Performance of Three Chemical Models on the High-Temperature

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Ind. Eng. Chem. Res. 2005, 44, 2931-2941

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Performance of Three Chemical Models on the High-Temperature Aqueous Al2(SO4)3-MgSO4-H2SO4-H2O System Jesu ´ s M. Casas,† Vladimiros G. Papangelakis,* and Haixia Liu Department of Chemical Engineering and Applied Chemistry, University of Toronto, 200 College Street, Toronto, Canada M5S 3E5

This work involves chemical modeling of concentrated aqueous sulfate solutions during an industrial process: pressure acid leaching of laterites at high temperature of interest to the metals and minerals industries. Equilibrium constants of Al and Mg complexes were estimated or extrapolated. Three activity coefficient models were used: the B-dot equation, the Pitzer model, and the Bromley-Zemaitis model. The B-dot and Pitzer models were implemented with EQ3/6 software (version 7.0), and the Bromley-Zemaitis model was implemented through OLI-Systems software (version 6.2). Original databases in all cases were modified in order to include the equilibrium constants of Al and Mg species. Calculated values are in good agreement with the experimental solubility data for MgSO4-H2SO4-H2O and Al2(SO4)-H2SO4-H2O ternary systems with all three models. However, significant differences were found in the predicted speciation and pH in both ternary and quaternary systems because of the different correlations and assumptions employed in the models. A self-consistent model and new thermodynamic data for high-temperature aqueous processes are highly recommended to handle concentrated solutions of interest to the process industry. Introduction In the minerals and metals industries, concentrated aqueous solutions of sulfuric acid and dissolved metals, such as Al, Mg, Ni, Mn, Cr, Co, and Fe, at 230-270 °C are encountered in the pressure acid leaching (PAL) process for Ni and Co recovery from laterite ores.1,2 Similar types of high-temperature electrolyte solutions are also encountered in many pressure oxidation processes operating at 150-230 °C for recovering precious metals, Ni, Cu, and Zn, from sulfide minerals.3-5 The knowledge of the ionic equilibria in solution and solid precipitation is important to understand the processes, optimize the production operations, and define the control strategies for impurities and contaminants present in the resulting leach effluents. The metals present in leach solutions are distributed as soluble species such as metal ion, neutral, or charged complexes.6 Process solutions in industrial applications contain high concentrations of acid and dissolved metals in order to minimize the equipment volume. In the aqueous processing of laterite ores (nickel oxide) at 250270 °C, the concentrations of free sulfuric acid and metal sulfates range from 5 to 80 g/L and from 5 to 20 g/L, respectively, as measured at room temperature.7 Consequently, high concentration comes with high nonideal thermodynamic behavior. Any attempt to chemically model the solutions presents significant challenges. The difficulty in predicting the behavior of electrolyte solutions is further increased at high temperatures and pressures: conditions at which many of the hydromet* To whom correspondence should be addressed. Tel.: 4169781093. Fax: 416-9788605. E-mail: [email protected]. † Present address: Department of Chemical Engineering, University of Chile, Beauchef 861, PC-6511266, Santiago, Chile. E-mail: [email protected]. Visiting professor at University of Toronto.

allurgical processes operate. Because of the lack of thermodynamic data and analytical techniques for in situ measurement of ions and ionic complexes at high temperature, the application of extrapolative chemical models is a promising way to predict the phase behavior provided that reliable models exist with acceptable predictive power based on limited available experimental data. The key question is, how reliable are the current chemical models of concentrated electrolyte solutions in predicting solution speciation and solidliquid equilibria (SLE) or vapor-liquid equilibria (VLE)? There have been significant recent developments in modeling the chemistry of the PAL process of nickeliferous laterites. Baghalha and Papangelakis8,9 proposed a new hybrid ion-interaction-association approach for calculating the solubilities of Al and Mg and the solution speciation in acid solutions at high temperature. Furthermore, Rubisov and Papangelakis10 attempted to model the PAL process where a multitude of different ions coexist by proposing a simplified speciation model, where only one dominant species per metal was considered. This work made it possible to apply electrolyte thermodynamics to real industrial solutions with acceptable predictive power at the expense of using many adjustable parameters. However, it also revealed that if we want to enhance this predictive power further, it is important to rely on a rigorous simulation package so that it can be easily and consistently used by industry. Modeling phase equilibria in electrolyte systems requires reliable standard state thermodynamic data for all species and a good activity coefficient model to describe the excess properties. In this work, the equilibrium constants (standard state properties) for Al and Mg species were collected and assessed, and three activity coefficient models were applied to simulate the solubilities and speciation of aqueous sulfuric acid solutions containing Mg and Al at or near saturation

10.1021/ie049535h CCC: $30.25 © 2005 American Chemical Society Published on Web 03/19/2005

