Crystallization and Agglomeration Kinetics of Hydromagnesite in the

Article pubs.acs.org/IECR

Crystallization and Agglomeration Kinetics of Hydromagnesite in the Reactive System MgCl2−Na2CO3−NaOH−H2O Junfeng Wang and Zhibao Li* Key Laboratory of Green Process and Engineering, National Engineering Laboratory for Hydrometallurgical Cleaner Production Technology, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, People's Republic of China S Supporting Information *

ABSTRACT: The reactive crystallization kinetics of hydromagnesite (4MgCO3·Mg(OH)2·4H2O) for the MgCl2−Na2CO3− NaOH−H2O system has been systematically investigated in a continuously operated mixed-suspension mixed-product removal (MSMPR) crystallizer for the first time. Determination of the effects of reactive temperature and OH− ion on magnesium carbonate hydrates in the above system was conducted through a batch crystallization experiment, and the crystallization temperature of 80 °C for the precipitation of regular spherical-like hydromagnesite was selected for the kinetics study. The relative supersaturation for hydromagnesite is obtained based on the activity coefficients calculated by the Pitzer model. The growth rate, nucleation rate, and agglomeration kernel are determined on the basis of the agglomeration population balance equation, and their kinetic equations are then correlated in terms of power law kinetic expressions. The orders of volume growth rate and linear growth rate with respect to the relative supersaturation are 1.55 and 0.95, respectively. The magma density has an important effect on the nucleation rate of hydromagnesite particles. However, the expression of β ∝ MT−0.39 for hydromagnesite agglomeration shows that the magma density has a negative effect on the agglomeration kernel. All of these will provide a basis for the design and analysis of industrial crystallizers.

1. INTRODUCTION The Qarham salt lake of Qinghai province in the western region of China is well-known for its huge reserves of potassium chloride, sodium chloride, and magnesium chloride. On one hand, potassium fertilizer of more than 3000 thousand tons has been annually produced through the decomposition of carnallite (KCl·MgCl2·6H2O), simultaneously generating about 30 000 thousand tons of magnesium chloride hexahydrate (MgCl2·6H2O) with high purity as byproduct or waste. On the other hand, an azodicarbonamide (ADC) foamer plant of 200 thousand tons per annum in this area, one of biggest ones in the world, has been currently established by use of NaCl deposit as raw material through urea technology. Unfortunately, about 600 thousand tons of sodium carbonate decahydrate (Na2CO3·10H2O), which contains 3.52% sodium hydroxide, 1.74% sodium chloride, and 7.74% unknown organic compounds, is discarded as waste in the cooling crystallization stage. Both valuable byproducts, MgCl2·6H2O and Na2CO3·10H2O, cannot be used effectively as yet and are discarded back into the saline lakes, causing a serious environmental problem. Therefore, from ecological and economic points of view, solution of the problem for effective utilization of the two byproducts is urgent. For this purpose, an attractive way as shown in Figure 1 to beneficiate the two byproducts has been proposed to prepare high-quality magnesium oxide (MgO) through the decomposition of magnesium carbonate hydrates obtained by the reaction of MgCl2·6H2O and Na2CO3·10H2O. In this process hydromagnesite, one of the magnesium carbonate hydrates generated from the MgCl2−Na2CO3−NaOH−H2O system, was selected as the precursor of MgO due to its excellent filterability.1 Reactive crystallization of hydromagnesite has been investigated by many researchers. Cheng and Li1 have synthesized rosette-like © 2012 American Chemical Society

Figure 1. Flow sheet of the process for MgO production through calcination of hydromagnesite.

4MgCO3·Mg(OH)2·4H2O spheres by reacting magnesium chloride and sodium carbonate at temperatures above 313.15 K. Mitsuhashi et al.2 have developed a procedure to generate microtube 4MgCO3·Mg(OH)2·4H2O by the carbonation of an Received: Revised: Accepted: Published: 7874

January 24, 2012 April 20, 2012 May 24, 2012 May 24, 2012 dx.doi.org/10.1021/ie300213c | Ind. Eng. Chem. Res. 2012, 51, 7874−7883

Industrial & Engineering Chemistry Research

Article

aqueous suspension of magnesium hydroxide with carbon dioxide. Fernández et al.3 have prepared hydromagnesite through the addition of MgO to a continuously stirred Mg(HCO3)2 solution obtained by carbonation of a MgOcontaining residue slurry. Rosa4 has described a procedure for obtaining hydromagnesite by carbonation of calcined dolomite and further heating of the magnesium bicarbonate solution formed after its filtration. Zhang et al.5 have synthesized the spherical-like hydromagnesite by the variation of pH values of the initial solution of K2CO3 and Mg(NO3)2 at 318 K. Li et al.6 have prepared hydromagnesite by reacting anhydrous magnesium sulfate and urea via a hydrothermal method. As can be seen from the above, the precipitation agents of a magnesium salt solution include mainly sodium carbonate, potassium carbonate, bicarbonate, etc. However, the byproduct sodium carbonate decahydrate from the ADC foamer production by urea method may be a suitable precipitation agent for preparing for the hydromagnesite and has never been reported in the literature. Among these impurities of the byproduct Na2CO3·10H2O, sodium hydroxide may have an important impact on hydromagnesite preparation. Therefore, the crystallization kinetics of hydromagnesite crystals from the reaction of magnesium chloride and alkali solution containing a mixture of sodium carbonate and sodium hydroxide is very necessary for the simulation, design, and analysis of industrial crystallizers. In this work, the effect of the reaction temperature and presence of OH− ion on the morphology of magnesium carbonate hydrates was first studied through a batch crystallization experiment. Then a steady-state mixed-suspension mixed-product removal (MSMPR) crystallizer was used to investigate the effect of feed concentration, the addition rate of the two reagents (magnesium chloride and the mixture of sodium carbonate and sodium hydroxide), and the mean residence time on the MgCl2−Na2CO3−NaOH−H2O reactive crystallization system. The activity coefficient of ions used to determine the relative supersaturation was strictly calculated by the Pitzer model embedded in AspenPlus. Conventional particle size distribution data of experimentally obtained hydromagnesite were transformed into crystal volume distribution data. The agglomerative population balance model based on the crystal volume distribution was used to simultaneously determine the growth rate, nucleation rate, and agglomeration kernel with moment transformation. The growth rate, nucleation rate, and agglomeration kernel were correlated with the corresponding kinetic equations.

