal of Crystal Growth 525 (2019) 125210
B. Zhou, et al.
ka = 9.948 × 10 41 × S 2.9353 × Gv 2.8167 × B0 0.00045
R2 = 0.960
(25)
For crystals larger than 10 μm, the experimental aggregation kernel has the order of magnitude of 10−28–10−26, and the value is much lower than the value of growth rate. The result implies that the crystal growth is more important for the enlargement of large crystals than the aggregation, and the aggregation of large crystals is negligible. The enhancement of the crystal size of MAH in this work is different from the MAH crystals obtained in the MSMPR crystallizer where crystal enlargement is mainly derived from crystal growth, rather than aggregation [6]. 4. Conclusions Nucleation, growth and aggregation kinetics of MAH from unseeded highly caustic aluminate solution with low supersaturation in a batch crystallizer was studied using a volume-independent growth aggregation model. Effects of parameters were also analyzed in detail. Temperature and initial αk had a positive effect on the growth of MAH crystal, but the agitation speed had an adverse effect. MAH had a slow growth rate due to the low supersaturation. The calculation of aggregation kernel was divided into two parts with crystal size of 10 μm as the boundary. It was found that small crystals below 10 μm aggregated more significantly than large crystals. The aggregation dominated the enhancement of the size of small crystals, but the growth was responsible for the enlargement of large crystals.
Fig. 9. Nucleation rate correlation.
Declaration of Competing Interest The authors declared that there is no conflict of interest. Acknowledgements This research was funded by the National Natural Science Foundation of China (No. 51674233), the Henan Transfer Project of CAS Scientific and Technological Achievements (No. 2019103), the Guangxi Natural Science Foundation (No. 2016GXNSFEA380002), the Shanxi Province Coal Based Low-carbon Technology Major Projects (No. MC2016-05), and Major Science and Technology Program for Water Pollution Control and Treatment (2018ZX07402005).
Fig. 10. Aggregation kernel correlation of crystals smaller than 10 μm.
References [1] S.T. Cao, Y.F. Zhang, Y. Zhang, Preparation of sodium aluminate from the leach liquor of diasporic bauxite in concentrated NaOH solution, Hydrometallurgy 98 (2009) 298–303. [2] L. Zhong, Y.F. Zhang, Y. Zhang, Extraction of alumina and sodium oxide from red mud by a mild hydro-chemical process, J. Hazard. Mater. 172 (2009) 1629–1634. [3] S.T. Cao, Y.F. Zhang, Y. Zhang, Nucleation and morphology of monosodium aluminate hydrate from concentrated sodium aluminate solutions, Cryst. Growth Des. 10 (2010) 1605–1610. [4] S.W. You, Y.F. Zhang, S.T. Cao, F.F. Chen, Y. Zhang, Crystallization of monosodium aluminate hydrate from a concentrated aluminate solution containing silica, Hydrometallurgy 115–116 (2012) 104–107. [5] S.W. You, T. Guo, P.F. Liu, X. Mao, Y.F. Zhang, Precipitation of monosodium aluminate hydrate from concentrated sodium aluminate solution, Hydrometallurgy 183 (2019) 125–129. [6] S.W. You, Y.F. Zhang, S.T. Cao, F.F. Chen, Y. Zhang, Crystallization kinetics of monosodium aluminate hydrate in concentrated sodium aluminate solutions, Ind. Eng. Chem. Res. 51 (2012) 7736–7741. [7] V.S. Sazhin, The crystallization of sodium aluminate, China Industry Press, Beijing, 1964. [8] V. Rayzman, I. Filipovich, L. Nisse, Y. Vlasenko, Sodium aluminate from aluminabearing intermediates and wastes, JOM 50 (1998) 32–37. [9] A.D. Randolph, M.A. Larson, Theory of particulate processes, analysis and techniques of continuous crystallization, New York, 1971. [10] A. Vancleef, S. Seurs, J. Jordens, T. Van Gerven, L.C.J. Thomassen, L. Braeken, Reducing the induction time using ultrasound and high-shear mixing in a continuous crystallization process, Crystals 8 (2018) 326. [11] J. Jordens, E. Canini, B. Gielen, T. Van Gerven, L. Braeken, Ultrasound assisted particle size control by continuous seed generation and batch growth, Crystals 7 (2017) 195. [12] J.B. Rawlings, S.M. Miller, W.R. Witkowski, Model identification and control of
Fig. 11. Aggregation kernel correlation of crystals larger than 10 μm.
