Experimental determination and modeling of gypsum and insoluble anhydrite solubility in the system CaSO 4 –H 2 SO 4 –H 2 O Wenlei Wang a , Dewen Zeng a,n , Qiyuan Chen a , Xia Yin b a College of Chemistry and Chemical Engineering, Central South University, Changsha, 410083, PR China b College of Chemistry and Chemical Engineering, Hunan University, Changsha, 410082, PR China HIGHLIGHTS Gypsum and anhydrite solubility in H 2 SO 4 aqueous solution has been measured. Kinetic transformation between gypsum and anhydrite has been studied. Stable formation fields of gypsum and anhydrite has been simulated. Anhydrite solubilities measured in this work are lower than those from literatures. Explanations are given for the errors of solubilities reported in literature. GRAPHICAL ABSTRACT article info Article history: Received 7 November 2012 Received in revised form 2 June 2013 Accepted 4 June 2013 Available online 15 June 2013 Keywords: Crystallization Computational chemistry Isothermal Kinetics Phase equilibria abstract The solubility isotherms of gypsum and insoluble anhydrite in the ternary system CaSO 4 –H 2 SO 4 –H 2 O were determined at T ¼(298.1, 323.1, 348.1, and 363.1) Kusing the isothermal method. The kinetics of the transformation between gypsum and insoluble anhydrite in H 2 SO 4 aqueous solutions at 298.1 and 363.1 K were also studied. Our measured solubility isotherms for gypsum are generally in good agreement with the literature solubility data. However, the solubilities of anhydrite measured in this work are much lower than those reported by Zdanovskii and Vlasov (1968b) [Zdanovskii, A.B., Vlasov, G.A., 1968b. Russ. J. Inorg. Chem. 13, 1418–1420.]. Kinetic experiments showed that the complete transformation from gypsum to anhydrite at 363.1 K takes at least 120 h in 0.5 mol kg -1 H 2 SO 4 aqueous solution and over 6 h for higher concentrations of H 2 SO 4 . Furthermore, much more time is needed for the Ca 2+ concentration in the solutions to equilibrate with the end solid phase “insoluble anhydrite” than for the complete transformation of gypsum to insoluble anhydrite. These kinetic results were used to identify why the insoluble anhydrite solubilities in H 2 SO 4 aqueous solution in the literature were higher than those in our results. A Pitzer thermodynamic model was chosen to simulate and predict the solubility isotherms of gypsum and insoluble anhydrite in this ternary system, and the good agreement between the experimental results and the model supports the reliability of the experimental solubility data obtained in this work. Finally, the stable fields for gypsum and insoluble anhydrite as a function of temperature and H 2 SO 4 concentration were constructed by the thermodynamic model. & 2013 Elsevier Ltd. All rights reserved. 1. Introduction Calcium sulfate, which has low solubility in water, is susceptible to scaling in many industrial processes, such as wet-process phosphoric acid production and hydrometallurgical processes involving heavy metal sulfates (Azimi and Papangelakis, 2010; Dutrizac, 2002; Dutrizac Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ces Chemical Engineering Science 0009-2509/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ces.2013.06.023 n Corresponding author. Tel.: +86 13618496806; fax: +86 731 88879616. E-mail addresses: [email protected], [email protected] (D. Zeng). Chemical Engineering Science 101 (2013) 120–129
Transcript
Chemical Engineering Science 101 (2013) 120–129
Contents lists available at ScienceDirect
Chemical Engineering Science
0009-25http://d
n CorrE-m
wenlei_
journal homepage: www.elsevier.com/locate/ces
Experimental determination and modeling of gypsum and insolubleanhydrite solubility in the system CaSO4–H2SO4–H2O
Wenlei Wang a, Dewen Zeng a,n, Qiyuan Chen a, Xia Yin b
a College of Chemistry and Chemical Engineering, Central South University, Changsha, 410083, PR Chinab College of Chemistry and Chemical Engineering, Hunan University, Changsha, 410082, PR China
H I G H L I G H T S
G R A P H I C A L A
� Gypsum and anhydrite solubility inH2SO4 aqueous solution has beenmeasured.
� Kinetic transformation betweengypsum and anhydrite has beenstudied.
� Stable formation fields of gypsumand anhydrite has been simulated.
� Anhydrite solubilities measured inthis work are lower than those fromliteratures.
� Explanations are given for the errorsof solubilities reported in literature.
09/$ - see front matter & 2013 Elsevier Ltd. Ax.doi.org/10.1016/j.ces.2013.06.023
The solubility isotherms of gypsum and insoluble anhydrite in the ternary system CaSO4–H2SO4–H2Owere determined at T¼(298.1, 323.1, 348.1, and 363.1) K using the isothermal method. The kinetics of thetransformation between gypsum and insoluble anhydrite in H2SO4 aqueous solutions at 298.1 and363.1 K were also studied. Our measured solubility isotherms for gypsum are generally in goodagreement with the literature solubility data. However, the solubilities of anhydrite measured in thiswork are much lower than those reported by Zdanovskii and Vlasov (1968b) [Zdanovskii, A.B., Vlasov, G.A.,1968b. Russ. J. Inorg. Chem. 13, 1418–1420.]. Kinetic experiments showed that the complete transformationfrom gypsum to anhydrite at 363.1 K takes at least 120 h in 0.5 mol kg−1H2SO4 aqueous solution and over 6 hfor higher concentrations of H2SO4. Furthermore, much more time is needed for the Ca2+ concentration inthe solutions to equilibrate with the end solid phase “insoluble anhydrite” than for the completetransformation of gypsum to insoluble anhydrite. These kinetic results were used to identify why theinsoluble anhydrite solubilities in H2SO4 aqueous solution in the literature were higher than those in ourresults. A Pitzer thermodynamic model was chosen to simulate and predict the solubility isotherms ofgypsum and insoluble anhydrite in this ternary system, and the good agreement between the experimentalresults and the model supports the reliability of the experimental solubility data obtained in this work.Finally, the stable fields for gypsum and insoluble anhydrite as a function of temperature and H2SO4
concentration were constructed by the thermodynamic model.& 2013 Elsevier Ltd. All rights reserved.
ll rights reserved.
