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Thermodynamic modeling and experimental measurement of calcium sulfate in complex aqueous solutions
Fluid Phase Equilibria 290 (2010) 88–94
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Fluid Phase Equilibria journal homepage: www.elsevier.com/locate/fluid
Thermodynamic modeling and experimental measurement of calcium sulfate in complex aqueous solutions G. Azimi, V.G. Papangelakis ∗ Department of Chemical Engineering and Applied Chemistry, University of Toronto, 200 College St., Toronto, ON, M5S 3E5 Canada
a r t i c l e
i n f o
Article history: Received 6 July 2009 Received in revised form 24 September 2009 Accepted 28 September 2009 Available online 7 October 2009 Keywords: Calcium sulfate Dihydrate (DH) Hemihydrate (HH) Anhydrite (AH) Phase transformation Solubility Chemical modeling
a b s t r a c t A newly developed database for the Mixed Solvent Electrolyte (MSE) model of the OLI Systems software was employed to model the solid and aqueous phase equilibria of calcium sulfate hydrates in electrolyte solutions containing NiSO4 , H2 SO4 , MgSO4 , Fe2 (SO4 )3 , LiCl and HCl from 25 to 90 ◦ C. The MSE model is a variant of an excess Gibbs free energy model for Mixed Solvent Electrolyte systems which takes into account long-range electrostatic interactions from a Pitzer–Debye–Hückel equation, middle-range interactions from a second virial coefficient-type equation and short-range interactions from the UNIQUAC model. The effect of cations with similar anions on the solubility was investigated and it was found that the solubility depends mainly on the anion type while the cation has a minor effect. The effect of acid addition and the acid type was also studied. The addition of both HCl and H2 SO4 increases the solubility; however H2 SO4 has a less pronounced effect due to the common ion effect. Furthermore, the effect of phase transitions between different calcium sulfate hydrates was studied. The transformation of CaSO4 dihydrate to anhydrite results in a significant decrease in the solubility, which complicates the chemistry of the system. Since it is not practical to measure solubility data under all conditions of interest, the model developed and the experimental results obtained serves the purpose of assessing the calcium sulfate scaling potential for a wide variety of complex aqueous industrial streams. © 2009 Elsevier B.V. All rights reserved.
1. Introduction The knowledge of the phase equilibria and solubility of inorganic salts in electrolyte solutions is essential in the development, design, optimization and operation of many chemical processes including environmental applications (gas treatment, wastewater treatment, or chemical disposal), separation processes (crystallization, extractive distillation and seawater desalination), electrochemical processes (corrosion or electrolysis), energy production sources (scaling in production wells) and hydrometallurgical processes [1]. Several inorganic salts exist in more than one crystalline form, the stability of which depends on the solution conditions in terms of temperature or composition. Calcium sulfate is one of the most common salts in this category, occurring as three different hydrates: dihydrate (DH: CaSO4 ·2H2 O), hemihydrate (HH: CaSO4 ·0.5H2 O) and anhydrite (AH: CaSO4 ). Many industrial processes including wastewater treatment, desalination, sulfur dioxide removal from the exhaust gas of coaldriven power plants [2,3] and hydrometallurgical processes [4–6]
∗ Corresponding author. E-mail address: [email protected] (V.G. Papangelakis). 0378-3812/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2009.09.023
are dealing with the formation of CaSO4 hydrates as undesirable byproducts, mostly as scale. As the scale layer becomes increasingly thicker, it reduces the production capacity and process efficiency because of increased heat transfer resistance, reduction of material flow and operating volumes, corrosion and wearing out of construction materials. The stability regions of the CaSO4 hydrates depend on the solution conditions. Each crystalline phase can be stable, metastable or unstable at certain temperatures and compositions. The transformation of calcium sulfate dihydrate (DH) to anhydrite (AH) results in a significant decrease in the solubility level that makes the prediction and control of calcium sulfate formation complicated. Therefore, understanding the chemistry of CaSO4 phase equilibria and being able to estimate its scaling potential in industrial processes involving electrolytes is of great theoretical significance and practical importance [5,7]. The purpose of this work is to use a recently developed database for the Mixed Solvent Electrolyte (MSE) model of the OLI Systems software [8,9] and map the effect of temperature and acidity as well as sulfate and chloride concentrations on the phase equilibria of CaSO4 hydrates and provide practical guidelines for solubility prediction of the thermodynamically stable phase under a particular solution composition and temperature. To this end, a number of experiments were conducted in electrolyte solutions containing
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2.3. Procedure
Fig. 1. Scheme of the glass reactor used in this work.
NiSO4 , H2 SO4 , MgSO4 , Fe2 (SO4 )3 , LiCl and HCl. The specific objectives are: • To investigate whether the type of cation has a significant effect on the solubility of calcium sulfate or all cations in the solution can be substituted with an arbitrary pseudo cation. • To study the effect of acid addition on the solubility of CaSO4 hydrates and to investigate the model performance in predicting the chemistry of calcium sulfate phase equilibria in acidic solutions. • To study the effect of the phase transformation on the solubility of calcium sulfate. 2. Experimental 2.1. Reagents In this work, all solutions were prepared by dissolving reagent grade chemicals directly without further purification. Both CaSO4 solids phases (DH and AH) used in this work were from J.T. Baker. Xray powder diffraction was carried out on both solids using a Philips PW3719 diffractometer. Result showed 100% dihydrate (DH) and anhydrite (AH), respectively. No traces of hemihydrate (HH) or anhydrite (AH) were found in the dihydrate (DH) solid powder. 2.2. Apparatus The experiments were performed inside 1 L double-layer glass reactors where heating was provided through a circulating oil jacket. Temperature was controlled within ±1 ◦ C of the set-point. The reactor slurry was kept suspended by a shaft stirrer. Samples were withdrawn through a dip rubber tube using preheated syringes, and filtrations were performed using 0.22 m PTFE syringe filters from Fisher. Fig. 1 represents a scheme of the experimental set-up used in this work. To avoid solution evaporation during the runs, the stirrer bushing was fully sealed using Dow Corning® high vacuum grease, which basically contains polydimethylsiloxane.