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during high-temperature acid leaching of laterites in the range of 235-270 °C. The three activity coefficient models are the extended Debye-Hu¨ckel equation denoted as the B-dot equation proposed by Helgeson,18,27 the Pitzer model with binary ion interaction parameters,11-13,18 and the Bromley-Zemaitis model.15-17 The first two models were tested through the EQ3/6 software package,18,19 whereas the third one was tested with OLISystems software.17 Original databases in both softwares were modified in order to include the equilibrium constants of Al and Mg solid phases appearing under the conditions of interest, as well as solution species that are not available in the original databases but have been reported to dominate in high-temperature sulfate systems. The aim of this work was essentially to compare and evaluate modern methodologies for chemical modeling of high-temperature aqueous industrial processes with a focus on the PAL of laterites. The actual systems investigated were (i) H2SO4-H2O, (ii) Al2(SO4)3-H2SO4-H2O, (iii) MgSO4-H2SO4-H2O, and (iv) Al2(SO4)3MgSO4-H2SO4-H2O. The comparison here is made on the models themselves as integrated packages rather than on their databases or their individual thermodynamic approaches. Equilibria in the Al2(SO4)3-MgSO4-H2SO4-H2O System In a simulation of the solubility and speciation of the complicated Al2(SO4)3-MgSO4-H2SO4-H2O system, in this work two types of equilibria are considered. SLE. In the MgSO4-H2SO4-H2O and Al2(SO4)3-H2SO4-H2O systems, the solid phases at high temperature (200-300 °C) are MgSO4‚H2O20 and (H3O)Al3(SO4)2(OH)6.8 The SLE reactions can be expressed as follows:

MgSO4‚H2O ) Mg2+ + SO42- + H2O

(1)

(H3O)Al3(SO4)2(OH)6 + 5H+ ) 3Al3+ + 2SO42- + 7H2O (2) The equilibrium constants for reactions 1 and 2 respectively are

K1 ) exp(-∆G1°/RT) ) aMg2+ aSO42-aH2O ) γMg2+mMg2+γSO42-mSO42-aH2O (3) K2 ) exp(-∆G2°/RT) )

aAl3+3aSO42-2aH2O7 aH+5

)

(γAl3+mAl3+)3(γSO42-mSO42-)2aH2O7 (γH+mH+)5

(4)

where a is the activity, γ is the activity coefficient, m is the concentration in terms of molality, and ∆G1° and ∆G2° are the standard Gibbs free energies of reactions 1 and 2. These equilibrium constants can be calculated from the standard Gibbs free energies of the reactions provided that the standard Gibbs free energies of formation for all individual species are available. However, these data are usually unavailable at high temperature. Alternatively, the same equilibrium constant can be regressed from experimental data. Baghalha and Papangelakis8 obtained these two equilibrium constants

by regression on experimental solubility data of MgSO4 and Al2(SO4)3 in H2SO4 solutions, using the Pitzer activity coefficient model. Aqueous Speciation Equilibria. Species selection for inclusion in a chemical model is not a straightforward issue particularly for high-temperature process solutions. The decision usually depends on identification studies performed at room temperature. However, new species may form under high temperature and high concentration for which prior knowledge at room temperature is not available.10 For many aqueous reactions, there is a lack of equilibrium constants for high temperatures. Even if they are available, there is often a big variation between different sources. For example, the reported values of log K at 250 °C for the reaction (which were calculated with different temperature extrapolation techniques)

AlOH2+ + H+ ) Al3+ + H2O are -1.49,21 -0.8,24 and 0.66.31 The Criss-Cobble method25,26 and the Helgeson-Kirkham-Flowers (HKF) model28-32 are two methods to calculate ∆Gi° (i represents a single species) at elevated temperature from room temperature data. However, the Criss-Cobble method is limited to temperatures below 200 °C and cannot be applied for certain types of complex species, e.g., neutral species, and metal oxyanions. The HKF model is currently the most accepted model to extrapolate standard thermodynamic properties at elevated temperatures and pressures.17,28 Numerous HKF parameters have been published for aqueous species.29,30 The HKF thermodynamic framework has been incorporated in commercial software like OLI,17 which is used in this work. Furthermore, equilibrium constants for some key Al and Mg complex species for which data were not available in the original databases of the EQ3/6 and OLI software were taken from literature data (see details below) if their determination was by direct measurements at high temperature (rather than extrapolation). The speciation reactions and equilibrium constants of the Al2(SO4)3-MgSO4-H2SO4-H2O system are presented in Table 1. The SLE reactions are also listed there. As an example, Figure 1 shows the extrapolation methodology adopted in this study for the case of the AlSO4+ complex. The equilibrium constant for AlSO4+ dissociation decreases with increasing temperature according to the experimental data of Ridley et al.33 at low temperatures, and the trend seems to be in agreement with the value proposed by Baghalha and Papangelakis8 at 250 °C. Hence, the log K values for AlSO4+ at different temperatures8,33 were combined and regressed with Mathematica (as shown by the curve in Figure 1) in the form of

log K ) A1 +

A2 + A3T + A4T 2 T

(5)

where A1-A4 are coefficients and T is the temperature in Kelvin. log K at any temperature can be calculated from the above equation, and values at 200, 250 and 300 °C are as shown in Table 1. Similarly, the dissociation equilibrium constant for Al(SO4)2-, as presented in Table 1, was estimated by the same nonlinear extrapolation (eq 5) of the experi-