: +86 731 88879616.
1. Introduction
Calcium sulfate, which has low solubility in water, is susceptible toscaling in many industrial processes, such as wet-process phosphoricacid production and hydrometallurgical processes involving heavymetal sulfates (Azimi and Papangelakis, 2010; Dutrizac, 2002; Dutrizac
W. Wang et al. / Chemical Engineering Science 101 (2013) 120–129 121
and Kuiper, 2008; Zeng and Wang, 2011; Wang et al., 2012; Farrahet al., 2007). A complete understanding of the solubility of calciumsulfate in H2SO4 aqueous solutions is essential for developingapproaches to avoid its negative effects. Calcium sulfate can crystallizeinto various crystal types, such as gypsum, hemihydrate, solubleanhydrite (hexagonal symmetry) and insoluble anhydrite (orthorhom-bic) (Freyer and Voigt, 2003), and its solubility varies by crystal type,temperature and H2SO4 concentration. Compared with the solubilityof the metastable phases, hemihydrate and soluble anhydrite, that ofthe stable phases, gypsum and insoluble anhydrite, have attractedmore attention and have been more extensively reported (Dutrizac,2002; Farrah et al., 2007; Marshall and Jones, 1966; Mecke, 1935;Zdanovskii and Vlasov, 1968a, 1968b). Although the solubility ofgypsum in H2SO4 aqueous solution is extensively reported (Dutrizac,2002; Marshall and Jones, 1966; Zdanovskii and Vlasov, 1968b) withgood agreement, those of insoluble anhydrite are essentially limited tothe results of Zdanovskii and Vlasov (1968a) at 298.1 K and 323.1 Kand Zdanovskii and Vlasov (1968b) 348.1 K and 368.1 K. Dutrizac(2002) have reported some solubility data of anhydrite mixed with asmall amount of gypsum, which should be considered as metastable.In the experiments performed by Zdanovskii and Vlasov (1968a,1968b), insoluble anhydrite was used as an initial solid phase at298.1 K and 323.1 K and gypsum at 348.1 K and 368.1 K, and theauthors assumed that gypsum is easily converted to the insolubleanhydrite at higher temperatures. In all their experiments (Zdanovskiiand Vlasov, 1968a, 1968b) a time of 5–8 h (counted from the time atwhich the initial solid phase was added to the solution) was used.Recently, Azimi and Papangelakis (2011) reported that the timeneeded for complete conversion from CaSO4 �2H2O to CaSO4 is atleast two days (48 h) in a 1.5 mol kg−1H2SO4 solution at 363.1 K.Consequently, the solubility data for insoluble anhydrite measuredby Zdanovskii and Vlasov (1968b) after 5–8 h could be unreliable. Thescattered solubility data of anhydrite in H2SO4 aqueous solution at363.1 K reported by Farrah et al. (2007) seems very anomalous, asreported in our previous work (Zeng and Wang, 2011).
In this paper, the solubility isotherms of gypsum and insolubleanhydrite in the system CaSO4–H2SO4–H2O have been determinedat T¼(298.1, 323.1, 348.1, and 363.1) K. Kinetic transformationsbetween gypsum and insoluble anhydrite in H2SO4 aqueoussolutions were also studied at 298.1 K and 363.1 K. A Pitzer modelwas used to simulate the solubility of gypsum and insolubleanhydrite in the system CaSO4–H2SO4–H2O, and their stableregions as a function of temperature and H2SO4 concentrationwere predicted with the model.
2. Experimental section
2.1. Materials and apparatus
Stock H2SO4 aqueous solutions of known concentration wereprepared with sulfuric acid (guaranteed reagent, China NationalPharmaceutical Industry Co. Ltd., China), as described in ourprevious work (Wang et al., 2012). The H2SO4 contents weredetermined by weighing BaSO4 precipitated by BaCl2 solution.Gypsumwas prepared by neutralizing calcium carbonate (purity inmass fraction 40.999, China National Pharmaceutical Industry Co.Ltd., China) with sulfuric acid (G.R.) and verified by X-ray Diffrac-tion (XRD). To convert the possible impurity anhydrite to gypsum,approximately 500 g of the prepared gypsum sample was mixedwith 4 kg of distilled water for 48 h and then filtered. Thisconversion process was repeated four times. The obtained gypsumsample was air-dried at room temperature for three days. Inso-luble anhydrite was prepared by placing the prepared gypsum inan oven at 760 1C for 16 h and then cooling the product in adesiccator. X-ray Diffraction analysis showed that the product
consists of insoluble anhydrite alone. Doubly distilled water(So1.2�10−4 S m−1) was used in the experiment.
The equilibrium experiments were carried out in a thermostat(Lauda E219, Germany) with temperature stability up to 70.01 Kat 298.1 K and 70.1 K at higher temperatures. A calibrated glassthermometer (Miller & Weber, Inc., USA) with an accuracy of70.01 K was used to determine the bath temperature. A SartoriusBS224S balance was used for weighing with an error of 70.1 mg.The Ca2+ analysis was performed by the standard addition methodwith an Inductively Coupled Plasma Optical Emission Spectro-meter (ICP-OES) (5300DV, Perkin-Elmer, USA). The type of solidphase in equilibrium with solution was determined by an X-raydiffractometer (D/Max-2500, Rigaku, Japan).
