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Thermodynamics and kinetics for mixed calcium carbonate and calcium sulfate precipitation
Chemical Engineering Science 56 (2001) 5391–5400
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Thermodynamics and kinetics for mixed calcium carbonate and calcium sulfate precipitation T. H. Chong, R. Sheikholeslami ∗ School of Chemical Engineering and Industrial Chemistry, The University of New South Wales, Sydney, 2052, Australia Received 30 August 2000; received in revised form 23 May 2001; accepted 25 May 2001
Abstract ◦
The e/ects of CaSO4 on CaCO3 precipitation were studied in the batch tests at 60, 70 and 80 C in mixtures having calcium carbonate as the dominant salt and at a given total initial calcium concentration of 0:03 M with sulfate concentration ranging from 0 to 0:01 M. Solubility products and rate constants were determined from thermodynamic and kinetic studies and the results indicated that even minute amounts of calcium sulfate a/ect the thermodynamics, kinetics and the scale structure and no longer the solubility data and rate constants for the pure salt were applicable. Presence of CaSO4 from 0.002 to 0:01 M increased the calcium carbonate solubility product more than an order of magnitude. The e/ect of salt mixture on the solubility constant of non-dominant salt (calcium sulfate) was reverse as calcium sulfate solubility increased to its pure value with increases in its molar ratio. In addition, the rate equation suggested in the literature (Nancollas and Reddy, J. Colloid Interface Sci. 37 (1971) 824; Reddy and Nancollas, J. Colloid Interface Sci. 36 (1971) 166) for pure salt was not applicable to the experimental data. The general observations indicated that the presence of CaSO4 had weakened the CaCO3 scale which is usually very adherent. The experimental results did take into account the e/ect of solution ionic strength, however, they suggest that data for pure salt precipitation seem not to be extendable to co-precipitation. ? 2001 Elsevier Science Ltd. All rights reserved. Keywords: Fouling; Precipitation; Co-precipitation; Calcium sulfate; Calcium carbonate; Composite fouling; Thermodynamics; Kinetics
1. Introduction Fouling is the accumulation of undesired solid materials at the phase interfaces. Build-up of fouling =lm leads to an increase in resistance and deteriorates the performance of process equipment such as membranes and heat exchangers and is costing industries billions of dollars annually. One of the major fouling phenomena encountered in the aqueous systems is scale formation due to precipitation of salts present in the water. Lots of metals and anions exist naturally in the water; among them, CaCO3 and CaSO4 are major fouling contributors. Both these salts have inverse solubility behaviour where the solubility decreases with increasing temperature and salts ∗
Corresponding author. Tel.: +61-2-9385-4343; fax: +61-29385-5966. E-mail address: [email protected] (R. Sheikholeslami).
precipitate on heat exchange surfaces when the solution becomes supersaturated. Crystallization has been studied for many years as shown in the two monographs by Mullin (1972, 1993). An immense body of information is available on thermodynamics and kinetics of crystallization of calcium carbonate (Augustin & Bohnet, 1995; Nancollas & Reddy, 1971; Plummer & Busenberg, 1982) and calcium sulfate (Liu & Nancollas, 1970; Nancollas, Eralp, & Gill, 1978; Zhang & Nancollas, 1992). The research in the area of crystallization fouling, including the dynamic e/ects, has also been extensive as covered in two comprehensive reviews (Hasson, 1981, 1999). However, due to the complexity of fouling process the research in this area usually involves fouling by a single precipitant. The area to which not much attention has been paid to is the interactive e/ect of co-precipitating salts with or without common ions. These include solubility e/ects, rate data, crystal structure and strength, inhibitor e/ects and also dynamic
0009-2509/01/$ - see front matter ? 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 0 1 ) 0 0 2 3 7 - 8
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e/ects. This is important for two reasons. One is that the mechanism of fouling might be di/erent for di/erent salts as it was shown to be di/erent for CaCO3 and CaSO4 (Bansal, Muller-Steinhagen, & Chen, 1997). The second is the fact that co-existence of salts might actually a/ect the thermodynamic and kinetic behaviour of each salt and therefore, the single salt data might not be applicable to the condition when the salts co-exist. The reviewed literatures on crystallization (Hasson, 1981, 1999) indicate that very little study has been devoted to the study of the co-precipitation phenomenon. There has been some qualitative research (Bramson, Hasson, & Semiat, 1996; Hasson & Karmon, 1984) on the strength and tenacity of co-precipitated calcium carbonate and sulfate. They found that a major factor a/ecting scale tenacity was the purity of the deposit. For calcium sulfate, the higher the impurities, the greater the strength of the scale; however, with calcium carbonate, adhesive strength was seen to decrease with increasing impurities. The most diGcult deposit to remove from heat transfer surfaces was calcium carbonate scale with impurities measuring less than 5% by mass; pure calcium sulfate deposits were found to be far less adherent than deposits containing co-precipitated calcium carbonate. The co-precipitated calcium carbonate seems to act as bonding cement, enhancing considerably the strength of calcium sulfate scale layer. In an earlier study, Morse and Knudsen (1977) also reported that for aggressive scale, the main constituent was calcium carbonate. In our recent work (Sudmalis & Sheikholeslami, 2000) on co-precipitation of CaCO3 and CaSO4 when they exist in comparable ratios, it has been qualitatively shown that co-precipitation a/ects thermodynamics and kinetics of precipitation as well as the scale structure. The objective of this study is to investigate and quantify co-precipitation process of CaCO3 and CaSO4 when CaCO3 is the predominant component at a constant total calcium concentration and to determine solubility constants, assess the reaction rate constants and therefore examine the applicability of data and mechanisms for pure precipitation to co-precipitation. 2. Background Understanding and developing kinetic and rate correlations and models for co-precipitation are built on the theories of single salt precipitation and hence crystallization theory and properties of CaCO3 and CaSO4 are brieJy discussed here. In general, crystallization is considered to be comprised of nucleation, growth and re-crystallization steps. There are various mechanisms for each step and a great degree of overlap among these steps (Sudmalis & Sheikholeslami, 2000). For crystallization to occur the solution has
to be supersaturated; however, supersaturation by itself is not suGcient to induce crystallization. There is a requirement for centers of crystallization that can take various forms such as seeds, embryos or foreign matter present in the solution to induce nucleation. Growth and re-crystallization follow the nucleation step. Usually, nucleation is the controlling step; once the critical nuclei are formed, the crystallization proceeds. A given salt may have di/erent crystal structures of which some might be more stable or more readily formed. Calcium carbonate occurs naturally in three crystal structures of calcite, aragonite and vaterite. Calcite is the most stable form of calcium carbonate. The aragonite polymorph is metastable and irreversibly changes to ◦ calcite when heated in dry air to about 400 C. Vaterite is metastable and least prevalent and transforms to calcite and aragonite under geological conditions (Reeder, 1990). The crystal forms of calcite are hexagonal whereas aragonite is in the orthorhombic system. Physical properties of the two more prevalent crystal polymorphs are given by Lepley (1984); corresponding values for vaterite are not available. The solubility product for calcium carbonate and the dissociation constants for carbonic acids are given by Bott (1995). Saturation solubility of calcium carbonate depends on the CO2 content and solution pH; Kemmer (1988) provides data showing the distribution of CO2 related ions and CO2 gas in solution as a function of pH. Calcium sulfate can exist in six di/erent solid phases (3 anhydrites, 2 hemihydrates and a dihydrate). Gypsum (CaSO4 :2H2 O), hemihydrates (CaSO4 :1=2H2 O), and anhydrite III and anhydrite II can exist at room tem◦ peratures whereas anhydrite I only exists above 1180 C. The physical properties of all polymorphs are given by Wirsching and Gipswerke (1985). Much research has been performed in an attempt to analyse the mechanism and determine the form of calcium sulfate at di/erent temperatures. Partridge and White (1929) found that gypsum is the usual precipitating phase in the range ◦ of 40 –98 C while anhydrite and hemihydrate are the ◦ species likely to precipitate above 98 C. Some others (Blount & Dickson, 1973; Hardie, 1967) indicated the transition temperature between anhydrite and gypsum to ◦ be in the range of 56 –58 C. This is incongruent with the results of Partridge and White (1929); however, all the works (Blount & Dickson, 1973; Hardie, 1967; Partridge & White, 1929) seemed to indicate that in the range of operation of majority of industrial heat exchangers, gypsum is the dominant phase. Furthermore, Hasson and Zahavi (1970) proposed a correlation for CaSO4 nucleation times and reported that nucleation of anhydrite is an extremely slow process in comparison to that of gypsum. This also justi=es considering gypsum as the dominant phase. Correlations for solubility products for di/erent forms of calcium sulfate, which may be adjusted
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4. Results and discussions
Table 1 Summary of batch tests conditions ◦
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Run
T ( C)
CaCO3 (M)
CaSO4 (M)
BT1 BT2 BT3 BT4 BT5 BT6 BT7 BT8 BT9 BT10 BT11 BT12 BM1 BM2
70 60 60 70 70 60 70 60 80 80 80 80 60 70
0.030 0.030 0.020 0.020 0.022 0.022 0.028 0.028 0.030 0.020 0.022 0.028 0.000 0.000
0.000 0.000 0.010 0.010 0.008 0.008 0.002 0.002 0.000 0.010 0.008 0.002 0.030 0.030
for the appropriate temperature, are available in the literature (EPRI, 1982; Marshall & Slusher, 1968; Nordstrom et al., 1990). 3. Experimental techniques Batch tests were carried out with model solutions with total calcium content of 0:03 M and sulfate concentrations ranging from 0 to 0:01 M at temperatures of 60, 70 and ◦ 80 C. Table 1 lists the chemical composition of model solutions used in experimentation. The supersaturated solutions of calcium sulfate (CaSO4 ) and calcium carbonate (CaCO3 ) were prepared by adding equimolar amounts of Na2 SO4 and CaCl2 , and CaCl2 and NaHCO3 , respectively. The solutions were prepared with analytical grade chemicals and with micro-=ltered (with 0:22 m Millipore =lter) distilled water. Solution pH was measured before mixing, then the mixture was carefully transferred to a series of 75 ml test tubes; which had been scrubbed, rinsed with concentrated hydrochloric acid and washed thoroughly with distilled water; to avoid air bubbles formation as the air bubbles will a/ect the equilibrium of CO2 hence the concentration of CO2− 3 in the solution. One tube sample was removed right after mixing the individual solutions, =ltered with 0:22 m =lter and was analysed for water quality. Water quality was determined by measurement of pH, total alkalinity, hardness (by complexometry), and sulfate (by chromatography) using the standard methods of water analysis. Remainders of the tubes were placed in the temperature baths. Water quality was monitored for each sample taken during the run. To ensure constant volume reaction for the kinetic data analysis, for each sample two solution-=lled tubes were removed from the bath and used for the analysis and monitoring during the run. The water quality tests were carried out until equilibrium had been achieved.
