Chemical Engineering Science 56 (2001) 53915400www.elsevier.com/locate/ces

Thermodynamics and kinetics for mixed calcium carbonate andcalcium 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 80C in mixtures having calcium car-

bonate as the dominant salt and at a given total initial calcium concentration of 0:03 M with sulfate concentration ranging from 0 to0:01 M. Solubility products and rate constants were determined from thermodynamic and kinetic studies and the results indicated thateven minute amounts of calcium sulfate a/ect the thermodynamics, kinetics and the scale structure and no longer the solubility dataand rate constants for the pure salt were applicable. Presence of CaSO4 from 0.002 to 0:01 M increased the calcium carbonate solubil-ity product more than an order of magnitude. The e/ect of salt mixture on the solubility constant of non-dominant salt (calcium sul-fate) was reverse as calcium sulfate solubility increased to its pure value with increases in its molar ratio. In addition, the rate equationsuggested in the literature (Nancollas and Reddy, J. Colloid Interface Sci. 37 (1971) 824; Reddy and Nancollas, J. Colloid InterfaceSci. 36 (1971) 166) for pure salt was not applicable to the experimental data. The general observations indicated that the presenceof CaSO4 had weakened the CaCO3 scale which is usually very adherent. The experimental results did take into account the e/ectof 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 materi-als at the phase interfaces. Build-up of fouling =lm leadsto an increase in resistance and deteriorates the perfor-mance of process equipment such as membranes and heatexchangers and is costing industries billions of dollarsannually. One of the major fouling phenomena encoun-tered in the aqueous systems is scale formation due toprecipitation of salts present in the water. Lots of met-als and anions exist naturally in the water; among them,CaCO3 and CaSO4 are major fouling contributors. Boththese salts have inverse solubility behaviour where thesolubility decreases with increasing temperature and salts

Corresponding author. Tel.: +61-2-9385-4343; fax: +61-2-9385-5966.E-mail address: r.sheikholeslami@unsw.edu.au

(R. Sheikholeslami).

precipitate on heat exchange surfaces when the solutionbecomes 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 thermo-dynamics and kinetics of crystallization of calcium car-bonate (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 ofcrystallization fouling, including the dynamic e/ects, hasalso been extensive as covered in two comprehensive re-views (Hasson, 1981, 1999). However, due to the com-plexity of fouling process the research in this area usuallyinvolves fouling by a single precipitant. The area to whichnot much attention has been paid to is the interactivee/ect of co-precipitating salts with or without commonions. These include solubility e/ects, rate data, crystalstructure and strength, inhibitor e/ects and also dynamic

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5392 T. H. Chong, R. Sheikholeslami / Chemical Engineering Science 56 (2001) 53915400

e/ects. This is important for two reasons. One is that themechanism of fouling might be di/erent for di/erent saltsas it was shown to be di/erent for CaCO3 and CaSO4(Bansal, Muller-Steinhagen, & Chen, 1997). The secondis the fact that co-existence of salts might actually a/ectthe thermodynamic and kinetic behaviour of each salt andtherefore, the single salt data might not be applicable tothe condition when the salts co-exist. The reviewed lit-eratures on crystallization (Hasson, 1981, 1999) indicatethat very little study has been devoted to the study ofthe co-precipitation phenomenon. There has been somequalitative research (Bramson, Hasson, & Semiat, 1996;Hasson & Karmon, 1984) on the strength and tenacityof co-precipitated calcium carbonate and sulfate. Theyfound that a major factor a/ecting scale tenacity was thepurity of the deposit. For calcium sulfate, the higher theimpurities, the greater the strength of the scale; however,with calcium carbonate, adhesive strength was seen to de-crease with increasing impurities. The most diGcult de-posit to remove from heat transfer surfaces was calciumcarbonate scale with impurities measuring less than 5%by mass; pure calcium sulfate deposits were found to befar less adherent than deposits containing co-precipitatedcalcium carbonate. The co-precipitated calcium carbon-ate seems to act as bonding cement, enhancing consid-erably the strength of calcium sulfate scale layer. In anearlier study, Morse and Knudsen (1977) also reportedthat for aggressive scale, the main constituent was cal-cium carbonate.In our recent work (Sudmalis & Sheikholeslami,