Solutions of known composition were placed in the reaction vessels with an excess of saturating solid phase. Experiments were started by heating the charged reactors to temperature under vigorous agitation and allowing sufficient time to reach equilibrium. Samples were withdrawn after equilibration, immediately filtered, and diluted by 5% HNO3 and kept in test tubes at room temperature. In the systems studied the solubility of calcium sulfate decreases with decreasing temperature. Therefore, samples withdrawn at higher temperatures, e.g., 90 ◦ C, will form dihydrate (DH) precipitate upon cooling to room temperature. In order to avoid this phenomenon, samples were diluted by 5% nitric acid. In each sampling step, 5 mL of the solution was withdrawn which does not affect the molarity of different elements in the system. The concentration of other elements than Ca was also monitored through out all experiments to confirm that the solution compositions remained unchanged. During solid samples withdrawal, only ∼1 g of the solid was taken, and since dihydrate was added in excess (∼50 g) initially, solid sampling would not have a significant effect on the overall composition of the solid phase. The Ca concentration was determined by Inductively Coupled Plasma (ICP-OES) analysis. The density of all liquid samples was measured at temperature using a portable density meter (DMA 35N ) from Anton Paar. Samples of the equilibrating solid phase were withdrawn at various temperatures for X-ray diffraction, thermo gravimetric (TGA) and scanning electron microscope (SEM) analysis. They were filtered, and washed with alcohol and dried at below 40 ◦ C in an oven under vacuum. 2.4. Equilibration time Equilibration time in solubility measurements varies from several hours to several days depending on the dissolution rate of the solid phase under applied conditions. In this work, several kinetic tests were conducted at various temperatures and the results showed that around 24 h was necessary to achieve saturation. Reproducibility tests showed that the experimentally measured data are accurate to within ±5%. 3. Theory The following reactions govern the solubility of CaSO4 hydrates: CaSO4 ·nH2 O(s) = Ca2+ + SO4 2− + nH2 O
(1)
Ca2+ + SO4 2− = CaSO4(aq) o
(2)
The solubility of calcium sulfate is: [Ca]total = [Ca2+ ] + [CaSO4(aq) o ]
(3)
To obtain the equilibrium constants of reactions (1) and (2) at temperature T and pressure P, the standard state chemical potentials of the products and reactants are required. These data are widely available in standard thermodynamic compilations. To extrapolate the standard state thermodynamic properties to high temperatures and pressures, the HKF model, developed by Tanger and Helgeson [10], embedded in the OLI software was employed. To account for the non-ideality (excess properties) of the electrolyte solutions studied, the MSE activity coefficient model [11,12], which is also embedded in the OLI Systems software, was used. In the end, a selfconsistent and calibrated model was produced. More details on the modeling methodology and the database developed are available elsewhere [8,9,13].
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Fig. 2. CaSO4 solubility as a function of MSO4 (M = Ni, Mg, Mn) concentration; MgSO4 experimental data are from [14–17]; NiSO4 experimental data are from [17,18]; MnSO4 experimental data are from [17,19]; curves are model predictions.
Fig. 3. CaSO4 solubility in CaSO4 –MgSO4 –HCl (0.5 M)–H2 O solution; experimental data are from this work, and curves are the model predictions.
4. Results and discussion 4.1. Effect of divalent cations on the solubility of CaSO4 hydrates Fig. 2 presents a comparison between the solubility of CaSO4 dihydrate (DH) in ternary solutions of CaSO4 –NiSO4 –H2 O, CaSO4 –MgSO4 –H2 O and CaSO4 –MnSO4 –H2 O along with the model “predictions” at two different temperatures: 25 and 75 ◦ C. It is clear that the difference between CaSO4 solubilities in these systems at both temperatures is always less than ∼15% indicating that the cation type does not have a dramatic effect on the CaSO4 solubility. For all three cations, as the metal sulfate concentration increases from pure water, the solubility initially drops and then increases gradually. After passing a maximum, the solubility decreases smoothly with further increasing the MSO4 (M = Mg, Mn, Ni) concentration. The initial drop is due to the common ion effect which shifts the dissolution reaction (Eq. (1)) to the left; the subsequent increase is attributable to the association of Ca2+ and SO4 2− ions and formation of calcium sulfate neutral species (Eq. (2)). The solubility decrease in concentrated solutions is due to the saltingout effect due to the decreased number of free water molecules in the solution to dissolve calcium sulfate.
In industrial applications, particularly in hydrometallurgy, solutions sometimes contain several cations for which there are no experimental data available. By knowing that cation type does not have a significant effect on the solubility level, all divalent cations can be substituted with a certain cation for which experimental data are available during the simulation of the process. 4.2. Effect of different acids on the solubility of CaSO4 hydrates To compare the effect of H2 SO4 and HCl on the solubility of calcium sulfate dihydrate (DH), two different sets of experiment were performed: first, the solubility was measured as a function of MgSO4 concentration in 0.5 M HCl solutions. Second, the solubility was measured as a function of NiSO4 concentration in 0.5 M H2 SO4 solutions. The measured data are presented in Tables 1 and 2. Figs. 3 and 4 show the measured solubility data in comparison with the model prediction results from 25 to 90 ◦ C. In both systems, the solubility first decreases with increasing MSO4 (M = Ni, Mg) concentration due to the common ion effect of the added SO4 2− ions. This effect is nullified by further increasing MSO4 concentration because of the association of Ca2+ and SO4 2− ions and
Table 1 Solubility of CaSO4 dihydrate in 0.5 M HCl solutions at various MgSO4 concentrations. MgSO4 (mol/L)
0.0 0.1 0.5 1.0 1.5
25 ◦ C
45 ◦ C
70 ◦ C
90 ◦ C
CaSO4 (mol/L)
Density (g/mL)
CaSO4 (mol/L)
Density (g/mL)
CaSO4 (mol/L)
Density (g/mL)
CaSO4 (mol/L)
Density (g/mL)
0.0810 0.0456 0.0168 0.0110 0.0087
1.007 1.021 1.057 1.112 1.162
0.0940 0.0594 0.0205 0.0139 0.0105
1.005 1.013 1.047 1.100 1.158
0.1300 0.0785 0.0231 0.0153 0.0113
1.004 1.008 1.038 1.105 1.102
0.1560 0.0987 0.0292 0.0188 0.0135
0.997 0.999 1.030 1.080 1.128
Table 2 Solubility of CaSO4 dihydrate in 0.5 M H2 SO4 solutions at various NiSO4 concentrations. NiSO4 (mol/L)
0.00 0.10 0.25 0.50 1.00 1.50
25 ◦ C
45 ◦ C
70 ◦ C
90 ◦ C
CaSO4 (mol/L)
Density (g/mL)
CaSO4 (mol/L)
Density (g/mL)
CaSO4 (mol/L)
Density (g/mL)
CaSO4 (mol/L)
Density (g/mL)
0.0190 0.0180 0.0166 0.0166 0.0148 0.0131
1.030 1.044 1.060 1.106 1.180 1.238
0.0258 0.0234 0.0210 0.0196 0.0172 0.0158
1.022 1.037 1.056 1.095 1.170 1.230
0.0403 0.0351 0.0298 0.0266 0.0234 0.0194
1.010 1.026 1.044 1.085 1.157 1.218
0.0545 0.0454 0.0383 0.0329 0.0314 0.0245
1.002 1.015 1.029 1.071 1.141 1.202
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Fig. 4. CaSO4 solubility in CaSO4 –NiSO4 –H2 SO4 (0.5 M)–H2 O solution; experimental data are from this work, and curves are the model predictions.
