Solution-Mediated Transformation Kinetics of Calcium Sulfate

Nov 8, 2013 - Figure 4 shows the simulation curve with simulated A0 = 1.0, B0 = 1.06 ..... in gypsum produced from flue gas desulfurization Fuel 2006,...
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Solution-Mediated Transformation Kinetics of Calcium Sulfate Dihydrate to α‑Calcium Sulfate Hemihydrate in CaCl2 Solutions at Elevated Temperature Hailu Fu,† Guangming Jiang,† Hao Wang,† Zhongbiao Wu,†,‡ and Baohong Guan*,† †

Department of Environmental Engineering, Zhejiang University, Hangzhou 310058, China Zhejiang Provincial Engineering Research Center of Industrial Boiler & Furnace Gas Pollution Control, Hangzhou 311202, China

‡

ABSTRACT: α-Calcium sulfate hemihydrate (α-HH), a kind of advanced cementitious material, can be prepared from calcium sulfate dihydrate (DH) in electrolyte solutions. The kinetics of the DH−α-HH transformation in CaCl2 solutions was investigated to better understand and, hence, control the transformation process. The results showed that the DH−α-HH transformation is a nucleation−growth limited process, following a dispersive kinetic model. The α-HH nucleation and growth were both promoted significantly with the increment of CaCl2 concentration and temperature. This is due to the enlarged activation entropy change and supersaturation, which were caused by the decreasing water activity and increasing solubility product ratio (Ksp,DH/Ksp,HH), respectively. The rate of DH−α-HH transformation in aqueous solutions can be effectively controlled by regulating water activity and temperature.

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INTRODUCTION Large quantities of flue gas desulfurization (FGD) gypsum produced by coal-burning power plants have continuously raised significant environmental concerns.1,2 The recycling and utilization of these gypsums become rather important for environmental protection and gypsum industry. FGD gypsum is composed mostly by calcium sulfate dihydrate (DH),3 which can be transformed into α-calcium sulfate hemihydrate (α-HH) in the presence of inorganic or organic additives in aqueous solutions.3−6 Hence, the preparation of α-HH from FGD gypsum could be a potential alternative for FGD gypsum utilization3,7 owing to the superior physical property of α-HH.8 DH dissolution, α-HH nucleation, and growth constitute the solution mediated transformation.7,9,10 Four principal transformation scenarios are classified on the basis of the solid and liquid component evolution, including dissolution control,11 growth control,12 nucleation−dissolution control,13 and nucleation−growth control.14 The identification of the limiting step is essential for the control of the DH transformation to αHH. The DH−α-HH conversion is driven by their solubility difference. According to dissolution equilibrium, solubility product and water activity are two important factors affecting the solubility, which depends heavily on temperature and stock solution.15−18 For a given temperature, there exists a critical water activity at which both DH and α-HH would reach dissolution equilibrium (i.e., having the same solubility).19,20 Low water activity makes DH prone to dehydration, attempting to increase availability of the free water molecules.21 The increment of temperature or acidity (hydrochloric acid concentration) could enlarge the solubility difference between DH and α-HH and, hence, accelerate the conversion.6,21 However, the underlying relationship between the driving force and operational factors (i.e., electrolyte concentration and temperature) is still not clear. © 2013 American Chemical Society

The transformation among calcium sulfate phases versus time generally presents a sigmoidal profile.8,22,23 Many kinetic models have been proposed to describe the S-shaped transformation curve.22−25 However, these models were constrained in application, owing to the limits of symmetrical S-shaped profile and obscure physical interpretation. Dispersive kinetic model is developed on the basis of the Maxwell− Boltzmann (M−B) distribution of activation energies to describe the nucleation or denucleation limited polymorphic transformation.26,27 It has only two parameters endowed with physical meanings and fits well to series x−t sigmoidal transients.28,29 Thus, this model is expected to help to explore the DH−α-HH conversion kinetics. In this paper, the solution mediated DH−α-HH transformation kinetics was studied by monitoring the solid and liquid component evolution and using dispersive kinetic model. The effect of temperature and CaCl2 concentration on the transformation kinetics was evaluated in 2.50−3.50 m CaCl2 solutions at 90.0−100.0 °C for better transformation control from DH to α-HH.