2000) on co-precipitation of CaCO3 and CaSO4 whenthey exist in comparable ratios, it has been qualita-tively shown that co-precipitation a/ects thermodynam-ics and kinetics of precipitation as well as the scalestructure. The objective of this study is to investi-gate and quantify co-precipitation process of CaCO3and CaSO4 when CaCO3 is the predominant com-ponent at a constant total calcium concentration andto determine solubility constants, assess the reactionrate constants and therefore examine the applicabil-ity of data and mechanisms for pure precipitation toco-precipitation.

2. Background

Understanding and developing kinetic and rate cor-relations and models for co-precipitation are builton the theories of single salt precipitation and hencecrystallization theory and properties of CaCO3 andCaSO4 are brieJy discussed here. In general, crystal-lization is considered to be comprised of nucleation,growth and re-crystallization steps. There are variousmechanisms for each step and a great degree of over-lap among these steps (Sudmalis & Sheikholeslami,2000). For crystallization to occur the solution has

to be supersaturated; however, supersaturation by it-self is not suGcient to induce crystallization. Thereis a requirement for centers of crystallization that cantake various forms such as seeds, embryos or foreignmatter present in the solution to induce nucleation.Growth and re-crystallization follow the nucleationstep. Usually, nucleation is the controlling step; oncethe critical nuclei are formed, the crystallizationproceeds.A given salt may have di/erent crystal structures

of which some might be more stable or more readilyformed. Calcium carbonate occurs naturally in three crys-tal structures of calcite, aragonite and vaterite. Calcite isthe most stable form of calcium carbonate. The arago-nite polymorph is metastable and irreversibly changes tocalcite when heated in dry air to about 400C. Vateriteis metastable and least prevalent and transforms to cal-cite and aragonite under geological conditions (Reeder,1990). The crystal forms of calcite are hexagonal whereasaragonite is in the orthorhombic system. Physical prop-erties of the two more prevalent crystal polymorphsare given by Lepley (1984); corresponding values forvaterite are not available. The solubility product forcalcium carbonate and the dissociation constants forcarbonic acids are given by Bott (1995). Saturation sol-ubility of calcium carbonate depends on the CO2 contentand solution pH; Kemmer (1988) provides data show-ing the distribution of CO2 related ions and CO2 gas insolution as a function of pH.Calcium sulfate can exist in six di/erent solid phases

(3 anhydrites, 2 hemihydrates and a dihydrate). Gyp-sum (CaSO4:2H2O), hemihydrates (CaSO4:1=2H2O),and anhydrite III and anhydrite II can exist at room tem-peratures whereas anhydrite I only exists above 1180C.The physical properties of all polymorphs are given byWirsching and Gipswerke (1985). Much research hasbeen performed in an attempt to analyse the mechanismand determine the form of calcium sulfate at di/erenttemperatures. Partridge and White (1929) found thatgypsum is the usual precipitating phase in the rangeof 4098C while anhydrite and hemihydrate are thespecies likely to precipitate above 98C. Some others(Blount & Dickson, 1973; Hardie, 1967) indicated thetransition temperature between anhydrite and gypsum tobe in the range of 5658C. This is incongruent with theresults of Partridge and White (1929); however, all theworks (Blount & Dickson, 1973; Hardie, 1967; Partridge& White, 1929) seemed to indicate that in the rangeof operation of majority of industrial heat exchangers,gypsum is the dominant phase. Furthermore, Hasson andZahavi (1970) proposed a correlation for CaSO4 nu-cleation times and reported that nucleation of anhydriteis an extremely slow process in comparison to that ofgypsum. This also justi=es considering gypsum as thedominant phase. Correlations for solubility products fordi/erent forms of calcium sulfate, which may be adjusted

