Development of an Improved Chemical Model for the Estimation of

Mar 25, 2006 - A self-consistent chemical model based on a single set of model parameters for all three CaSO4 modificationss namely, dihydrate, hemihy...
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Ind. Eng. Chem. Res. 2006, 45, 2914-2922

APPLIED CHEMISTRY Development of an Improved Chemical Model for the Estimation of CaSO4 Solubilities in the HCl-CaCl2-H2O System up to 100 °C Zhibao Li and George P. Demopoulos* Department of Mining, Metals and Materials Engineering, McGill UniVersity, 3610 UniVersity Street, Montreal, Quebec, H3A 2B2, Canada

A self-consistent chemical model based on a single set of model parameters for all three CaSO4 modificationss namely, dihydrate, hemihydrate, and anhydriteswas developed and described in this work. The model was successfully tested for the estimation of CaSO4 solubilities in concentrated (up to 20 m) mixed HCl-CaCl2H2O systems up to 100 °C. The new model makes use of the OLI Systems software platform. Via regression of experimental solubility data, new Bromley-Zemaitis model parameters were determined for the Ca2+SO42- and Ca2+-HSO4- ion pairs. Moreover, for the first time, the new model incorporates data for hemihydrate modification (CaSO4‚1/2H2O). After validation, the model was calibrated by determining new temperaturedependent parameters of the solubility product constants of the hemihydrate and anhydrite. With the aid of the newly developed model, the bell-shaped solubility curves for dihydrate and anhydrite, as a function of HCl concentration, were successfully explained, based on the bisulfate ion formation and ion-activity coefficient. Introduction The prediction or estimation of the solubilities of calcium sulfate (CaSO4) and its various modifications, dihydrate (DH, CaSO4‚2H2O), hemihydrate (HH, CaSO4‚1/2H2O), and anhydrite (AH, CaSO4) in hot and highly concentrated chloride solutions is an important requirement in developing, designing, and optimizing various industrial processes in which calcium sulfate precipitation may be involved.1 Reliable estimation of CaSO4 solubilities can prove invaluable in predicting CaSO4 scale formation2 or in determining and controlling supersaturation in a crystallization process.3 A new process currently under development in which the estimation of CaSO4 solubilities is a requirement involves the regeneration of hydrochloric acid (HCl, up to 6 M strength) from spent CaCl2 brine solutions (up to 4 M strength) by reaction with concentrated H2SO4 under atmospheric pressure:4

CaCl2(aq) + H2SO4(aq) + xH2O T CaSO4·xH2O(s) + 2HCl(aq) (1) The process may be controlled to produce dihydrate (x ) 2) or hemihydrate (x ) 0.5), the alpha variety of which is a highvalue material.5 Experimental determination of CaSO4 solubilities in a particular system of interest is, of course, an option; however, this is a time-consuming enterprise, not to mention that it is not feasible to test all possible combinations of conditions. Development and validation of a chemical model capable of providing a reliable estimation of CaSO4 solubilities in concentrated and multicomponent electrolyte solutions is preferred instead. * To whom correspondence should be addressed. Fax: (514) 3984492. E-mail: [email protected].

Chemical modeling works have been undertaken to either develop empirical or theoretical solubility models for calcium sulfate in pure or multicomponent electrolyte aqueous solutions with variable degrees of success in the past. Marshall and his associates6-8 proposed an empirical model based on the extended Debye-Huckel limiting-law expression to correlate the solubility of calcium sulfate in seawater and concentrated brines. This empirical model can give a satisfactory solubility estimation of the dihydrate, hemihydrate, and anhydrite in electrolytes (such as NaCl, Na2SO4, and MgSO4) and their mixed solutions, as well as saline water. However, their model takes into account only the total dissolved solids (TDS) and not the individual ions; hence, this is not applicable to acidic media (in which the HSO4- species dominates), because the HCl-CaCl2 system is investigated in this work. As a consequence, the same calcium sulfate solubility is predicted in the presence of both chloride and nitrate salts, whereas the experimental data show a remarkable difference in the two cases.9 Finally, according to Barba et al.,9,10 Marshall’s model becomes unsatisfactory when it is used for solutions with a high sulfate/magnesium ratio. Barba et al.9,10 developed a thermodynamic model to describe the solubility of calcium sulfate in saltwatersthat is, relatively dilute but consisting of several components. The model is based on the local compositions of the nonrandom two-liquid (NRTL) theory. Using only binary parameters, their model yields good agreement between the experimental and predicted values of calcium sulfate dihydrate solubility in seawater and in natural and synthetic water at 298 K. However, for concentrated multicomponent solutions with a high sodium chloride (NaCl) content, new binary parameters should be regressed to improve the calculation. Moreover, it cannot be used at elevated temperatures, because of the omission to consider hemihydrate. The ion-specific interaction approach originally proposed by Pitzer11 was used to model the solubility of CaSO4 in electrolyte