Ind. Eng. Chem. Res., Vol. 44, No. 9, 2005 2933 Table 1. Equilibrium Constants for the System Al2(SO4)3-MgSO4-H2SO4-H2O log KT species

dissociation reaction

200 °C

250 °C

300 °C

ref

AlSO4+ Al(SO4)2AlHSO42+ Al2(SO4)30 (H3O)Al3(SO4)2(OH)6 MgSO40 MgHSO4+ MgSO4‚H2O

AlSO4+ ) Al3+ + SO42Al(SO4)2- ) Al3+ + 2SO42AlHSO42+ ) Al3+ + H+ + SO42Al2(SO4)30 ) 2Al3+ + 3SO42(H3O)Al3(SO4)2(OH)6 + 5H+ ) 3Al3+ + 2SO42- + 7H2O MgSO40 ) Mg2+ + SO42MgHSO4+ ) Mg2+ + H+ + SO42MgSO4‚H2O ) Mg2+ + SO42- + H2O

-9.4 -13.4 -7.8

-12.0 -17.4 -10.3 -31.7 -32.7 -4.6 -6.6 -6.6

-14.6 -22.0 -12.9

8, 33 33 22a 8 8 8 a 8, 23

a

-4.0 -5.3 -5.2

-5.5 -7.9 -8.1

See text. Table 2. B-dot Parameters as a Function of the Temperature18 temperature, Aγ, Bγ, B˙ , kg0.5 mol-0.5 (×10-8) kg0.5 mol-0.5 cm-1 kg mol-1 °C 0 25 60 100 150 200 250 300

Figure 1. Equilibrium constant as a function of the temperature for dissociation reaction AlSO4+ ) Al3+ + SO42-: (O) Ridley et al.;33 (9) Baghalha and Papangelakis.8

mental data of Ridley et al.33 within the temperature range of 25-125 °C. The equilibrium constant of AlHSO42+ dissociation is reported only at 25 °C.22 Its temperature dependence was estimated from the Criss-Cobble method through HSC software.34 The equilibrium constant for MgHSO4+ dissociation between 200 and 300 °C was obtained by fitting the Mg solubility data reported by Marshall and Slusher20 with EQ3/6 software and the B-dot model.18 This procedure was used because the thermodynamic data for MgHSO4+ have never been reported in the literature. Consideration of bisulfate complexes arises from the fact that H2SO4 solutions at high temperature are dominated by HSO4- ions.12,14 Although studies with Raman spectrophotometry have not identified contact ion pairing of Al3+HSO4- 37 and Fe2+HSO4- 38 in aqueous solutions, the two bisulfate complexes, AlHSO42+ and MgHSO4+, were considered as possible species. The main reason was that poor solubility prediction could be achieved with the B-dot model in the MgSO4-H2SO4H2O system without the inclusion of MgHSO4+. Furthermore, Raman spectrophotometry is only sensitive to contact ion-pair complexes (Fe2+SO42-) but not to hydrated (outer sphere) complexes such as Fe2+(H2O)nHSO4-, which might exist.38 The solubility product for the mineral MgSO4‚H2O was estimated by linear extrapolation from the data reported by Harvie et al.23 at 25 °C and Baghalha and Papangelakis8 at 235 and 270 °C. Finally, the equilibrium constants for Al2(SO4)30, (H3O)Al3(SO4)2(OH)6, and MgSO40 dissociation at 250 °C were taken directly from the work of Baghalha and Papangelakis.8 The assembled equilibrium constant data of complex dissociation and mineral precipitation reactions were then entered into the databases of EQ3/6 and OLI software.

