Kinetics of magnesium hydroxide precipitation from

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Chemical Engineering and Processing 47 (2008) 215–221

Kinetics of magnesium hydroxide precipitation from sea bittern A. Alamdari ∗ , M.R. Rahimpour, N. Esfandiari, E. Nourafkan Department of Chemical Engineering, School of Engineering, Shiraz University, Post Code 7134851154, Shiraz, Iran Received 23 May 2006; received in revised form 8 December 2006; accepted 13 February 2007 Available online 28 February 2007

Abstract Magnesium hydroxide is a valuable chemical produced almost in pure form from seawater and its bitterns through precipitation process. Product size distribution of magnesium hydroxide affects the ease of downstream processes of filtration and drying. Therefore, gaining insight into kinetic information in order to improve the size distribution of product particles is essential. In this work, a mechanistic model has been developed for precipitation of magnesium hydroxide from sea bittern. The parameters of model equations based on the population balance concept have been determined using the experimental data of precipitation from a pure synthetic solution containing 3% Mg2+ and a sea bittern from salt production unit of a local petrochemical complex. The model suggests a higher nucleation rate coefficient and a lower growth rate coefficient for precipitation from the sea bittern compared to that from pure synthetic solution. The nucleation increase and growth decrease which were attributed to the effects of impurities in the bittern, would decrease the settling velocity of the product particles and therefore make the filtration process in industrial use more difficult. However, a larger coefficient of agglomeration rate was predicted by the model for precipitation from the bittern favor to product settling. © 2007 Elsevier B.V. All rights reserved. Keywords: Magnesium hydroxide; Reactive crystallization; Precipitation; Particle growth; Nucleation; Agglomeration

1. Introduction Magnesium hydroxide, the intermediate of magnesium oxide, is used mainly in industries of pharmaceutical, refractory, water and wastewater treatment and desulphurization of fuel gases [1]. Seawater is the main source for production of Mg(OH)2 due to containing of soluble salts of magnesium such as MgCl2 and MgSO4 . The concentration of magnesium ion is about 1272 ppm in seawater and about 30,000 ppm in the end bitterns of NaCl production units from seawater [2]. A chemical reaction between magnesium ions of seawater and an alkaline such as caustic soda will result in magnesium hydroxide precipitates as: Mg2+ + 2NaOH → Mg(OH)2 + 2Na+

(1)

Lime milk may also be used instead of caustic soda [2], but due to a low solubility of lime in water (0.159 g/100g H2 O at 25 ◦ C, [3]), however, lime particles and insoluble impurities in lime may enter the solid product of magnesium hydroxide caus∗

Corresponding author. Tel.: +98 711 2303071; fax: +98 711 6287294. E-mail address: [email protected] (A. Alamdari).

0255-2701/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.cep.2007.02.012

ing a detrimental effect on product purity. Use of lime as an alkaline solution in precipitation of magnesium hydroxide may also result in precipitation of calcium sulfate when the solution contains a high concentration of sulfate ions. Desulfation may be necessary when lime is used as a reagent for introduction of hydroxyl ions to the solution containing Mg2+ . Rabadzhieva et al. [2] desulfated natural brine using CaCl2 solution prior to precipitation of magnesium hydroxide. However, the impurity content of the product they obtained was high. Therefore, use of caustic soda as alkaline is more reasonable than lime when a very high pure product is desirable and when calcium compounds in the product have a detrimental effect on Mg(OH)2 applications as in refractory industry. Turek and Gnot [4] investigated the effect of temperature on the precipitation of Mg(OH)2 in the range 10–40 ◦ C when the precipitating agent was NaOH. They observed that precipitation at higher temperatures reduced the sedimentation rate and increased the humidity of the filter cake. These observations were apparently due to higher rates of reaction and consequently higher rates of supersaturation release and nucleation at higher temperatures. However, a higher rate of diffusion at higher temperature due to a lower viscosity increases the mass deposition on precipitates.