4.1. General observations For all the runs when the solutions of CaCl2 ; NaHCO3 and Na2 SO4 were mixed, the mixture immediately turned into a cloudy solution. This indicated the formation of a white colour CaCO3 precipitate and also a very insignificant nucleation or induction period that is reasonable for such a supersaturated solution. Besides, the amount of precipitate collected during =ltering of pure CaCO3 was less compared to the mixture of CaCO3 + CaSO4 . In addition, as the concentration of CaSO4 increased, the amount of precipitate collected increased as well. This was due to the fact that pure CaCO3 is a very adherent scale, where most of the precipitate stuck to the wall of test tube as was observed. The presence of CaSO4 weakened the CaCO3 scale, making the precipitate less tenacious and freely moving in the solution. Therefore, the scale formed from the mixture could be more easily removed than that of the pure CaCO3 scale. This is consistent with previous =ndings of Bramson et al. (1996) in their study of composite fouling of CaCO3 and CaSO4 on a heat transfer surface in turbulent Jow of a falling =lm. 4.2. Scale morphology The CaCO3 scale was a powdery-like precipitate while CaSO4 had a needle shape. The pure CaCO3 crystal had a hexagonal structure, which indicated that the CaCO3 was in the form of calcite and proves that it was the favourable form of calcium carbonate precipitation phase. When CaSO4 was added to the CaCO3 , the needle shape crystals grow on the hexagonal crystal. The pure CaCO3 crystals were more tenacious and compact than the mixed solutions. Also, more crystals were grown in the pure CaCO3 as compared to the mixture. 4.3. E4ect of sulfate ion and temperature on calcium decline Total calcium concentration of the solutions was monitored in order to investigate the co-precipitation e/ects and to determine the solubility constants for salt mixtures. The e/ect of solution composition at given temperatures are shown in Fig. 1. The change in total cal◦ cium concentration for all solutions at 60 C are shown in Fig. 1(a) and shows that the crystallisation process exhibited no induction period; all the curves have a steep decrease in Ca2+ at the initial stage of the experiment before reaching equilibrium. The e/ect of sulfate on precipitation is compared with that of pure CaCO3 solution (BT2) in which Ca2+ concentration decreased from the initial value of 1200 ppm (0:03 M) to the equilibrium concentration of 552 ppm (0:0138 M) in about 500 h indicating
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sulfate concentration increases, the solubility concentration of calcium increases as well and the e/ect of sulfate gradually levels-o/ as its concentration increases. Figs. 1(b) and (c), respectively show the e/ect of co◦ ◦ precipitation at 70 C and 80 C and Table 2 summarizes increases in =nal calcium concentration and the percent◦ age drop in precipitate for all the runs. Again, at 70 C and ◦ 80 C, presence of sulfate increased the equilibrium concentration of calcium and reduced the amount of precipitation but the e/ect levelled-o/ as it approached 0.008– ◦ 0:010 M. The only di/erence was that at 80 C, the amount of precipitate for the solution with 0:008 M of SO2− 4 was slightly (less than 1%) higher than that for the solution with 0:010 M of SO2− 4 . This is very likely due to experimental errors and is negligible. The e/ect of temperature at given concentrations are shown in Fig. 2. As expected for inverse solubility salts, the equilibrium concentration for calcium decreased as the solution temperature was increased irrespective of concentration of SO2− 4 and the solution composition. 4.4. Decline in concentrations of anions and SO2− Concentrations of anions (CO2− 3 4 ) are required to determine the solubility products for CaCO3 and CaSO4 salts in the co-precipitation process. The CO2− 3 were calculated from the distribution of carbonic species in solution based on the total alkalinity and pH of the solution as follows [CO2− 3 ]= 2− Fig. 1. E/ect of composition ( at 0:000 M SO2− 4 , at 0:002 M SO4 , 2− 2− 4 at 0:008 M SO2− , at 0:010 M SO and ∗ at 0:002 M SO 4 4 4 ) at given temperatures.
approximately 54% (648 ppm) had precipitated. When 0:002 M of SO2− 4 was introduced to the CaCO3 solution (BT8), the equilibrium concentration for Ca2+ shifted to 632 ppm indicating a decline of 7% in the amount of precipitate (568 ppm) from 54% to 47%. Further increase in sulfate concentration to 0.008 (BT6) and 0:01 M (BT3) reduced the total amount of calcium precipitated to, respectively, 468 and 460 ppm. This indicates as the
[T:A:] + [H+ ] − [OH− ] ; 2(1 + [H+ ]=2K2 )
[HCO2− 3 ]= [CO2 ] =
(1)
[T:A:] + [H+ ] − [OH− ] ; (1 + 2K2 =[H+ ])
(2)
[T:A:] + [H+ ] − [OH− ] ; K1 =[H+ ](1 + 2K2 =[H+ ])
(3)
2− CT = [HCO− 3 ] + [H2 CO3 ] + [CO3 ]:
(4)
Based on the electroneutrality condition through the proton balance equation, the Total Alkalinity (T.A.) of water with a total carbon species CT is 2− − + [T:A:] = [HCO− 3 ] + 2[CO3 ] + [OH ] − [H ]:
(5)
Table 2 − on Ca++ concentration in solution and precipitation E/ect of SO− 4 ◦
◦
◦
SO2− 4
60 C
(M)
Final Ca++ (ppm)
Precipitate % decrease
Final Ca++ (ppm)
Precipitate % decrease
Final Ca++ (ppm)
Precipitate % decrease
0.000 0.002 0.008 0.010
552 632 732 740
0 7 15 16
520 592 700 716
0 6 15 16
512 552 700 696
0 3 16 15
70 C
80 C
T. H. Chong, R. Sheikholeslami / Chemical Engineering Science 56 (2001) 5391–5400
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Fig. 3. Carbonate ion concentrations in the solutions ( at 2− 2− and at 0:000 M SO2− 4 , ∗ at 0:002 M SO4 , 4 at 0:008 M SO4 2− 0:010 M SO4 ).
Fig. 2. E/ect of temperature ( at given compositions.
◦
◦
◦
at 60 C, at 70 C, and 4 at 80 C)
By combining Eqs. (1) – (5) the concentration of each carbon species can be obtained. The declines in concentrations of anions are represented in Figs. 3 and 4, re◦ 2− spectively for CO2− 3 and SO4 at 60, 70 and 80 C. The 2− initial quantity of CO3 in the solution was unknown because the HCO− 3 in the solution prepared from sodium and CO2 bicarbonate powder will dissociate to CO2− 3
according to the chemistry of carbonic acid which is pH dependent. We cannot obtain this value by using relationships for pure sodium carbonate as the pH of concentration upon solution changes and a/ects CO2− 3 mixing sodium bicarbonate and calcium chloride solutions. So though the exact initial value could not be determined, the instantaneous values were calculated and plots exhibare shown in Fig. 3. In general, the CO2− 3 ited similar trends to those of Ca2+ . By increasing the ions or in other words decreasing the CO2− in SO2− 4 3 had the solution, the equilibrium concentration of CO2− 3 had suppressed been increased. The presence of SO2− 4 ions the crystallisation of CaCO3 , leaving more CO2− 3 in the solution. This indicates that the e/ect of sulfate on CaCO3 solubility is not due to pH e/ects as both Ca2+ and CO2− 3 solubilities are increased in presence of sulfate.
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4.5. Solubility product
Fig. 4. Sulphate ion concentrations in the solutions (4 at at 0:008 M SO2− and at 0:010 M SO2− 0:002 M SO2− 4 , 4 4 ).
The change in SO2− 4 content in the solution with time (Fig. 4) was less pronounced than that of CO2− 3 . The at lowest sulfate concenaverage total change of SO2− 4 tration of 0:002 M was about 30 ppm only. At highest sulfate concentration of 0:01 M, the amount precipitated had was more signi=cant and about 250 ppm of SO2− 4 crystallized with Ca2+ .