Figure 2. Schematic diagram of the experimental apparatus. (A) MSMPR crystallizer; (B) water bath; (C) magnesium chloride solution tank; (D) peristaltic pump; (E) thermometer; (F) peristaltic pump; (G) alkali solution tank; (H) pump; (I) product; (J) electrode.

(MSMPR) crystallizer equipped with propeller agitator responsible for internal circulation of the suspension. It was a jacketed glass-made crystallizer (A), inside which a three-paddle propeller mixer of standard geometric proportions was located. The crystallizer’s internal diameter was 100 mm and its height was 125 mm. The stirrer speed was kept at 300 rpm in experiments satisfying the hydrodynamic requirements of maintaining a stable and intensive enough circulation of suspension inside the crystallizer working volume. The temperature of the solution in the crystallizer was held constant at 80 °C by the circulation of heating water from a water bath with a thermoelectric controller (B) to the jacket of the crystallizer, while the temperature of the reactants was held constant at 60 °C. The digital peristaltic pumps (D and F) were used to carry the alkaline solution from tank C and magnesium chloride solution from tank G to the crystallizer, respectively. Withdrawal was carried out through a pump (H) working intermittently at high flow rate, and the slurry withdrawn was pumped to the product tank (I). The pH was measured using an electrode (J). 2.3. Temperature Effect on the Crystallization of Magnesium Carbonate Hydrates. First, a batch crystallization experiment was carried out to study the effect of reaction temperature on the crystallization of magnesium carbonate hydrates from the MgCl2−Na2CO3−NaOH−H2O reactive crystallization system. A standard volume of MgCl2 solution (300 mL, 1 mol/L) was transferred to a 1-L double-jacketed glass reactor connected to a water circulator and was heated to the desired temperature. The solution temperature was monitored with a thermometer. Upon attainment of the desired temperature, the alkaline solution (300 mL, mixture of 1 mol/L sodium carbonate and 0.28 mol/L sodium hydroxide) was added to the vigorously stirred (300 rpm) MgCl2 solution at 5 mL·min−1. The mixture was further stirred for 2 h. After that, a white precipitate was collected, filtered off, and washed with double distilled water and ethanol several times. The obtained particles were dried in an oven at 50 °C for 10 h. The dried particles were photographed by the scanning electron microscope (SEM) JEOL JSM-820. The crystal phase of the dried crystal was analyzed using a Siemens D5000 X-ray diffractometer with Cu Kα radiation. 2.4. Experimental Procedure of Crystallization Kinetics for Hydromagnesite. When the desired operating temperature was reached, the two reactant solutions were continuously and simultaneously fed to the MSMPR crystallizer from their own inlet tubes located on opposite sides of the impeller. The volumetric flow rates of reactant solutions provide the required

2. EXPERIMENTAL SECTION 2.1. Experimental Materials. The chemicals magnesium chloride hexahydrate, sodium carbonate, and sodium hydroxide were supplied by Beijing Chemical Reagent Co. and were used without further purification. All were of analytical research grade with a purity of 99.0%. A series of magnesium chloride solutions, concentrations ranging from 0.5 to 1.25 mol/L with an interval of 0.25 mol/L, were prepared by dissolving magnesium chloride hexahydrate in double distilled water (conductivity < 0.1 μS/ cm). A series of alkaline solutions containing a mixture of sodium carbonate and sodium hydroxide were prepared by dissolving sodium carbonate and sodium hydroxide in double distilled water. 2.2. Experimental Setup. A schematic representation of the laboratory system used for the experiments is presented in Figure 2. The main element of the experimental setup was a laboratoryscale continuous mixed-suspension mixed-product removal 7875