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The size enlargement of product is desired in industrial production of Mg(OH)2 due to difficult filtration of very fine particles. Products containing a large portion of fine particles will also cause dustiness problems in the drying process. Therefore, in industrial applications every effort is made to produce a relatively coarse product with a size distribution as narrow as possible. Gaining insight into kinetic information in order to increase the average size of product particles and improve the distribution is, therefore, indispensable. The present investigation is aimed at gaining kinetic information of magnesium hydroxide precipitation from sea bittern, wasted from salt production units. Kinetic information is helpful in design and optimization of the precipitation process in industrial production of magnesium hydroxide. 2. Experimental Experiments were carried out both batch and semi-batch wise at room temperature in a one-liter crystallizer equipped with a stirrer using both synthetic solution and sea bittern. Caustic solution (250 ml, 1N) was added drop-wise by a burette to the crystallizer containing 100 ml of sea bittern or synthetic 3% Mg2+ solution. Preliminary precipitation experiments were carried out to adjust the supersaturation release rate at which the primary nucleation was not dominant. Therefore, the flow rate of caustic addition thereafter was adjusted to 4 ml/min to avoid primary nucleation. In order to prevent excessive nucleation, enough mass of Mg(OH)2 powder as seed (15 g) was added to the solution prior to commencement of the reaction. This amount of seed provides a suspension density of around 15% at the commencement of the precipitation runs, almost the common suspension density utilized in industrial trials. The size distribution of seed particles is shown in Fig. 1. After addition of the first half of the caustic soda solution (31 min), the reaction was paused and the suspension in the crystallizer was filtered. The filter cake was washed and the size distribution of particles was analyzed. Then, the particles were returned to the mother solution in the crystallizer, and the reaction was restarted with the same flow rate of caustic

addition. The reaction was terminated when the second half of the caustic solution had been consumed (62 min). The product particles were filtered and analyzed for size distribution. During the course of reaction at specified time intervals the mother solution was sampled and analyzed for pH and the magnesium ion concentration. The method of titration with EDTA was used to determine the concentration of Mg2+ in the mother solutions. Due to measurement limitations of the sieve set for fine size ranges of particles, size distribution was analyzed by the hydrometry method where size is calculated based on measurements of suspension density changes with time due to settling of particles in a fluid. Hydrometry is a standard method for measuring sizes of particles less than 75 ␮m [5]. In order to verify the consistency of hydrometry method with sieve analysis, an initial powder sample of magnesium hydroxide was split into two almost identical samples using method of multiple divisions and then the resulting two samples were analyzed by wet screening and hydrometry. In order to find how the particles are agglomerated together the method of Scanning Electron Microscopy (SEM) was performed using an Oxford 5526 (Link Pentafet) microscope operating at 20 kV. 3. Mathematical modeling Equations of mass and population balances were coupled together with appropriate initial and boundary conditions in order to model the precipitation of Mg(OH)2 . Considering an interval of particle size and number of particles entering and exiting the interval because of growth and agglomeration, the population balance equation for a batch or semi-batch precipitation process in the absence of particle breakage is written as [6]: ∂n(v, t) ∂(n(v, t)Gv ) + ∂t ∂v  v 1 = C(t, u, v − u)n(v − u, t)n(u, t) du 2 0  ∞ −n(v, t) C(t, v, u)n(u, t) du

(2)

0

Fig. 1. Experimental size evolution of particles during the course of precipitation from sea bittern.

where n(v, t) is the population density of v size particles at time t, Gv the growth rate defined based on particle volume as size, C the agglomeration kernel, and u is a dummy variable of size. The first term on the right side of Eq. (2) represents the rate of formation of new v size particles by agglomeration of smaller ones. The second term on the right is for death of v size particles which agglomerate with other particles. The kernel function C(t, v, u) represents the frequency at which particles of size v and size u collide and then agglomerate. The relation between mass deposition on Mg(OH)2 particles and the changes in Mg2+ concentrations in solution is represented by the mass balance equation. The reaction between Mg2+ and NaOH generates solute mass in the solution and the particle growth consumes mass from the solution and deposits it on the solid phase. Since there is no outflow of mass from the solution, the mole balance equations on ions of OH− and Mg2+

