Article pubs.acs.org/IECR
Experimental Determination and Modeling of the Solubility of CaSO4·2H2O and CaSO4 in the Quaternary System CaSO4 + MgSO4 + H2SO4 + H2O Wenlei Wang,†,‡ Dewen Zeng,*,‡ Juntao Wang,‡ Hongliang Li,‡ and Lichao Wu§ †
College of Science, and §Key Laboratory of Cultivation and Protection for Non-Wood Forest Trees, Ministry of Education, Central South University of Forestry and Technology, Changsha 410004, P. R. China ‡ College of Chemistry and Chemical Engineering, Central South University, Changsha 410083, P. R. China ABSTRACT: A theoretical and experimental investigation of solubility of gypsum and anhydrite II in the complex system CaSO4 + MgSO4 + H2SO4 + H2O was conducted from 298.1 to 363.1 K. The solubility of anhydrite II in (MgSO4 + H2SO4) aqueous solutions was determined at 348.1 and 363.1 K by an isothermal method. A Pitzer thermodynamic model was selected to predict the solubility of gypsum and anhydrite II in the titled quaternary system. Good agreement between the experimental and the model values was observed, which supports the reliability of the model prediction. As predicted by the model, the transfer temperature from gypsum to anhydrite II decreases with increasing H2SO4 and MgSO4 concentrations, and the solubilities of gypsum and anhydrite II decrease monotonically with increasing MgSO4 concentration if H2SO4 concentration is higher than 0.5 mol·kg−1. On the basis of the results obtained, several suggestions for avoiding calcium sulfate scaling in the industrial process were proposed.
1. INTRODUCTION A large amount of magnesium sulfate waste liquid is produced in the laterite nickel ore hydrometallurgical process.1 In the MgSO4·7H2O production process by the condensation− crystallization method, calcium sulfate scaling is often encountered on the walls of reactors or pipelines. As we know, the condensation−crystallization process is accompanied by change in the CaSO4, H2SO4, and MgSO4 concentrations, as well as the temperature and calcium sulfate crystal types. To understand the scaling mechanism of calcium sulfate and develop a new approach to avoid scaling formation, it is necessary to know the solubility of calcium sulfate in the quaternary system CaSO4 + MgSO4 + H2SO4 + H2O. However, the solubility of calcium sulfate in any of its various hydrate types has never been reported in the quaternary system before, except in the related binary and ternary systems. As is well-known, calcium sulfate exists in a single salt aqueous solution in various crystal types, i.e., gypsum (CaSO4·2H2O), hemihydrate (CaSO4·0.5H2O), soluble anhydrite (hexagonal symmetry, γ-CaSO 4 ) and anhydrite II (orthorhombic, CaSO4),2,3 among which only gypsum and anhydrite II are stable phases, depending on their equilibrium temperature. Wollmann and Voigt4 reported the gypsum solubility in the ternary system CaSO4 + MgSO4 + H2O at (298.15 and 313.15) K. Azimi and Papangelakis5 reported the anhydrite solubilities in MgSO4 (0−0.8 mol·kg−1) aqueous solutions at 423 and 448 K. In our previous work, the gypsum and anhydrite II solubilities in the ternary system CaSO4 + H2SO4 + H2O were carefully studied over the temperature range from 298 to 373 K.6 Filippov and Antonova7 reported the solubility of MgSO4· 7H2O in the ternary system MgSO4 + H2SO4 + H2O at 298 K, and Zdanovskii and Murav’eva8 reported that of MgSO4·H2O at 348 K. All of the experimental data form a basis for solubility determination of the quaternary system. © 2014 American Chemical Society
In this work, the solubility of anhydrite II in the CaSO4 + MgSO4 + H2O and CaSO4 + MgSO4 + H2SO4 + H2O systems have been determined at T = (348.1 and 363.1) K. On the basis of the available literature and newly obtained experimental data, a thermodynamic model was applied to simulate and predict the solubility phase behavior of calcium sulfate in the MgSO4 + H2SO4 aqueous solutions over a wide temperature range. Finally, several possible industrial applications to prevent calcium sulfate scaling were discussed.