dx.doi.org/10.1021/ie300213c | Ind. Eng. Chem. Res. 2012, 51, 7874−7883


Article

residence time in a crystallizer space, τ. In a typical run, once the working volume of the slurry within the crystallizer was achieved, the slurry in the reactor was discharged intermittently by a peristaltic pump, and the withdrawal pipe of product slurry was located approximately halfway up the side of the crystallizer. Every slurry sample withdrawn from the crystallizer was 30−35 mL. The crystallizer was operated to reach steady state, which was found to be assured after at least 8−10 residence times (τ). Sample volumes of slurry were taken rapidly within the crystallizer to avoid crystal classification. They were filtered immediately using a 0.2 μm filter membrane. One part of the clear filtrate was added into a 25-mL volumetric flask which was kept in the water bath to measure the density of solution. The other part of the clear filtrate was used to measure the concentrations of Mg2+, CO32−, and HCO3− ions for obtaining the supersaturation of the solution. The total magnesium content was determined by complexometric titration with EDTA at pH 9.5−10 (ammonia buffer), using black T as the indicator. The CO32− and HCO3− contents in solution were determined by titration with standardized 0.025 M HCl and phenolphthalein and methyl orange as indicators. The crystal mass was washed with water and was air-desiccated at 80 °C for 10 h to determine the suspension density. The dried 4MgCO3·Mg(OH)2·4H2O particles were photographed with the SEM JEOL JSM-820. The crystal phase of the dried hydromagnesite crystals was analyzed using the Siemens D5000 X-ray diffractometer with Cu Kα radiation. Finally, a 20 mL sample of the slurry was withdrawn from the crystallizer for particle size distribution (PSD) analysis using the Malvern Mastersizer Hydro 2000MU. The operating conditions of the reactive crystallization are listed in Table 1.

(4)

The concentrations of the chemical species Mg2+, CO32−, and OH− in eq 5 were already tested in this work. In order to calculate the relative supersaturation, the solubility product constant of hydromagnesite and the activity coefficients (γMg2+, γCO32−, and γOH−) need to be obtained. 3.3. Determination of Equilibrium Constants. The solubility product constant of hydromagnesite is calculated by integrating the van’t Hoff equation: d ln K ΔH ° = dt RT 2

(6)

Assuming ΔH° is a constant, then integration yields ln KT = ln K 298.15 +

ΔH ° ⎛ 1 1⎞ ⎜ − ⎟ ⎝ R 298.15 T⎠

(7)

For hydromagnesite, ln K298.15 = −84.665 and ΔH° = −106.93 kJ/mol from Drever7 are used in this study. More recently, Xiong8 has reported the solubility constants of hydromagnesite determined in NaCl solutions with a wide range of ionic strengths. The solubility product constant of hydromagnesite converted into the form of the literature8 is 57.97, which is excellent agreement with the value of 57.93 obtained by Xiong.8 The calculated results indicate the reliability of the Ksp values. The solubility product constants of 4MgCO3·Mg(OH)2·4H2O at different temperatures are calculated by eq 7 and correlated in terms of temperature by means of eq 8. The values of coefficients a1−a4 thus obtained are listed in Table 2. a ln KT = a1 + 2 + a3 ln T + a4T (8) T

3. THEORETICAL BACKGROUND 3.1. Reaction System. For the MgCl2−Na2CO3−NaOH− H2O system, the following main reactions are considered.

For the system studied, the other thermodynamic constants of H2O, MgOH+, and MgCO3 are taken from the literature9,10 and are also listed in the Table 2. 3.4. Calculation of Activity Coefficients. The Pitzer activity coefficient model has already been used to adequately represent thermodynamic properties of the system Na−K−Ca−

5Mg 2 + + 4CO32 − + 2OH− + 4H 2O (1)

H 2O ⇄ H+ + OH−

Mg 2 + + CO32 − ⇄ MgCO3

⎡ (γ 2 +m 2 +)5 (γ 2 −m 2 −)4 (γ −m −)2 α 4 ⎤1/15 Mg CO3 OH H2O Mg CO3 OH ⎥ σ=⎢ −1 ⎢ ⎥ K sp ⎣ ⎦ (5)

80 1800−5400 300 0.5−1.25 0.5−1.25 3.5 600 20.88−62.20 3.12−9.37 0.524

⇄ 4MgCO3 · Mg(OH)2 ·4H 2O

(3)

The solubility product constant of 4MgCO3·Mg(OH)2·4H2O is designated as Ksp. The thermodynamic dissociation constant of H2O is designated as K1. The thermodynamic association constants for the formation of ion pairs are designated as K2 for MgOH+ and K3 for MgCO3. 3.2. Determination of the Relative Supersaturation. The relative supersaturation, σ, for hydromagnesite in the system can be defined as

Table 1. Operating Conditions Maintained in This Work working temp (°C) mean residence time (s) stirrer speed (rpm) init concn of MgCl2 (mol/L) init concn of Na2CO3 (mol/L) Na2CO3/NaOH molar ratio in alkali soln crystallization vol (mL) magma density (kg/m3) relative supersaturation (σ) shape factor

Mg 2 + + OH− ⇄ MgOH+

(2)