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respectively, are: dMTot 2 Q d(V [OH− ]) − = dt MWNaOH MWMg(OH)2 dt

(3)

dMTot d(V [Mg2+ ]) 1 + =0 dt MWMg(OH)2 dt

(4)

where [OH− ] and [Mg2+ ] are concentrations of hydroxyl and magnesium ions in mol/l, respectively. V is the volume of solution, Q the mass flow rate of NaOH on dry basis, and MTot represents the total mass of particles suspended in the solution. The dimensionless supersaturation is represented as [7]: [Mg2+ ][OH− ] − ksp ksp

Fig. 2. Accuracy of numerical solution with changes in time increment.

2

S=

(5)

where ksp is the solubility constant of Mg(OH)2 . Nucleation and growth rates (B◦ and GL ) were correlated to supersaturation, respectively, as: B◦ = kn S b MT

(6)

GL = kg S g

(7)

where kg is the coefficient of growth rate equation. The supersaturation at the commencement of reaction and the seed mass and size distribution were the initial conditions. The boundary conditions for solving the mass and population equations are n(t, vmax ) = 0 n(t, vmin ) =

B◦ Gv

(8) (9)

where vmin and vmax are the minimum and maximum sizes in the distribution, respectively. The growth rate based upon particle volume as size is Gv = 3kg kv1/3 S g v2/3

(10)

where kv is the volume shape factor of particles. Simultaneous solution of mass and population equations, using numerical implicit method of Crank–Nicolson [8], calculated population density of particles and size distributions of product at various times. The partial derivatives in the population balance equation were replaced by the following difference approximations: ∂n ni+1,j − ni,j = ∂t t   ∂n log e 1 ni,j+1 − ni,j−1 ni+1,j+1 − ni+1,j−1 = + ∂v v 2 2  log v 2  log v

(11) (12)

Logarithmic size increments were chosen to expand small size ranges which include highest number of particles in the distribution. The particle size domain (from 4 to 57 ␮m) was divided to 55 geometrically progressive intervals ( log v = 0.065). This increases the size range by around 5% for the succeeding interval. Due to nonlinear nature of nucleation, growth and agglomeration functions the analytical solution for balance equations

was unattainable. However, for some simplified cases of population equation the analytical solutions have been reported [9]. The numerical solution was verified by comparing the distributions generated by the numerical method with those generated through analytical solution for some limited conditions where analytical solutions were available. The accuracy of numerical solution increases as the value of time increment is reduced, on the other hand applying a very short time increment, necessitates much longer calculations. Tending to find an optimum value for t, an objective function of difference between analytical solution and numerical solution was defined. Fig. 2 shows variations of objective function as the time increment is changed. As the figure shows, a time increment less than 30 s does not improve the accuracy of numerical solution further. Therefore a time increment of 30 s was chosen to run the program. 3.1. Estimation of parameters The model parameters need to be evaluated in order to enable the model to predict the size distribution of product. Therefore, the initial values of parameters were guessed and later corrected in order the size distributions generated by the model be fitted to the experimental results. This trial and error procedure optimizes the values of kinetic parameters. The objective function representing the closeness of model and experimental results includes information from both solid and liquid phases as:  nM    Mexp (i) − Mmodel (i)    fobj (kg , kn , ka , g, b, a) =   Mexp (i) i=1

 nS    Sexp (j) − Smodel (j)    ×   S (j) j=1

(13)

exp

The first part on the right side of Eq. (13) is solid information in terms of difference between the model calculated mass distribution and those calculated from the experimental measurements and the second part is liquid information in terms of difference between the model calculated supersaturations of magnesium hydroxide and the supersaturations calculated from the concentrations measured by pH and titration. nM is the number of readings in hydrometry method. Each reading corresponds to a