10.1021/ie0508280 CCC: $33.50 © 2006 American Chemical Society Published on Web 03/25/2006

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solutions. Thus, Harvie et al.,12 using Pitzer’s framework, developed a chemical model for predicting mineral solubilities in brines from zero to high ionic strength (I > 20 m) at 298 K. In their modeling, the single electrolyte parameters were taken from the Pitzer parametrization, whereas the third virial coefficient mixing parameters were chosen by fitting ternary common ion solubility data. The calculated solubility of gypsum in NaCl solution was in good agreement with the experiment. Pitzer’s equations were also used by Meijer and Rosmalen,13 who proposed a computer program to calculate the solubility and supersaturation of CaSO4 in seawater, this time extending the calculations to elevated temperatures (up to 100 °C). Zemaitis et al.14 evaluated the various activity coefficient models, such as the Bromley, Meissner, and Pitzer models, by calculating the solubility of calcium sulfate dihydrate in NaCl, CaCl2, and HCl aqueous solutions. Their results showed that interaction parameters based on the solubility data of gypsum in pure water cannot be used in predicting the solubility of gypsum in multicomponent electrolyte solutions. Demopoulos et al.15 used Meissner’s method to predict the solubility of gypsum in the concentrated (up to saturation) NaCl-H2O system with satisfactory results. The major difference, with reference to Zemaitis et al.’s work, was that they made use of a new Meissner’s parameter for CaSO4, with a value of 0.108. All of the CaSO4 solubility modeling works previously described are based on the assumption of complete electrolyte dissociation; i.e., they adopt a nonspeciation approach,16 which is normally accurate for simple electrolyte systems or limited only to vapor-liquid-equilibria (VLE)-type phase equilibrium calculations.17 However, the formation of solution complexes occurs in most concentrated aqueous electrolyte systems (with the exception, perhaps, of single univalent metal chlorides); hence, a speciation-based approach becomes the preferred methodology in thermodynamic modeling.18,19 The speciation modeling approach was used by Scrivner and Staples16 to model the solubility of gypsum in NaCl, mixed NaCl and Na2SO4, and HCl aqueous solutions, with the aid of the ECES computer program that was developed by OLI Systems. The activity coefficient for CaSO4 was estimated using Bromley’s correlation20 at low ionic strength and Meissner’s universal plot14 at high ionic strength. Reasonable results were obtained for the NaCl and NaCl-Na2SO4 systems but not for the HCl system. More recently, Raju and Atkinson2 used a modified Pitzer equation to calculate the solubility of both gypsum and anhydrite in NaCl solutions with good agreement. However, the model that they developed was not self-consistent, as two separate sets of model parameters (12 in total for each phase) were used for gypsum and anhydrite. Moreover, the model was not demonstrated to be applicable to mixed electrolyte systems or HCl media. Another thermodynamic model based on the speciation approach that potentially can be used for the estimation of CaSO4 solubilities in concentrated and hot CaCl2-HCl media is the one that forms the basis of OLI Systems.21 Activity coefficient estimation in this model is done via the BromleyZemaitis equation.20,22 Preliminary estimations of CaSO4 dihydrate solubilities using OLI’s StreamAnalyzer software package (version 1.1) and comparison with experimental data generated by the authors yielded poor results,23 not to mention OLI’s inability to address calcium sulfate hemihydrate phase(s). Given, however, the attractiveness of the speciation-based modeling approach that characterizes the OLI platform and the userfriendly interface of it, further work was undertaken with the purpose of improving OLI’s solubility estimation capability via

Table 1. Chemical Species and Their Speciation Reactions in the CaSO4-HCl-CaCl2-H2O System species

dissociation reaction

H2O CaCl2(aq) CaCl+ CaOH+ HCl(aq) H2SO4(aq) HSO4CaSO4(aq) CaSO4(s) (AH) CaSO4‚0.5H2O(s) (HH) CaSO4‚2H2O(s) (DH)