Table 2. Coefficients for Equilibrium Constants of H2O, MgOH+, MgCO3, 4MgCO3·Mg(OH)2·4H2O, and MgCO3·3H2O ln K18 ln K28 ln K39 ln Ksp7 ln Knesquehonite14

a1

a2

a3

a4

T (K) range

148.9802 −8.9110 −2.3671 −127.801 111.7574

−13 847.26 1154.9770 0 12 861.00 68.0279

−23.6521 0 0 0 −24.5756

0 0 −0.0152 0 0.0533

273.15−353.15 273.15−353.15 273.15−353.15 273.15−373.15 273.15−313.15

7876



Article

Mg−H−Cl−HSO4−SO4−OH−HCO3−CO3−CO2−H2O in solutions from 0 to 90 °C.11 Therefore, the Pitzer equation embedded in Aspen Plus was selected to calculate the activity coefficients of the chemical species for the Mg−Na−Cl−OH− CO3−HCO3−H2O system in this work. The Pitzer ioninteraction parameters of β(0), β(1), Cϕ, θ, and ψ needed for the system are available from the literature9,11−14 and provided in the Supporting Information. Based on the solubility product constant and the Pitzer ion-interaction parameters mentioned above, the thermodynamic model for the Na−K−Mg−Ca−H− Cl−SO4−OH−HCO3−CO3−CO2−H2O system which has been developed by Marion15 can accurately calculate the solubility of MgCO3 in water. In this study, in order to further test whether the model parameters and equilibrium constants in the system interest perform well, the solubility data of nesquehonite in the NaCl−H2O system taken from the literature16 are predicted. Figure 3 shows that the calculated

According to the classical work of Smoluchowski,17 the empirical birth function Ba and death function Da can be represented by the following equations: Ba =

1 2

∫0

Da = n(v)

v

β(u , v − u) n(u , t ) n(v − u) du

∫0

∞

β(u , v) n(u) du

results agree well with the experimental solubility data for nesquehonite in the NaCl−H2O system. The results indicate the Pitzer model with these parameters is suitable to calculate the activity coefficients of chemical species for the Mg−Na−Cl− OH−CO3−HCO3−H2O system. 3.5. Population Balance. For an MSMPR crystallizer, the population balance equation proposed by Randolph and Larson16 can be expressed in terms of volume coordinated as

μ1 τ

μ2 τ

d log V ∂(Gvn) ∂n + +n dτ ∂τ ∂v k

= Gvμ0

(16)

= 2Gvμ1 + βμ12

(17)

The moments of the distribution represent the average and total properties of the solid phase. The moments can be evaluated numerically as

Q knk V

(9)

μi =

The population density, n, as a function of particle volume can be evaluated as follows: ΔwM T n= ρc v ̅ Δv

(10)

∑ k

Q knk V

∫0

∞

n(v)v i dv

(18)

3.7. Crystallization and Agglomeration Kinetics. The experimentally determined population data at steady state can be converted into the moments with respect to volume using eq 18. The volume growth rate, nucleation rate, and agglomeration kernel relations can be derived from the moment equations (eqs 15−17) and can be used to determine the rates from the moments of experimental population density data obtained during the course of an MSMPR experiment.

In general, the rupture term is negligible; then eq 9 becomes d log V ∂(Gvn) ∂n + +n = Ba − Da − ∂τ ∂v dτ

(14)

In this work, following the treatment proposed by Hulburt and Katz,23 for the moment transformation of the population balance equation (eq 14), i.e., substituting eqs 12 and 13 into eq 14, then eq 14 multiplies vi and integrates each term with respect to v over the entire particle volume range from zero to infinity, yielding a set of algebraic equations. From the equation, moment equations for the first three moments (up to second order) are then μ 1 −B0 + 0 = − βμ0 2 (15) τ 2

Figure 3. Solubility of MgCO3·3H2O in NaCl−H2O system at different temperatures: □, 288.15 K; △, 298.15 K; ◊, 308.15 K; ―, calculated in this work.

∑

(13)

The agglomeration kernel β(u,v−u), expressed as a function of particle volume, is a measure of the frequency of collisions between particles of volumes u and v − u that are successful in producing a particle of volume v. The factor 1/2 in eq 12 ensures that collisions are not counted twice. The agglomeration kernel β(u,v−u) depends on the environment and accounts for the physical forces that are instrumental in the mechanism of aggregation, which decides its functional form. Many theoretical and empirical formulations of the agglomeration kernel are available to describe various mechanisms of aggregation.16,18−22 3.6. Moment Transformation. In order to predict the PSD, the particle population balance equation (eq 11) needs to be solved. However, direct solution of the partial differential equation for the population balance requires extensive computational time. Instead, the moment transformation approach is an alternative that avoids expensive computational effort, and it is sufficient to provide information useful for engineering and design purposes. The moment transformation of the population balance assumes that the growth rate is independent of the particle volume, and eq 11 becomes Gv dn n + = Ba − Da dv τ

= Ba − Da + Bd − Dd −

(12)

(11) 7877



Article

Figure 4. Typical X-ray diffraction patterns of hydromagnesite particles at different reaction temperatures.

Figure 5. Typical SEM morphologies for hydromagnesite particles at different temperatures.

Gv =

β=

B0 =

μ1

β = kβGv hB0 pτ q

μ0 τ μ2 τμ12

(24)

(19)

2Gv 1⎛ μ 2⎞ − = ⎜⎜ 22 − ⎟⎟ μ1 τ ⎝ μ1 μ0 ⎠

μ μμ2 1 βμ0 2 + 0 = 2 02 2 τ 2τμ1

4. RESULTS AND DISCUSSION 4.1. Relative Supersaturation. The relative supersaturation values are calculated based on the available concentrations and activity coefficients of Mg2+, CO32−, and OH− ions by eq 5 and are provided in the Supporting Information. The relative supersaturation increases with increasing initial concentration of reactants because many ions are fed to the crystallizer. The experimental values of relative supersaturation versus mean residence time (runs 3, 7, 11, 15, and 19) are fitted by the leastsquares method, and an empirical equation