0.4939 0.5114 0.5465 0.5995 0.6855 0.7994 0.9593 1.2180

0.3253 0.3288 0.3346 0.3421 0.3525 0.3639 0.3766 0.3925

0.0394 0.0410 0.0438 0.0460 0.0470 0.0470 0.0340 0.0150

The equilibrium constants were then used with different activity models. A brief description of the three activity coefficient models used is given below. Some additional changes were also made and explained where appropriate. The AlHSO42+, Al(SO4)2-, and MgHSO4+ complexes were not considered in the Pitzer-based model proposed by Balghala and Papangelakis.8 Hence, they are not included in the EQ3/6 Pitzer model. Also, MgSO40 and MgHSO4+ were not entered into OLI’s database because the former exists in the default database and the latter did not give good solubility prediction of MgSO4. Activity Coefficient Models B-Dot Equation. Helgeson27 proposed a simple extended Debye-Hu¨ckel equation known as the B-dot equation to calculate the activity coefficient in the ranges 0-1000 °C, 10-3-105 kbar, and I < 1 m:

log γi ) -

Aγzi2xI 1 + a˚ iBγxI

+ B˙ I

(6)

where a˚ i is the hard-core diameter of species i, zi is the charge, Aγ and Bγ are Debye-Hu¨ckel parameters, I is the ionic strength of the solution, and B˙ is the characteristic B-dot parameter, which depends only on the temperature. Aγ, Bγ, and B˙ values as a function of temperature are listed in Table 2. Equation 6 is embedded in EQ3/6 software. All of the species and their equilibrium constants listed in Table 1 were entered into the EQ3/6 database for the B-dot model. The only species-specific parameter is the hard-core parameter a˚ , which is provided for almost 1000 aqueous species in the default EQ3/6 database. For newly added species that were not included in the database, reasonable estimates were assigned. For example, we adopted an a˚ value for AlSO4+ equal to that of FeSO4+, which is 4.0 Å. For neutral species, the a˚ value in EQ3/6 is usually 3.0 Å. In Table 1, the a˚ value for AlSO4+, Al(SO4)2-, and MgHSO4+ was assigned a value of 4.0 Å, whereas that

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for Al2(SO4)30 and MgSO40 was 3.0 Å and that for AlHSO42+ 4.5 Å. Pitzer Model. In this work, a simplified form of the Pitzer model was used in which only the second-order interaction coefficients together with the long-range electrostatic interactions were considered. Thus, the activity coefficient for ion i is calculated by the following equation:13,18

log γi )

() zi2 2

∑j λij(I) mj +

f ′(I) + 2

0 -3 (T - 25) βMg 2+-HSO - ) 0.244 - 1.37 × 10 4

[( ) ] zi

2

λ′jk(I) mjmk (7)

where m is the molal concentration, z is the charge, i, j, and k are ions,

f ′(I) ) -2Aφ

(

)

xI 2 ln(1 + bxI) + b 1 + bxI

Aφ ) (Aγ/3) ln 10, where Aγ is the same as that in the B-dot equation, b is assigned a constant value of 1.2, λ′ is the derivative of λ with respect to I, and λ is the second-order interaction coefficient between ions i and j. It is a function of the ionic strength and can be expressed as

2β(1) ij λij(I) ) β(0) + [1 - (1 + R1xI) exp(-R1I)] + ij 2 R1 I

For 1:1, 2:1, 3:1, and 4:1 electrolytes, the β(2) term is omitted, R1 has a value of 2.0, and the adjustable parameters become β(0) and β(1). For 2:2 electrolytes, R1 ) 1.2, R2 ) 12.0, and there are three adjustable parameters β(0), β(1), and β(2). For higher charge types of electrolytes such as 3:2, R1 and R2 may have different values.13 So, the mean activity coefficient of a single electrolyte is

{

|z+z-| 2β f ′(I) + m 2β(0) + 2 [1 - (1 + R1 2 R I (1)

1

2β(2) 0.5R1 ) exp(-R2xI)] + 2 [1 - (1 + R2 R2 I

0 βAlSO - ) 0.1060 + 4 -HSO4

Bromley-Zemaitis Model. The activity coefficient model proposed by Bromley15 and modified by Zemaitis et al.16,17 has received special attention by OLI Systems17 due to good results obtained in the simulations of multiphase and multicomponent inorganic systems. This model can describe the solution speciation over a wide range of concentration (0.1 to 30 molal) and temperature (-50 to +300 °C), by using the following relationship for a single electrolyte:

log γ( ) -

A|z+z-|xI 1 + xI

+

(0.06 + 0.6B)|z+z-|I + BI + 1.5 2 I 1+ |z+z-|

(

)

CI2 + DI3 (10)

2β(2) ij [1 - (1 + R2xI) exp(-R2I)] 2 R2 I

log γ( )

0 -4 βH (T - 25) +-HSO - ) 0.2106 - 5.05 × 10 4 1 -4 βH (T - 25) +-HSO - ) 0.4200 - 2.05 × 10 4

2

∑j ∑k

with the Pitzer model. The following Pitzer parameters were entered into EQ3/6 to account for the activity coefficient calculations at 250 °C of the system studied in this work8,12,14 (other parameters are available in the software database18):

where A is the Debye-Hu¨ckel constant and B, C, and D are Bromley parameters for one pair of cation-anion. Each of the B, C, and D parameters has the following temperature dependence:

B ) B1 + B2T + B3T 2 C ) C1 + C2T + C3T 2 D ) D1 + D2T + D3T 2 (where T is the temperature in degrees Celsius). A large number of Bromley parameters are being provided in OLI’s default database. In this work, no new Bromley parameters were entered into the software other than those existing in OLI’s default database.