H2O ) + OHCaCl2(aq) ) CaCl+ + ClCaCl+ ) Ca2+ + ClCaOH+ ) Ca2+ + OHHCl(aq) ) H+ + ClH2SO4(aq) ) H+ + HSO4HSO4- ) H+ + SO42CaSO4(aq) ) Ca2+ + SO42CaSO4(s) ) Ca2+ + SO42CaSO4‚0.5H2O(s) ) Ca2+ + SO42- + 0.5H2O CaSO4‚2H2O(s) ) Ca2+ + SO42- + 2H2O H+

determination and validation of new model parameters. For the determination of the new model parameters, the experimental solubility data recently generated for all three CaSO4 modifications (DH, HH, and AH)24 in CaCl2-HCl media from 10 °C to 80 °C were used, along with OLI’s regression module ESP V-6.6.0.6.25 With this regression, an internally self-consistent model that made use of a single set of model parameters was developed for solubility estimation of all three CaSO4 modifications, namely, DH, HH, and AH. Modeling Methodology Equilibrium Relationships and Data. The solubility equilibrium of CaSO4 in electrolyte solutions can be described by the following dissolution reaction:

CaSO4·nH2O(s) T Ca2+(aq) + SO42-(aq) + nH2O(l)

(2)

where n ) 0, 0.5, and 2 for anhydrite (AH), hemihydrate (HH), and dihydrate (DH), respectively. The thermodynamic equilibrium constant (KSP) for CaSO4 solids takes the form

KSP ) aCa2+aSO42-aH2On ) (mCa2+γCa2+)(mSO42-γSO42-)aH2On (3) where mCa2+ and mSO42- are the molal concentrations of the cation Ca2+ and the anion SO42- in solution, γCa2+ and γSO42- are the ion activity coefficients, and aH2O is the activity of water. The experimental CaSO4 solubility, s (expressed in units of mol/ kg) in pure water is simply s ) mCa2+ ) mSO42- , but in mixed CaCl2-HCl media, the solubility becomes s ) ∑ m“SO4”, i.e., s is taken as the sum of all “SO4”-containing species. This explains why the speciation modeling approach makes sense in this context. Table 1 provides a list with all species and their dissociation reactions considered in this system. As an example, the second dissociation of H2SO4 is given as follows:

HSO4- ) H+ + SO42-

(4)

The thermodynamic equilibrium constant for this reaction is

KHSO4- )

(mH+ γH+)(mSO42- γSO42- ) mHSO4- γHSO4-

(5)

Determination of the concentration of the various chemical species calls for setting up and solving N number of equations equal to the number of unknown species.29 Of these N equations, M corresponds to the chemical equilibrium equations (such as eqs 3 and 5), N - M - 1 are mass balance equations and one is the charge balance equation.

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Table 2. Parameters for Species Whose Equilibrium Constant Has Been Calculated with the Aid of eq 6a species

A -46.242 2.40192 34.31792 13.9312 32.1499 19.12274 40.11184

CaCl2(aq) CaCl+ CaSO4(aq) H2SO4(aq) HCl(aq) CaSO4(s) (AH) CaSO4‚2H2O(s) (DH) a

B

C 4.08507 × -1.36144 × 10-2 -8.84494 × 10-2 -2.916 × 10-3 -1.0083 × 10-1 -4.785357 × 10-2 -1.15199 × 10-1

14154.1 1871.39 -4403.012 -704.65 -1328.3 -3066.119 -5481.185

0.0 0.0 5.89741 × 10-5 -3.24087 × 10-6 9.66894 × 10-5 1.20537 × 10-5 9.1384 × 10-5

Data taken from the OLI databank.