(20)

(21)

Crystal growth, nucleation rates, and agglomeration kernel obtained from a series of experiments can be correlated by empirical kinetic relations in terms of most significant and observable variables. In this work, the applicable power law kinetic correlations are Gv = kgσ g

(22)

B0 = kRGv iM T j

(23)

σ = 65.68τ −0.26

(25)

is obtained. Eq 25 is applicable when the feed concentration remains unchanged and the system is isothermal. The relativity coefficient between the mean residence time and relative supersaturation is 0.9960, indicating a high relativity. As can be seen from eq 25, the relative supersaturation decreases with the 7878



Article

increase of the mean residence time because the concentration of ions fed to the MSMPR crystallizer per unit time decreases. 4.2. Crystal Characteristics. 4.2.1. Magnesium Carbonate Hydrates from Batch Crystallization Experiment. Typical X-ray diffraction patterns of the particles from different reaction temperatures are shown in Figure 4. It is evident that the precipitate has a formula of MgCO3·3H2O confirmed from the reported data (JCPDS file no. 01-070-1433) at the reaction temperatures below 40 °C. When the reaction temperatures are 80 and 90 °C, all diffraction peaks in the XRD patterns are indexed to be 4MgCO3·Mg(OH) 2·4H2 O with unit cell parameters of a = 10.11, b = 8.94, and c = 8.38 Å and β = 114.58° as confirmed from the reported data (JCPDS file no. 250513). However, in the reaction temperature range from 40 to 70 °C, 4MgCO3·Mg(OH)2·4H2O and 4MgCO3·Mg(OH)2·5H2O coexist. Figure 5 provides a set of typical SEM images corresponding to the samples from different reaction temperatures. The various surface structures in Figure 5 illustrate that the reaction temperature has a significant influence on the anisotropy of growth rates, so the particles display different macroscopic shapes with the variation of the reaction temperature. As can be observed, needlelike particles are obtained at 25 and 35 °C, whereas the precipitate becomes amorphous at 40 °C. When the reaction temperature increases to 50 °C, the amorphous particles become irregular spherical particles. When the reaction temperature increases from 50 to 90 °C, the diameter of spherical-like particles gradually increases. Therefore, the reaction temperature of 80 °C is selected for the study of crystallization kinetics of hydromagnesite crystals due to their excellent filterability. 4.2.2. Hydromagnesite from Continuous Crystallization Experiment. From the detailed view of an individual particle as shown in Figure 6, it can be observed that these spherical-like

Figure 7. Evolution of mean crystal size with mean residence time.

4500 s (runs 13−16). This case could be explained as follows: in the solution with lower supersaturation, the growth rate of nuclei is superior to the nucleation rate, and the nuclei are more prone to assemble into larger particles. However, in the solution with higher supersaturation which has more influence on the nucleation rate than on the growth rate, the nucleation rate of Mg2+, CO32−, and OH− gradually increases, and the particles have less time to aggregate. Therefore, the mean crystal size decreases with further increasing supersaturation. This can be confirmed in section 4.4.3. 4.3. Population Density Distributions. A typical experimental population density plot in size coordinates is given in Figure 10. The plot deviates from the ideal MSMPR theory especially at the smaller sizes. The nonlinear behavior of log n vs L indicates that the hydromagnesite crystal growth rate is not constant. As explained above, the spherical-like hydromagnesite particles precipitated in the reactive crystallization process are agglomerated by a number of thin sheets of crystalline walls growing out from a common center. Moreover, for the reactive crystallization, agglomeration is unavoidable and becomes a problem because the crystal size distribution is strongly affected by agglomeration. Therefore, for all experiments of interest, the considerable upward concave curvature over the small size range is mainly attributed to the agglomeration. The population density versus crystal size for the small particles ranging from 0 to 2.14 × 10−5 m in Figure 10 is fitted and an empirical equation is obtained.

Figure 6. Scanning electron microscope of the hydromagnesite particles precipitated at the supersaturation of 5.96 and residence time of 5400 s.

particles exhibit the crystal morphology of an agglomerate of a large number of thin sheets interconnected to each other. The PSD for the hydromagnesite particles was obtained for each experiment. Figure 7 shows the effect of mean residence time on the mean crystal size D0.5. In Figure 7, elongation of the mean residence time from 1800 to 5400 s (runs 3, 7, 11, 15, and 19) results in an increase of mean crystal size D0.5 ranging from 32.07 to 55.31 μm. The results can also be confirmed from the scanning electron microscopic images of hydromagnesite crystals (Figure 8) produced under the same experimental conditions. This case could be ascribed to the fact that a higher mean residence time results in a higher slurry density because of lower supersaturation, so more crystal surface is available with increasing slurry density and the nuclei are prone to assemble into larger particles. It can also be observed from Figure 9 that the mean crystal size D0.5 initially increases and then decreases with increasing supersaturation at the same mean residence time of

ln(nL) = −3.67 ln(L) + 2.37

(26)

The correlation coefficient is 0.9957. Meanwhile, the PSD curve with the size range from 2.14 × 10−5 to 1.70 × 10−4 m can be well regressed as a linear equation of ln(nL) = −53619L + 42.21 with the correlation coefficient of 0.9989. Size distribution data were also translated into volume population density according to eq 10. Results of volume population density calculations for hydromagnesite particles, which were translated from its population density in the size coordinates shown in Figure 10, are shown in Figure 11 as a population density plot (ln n versus v on a logarithmic scale). The volume population density versus crystal volume over the entire range is fitted and an logarithmic function is obtained. 7879



Article

Figure 8. Scanning electron microscopic images of hydromagnesite particles precipitated at initial MgCl2 concentration of 1.0 mol/L and different residence times.