T. H. Chong, R. Sheikholeslami / Chemical Engineering Science 56 (2001) 53915400 5393

Table 1Summary of batch tests conditions

Run T (C) CaCO3 (M) CaSO4 (M)

BT1 70 0.030 0.000BT2 60 0.030 0.000BT3 60 0.020 0.010BT4 70 0.020 0.010BT5 70 0.022 0.008BT6 60 0.022 0.008BT7 70 0.028 0.002BT8 60 0.028 0.002BT9 80 0.030 0.000BT10 80 0.020 0.010BT11 80 0.022 0.008BT12 80 0.028 0.002BM1 60 0.000 0.030BM2 70 0.000 0.030

for the appropriate temperature, are available in theliterature (EPRI, 1982; Marshall & Slusher, 1968;Nordstrom et al., 1990).

3. Experimental techniques

Batch tests were carried out with model solutions withtotal calcium content of 0:03 M and sulfate concentrationsranging from 0 to 0:01 M at temperatures of 60, 70 and80C. Table 1 lists the chemical composition of modelsolutions used in experimentation.The supersaturated solutions of calcium sulfate

(CaSO4) and calcium carbonate (CaCO3) were preparedby adding equimolar amounts of Na2SO4 and CaCl2,and CaCl2 and NaHCO3, respectively. The solutionswere prepared with analytical grade chemicals and withmicro-=ltered (with 0:22 m Millipore =lter) distilledwater. Solution pH was measured before mixing, thenthe mixture was carefully transferred to a series of 75 mltest tubes; which had been scrubbed, rinsed with con-centrated hydrochloric acid and washed thoroughly withdistilled water; to avoid air bubbles formation as the airbubbles will a/ect the equilibrium of CO2 hence theconcentration of CO23 in the solution. One tube samplewas removed right after mixing the individual solutions,=ltered with 0:22 m =lter and was analysed for waterquality. Water quality was determined by measurementof pH, total alkalinity, hardness (by complexometry),and sulfate (by chromatography) using the standardmethods of water analysis. Remainders of the tubes wereplaced in the temperature baths. Water quality was mon-itored for each sample taken during the run. To ensureconstant volume reaction for the kinetic data analysis,for each sample two solution-=lled tubes were removedfrom the bath and used for the analysis and monitoringduring the run. The water quality tests were carried outuntil equilibrium had been achieved.

4. Results and discussions

4.1. General observations

For all the runs when the solutions of CaCl2; NaHCO3and Na2SO4 were mixed, the mixture immediately turnedinto a cloudy solution. This indicated the formation of awhite colour CaCO3 precipitate and also a very insignif-icant nucleation or induction period that is reasonablefor such a supersaturated solution. Besides, the amountof precipitate collected during =ltering of pure CaCO3was less compared to the mixture of CaCO3 + CaSO4.In addition, as the concentration of CaSO4 increased, theamount of precipitate collected increased as well. Thiswas due to the fact that pure CaCO3 is a very adherentscale, where most of the precipitate stuck to the wall oftest tube as was observed. The presence of CaSO4 weak-ened the CaCO3 scale, making the precipitate less tena-cious and freely moving in the solution. Therefore, thescale formed from the mixture could be more easily re-moved than that of the pure CaCO3 scale. This is consis-tent with previous =ndings of Bramson et al. (1996) intheir study of composite fouling of CaCO3 and CaSO4 ona heat transfer surface in turbulent Jow of a falling =lm.