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specific size in the distribution, and nS is the number of measured Mg2+ concentrations in solution. Using an optimization routine “fminsearch” for minimization of the objective function, the best values of kinetic parameters of nucleation, agglomeration, and growth rates were estimated. The unconstrained nonlinear optimization routine “fminsearch” uses the simplex search method to find the minimum of a scalar function of several variables starting at an initial estimate [10]. In order to make the values of objective function reasonable and dimensionless, the difference values in the definition of function were divided by the experimental values. Use of solid and liquid phase information in objective function for parameter estimation gives more reliable parameters than the case using information only from one phase. 4. Results and discussion Preliminary experiments showed that seeding in precipitation of Mg(OH)2 improves the filterability of product. Therefore, the later experiments were carried out in the presence of seed particles, which provided enough surface area for supersaturation release and prevented primary nucleation. Results of particle size analysis of two almost identical powder samples of Mg(OH)2 , using methods of wet screening and hydrometry, showed that results of particle size measurement by hydrometry is consistent with those by wet screening. However, hydrometry is able to measure particles in a finer size range (Fig. 3). Products of batch experiments in which reactant solutions of MgCl2 and NaOH were intermixed instantly in stoichiometric portions, were very fine due to creation of a large amount of supersaturation in a very short time which caused primary nucleation. Semi-batch operations in which the caustic soda solution was added gradually to the magnesium chloride solution at a constant rate resulted in coarser products than those produced in batch experiments. Gradual intermixing of the two reactants prevented spontaneous generation of extensive supersaturation and massive nucleation, and consequently caused the consumption of supersaturation mainly on growth of particles rather than on nucleation. In these preliminary experiments, at flow rates

Fig. 3. Comparison of size measurements by methods of hydrometry and sieve analysis.

Fig. 4. Supersaturations calculated from experimental data during the courses of precipitation from sea bittern.

of caustic addition higher than 4 ml/min, the clear solution in the vicinity of flow inlet turned turbid immediately after starting caustic addition, but at caustic flow rates of 4 ml/min the solution remained transparent. This observation suggested that primary nucleation was prevented at low caustic addition. The product particles of preliminary experiments were very fine and did not settle even after several days. Production of coarser particles in semi-batch experiments of this study in which the Mg2+ ions was in excess at initial stages of experiment course was consistent with the conclusions made by Turek and Gnot [4] which stated that precipitation of Mg(OH)2 in presence of excess OH− resulted in product with a lower sedimentation rate than in presence of excess Mg2+ . Each semi-batch experiment was performed 3 times. Product size distributions of 3 experiments at the end of both halves after 31 min and after 62 min and supersaturations during the courses of 3 runs were consistent with each other (Figs. 1 and 4). This consistency of experimental results suggests that the particle size distribution of products are almost reproducible. Small value of ksp for Mg(OH)2 increases the micromixing effects. However, low viscosity of solution, intensive agitation resulting high energy dissipation rate in a small volume of suspension, and very low flow rate of reagent addition are factors which reduce the micromixing effects [11]. Fig. 5 shows two representative micrographs of Mg(OH)2 particles grown from synthetic solution and sea bittern in this study. As the micrographs show the appearance of agglomerated secondary particles is conglomerate. The shape of secondary particles produced in this study is in good agreement with the shape of particles produced in another study by reaction between sodium hydroxide and magnesium chloride [12]. The conglomerate shape of particles suggests an approximate shape factor of π/6 necessary in calculating the growth rate based upon particle volume as size. Tending to have integer orders of rate dependency of mechanisms with respect to their driving forces, the optimization process were carried out in two stages; firstly, all parameters were allowed to freely be optimized, and secondly, the order

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Table 1 Estimated kinetic parameters of growth, nucleation, and agglomeration rates of magnesium hydroxide precipitation from synthetic liquor and from sea bittern Parameter

Synthetic solution

Growth rate coefficient, kg (␮m s−1 ) Mean value Standard error

3.01 × 10−5 0.080 × 10−5

Sea bittern 2.13 × 10−5 0.142 × 10−5

Growth rate order with respect to 1 supersaturation, g Nucleation rate coefficient, kn (# s−1 gcrystal −1 ) Mean value 0.335 Standard error 0.0595