Figure 11. Volume population density data for hydromagnesite particles precipitated under supersaturation of 5.96 and residence time of 5400 s.

Figure 9. Evolution of mean crystal size with relative supersaturation at the same residence time.

rate, and agglomeration kernel using eqs 19, 20, and 21, respectively. In addition, the linear growth rate can also be calculated.24 The values of the calculated volume growth rate, linear growth rate, nucleation rate, and agglomeration kernel for all experiments are provided in the Supporting Information. As can be seen from Table 3 in the Supporting Information, the calculated volume growth rates and linear growth rates range from 0.28 × 10−19 to 2.57 × 10−19 m3/s and from 0.92 × 10−9 to 3.29 × 10−9 m/s, respectively. 4.4.1. Growth Kinetics Correlation. The crystal volume growth rates of hydromagnesite particles are correlated using a linear least-squares technique by the empirical power equation (eq 22). The regressed correlation in volume coordinate is expressed as Gv = 5.41 × 10−21σ 1.55

In addition, using the same method as above, the linear growth rates of hydromagnesite particles can be expressed in terms of the relative supersaturation σ as follows:

Figure 10. Typical population density distribution of produced hydromagnesite at supersaturation of 5.96 and residence time of 5400 s.

ln(nv) = −1.81 ln(v) + 3.52

(28)

GL = 3.42 × 10−10σ 0.95

(27)

(29)

The mean square errors of eqs 28 and 29 are 2.47 and 1.26%, respectively. Figure 12 shows the comparison of the growth rates between the calculations and the experiments. It is clear that the deviation basically evenly occurred in experiments, and the calculation results basically coincide with the experimental results. By substituting eq 25 into eq 28, the following expression is obtained.

The correlation coefficient is 0.9962. As shown in Figure 11, the population density data in volume coordinates show a slightly downward convex curvature at large size. 4.4. Determination of Crystallization Kinetics Parameters for Hydromagnesite. All these population density data in crystal volume coordinates were used to calculate numerically the moments with respect to crystal volume up to second order using eq 18. The calculated moments were then used to determine the crystal volume growth rate, apparent nucleation

Gv ∝ τ −0.40 7880

(30) dx.doi.org/10.1021/ie300213c | Ind. Eng. Chem. Res. 2012, 51, 7874−7883


Article

relationship of the nucleation rate with respect to the volume growth rates and magma density (eq 31) is applicable for the systems studied, as deviation from the diagonal of Figure 13 basically evenly occurred in all experiments. The exponent of Gv is −1.51 in eq 31. A negative kinetic order is probably a characteristic of size-limiting nucleation phenomena found in MSMPR studies, as described by Randolph25 and Youngquist.26 The magma density has an important influence on the nucleation rate. Furthermore, through eq 31, the nucleation rate increases with the increase of magma density. 4.4.3. Agglomeration Kinetics Correlation. Agglomeration kernels obtained in all the experiments are correlated by the

Figure 12. Growth rate correlation for hydromagnesite.

This result shows that the mean residence time has a negative effect on the volume growth rate of hydromagnesite at the other same experimental conditions. From eqs 28 and 29, it can be seen that the exponential rates of Gv and GL to σ are 1.55 and 0.95, respectively. This shows that the crystal growth rate increase with the increase of the relative supersaturation, but the volume growth rate increases more sharply. The volume growth kinetic exponent in relative supersatureation is 1.55 (eq 28), which is in the range of 1−2. This indicates that the volume growth mechanism of hydromagnesite is controlled by both masstransfer and surface-integrated mechanisms. A near-unity exponent of σ in the linear growth kinetics (eq 29) indicates that the linear growth mechanism of hydromagnesite at higher temperature (80 °C) may be controlled by mass transfer. 4.4.2. Nucleation Kinetics Correlation. Nucleation kinetics for MSMPR experiments are usually correlated empirically by eq 23, and parameter estimates obtained by multiple linear regression analysis of all the nucleation rate data gave the correlation B0 = 6.71 × 10−21Gv−1.51M T 3.58

Figure 14. Agglomeration kernel correlation for hydromagnesite.

empirical power law relationship (eq 24) as shown in Figure 14. The regressed correlation is expressed as β = 4.30 × 10−38Gv−1.27B0−0.11τ −0.56

(32)