2. EXPERIMENTAL SECTION 2.1. Materials and Apparatus. MgSO4·7H2O was purified three times by crystallization with 50% salt recovery of the analytical grade reagent in each case (China National Pharmaceutical Industry Co., Ltd., China). H2SO4 was guaranteed reagent grade (China National Pharmaceutical Industry Co., Ltd., China). The MgSO4 and H2SO4 stock aqueous solutions were prepared with the chemical agents mentioned. The contents were determined by gravimetric analysis using a BaCl2 solution. Anhydrite II was prepared with the method described in our previous work.6 X-ray diffraction analysis showed that the product consists of anhydrite II alone. Doubly distilled water (κ < 1.2 × 10−4 S·m−1) was used in the experiment. The equilibrium experiments were performed in a thermostat (Lauda E219, Germany) with temperature stability up to ±0.1 K at high temperatures. The bath temperature was determined by a calibrated glass thermometer (Miller & Weber, Inc., USA) with an accuracy of ±0.01 K. All weighing was operated Received: Revised: Accepted: Published: 12839
May 26, 2014 July 11, 2014 July 15, 2014 July 15, 2014 dx.doi.org/10.1021/ie5021365 | Ind. Eng. Chem. Res. 2014, 53, 12839−12847
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Table 1. Experimental Solubility Data of Anhydrite II in the CaSO4 + MgSO4 + H2O and CaSO4 + MgSO4 + H2SO4 + H2O Systems at 348.1 and 363.1 K composition (mol·kg−1) m(H2SO4)
m(MgSO4)
composition (mol·kg−1) m(CaSO4)
m(H2SO4)
T = 348.1 K
m(MgSO4)
m(CaSO4)
T = 363.1 K
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0.016 0.039 0.064 0.097 0.118 0.214 0.402 0.836 1.135 1.154 1.569 2.002 2.752 3.457 3.597
0.0085 0.0066 0.0061 0.0065 0.0056 0.0059 0.0069 0.0079 0.0087 0.0084 0.0090 0.0094 0.0080 0.0062 0.0052 0.0047
0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.5 1.5 1.5 1.5 1.5 1.5 1.5
0.050 0.131 0.250 0.500 1.001 1.501 2.001 2.502 3.252 4.002 0.150 0.301 0.501 1.001 1.501 2.001 2.502 3.502 4.000 0.251 0.500 1.001 1.507 1.999 2.752 4.001 0.150 0.302 0.503 1.001 1.501 2.752 4.001
0.0165 0.0131 0.0103 0.0086 0.0083 0.0078 0.0070 0.0065 0.0048 0.0032 0.0178 0.0140 0.0117 0.0086 0.0077 0.0069 0.0057 0.0038 0.0028 0.0206 0.0162 0.0106 0.0078 0.0061 0.0043 0.0024 0.0251 0.0216 0.0173 0.0091 0.0073 0.0040 0.0020
in a Sartorius BS224S balance with an error of ±0.1 mg. The Ca2+ analysis was performed by the standard addition method with an inductively coupled plasma optical emission spectrometer (ICP-OES) (5300DV, PerkinElmer, USA). The solid phase was determined by an X-ray diffractometer (D/Max-2500, Rigaku, Japan).