formation of calcium sulfate neutral species. Also, the solubility of dihydrate (DH) is significantly higher in the presence of HCl (Fig. 3) compared to that in H2 SO4 (Fig. 4). This effect is most pronounced near zero metal sulfate concentrations. The addition of both H2 SO4 and HCl increases the solubility of CaSO4 dihydrate (DH) due to the formation of bisulfate ions; however, in the case of H2 SO4 , there is a common ion effect due to the produced SO4 2− from the second dissociation of H2 SO4 hindering the dissolution reaction. In both systems, model “predictions” are in good agreement with the experimental data. It should be emphasized that no extra fitting were perfumed in these systems which proves the predictability of the model in multicomponent systems using the interaction parameters obtained in binary and ternary systems, i.e., CaSO4 –H2 O, CaSO4 –MgSO4 –H2 O, CaSO4 –NiSO4 –H2 O, CaSO4 –HCl–H2 O and CaSO4 –H2 SO4 –H2 O which have been studied previously [8,9].
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Fig. 5. CaSO4 solubility in CaSO4 –NiSO4 (1.4 M)–H2 SO4 (1 M)–Fe2 (SO4 )3 (0.2 M)–LiCl (0.3 M)–H2 O solutions at various retention times and different temperatures.
the equilibrating solid phase was estimated semi-quantitatively by measuring the peak intensities of the different X-ray diffraction patterns and was confirmed by thermo gravimetric analysis (TGA). Hemihydrate was not detected in any of the samples despite a careful search for this phase. The experimentally measured solubility
4.3. Effect of phase transition on the solubility of CaSO4 hydrates 4.3.1. CaSO4 –NiSO4 –H2 SO4 –Fe2 (SO4 )3 –LiCl–H2 O System Nickel processing solutions typically contain NiSO4 , H2 SO4 , Fe2 (SO4 )3 and small amounts of a chloride salt. In this work, the solubility of calcium sulfate dihydrate (DH) was measured in a solution of 1.4 M NiSO4 , 1 M H2 SO4 , 0.2 M Fe2 (SO4 )3 and 0.3 M LiCl. Solubility measurements were carried out based on heating from 25 to 90 ◦ C followed by subsequent cooling. At a given temperature, the relative amount of dihydrate (DH) and anhydrite (AH) in
Fig. 6. CaSO4 solubility in CaSO4 –NiSO4 (1.4 M)–H2 SO4 (1 M)–Fe2 (SO4 )3 (0.2 M)–LiCl (0.3 M)–H2 O solutions; solid curves are the model predictions, and the dashed line shows the phase transition region.
Table 3 Calcium sulfate concentration, saturated solution density and solid phase composition in 1.4 M NiSO4 , 1 M H2 SO4 , 0.2 M Fe2 (SO4 )3 , 0.3 M LiCl solutions at various temperatures and retention times. Time (h)
T (◦ C)
Density (g/mL)
CaSO4 (mol/L)
Method
Solid phase composition
24 48 72 96 120 144 168 192 216 240 264
25 45 60 70 70 70 90 80 60 35 25
1.333 1.318 1.315 1.305 1.305 1.305 1.298 1.300 1.315 1.326 1.333
0.0079 0.0106 0.0136 0.0155 0.0127 0.0089 0.0085 0.0084 0.0082 0.0082 0.0080
Heating Heating Heating Heating Heating Heating Heating Cooling Cooling Cooling Cooling
100% DH 100% DH 100% DH 100% DH 80% DH + 20% AH 100% AH 100% AH 100% AH 100% AH 100% AH 25% DH + 75% AH
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Fig. 8. CaSO4 solubility vs. temperature in CaSO4 –MnSO4 –H2 SO4 –H2 O solutions; the experimental data are from [20]; the solid curves are the predicted values and the dashed lines show the phase transition region.
Fig. 7. SEM images of the solid phases at 70 ◦ C showing the different crystal morphologies of (a) 100% dihydrate (DH) withdrawn after 24 h retention time (b) transitional of 80% dihydrate (DH)–20% anhydrite (AH) mixture withdrawn after 48 h and (c) 100% anhydrite withdrawn after 72 h.
data, saturated solution densities and solid phase compositions at various temperatures are summarized in Table 3. Fig. 5 presents the solubility data as a function of the retention time along with solid sample compositions at different temperatures. As is shown, the solubility increases with temperature up to 70 ◦ C. The system was kept at 70 ◦ C for 3 days and slurries were periodically sampled. The results showed a gradual decrease in the solubility in the second and the third samples at 70 ◦ C withdrawn on the day 2 and day 3, respectively. The solubility values measured at 90 ◦ C had the same order of magnitude as the third sample withdrawn at 70 ◦ C after 3 days. On cooling, a relatively flat solubility curve is noted up to 25 ◦ C.