4.2. Scale morphology

The CaCO3 scale was a powdery-like precipitate whileCaSO4 had a needle shape. The pure CaCO3 crystal hada hexagonal structure, which indicated that the CaCO3was in the form of calcite and proves that it was thefavourable form of calcium carbonate precipitation phase.When CaSO4 was added to the CaCO3, the needle shapecrystals grow on the hexagonal crystal. The pure CaCO3crystals were more tenacious and compact than the mixedsolutions. Also, more crystals were grown in the pureCaCO3 as compared to the mixture.

4.3. E4ect of sulfate ion and temperature on calciumdecline

Total calcium concentration of the solutions was mon-itored in order to investigate the co-precipitation e/ectsand to determine the solubility constants for salt mix-tures. The e/ect of solution composition at given tem-peratures are shown in Fig. 1. The change in total cal-cium concentration for all solutions at 60C are shown inFig. 1(a) and shows that the crystallisation process exhib-ited no induction period; all the curves have a steep de-crease in Ca2+ at the initial stage of the experiment beforereaching equilibrium. The e/ect of sulfate on precipita-tion is compared with that of pure CaCO3 solution (BT2)in which Ca2+ concentration decreased from the initialvalue of 1200 ppm (0:03 M) to the equilibrium concen-tration of 552 ppm (0:0138 M) in about 500 h indicating

5394 T. H. Chong, R. Sheikholeslami / Chemical Engineering Science 56 (2001) 53915400

Fig. 1. E/ect of composition ( at 0:000 M SO24 , at 0:002 M SO24 ,

4 at 0:008 M SO24 , at 0:010 M SO24 and at 0:002 M SO24 )

at given temperatures.

approximately 54% (648 ppm) had precipitated. When0:002 M of SO24 was introduced to the CaCO3 solution(BT8), the equilibrium concentration for Ca2+ shiftedto 632 ppm indicating a decline of 7% in the amountof precipitate (568 ppm) from 54% to 47%. Further in-crease in sulfate concentration to 0.008 (BT6) and 0:01 M(BT3) reduced the total amount of calcium precipitatedto, respectively, 468 and 460 ppm. This indicates as the

Table 2E/ect of SO4 on Ca

++ concentration in solution and precipitation

SO24 60C 70C 80C

(M) Final Ca++ Precipitate Final Ca++ Precipitate Final Ca++ Precipitate(ppm) % decrease (ppm) % decrease (ppm) % decrease

0.000 552 0 520 0 512 00.002 632 7 592 6 552 30.008 732 15 700 15 700 160.010 740 16 716 16 696 15

sulfate concentration increases, the solubility concentra-tion of calcium increases as well and the e/ect of sulfategradually levels-o/ as its concentration increases.Figs. 1(b) and (c), respectively show the e/ect of co-

precipitation at 70C and 80C and Table 2 summarizesincreases in =nal calcium concentration and the percent-age drop in precipitate for all the runs. Again, at 70C and80C, presence of sulfate increased the equilibrium con-centration of calcium and reduced the amount of precip-itation but the e/ect levelled-o/ as it approached 0.0080:010 M. The only di/erence was that at 80C, the amountof precipitate for the solution with 0:008 M of SO24 wasslightly (less than 1%) higher than that for the solutionwith 0:010 M of SO24 . This is very likely due to experi-mental 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 asthe solution temperature was increased irrespective ofconcentration of SO24 and the solution composition.

4.4. Decline in concentrations of anions

Concentrations of anions (CO23 and SO24 ) are re-

quired to determine the solubility products for CaCO3 andCaSO4 salts in the co-precipitation process. The CO

23

were calculated from the distribution of carbonic speciesin solution based on the total alkalinity and pH of thesolution as follows

[CO23 ]=[T:A:] + [H+] [OH]

2(1 + [H+]=2K2); (1)

[HCO23 ]=[T:A:] + [H+] [OH]

(1 + 2K2=[H+]); (2)

[CO2]=[T:A:] + [H+] [OH]K1=[H+](1 + 2K2=[H+])

; (3)

CT = [HCO3 ] + [H2CO3] + [CO

23 ]: (4)

Based on the electroneutrality condition through the pro-ton balance equation, the Total Alkalinity (T.A.) of waterwith a total carbon species CT is

[T:A:] = [HCO3 ] + 2[CO23 ] + [OH

] [H+]: (5)

T. H. Chong, R. Sheikholeslami / Chemical Engineering Science 56 (2001) 53915400 5395

Fig. 2. E/ect of temperature ( at 60C, at 70C, and 4 at 80C)at given compositions.