Table 3 summarizes the results for solubility products of pure salts and mixed solutions. Also pure salt data determined in this study are compared with the published (Bott, 1995; Marshall & Slusher, 1968) values. The measured values for pure CaCO3 are greater than those of literature (Bott, 1995) and for pure CaSO4 are lower than those in the literature (Marshall & Slusher, 1968). The di/erence can be due to the method of solution preparation and analysis; in this study, all CaCO3 and CaSO4 solutions were obtained by mixing CaCl2 , NaHCO3 and Na2 SO4 solutions while the previous researchers determined the Ksp from pure crystals. In the following discussion, the measured values are used to compare the solubility constants in mixtures with those in pure salts to ensure consistency; however, this would not have any e/ect on the trends obtained even if the literature values were to be used. The results show that the solubility product of CaCO3 in the co-precipitation process is greatly a/ected by the presence of CaSO4 . For example, by introducing 0:002 M ◦ SO2− 4 into the solution at 70 C the Ksp value for CaCO3 −8 increased to 1:943 × 10 , by about 500% from the Ksp (3:00×10−9 ) for pure salt. The Ksp of CaCO3 in mixed so◦ lutions with 0.008 and 0:01 M CaSO4 at 70 C increased, respectively, by 1205% and 1329% from that of pure CaCO3 . The Ksp for CaSO4 was also calculated for all the ◦ runs with sulfate. The Ksp for pure CaSO4 at 70 C was 1:760×10−5 while in a mixed solution with minor amount of sulfate (0:002 M) the Ksp had dropped by about 75% to 4:308 × 10−6 . While for the solutions with higher concentrations of sulfate (0.008 and 0:01 M), the Ksp in mixed solutions were very close (between 1% and 10%) to of those in pure calcium sulfate solution. Fig. 5 shows a graphical representation of the trend between the Ksp ’s at ◦ 60 C for each salt in the mixed solution in comparison to those of pure salts. The same trends were observed at other temperatures. It is very clear that the solubility constant of the dominant calcium carbonate is greatly a/ected by presence of calcium sulfate and the e/ect levels-o/ as the concentration of the non-dominant anion increases.
Table 3 Solubility product for CaCO3 and CaSO4 (CaCO3 Dominant) Ksp for CaCO3 ◦
Ksp for CaSO4 ◦
◦
Solution
60 C
70 C
80 C
CaCO3 (Bott) 0:030 M CaCO3 (measured) 0:028 M CaCO3 + 0:002 M CaSO4 0:022 M CaCO3 + 0:008 M CaSO4 0:020 M CaCO3 + 0:010 M CaSO4 0:030 M CaSO4 (measured) CaSO4 (Marshall and Slusher)
1.821E-09 4.011E-09 1.962E-08 4.000E-08 4.408E-08
1.386E-09 3.000E-09 1.943E-08 3.915E-08 4.288E-08
1.056E-09 1.910E-09 1.715E-08 3.415E-08 3.557E-08
◦
◦
◦
60 C
70 C
80 C
5.051E-06 1.907E-05 2.076E-05 1.930E-05 3.594E-05
4.308E-06 1.795E-05 1.921E-05 1.760E-05 3.244E-05
3.615E-06 1.692E-05 1.870E-05 2.889E-05
T. H. Chong, R. Sheikholeslami / Chemical Engineering Science 56 (2001) 5391–5400
As seen in previous discussion, the equilibrium concentration of both Ca2+ and CO2− 3 ions has increased in presence of sulfate. The e/ect on the non-dominant ion is much less though cannot be neglected at some ratios of non-dominant to dominant ions. This means the Ksp values for the pure salts are not suitable to be used when predicting the equilibrium established in a co-precipitating system. The e/ect of presence of foreign coprecipitating ionic species upon the thermodynamic solubility constant of pure salt could be explained from the thermodynamic aspect. The formation of pure CaCO3 from Ca2+ and CO2− 3 proceeds according to the reaction below Ca2+ + CO2− 3 CaCO3 (s):
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Fig. 5. Comparison of Ksp for both salts in pure and mixed solutions.
(6)
At equilibrium, the Gibbs free energy of reaction (Rr G) is zero. Therefore based on Eq. (7), at equilibrium the thermodynamic solubility constant will be related to the standard molar Gibbs free energy of reaction (Rr G ) according to Eq. (8) a 2+ a 2− Ca CO3 ; (7) Rr G = Rr G + RT ln aCaCO3 − RT ln(Ksp ) = Rr G :
(8)
a is the activity of ions or salt, R is the universal gas constant and T is temperature in Kelvin. By de=nition, Rr G is the di/erence between the total standard Gibbs free energy of formation of products Rf G (products) and the reactants Rf G (reactants). For the formation of CaCO3 , the following equation can be written: Rr G = Rf G (CaCO3 ) − {Rf G (Ca2+ ) +Rf G (CO2− 3 )}:
(9)
In the coprecipitation process, the product di/ers from that of single salt precipitation. This is supported by the scale morphology of salt forms from mixture where the needle-shaped CaSO4 grows in the hexagonal-shaped CaCO3 . For the sake of reference, the product in co-precipitation is denoted by an asterisk (CaCO∗3 ). Since the standard Gibbs free energy of formation of that mixed salt Rf G (CaCO∗3 ) is di/erent from that of the pure salt Rf G (CaCO3 ), hence the thermodynamic equilibrium constant of the coprecipitation is di/erent from that of single salt precipitation. The solubility product of salts for all solutions decreased with increasing temperature, as both salts are of inverse solubility characteristic. For the pure CaCO3 , the Ksp determined from the experimental data was 4:011 × ◦ ◦ 10−9 and decreased by 25% and 52% for 70 C and 80 C, respectively. As mentioned previously, the di/erence in the measured and literature values for pure salts are expected to be due to the e/ect of sample preparations. The solubility constants for both salts were =tted to van’t Ho/ equation (Atkins, 1995) to obtain correlations
Fig. 6. Solubility constants for both salts.
with respect to temperature and also to obtain the heat of precipitation (RHR ) based on the following relationship: d ln(Ksp ) RHR =− : (10) d(1=T ) R The plot of −ln(Ksp ) vs. 1=T should yield a straight line with a slope equal to −RHR =R, where R is the universal gas constant. Fig. 6 shows the plots for both CaCO3 and CaSO4 . The correlations showing the e/ect of temperature are given in Table 4. As seen in Fig. 6(a), the slope of the curves for pure measured and literature (Bott, 1995) values of CaCO3 were very similar though the Ksp values were slightly higher. This indicates comparable heats of precipitation. In addition, Table 4 shows that the heats
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Table 4 Equations of Ksp for CaCO3 and CaSO4 (CaCO3 Dominant) Solution composition CaSO4
CaCO3
0:000 M 0:002 M 0:008 M 0:010 M
0:030 M 0:028 M 0:022 M 0:020 M
Ksp (CaCO3 )
Ksp (CaSO4 )
−ln(Ksp ) = − 4:353 × 103 =T + 32:37 −ln(Ksp ) = − 7:858 × 102 =T + 20:09 −ln(Ksp ) = − 1:195 × 103 =T + 20:35 −ln(Ksp ) = − 1:252 × 103 =T + 20:67
−ln(Ksp ) = − 1:966 × 103 =T + 18:09 −ln(Ksp ) = − 7:036 × 102 =T + 12:98 −ln(Ksp ) = − 6:175 × 102 =T + 12:64
of precipitation for both CaCO3 in solutions with 0.008 and 0:01 M CaSO4 were almost the same. Likewise, the heats of precipitations for CaSO4 in these solutions were almost the same. These were the solutions that exhibited almost the same Ksp values at given temperatures. So, one hypothesis might be that the presence of a co-precipitating salt with a common cation somewhat a/ects the heat of precipitation and therefore the extent of precipitation and this as discussed before can be explained from the standard Gibbs free energy of the substance produced. 4.6. Rate of precipitation for CaCO3 Fig. 2 shows that there was a sharp decline in the concentration of Ca2+ initially right after the solutions were mixed; for example in Run BT8, Ca2+ in the solution dropped to 0:0212 M and 29% of initial Ca2+ precipitated in less than 2 min. The decline in Ca2+ became more gradual as the time progressed. Runs (BT1, BT2, BT7, BT8, BT9 and BT12) with high levels (0.03 and 0:028 M) of CaCO3 showed a rapid decrease in the =rst 50 h before approaching equilibrium. To study CaCO3 precipitation process under the inJuence of CaSO4 and temperature, the rate constant associated with each run was calculated. The initial attempt was to use the integral approach and to =t the data to 2nd order reaction that had been suggested (Nancollas & Reddy, 1971) for pure calcium carbonate. Therefore, according to a second-order reaction (Eq. 12) between Ca2+ and CO2− 3 (Eq. 11), the plot of −log(−d[Ca2+ ]=dt) vs. −log({[Ca2+ ][CO2− 3 ] − Ksp }) should yield a straight line with the slope of 1 and the intercept of −log(kr ). k
r Ca2+ + CO2− 3 → CaCO3 (s);
−
d[Ca2+ ] = kr {[Ca2+ ][CO2− 3 ] − Ksp }: dt
(11) (12)
in Eq. (12) is the concentration product of Ca2+ and Ksp 2− CO3 at equilibrium. The experimental data shown in Fig. 7 (a) indicated that there was a region, known as initial surge growth, where the crystallisation rate could not be predicted by Eq. (12). This initial surge was also noted by Nancollas and Reddy (1971) who thus suggested applying Eq. (12) to the rate of crystallization but
Fig. 7. Assessment of rate of precipitation for calcium carbonate ( ◦ ◦ ◦ at 60 C, at 70 C, and 4 at 80 C).