Powder X-ray diffraction analysis of the equilibrating solid phase showed only dihydrate (DH) during heating up to 70 ◦ C; however, the solid sample withdrawn at 70 ◦ C after 3 days retention time and the one withdrawn at 90 ◦ C showed 100% anhydrite (AH) in the composition. The solid sample withdrawn at 70 ◦ C after 2 days retention time contained a mixture of dihydrate (DH) and anhydrite (AH). On cooling, anhydrite remained the dominant equilibrating solid phase above 25 ◦ C, but at 25 ◦ C the conversion of anhydrite (AH) to dihydrate (DH) occurred. Thus, the major drop in the solubility of calcium sulfate is due to the transformation of dihydrate (DH) into anhydrite (AH), a phase which has a significantly different solubility–temperature relationship. Fig. 6 shows CaSO4 solubility data as a function of temperature along with the model predictions. As can be seen, the model predicts the solubility of dihydrate and anhydrite precisely. However, the phase transition area, which is not thermodynamically stable, cannot be predicted by the model and is marked by a dashed line in the figure. The SEM images of the solid samples withdrawn at 70 ◦ C after 24, 48 and 72 h retention times are presented in Fig. 7(a)–(c), respectively. As mentioned above, the first solid sample presented in Fig. 7(a) shows 100% dihydrate in composition, whereas, the sample shown in Fig. 7(b) reveals a mixture of 80% DH and 20% AH, as estimated from XRD and TGA. Fig. 7(c) presents a solid sample with 100% AH after complete transformation of dihydrate in the system. As is clear, the morphologies of calcium sulfate dihydrate and anhydrite are very different: DH crystals are in a monoclinic form, whereas AH crystals have an orthorhombic structure and are needle shaped. 4.3.2. CaSO4 –H2 SO4 –MnSO4 –H2 O system There are some difficulties involved in the electrolytic process for the winning of manganese dioxide from H2 SO4 /Mn2+ electrolytes where CaSO4 scale develops in heat exchangers, pipes and other equipment. These processes require regular cleaning to maintain efficient process operation. Farrah et al. [20] studied the effect of H2 SO4 , MnSO4 and temperature on the solubility of CaSO4 hydrates over the temperature range of 30–105 ◦ C. Fig. 8 shows their experimental solubility data along with the predicted results obtained from the new model, which are in very good agreement. It is obvious from the figure that dihydrate (DH)
G. Azimi, V.G. Papangelakis / Fluid Phase Equilibria 290 (2010) 88–94
solubility decreases with an increase in MnSO4 concentration at fixed H2 SO4 concentrations due to the common ion effect. Also, there is a systematic increase in the solubility with temperature in the presence of MnSO4 up to 80 ◦ C because of the tendency of the sulfate ions to form bisulfate. Above 80 ◦ C, calcium sulfate solubility declines sharply as a result of dihydrate (DH) to anhydrite (AH) transformation. It can be seen from the figure that the solubility of anhydrite is also depressed by subsequent addition of MnSO4 . 5. Conclusions Many industries are dealing with calcium sulfate scale formation and need regular removal of precipitated calcium sulfate hydrates. At elevated temperatures, the transformation between the calcium sulfate phases has a complex effect on the solubility, making the behaviour of calcium sulfate difficult to predict and control. In this work, a recently developed database for the MSE model of the OLI Systems software was used to study the effect of different electrolytes on the CaSO4 solubility. It was found out that it is mainly the anion which controls the solubility of calcium sulfate, while cations have a minor effect. The solubility behaviour of CaSO4 is the same in all metal sulfate electrolytes with different cations: as the metal sulfate concentration increases from pure water, the solubility initially drops due to the common ion effect and then increases gradually due to the formation of calcium sulfate neutral species. After passing a maximum, solubility decreases smoothly with a further increase in the concentration due to the salting-out effect and decreased number of free water molecules in the solution. The solubility of CaSO4 dihydrate was measured in solutions containing NiSO4 , H2 SO4 , MgSO4 and HCl. It was found that the
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solubility is significantly higher in the presence of HCl compared to that in H2 SO4 because in the case of H2 SO4 , there is a common ion effect due to the produced SO4 2− from the second dissociation of H2 SO4 hindering the dissolution reaction. Furthermore, the effect of the phase transformation of calcium sulfate dihydrate (DH) into anhydrite (AH) on the solubility was studied. The transformation takes place at higher temperatures and acid concentrations and has a complex effect on the solubility. In this work, complete transformation was achieved at 70 ◦ C after 3 days retention time in the presence of 1 M H2 SO4 . The solubility of anhydrite is much lower than that of dihydrate (∼50–80% lower); therefore process solutions which are saturated with dihydrate (DH) at ambient temperature and are recycled to autoclaves, operating at temperatures above 100 ◦ C, need to be processed to decrease their calcium content and make it less than anhydrite saturation level inside an autoclave. Otherwise, scale formation will be unavoidable. Chemical modeling is a practical asset to map calcium sulfate chemistry in electrolyte solutions over wide ranges of temperature and concentration. This, in turn, results in gaining comprehensive insight for process improvements and optimization in various processes. Acknowledgements The authors would like to acknowledge the financial support provided by Anglo American plc., Barrick Gold Corporation, OLI Systems Inc., Sherritt International Corporation, Vale Inco Ltd., the Ontario Graduate Scholarship (OGS) and the Natural Sciences and Engineering Research Council of Canada (NSERC) for this project. Appendix A. MSE middle-range interaction parameters (OLI-version 8.1.3)
Species i
Species j
BMD0
BMD1
BMD2
CMD0
CMD1
MnSO4 –H2 O CaSO4 –H2 O
Mn2+ Ca2+
SO4 2− SO4 2−
−716.157 10887.73
0.9059 −16.973
93031.7 −1770400
255.511 −15416.42
– 24.215
CaSO4 –MnSO4 –H2 O
Ca2+ CaSO4(aq)
Mn2+ Mn2+
683.490 2134.468
−2.0005 −2.8306
2+
−2602.165 678.644
4.8761 −1.529
2+
CaSO4 –MgSO4 –H2 O
Ca CaSO4(aq)
Mg Mg2+
CaSO4 –Na2 SO4 –H2 O
Ca2+
Na+
– −394938 333009 −62232.5
−868.843 – 3630.73 −562.19
CMD2
Temperature range (◦ C)
– 2508590
2.5173 –
– –
25–100
−6.8234 1.7298
−462726 –
25–175
25.171
−0.0262
CaSO4 –H2 SO4 –H2 O
Ca CaSO4(aq)
HSO4 − HSO4 −
3715.460 393.149
−6.0144 −1.6809
−618224 11323.61
CaSO4 –CaCl2 –H2 O/CaSO4 – HCl–H2 O/CaSO4 –NaCl– H2 O/CaSO4 –MgCl2 –H2 O
Cl− Cl− Cl−
SO4 2− HSO4 − CaSO4(aq)
465.363 −148.074 9.4550
−0.8069 0.3573 0.0367
−62105.4 – –
CaSO4 –NiSO4 –H2 O
Ca2+ CaSO4(aq)
Ni2+ Ni2+
269.924 −656.530
−0.7478 1.5199
97192 –
−1160.872 863.322
1.9865 −1.8770
– –
CaSO4 –Fe2 (SO4 )3 – ZnSO4 –H2 SO4 –H2 O
Ca2+ CaSO4(aq)
Fe3+ Fe3+
−172.067 663.006