2.2. Experimental procedures
Measurements were carried out in a 150 cm3 Erlenmeyer flaskimmersed in a thermostatted glycol–water bath. Approximately 130 gof sulfuric acid aqueous solution of known composition prepared fromthe H2SO4 stock solutions was placed in the Erlenmeyer flask with anexcess 5 g of gypsum or insoluble anhydrite as the saturating solidphase. The solution and solid phase in the flask were stirred with amagnetic stirrer outside the glycol–water bath. For gypsum at 298.1 Kand insoluble anhydrite at (323.1, 348.1, and 363.1) K, each sample wasstirred at constant temperature for 120 h and then kept static for 8 h.The time of 120 h should be sufficient for the two types of solids toreach equilibrium with their respective solution, as we tested in ourprevious work (Zeng and Wang, 2011). The clear top layer of thesolutionwas directly transported into aweighed vacuum tubemade ofglass that had been heated in an oven to the equilibrium temperaturebefore sampling. The removed sample solution was diluted with aknown amount of distilled water to avoid crystallization. The wellmixed diluted solution was pipetted equally into four weighed 100 mlvolumetric flasks. To avoid the possible hydrolysis or precipitation ofCaSO4, 3 ml of 65% HNO3 was added to each flask. Different amountsof CaCl2 standard solution were added to three of the four flasks.Distilled water was added to each volumetric flask to the 100 ml line.The solution in each flask was mixed well by shaking and thenanalyzed by ICP-OES with the analysis strategy as described in detail inour previous work (Wang et al., 2012).
When the equilibrium solid phase was considered unstable andcould be converted to other crystal types in the H2SO4 aqueoussolution, the sample solution was removed with a pipet covered withglass cloth as a filter at regular intervals. Each removed samplesolution was diluted, mixed well and pipetted into four volumetricflasks and subjected to the procedures described above. The highestconcentration measured during each experimental run was assignedas the equilibrium concentration of the unstable phase.
2.3. Analytical accuracy
To ensure a high accuracy for Ca2+, the Ca2+ concentration of thestandard solution added to the initial sample solution was alwayscomparable with that in the sample solution. The measured results ineach analysis run possess a correlation coefficient higher than 0.9999.The relative error for the analyzed Ca2+ content can be controlledwithin 2% in most cases and within 0.1% for SO4
2−.
3. Experimental results and discussion
3.1. Solubility isotherms of gypsum and insoluble anhydrite
The experimental solubility data of gypsum and insolubleanhydrite in the ternary system CaSO4–H2SO4–H2O at T¼(298.1,
Table 3Solubility data of gypsum and insoluble anhydrite in the ternary systemCaSO4–H2SO4–H2O at 348.1 K.
n Excess H2SO4, no contribution from the dissolution of CaSO4.nn G¼gypsum; A¼ insoluble anhydrite.nnn Metastable phases.
W. Wang et al. / Chemical Engineering Science 101 (2013) 120–129122
323.1, 348.1, and 363.1) K are tabulated in Tables 1–4 and plotted inFigs. 1 and 2, respectively.
At high temperatures and H2SO4 concentrations, gypsum incontact with the solution is easily converted to the less solubleinsoluble anhydrite and vice versa at low temperature and H2SO4
concentrations. In each experimental run, we found that the Ca2+
concentration first increases and then decreases with time.The maximum values are provisionally assigned as the equilibriumconcentration relative to the metastable phase in this work.
The equilibrium concentrations of gypsum measured in thiswork agree with the literature solubility data (Dutrizac, 2002;Marshall and Jones, 1966; Zdanovskii and Vlasov, 1968b) very wellon the whole temperature range, as shown in Fig. 1, although theso-called equilibrium concentrations were taken from the max-imum concentration of calcium since gypsum was added into thesolution. The solubility isotherms of gypsum show the sametendency at each temperature, first increasing and then decreasingwith increasing H2SO4 concentration. The solubility of gypsumincreases monotonously with increasing temperature at a constantH2SO4 concentration.
The solubilities of insoluble anhydrite in the ternary systemCaSO4–H2SO4–H2O at different temperatures were reported in two
Table 1Solubility data of gypsum and insoluble anhydrite in the ternary system CaSO4–
n Excess H2SO4, no contribution from the dissolution of CaSO4.nn G¼gypsum; A¼ insoluble anhydrite.nnn Metastable phases.
Fig. 1. Solubility phase diagram of gypsum in the system CaSO4–H2SO4–H2O.Symbols are experimental data. 298.1 K: (−□−), Dutrizac (2002), Marshall andJones (1966) and Zdanovskii and Vlasov (1968b); ■, this work. 323.1 K: (−○−),Dutrizac (2002) and Zdanovskii and Vlasov (1968b); ●, this work. 348.1 K: (−Δ−),Dutrizac (2002) and Zdanovskii and Vlasov (1968b); ▲, this work. 363.1 K: (−◇−),Dutrizac (2002); ◆, this work.
Fig. 2. Solubility phase diagram of insoluble anhydrite in the system CaSO4–H2SO4–
H2O. Symbols are experimental data. 298.1 K: (−□−), Zdanovskii and Vlasov(1968a); ■, this work. 323.1 K: (−○−), Zdanovskii and Vlasov (1968a); ●, this work.348.1 K: (−Δ−), Zdanovskii and Vlasov (1968b); ▲, this work. 363.1 K: ◆, this work.368.1 K: (−☆−), Zdanovskii and Vlasov (1968b).
Fig. 3. Transformation of insoluble anhydrite to gypsum as a function of time at298.1 K in contact with H2SO4 aqueous solution: (−■−), 0.5 mol kg−1; (−●−),1.5 mol kg−1; (−▲−), 3.0 mol kg−1; (−◆−), 4.0 mol kg−1.
Fig. 4. Calcium sulfate concentrations as a function of time at 298.1 K afterinsoluble anhydrite was added to H2SO4 aqueous solution: (−■−), 0.5 mol kg−1;(−●−), 1.5 mol kg−1; (−▲−), 3.0 mol kg−1; (−◆−), 4.0 mol kg−1.