1

Nucleation rate order with respect to 3 supersaturation, b Agglomeration rate coefficient, ka (gsolution #−1 s−1 ␮m−3 ) Mean value 9.55 × 10−17 Standard error 1.45 × 10−17

3

Agglomeration rate order with respect to supersaturation, a

1

0.418 0.0764

11.25 × 10−17 0.65 × 10−17 1

31 min. The average relative error between the model calculated and the experimental data was 3.24%. This error was calculated as:  nM   Mexp (i) − Mmod (i)  1    × 100 Error = (17)   nM Mexp (i) i=1

Fig. 5. Representative micrographs showing particles precipitated from: (top) seed in synthetic liquor; (bottom) seed in bittern.

parameters were fixed to the closest integers obtained at first stage of optimization and then the coefficient parameters were allowed to freely be optimized for the second time. The optimization process was individually carried out using data from each run of experiments and mean value and standard error of obtained parameters were calculated. The mean values and the standard error of kinetic parameters of growth, nucleation, and agglomeration rates, for precipitation from both synthetic pure liquor and sea bittern are reported in Table 1. Mean value and standard error of parameters were calculated from the following equations: ne xi x¯ = i=1 (14) ne  ne ¯ )2 /(ne − 1) i=1 (xi − x (15) S.E. = √ ne

Fig. 1 shows the seed size distribution used as the initial condition for model solution and the experimental size evolution of particles during the course of precipitation from sea bittern. According to the mean values of kinetic parameters higher nucleation and agglomeration rates and a lower growth rate is anticipated for precipitation from the sea bittern than from the synthetic pure liquor at the identical conditions. These effects may be attributed to the adsorption of impurities present in the bittern on the active sites of magnesium hydroxide particles. An almost extensive literature survey revealed no previous estimation for parameters of precipitation mechanisms of Mg(OH)2 to be compared to the values of parameters obtained in this study.

where xi represents the optimum value of each parameter and ne is the number of repetition of each experiment. Note that among the agglomeration kernels of shear flow, turbulent and size independent which were examined the turbulent kernel function [13] C(t, u, v) = ka S a (u1/3 + v1/3 )|u2/3 − v2/3 |

(16)

best fitted to experimental data. This experimental data was the size distribution of the product filtered after the addition of the first half of the caustic soda solution. Fig. 6 shows the PSD calculated by the model and that measured in the experiment after

Fig. 6. Illustration of model fitting of mass distribution to the corresponding experimental data of precipitation from sea bittern after 31 min.

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Fig. 7. Comparison of mass distribution of product predicted by the model beyond the conditions at which the parameters were tuned with the corresponding experimental data of precipitation from sea bittern.

4.1. Model verification The model was verified for prediction of product PSD, total mass of solid, and supersaturation in the solution beyond the range at which the parameters had been tuned. Experimental data obtained at the end of the second half of the caustic addition period was used for this verification. Product of the first half period was considered as seed (initial condition) and the model was allowed to run for next 31 min with the same rate of caustic addition and to predict the product size distribution, total mass and supersaturation. Fig. 7 shows the product size distribution at end of the second half of caustic addition period for both experimental and model runs. Closeness of model predictions to experimental data represents the accuracy of the values of parameters. The difference between the model predictions and the experimental data was 12.63%. Fig. 8 shows the model predicted supersaturations and those calculated from experimental data both during the first and second halves of caustic addi-

Fig. 9. Comparison of total mass predicted by the model for the first half period and for the second half period beyond the conditions at which the parameters were tuned with the corresponding experimental data of precipitation from sea bittern.

tion period. The declining trend of supersaturation is because Mg2+ concentration reduced with time due to precipitation of Mg(OH)2 . However, caustic addition compensates the consumption of hydroxyl ion through precipitation. Therefore, the pH of the solution remains almost constant in the range 9.2–9.4 during the course of caustic addition as practically observed. However, minute changes in pH may be due to increase in the volume of solution. Closeness of model predictions with the experimental data for both PSD and supersaturation beyond the conditions at which the parameters were tuned verifies the validity of the model. However, predicted supersaturations by the model deviated to some extent from the experimental data at the last stages of the second period as shown in Fig. 8. Comparison of total mass predicted by the model with the experimental data of precipitation from sea bittern during the first half of caustic addition and beyond the conditions at which the parameters were tuned during the second half is shown in Fig. 9. It is of note that in minimization of difference between the model calculated and the experimental data, the mass distribution of particles at the end of the first half and the supersaturations of magnesium hydroxide in the course of the first half were included in the definition of objective function. 5. Conclusions