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EXPERIMENTAL SECTION DH−α-HH Transformation. The transformation from DH to α-HH was performed at 90.0−100.0 °C in 2.50−3.50 m CaCl2 solutions, which were prepared by mixing analyticalgrade CaCl2 (Sinopharm Chemical Reagent Co., Ltd.) with deionized water. The solution of 1.0 L was transferred into a double-walled jacket reactor equipped with a condenser on top of it and a Teflon impeller. Temperature was monitored by a thermometer inserted into the reactor and kept at within ±0.2 Received: Revised: Accepted: Published: 17134

August 19, 2013 October 14, 2013 November 8, 2013 November 8, 2013 dx.doi.org/10.1021/ie402716d | Ind. Eng. Chem. Res. 2013, 52, 17134−17139

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°C of the desired temperature by circulating oil through the jacket. DH was added into the CaCl2 solution, and the conversion was monitored. Samples of suspension were withdrawn at different time intervals with the upper liquid being filtered through 0.22 μm membrane to test the SO42− ions concentration and the bottom slurry being quickly vacuum filtered. The solid was immediately washed with boiling water four times, rinsed with acetone once, and then dried at 45 °C in an oven for 12 h. On the basis of the crystal water content, the mole fractions of DH and α-HH in the solids were calculated. SO42− Ion Concentration Measurement and Solid Characterization. To determine the driving force for the conversion of DH to α-HH, the solubility was determined by measuring SO42− ion concentration at dissolution equilibrium. The SO42− ion concentration was measured by PCMultidirect COD Vario Moving Laboratories (ET99731, Tintometer GmbH Germany) at a wavelength of 450 nm according to the turbidity method.30 Thermogravimetry and differential scanning calorimetry (TG-DSC, STA-409PC, NET-ZSCH, Germany) was performed for phase identification and crystal water content determination. For TG-DSC measurements, about 8 mg of solid was sealed in a lidded Al2O3 crucible and scanned at a rate of 10 °C min−1 under an N2 gas atmosphere. The crystal morphologies were investigated by scanning electron microscopy (SEM, HITACHI S-4800 Japan).

Figure 2. SEM images of the solids withdrawn at 0 h (a), 5.0 h (b), 6.5 h (c), and 7.5h (d) during the DH−α-HH transformation in a 3.00 m CaCl2 solution at 90.0 °C.

a plate-like morphology with irregular shapes, but some show an elongated column-like morphology (Figure 2a). Short column α-HH crystals, which exhibit relatively smooth side faces and coarse end faces, are observed (Figure 2b) at 5.0 h. The growth of α-HH on DH surface is not observed. More αHH crystals aggregating together appear after 6.5 h reaction (Figure 2c). At the end of the conversion, the solid mainly consists of column-like α-HH crystals (Figure 2d). It is to be noted that a considerable amount of α-HH crystals interlock with each other, and some α-HH crystals are not well developed with defined crystal faces. The deformity of crystal lattice may be responsible for the disappearance of the α-HH characteristic exotherm in the DSC curves.9,31 The mole fraction of α-HH is calculated on the basis of crystal water content that was determined by the TG analysis. Figure 3 shows the profile of α-HH mole fraction is an

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RESULTS AND DISCUSSION Solution Mediated Transformation of DH−α-HH. Figure 1 tracks the transformation from DH to α-HH by

Figure 1. DSC patterns of the solids withdrawn at different time intervals during the DH−α-HH transformation in a 3.00 m CaCl2 solution at 90.0 °C.