W. Wang et al. / Chemical Engineering Science 101 (2013) 120–129 123
studies (Zdanovskii and Vlasov, 1968a, 1968b). As shown in Fig. 2,our solubility data for insoluble anhydrite are in good agreementwith those reported by Zdanovskii and Vlasov (1968a) at 323.1 Kand slightly higher than their data at 298.1 K. However, thesolubility data of insoluble anhydrite in aqueous H2SO4 solutionsat 348.1 K and 363.1 K obtained in this work were much lowerthan those reported by Zdanovskii and Vlasov (1968b), whomeasured the solubility of insoluble anhydrite at 348.1 K and368.1 K using a kinetic method. In each run of their experiment,gypsum was added to H2SO4 aqueous solution as an initial solidphase and only 5–8 h was allowed for the transformation fromgypsum to insoluble anhydrite and for the insoluble anhydrite-liquid equilibration. According to the experiment on the transfor-mation from gypsum to insoluble anhydrite in sulfuric acidsolutions performed by Azimi and Papangelakis (2011), 5–8 hwas insufficient for complete conversion from CaSO4 �2H2O toCaSO4 in H2SO4 aqueous solution at 363.1 K, much less 348.1 K.
Fig. 2 shows that the sulfuric acid concentration has the sameeffect on the solubilities of insoluble anhydrite and gypsum. Thesolubility isotherms of insoluble anhydrite first increase and thendecrease with increasing H2SO4 concentration at each tempera-ture. However, the solubility of insoluble anhydrite does notalways increase with temperature for a constant concentration ofH2SO4: it decreases when mH2SO4 o0.5 mol kg−1 and increaseswhen mH2SO4 40.5 mol kg−1.
3.2. Transformation between gypsum and insoluble anhydrite
To understand the effects of sulfuric acid concentration andtemperature on the transformation between insoluble anhydriteand gypsum, we added insoluble anhydrite and gypsum as aninitial solid phase into an aqueous solution with a known H2SO4
concentration at 298.1 K and 363.1 K and then measured the Ca2+
concentration in the solution by ICP-OES in regular intervals.Meanwhile, the relative amounts of each type of calcium sulfatein the solid samples were estimated by Rietveld refinement, whichis embedded in the XRD analysis software.
Fig. 3 presents the influence of H2SO4 concentration on thetransformation rate of insoluble anhydrite to gypsum at 298.1 K. It iswell known that gypsum is stable in aqueous solution withmH2SO4 ¼0mol kg−1 at 298.1 K (Wang et al., 2012). In 0.5 mol kg−1
H2SO4 solution, insoluble anhydrite begins transforming to gypsum
after 12 h and completely transforms to gypsum after five days.In 3.0 mol kg−1H2SO4 solution, insoluble anhydrite is stable in the first2.5 days. However, insoluble anhydrite remains unchanged even aftersix days in a 4.0 mol kg−1H2SO4 solution. The calcium sulfate concen-tration in the transformation process was measured and is presentedin Fig. 4. In each experimental run, the Ca2+ concentration in theH2SO4 solution first increases and then decreases. The increasingsection can be understood as the result of the dissolution of insolubleanhydrite and the decreasing section as that of the formation ofgypsum with lower solubility. The highest concentrations detectedduring each experimental process were assigned as the solubility ofthe initial solid phase (insoluble anhydrite) in this work. Generally, oneor two days are needed for the insoluble anhydrite to reach itssolubility limit, which can explain why the solubilities of insolubleanhydrite at 298.1 K in Fig. 2 measured by Zdanovskii andVlasov (1968a) over 5–6 h are generally lower than our results.
In sulfuric acid solutions at 363.1 K, the transition from theinitial solid phase gypsum to insoluble anhydrite is very rapid(a few minutes to several hours), as shown in Fig. 5. The timerequired for complete transformation depends on the H2SO4
concentration. For instance, gypsum began to transform into
Fig. 5. Transformation of gypsum to insoluble anhydrite as a function of time at363.1 K in contact with H2SO4 aqueous solutions at different concentrations: (−■−),0.5 mol kg−1; (−●−), 1.5 mol kg−1; (−▲−), 3.0 mol kg−1; (−◆−), 4.0 mol kg−1.
Fig. 6. Calcium sulfate concentrations as a function of time at 363.1 K after gypsumwas added to H2SO4 aqueous solution: (−■−), 0.5 mol kg– 1; (−●−), 1.5 mol kg−1;(−▲−), 3.0 mol kg−1; (−◆−), 4.0 mol kg−1.
W. Wang et al. / Chemical Engineering Science 101 (2013) 120–129124
insoluble anhydrite after 10 h and completely transformed intoinsoluble anhydrite at five days after being placed into the0.5 mol kg−1H2SO4 solution and gypsum completely transformedto insoluble anhydrite after 6 h in the 4.0 mol kg−1H2SO4 solution.The Ca2+ concentration in the H2SO4 aqueous solution during thetransformation process as a function of time is presented in Fig. 6.Similarly to 298.1 K, the Ca2+ concentration first increases andthen decreases at 363.1 K. The maximum values are assigned asthe solubility of the initial solid phase gypsum. At least 12 h wasneeded for the solution with insoluble anhydrite to equilibrate ifgypsum was added to the solution as the initial solid phase in a3.0 mol kg−1H2SO4 aqueous solution, and at least two days and fivedays were needed for 1.5 mol kg−1 and 0.5 mol kg−1H2SO4 aqueoussolution, respectively. Zdanovskii and Vlasov (1968b) measuredthe solubility of insoluble anhydrite at 368.1 K, as shown in Fig. 2.In their experiments, the Ca2+ concentration in the solution wasanalyzed 5–8 h after the gypsum was added to the solution as theinitial solid phase, which was assigned as the solubility ofinsoluble anhydrite. According to the kinetic research in this workat 363.1 K, the Ca2+ concentration measured at 5–8 h after gypsumwas added to the solution should not be assigned as the solubilityof insoluble anhydrite; more equilibration time was needed. Thus,
their solubility data (Zdanovskii and Vlasov, 1968b) for insolubleanhydrite at high temperatures are higher than ours.