2

0.5R22) exp(-R2xI)]

}

Results and Discussion

(8)

The temperature dependence of the Pitzer parameters β(0) and β(1) (b, R1, and R2 are treated as constants) follows a linear relationship19 with temperature in degrees Celsius.

x(T) ) x0 +

dx (dT )

T0

(T - T0)

(9)

where T0 is 25 °C. In the previous work of Balghala and Papangelakis,8 the species AlHSO42+, Al(SO4)2-, and MgHSO4+ complexes were not considered in the Pitzer-based model. Therefore, they were not included in the EQ3/6 database

The equilibrium constants shown in Table 1 were entered as discrete values in the database of EQ3/6 software “data0.com”. In the case of the OLI database, eq 5 is used. If the equilibrium constant data exist only for one temperature, then A2, A3, and A4 are set to 0. Model comparisons of Al and Mg solubilities in aqueous solutions of sulfuric acid at high temperature are presented for the following aqueous systems. (i) Binary system: H2SO4-H2O, 25-300 °C. (ii) Ternary system: MgSO4-H2SO4-H2O, 235-270 °C. (iii) Ternary system: Al2(SO4)3-H2SO4-H2O, 250 °C. (iv) Quaternary system: MgSO4-Al2(SO4)3-H2SO4H2O, 250 °C. The pH and speciation for the above systems are calculated and compared among the three models. The calculated solubilities of MgSO4 and Al2(SO4)3 with the

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Figure 2. Calculated pH at 25-300 °C in a 0.5 m H2SO4 solution.

Figure 3. Calculated pH in H2SO4 solutions at 250 °C.

three models are also compared against available experimental measurements at high temperature. H2SO4-H2O System. The pH in a 0.5 m H2SO4 solution from 25 to 300 °C was calculated with all three models, as shown in Figure 2. The calculated pH values with all three models correctly show the same general tendency, i.e., increases with increasing temperature due to a decrease of the second dissociation constant of H2SO4 with temperature.12,36 However, the B-dot and Bromley-Zemaitis models give a higher pH than the Pitzer model over the whole temperature range. To compare the pH variation with the H2SO4 concentration at 250 °C, plots of the pH calculated by each activity model are shown in Figure 3. The pH decreases with increasing acidity with all three models. At the same acidity, the pH from the Bromley-Zemaitis model is again the highest. Each model, however, calculates the equilibria based on a different speciation. The speciation of the H2SO4H2O system at 250 °C is also shown in Figure 4. As can be seen, although H+ and HSO4- are dominant species in all three models, H+ and HSO4- have equal concentrations in the B-dot and Bromley-Zemaitis models, as shown in Figure 4a,c. On the other hand, H2SO4(aq) has an importance in the B-dot model and SO42- in the Pitzer model, whereas in the Bromley-Zemaitis model, both H2SO4(aq) and SO42- are negligible. Therefore, the pH difference among the three models is due to the difference between both the concentration and activity coefficient of H+ because the pH is defined as -log(γH+mH+). For example, the activity coefficient of H+ as a function of the ionic strength in a H2SO4 solution at 250 °C is shown in Figure 5. The Bromley-

Figure 4. Calculated species concentrations in the H2SO4-H2O system at 250 °C: (a) B-dot; (b) Pitzer; (c) Bromley-Zemaitis.

Zemaitis model consistently gives the lowest value. This explains why the pH (shown in Figure 3) follows the order of Bromley-Zemaitis > B-dot > Pitzer when the concentrations of H+ (Figure 5) with all three models are comparable. It can also be seen from Figure 5 that the activity coefficient of H+ drops with increasing ionic strength up to 0.4 m and then stays almost constant, indicating that the pH value mainly depends on the concentration of H+ in concentrated solutions, which is determined by the speciation. This relationship between the activity coefficient of H+ and the ionic strength also holds true in the presence of MgSO4 and/or Al2(SO4)3. MgSO4-H2SO4-H2O System. Figure 6 shows the calculated solubility of MgSO4 as a function of the free H2SO4 concentration in the range of 0-1.5 m at 250 °C together with experimental data at 235 and 270 °C from Marshall and Slusher.20 Although there are no experi-

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Figure 5. Activity coefficient of H+ as a function of the ionic strength in a H2SO4 solution at 250 °C.