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
0 0.014 0.039 0.068 0.107 0.122 0.203 0.299 0.844 0.857 1.097 1.461 1.894 2.525 3.305 3.541 4.002 0.063 0.130 0.250 0.522 1.002 1.500 2.001 2.502 3.252 4.000 0.150 0.301 0.500 1.001 1.498 2.001 2.506 4.000
0.0061 0.0046 0.0041 0.0044 0.0041 0.0041 0.0049 0.0056 0.0069 0.0070 0.0071 0.0074 0.0071 0.0066 0.0053 0.0047 0.0036 0.0153 0.0109 0.0082 0.0072 0.0073 0.0075 0.0075 0.0060 0.0048 0.0036 0.0207 0.0152 0.0093 0.0085 0.0078 0.0061 0.0054 0.0033
1.0 1.0 1.0 1.0 1.0 1.0
0.251 0.501 1.002 1.507 2.752 4.000
0.0251 0.0188 0.0114 0.0072 0.0045 0.0027
1.5 1.5 1.5 1.5 1.5 1.5 1.5
0.150 0.301 0.502 1.001 1.501 2.752 4.001
0.0254 0.0226 0.0186 0.0099 0.0077 0.0045 0.0024
2.2. Experimental Procedures. Specific amounts of MgSO4 and H2SO4 stock aqueous solutions were weighed and transferred into a 150 cm3 Erlenmeyer flask. The content of the mixture was set to a standard value by diluting or evaporating the mixture. Then, 5 g of anhydrite II was added to the solution. Each sample was placed into a glycol−water bath 12840
dx.doi.org/10.1021/ie5021365 | Ind. Eng. Chem. Res. 2014, 53, 12839−12847
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Figure 1. Comparison of the calculated and experimental wateractivity data14−17 in the MgSO4 + H2O system.
Figure 2. Comparison of the calculated and experimental data of the magnesium sulfate solubility18 in the system MgSO4 + H2O.
thermostat and stirred by a magnetic stirrer outside the bath for 120 h, which can guarantee the equilibrium, according our experience.9 After equilibrium, each sample was kept static for 8 h. The clear top layer of the solution was transferred out to a weighed vacuum tube. The removed sample solution was diluted with a known amount of distilled water to avoid crystallization. The well-mixed diluted solution was pipetted with same quantity into four weighed 100-ml volumetric flasks. Three milliliters of 65% HNO3 were added to each flask to avoid the hydrolysis of CaSO4. Different amounts of the CaCl2 standard solution were added to three of the four flasks, respectively. Distilled water was added to each volumetric flask to the 100-mL line. The solution in each flask was mixed well by shaking and then analyzed by ICP-OES using the analysis strategy described in detail in our previous work.10 The relative error for the analyzed Ca2+ content can be controlled within 2% in most cases and within 0.1% for SO42−. 2.3. Experimental Results. The experimental solubility data of anhydrite II in the ternary system CaSO4 + MgSO4 + H2O and the quaternary system CaSO4 + MgSO4 + H2SO4 + H2O at T = (348.1 and 363.1) K are tabulated in Table 1.
Pitzer model, as summarized by Harvie et al.,11 is used in this work for modeling. For simplification, the model equations are not repeated here. The binary and ternary mixing parameters at various temperatures were obtained by regressing the thermodynamic properties of the binary and ternary systems, such as the water activity, solubility, and enthalpy. The temperature dependence of the parameters is incorporated into the model according to the following equation: parameter (T ) = a1 + a 2(T /K − 298.15)
(1)
3.2. Chemical Equilibrium Relationships. Usually, the first-order dissociation of H2SO4 (eq 2) is considered to be complete, and the second-order dissociation (eq 3) partially complete with a certain dissociation constant.12,13 H 2SO4(aq) = H+(aq) + HSO4−(aq)
(2)
HSO4 −(aq) = H+(aq) + SO4 2 −(aq)
(3)
The solid−liquid equilibrium constants k for the two types of equilibria (eqs 4 and 5) are expressed by eq 6.