excluding the initial surge period and through this obtained linear relationship with slope of unity. Therefore, the same approach of excluding the initial surge period was used (as shown in Fig. 7(b)); however, the slopes of the plots were greatly di/erent from unity. This would mean that the crystallisation rate of calcium carbonate in presence of calcium sulfate could not simply be modelled as a second order reaction. This suggests that using the rate equations suggested for a single salt crystallization to crystallization of mixed salts might as well be questionable. Controlled experiments and possibly continuous monitoring of calcium concentration (e.g. by calcium electrode) is necessary to provide more precise measurements for kinetic analysis during the very early stages and hence determining the rate and order of reaction. 5. Concluding remarks The e/ect of water quality is of great importance on induction times and precipitation of calcium carbonate. Also the presence of other cations or anions that may form
T. H. Chong, R. Sheikholeslami / Chemical Engineering Science 56 (2001) 5391–5400
particulate matter plays a signi=cant role in promoting precipitation of a salt solution due to the aGnity that the salt has to precipitate on other particulate matter in preference to, say, the heat transfer surface. The species will tend to do this long before homogeneous nucleation becomes a viable option. Nevertheless work has mainly been in the absence of other precipitating species and correlations have been established where nucleation has been achieved homogeneously. In this study, the e/ect of co-precipitation of calcium carbonate and calcium sulfate in a solution having CaCO3 ◦ as the dominant salt was investigated at 60, 70 and 80 C. In presence of CaSO4 , the CaCO3 scale which is usually very adherent and tenacious loses its strength and becomes less adherent and more freely moving. Also, in solution increases the equilibrium presence of SO2− 4 concentration of both Ca2+ and CO2− 3 and therefore the solubility constant for CaCO3 . The thermodynamic solubility constant of pure salt precipitation is di/erent from that of the co-precipitation due to the fact that the product of co-precipitation di/ers from that of single salt precipitation; based on thermodynamic principles, it is hypothesized that this is related to the change in standard molar Gibbs free energy of reaction Rr G . This is evident from the structure of the product of mixed calcium carbonate and sulfate solution that showed the growth of needle-shaped CaSO4 in the hexagonal-shaped CaCO3 . The solubility constant for CaCO3 increases with increase in sulfate ion but there seems to be a limit to the e/ect of CaSO4 on CaCO3 precipitation. This is evident from the experimental runs with 0.008 and 0:01 M CaSO4 where the e/ect of SO2− had levelled-o/. Presence of 4 CaCO3 had a di/erent e/ect on CaSO4 solubility. In solutions with minute amounts of sulfate (0:002 M), the CaSO4 solubility product in the mixture was much less than that of pure salt. However, further increases in the sulfate concentration to 0:01 M, has increased the CaSO4 solubility constant in the mixture to that of pure salt. Therefore, these suggest that the thermodynamic data for pure salts are not extendable to co-precipitation; also it seems that the e/ect depends on the dominance as well. Experimental measurements are necessary until theoretical studies will address the co-precipitation issue. Also additional tests are necessary to verify the existence of critical composition range where Ksp ’s are una/ected by composition. The solubility product of pure CaCO3 determined experimentally was slightly higher than those reported by Bott (1995) while that of pure CaSO4 was slightly lower than those reported by Marshall and Slusher (1968). This di/erence could be due to the e/ect of sample preparation; in this study, all CaCO3 and CaSO4 solutions were obtained by mixing CaCl2 ; NaHCO3 and Na2 SO4 solutions while the previous researchers determined the Ksp from pure crystals of calcium carbonate and calcium
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sulfate. This suggests that there are two di/erent constants for dissociation and association of salt. Solubility products for both salts were correlated with temperature using van’t Ho/ relationship (Atkins, 1995). Heat of reaction was similar for solutions with 0.008 and 0:01 M of CaSO4 that exhibited similar solubility constants. This again may suggest and reinforce the hypothesis that presence of non-dominant ion a/ects the heat of precipitation. Kinetic data for calcium carbonate did not correspond to a second-order reaction as suggested in the literature (Nancollas & Reddy, 1971). But from the concentration pro=le of the species, it was shown that there was an initial surge followed by an exponential decrease before reaching equilibrium. It is possible that the extent of supersaturation had caused this. It is highly recommended to study the change in [Ca2+ ] and [CO2− 3 ] at the initial stage of crystallisation to examine what is the extent of the surging process. Also the applicability of 2nd order reaction rate should be examined with either less supersaturated solutions or with Ca2+ monitoring with electrochemical method that would permit more accurate measurements during initial periods. References Atkins, P. W. (1995). Physical Chemistry. Oxford: Oxford University Press. Augustin, W., & Bohnet, M. (1995). InJuence of the ratio of free hydrogen ions on crystallisation fouling. Chemical Engineering and Processing, 34, 79–85. Bansal, B., Muller-Steinhagen, H., & Chen, X. D. (1997). E/ect of suspended particles on crystallisation fouling in plate heat exchangers. ASME Journal of Heat Transfer, 119, 568–574. Blount, C. W., & Dickson, F. W. (1973). Gypsum anhydrite equilibria in systems CaSO4 -H2 O and CaCO3 -NaCl-H2 O. The American Minerologist, 58, 323–331. Bott, T. R. (1995). Fouling of heat exchangers. Amsterdam: Elsevier. Bramson, D., Hasson, D., & Semiat, R. (1996). The roles of gas bubbling, wall crystallization, and particulate deposition in CaSO4 scale formation. Desalination, 100, 105–113. EPRI, 1982. (Ed.) Design and operating guidelines manual for cooling water treatment: treatment of recirculating water. Electric Power Research Institute, Palo Alto, California. Hardie, L. A. (1967). The gypsum-anhydrite equilibrium at one atmosphere pressure. The American Mineralogist, Vol. 52, p. 171–200. Hasson, D. (1981). Precipitation fouling—A review. In E. F. C. Somerscales, J. G. Knudsen (Eds.), Fouling of heat transfer equipment, (p. 527–568). New York: Hemisphere Publishing Corporation. Hasson, D. (1999). Progress in precipitation fouling research, A review. In R. Bott (Ed.), Proceedings of engineering foundation conference, understanding heat exchanger fouling and its mitigation (p. 67–89). New York: Begell House. Hasson, D., & Karmon, M. (1984). Novel process for lining water mains by controlled calcite deposition. Corrosion Prevention and Control, 31, 9–17. Hasson, D., & Zahavi, J. (1970). Mechanism of calcium sulfate scale deposition on heat-transfer surfaces. Industrial and Engineering Chemistry Fundamentals, 9(1), 1–10.
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Kemmer, F. N. (1988). The nalco water handbook. New York: McGraw-Hill Book Co. Lepley, R. H. (1984). Calcium compounds–calcium carbonate. In M. Grayson, D. Ekroth (Eds.), Kirk–Othmer Encyclopedia of Chemical Technology (3 edn, vol. 4, pp. 427– 432). New York: John Wiley & Sons. Liu, S. T., & Nancollas, G. H. (1970). The kinetics of crystal growth of calcium sulfate dihydrate. Journal of Crystal Growth, 6, 281–289. Marshall, W. L., & Slusher, R. (1968). Aqueous systems at high temperature. Journal of Chemical and Engineering Data, 13(1), 83–93. Morse, R. W., & Knudsen, J. G. (1977). E/ect of alkalinity on the scaling of stimulated cooling tower water. Canadian Journal of Chemical Engineering, 55, 272–278. Mullin, J. W. (1972). Crystallization. London: Butterworths. Mullin, J. W. (1993). Crystallization. Oxford: ButterworthsHeinemann. Nancollas, G. H., Eralp, A. E., & Gill, J. S. (1978). Calcium sulfate scale formation: A kinetic approach. Society of Petroleum Engineering Journal, 18, 133–138. Nancollas, G. H., & Reddy, M. N. (1971). The crystallization of calcium carbonate II. Calcite growth mechanism. Journal of Colloid Interface Science, 37, 824–830. Nordstrom, D. K. Plummer, L. N., Langmuir, D., Busenberg, E., May, H. M., Jones, B. F., & Parkhurst, D. L. (1990). Revised chemical equilibrium data from major mineral reactions and their limitations. In D. C. Melchior, R. L. Bassett (Eds.), ACS Symposium Series 416–Chemical modeling of aqueous
systems II (p. 398– 413). Washington, DC: American Chemical Society. Partridge, E. P., & White, A. H. (1929). The solubility of calcium ◦ sulfate from 0 to 200 C. Journal of American Chemical Society, 51, 360–370. Plummer, N. L., & Busenberg, E. (1982). The solubilities of calcite, aragonite and vaterite in CO2 -H2 O solutions between 0 and 90◦ C, and an evaluation of the aqueous model for the system CaCO3 -CO2 -H2 O. Geochimica Cosmochimica Acta, 46, 1011– 1040. Reddy, M. M., & Nancollas, G. H. (1971). The crystallization calcium carbonate, I. Isotopic exchange and kinetics. Journal of Colloid Interface Science, 36, 166–172. Reeder, R. J. (1990). Carbonates, mineralogy and chemistry. Washington DC: Mineralogy Society of America. Sudmalis, M., & Sheikholeslami, R. (2000). Precipitation and co-precipitation of CaCO3 and CaSO4 . Canadian Journal of Chemical Engineering, 78, 21–31. Wirsching, F., & Gipswerke, G. K. W. (1985). Calcium Sulfate. In W. Gerhartz, Y. S. Yamamoto, F. T. Campbell, R. Pfe/erkorn, J. F. Rounsaville (Eds.) Ullmann’s Encyclopedia of Industrial Chemistry (5 edn, vol. 4, p. 556 –558). Weinheim: VCH Verlagsgesellschaft. Zhang, J., & Nancollas, G. H. (1992). InJuence of calcium=sulfate molar ratio on the growth rate of calcium sulfate dihydrate at constant supersaturation. Journal of Crystal Growth, 118, 287– 294.