For the calculation of the constants of aqueous speciation equilibria (e.g., KHSO4-) the standard-state thermodynamic parameters of each aqueous species are required. In the OLI software,25 two alternative methods are used to accomplish this task. The first method makes use of the revised HKF equation of state originally proposed by Helgeson and co-workers,26,30-33 whereas the second method makes use of an empirical equation of the form

log10 K ) A +

B + CT + DT2 T

(6)

Table 3. Thermochemical Data26 Used by OLI To Calculate Equilibrium Constants with the HKF Method species

∆G h °f,25 (kJ/mol)

∆H h °f,25 (kJ/mol)

Sh°f,25 (J K-1 mol-1)

C°p,25 (J K-1 mol-1)

H+ OHH2Oa SO42HSO4Ca2+ CaOH-b Cl-

0 -157.29 -237.18 -744.46 -755.76 -552.79 -717.138 -131.29

0 -230.0 -285.85 -909.6 -889.1 -543.083 -764.417 -167.08

0 -10.7 69.95 18.83 125.52 -56.48 -14.4683 56.735

0 -137.19 75.35 -269.37 22.18 -31.50 89.45 -123.177

a

The aforementioned equation may be applied to either solubility product constants or to dissociation constants of solution complexes. A, B, C, and D are empirical parameters obtained via fitting to experimental solubility data. Table 2 lists the species whose K (solubility product or dissociation constants) is calculated by the OLI software with the aid of eq 6. Table 3 lists the thermodynamic data of the relating species used by the OLI software to calculate equilibrium constants with the aid of the HKF equation. Ion Activity Coefficient and Water Activity Relationships. It is clear from eqs 3 and 5 that determination of the CaSO4 solubility or the abundance of solution species necessitates knowledge of the relevant ion activity coefficients and activity of water. There are different types of coefficient models that may be used in this context.21,22 The Bromley-Zemaitis activity coefficient model21,25 developed by Bromley20 and empirically modified by Zemaitis22 is used in the OLI software. This model has been successfully used for highly concentrated electrolytes (up to 30 m) and elevated temperature (up to 473 K);25 hence, it is appropriate for the present system, which is up to 20 m and 373 K. The Bromley-Zemaitis activity coefficient model for the case of cation i in a multicomponent electrolyte solution is expressed by eq 7: log γi )

∑ j

D 10-2

-AZi2xI

[(

1.5I

)

|ZiZj|

regression of the electrolyte solution properties, such as osmotic coefficient data or solubility data. In the case of neutral aqueous species, e.g., CaSO40, the Bromley-Zemaitis model (eq 7) cannot be used. In this case, the expression proposed by Pitzer25 is used to obtain the activity coefficient:

ln γaq ) 2β0(m-m) + 2β1(m-s)ms

(8)

where β0(m-m) is the adjustable parameter for moleculemolecule interactions; β1(m-s) represents the adjustable parameter for molecule-ion interactions; and ms is the concentration of the neutral species. Finally, for the activity of water in a multicomponent system, the formulation proposed by Meissner and Kusik34 is adopted in OLI’s thermodynamic framework:

log(aw)mix )

∑i ∑j XiYj log(aw0)ij

(9)

where (aw0) is the hypothetical water activity of pure electrolyte ij (where i is an odd number for all cations and j is an even number for all anions), Xi represents cationic fraction (Xi ) Ii/ Ic), and Yj represents the anionic fraction (Yj ) Ij/Ia). Results and Discussion

+

1 + xI (0.06 + 0.6Bij)|ZiZj| 1+

From ref 27. b From ref 28.

2

+ Bij + CijI + DijI2

]

(

)

|Zi| + |Zj| 2

2

mj (7)

where j indicates all anions in solution; A is the Debye-Huckel parameter; I is the ionic strength of the solution; B, C, and D are temperature-dependent empirical coefficients; and Zi and Zj are the cation and anion charges, respectively. Bij ) B1ij + B2ijT + B3ijT 2 (where T is the temperature, in Celsius), and the other coefficients C and D have similar forms of temperature dependence. For the activity coefficient of an anion, the subscript i represents that anion and the subscript j then represents all cations in the solution. Each ion pair is described with this nineparameter equation. The nine parameters are determined via

Solubility Estimation with Existing Model. The accuracy of OLI’s existing model (available as software package StreamAnalyzer 1.2) in estimating CaSO4 solubilities in HCl-CaCl2 aqueous solutions was first evaluated by comparing OLI’s prediction to experimental data generated by the authors.24 Both sets of data (model predictions and experimental) are plotted in Figure 1 for the case of the solubility of calcium sulfate dihydrate in 0.0-5.5 m HCl solutions in the 283-353 K temperature range. As it can be observed, a significant deviation of OLI prediction from experiments is observed at the concentrated HCl range, and this is enlarged at elevated temperature. Figures 2 and 3 provide further comparisons between the OLI solubility prediction and the experiment in the case of DH solubility in mixed HCl-CaCl2 solutions. While the comparison is satisfactory at low acid concentrations, the deviation becomes significant at higher HCl concentrations. For example, the

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Figure 1. Comparison of the solubility of calcium sulfate dihydrate in HCl solutions between experimental data24 (given as data points) and the OLI prediction (given as lines): (9) 283 K, (b) 295 K, (2) 313 K, (4) 333 K, and (O) 353 K.