−9.8085 −1.1448
955584 −104326
313.487 1099.014
13.8038 −1.1435
−1362390 −202962
2+
–
0–180 0–400
−33.189
0.0210
–
25–300
−4472.033 −671.232
7.3066 2.5821
733093 –
25–300
−511.001 176.162 −55.0627
0.9236 −0.4188 0.02547
64179.32 – –
22–300
25–175 25–90
94
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Fluid Phase Equilibria journal homepage: www.elsevier.com/locate/fluid
Thermodynamic modeling and experimental measurement of calcium sulfate in complex aqueous solutions G. Azimi, V.G. Papangelakis ∗ Department of Chemical Engineering and Applied Chemistry, University of Toronto, 200 College St., Toronto, ON, M5S 3E5 Canada
a r t i c l e
i n f o
Article history: Received 6 July 2009 Received in revised form 24 September 2009 Accepted 28 September 2009 Available online 7 October 2009 Keywords: Calcium sulfate Dihydrate (DH) Hemihydrate (HH) Anhydrite (AH) Phase transformation Solubility Chemical modeling
a b s t r a c t A newly developed database for the Mixed Solvent Electrolyte (MSE) model of the OLI Systems software was employed to model the solid and aqueous phase equilibria of calcium sulfate hydrates in electrolyte solutions containing NiSO4 , H2 SO4 , MgSO4 , Fe2 (SO4 )3 , LiCl and HCl from 25 to 90 ◦ C. The MSE model is a variant of an excess Gibbs free energy model for Mixed Solvent Electrolyte systems which takes into account long-range electrostatic interactions from a Pitzer–Debye–Hückel equation, middle-range interactions from a second virial coefficient-type equation and short-range interactions from the UNIQUAC model. The effect of cations with similar anions on the solubility was investigated and it was found that the solubility depends mainly on the anion type while the cation has a minor effect. The effect of acid addition and the acid type was also studied. The addition of both HCl and H2 SO4 increases the solubility; however H2 SO4 has a less pronounced effect due to the common ion effect. Furthermore, the effect of phase transitions between different calcium sulfate hydrates was studied. The transformation of CaSO4 dihydrate to anhydrite results in a significant decrease in the solubility, which complicates the chemistry of the system. Since it is not practical to measure solubility data under all conditions of interest, the model developed and the experimental results obtained serves the purpose of assessing the calcium sulfate scaling potential for a wide variety of complex aqueous industrial streams. © 2009 Elsevier B.V. All rights reserved.
1. Introduction The knowledge of the phase equilibria and solubility of inorganic salts in electrolyte solutions is essential in the development, design, optimization and operation of many chemical processes including environmental applications (gas treatment, wastewater treatment, or chemical disposal), separation processes (crystallization, extractive distillation and seawater desalination), electrochemical processes (corrosion or electrolysis), energy production sources (scaling in production wells) and hydrometallurgical processes [1]. Several inorganic salts exist in more than one crystalline form, the stability of which depends on the solution conditions in terms of temperature or composition. Calcium sulfate is one of the most common salts in this category, occurring as three different hydrates: dihydrate (DH: CaSO4 ·2H2 O), hemihydrate (HH: CaSO4 ·0.5H2 O) and anhydrite (AH: CaSO4 ). Many industrial processes including wastewater treatment, desalination, sulfur dioxide removal from the exhaust gas of coaldriven power plants [2,3] and hydrometallurgical processes [4–6]
∗ Corresponding author. E-mail address: [email protected] (V.G. Papangelakis). 0378-3812/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2009.09.023
are dealing with the formation of CaSO4 hydrates as undesirable byproducts, mostly as scale. As the scale layer becomes increasingly thicker, it reduces the production capacity and process efficiency because of increased heat transfer resistance, reduction of material flow and operating volumes, corrosion and wearing out of construction materials. The stability regions of the CaSO4 hydrates depend on the solution conditions. Each crystalline phase can be stable, metastable or unstable at certain temperatures and compositions. The transformation of calcium sulfate dihydrate (DH) to anhydrite (AH) results in a significant decrease in the solubility level that makes the prediction and control of calcium sulfate formation complicated. Therefore, understanding the chemistry of CaSO4 phase equilibria and being able to estimate its scaling potential in industrial processes involving electrolytes is of great theoretical significance and practical importance [5,7]. The purpose of this work is to use a recently developed database for the Mixed Solvent Electrolyte (MSE) model of the OLI Systems software [8,9] and map the effect of temperature and acidity as well as sulfate and chloride concentrations on the phase equilibria of CaSO4 hydrates and provide practical guidelines for solubility prediction of the thermodynamically stable phase under a particular solution composition and temperature. To this end, a number of experiments were conducted in electrolyte solutions containing
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2.3. Procedure
Fig. 1. Scheme of the glass reactor used in this work.
NiSO4 , H2 SO4 , MgSO4 , Fe2 (SO4 )3 , LiCl and HCl. The specific objectives are: • To investigate whether the type of cation has a significant effect on the solubility of calcium sulfate or all cations in the solution can be substituted with an arbitrary pseudo cation. • To study the effect of acid addition on the solubility of CaSO4 hydrates and to investigate the model performance in predicting the chemistry of calcium sulfate phase equilibria in acidic solutions. • To study the effect of the phase transformation on the solubility of calcium sulfate. 2. Experimental 2.1. Reagents In this work, all solutions were prepared by dissolving reagent grade chemicals directly without further purification. Both CaSO4 solids phases (DH and AH) used in this work were from J.T. Baker. Xray powder diffraction was carried out on both solids using a Philips PW3719 diffractometer. Result showed 100% dihydrate (DH) and anhydrite (AH), respectively. No traces of hemihydrate (HH) or anhydrite (AH) were found in the dihydrate (DH) solid powder. 2.2. Apparatus The experiments were performed inside 1 L double-layer glass reactors where heating was provided through a circulating oil jacket. Temperature was controlled within ±1 ◦ C of the set-point. The reactor slurry was kept suspended by a shaft stirrer. Samples were withdrawn through a dip rubber tube using preheated syringes, and filtrations were performed using 0.22 m PTFE syringe filters from Fisher. Fig. 1 represents a scheme of the experimental set-up used in this work. To avoid solution evaporation during the runs, the stirrer bushing was fully sealed using Dow Corning® high vacuum grease, which basically contains polydimethylsiloxane.