www.elsevier.com/locate/ces
Thermodynamics and kinetics for mixed calcium carbonate and calcium sulfate precipitation T. H. Chong, R. Sheikholeslami ∗ School of Chemical Engineering and Industrial Chemistry, The University of New South Wales, Sydney, 2052, Australia Received 30 August 2000; received in revised form 23 May 2001; accepted 25 May 2001
Abstract ◦
The e/ects of CaSO4 on CaCO3 precipitation were studied in the batch tests at 60, 70 and 80 C in mixtures having calcium carbonate as the dominant salt and at a given total initial calcium concentration of 0:03 M with sulfate concentration ranging from 0 to 0:01 M. Solubility products and rate constants were determined from thermodynamic and kinetic studies and the results indicated that even minute amounts of calcium sulfate a/ect the thermodynamics, kinetics and the scale structure and no longer the solubility data and rate constants for the pure salt were applicable. Presence of CaSO4 from 0.002 to 0:01 M increased the calcium carbonate solubility product more than an order of magnitude. The e/ect of salt mixture on the solubility constant of non-dominant salt (calcium sulfate) was reverse as calcium sulfate solubility increased to its pure value with increases in its molar ratio. In addition, the rate equation suggested in the literature (Nancollas and Reddy, J. Colloid Interface Sci. 37 (1971) 824; Reddy and Nancollas, J. Colloid Interface Sci. 36 (1971) 166) for pure salt was not applicable to the experimental data. The general observations indicated that the presence of CaSO4 had weakened the CaCO3 scale which is usually very adherent. The experimental results did take into account the e/ect of solution ionic strength, however, they suggest that data for pure salt precipitation seem not to be extendable to co-precipitation. ? 2001 Elsevier Science Ltd. All rights reserved. Keywords: Fouling; Precipitation; Co-precipitation; Calcium sulfate; Calcium carbonate; Composite fouling; Thermodynamics; Kinetics
1. Introduction Fouling is the accumulation of undesired solid materials at the phase interfaces. Build-up of fouling =lm leads to an increase in resistance and deteriorates the performance of process equipment such as membranes and heat exchangers and is costing industries billions of dollars annually. One of the major fouling phenomena encountered in the aqueous systems is scale formation due to precipitation of salts present in the water. Lots of metals and anions exist naturally in the water; among them, CaCO3 and CaSO4 are major fouling contributors. Both these salts have inverse solubility behaviour where the solubility decreases with increasing temperature and salts ∗
Corresponding author. Tel.: +61-2-9385-4343; fax: +61-29385-5966. E-mail address: [email protected] (R. Sheikholeslami).
precipitate on heat exchange surfaces when the solution becomes supersaturated. Crystallization has been studied for many years as shown in the two monographs by Mullin (1972, 1993). An immense body of information is available on thermodynamics and kinetics of crystallization of calcium carbonate (Augustin & Bohnet, 1995; Nancollas & Reddy, 1971; Plummer & Busenberg, 1982) and calcium sulfate (Liu & Nancollas, 1970; Nancollas, Eralp, & Gill, 1978; Zhang & Nancollas, 1992). The research in the area of crystallization fouling, including the dynamic e/ects, has also been extensive as covered in two comprehensive reviews (Hasson, 1981, 1999). However, due to the complexity of fouling process the research in this area usually involves fouling by a single precipitant. The area to which not much attention has been paid to is the interactive e/ect of co-precipitating salts with or without common ions. These include solubility e/ects, rate data, crystal structure and strength, inhibitor e/ects and also dynamic
0009-2509/01/$ - see front matter ? 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 0 1 ) 0 0 2 3 7 - 8
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e/ects. This is important for two reasons. One is that the mechanism of fouling might be di/erent for di/erent salts as it was shown to be di/erent for CaCO3 and CaSO4 (Bansal, Muller-Steinhagen, & Chen, 1997). The second is the fact that co-existence of salts might actually a/ect the thermodynamic and kinetic behaviour of each salt and therefore, the single salt data might not be applicable to the condition when the salts co-exist. The reviewed literatures on crystallization (Hasson, 1981, 1999) indicate that very little study has been devoted to the study of the co-precipitation phenomenon. There has been some qualitative research (Bramson, Hasson, & Semiat, 1996; Hasson & Karmon, 1984) on the strength and tenacity of co-precipitated calcium carbonate and sulfate. They found that a major factor a/ecting scale tenacity was the purity of the deposit. For calcium sulfate, the higher the impurities, the greater the strength of the scale; however, with calcium carbonate, adhesive strength was seen to decrease with increasing impurities. The most diGcult deposit to remove from heat transfer surfaces was calcium carbonate scale with impurities measuring less than 5% by mass; pure calcium sulfate deposits were found to be far less adherent than deposits containing co-precipitated calcium carbonate. The co-precipitated calcium carbonate seems to act as bonding cement, enhancing considerably the strength of calcium sulfate scale layer. In an earlier study, Morse and Knudsen (1977) also reported that for aggressive scale, the main constituent was calcium carbonate. In our recent work (Sudmalis & Sheikholeslami, 2000) on co-precipitation of CaCO3 and CaSO4 when they exist in comparable ratios, it has been qualitatively shown that co-precipitation a/ects thermodynamics and kinetics of precipitation as well as the scale structure. The objective of this study is to investigate and quantify co-precipitation process of CaCO3 and CaSO4 when CaCO3 is the predominant component at a constant total calcium concentration and to determine solubility constants, assess the reaction rate constants and therefore examine the applicability of data and mechanisms for pure precipitation to co-precipitation. 2. Background Understanding and developing kinetic and rate correlations and models for co-precipitation are built on the theories of single salt precipitation and hence crystallization theory and properties of CaCO3 and CaSO4 are brieJy discussed here. In general, crystallization is considered to be comprised of nucleation, growth and re-crystallization steps. There are various mechanisms for each step and a great degree of overlap among these steps (Sudmalis & Sheikholeslami, 2000). For crystallization to occur the solution has
to be supersaturated; however, supersaturation by itself is not suGcient to induce crystallization. There is a requirement for centers of crystallization that can take various forms such as seeds, embryos or foreign matter present in the solution to induce nucleation. Growth and re-crystallization follow the nucleation step. Usually, nucleation is the controlling step; once the critical nuclei are formed, the crystallization proceeds. A given salt may have di/erent crystal structures of which some might be more stable or more readily formed. Calcium carbonate occurs naturally in three crystal structures of calcite, aragonite and vaterite. Calcite is the most stable form of calcium carbonate. The aragonite polymorph is metastable and irreversibly changes to ◦ calcite when heated in dry air to about 400 C. Vaterite is metastable and least prevalent and transforms to calcite and aragonite under geological conditions (Reeder, 1990). The crystal forms of calcite are hexagonal whereas aragonite is in the orthorhombic system. Physical properties of the two more prevalent crystal polymorphs are given by Lepley (1984); corresponding values for vaterite are not available. The solubility product for calcium carbonate and the dissociation constants for carbonic acids are given by Bott (1995). Saturation solubility of calcium carbonate depends on the CO2 content and solution pH; Kemmer (1988) provides data showing the distribution of CO2 related ions and CO2 gas in solution as a function of pH. Calcium sulfate can exist in six di/erent solid phases (3 anhydrites, 2 hemihydrates and a dihydrate). Gypsum (CaSO4 :2H2 O), hemihydrates (CaSO4 :1=2H2 O), and anhydrite III and anhydrite II can exist at room tem◦ peratures whereas anhydrite I only exists above 1180 C. The physical properties of all polymorphs are given by Wirsching and Gipswerke (1985). Much research has been performed in an attempt to analyse the mechanism and determine the form of calcium sulfate at di/erent temperatures. Partridge and White (1929) found that gypsum is the usual precipitating phase in the range ◦ of 40 –98 C while anhydrite and hemihydrate are the ◦ species likely to precipitate above 98 C. Some others (Blount & Dickson, 1973; Hardie, 1967) indicated the transition temperature between anhydrite and gypsum to ◦ be in the range of 56 –58 C. This is incongruent with the results of Partridge and White (1929); however, all the works (Blount & Dickson, 1973; Hardie, 1967; Partridge & White, 1929) seemed to indicate that in the range of operation of majority of industrial heat exchangers, gypsum is the dominant phase. Furthermore, Hasson and Zahavi (1970) proposed a correlation for CaSO4 nucleation times and reported that nucleation of anhydrite is an extremely slow process in comparison to that of gypsum. This also justi=es considering gypsum as the dominant phase. Correlations for solubility products for di/erent forms of calcium sulfate, which may be adjusted
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4. Results and discussions
Table 1 Summary of batch tests conditions ◦
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Run
T ( C)
CaCO3 (M)
CaSO4 (M)
BT1 BT2 BT3 BT4 BT5 BT6 BT7 BT8 BT9 BT10 BT11 BT12 BM1 BM2
70 60 60 70 70 60 70 60 80 80 80 80 60 70
0.030 0.030 0.020 0.020 0.022 0.022 0.028 0.028 0.030 0.020 0.022 0.028 0.000 0.000
0.000 0.000 0.010 0.010 0.008 0.008 0.002 0.002 0.000 0.010 0.008 0.002 0.030 0.030
for the appropriate temperature, are available in the literature (EPRI, 1982; Marshall & Slusher, 1968; Nordstrom et al., 1990). 3. Experimental techniques Batch tests were carried out with model solutions with total calcium content of 0:03 M and sulfate concentrations ranging from 0 to 0:01 M at temperatures of 60, 70 and ◦ 80 C. Table 1 lists the chemical composition of model solutions used in experimentation. The supersaturated solutions of calcium sulfate (CaSO4 ) and calcium carbonate (CaCO3 ) were prepared by adding equimolar amounts of Na2 SO4 and CaCl2 , and CaCl2 and NaHCO3 , respectively. The solutions were prepared with analytical grade chemicals and with micro-=ltered (with 0:22 m Millipore =lter) distilled water. Solution pH was measured before mixing, then the mixture was carefully transferred to a series of 75 ml test tubes; which had been scrubbed, rinsed with concentrated hydrochloric acid and washed thoroughly with distilled water; to avoid air bubbles formation as the air bubbles will a/ect the equilibrium of CO2 hence the concentration of CO2− 3 in the solution. One tube sample was removed right after mixing the individual solutions, =ltered with 0:22 m =lter and was analysed for water quality. Water quality was determined by measurement of pH, total alkalinity, hardness (by complexometry), and sulfate (by chromatography) using the standard methods of water analysis. Remainders of the tubes were placed in the temperature baths. Water quality was monitored for each sample taken during the run. To ensure constant volume reaction for the kinetic data analysis, for each sample two solution-=lled tubes were removed from the bath and used for the analysis and monitoring during the run. The water quality tests were carried out until equilibrium had been achieved.