In this correlating equation, the exponents of Gv, B0, and τ are −1.27, −0.11, and −0.56, respectively. Generally speaking, the volume growth rate Gv can be taken as the measure of the solution supersaturation, while the nucleation rate B0 provides a total rate measurement of newly generated particles, and the mean residence time τ provides a measurement of the probability of a particle staying within an MSMPR crystallizer. Therefore, the products of Gvτ and B0τ can provide the mean crystal volume of a particle from the slurry and the number of crystals of newly generated particles in the MSMPR crystallizer. By substituting eq 31 into eq 32, the expression of β ∝ MT−0.39 for hydromagnesite agglomeration in this work is obtained. The magma density shows a negative effect, perhaps indicating that increasingly frequent and energetic collisions at high solid concentrations have an effect in breaking down the agglomerates. However, by substituting eq 30 in eq 32, the expression of β ∝ τ0.23 for runs 3, 7, 11, 15, and 19 provided in the Supporting Information is obtained. The mean residence time shows a positive effect on hydromagnesite agglomeration at the same experimental conditions. In addition, through the correlation equation (eq 32), compared to the volume growth rate Gv and mean residence time τ, the nucleation rate appears have less effect on the agglomeration kernel. Therefore, the increase of crystal size with increasing mean residence time is mainly attributed to the agglomeration between two particles (as shown in Figure 7). The agglomeration is significantly more than the

(31)

In order to show the overall prediction performance, the predicted and the experimental nucleation rates are compared and plotted in Figure 13. The results indicate that the

Figure 13. Nucleation rate correlation for hydromagnesite. 7881



Article

breakage caused by the collision between particles in the reactive crystallization system for hydromagnesite. Furthermore, the expression of β/B0 ∝ σ−0.54 for runs 13−16 can be obtained. The results indicate that the nucleation rate is superior to the aggregation rate of nuclei in the solution with higher supersaturation. Therefore, there is less time for the aggregated particles to grow, which induces the decrease of the mean particle size (as shown in Figure 9).

5. CONCLUSIONS The crystallization kinetics of hydromagnesite from the MgCl2− Na2CO3−NaOH−H2O system was systematically investigated in a steady-state MSMPR crystallizer. The experimental results showed that the mean crystal size first increased and then decreased with increasing supersaturation at the same mean residence time, and the optimal concentrations of MgCl2, Na2CO3, and NaOH were found to be 1.0, 1.0, and 0.28 mol/L, respectively. The volume growth rate, secondary nucleation rates, and agglomeration kernels of hydromagnesite were obtained as 0.28 × 10−19−2.57 × 10−19 m3/s, 0.26 × 1014− 5.84 × 1014 number/m3 s, and 0.72 × 10−17−5.61 × 10−17 m3/ number·s, respectively. The positive order of the mean residence time in the expression of β ∝ τ0.23 for hydromagnesite agglomeration in the reactive system indicates that the agglomeration increases with increasing mean residence time. The agglomeration is significantly more than the breakage caused by the collision between particles in the reactive crystallization system for hydromagnesite. The experimental data and their kinetic interpretation can be a useful reference material providing a basis for reaction crystallization of hydromagnesite by reacting the two byproducts, MgCl2·6H2O from the potassium fertilizer production and Na2CO3·10H2O from the ADC foamer production, in modern industrial-scale technologies.

■

■

ASSOCIATED CONTENT

S Supporting Information *

Table 1 listing the temperature coefficients of β(0), β(1), and Cϕ in the Pitzer model for the Na−Mg−Cl−OH−CO3−HCO3−H2O system; Table 2 listing the Pitzer ion-interaction parameters, θ and ψ, for Na−Mg−Cl−OH−CO3−HCO3−H2O system; Table 3 listing the experimentally measured and calculated parameters for 4MgCO3·Mg(OH)2·4H2O. This material is available free of charge via the Internet at http://pubs.acs.org.

■

ρc = crystal density (kg/m3) Li = average size of the ith crystal fraction (m) ΔLi = size range of the ith crystal fraction (m) V = crystallizer working volume (m3) kg, kR, and kβ = empirical constants accounting for other significant variables n = volume population density (number/m3) nL = population density (number/m3) v = crystal volume (m3) τ = mean residence time (s) Gv = volume growth rate (m3/s) GL = linear growth rate (m/s) Ba = empirical birth function over a volume v and v + dv Da = empirical death function over a volume v and v + dv Ba − Da = agglomeration term Bd − Dd = rupture term MT = slurry density (kg·m−3) Δw = weight fraction between vi and vi+1 Δv = volume interval between vi and vi+1 (m3) v ̅ = mean crystal volume between vi and vi+1 (m3) σ = relative supersaturation B0 = nucleation rate (number/m3 s) β = agglomeration kernel (m3/number·s) μi = ith moment of distribution (number·m3i/m3) Ksp = solubility product of hydromagnesite m2 = second moment (μm2/L) m3 = third moment (μm3/L) T = absolute temperature (K) R = universal gas constant (J/mol K) ΔH° = standard state enthalpy change (J/mol) aH2O = activity of water ϕ = osmotic coefficient γ = activity coefficient of ions m = molality of ions in eq 4 (mol/kg)