Solutions of known composition were placed in the reaction vessels with an excess of saturating solid phase. Experiments were started by heating the charged reactors to temperature under vigorous agitation and allowing sufficient time to reach equilibrium. Samples were withdrawn after equilibration, immediately filtered, and diluted by 5% HNO3 and kept in test tubes at room temperature. In the systems studied the solubility of calcium sulfate decreases with decreasing temperature. Therefore, samples withdrawn at higher temperatures, e.g., 90 ◦ C, will form dihydrate (DH) precipitate upon cooling to room temperature. In order to avoid this phenomenon, samples were diluted by 5% nitric acid. In each sampling step, 5 mL of the solution was withdrawn which does not affect the molarity of different elements in the system. The concentration of other elements than Ca was also monitored through out all experiments to confirm that the solution compositions remained unchanged. During solid samples withdrawal, only ∼1 g of the solid was taken, and since dihydrate was added in excess (∼50 g) initially, solid sampling would not have a significant effect on the overall composition of the solid phase. The Ca concentration was determined by Inductively Coupled Plasma (ICP-OES) analysis. The density of all liquid samples was measured at temperature using a portable density meter (DMA 35N ) from Anton Paar. Samples of the equilibrating solid phase were withdrawn at various temperatures for X-ray diffraction, thermo gravimetric (TGA) and scanning electron microscope (SEM) analysis. They were filtered, and washed with alcohol and dried at below 40 ◦ C in an oven under vacuum. 2.4. Equilibration time Equilibration time in solubility measurements varies from several hours to several days depending on the dissolution rate of the solid phase under applied conditions. In this work, several kinetic tests were conducted at various temperatures and the results showed that around 24 h was necessary to achieve saturation. Reproducibility tests showed that the experimentally measured data are accurate to within ±5%. 3. Theory The following reactions govern the solubility of CaSO4 hydrates: CaSO4 ·nH2 O(s) = Ca2+ + SO4 2− + nH2 O
(1)
Ca2+ + SO4 2− = CaSO4(aq) o
(2)
The solubility of calcium sulfate is: [Ca]total = [Ca2+ ] + [CaSO4(aq) o ]
(3)
To obtain the equilibrium constants of reactions (1) and (2) at temperature T and pressure P, the standard state chemical potentials of the products and reactants are required. These data are widely available in standard thermodynamic compilations. To extrapolate the standard state thermodynamic properties to high temperatures and pressures, the HKF model, developed by Tanger and Helgeson [10], embedded in the OLI software was employed. To account for the non-ideality (excess properties) of the electrolyte solutions studied, the MSE activity coefficient model [11,12], which is also embedded in the OLI Systems software, was used. In the end, a selfconsistent and calibrated model was produced. More details on the modeling methodology and the database developed are available elsewhere [8,9,13].
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Fig. 2. CaSO4 solubility as a function of MSO4 (M = Ni, Mg, Mn) concentration; MgSO4 experimental data are from [14–17]; NiSO4 experimental data are from [17,18]; MnSO4 experimental data are from [17,19]; curves are model predictions.
Fig. 3. CaSO4 solubility in CaSO4 –MgSO4 –HCl (0.5 M)–H2 O solution; experimental data are from this work, and curves are the model predictions.
4. Results and discussion 4.1. Effect of divalent cations on the solubility of CaSO4 hydrates Fig. 2 presents a comparison between the solubility of CaSO4 dihydrate (DH) in ternary solutions of CaSO4 –NiSO4 –H2 O, CaSO4 –MgSO4 –H2 O and CaSO4 –MnSO4 –H2 O along with the model “predictions” at two different temperatures: 25 and 75 ◦ C. It is clear that the difference between CaSO4 solubilities in these systems at both temperatures is always less than ∼15% indicating that the cation type does not have a dramatic effect on the CaSO4 solubility. For all three cations, as the metal sulfate concentration increases from pure water, the solubility initially drops and then increases gradually. After passing a maximum, the solubility decreases smoothly with further increasing the MSO4 (M = Mg, Mn, Ni) concentration. The initial drop is due to the common ion effect which shifts the dissolution reaction (Eq. (1)) to the left; the subsequent increase is attributable to the association of Ca2+ and SO4 2− ions and formation of calcium sulfate neutral species (Eq. (2)). The solubility decrease in concentrated solutions is due to the saltingout effect due to the decreased number of free water molecules in the solution to dissolve calcium sulfate.
In industrial applications, particularly in hydrometallurgy, solutions sometimes contain several cations for which there are no experimental data available. By knowing that cation type does not have a significant effect on the solubility level, all divalent cations can be substituted with a certain cation for which experimental data are available during the simulation of the process. 4.2. Effect of different acids on the solubility of CaSO4 hydrates To compare the effect of H2 SO4 and HCl on the solubility of calcium sulfate dihydrate (DH), two different sets of experiment were performed: first, the solubility was measured as a function of MgSO4 concentration in 0.5 M HCl solutions. Second, the solubility was measured as a function of NiSO4 concentration in 0.5 M H2 SO4 solutions. The measured data are presented in Tables 1 and 2. Figs. 3 and 4 show the measured solubility data in comparison with the model prediction results from 25 to 90 ◦ C. In both systems, the solubility first decreases with increasing MSO4 (M = Ni, Mg) concentration due to the common ion effect of the added SO4 2− ions. This effect is nullified by further increasing MSO4 concentration because of the association of Ca2+ and SO4 2− ions and
Table 1 Solubility of CaSO4 dihydrate in 0.5 M HCl solutions at various MgSO4 concentrations. MgSO4 (mol/L)
0.0 0.1 0.5 1.0 1.5
25 ◦ C
45 ◦ C
70 ◦ C
90 ◦ C
CaSO4 (mol/L)
Density (g/mL)
CaSO4 (mol/L)
Density (g/mL)
CaSO4 (mol/L)
Density (g/mL)
CaSO4 (mol/L)
Density (g/mL)
0.0810 0.0456 0.0168 0.0110 0.0087
1.007 1.021 1.057 1.112 1.162
0.0940 0.0594 0.0205 0.0139 0.0105
1.005 1.013 1.047 1.100 1.158
0.1300 0.0785 0.0231 0.0153 0.0113
1.004 1.008 1.038 1.105 1.102
0.1560 0.0987 0.0292 0.0188 0.0135
0.997 0.999 1.030 1.080 1.128
Table 2 Solubility of CaSO4 dihydrate in 0.5 M H2 SO4 solutions at various NiSO4 concentrations. NiSO4 (mol/L)
0.00 0.10 0.25 0.50 1.00 1.50
25 ◦ C
45 ◦ C
70 ◦ C
90 ◦ C
CaSO4 (mol/L)
Density (g/mL)
CaSO4 (mol/L)
Density (g/mL)
CaSO4 (mol/L)
Density (g/mL)
CaSO4 (mol/L)
Density (g/mL)
0.0190 0.0180 0.0166 0.0166 0.0148 0.0131
1.030 1.044 1.060 1.106 1.180 1.238
0.0258 0.0234 0.0210 0.0196 0.0172 0.0158
1.022 1.037 1.056 1.095 1.170 1.230
0.0403 0.0351 0.0298 0.0266 0.0234 0.0194
1.010 1.026 1.044 1.085 1.157 1.218
0.0545 0.0454 0.0383 0.0329 0.0314 0.0245
1.002 1.015 1.029 1.071 1.141 1.202
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Fig. 4. CaSO4 solubility in CaSO4 –NiSO4 –H2 SO4 (0.5 M)–H2 O solution; experimental data are from this work, and curves are the model predictions.