3. MODELING 3.1. Modeling Methodology. Because the substance concentrations in this system are not too high, a molality-based
CaSO4 ·nH 2O(s) = Ca 2 +(aq) + SO4 2 −(aq) + nH 2O(aq)
(n = 0, 2) (4)
Table 2. Binary and Ternary Parameters of the Pitzer Model coefficients ionic interactions
a
parametersa
Mg2+
HSO4−
Mg2+
SO42−
Ca2+ H+ Ca2+
Mg2+ Mg2+ Mg2+
β(0) ca β(1) ca β(2) ca Cϕca β(0) ca β(1) ca β(2) ca Cϕca θcc′ θcc′ ψSO2− 4
Ca2+
Mg2+
ψHSO2− 4
a1 0.475 1.73
0.2120 3.343 −37.23 0.0250 −0.150
a2
ref
−0.0003 0.0288
Pitzer21
−0.000173 0.0104 −0.707 −0.00 008 273 0.0031 0.0064 −0.002 08
Holmes and Mesmer15
this work this work this work
−0.001 38
this work
X(T) = a1 + a2(T/K − 298.15). 12841
dx.doi.org/10.1021/ie5021365 | Ind. Eng. Chem. Res. 2014, 53, 12839−12847
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Figure 3. Comparison of the calculated and experimental solubility data of gypsum (a) and anhydrite II (b) in the system CaSO4 + MgSO4 + H2O.
Figure 4. Equilibrium Ca2+concentration and calculated values of γCa2+, aSO42− and γCa2+·aSO42−·a2W as a function of MgSO4 concentrations in CaSO4·2H2O saturation solutions at 298.1 K.
Figure 5. Equilibrium Ca2+ concentration and calculated values of γCa2+, SO42−, and γCa2+·aSO42−·a2W as a function of MgSO4 concentrations in CaSO4 saturation solutions at 298.1 K.
2+ MgSO4 ·nH 2O(S) = Mg(aq) + SO24(aq) + nH 2O(aq)
(n = 7, 6, 1)
solutions; however, Holmes and Mesmer15 evaluated their parameters by fitting to experimental data of solutions up to solubility limit. Thus, the binary parameters for MgSO4 reported by Holmes and Mesmer15 were used in this work. The solubility products for the solid phases (MgSO4·H2O, MgSO4·6H2O, and MgSO4·7H2O) were determined using the experimental solubility data from Linke and Seidell.18 With the binary parameters in Table 2 and the solubility products, the solubility phase diagrams were calculated (see Figure 2). The calculated results are in good agreement with the experimental data. 3.4. Ternary Parameter Estimation. 3.4.1. The CaSO4 + H2SO4 + H2O System. The mixing parameters for the ternary system are the same as in our previous work.6 3.4.2. The MgSO4 + CaSO4 + H2O System. The gypsum solubility in the MgSO4 aqueous solution at various temperatures was measured by several researchers,4,19 and the anhydrite II solubility was measured in this work at 348.1 and 363.1 K. All of the experimental data were used for the model parametrization. The obtained parameters are listed in Table 2. The solubility isotherms of gypsum and anhydrite II in the CaSO4 + MgSO4 + H2O system were predicted with the binary parameters only and are presented as dashed lines in Figure 3. The calculated gypsum solubilities agree with the literature solubility
(5)
ln K MV+XV−·nH2O(S) = V+ ln a M v+ + V −ln a X v− + n ln aW (6)
3.3. Binary Parameter Estimation. The binary Pitzer model parameters for the systems H2SO4 + H2O and CaSO4 + H2O with the dissociation constant for the second-order dissociation equilibrium HSO−4 (aq) = H + (aq) + SO2− 4 (aq) and the solubility product of CaSO4 were taken from our previous work.6 The binary parameters for MgSO4 have been determined by fitting the thermodynamic properties of the single salt by Silvester and Pitzer14 and Holmes and Mesmer,15 respectively. To test the reliability of these available binary parameters, the water activities of the system MgSO4 + H2O were calculated. The calculated results were presented as dashed lines (Silvester and Pitzer14) and solid lines (Holmes and Mesmer15) in Figure 1 and compared with other experimental data from the literature.15−17 The calculated results of Silvester and Pitzer14 deviate largely from the experimental data, whereas those of Holmes and Mesmer15 are in good agreement with them. The possible reason lies in that Silvester and Pitzer14 determined the parameters by fitting them to experimental data of