DSC measurement. Two sequential endotherms demonstrate that the solid is mainly composed of DH at 4.0 h. The first endotherm denotes 1.5 H2O crystal water loss from DH, indicating a dehydration of DH into HH, and the second endotherm denotes 0.5 H2O crystal water loss from HH, indicating a dehydration of HH into soluble calcium sulfate anhydrite (AH-III). The first endotherm shrinks with time and disappears at 7.5 h, which means α-HH grows at the expense of DH and makes the only solid at 7.5 h. However, the characteristic sharp exotherm of α-HH that denotes AH-III conversion to insoluble anhydrite (AH-II)3 is not observed. The morphological evolution of the solid during DH−α-HH transformation is shown in Figure 2. Most DH crystals present

Figure 3. Evolution of the α-HH mole fraction and SO42− ion concentration during the DH−α-HH transformation in a 3.00 m CaCl2 solution at 90.0 °C.

asymmetrical S-shaped curve. No phase change is observed within the first 3.0 h. The α-HH mole fraction increases gradually to 0.027 after 4.0 h reaction, which implies that the main component is DH. This is consistent with the corresponding DSC curve. The DH−α-HH transition accelerates in the subsequent 2.5 h, showing an exponential 17135

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parameter, and β [h−2] is an activation entropy-related timedependent parameter. α and β are expressed as eqs 3 and 4

increasing trend. α-HH reaches a mole fraction of 0.97 at 7.5 h till it becomes the only solid. During the transformation, DH dissolves and releases SO42− ions into the solution, reaching a supersaturated state with respect to α-HH. After certain induction time, α-HH precipitates out from the solution. To explore the phase transformation kinetics, the SO42− ion concentration was monitored and shown in Figure 3. The SO 4 2− ion concentration over the whole process fluctuates around the solubility of DH (4.36 × 10−3 M), which is far higher than that of α-HH at 3.68 × 10−3 M. The driving force for α-HH crystallization stays almost constant through the conversion, which indicates that the rate controlling step is α-HH nucleation−growth. The sulfate concentration would decrease owing to the growth of α-HH if a longer time were provided. Simulation of the DH−α-HH Transformation Kinetics. The transformation among different calcium sulfate phases is often considered to be a crystal seed-catalyzed process, which can be described by the autocatalytic model (eq 1)22,23,32−34 y=

0

( )exp[(kA B0 A0

0

+ B0 )t ]

β=

(1)

k = α e βt

2

(5) (6)

Figure 4 shows that the dispersive kinetic model well fits the experimental data with α = 2.88 × 10−2 h, β = 1.22 × 10−1 h−2, and R2 = 0.9974. The fitting curve presents an asymmetric S shape, which coincides well with the evolution of experimental results. It precisely reflects the DH−α-HH transformation at the initiating and ending periods, avoiding the simulation deviation at 4.0, 5.0, 7.5, and 8.0 h by the autocatalytic model. The positive value of β suggests that the conversion from DH to α-HH is a nucleation-limited process.26,28 The activation energy barrier (Ea) drops down, and the reaction rate coefficient increases with time, which accounts for the faster DH−α-HH transformation with time. Effect of Temperature and CaCl2 on DH−α-HH Transformation Kinetics. Figure 5 shows the DH−α-HH transformation in 2.50−3.50 m CaCl2 solutions at 90.0−100.0 °C. The transformation accelerates significantly with the increase in CaCl2 concentration and temperature. The conversion time shrank from 11.0 to 1.0 h with the CaCl2 concentration increasing from 2.50 to 3.50 m at 95.0 °C. Similarly, the time required to complete the DH−α-HH conversion reduced from 7.50 to 1.0 h as the temperature increased from 90.0 to 100.0 °C in a 3.00 m CaCl2 solution. To investigate the kinetics, the transformation is divided into two stages. The first one is the induction time, which is defined as the time consumed to accomplish the first 10 mol % transformation.23 The second one is the crystals growth time consumed to cover the remaining 90 mol % transformation. The induction time is inversely proportional to the nucleation rate. Both the induction and growth time shrink with the increment of CaCl2 concentration and temperature, indicating a facilitation of α-HH nucleation and growth. Supersaturation, which is dominated by CaCl2 concentration and temperature, plays an important role in determining the αHH nucleation and growth rate. In aqueous solutions, dissolution of DH and α-HH follows the following relationships:

shows the simulation curve with simulated A0 = 1.0, B0 = 1.06 × 10−6, k = 2.16 h−1, and R2 = 0.9956. Though the simulation well fits the experimental data as a whole, it deviated clearly at 4.0, 5.0, 7.5, and 8.0 h. It could not precisely reflect the slow reaction before an explosive increment of α-HH occurs. Also, it slows down the final stage transformation. The autocatalytic simulation presents a symmetrical sigmoidal curve, which did not match the experimental results. To interpret the asymmetrical mole fraction evolution, the transformation kinetics was simulated with the dispersive kinetic model (eq 2)26,27

}

(4)

Ea = Ea0 − RTβt 2

Figure 4. Mole fraction evolution of α-HH in the solids simulated by the autocatalytic model and dispersive kinetic model.

{

ΔS* Rt 2

where R is the gas constant and ΔS* is the time-dependent activation entropy. The activation energy barrier is defined as the difference of the ground and activated state Gibbs free energy, which can be decomposed into activation enthalpy (Ea0) and activation entropy. The time and temperature dependent activation energy barrier and reaction rate coefficient are expressed as eqs 5 and 6

where A0 and B0 are the mole fractions of the reactant A and the product B at zero time, k is the rate constant, t is the time, and y is the increment of product B. A plot of y versus t gives a sigmoidal curve characterizing autocatalytic reactions. Figure 4

α x = exp − [exp(βt 2) − 1] t

(3)

where A is an Arrhenius-like frequency factor without entropic considerations, n is a constant that correlates to the dimensionality of the system, which is assumed to be 0 in eq 3, Ea0 is the Arrhenius-like time-independent portion of activation energy barrier, ΔH* is the corresponding activation enthalpy.

B0{exp[(kA 0 + B0 )t ] − 1} 1+

*

α = An − 1e 2e−Ea / RT = An − 1e−ΔH / RT

(2)

where x is the mole fraction of product, t [h] is the conversion time, α [h] is an activation enthalpy related time-independent 17136

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ratio of DH to α-HH can be derived (combining eqs 9 and 10) as K sp,DH ce,DH SHH = = ce,HH K sp,HHa w1.5 (11) Supersaturation is associated with solubility product and water activity. In this paper, solubility product was obtained from ref 10, and the water activity was determined by vapor balance method.19 Table 1 lists the solubility products and Table 1. Solubility Product (Ksp) of DH and α-HH and Water Activity (aw) in 2.50−3.50 m CaCl2 Solutions at 90.0− 100.0 °C batch 1 2 3 4 5

2+

)a(SO24 −)DH a w2

a w,crit

= γ(Ca 2 +)m(Ca 2 +)γ(SO24 −)m(SO24 −)a w2 K sp,HH = a(Ca

(7)

)a(SO24 −)HH a w0.5 (8)

where Ksp,DH and Ksp,HH are the solubility products of DH and α-HH, respectively, m(Ca2+) and m(SO42‑) are the molal concentrations of Ca2+ ion and SO42− ion in solution, respectively, γ(Ca2+) and γ(SO42‑) are the ion activity coefficients, and aw is the water activity. The solubility of DH and α-HH can be expressed as eqs 9 and 10: ce,DH = m(SO24 −)DH =

ce,HH = m(SO24 −)HH =

K sp,DH 2+

γ(Ca )γ(SO24 −)m(Ca 2 +)a w2

90.0 95.0

3.00 2.50 3.00 3.50 3.00

100.0

Ksp, DH

Ksp, HH

aw

1.72 × 10−5 1.58 × 10−5

2.14 × 10−5 1.77 × 10−5

1.45 × 10−5

1.46 × 10−5

0.75 0.81 0.75 0.69 0.75

⎛ K sp,DH ⎞2/3 ⎟⎟ = ⎜⎜ ⎝ K sp,HH ⎠

(12)