formation of calcium sulfate neutral species. Also, the solubility of dihydrate (DH) is significantly higher in the presence of HCl (Fig. 3) compared to that in H2 SO4 (Fig. 4). This effect is most pronounced near zero metal sulfate concentrations. The addition of both H2 SO4 and HCl increases the solubility of CaSO4 dihydrate (DH) due to the formation of bisulfate ions; however, in the case of H2 SO4 , there is a common ion effect due to the produced SO4 2− from the second dissociation of H2 SO4 hindering the dissolution reaction. In both systems, model “predictions” are in good agreement with the experimental data. It should be emphasized that no extra fitting were perfumed in these systems which proves the predictability of the model in multicomponent systems using the interaction parameters obtained in binary and ternary systems, i.e., CaSO4 –H2 O, CaSO4 –MgSO4 –H2 O, CaSO4 –NiSO4 –H2 O, CaSO4 –HCl–H2 O and CaSO4 –H2 SO4 –H2 O which have been studied previously [8,9].
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Fig. 5. CaSO4 solubility in CaSO4 –NiSO4 (1.4 M)–H2 SO4 (1 M)–Fe2 (SO4 )3 (0.2 M)–LiCl (0.3 M)–H2 O solutions at various retention times and different temperatures.
the equilibrating solid phase was estimated semi-quantitatively by measuring the peak intensities of the different X-ray diffraction patterns and was confirmed by thermo gravimetric analysis (TGA). Hemihydrate was not detected in any of the samples despite a careful search for this phase. The experimentally measured solubility
4.3. Effect of phase transition on the solubility of CaSO4 hydrates 4.3.1. CaSO4 –NiSO4 –H2 SO4 –Fe2 (SO4 )3 –LiCl–H2 O System Nickel processing solutions typically contain NiSO4 , H2 SO4 , Fe2 (SO4 )3 and small amounts of a chloride salt. In this work, the solubility of calcium sulfate dihydrate (DH) was measured in a solution of 1.4 M NiSO4 , 1 M H2 SO4 , 0.2 M Fe2 (SO4 )3 and 0.3 M LiCl. Solubility measurements were carried out based on heating from 25 to 90 ◦ C followed by subsequent cooling. At a given temperature, the relative amount of dihydrate (DH) and anhydrite (AH) in
Fig. 6. CaSO4 solubility in CaSO4 –NiSO4 (1.4 M)–H2 SO4 (1 M)–Fe2 (SO4 )3 (0.2 M)–LiCl (0.3 M)–H2 O solutions; solid curves are the model predictions, and the dashed line shows the phase transition region.
Table 3 Calcium sulfate concentration, saturated solution density and solid phase composition in 1.4 M NiSO4 , 1 M H2 SO4 , 0.2 M Fe2 (SO4 )3 , 0.3 M LiCl solutions at various temperatures and retention times. Time (h)
T (◦ C)
Density (g/mL)
CaSO4 (mol/L)
Method
Solid phase composition
24 48 72 96 120 144 168 192 216 240 264
25 45 60 70 70 70 90 80 60 35 25
1.333 1.318 1.315 1.305 1.305 1.305 1.298 1.300 1.315 1.326 1.333
0.0079 0.0106 0.0136 0.0155 0.0127 0.0089 0.0085 0.0084 0.0082 0.0082 0.0080
Heating Heating Heating Heating Heating Heating Heating Cooling Cooling Cooling Cooling
100% DH 100% DH 100% DH 100% DH 80% DH + 20% AH 100% AH 100% AH 100% AH 100% AH 100% AH 25% DH + 75% AH
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Fig. 8. CaSO4 solubility vs. temperature in CaSO4 –MnSO4 –H2 SO4 –H2 O solutions; the experimental data are from [20]; the solid curves are the predicted values and the dashed lines show the phase transition region.
Fig. 7. SEM images of the solid phases at 70 ◦ C showing the different crystal morphologies of (a) 100% dihydrate (DH) withdrawn after 24 h retention time (b) transitional of 80% dihydrate (DH)–20% anhydrite (AH) mixture withdrawn after 48 h and (c) 100% anhydrite withdrawn after 72 h.
data, saturated solution densities and solid phase compositions at various temperatures are summarized in Table 3. Fig. 5 presents the solubility data as a function of the retention time along with solid sample compositions at different temperatures. As is shown, the solubility increases with temperature up to 70 ◦ C. The system was kept at 70 ◦ C for 3 days and slurries were periodically sampled. The results showed a gradual decrease in the solubility in the second and the third samples at 70 ◦ C withdrawn on the day 2 and day 3, respectively. The solubility values measured at 90 ◦ C had the same order of magnitude as the third sample withdrawn at 70 ◦ C after 3 days. On cooling, a relatively flat solubility curve is noted up to 25 ◦ C.