In the transition process from gypsum to insoluble anhydrite inH2SO4 aqueous solutions at 363.1 K, no hemihydrate or γ-CaSO4
(soluble anhydrite) were detected. Azimi and Papangelakis (2011)observed the same phenomenon in their transformation experimentin 1.5 M H2SO4 solution at 363.1 K. However, Zdanovskii and Vlasov(1968b) reported that the transition process occurred as CaSO4 �2H2O-CaSO4 �0.5H2O-γ-CaSO4 in H2SO4 (20%, 30%, 40%) solutionsat 368.1 K, but gave no details on the solid characterization.
4. Thermodynamic modeling
4.1. Modeling methodology
To construct the stable regions of insoluble anhydrite andgypsum as a function of temperature and H2SO4 concentration, athermodynamic model is necessary to simulate and predict thethermodynamic properties of the binary and ternary systems (Liand Demopoulos, 2006). As discussed in our previous work (Wanget al., 2012), the Pitzer thermodynamic model summarized byHarvie et al. (1984) is sufficient for this task.
The expressions of the osmotic coefficient ϕ or water activityand ionic activity coefficients are given as follows:
ðϕ−1Þ ¼ 2ð∑imiÞ
ð− AϕI3=2
1þ bI1=2þ∑
c∑amcmaðBϕ
ca þ ZCcaÞ
þ∑c
∑c0 o c
mcmc0 ðΦϕcc0 þ∑
amaψ cc0aÞ
þ∑a
∑a0 oa
mama0 ðΦϕaa0 þ∑
cmcψaa0cÞÞ ð1Þ
aw ¼ expð−ðMH2O=1000Þϕ∑jmjÞ ð2Þ
The cation activity coefficients are
ln γM ¼ z2MF þ∑amað2BMa þ ZCMaÞ þ∑
cmcð2ΦMc þ∑
amaψMcaÞ
þ∑a
∑a′oa
mama′ψaa0M þ jzM j∑c∑amcmaCca ð3Þ
and the anion activity coefficients are
ln γX ¼ z2XF þ∑cmcð2BcX þ ZCcXÞ
þ∑amað2ΦXa þ∑
cmcψXacÞ þ∑
c∑
c′o cmcmc′ψ cc′X
þjzX j∑c∑amcmaCca ð4Þ
where
F ¼−Aϕ
ffiffiI
p
1þ bffiffiI
p þ 2blnð1þ b
ffiffiI
pÞ
" #
þ∑c∑amcmaB′ca þ∑
c∑
c′o cmcmc′Φ′cc′ þ∑
a∑
a′oamama′Φ′aa′ ð5Þ
Aϕ is one-third of the Debye–Hückel limiting slope.The BMX coefficients are functions of ionic strength (Pitzer, 1973)
BMX ¼ βð0ÞMX þ βð1ÞMXgðα1ffiffiI
pÞþ β 2ð Þ
MXgðα2ffiffiI
pÞ ð6Þ
BMX0 ¼ βð1ÞMXg′ðα1
ffiffiI
pÞþ βð2ÞMXg′ðα2
ffiffiI
pÞ ð7Þ
For 1–1 and 1–2 electrolytes, α1¼2, α2¼0. For 2–2 or highervalence pairs, α1¼1.4, α2¼12.0. In most cases, βð2Þ ¼0 for univalentpairs. For 2–2 electrolytes, a nonzero βð2Þ is more common.
The mixing parameter Φ, which depends on ionic strength, isgiven in the following form (Pitzer, 1975):
Φij ¼ θij þ θEijðIÞ ð8Þ
Table 5Binary and ternary parameters of the Pitzer model.
Reference Ion interactions Coefficientsn a1 a2 a3 a4 Temperature range (K)
This work Ca2+ HSO4−
βð0Þca2.145�10−1 − − 3.01�10−3 298−363
βð1Þca3.14 − − −1.776�10−2
βð2Þca− − − −
Cφca − − − −
This work Ca2+ SO42−
βð0Þca2.0�10−1 − − −7.7�10−4 298−363
βð1Þca2.65 − − 5.38�10−3
βð2Þca−55.7 − − 9.031�10−1
Cφca − − − −
Reardon and Bechie (1987) H+ HSO4−
βð0Þca2.106�10−1 4.801�102 − − 298−373
βð1Þca5.320�10−1 1.183�103 2.364 −
βð2Þca− − − −
Cφca − − − −
Reardon and Bechie (1987) H+ SO42−
βð0Þca2.17�10−2 5.833�101 − − 298−373
βð1Þca− − − −
βð2Þca− − − −
Cφca 4.11�10−2 5.865�101 − −
This work Ca2+ H+ θcc0 4.4�10−2 − −6.8�10−4 298−363Reardon and Bechie (1987) H+ HSO4
− ψSO42− − − − − 298−373
n XðT=KÞ ¼ a1 þ a2ð1=ðT=KÞ−1=298:15Þ þ a3nlnððT=KÞ=298:15Þ þ a4nððT=KÞ−298:15Þ.
Fig. 7. Calculated water activities for the system H2SO4–H2O compared withliterature data. Symbols are the literature experimental data: ○, Hovey et al.(1993). All lines are calculated values: −, 298.1 K; —, 323.1 K; - � -, 348.1 K; � � � ,373.1 K.
Table 6Parameter ln Kn of solid phase in the ternary system CaSO4–H2SO4–H2O.
W. Wang et al. / Chemical Engineering Science 101 (2013) 120–129 125
Φij0 ¼ θE′ij ðIÞ ð9Þ
θEij and θE0
ij are functions of ionic strength and electrolyte pairtype alone.
For details of the expressions, one can refer to the literature(Harvie et al., 1984).