REFERENCES

(1) Cheng, W. T.; Li, Z. B. Controlled supersaturation precipitation of hydromagnesite for the MgCl2-Na2CO3 system at elevated temperatures. Ind. Eng. Chem. Res. 2010, 49, 1961−1974. (2) Mitsuhashi, K.; Tagami, N.; Tanabe, K.; Ohkubo, T.; Sakai, H.; Koishi, M.; Abe, M. Synthesis of microtubes with a surface of “House of Cards” structure via needlelike particles and control of their pore size. Langmuir 2005, 21, 3659−3663. (3) Fernández, A. I.; Chimenos, J. M.; Segarra, M.; Fernández, M. A.; Espiell, F. Procedure to obtain hydromagnesite from a MgO-containing residue. Kinetic study. Ind. Eng. Chem. Res. 2000, 39, 3653−3658. (4) Rosa, R. Procede de production de derives du magnesium. EP0732304A1, 1996. (5) Zhang, Z. P.; Zheng, Y. J.; Ni, Y. W.; Liu, Z. M.; Chen, J. P.; Liang, X. M. Temperature- and pH-dependent morphology and FT-IR analysis of magnesium carbonate hydrates. J. Phys. Chem. B 2006, 110, 12969− 12973. (6) Li, Q.; Ding, Y.; Yu, G. H.; Li, F. Q.; Qian, Y. T. Fabrication of lightemitting porous hydromagnesite with rosette-like architecture. Solid State Commun. 2003, 125, 117−120. (7) Drever, J. I. The Geochemistry of Natural Water. Surface and Groundwater Environments, 3rd ed.; Prentice Hall: Upper Saddle River, NJ, USA, 1997. (8) Xiong, Y. L. Experimental determination of solubility constant of hydromagnesite (5424) in NaCl solutions up to 4.4 m at room temperature. Chem. Geol. 2011, 284, 262−269. (9) Millero, F. J.; Pierrot, D. A chemical equilibrium model for natural waters. Aquat. Geochem. 1998, 4, 153−199. (10) Millero, F. J.; Roy, R. A chemical model for the carbonate system in natural waters. Croat. Chem. Acta 1997, 70, 1−38.

AUTHOR INFORMATION

Corresponding Author

*Tel./fax: +86-10-62551557. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors are grateful for financial support from the National Basic Research Program of China (973 Program, 2009CB219904), the National Natural Science Foundation of China (21076213, 21076212, and 21146006), and the Key Program in Science & Technology of Qinghai Province (Grant 2010-G-A4).

■

NOTATION α = crystal volumetric shape factor Mi = mass of the ith crystal fraction (kg) Vi = volume of the ith crystal fraction (m3) 7882



Article

(11) He, S.; Morse, J. W. The carbonic acid system and calcite solubility in aqueous Na-K-Ca-Mg-Cl-SO4 solutions from 0 to 90 °C. Geochim. Cosmochim. Acta 1993, 57, 3533−3554. (12) Pitzer, K. S.; Peiper, J. C.; Busey, R. H. Thermodynamic properties of aqueous sodium chloride solutions. J. Phys. Chem. Ref. Data 1984, 13, 1−102. (13) Pabalan, R. T.; Pitzer, K. S. Thermodynamics of concentrated electrolyte mixtures and the prediction of mineral solubilities to high temperatures for mixtures in the system Na-K-Mg-Cl-SO4-OH-H2O. Geochim. Cosmochim. Acta 1987, 51, 2429−2443. (14) Harvie, C. E.; Møller, N.; Weare, J. H. The prediction of mineral solubilities in natural waters: The Na-K-Mg-Ca-H-Cl-SO4-OH-HCO3CO3-CO2-H2O system to high ionic strengths at 25 °C. Geochim. Cosmochim. Acta 1984, 48, 723−752. (15) Marion, G. M. Carbonate mineral solubility at low temperatures in the Na-K-Mg-Ca-H-Cl-SO4-OH-HCO3-CO3-CO2-H2O system. Geochim. Cosmochim. Acta 2001, 65 (12), 1883−1896. (16) Randolph, A. D.; Larson, M. A. Theory of Particulate Processes; Academic Press: New York, 1988. (17) Smoluchowski, M. Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Lösungen. Z. Phys. Chem. 1917, 92, 129− 168. (18) Tavare, N. S.; Patwardhan, V. Agglomeration in a continuous MSMPR crystallizer. AIChE J. 1992, 38, 377−384. (19) Hounslow, M. J.; Ryall, R. L.; Marshall, V. R. A discretized population balance for nucleation, growth, and aggregation. AIChE J. 1988, 34 (11), 1821−1832. (20) Liao, P. F.; Hulburt, H. M. Agglomeration processes in suspension crystallization. Presented at the AIChE Meeting, Chicago, IL, USA, December 1976. (21) Tavare, N. S. Mixing in continuous crystallizers. AIChE J. 1986, 32 (5), 705−732. (22) Chen, P.-C.; Chen, C. C.; Fun, M. H.; Liao, O. Y.; Jiang, J. J.; Wang, Y. S.; Chen, C. S. Mixing and crystallization kinetics in gas-liquid reactive crystallization. Chem. Eng. Technol. 2004, 27, 519−528. (23) Hulburt, H. M.; Katz, S. Some problems in particle technology: a statistical mechanical formulation. Chem. Eng. Sci. 1964, 19, 555−574. (24) Yin, Q. X.; Wang, J. K.; Xu, Z.; Li, G. Z. Analysis of concentration multiplicity patterns of continuous isothermal mixed suspension-mixed product removal reactive precipitators. Ind. Eng. Chem. Res. 2000, 39, 1437−1442. (25) Randolph, A. D.; Cite, M. D. Nucleation kinetics of the potassium sulfate-water system. AIChE J. 1972, 18, 798−807. (26) Youngquist, G. R.; Randolph, A. D. Secondary nucleation in a class II system: ammonium sulfate-water. AIChE J. 1972, 18, 421−429.

7883


Crystallization and Agglomeration Kinetics of Hydromagnesite in the

Recommend Documents