According to eq 12, the critical water activity at 90.0, 95.0, and 100.0 °C is 0.86, 0.93, and 1.00, respectively. In all experiments, the water activities are smaller than the corresponding critical water activities, which enables DH to have a larger solubility than α-HH, making the DH−α-HH transformation occur. As revealed in Table 1, temperature mainly affects the solubility product and has no effect on the water activity. The solubility products of both DH and α-HH decrease with the increase in temperature. However, the solubility product of αHH decreases to a larger extent with temperature. Consequently, the solubility product ratio of DH to α-HH (Ksp,DH/ Ksp,HH) increases from 0.80 at 90.0 °C to 0.99 at 100.0 °C. CaCl2 mainly influences the water activity, which decreases from 0.81 to 0.69 as the CaCl2 concentration varied from 2.50 to 3.50 m. Table 2 shows the evolution of the supersaturation, induction time, and apparent growth rate depending upon CaCl2 concentration and temperature. The apparent growth rate is defined as mole fraction increment of α-HH in a unit time during the second transformation stage. The supersaturation increases from 1.22 to 1.56 as the CaCl2 concentration changed from 2.50 to 3.50 m at 95.0 °C. Meanwhile, the supersaturation increases from 1.24 to 1.54 as the temperature varied from 90.0 to 100.0 °C in a 3.00 m CaCl2 solution. Higher supersaturation

2+

= γ(Ca 2 +)m(Ca 2 +)γ(SO24 −)m(SO24 −)a w0.5

CaCl2 (m)

water activities under different thermodynamic conditions. The calculated supersaturation in a 2.50 m CaCl2 solution at 95.0 °C according to eq 11 is 1.22. To verify the validity of eq 11, the actual solubility was determined by measuring the equilibrium SO42− ion concentration. The solubilities of DH and α-HH in 2.50 m CaCl2 solutions at 95.0 °C are 6.09 × 10−3 M and 5.00 × 10−3 M, respectively. Therefore, the actual supersaturation (i.e., ce, DH/ce, HH) for α-HH nucleation is 1.22, which indicates that the eq 11 is reasonable. When SHH equals 1.0 (i.e., DH and α-HH have the same solubility), the critical water activity (aw,crit) can be expressed as:

Figure 5. Evolution of α-HH mole fraction during the DH−α-HH transformation (a) in a 3.00 m CaCl2 solution at 90.0−100.0 °C and (b) in 2.50−3.50 m CaCl2 solutions at 95.0 °C.

K sp,DH = a(Ca

temperature (°C)

(9)

K sp,HH 2+

γ(Ca )γ(SO24 −)m(Ca 2 +)a w0.5 (10)

According to the extended Debye−Hückel equation, the ion activity coefficient is mainly influenced by ionic strength. In concentrated CaCl2 solution, the contribution of ions from DH or α-HH dissolution to the whole ionic strength can be neglected because they are sparingly soluble. Consequently, the supersaturation for α-HH nucleation defined by the solubility 17137

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4. CONCLUSIONS Solution-mediated transformation from DH to α-HH is a nucleation−growth limited process that can be fitted well by the dispersive kinetic model. The decrease in activation energy accounts for the increasing conversion rate upon time. The water activity lowers down with the increase in CaCl2 concentration. The solubility product ratio (Ksp,DH/Ksp,HH) increases with the increase in temperature. Both of them enlarge the activation entropy change and the supersaturation for α-HH nucleation−growth, expediting the DH−α-HH transformation. This paper shows the elevation of temperature and reduction of water activity can promote the DH−α-HH conversion effectively, which provides significant guidance for the α-HH production in aqueous solutions.