4.2. Binary parameter determination
4.2.1. H2SO4–H2O systemIn sulfuric acid solution, the first-order dissociation equilibrium
H2SO4ðaqÞ ¼HþðaqÞ þ HSO−
4ðaqÞ is considered complete and thesecond-order dissociation equilibrium HSO−
4ðaqÞ ¼HþðaqÞ þ SO2−
4ðaqÞ ispartially completed with a dissociation constant K2 (Pitzer andRoy, 1977; Reardon and Bechie, 1987):
ln K2 ¼ lnðaHþðaqÞ
aSO2−4ðaqÞ
=aHSO−4ðaqÞ Þ ð10Þ
Binary model parameters for H2SO4 from 298.1 K to 363.1 K,listed in Table 5, were given by Reardon and Bechie (1987)including HSO4
− species in the dissociation equilibrium,HSO−
4ðaqÞ ¼HþðaqÞ þ SO2−
4ðaqÞ, using the familiar dissociation constantln K2¼−14.0321+2825.2/(T/K) (298.1 K−373.1 K). The calculatedwater activity curves of the system H2SO4–H2O are presented inFig. 7 and agree well with other literature data (Hovey et al., 1993).
4.2.2. CaSO4–H2O systemThe equilibrium constant lnK parameters for each solid phase
(gypsum and insoluble anhydrite) are determined by calculatingthe activities of each component (Eq. (11)) at the saturation pointusing the following equilibrium:
The binary parameters for CaSO4 at 298.1 K evaluated by Pitzerand Mayorga (1974) were used in this work. Because of a lack ofdata for the activity and osmotic coefficients for CaSO4 at differenttemperatures, Silvester and Pitzer (1978) calculated the tempera-ture derivation of each binary parameter for CaSO4 by fittingthe thermodynamic properties of pure electrolyte solution. How-ever, these parameters for high temperatures are limited to0.02 mol kg−1. To improve the application range of the parameters,
we refitted the binary parameters. Because Alai et al. (2005) havegiven binary parameters for CaSO4 at 368.1 K and used them tosuccessfully calculate the complex system Na–Cl–NO3–K–Ca–SO4–
Mg–Si, their data at 368.1 K, along with that at 298.1 K given byPitzer and Mayorga (1974), were applied to determine the tem-perature function of the parameters in this work, and the obtainedresults are presented in Table 5. The lnK parameters for gypsumand insoluble anhydrite from 298.1 K to 363.1 K were determinedusing literature solubility data in pure electrolyte solutions (Hulettand Allen, 1902; Partridge and White, 1929) with Eq. (11) and
W. Wang et al. / Chemical Engineering Science 101 (2013) 120–129126
consequently fitted with a temperature function (see Table 6).Again, applying the binary parameters, we calculated the solubilityisotherms of gypsum and insoluble anhydrite by the Pitzerthermodynamic model and presented them in Fig. 8. Naturally,the calculated results were in excellent agreement with theexperimental solubility data.
Fig. 10. Solubility isotherms of insoluble anhydrite in the system CaSO4–H2SO4–
H O. All lines are model values: —, isotherms predicted with binary parameters
4.3. Ternary parameter determination and solubility prediction
Applying the binary parameters in Table 5, we predicted thesolubility isotherms of gypsum and insoluble anhydrite in the ternarysystem CaSO4–H2SO4–H2O at (298.1–363.1) K (Figs. 9 and 10), whichdeviate largely from our experimental data. The ternary modelparameters are apparently necessary to describe the properties ofthe system. To simplify the fitting procedure and improve theprediction ability of the thermodynamic model, we evaluated themixing parameters βð0ÞCa−HSO4
, βð1ÞCa−HSO4and θCa−H by regressing the
solubilities of the stable phases, i.e., gypsum at 298.1 K and insolubleanhydrite at 363.1 K in the system CaSO4–H2SO4–H2O. The max
Fig. 8. Comparison of the calculated and experimental solubilities for gypsum andinsoluble anhydrite in the system CaSO4–H2O. Experimental data are from Hulettand Allen (1902) and Partridge and White (1929): □, gypsum; ○, insolubleanhydrite. All lines are model values.
Fig. 9. Solubility isotherms of gypsum in the system CaSO4–H2SO4–H2O. All linesare model values: —, isotherms predicted with binary parameters only; —,isotherms calculated with both binary and ternary parameters; − �−, isothermspredicted with both binary and ternary parameters. All symbols are experimentalvalues from this work: ■, 298.1 K; ●, 323.1 K; ▲, 348.1 K and ◆, 363.1 K.
2
only; —, isotherms calculated with both binary and ternary parameters; − �−,isotherms predicted with both binary and ternary parameters. All symbols areexperimental values from this work: ■, 298.1 K; ●, 323.1 K; ▲, 348.1 K and ◆,363.1 K.
Table 7Comparison of predicted values and literature experimental solubility data ofanhydrite in the system CaSO4–H2SO4–H2O.
T/K m(H2SO4)/mol kg−1
m(CaSO4)/mol kg−1 Solidphasennn
Deviation(%)nnnn
Exp.n Predictednn
298.1 0.2622 0.02108 0.02434 A −15.460.5383 0.02265 0.02574 A −13.640.8293 0.02294 0.02610 A −13.771.1364 0.02235 0.02595 A −16.111.8042 0.01941 0.02307 A −18.862.5545 0.01527 0.01765 A −15.594.3746 0.00756 0.00809 A 7.01
323.1 0.2623 0.02297 0.02356 A −2.570.5386 0.02701 0.02664 A 1.370.8300 0.02878 0.02784 A 3.271.1373 0.02818 0.02787 A 1.101.8057 0.02541 0.02610 A −2.722.5567 0.02164 0.02178 A −0.654.3771 0.01177 0.01113 A 5.44
n Experimental data from Zdanovskii and Vlasov (1968a).nn Calculated and predicted with the binary and ternary parameters in
concentrations of the metastable phases, i.e., gypsum at 323.1 K,348.1 K, 363.1 K and insoluble anhydrite at 298.1 K, were not used inthe regression. The obtained mixing parameters were presented as afunction of temperature in Table 5. The solubility isotherms ofgypsum at 298.1 K and insoluble anhydrite at 363.1 K, which werecalculated by the ternary parameters, are presented as solid curves inFigs. 9 and 10, respectively. At other temperatures, the solubilityisotherms predicted by the binary and ternary parameters are ingood agreement with our experimental solubility data (see the dash-dotted lines in Figs. 9 and 10), including the data taken from themaximal values for the metastable phases gypsum at 323.1 K,348.1 K, and 363.1 K and partial insoluble anhydrite at 298.1 K. Theaverage relative deviation between our experimental data and thepredicted values in the system CaSO4–H2SO4–H2O are 1.8% (1.3%),
Table 8Comparison of predicted values and literature experimental solubility data ofgypsum and insoluble anhydrite in the system CaSO4–H2SO4–H2O.