4.1. General observations For all the runs when the solutions of CaCl2 ; NaHCO3 and Na2 SO4 were mixed, the mixture immediately turned into a cloudy solution. This indicated the formation of a white colour CaCO3 precipitate and also a very insignificant nucleation or induction period that is reasonable for such a supersaturated solution. Besides, the amount of precipitate collected during =ltering of pure CaCO3 was less compared to the mixture of CaCO3 + CaSO4 . In addition, as the concentration of CaSO4 increased, the amount of precipitate collected increased as well. This was due to the fact that pure CaCO3 is a very adherent scale, where most of the precipitate stuck to the wall of test tube as was observed. The presence of CaSO4 weakened the CaCO3 scale, making the precipitate less tenacious and freely moving in the solution. Therefore, the scale formed from the mixture could be more easily removed than that of the pure CaCO3 scale. This is consistent with previous =ndings of Bramson et al. (1996) in their study of composite fouling of CaCO3 and CaSO4 on a heat transfer surface in turbulent Jow of a falling =lm. 4.2. Scale morphology The CaCO3 scale was a powdery-like precipitate while CaSO4 had a needle shape. The pure CaCO3 crystal had a hexagonal structure, which indicated that the CaCO3 was in the form of calcite and proves that it was the favourable form of calcium carbonate precipitation phase. When CaSO4 was added to the CaCO3 , the needle shape crystals grow on the hexagonal crystal. The pure CaCO3 crystals were more tenacious and compact than the mixed solutions. Also, more crystals were grown in the pure CaCO3 as compared to the mixture. 4.3. E4ect of sulfate ion and temperature on calcium decline Total calcium concentration of the solutions was monitored in order to investigate the co-precipitation e/ects and to determine the solubility constants for salt mixtures. The e/ect of solution composition at given temperatures are shown in Fig. 1. The change in total cal◦ cium concentration for all solutions at 60 C are shown in Fig. 1(a) and shows that the crystallisation process exhibited no induction period; all the curves have a steep decrease in Ca2+ at the initial stage of the experiment before reaching equilibrium. The e/ect of sulfate on precipitation is compared with that of pure CaCO3 solution (BT2) in which Ca2+ concentration decreased from the initial value of 1200 ppm (0:03 M) to the equilibrium concentration of 552 ppm (0:0138 M) in about 500 h indicating
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sulfate concentration increases, the solubility concentration of calcium increases as well and the e/ect of sulfate gradually levels-o/ as its concentration increases. Figs. 1(b) and (c), respectively show the e/ect of co◦ ◦ precipitation at 70 C and 80 C and Table 2 summarizes increases in =nal calcium concentration and the percent◦ age drop in precipitate for all the runs. Again, at 70 C and ◦ 80 C, presence of sulfate increased the equilibrium concentration of calcium and reduced the amount of precipitation but the e/ect levelled-o/ as it approached 0.008– ◦ 0:010 M. The only di/erence was that at 80 C, the amount of precipitate for the solution with 0:008 M of SO2− 4 was slightly (less than 1%) higher than that for the solution with 0:010 M of SO2− 4 . This is very likely due to experimental errors and is negligible. The e/ect of temperature at given concentrations are shown in Fig. 2. As expected for inverse solubility salts, the equilibrium concentration for calcium decreased as the solution temperature was increased irrespective of concentration of SO2− 4 and the solution composition. 4.4. Decline in concentrations of anions and SO2− Concentrations of anions (CO2− 3 4 ) are required to determine the solubility products for CaCO3 and CaSO4 salts in the co-precipitation process. The CO2− 3 were calculated from the distribution of carbonic species in solution based on the total alkalinity and pH of the solution as follows [CO2− 3 ]= 2− Fig. 1. E/ect of composition ( at 0:000 M SO2− 4 , at 0:002 M SO4 , 2− 2− 4 at 0:008 M SO2− , at 0:010 M SO and ∗ at 0:002 M SO 4 4 4 ) at given temperatures.
approximately 54% (648 ppm) had precipitated. When 0:002 M of SO2− 4 was introduced to the CaCO3 solution (BT8), the equilibrium concentration for Ca2+ shifted to 632 ppm indicating a decline of 7% in the amount of precipitate (568 ppm) from 54% to 47%. Further increase in sulfate concentration to 0.008 (BT6) and 0:01 M (BT3) reduced the total amount of calcium precipitated to, respectively, 468 and 460 ppm. This indicates as the
[T:A:] + [H+ ] − [OH− ] ; 2(1 + [H+ ]=2K2 )
[HCO2− 3 ]= [CO2 ] =
(1)
[T:A:] + [H+ ] − [OH− ] ; (1 + 2K2 =[H+ ])
(2)
[T:A:] + [H+ ] − [OH− ] ; K1 =[H+ ](1 + 2K2 =[H+ ])
(3)
2− CT = [HCO− 3 ] + [H2 CO3 ] + [CO3 ]:
(4)
Based on the electroneutrality condition through the proton balance equation, the Total Alkalinity (T.A.) of water with a total carbon species CT is 2− − + [T:A:] = [HCO− 3 ] + 2[CO3 ] + [OH ] − [H ]:
(5)
Table 2 − on Ca++ concentration in solution and precipitation E/ect of SO− 4 ◦
◦
◦
SO2− 4
60 C
(M)
Final Ca++ (ppm)
Precipitate % decrease
Final Ca++ (ppm)
Precipitate % decrease
Final Ca++ (ppm)
Precipitate % decrease
0.000 0.002 0.008 0.010
552 632 732 740
0 7 15 16
520 592 700 716
0 6 15 16
512 552 700 696
0 3 16 15
70 C
80 C
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5395
Fig. 3. Carbonate ion concentrations in the solutions ( at 2− 2− and at 0:000 M SO2− 4 , ∗ at 0:002 M SO4 , 4 at 0:008 M SO4 2− 0:010 M SO4 ).
Fig. 2. E/ect of temperature ( at given compositions.
◦
◦
◦
at 60 C, at 70 C, and 4 at 80 C)
By combining Eqs. (1) – (5) the concentration of each carbon species can be obtained. The declines in concentrations of anions are represented in Figs. 3 and 4, re◦ 2− spectively for CO2− 3 and SO4 at 60, 70 and 80 C. The 2− initial quantity of CO3 in the solution was unknown because the HCO− 3 in the solution prepared from sodium and CO2 bicarbonate powder will dissociate to CO2− 3
according to the chemistry of carbonic acid which is pH dependent. We cannot obtain this value by using relationships for pure sodium carbonate as the pH of concentration upon solution changes and a/ects CO2− 3 mixing sodium bicarbonate and calcium chloride solutions. So though the exact initial value could not be determined, the instantaneous values were calculated and plots exhibare shown in Fig. 3. In general, the CO2− 3 ited similar trends to those of Ca2+ . By increasing the ions or in other words decreasing the CO2− in SO2− 4 3 had the solution, the equilibrium concentration of CO2− 3 had suppressed been increased. The presence of SO2− 4 ions the crystallisation of CaCO3 , leaving more CO2− 3 in the solution. This indicates that the e/ect of sulfate on CaCO3 solubility is not due to pH e/ects as both Ca2+ and CO2− 3 solubilities are increased in presence of sulfate.
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4.5. Solubility product
Fig. 4. Sulphate ion concentrations in the solutions (4 at at 0:008 M SO2− and at 0:010 M SO2− 0:002 M SO2− 4 , 4 4 ).
The change in SO2− 4 content in the solution with time (Fig. 4) was less pronounced than that of CO2− 3 . The at lowest sulfate concenaverage total change of SO2− 4 tration of 0:002 M was about 30 ppm only. At highest sulfate concentration of 0:01 M, the amount precipitated had was more signi=cant and about 250 ppm of SO2− 4 crystallized with Ca2+ .