Powder X-ray diffraction analysis of the equilibrating solid phase showed only dihydrate (DH) during heating up to 70 ◦ C; however, the solid sample withdrawn at 70 ◦ C after 3 days retention time and the one withdrawn at 90 ◦ C showed 100% anhydrite (AH) in the composition. The solid sample withdrawn at 70 ◦ C after 2 days retention time contained a mixture of dihydrate (DH) and anhydrite (AH). On cooling, anhydrite remained the dominant equilibrating solid phase above 25 ◦ C, but at 25 ◦ C the conversion of anhydrite (AH) to dihydrate (DH) occurred. Thus, the major drop in the solubility of calcium sulfate is due to the transformation of dihydrate (DH) into anhydrite (AH), a phase which has a significantly different solubility–temperature relationship. Fig. 6 shows CaSO4 solubility data as a function of temperature along with the model predictions. As can be seen, the model predicts the solubility of dihydrate and anhydrite precisely. However, the phase transition area, which is not thermodynamically stable, cannot be predicted by the model and is marked by a dashed line in the figure. The SEM images of the solid samples withdrawn at 70 ◦ C after 24, 48 and 72 h retention times are presented in Fig. 7(a)–(c), respectively. As mentioned above, the first solid sample presented in Fig. 7(a) shows 100% dihydrate in composition, whereas, the sample shown in Fig. 7(b) reveals a mixture of 80% DH and 20% AH, as estimated from XRD and TGA. Fig. 7(c) presents a solid sample with 100% AH after complete transformation of dihydrate in the system. As is clear, the morphologies of calcium sulfate dihydrate and anhydrite are very different: DH crystals are in a monoclinic form, whereas AH crystals have an orthorhombic structure and are needle shaped. 4.3.2. CaSO4 –H2 SO4 –MnSO4 –H2 O system There are some difficulties involved in the electrolytic process for the winning of manganese dioxide from H2 SO4 /Mn2+ electrolytes where CaSO4 scale develops in heat exchangers, pipes and other equipment. These processes require regular cleaning to maintain efficient process operation. Farrah et al. [20] studied the effect of H2 SO4 , MnSO4 and temperature on the solubility of CaSO4 hydrates over the temperature range of 30–105 ◦ C. Fig. 8 shows their experimental solubility data along with the predicted results obtained from the new model, which are in very good agreement. It is obvious from the figure that dihydrate (DH)
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solubility decreases with an increase in MnSO4 concentration at fixed H2 SO4 concentrations due to the common ion effect. Also, there is a systematic increase in the solubility with temperature in the presence of MnSO4 up to 80 ◦ C because of the tendency of the sulfate ions to form bisulfate. Above 80 ◦ C, calcium sulfate solubility declines sharply as a result of dihydrate (DH) to anhydrite (AH) transformation. It can be seen from the figure that the solubility of anhydrite is also depressed by subsequent addition of MnSO4 . 5. Conclusions Many industries are dealing with calcium sulfate scale formation and need regular removal of precipitated calcium sulfate hydrates. At elevated temperatures, the transformation between the calcium sulfate phases has a complex effect on the solubility, making the behaviour of calcium sulfate difficult to predict and control. In this work, a recently developed database for the MSE model of the OLI Systems software was used to study the effect of different electrolytes on the CaSO4 solubility. It was found out that it is mainly the anion which controls the solubility of calcium sulfate, while cations have a minor effect. The solubility behaviour of CaSO4 is the same in all metal sulfate electrolytes with different cations: as the metal sulfate concentration increases from pure water, the solubility initially drops due to the common ion effect and then increases gradually due to the formation of calcium sulfate neutral species. After passing a maximum, solubility decreases smoothly with a further increase in the concentration due to the salting-out effect and decreased number of free water molecules in the solution. The solubility of CaSO4 dihydrate was measured in solutions containing NiSO4 , H2 SO4 , MgSO4 and HCl. It was found that the
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solubility is significantly higher in the presence of HCl compared to that in H2 SO4 because in the case of H2 SO4 , there is a common ion effect due to the produced SO4 2− from the second dissociation of H2 SO4 hindering the dissolution reaction. Furthermore, the effect of the phase transformation of calcium sulfate dihydrate (DH) into anhydrite (AH) on the solubility was studied. The transformation takes place at higher temperatures and acid concentrations and has a complex effect on the solubility. In this work, complete transformation was achieved at 70 ◦ C after 3 days retention time in the presence of 1 M H2 SO4 . The solubility of anhydrite is much lower than that of dihydrate (∼50–80% lower); therefore process solutions which are saturated with dihydrate (DH) at ambient temperature and are recycled to autoclaves, operating at temperatures above 100 ◦ C, need to be processed to decrease their calcium content and make it less than anhydrite saturation level inside an autoclave. Otherwise, scale formation will be unavoidable. Chemical modeling is a practical asset to map calcium sulfate chemistry in electrolyte solutions over wide ranges of temperature and concentration. This, in turn, results in gaining comprehensive insight for process improvements and optimization in various processes. Acknowledgements The authors would like to acknowledge the financial support provided by Anglo American plc., Barrick Gold Corporation, OLI Systems Inc., Sherritt International Corporation, Vale Inco Ltd., the Ontario Graduate Scholarship (OGS) and the Natural Sciences and Engineering Research Council of Canada (NSERC) for this project. Appendix A. MSE middle-range interaction parameters (OLI-version 8.1.3)
Species i
Species j
BMD0
BMD1
BMD2
CMD0
CMD1
MnSO4 –H2 O CaSO4 –H2 O
Mn2+ Ca2+
SO4 2− SO4 2−
−716.157 10887.73
0.9059 −16.973
93031.7 −1770400
255.511 −15416.42
– 24.215
CaSO4 –MnSO4 –H2 O
Ca2+ CaSO4(aq)
Mn2+ Mn2+
683.490 2134.468
−2.0005 −2.8306
2+
−2602.165 678.644
4.8761 −1.529
2+
CaSO4 –MgSO4 –H2 O
Ca CaSO4(aq)
Mg Mg2+
CaSO4 –Na2 SO4 –H2 O
Ca2+
Na+
– −394938 333009 −62232.5
−868.843 – 3630.73 −562.19
CMD2
Temperature range (◦ C)
– 2508590
2.5173 –
– –
25–100
−6.8234 1.7298
−462726 –
25–175
25.171
−0.0262
CaSO4 –H2 SO4 –H2 O
Ca CaSO4(aq)
HSO4 − HSO4 −
3715.460 393.149
−6.0144 −1.6809
−618224 11323.61
CaSO4 –CaCl2 –H2 O/CaSO4 – HCl–H2 O/CaSO4 –NaCl– H2 O/CaSO4 –MgCl2 –H2 O
Cl− Cl− Cl−
SO4 2− HSO4 − CaSO4(aq)
465.363 −148.074 9.4550
−0.8069 0.3573 0.0367
−62105.4 – –
CaSO4 –NiSO4 –H2 O
Ca2+ CaSO4(aq)
Ni2+ Ni2+
269.924 −656.530
−0.7478 1.5199
97192 –
−1160.872 863.322
1.9865 −1.8770
– –
CaSO4 –Fe2 (SO4 )3 – ZnSO4 –H2 SO4 –H2 O
Ca2+ CaSO4(aq)
Fe3+ Fe3+
−172.067 663.006
−9.8085 −1.1448
955584 −104326
313.487 1099.014
13.8038 −1.1435
−1362390 −202962
2+
–
0–180 0–400
−33.189
0.0210
–
25–300
−4472.033 −671.232
7.3066 2.5821
733093 –
25–300
−511.001 176.162 −55.0627
0.9236 −0.4188 0.02547
64179.32 – –
22–300
25–175 25–90
94
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