T/K m(H2SO4)/mol kg−1
m(CaSO4)/mol kg−1 Solidphasennn
deviation(%)nnnn
Exp.n Predictednn
298.1 0 0.01553 0.01514 G 2.510.2621 0.01782 0.01758 G 1.350.5381 0.01961 0.01942 G 0.970.8291 0.02039 0.02009 G 1.471.1361 0.02038 0.01991 G 2.311.8040 0.01854 0.01745 G 5.882.5546 0.01546 0.01393 G 9.904.3750 0.00830 0.00731 G 11.93
323.1 0 0.01612 0.01530 G 5.090.2624 0.02616 0.02670 G −2.060.5390 0.03168 0.03203 G −1.100.8306 0.03398 0.03450 G −1.531.1381 0.03353 0.03580 G −6.771.8069 0.03037 0.03442 G −13.342.5582 0.02598 0.02989 G −15.054.3784 0.01409 0.01737 G −23.78
348.1 0 0.01531 0.01399 G 8.620.2628 0.03900 0.03790 G 2.820.5404 0.05147 0.04861 G 5.560.8330 0.05561 0.05557 G 0.071.1419 0.05799 0.05977 G −3.071.8137 0.05836 0.06013 G −3.032.5679 0.05392 0.05447 G −1.024.3929 0.03840 0.03142 G 18.180 0.01035 0.00854 A 17.490.2652 0.02283 0.02293 A −0.440.5465 0.02947 0.02709 A 8.080.8357 0.03265 0.02897 A 11.271.1491 0.03504 0.02962 A 15.471.8161 0.03558 0.02834 A 20.352.5714 0.02681 0.02470 A 7.87
368.1 0.2552 0.02355 0.02147 A 8.830.5359 0.03561 0.02709 A 23.920.8422 0.04150 0.03007 A 27.541.1399 0.04402 0.03145 A 28.551.8204 0.04093 0.03108 A 24.062.5605 0.02579 0.02785 A −7.99
n Experimental data from Zdanovskii and Vlasov (1968b).nn Calculated and predicted with the binary and ternary parameters in
Table 9Comparison of predicted values and literature experimental solubility data ofgypsum in the system CaSO4–H2SO4–H2O.
T/K m(H2SO4)/mol kg−1
m(CaSO4)/mol kg−1 Solidphasennn
Deviation(%)nnnn
Exp.n Predictednn
298.1 0.0990 0.01511 0.01593 G −5.430.2005 0.01697 0.01715 G −1.060.4055 0.01862 0.01874 G −0.640.6139 0.01976 0.01961 G 0.760.8211 0.01997 0.02016 G −0.951.0274 0.02002 0.02005 G −0.151.2467 0.01969 0.01976 G −0.361.4601 0.01838 0.01908 G −3.811.6826 0.01796 0.01818 G −1.221.9200 0.01714 0.01705 G 0.52
323.1 0.0999 0.02071 0.02155 G −4.060.2028 0.02506 0.02509 G −0.120.4096 0.02951 0.02980 G −0.980.6207 0.03211 0.03279 G −2.120.8300 0.03277 0.03466 G −5.771.0392 0.03298 0.03566 G −8.131.2635 0.03315 0.03579 G −7.961.4811 0.03274 0.03567 G −8.951.7068 0.03172 0.03504 G −10.471.9425 0.03026 0.03391 G −12.06
348.1 0.1013 0.02733 0.02670 G 2.300.2059 0.03598 0.03382 G 6.000.4158 0.04615 0.04400 G 4.660.6296 0.05269 0.05108 G 3.060.8441 0.05651 0.05596 G 0.971.0592 0.05892 0.05880 G 0.201.2898 0.06034 0.06063 G −0.481.5108 0.06046 0.06104 G −0.961.7403 0.06021 0.06083 G −1.031.9810 0.05835 0.05921 G −1.47
363.1 0.1024 0.03184 0.02936 G 7.790.2081 0.04398 0.03973 G 9.660.4205 0.05910 0.05736 G 2.940.6361 0.06920 0.06774 G 2.110.8553 0.07640 0.07526 G 1.491.0754 0.08124 0.08098 G 0.321.3106 0.08382 0.08384 G −0.021.5332 0.08402 0.08527 G −1.491.7654 0.08489 0.08528 G −0.462.0125 0.08302 0.08385 G −1.00
n Experimental data from Dutrizac (2002) in volumetric concentration andsolution density.
nn Calculated and predicted with the binary and ternary parameters inTable 5.
W. Wang et al. / Chemical Engineering Science 101 (2013) 120–129 127
1.2% (1.6%), 2.3% (2.0%), and 3.7% (1.1%) for gypsum (insolubleanhydrite) at 298.1 K, 323.1 K, 348.1 K, and 363.1 K, respectively.