Figure 2. Comparison of the solubility of calcium sulfate dihydrate in mixed HCl (1 M)-CaCl2 solutions between experimental data24 (given as data points) and the OLI prediction (given as lines): (b) 295 K, (2) 313 K, (4) 333 K, and (O) 353 K.

Figure 3. Comparison of the solubility of calcium sulfate dihydrate in mixed HCl (5 M)-CaCl2 solutions between experimental data24 (given as data points) and the OLI prediction (given as lines): (b) 295 K, (2) 313 K, and (4) 333 K.

average relative deviation is 11%, 25%, and 34% as the HCl concentration increases from 1 M to 3 M to 5 M, respectively. Similarly, with DH, OLI yielded a relatively large deviation when the solubility of anhydrite in HCl was estimated (see Figure 4). The relative deviations are 10%, 16%, 22%, and 25% at 298 K, 313 K, 333 K, and 353 K, respectively. The accuracy of the OLI predictions is strongly dependent on the availability

Figure 4. Comparison of the solubility of calcium sulfate anhydrite in mixed HCl solutions between experimental data24 (given as data points) and the OLI prediction (given as lines): (b) 298 K, (2) 313 K, (4) 333 K, and (O) 353 K.

of experimental data on the basis of which the model is built. There is limited solubility data available in the literature for calcium sulfate anhydrite in concentrated HCl solutions, hence the observed large deviation. Finally, as mentioned previously, no estimation of hemihydrate solubility is possible with the current OLI model. New Model Parameter Estimation. With the purpose of improving the OLI System’s prediction capability, in regard to CaSO4 solubilities in HCl-CaCl2 media, new model parameters were determined via the regression of experimental data recently produced by the authors.24 In this regression, the model parameters are obtained by minimizing the sum of squared deviations between the experimental and calculated values of solubility of CaSO4. In particular, the parameters of two model equations were scrutinized and modified (when necessary): the Bromley-Zemaitis activity coefficient model parameters in eq 7 and the empirical parameters in an equilibrium constant relationship (eq 6). The main aqueous species or ions that are present in the CaSO4-HCl-CaCl2-H2O system are two cations (H+, Ca2+) and three anions (Cl-, SO42-, and HSO4-), as listed in Table 1. According to the Bromley-Zemaitis model (eq 7), to calculate the activity coefficient of each ion (and the activity of water), we must know six pairs of ion-interaction parameters. Among the six possible ion pairs, only the Bromley-Zemaitis parameters for two pairssnamely, Ca2+-SO42- and Ca2+HSO4-swere regressed with the model parameters, with all other ion pairs kept the same as in OLI’s default databank. These ion pairs were selected because they were intuitively thought to directly impact on the solubility of CaSO4. The new Bromley-Zemaitis interaction parameters for these two ion pairs were determined by regressing the DH experimental solubility data published elsewhere.24 The best fit was obtained when the dissociation constant of the HSO4- ion was expressed with the aid of eq 6 and not by the HKF method, as done in the original version of the OLI software. The adopted equation for the dissociation constant of HSO4- is given below:

log10 KHSO4- ) -66.6422 +

7402.28 + 0.200352T T 2.20974 × 10-4T 2 (10)

It is considered important to evaluate the validity of the adopted eq 10 by comparing the temperature dependency of the dissociation constant of HSO4- calculated using it to the values calculated by OLI’s HKF method25 and other values reported

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Figure 5. Dissociation constant of bisulfate, as a function of temperature: (s) Dickson et al.,35 (0) OLI (HKF),25 (O) this work, (9) Marshall et al.,7 and (4) Hovey et al.36

Figure 6. Calculated pH at 323 K in a 0.5 m H2SO4 solution: (O) this work and (9) OLI.