Fig. 8. Comparison of supersaturation predicted by the model for the first half period and for the second half period beyond the conditions at which the parameters were tuned with the corresponding experimental data of precipitation from sea bittern.

Precipitation process of magnesium hydroxide from both a synthetic solution of 3% Mg2+ ions and an industrial sea bittern was experimentally studied focusing on particle growth and size enlargement. Gradual intermixing of reactants, leading to slow release of supersaturation, resulted in a coarser product. Using mass and population balances, the process was formulated and the model parameters were estimated by best fitting the model predictions to the experimental data. The nucleation rate equations for precipitation from synthetic solution and the bittern suggested by the model were B◦ = 0.335S3 MT and B◦ = 0.418S3 MT , respectively, and the growth rate equations for these solutions were GL = 3.01 × 10−5 S and GL = 2.13 × 10−5 S,

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respectively. A turbulent kernel function of agglomeration with an order of 1 with respect to supersaturation and coefficients of ka = 9.55 × 10−17 and 11.25 × 10−17 for synthetic solution and the bittern, respectively, best fitted to experimental data. The performance of the model was verified by comparison of the model predictions with the experimental data beyond the data range in which the parameters were optimized. A greater estimated value for the order parameter of nucleation rate (3) than that for growth rate (1) indicates that nucleation is the dominant mechanism in magnesium hydroxide precipitation from both synthetic liquor and sea bittern. Higher nucleation and agglomeration rate coefficients and lower growth rate coefficient for precipitation from the sea bittern compared to those from the synthetic pure liquor are attributed to the impurities in the bittern. These effects are likely to increase the inclusion of impurities between the product particles and reduce the mechanical strength of the grains in an industrial plant of magnesium hydroxide recovery from sea bittern. However, a larger coefficient of agglomeration rate predicted by the model for particles precipitated from the bittern favors particle enlargement and settling which is diminished by a higher coefficient of nucleation rate and a lower coefficient of growth rate. Appendix A. Nomenclature

b B◦ C f

nucleation rate order with respect to supersaturation nucleation rate (# s−1 gsolution −1 ) agglomeration kernel (gsolution #−1 s−1 ) objective function representing the closeness of model predictions with experimental data g growth rate order with respect to supersaturation GL growth rate defined based on particle linear size (␮m s−1 ) growth rate defined based on particle volume as size Gv (␮m3 s−1 ) ka coefficient of agglomeration rate equation (gsolution #−1 s−1 ␮m−3 ) kg coefficient of growth rate equation (␮m s−1 ) kn coefficient of nucleation rate equation (# s−1 gcrystal −1 ) ksp solubility product constant (mol l−1 )3 kv volume shape factor of particles [Mg2+ ] concentration of magnesium ion (mol l−1 ) magma density (gcrystal gsolution −1 ) MT MTot total mass of particles in solution (gcrystal ) n population density of v size particles (# ␮m−3 gsolution −1 )

221

experimentally measured population density (# ␮m−3 gsolution −1 ) number of repetition of each experiment ne number of readings in hydrometry method correspondnM ing to a specific size in the distribution nmod model predicted population density (# ␮m−3 gsolution −1 ) nS number of samples from liquid phase for titration [OH− ] concentration of hydroxyl ion (mol l−1 ) Q mass flow rate of net caustic soda (gNaOH s−1 ) S supersaturation S.E. standard error of parameters t time (s) u a dummy particle size (␮m3 ) v particle size (␮m3 ) vmax maximum particle size of distribution (␮m3 ) minimum particle size of distribution (␮m3 ) vmin V volume of solution (l) xi the optimum value of each parameter

nexp

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