Table 3 summarizes the results for solubility products of pure salts and mixed solutions. Also pure salt data determined in this study are compared with the published (Bott, 1995; Marshall & Slusher, 1968) values. The measured values for pure CaCO3 are greater than those of literature (Bott, 1995) and for pure CaSO4 are lower than those in the literature (Marshall & Slusher, 1968). The di/erence can be due to the method of solution preparation and analysis; in this study, all CaCO3 and CaSO4 solutions were obtained by mixing CaCl2 , NaHCO3 and Na2 SO4 solutions while the previous researchers determined the Ksp from pure crystals. In the following discussion, the measured values are used to compare the solubility constants in mixtures with those in pure salts to ensure consistency; however, this would not have any e/ect on the trends obtained even if the literature values were to be used. The results show that the solubility product of CaCO3 in the co-precipitation process is greatly a/ected by the presence of CaSO4 . For example, by introducing 0:002 M ◦ SO2− 4 into the solution at 70 C the Ksp value for CaCO3 −8 increased to 1:943 × 10 , by about 500% from the Ksp (3:00×10−9 ) for pure salt. The Ksp of CaCO3 in mixed so◦ lutions with 0.008 and 0:01 M CaSO4 at 70 C increased, respectively, by 1205% and 1329% from that of pure CaCO3 . The Ksp for CaSO4 was also calculated for all the ◦ runs with sulfate. The Ksp for pure CaSO4 at 70 C was 1:760×10−5 while in a mixed solution with minor amount of sulfate (0:002 M) the Ksp had dropped by about 75% to 4:308 × 10−6 . While for the solutions with higher concentrations of sulfate (0.008 and 0:01 M), the Ksp in mixed solutions were very close (between 1% and 10%) to of those in pure calcium sulfate solution. Fig. 5 shows a graphical representation of the trend between the Ksp ’s at ◦ 60 C for each salt in the mixed solution in comparison to those of pure salts. The same trends were observed at other temperatures. It is very clear that the solubility constant of the dominant calcium carbonate is greatly a/ected by presence of calcium sulfate and the e/ect levels-o/ as the concentration of the non-dominant anion increases.
Table 3 Solubility product for CaCO3 and CaSO4 (CaCO3 Dominant) Ksp for CaCO3 ◦
Ksp for CaSO4 ◦
◦
Solution
60 C
70 C
80 C
CaCO3 (Bott) 0:030 M CaCO3 (measured) 0:028 M CaCO3 + 0:002 M CaSO4 0:022 M CaCO3 + 0:008 M CaSO4 0:020 M CaCO3 + 0:010 M CaSO4 0:030 M CaSO4 (measured) CaSO4 (Marshall and Slusher)
1.821E-09 4.011E-09 1.962E-08 4.000E-08 4.408E-08
1.386E-09 3.000E-09 1.943E-08 3.915E-08 4.288E-08
1.056E-09 1.910E-09 1.715E-08 3.415E-08 3.557E-08
◦
◦
◦
60 C
70 C
80 C
5.051E-06 1.907E-05 2.076E-05 1.930E-05 3.594E-05
4.308E-06 1.795E-05 1.921E-05 1.760E-05 3.244E-05
3.615E-06 1.692E-05 1.870E-05 2.889E-05
T. H. Chong, R. Sheikholeslami / Chemical Engineering Science 56 (2001) 5391–5400
As seen in previous discussion, the equilibrium concentration of both Ca2+ and CO2− 3 ions has increased in presence of sulfate. The e/ect on the non-dominant ion is much less though cannot be neglected at some ratios of non-dominant to dominant ions. This means the Ksp values for the pure salts are not suitable to be used when predicting the equilibrium established in a co-precipitating system. The e/ect of presence of foreign coprecipitating ionic species upon the thermodynamic solubility constant of pure salt could be explained from the thermodynamic aspect. The formation of pure CaCO3 from Ca2+ and CO2− 3 proceeds according to the reaction below Ca2+ + CO2− 3 CaCO3 (s):
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Fig. 5. Comparison of Ksp for both salts in pure and mixed solutions.
(6)
At equilibrium, the Gibbs free energy of reaction (Rr G) is zero. Therefore based on Eq. (7), at equilibrium the thermodynamic solubility constant will be related to the standard molar Gibbs free energy of reaction (Rr G ) according to Eq. (8) a 2+ a 2− Ca CO3 ; (7) Rr G = Rr G + RT ln aCaCO3 − RT ln(Ksp ) = Rr G :
(8)
a is the activity of ions or salt, R is the universal gas constant and T is temperature in Kelvin. By de=nition, Rr G is the di/erence between the total standard Gibbs free energy of formation of products Rf G (products) and the reactants Rf G (reactants). For the formation of CaCO3 , the following equation can be written: Rr G = Rf G (CaCO3 ) − {Rf G (Ca2+ ) +Rf G (CO2− 3 )}:
(9)
In the coprecipitation process, the product di/ers from that of single salt precipitation. This is supported by the scale morphology of salt forms from mixture where the needle-shaped CaSO4 grows in the hexagonal-shaped CaCO3 . For the sake of reference, the product in co-precipitation is denoted by an asterisk (CaCO∗3 ). Since the standard Gibbs free energy of formation of that mixed salt Rf G (CaCO∗3 ) is di/erent from that of the pure salt Rf G (CaCO3 ), hence the thermodynamic equilibrium constant of the coprecipitation is di/erent from that of single salt precipitation. The solubility product of salts for all solutions decreased with increasing temperature, as both salts are of inverse solubility characteristic. For the pure CaCO3 , the Ksp determined from the experimental data was 4:011 × ◦ ◦ 10−9 and decreased by 25% and 52% for 70 C and 80 C, respectively. As mentioned previously, the di/erence in the measured and literature values for pure salts are expected to be due to the e/ect of sample preparations. The solubility constants for both salts were =tted to van’t Ho/ equation (Atkins, 1995) to obtain correlations
Fig. 6. Solubility constants for both salts.
with respect to temperature and also to obtain the heat of precipitation (RHR ) based on the following relationship: d ln(Ksp ) RHR =− : (10) d(1=T ) R The plot of −ln(Ksp ) vs. 1=T should yield a straight line with a slope equal to −RHR =R, where R is the universal gas constant. Fig. 6 shows the plots for both CaCO3 and CaSO4 . The correlations showing the e/ect of temperature are given in Table 4. As seen in Fig. 6(a), the slope of the curves for pure measured and literature (Bott, 1995) values of CaCO3 were very similar though the Ksp values were slightly higher. This indicates comparable heats of precipitation. In addition, Table 4 shows that the heats
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T. H. Chong, R. Sheikholeslami / Chemical Engineering Science 56 (2001) 5391–5400
Table 4 Equations of Ksp for CaCO3 and CaSO4 (CaCO3 Dominant) Solution composition CaSO4
CaCO3
0:000 M 0:002 M 0:008 M 0:010 M
0:030 M 0:028 M 0:022 M 0:020 M
Ksp (CaCO3 )
Ksp (CaSO4 )
−ln(Ksp ) = − 4:353 × 103 =T + 32:37 −ln(Ksp ) = − 7:858 × 102 =T + 20:09 −ln(Ksp ) = − 1:195 × 103 =T + 20:35 −ln(Ksp ) = − 1:252 × 103 =T + 20:67
−ln(Ksp ) = − 1:966 × 103 =T + 18:09 −ln(Ksp ) = − 7:036 × 102 =T + 12:98 −ln(Ksp ) = − 6:175 × 102 =T + 12:64
of precipitation for both CaCO3 in solutions with 0.008 and 0:01 M CaSO4 were almost the same. Likewise, the heats of precipitations for CaSO4 in these solutions were almost the same. These were the solutions that exhibited almost the same Ksp values at given temperatures. So, one hypothesis might be that the presence of a co-precipitating salt with a common cation somewhat a/ects the heat of precipitation and therefore the extent of precipitation and this as discussed before can be explained from the standard Gibbs free energy of the substance produced. 4.6. Rate of precipitation for CaCO3 Fig. 2 shows that there was a sharp decline in the concentration of Ca2+ initially right after the solutions were mixed; for example in Run BT8, Ca2+ in the solution dropped to 0:0212 M and 29% of initial Ca2+ precipitated in less than 2 min. The decline in Ca2+ became more gradual as the time progressed. Runs (BT1, BT2, BT7, BT8, BT9 and BT12) with high levels (0.03 and 0:028 M) of CaCO3 showed a rapid decrease in the =rst 50 h before approaching equilibrium. To study CaCO3 precipitation process under the inJuence of CaSO4 and temperature, the rate constant associated with each run was calculated. The initial attempt was to use the integral approach and to =t the data to 2nd order reaction that had been suggested (Nancollas & Reddy, 1971) for pure calcium carbonate. Therefore, according to a second-order reaction (Eq. 12) between Ca2+ and CO2− 3 (Eq. 11), the plot of −log(−d[Ca2+ ]=dt) vs. −log({[Ca2+ ][CO2− 3 ] − Ksp }) should yield a straight line with the slope of 1 and the intercept of −log(kr ). k
r Ca2+ + CO2− 3 → CaCO3 (s);
−
d[Ca2+ ] = kr {[Ca2+ ][CO2− 3 ] − Ksp }: dt
(11) (12)
in Eq. (12) is the concentration product of Ca2+ and Ksp 2− CO3 at equilibrium. The experimental data shown in Fig. 7 (a) indicated that there was a region, known as initial surge growth, where the crystallisation rate could not be predicted by Eq. (12). This initial surge was also noted by Nancollas and Reddy (1971) who thus suggested applying Eq. (12) to the rate of crystallization but
Fig. 7. Assessment of rate of precipitation for calcium carbonate ( ◦ ◦ ◦ at 60 C, at 70 C, and 4 at 80 C).