in the literature.7,35,36 This is done in Figure 5. As can be observed, eq 10 gives marginally lower values of -log KHSO4than the HKF method of OLI25 but within the range of values reported in the literature. The validity of eq 10 was further tested by calculating and comparing the pH for the 0.5 m H2SO4H2O system from 10 °C to 100 °C with that calculated by OLI. Figure 6 shows that the pH values determined by both methods are very close. It is not surprising that the bisulfate ion has a central role in this system, because it was qualitatively discussed elsewhere.24 The critical role of HSO4- in affecting the solubility of CaSO4 phases explains the failure of earlier efforts16 in modeling solubility equilibria in strong HCl-containing solutions. The new Bromley-Zemaitis model parameters obtained via the regression of the DH solubility data (see Figures 7 and 8) are tabulated in Table 4. The total average relative deviation between DH experimental data and new OLI model obtained by regression model is 2.7%. Model Validation. Having successfully modeled the solubility data of calcium sulfate dihydrate in HCl-CaCl2 solutions, we proceeded to test the new model in the case of hemihydrate and anhydrite solubilities. Toward this end, a new databank was created, called “OLI-McGill”, in which the newly obtained Bromley-Zemaitis parameters shown in Table 4 and the new parameters of the dissociation equilibrium constant of bisulfate ion (eq 10) were added. To calculate the solubility of hemihydrate, the solubility product of hemihydrate is required. This is not available in the current OLI databank. Initially, the solubility data37 of calcium sulfate hemihydrate in pure water at various

Figure 7. Comparison of regressed (solid lines) and experimental24 (symbols) solubility of calcium sulfate dihydrate in HCl solutions: (9) 283 K, (b) 295 K, (2) 313 K, (4) 333 K, and (O) 353 K.

Figure 8. Comparison of regressed (solid lines) and experimental24 (symbols) solubility of calcium sulfate dihydrate in mixed HCl (5 M)CaCl2 solutions: (b) 295 K, (2) 313 K, and (4) 333 K. Table 4. Newly Regressed Bromley-Zemaitis Model Parameters for Ca2+-SO42- and Ca2+-HSO4- Interactions parameter

Ca2+-SO42-

Ca2+-HSO4-

B1 B2 B3 C1 C2 C3 D1 D2 D3

-2.46708 × 10-1 3.5632 × 10-3 -5.12319 × 10-5 7.31743 × 10-2 -1.07027 × 10-3 1.15506 × 10-5 1.0482 × 10-2 -2.91146 × 10-5 1.28589 × 10-6

-8.16875 × 10-2 3.96067 × 10-4 1.65505 × 10-5 6.17896 × 10-3 6.64883 × 10-4 -1.07042 × 10-5 1.49402 × 10-3 -8.87896 × 10-5 1.05082 × 10-6

temperatures was used to obtain the hemihydrate solubility product parameters (refer to eq 6):

log10 KHH ) -65.7208 -

7758.18 - 0.199782T + T 1.77968 × 10-5T 2 (11)

With the aid of eq 11 and the new model parameters (Table 4 and eq 10), the solubility of hemihydrate was calculated using the StreamAnalyzer 1.2 program. A comparison of experimental and predicted HH solubility values is presented in Figures 9 and 10. Figure 9 shows the excellent agreement between the literature value38 and the predicted solubility of R-calcium sulfate hemihydrate in pure HCl solutions at 373 K. Equally good agreement is observed between the experimental data and the model predictions in Figures 9 and 10. All of these results serve

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Figure 9. Comparison of predicted (solid lines) and literature (symbols) solubility values of calcium sulfate hemihydrate in HCl solutions: (9) HH at 298 K,39 (b) β-HH at 298 K,24 (3) R-HH at 298 K,24 (O) β-HH at 323 K,24 and (0) R-HH at 373 K.38

as validation of the newly developed model, because it proved capable in making good solubility predictions for a CaSO4 phase (hemihydrate) other than the one (dihydrate) used to determine the model parameters in a range of conditions outside the regression zone, i.e., T > 353 K and [HCl] > 6 M. The new model was further validated by comparing its predictions to anhydrite solubility data24 (Figure 11). Predictions are now much better than those obtained with the current version (1.2) of OLI’s StreamAnalyzer program. Model Calibration. The developed model was subjected to calibration by retaining the new set of Bromley-Zemaitis parameters that were obtained by regression of the dihydrate solubility data (Table 4), but this time, the KSP equation parameters (eq 6) for hemihydrate and anhydrite were adjusted slightly. The eq 6 parameters were recalculated by performing regression using the HH and AH solubility data generated by the authors,24 instead of using the AH default values in the OLI databank or the parameters obtained from the regression of HH solubility data in water (eq 11). As a result of this regression-calibration work, the following two solubility product equations were derived for hemihydrate and anhydrite, respectively:

Figure 10. Comparison of predicted (solid lines) and experimental24 (symbols) solubility of calcium sulfate hemihydrate in mixed HCl-CaCl2 solutions: (b) in 6 M HCl at 333 K and (2) in 3 M HCl at 353 K.

Figure 11. Comparison of the solubility of calcium sulfate anhydrite in concentrated HCl solutions at 353 K: (- - -) predicted by OLI, (s) predicted by OLI equipped with new model parameters (Table 4 and eq 10), and (9) experimental data.24

4939.1 - 0.0870353T + T (0 < T < 100 °C) (12) 4.59692 × 10-5 T 2

log10 KSP(HH) ) 34.4739 -

8775.05 + 0.261521T T (20 < T < 100 °C) (13) 2.93598 × 10-4 T 2

log10 KSP(AH) ) -85.601 +

The solubility product constant (Ksp) values for anhydrite, obtained with eq 13 at various temperatures, are shown in Figure 12. In the same figure, the Ksp values reported by Ling and Demopoulos,40 Raju and Atkinson,2 Marshall and Slusher,8 and Langmuir and Melchior41 are also plotted for comparison, as well as values stored in the OLI databank. The OLI values are less than ours at lower temperatures and greater than ours at higher temperatures. The values obtained in this work are in very good agreement with those of Raju and Atkinson2 and are in good agreement overall with those of Langmuir and Melchior. The data reported in other sources, as shown in Figure 12, are consistently greater than ours. The new solubility product parameters for hemihydrate and anhydrite shown in eqs 12 and 13 were finally retained along the set of new Bromley-Zemaitis model parameters (Table 4)

Figure 12. Plot of log KSP vs T for calcium sulfate anhydrite: (s) this work, (0) OLI, (O) Ling and Demopoulos,40 (4) Raju and Atkinson,2 (b) Marshall and Slusher,8 and (2) Langmuir and Melchior.41

and eq 10 to formulate the improved OLI-McGill model for the estimation of CaSO4 solubilities in mixed HCl-CaCl2 media in the temperature range up to 100 °C. The excellent agreement of the calibrated model’s predictions with experimental data is exemplified with the data plotted in Figure 13. The relative deviation from experimental data as described in Figure 13 is only 1.48%.

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Figure 13. Comparison of the solubility of calcium sulfate anhydrite in concentrated HCl solutions at various temperatures: (s) predicted by OLI equipped with new model parameters (Table 4 and eqs 10 and 13), (9) 298 K, (b) 313 K, (4) 333 K, and (O) 353 K.

Figure 15. Sulfate speciation, as a function of temperature, for a hemihydrate-saturated solution containing 5 m HCl and 1 m CaCl2.

Figure 16. Sulfate speciation at 298 K, as a function of concentration, for a dihydrate-saturated HCl solution with 0.5 m CaCl2. Figure 14. Sulfate speciation, as a function of temperature, for a hemihydrate-saturated solution containing 5 m HCl.

Speciation Calculations and Thermodynamic Interpretation. OLI’s StreamAnalyzer 1.2 program, equipped with the new model parameters developed in this work, was used to study and analyze the concentration and temperature effects on species distribution as well as in interpreting the observed CaSO4 solubility behavior in the CaSO4-HCl-CaCl2-H2O system. 1. Temperature Effects. Figure 14 shows the relative concentration of sulfate species, CaSO4(aq), HSO4-, and SO42in HH-saturated 5 m HCl solutions, as a function of temperature. In this case, the solubility of hemihydrate is equal to the total concentration of these sulfate species in the solution. It is obvious that the relative concentration of HSO4- increases as the temperature increases, indicating an increase in the degree of ion association. Simultaneously, the concentration of the SO42- ion decreases with temperature. The relative concentration of HSO4- and SO42- are 81% and 17%, respectively, at 303 K, but 98% and 0.7%, respectively, at 353 K. The CaSO4(aq) is present in