parts: aggregation kernel in the range of smaller than 10 μm and that of larger than 10 μm. As shown in Figs. 10 and 11, the experimental aggregation kernels in the range of smaller than 10 μm have the order of magnitude of 10−18–10−20 that are much higher than the order of magnitude of 10−28–10−26 of crystals larger than 10 μm. The value of aggregation kernel below 10 μm is greater than the value of growth rate which has the order of magnitude of 10−23–10−22. It can be concluded that small crystals aggregate more significantly than large crystals and the aggregation is responsible for the enlargement of small crystals. The correlated expression aggregation kernel of crystals smaller than 10 μm is shown as follows:
6
Journal of Crystal Growth 525 (2019) 125210
B. Zhou, et al.
[13]
[14] [15]
[16]
[17]
[18]
[19] [20] [21] [22]
[23] S.T. Cao, Applied and fundamental research for crystallization of monosodium aluminate hydrate. Beijing, 2010. [24] T. Guo, S.W. You, B. Yang, S.T. Cao, Y. Zhang, Crystallization kinetics of Na2CO3 in Bayer aluminate solutions during the evaporation process, CrystEngComm 20 (2018) 3722–3727. [25] X. Zhang, G. Qian, X. Zhou, Kinetic modeling on batch-cooling crystallization of zinc lactate: The influence of malic acid, J. Cryst. Growth 463 (2017) 162–167. [26] H.M. Omar, S. Rohani, Crystal population balance formulation and solution methods: a review, Cryst. Growth Des. 17 (2017) 4028–4041. [27] J.A. Wojcik, A.G. Jones, Particle disruption of precipitated CaCO3 crystal agglomerates in turbulently agitated suspensions, Chem. Eng. Sci. 53 (1998) 1097–1101. [28] D.M. Ginter, S.K. Loyalka, Apparent size-dependent growth in aggregating crystallizers, Chem. Eng. Sci. 51 (1996) 3685–3695. [29] J.A. Wójcik, A.G. Jones, Experimental investigation into dynamics and stability of continuous MSMPR agglomerative precipitation of CaCO3 crystals, Chem. Eng. Res. Des. 75 (1997) 113–118. [30] N.S. Tavare, A.V. Patwardhan, Agglomeration in a continuous MSMPR crystallizer, AlChE J. 38 (1992) 377–384. [31] A.G. Jones, J. Hostomsky, S. Wachi, Modelling and analysis of particle formation during agglomerative crystal precipitation processes, Chem. Eng. Commun. 146 (1996) 105–130. [32] J.F. Wang, Z.B. Li, Crystallization and agglomeration kinetics of hydromagnesite in the reactive system MgCl2-Na2CO3-NaOH-H2O, Ind. Eng. Chem. Res. 51 (2012) 7874–7883. [33] J.S. Wey, J.P. Terwilliger, Effect of temperature on suspension crystallization process, Chem. Eng. Sci. 2–3 (1980) 297–305.
solution crystallization processes: a review, Ind. Eng. Chem. Res. 32 (1993) 1275–1296. F. Castro, A. Ferreira, J.A. Teixeira, F. Rocha, Influence of mixing intensity on lysozyme crystallization in a meso oscillatory flow reactor, Cryst. Growth Des. 18 (2018) 5940–5946. Z. Amjad, Mineral scales in biological and industrial systems, CRC Press, Boca Raton, 2013. G. Capellades, P.U. Joshi, K. Dam-Johansen, M.J. Mealy, T.V. Christensen, S. Kiil, Characterization of a multistage continuous MSMPR crystallization process assisted by image analysis of elongated crystals, Cryst. Growth Des. 18 (2018) 6455–6469. S.W. You, Y. Li, Y.F. Zhang, C. Yang, Y. Zhang, Synthesis of uniformly spherical bayerite from a sodium aluminate solution reacted with sodium bicarbonate, Ind. Eng. Chem. Res. 52 (2013) 12710–12716. R.Q. Liu, M. Huang, X.L. Yao, S. Chen, S. Wang, Z.R. Suo, Gas-liquid reactive crystallization kinetics of 2,4,6-triamino-1,3,5-trinitrobenzene in the semi-batch procedure, J. Cryst. Growth 491 (2018) 6–15. S. Shayanfar, V. Aghazadeh, A. Saravari, P. Hasanpour, Aluminum hydroxide crystallization from aluminate solution using carbon dioxide gas: effect of temperature and time, J. Cryst. Growth 496–497 (2018) 1–9. J.W. Mullin, Crystallization, fourth ed., Butterworth-Heinemann, Oxford, 2001. H. Peng, J. Vaughan, Aluminate effect on desilication product phase transformation, J. Cryst. Growth 492 (2018) 84–91. Α.Α. Aгpaнoвcкий, Alumina Production Handbook, Metallurgical Industry Press, Beijing, 1974. Y.F. Zhang, Y.H. Li, Y. Zhang, Phase diagram for the system Na2O-Al2O3-H2O at high alkali concentration, J. Chem. Eng. Data 48 (2003) 617–620.
7