Table 2. Supersaturation (SHH), Induction Time (tind), and Apparent Growth Rate (v) Evolution under Different Thermodynamic Conditions batch

temperature (°C)

CaCl2 (m)

SHH

tind (h)

v (h−1)

1 2 3 4 5

90.0 95.0

3.00 2.50 3.00 3.50 3.00

1.24 1.22 1.38 1.56 1.53

4.90 6.10 2.07 0.28 0.39

0..32 0.20 0.62 1.39 1.64

100.0

accounts for the shrinkage of induction time and increment of apparent growth rate at a higher CaCl2 molality or temperature. The induction time (i.e., tind = 4.90 h) in a 3.00 m CaCl2 solution at 90.0 °C (batch 1) is shorter than that (i.e., tind = 6.10 h) in a 2.50 m CaCl2 solution at 95.0 °C (batch 2). Besides, the apparent growth rate of batch 1 (i.e., v = 0.32 h−1) is faster than that of batch 2 (i.e., v = 0.20 h−1). These can be ascribed to the larger supersaturation of batch 1 (i.e., SHH = 1.24) compared to that of batch 2 (i.e., SHH = 1.22). The supersaturation in a 3.50 m CaCl2 at 95.0 °C (batch 4) is 1.56, which is larger than that in a 3.00 m CaCl2 at 100.0 °C (i.e., SHH = 1.53; batch 5). Correspondingly, the induction time of batch 4 is shorter than that of batch 5. However, the apparent growth rates of the two batches vary in an opposite order. This may be due to the limited experimental data for the determination of the transformation finishing point. Elevating temperature and lowering water activity are two important ways to promote the DH−α-HH transformation by enlarging the supersaturation for α-HH nucleation and growth. Table 3 shows the kinetic parameters fitted by the dispersive kinetic model in a 2.50−3.50 m CaCl2 solution at 90.0−100.0 °C. CaCl2 concentration and temperature exert a pronounced effect on parameter β. Parameter β changes notably from 1.22 × 10−1 to 7.15 h−2 (almost 60 times larger) as temperature increases from 90.0 to 100.0 °C in a 3.00 m CaCl2 solution, whereas little change occurred in parameter α. The bigger β means the activation entropy change within the same time unit is larger at higher temperature, which brings down the activation energy barrier more rapidly with time. Hence, the conversion time is significantly reduced with the increase in temperature. Parameter β increases considerably and parameter α decreases slightly with the CaCl2 concentration increasing from 2.50 to 3.50 m at 95.0 °C. The decrease in α indicates the time-independent Ea0 or activation enthalpy elevates with CaCl2 concentration, favoring the rise of activation energy barrier. The combined effect of activation enthalpy and entropy change contributes to lower activation energy barriers in more concentrated CaCl2 solutions. Overall, the larger activation entropy change leads to the higher transformation rate at a higher CaCl2 concentration and temperature.

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AUTHOR INFORMATION

Corresponding Author

*B. Guan. E-mail: [email protected]. Phone: +86 571 8898 2026. Fax: +86 571 8827 3687. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully appreciate Project 21176219 supported by NSFC and the Changjiang Scholar Incentive Program (Ministry of Education, China, 2009).

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REFERENCES

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Table 3. Kinetic Parameters for the Transformation from DH to α-HH in 2.50−3.50 m CaCl2 Solutions at 90.0−100.0 °C batch 1 2 3 4 5

T (°C) 90.0 95.0

100.0

3.00 2.50 3.00 3.50 3.00

β (h−2)

α (h)

CaCl2 (m) 2.88 1.26 2.86 4.25 1.88

× × × × ×

−2

10 10−1 10−2 10−2 10−2

± ± ± ±

5.20 1.06 8.71 4.83

17138

× × × ×

−5

10 10−3 10−5 10−6

1.22 4.94 5.02 6.44 7.15

−1

adjusted R2 −5

× 10 ± 4.41 × 10 × 10−1 ± 5.22 × 10−5 × 10−1 ± 3.40 × 10−4 ± 6.73 × 10−5

0.9974 0.9963 0.9987 0.9990 0.9995

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dx.doi.org/10.1021/ie402716d | Ind. Eng. Chem. Res. 2013, 52, 17134−17139