Figure 6. Calculated MgSO4 solubility with three models in H2SO4 solutions at 250 °C. Experimental data are from Marshall and Slusher.20

Figure 8. Calculated species concentrations in saturated MgSO4H2SO4 at 250 °C: (a) B-dot; (b) Pitzer; (c) Bromley-Zemaitis.

Figure 7. Calculated pH in the saturated MgSO4-H2SO4-H2O system at 250 °C.

mental data at 250 °C to compare with the calculated values, the results seem very reasonable because they fall between the measured data at 235 and 270 °C. The B-dot equation and the Bromley-Zemaitis model perform similarly within the entire acidity range, as shown in Figure 6. The Pitzer model presented a good agreement with the other models but only up to 1 m H2SO4. The calculated pH along the saturation curves of Figure 6 is shown in Figure 7. A comparison with Figure 3 shows that the pH increases in the presence of MgSO4 in the solution. Although all three models give similar solubility predictions, this is not the case when it comes

to the pH. Significant differences are observed among the three models. Again, the Bromley-Zemaitis model gives much higher pH values. Figure 8 shows calculated species concentrations versus the acid concentration, along the solubility curve at 250 °C (Figure 6). As can be observed, Mg favors the formation of HSO4- and thus decreases the concentration of H+, which explains the increase of the pH (Figure 7) as compared to pure H2SO4 solutions (Figure 3). As seen in Figure 8a, MgHSO4+ is a necessary species only in the B-dot model. Mg2+ is the only dominant species in the Pitzer and Bromley-Zemaitis models and MgSO40 is not important with any of the three models. Thus, the speciation is markedly different, affecting the solution pH value depending on which model is used but not affecting the MgSO4 solubility prediction. Al2(SO4)3-H2SO4-H2O System. The solution speciation and Al2(SO4)3 solubilities in the Al2(SO4)3-H2SO4-H2O system at 250 °C were also compared using three activity coefficient models. The comparison is against experimental solubility data reported by Baghalha and Papangelakis.8 Figure 9 shows the solubility of Al2(SO4)3 at 250 °C versus the H2SO4 concentration in the range of 0-0.8 m. An exponential increase of solubility with solution acidity is observed. All models can fit equally well with

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Figure 9. Al2(SO4)3 solubility in H2SO4 solutions at 250 °C with three models. Experimental data are from Baghalha and Papangelakis.8

Figure 10. Calculated pH in the saturated Al2(SO4)3-H2SO4H2O system at 250 °C.

the solubility data and are in good agreement with the experimental data within the complete solution acidity range covered in Figure 9. Figure 10 shows the calculated pH at 250 °C versus the H2SO4 concentration in the range of 0-0.8 m. In general, the presence of Al2(SO4)3 increases the pH as compared to pure acid (Figure 3) but not as much as the presence of MgSO4 solutions. The B-dot and Bromley-Zemaitis models show similar results, whereas for higher than 0.4 m H2SO4, the Pitzer model gives substantially higher pH values than the other two, indicating that ionic interactions in the Pitzer model are more sensitive as the solution becomes more concentrated. Figure 11 shows calculated species concentrations versus H2SO4, along the solubility curve at 250 °C. In the B-dot model, Al2(SO4)3 has little impact on the equilibria of H2SO4, while in the Pitzer model, Al2(SO4)3 has a significant effect on the equilibria of H2SO4. Although the same speciation of Al were calculated with the B-dot and Bromley-Zemaitis models, and with the same species equilibrium constant values, the order of dominant species is different. In the B-dot model, Al2(SO4)30 is the most abundant followed by AlSO4+, Al(SO4)2-, and AlHSO42+. In the Bromley-Zemaitis model, the order is Al2(SO4)30 > AlHSO42+ > Al(SO4)2> AlSO4+. Because the dominant species Al2(SO4)30 does not contribute to the ionic strength, the pH (Figure 10) does not change as compared to pure H2SO4 solutions (Figure 3). In the case of the Pitzer model, only two Al-

Figure 11. Calculated species concentrations in the saturated Al2(SO4)3-H2SO4 solutions at 250 °C: (a) B-dot; (b) Pitzer; (c) Bromley-Zemaitis.