excluding the initial surge period and through this obtained linear relationship with slope of unity. Therefore, the same approach of excluding the initial surge period was used (as shown in Fig. 7(b)); however, the slopes of the plots were greatly di/erent from unity. This would mean that the crystallisation rate of calcium carbonate in presence of calcium sulfate could not simply be modelled as a second order reaction. This suggests that using the rate equations suggested for a single salt crystallization to crystallization of mixed salts might as well be questionable. Controlled experiments and possibly continuous monitoring of calcium concentration (e.g. by calcium electrode) is necessary to provide more precise measurements for kinetic analysis during the very early stages and hence determining the rate and order of reaction. 5. Concluding remarks The e/ect of water quality is of great importance on induction times and precipitation of calcium carbonate. Also the presence of other cations or anions that may form
T. H. Chong, R. Sheikholeslami / Chemical Engineering Science 56 (2001) 5391–5400
particulate matter plays a signi=cant role in promoting precipitation of a salt solution due to the aGnity that the salt has to precipitate on other particulate matter in preference to, say, the heat transfer surface. The species will tend to do this long before homogeneous nucleation becomes a viable option. Nevertheless work has mainly been in the absence of other precipitating species and correlations have been established where nucleation has been achieved homogeneously. In this study, the e/ect of co-precipitation of calcium carbonate and calcium sulfate in a solution having CaCO3 ◦ as the dominant salt was investigated at 60, 70 and 80 C. In presence of CaSO4 , the CaCO3 scale which is usually very adherent and tenacious loses its strength and becomes less adherent and more freely moving. Also, in solution increases the equilibrium presence of SO2− 4 concentration of both Ca2+ and CO2− 3 and therefore the solubility constant for CaCO3 . The thermodynamic solubility constant of pure salt precipitation is di/erent from that of the co-precipitation due to the fact that the product of co-precipitation di/ers from that of single salt precipitation; based on thermodynamic principles, it is hypothesized that this is related to the change in standard molar Gibbs free energy of reaction Rr G . This is evident from the structure of the product of mixed calcium carbonate and sulfate solution that showed the growth of needle-shaped CaSO4 in the hexagonal-shaped CaCO3 . The solubility constant for CaCO3 increases with increase in sulfate ion but there seems to be a limit to the e/ect of CaSO4 on CaCO3 precipitation. This is evident from the experimental runs with 0.008 and 0:01 M CaSO4 where the e/ect of SO2− had levelled-o/. Presence of 4 CaCO3 had a di/erent e/ect on CaSO4 solubility. In solutions with minute amounts of sulfate (0:002 M), the CaSO4 solubility product in the mixture was much less than that of pure salt. However, further increases in the sulfate concentration to 0:01 M, has increased the CaSO4 solubility constant in the mixture to that of pure salt. Therefore, these suggest that the thermodynamic data for pure salts are not extendable to co-precipitation; also it seems that the e/ect depends on the dominance as well. Experimental measurements are necessary until theoretical studies will address the co-precipitation issue. Also additional tests are necessary to verify the existence of critical composition range where Ksp ’s are una/ected by composition. The solubility product of pure CaCO3 determined experimentally was slightly higher than those reported by Bott (1995) while that of pure CaSO4 was slightly lower than those reported by Marshall and Slusher (1968). This di/erence could be due to the e/ect of sample preparation; in this study, all CaCO3 and CaSO4 solutions were obtained by mixing CaCl2 ; NaHCO3 and Na2 SO4 solutions while the previous researchers determined the Ksp from pure crystals of calcium carbonate and calcium
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sulfate. This suggests that there are two di/erent constants for dissociation and association of salt. Solubility products for both salts were correlated with temperature using van’t Ho/ relationship (Atkins, 1995). Heat of reaction was similar for solutions with 0.008 and 0:01 M of CaSO4 that exhibited similar solubility constants. This again may suggest and reinforce the hypothesis that presence of non-dominant ion a/ects the heat of precipitation. Kinetic data for calcium carbonate did not correspond to a second-order reaction as suggested in the literature (Nancollas & Reddy, 1971). But from the concentration pro=le of the species, it was shown that there was an initial surge followed by an exponential decrease before reaching equilibrium. It is possible that the extent of supersaturation had caused this. It is highly recommended to study the change in [Ca2+ ] and [CO2− 3 ] at the initial stage of crystallisation to examine what is the extent of the surging process. Also the applicability of 2nd order reaction rate should be examined with either less supersaturated solutions or with Ca2+ monitoring with electrochemical method that would permit more accurate measurements during initial periods. References Atkins, P. W. (1995). Physical Chemistry. Oxford: Oxford University Press. Augustin, W., & Bohnet, M. (1995). InJuence of the ratio of free hydrogen ions on crystallisation fouling. Chemical Engineering and Processing, 34, 79–85. Bansal, B., Muller-Steinhagen, H., & Chen, X. D. (1997). E/ect of suspended particles on crystallisation fouling in plate heat exchangers. ASME Journal of Heat Transfer, 119, 568–574. Blount, C. W., & Dickson, F. W. (1973). Gypsum anhydrite equilibria in systems CaSO4 -H2 O and CaCO3 -NaCl-H2 O. The American Minerologist, 58, 323–331. Bott, T. R. (1995). Fouling of heat exchangers. Amsterdam: Elsevier. Bramson, D., Hasson, D., & Semiat, R. (1996). The roles of gas bubbling, wall crystallization, and particulate deposition in CaSO4 scale formation. Desalination, 100, 105–113. EPRI, 1982. (Ed.) Design and operating guidelines manual for cooling water treatment: treatment of recirculating water. Electric Power Research Institute, Palo Alto, California. Hardie, L. A. (1967). The gypsum-anhydrite equilibrium at one atmosphere pressure. The American Mineralogist, Vol. 52, p. 171–200. Hasson, D. (1981). Precipitation fouling—A review. In E. F. C. Somerscales, J. G. Knudsen (Eds.), Fouling of heat transfer equipment, (p. 527–568). New York: Hemisphere Publishing Corporation. Hasson, D. (1999). Progress in precipitation fouling research, A review. In R. Bott (Ed.), Proceedings of engineering foundation conference, understanding heat exchanger fouling and its mitigation (p. 67–89). New York: Begell House. Hasson, D., & Karmon, M. (1984). Novel process for lining water mains by controlled calcite deposition. Corrosion Prevention and Control, 31, 9–17. Hasson, D., & Zahavi, J. (1970). Mechanism of calcium sulfate scale deposition on heat-transfer surfaces. Industrial and Engineering Chemistry Fundamentals, 9(1), 1–10.
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Kemmer, F. N. (1988). The nalco water handbook. New York: McGraw-Hill Book Co. Lepley, R. H. (1984). Calcium compounds–calcium carbonate. In M. Grayson, D. Ekroth (Eds.), Kirk–Othmer Encyclopedia of Chemical Technology (3 edn, vol. 4, pp. 427– 432). New York: John Wiley & Sons. Liu, S. T., & Nancollas, G. H. (1970). The kinetics of crystal growth of calcium sulfate dihydrate. Journal of Crystal Growth, 6, 281–289. Marshall, W. L., & Slusher, R. (1968). Aqueous systems at high temperature. Journal of Chemical and Engineering Data, 13(1), 83–93. Morse, R. W., & Knudsen, J. G. (1977). E/ect of alkalinity on the scaling of stimulated cooling tower water. Canadian Journal of Chemical Engineering, 55, 272–278. Mullin, J. W. (1972). Crystallization. London: Butterworths. Mullin, J. W. (1993). Crystallization. Oxford: ButterworthsHeinemann. Nancollas, G. H., Eralp, A. E., & Gill, J. S. (1978). Calcium sulfate scale formation: A kinetic approach. Society of Petroleum Engineering Journal, 18, 133–138. Nancollas, G. H., & Reddy, M. N. (1971). The crystallization of calcium carbonate II. Calcite growth mechanism. Journal of Colloid Interface Science, 37, 824–830. Nordstrom, D. K. Plummer, L. N., Langmuir, D., Busenberg, E., May, H. M., Jones, B. F., & Parkhurst, D. L. (1990). Revised chemical equilibrium data from major mineral reactions and their limitations. In D. C. Melchior, R. L. Bassett (Eds.), ACS Symposium Series 416–Chemical modeling of aqueous
systems II (p. 398– 413). Washington, DC: American Chemical Society. Partridge, E. P., & White, A. H. (1929). The solubility of calcium ◦ sulfate from 0 to 200 C. Journal of American Chemical Society, 51, 360–370. Plummer, N. L., & Busenberg, E. (1982). The solubilities of calcite, aragonite and vaterite in CO2 -H2 O solutions between 0 and 90◦ C, and an evaluation of the aqueous model for the system CaCO3 -CO2 -H2 O. Geochimica Cosmochimica Acta, 46, 1011– 1040. Reddy, M. M., & Nancollas, G. H. (1971). The crystallization calcium carbonate, I. Isotopic exchange and kinetics. Journal of Colloid Interface Science, 36, 166–172. Reeder, R. J. (1990). Carbonates, mineralogy and chemistry. Washington DC: Mineralogy Society of America. Sudmalis, M., & Sheikholeslami, R. (2000). Precipitation and co-precipitation of CaCO3 and CaSO4 . Canadian Journal of Chemical Engineering, 78, 21–31. Wirsching, F., & Gipswerke, G. K. W. (1985). Calcium Sulfate. In W. Gerhartz, Y. S. Yamamoto, F. T. Campbell, R. Pfe/erkorn, J. F. Rounsaville (Eds.) Ullmann’s Encyclopedia of Industrial Chemistry (5 edn, vol. 4, p. 556 –558). Weinheim: VCH Verlagsgesellschaft. Zhang, J., & Nancollas, G. H. (1992). InJuence of calcium=sulfate molar ratio on the growth rate of calcium sulfate dihydrate at constant supersaturation. Journal of Crystal Growth, 118, 287– 294.