Comparing the predicted values with the experimental solubi-lity data reported by other authors (Dutrizac, 2002; Zdanovskiiand Vlasov, 1968a, 1968b), the model values deviate strongly fromthose reported by Zdanovskii and Vlasov (1968a, 1968b). In mostcases, the relative deviation are greater than 5% (see Tables 7 and8); however, our model values agree with the experimental datameasured by Dutrizac (2002) with an average relative deviation3.1% (see Table 9), near the experimental uncertainty.
Furthermore, we calculated the solubility surfaces of gypsumand insoluble anhydrite as functions of temperature and H2SO4
concentration, as shown in Fig. 11. The solid phase with the lowestsolubility is usually the stable phase at a specified temperatureand H2SO4 concentration. The stable regions of the two solidphases, gypsum and insoluble anhydrite, were constructed basedon the calculated results and presented in Fig. 12. Gypsum isgenerally stable in H2SO4 aqueous solution at relatively lowtemperatures, and insoluble anhydrite is generally stable at hightemperatures. Zdanovskii and Vlasov (1968a) reported data for
some individual transformation temperature-H2SO4 concentrationpairs, which were presented in the Fig. 12 for comparison. Theirdata strongly deviate from our model. For instance, Zdanovskiiand Vlasov (1968a) reported that the transformation point is at2.55 mol kg−1 at 298.1 K, which should be 3.2 mol kg−1 accordingto our model. According to Zdanovskii and Vlasov's data, the stablephase in a 3.0 mol kg−1 H2SO4 solution should be insolubleanhydrite. Our Kinetic transformation experiments (Fig. 3) showthat the initial solid phase insoluble anhydrite will begin toconvert into the solid phase gypsum at 2.5 days after being addedto a 3 mol kg−1 H2SO4 solution. Thus, gypsum, rather than inso-luble anhydrite, is the stable solid phase in 3 mol kg−1 H2SO4,which is consistent with our thermodynamic model. The experi-mental conclusion of Zdanovskii and Vlasov (1968a), drawn from5–8 h equilibrium experiments, represented only the Kineticaspects of the concerned system, based on which the simulatedresults reported by Azimi et al. (2007) are also questionable.
Fig. 11. The integrated solubility phase diagram for gypsum and insoluble anhy-drite in (0–5) mol kg−1H2SO4 from 298.1 K to 363.1 K in the system CaSO4–H2SO4–
H2O.
Fig. 12. Predicted stable region of calcium sulfate as function of H2SO4 concentra-tion and temperature. ––: model value from this work; ●: individual model valuesfrom this work; □: literature values from Zdanovskii and Vlasov (1968a).
W. Wang et al. / Chemical Engineering Science 101 (2013) 120–129128
5. Summary
The solubility isotherms of gypsum and insoluble anhydrite inthe system CaSO4–H2SO4–H2O were measured by static and kineticequilibrium methods at T¼(298.1, 323.1, 348.1, and 363.1) K. Thetransformation between gypsum and insoluble anhydrite was alsostudied as a function of time at 298.1 K and 363.1 K. The experi-mental data obtained in this work were compared with literaturevalues, and possible explanations of the differences between ourdata and the literature data were given based on the kinetics of theconversion between the two solid phases. A Pitzer model was usedto simulate and predict the solubility isotherms of gypsum andinsoluble anhydrite in the studied system, and good thermody-namic agreement has been achieved. A stable region diagram wasconstructed using the model calculations. The following conclu-sions have been drawn:
1.
Generally, the solubility isotherms for gypsum in H2SO4 aqu-eous solution measured in this work were in good agreement
with literature solubility data over a large temperature range ofT¼(298.1–363.1) K.
2.
The solubility data for insoluble anhydrite measured in this workat 298.1 K are generally higher than those reported by Zdanovskiiand Vlasov (1968a). The 5–8 h equilibrium time applied in thelatter case was insufficient for the solution to equilibrate with theinitial solid phase insoluble anhydrite, producing overly low values.
3.
The solubility data for insoluble anhydrite measured in thiswork at temperatures above 323.1 K are generally lower thanthose reported by Zdanovskii and Vlasov (1968b). The 5–8 hequilibrium time used in the latter case was insufficient for theinitial solid phase gypsum to completely convert to insolubleanhydrite, which results overly high values.
Nomenclature
ai activity of species iAϕ one-third of the Debye–Hückel limiting slopeb a parameter in Pitzer's equations with an fixed value of
1.2BMX observable second-order interaction coefficient for neu-
tral elect rolyte MX(M¼cation,X¼anion)BMX0 derivative of BMX with respect to ionic strength
CϕMX third-order interaction coefficient for the neutral elec-
pF sum of the Debye–Hückel termsI ionic strength, mol kg−1
k electric conductivityK thermodynamic equilibrium constantm molality concentration, mol kg−1
n stoichiometric number of water molecules in asolid phase
R ideal gas constant, 8.314 J mol−1 K−1
T temperature, KMH2O molecular weight of water, 18.0152 g mol−1
Z coefficient for CϕMX
a1, a2 parameters appearing in Pitzer's equationβð0ÞMX ,β
ð1ÞMX ,β
ð2ÞMX observable second-order interaction coefficientparameters for neutral electrolyte MX
γi activity coefficient of the solute speciesθij observable second-order interaction coefficient for each
cation–cation or anion–anion pairθEij electrostatic part of θijθE′ij derivative of θEijψ ijk observable third-order interaction coefficient for each
cation–cation–anion or anion–anion–cation tripletϕ osmotic coefficient of the aqueous solutionΦ equation for θijΦ′ derivative of Φψ observable third-order interaction coefficient for triple-
ion interactions
Subscripts
M, c and c′ symbols denoting cationsX, a and a′ symbols denoting anions
Acknowledgments
This work was financially supported by the National NatureScience Foundation of China under Contract nos. 21176261 and
W. Wang et al. / Chemical Engineering Science 101 (2013) 120–129 129
51134007, the Nature Science Foundation of Hunan Province underContract no. 11JJ2011, and the Hunan Innovation Foundation forPostgraduate under Contract no. CX2012B118.
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