SO4 complexes, namely, Al2(SO4)30 and AlSO4+, were taken into account in the calculations. Nevertheless, AlSO4+ is the only dominant species, and Al2(SO4)30 is negligible. The dominance of AlSO4+ changes the equilibrium of H2SO4 (compare to Figure 4) significantly, especially at H2SO4 higher than 0.3 m. At these levels of H2SO4, the concentration of H+ begins to drop, which explains the increase of the pH at this point, as shown in Figure 10. Again, the solution speciation is markedly different depending on the model used. Al2(SO4)3-MgSO4-H2SO4-H2O System. Two ternary systems, Al2(SO4)3-H2SO4-H2O and MgSO4-H2SO4-H2O, were well predicted with the three activity coefficient models. Our aim is to test the goodness of the three models in quaternary or multicomponent systems because of industrial relevance so that the model can be applied to industry for process control and optimization. The solution speciation and the solubilities of Al2(SO4)3 and MgSO4 in the quaternary Al2(SO4)3-MgSO4H2SO4-H2O system at 250 °C were calculated and

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Figure 12. Calculated MgSO4 solubility with saturated Al in MgSO4-Al2(SO4)3-H2SO4 solutions at 250 °C. Experimental data are from Baghalha and Papangelakis.8

Figure 13. Calculated Al2(SO4)3 solubility with saturated Mg in the Al2(SO4)3-MgSO4-H2SO4 solution at 250 °C. Experimental data are from Baghalha and Papangelakis.8

compared using the three activity coefficient models. The solubility data are from Baghalha and Papangelakis.8 Figure 12 shows the MgSO4 solubility in the Al2(SO4)3 saturated system as a function of free H2SO4 within the range of 0-1 m at 250 °C. From experimental measurements, it is known that the solubility of MgSO4 does not change much in the presence of Al2(SO4)3.8,20 For acid concentrations lower than 0.4 m, all models predict the same MgSO4 solubility and are in good agreement with the experimental measurements at high temperature. At higher acid concentrations, a positive deviation is observed with the Bromley-Zemaitis model and a negative one by the Pitzer model. Figure 13 shows the Al2(SO4)3 solubility in the quaternary Al2(SO4)3-MgSO4-H2SO4-H2O system as a function of free H2SO4 within the range of 0-1 m at 250 °C. For comparison, the solubility of Al2(SO4)3 in the ternary Al2(SO4)3-H2SO4-H2O (solid triangles) is also shown here. In contrast to MgSO4, the experimental data show a decrease of about 5 times the solubility of Al2(SO4)3 in the quaternary system as compared to the ternary system. Huge differences exist between the experimental and calculated solubilities, as seen in Figure 13. Only the Bromley-Zemaitis model can represent the experimental data up to a solution acidity of about 0.5 m free H2SO4. At higher acid concentrations, all models overestimate the Al2(SO4)3 solubility, with the worst performer being the B-dot model.

Figure 14. Calculated pH in the Al2(SO4)3-MgSO4-H2SO4-H2O system at 250 °C with saturated Al and Mg.

Figure 14 shows the differences in the pH as predicted by the three models. In general, pH decreases with an increase in the solution acidity from 0.05 to 1 m. The Pitzer model, however, shows a reverse tendency of pH at concentrations higher than 0.35 m compared to that in the ternary Al2(SO4)3-H2SO4-H2O system in Figure 10. Figure 15 shows species concentrations versus H2SO4, along the solubility curves for both electrolytes at 250 °C. In the B-dot model (Figure 15a), neither Mg nor Al speciation changes much (compared to Figures 8a and 11a), and thus a good prediction of the MgSO4 solubility is obtained, as shown in Figure 12. There is only a small drop in the solubility of Al2(SO4)3 with saturated MgSO4 (Figure 13) compared to that in the ternary Al2(SO4)3H2SO4-H2O (the experimental data in Figure 13 under no MgSO4). In the Pitzer model, however, only Mg2+ and AlSO4+ are dominant and H+ becomes negligible (compared to Figures 8b and 11b) in the presence of Al and Mg. In the Bromley-Zemaitis model, Al speciation changes dramatically compared to that in the ternary Al2(SO4)3-H2SO4-H2O (Figure 11c). Al(SO4)2- becomes more dominant than Al2(SO4)0, whereas two other Al complexes, AlSO4+ and AlHSO42+, disappear. Nevertheless, the Bromley-Zemaitis model has the best overall performance when it comes to Al2(SO4)3 solubility prediction at 250 °C. In summary, each model tells its own story. Different speciation and activity coefficient models give different solution compositions. Common in all models is that the pH increases with increasing temperature and Mg concentration, Al does not change the pH, and solubility models can predict the experimental data up to ternary systems but not quaternary. Prediction ability deteriorates with increasing components in solution. Although the general trends are consistent with all models, the speciation is markedly different, producing a pH difference of more than one unit in progressively concentrated H2SO4 solutions. Hence, there is a need for an internally consistent model to be calibrated and used as the reference point. The OLI model seems to be more capable of handling concentrated multicomponent systems at high temperature of interest to industrial application. Although not examined in the present work, OLI software allows for further calibration by allowing regression of equilibrium constant and activity model parameters.35

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Figure 15. Calculated species concentrations in the Al2(SO4)3MgSO4-H2SO4-H2O system at 250 °C with saturated Al and Mg: (a) B-dot; (b) Pitzer; (c) Bromley-Zemaitis.

Conclusions In this work, ion association and ion interaction electrolyte models were used to simulate the thermodynamic behavior of aqueous H2SO4 solutions containing Mg and Al under conditions of high-temperature acid leaching of laterites in the range of 235-270 °C. Known and new complex species were accounted for along with their equilibrium constants and three different activity coefficient models to fit and predict the solubility data. The three activity coefficient models were the extended Debye-Hu¨ckel equation denoted as the B-dot equation, the Pitzer model with binary ion interaction parameters, and the Bromley-Zemaitis model. The first two models were tested through the EQ3/6 software package, and the third one was tested with OLI software. The main advantage of the B-dot equation is its simplicity. The three temperature-dependent parameters, Aγ, Bγ, and B˙ , are known, so there is only one

species-specific parameter, the hard-core diameter a˚ , which can be assigned a reasonable value. The advantage of the Pitzer model is that it can theoretically simulate highly concentrated systems (up to 10 m in ionic strength). However, its major disadvantage is its requirement of a large number of temperature-dependent parameters to quantify the physicochemical interactions among all of the components present in solution. Hence, considerable simplification by omission of several interaction parameters was necessary, with a resulting loss in predictive ability. Furthermore, the inclusion of distinct complex species (with all of the accompanying interaction parameters) was also necessary before an acceptable performance could be achieved in strongly associating systems.8 The Bromley-Zemaitis model embodied within OLI software presented the most convenient way to simulate multiphase and multicomponent systems and produced more consistent predictions. In the H2SO4-H2O system, all models gave similar speciation. In the ternary MgSO4-H2SO4-H2O and Al2(SO4)3-H2SO4-H2O systems, all three models had a good ability to predict the solubility of MgSO4 and Al2(SO4)3. It was found that MgSO4 increases the pH and the Bromeley-Zemaitis model gave the most significant difference. MgHSO4+ and Mg2+ were dominant Mg species in the B-dot model, while Mg2+ was the only dominant species with the Pitzer and Bromley-Zemaitis models. AlSO4+ was the only dominant species in the Pitzer model, and Al2(SO4)30, AlSO4+, Al(SO4)2-, and AlHSO42+ were the main species in the B-dot and Bromley-Zemaitis models. The three models demonstrated almost the same ability to fit the solubility of Mg and Al in ternary systems, indicating that ion interactions can make up for the differences in speciation. However, in the quaternary Al2(SO4)3-MgSO4-H2SO4-H2O system, using the same model parameters as those in the ternary systems, only the BromleyZemaitis model gave a reasonable prediction below H2SO4 of 0.5 m. All three models fail to predict the solubility of Al2(SO4)3 in MgSO4-H2SO4-H2O at high H2SO4 concentrations. It can be seen from the simulation with three models that there is a great variation with the obtained results. It seems that, in order to implement aqueous electrolyte modeling into a process simulator for the process industries, simulators must be sufficiently flexible to allow users to input model parameters either from literature sources or by regression of experimental data into the databases. OLI-Systems seems to offer these abilities, allowing users to evaluate new experimental data and generate new thermodynamic data. With better thermodynamic data, it is possible to provide more accurate predictions, as we showed recently.35 Acknowledgment The authors acknowledge the Centre for Chemical Process Metallurgy of University of Toronto, the Natural Science and Engineering Research Council of Canada (NSERC), and University of Chile for providing financial and other support. Nomenclature a ) activity, mol kg-1 a˚ ) hard-core diameter of the solvated ion, cm

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A1, ..., A4 ) coefficients for the log K expression in OLI software A ) Debye-Hu¨ckel constant, kg0.5 mol-0.5 Aγ ) Debye-Hu¨ckel constant according to Helgeson, kg0.5 mol-0.5 Aφ ) Debye-Hu¨ckel constant according to Pitzer, kg0.5 mol-0.5 b ) Pitzer constant B ) Bromley’s model parameter Bγ ) Debye-Hu¨ckel constant according to Helgeson, kg0.5 mol-0.5 cm-1 B˙ ) B-dot parameter, kg mol-1 C ) Bromley model parameter D ) Bromley model parameter G ) Gibbs free energy, kJ mol-1 I ) ionic strength, mol kg-1 K ) equilibrium constant in terms of molality m ) molal concentration, mol kg-1 T ) temperature, K z ) charge of the ionic species R1, R2 ) Pitzer’s model parameters, constant β ) Pitzer’s model parameter γ ) activity coefficient ν ) stoichiometric coefficient λ ) Pitzer’s model parameter for second-order binary interactions

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Received for review May 28, 2004 Revised manuscript received January 14, 2005 Accepted February 18, 2005 IE049535H