By combining Eqs. (1)(5) the concentration of eachcarbon species can be obtained. The declines in concen-trations of anions are represented in Figs. 3 and 4, re-spectively for CO23 and SO

24 at 60, 70 and 80

C. Theinitial quantity of CO23 in the solution was unknown be-cause the HCO3 in the solution prepared from sodiumbicarbonate powder will dissociate to CO23 and CO2

Fig. 3. Carbonate ion concentrations in the solutions ( at0:000 M SO24 , at 0:002 M SO24 , 4 at 0:008 M SO24 and at0:010 M SO24 ).

according to the chemistry of carbonic acid which ispH dependent. We cannot obtain this value by usingrelationships for pure sodium carbonate as the pH ofsolution changes and a/ects CO23 concentration uponmixing sodium bicarbonate and calcium chloride solu-tions. So though the exact initial value could not be de-termined, the instantaneous values were calculated andare shown in Fig. 3. In general, the CO23 plots exhib-ited similar trends to those of Ca2+. By increasing theSO24 ions or in other words decreasing the CO

23 in

the solution, the equilibrium concentration of CO23 hadbeen increased. The presence of SO24 had suppressedthe crystallisation of CaCO3, leaving more CO

23 ions

in the solution. This indicates that the e/ect of sulfateon CaCO3 solubility is not due to pH e/ects as bothCa2+ and CO23 solubilities are increased in presence ofsulfate.

5396 T. H. Chong, R. Sheikholeslami / Chemical Engineering Science 56 (2001) 53915400

Fig. 4. Sulphate ion concentrations in the solutions (4 at0:002 M SO24 , at 0:008 M SO

24 and at 0:010 M SO

24 ).

The change in SO24 content in the solution with time(Fig. 4) was less pronounced than that of CO23 . Theaverage total change of SO24 at lowest sulfate concen-tration of 0:002 M was about 30 ppm only. At highestsulfate concentration of 0:01 M, the amount precipitatedwas more signi=cant and about 250 ppm of SO24 hadcrystallized with Ca2+.

Table 3Solubility product for CaCO3 and CaSO4 (CaCO3 Dominant)

Ksp for CaCO3 Ksp for CaSO4

Solution 60C 70C 80C 60C 70C 80C

CaCO3 (Bott) 1.821E-09 1.386E-09 1.056E-090:030 M CaCO3 (measured) 4.011E-09 3.000E-09 1.910E-090:028 M CaCO3 + 0:002 M CaSO4 1.962E-08 1.943E-08 1.715E-08 5.051E-06 4.308E-06 3.615E-060:022 M CaCO3 + 0:008 M CaSO4 4.000E-08 3.915E-08 3.415E-08 1.907E-05 1.795E-05 1.692E-050:020 M CaCO3 + 0:010 M CaSO4 4.408E-08 4.288E-08 3.557E-08 2.076E-05 1.921E-05 1.870E-050:030 M CaSO4 (measured) 1.930E-05 1.760E-05CaSO4 (Marshall and Slusher) 3.594E-05 3.244E-05 2.889E-05

4.5. Solubility product

Table 3 summarizes the results for solubility productsof pure salts and mixed solutions. Also pure salt data de-termined in this study are compared with the published(Bott, 1995; Marshall & Slusher, 1968) values. The mea-sured values for pure CaCO3 are greater than those ofliterature (Bott, 1995) and for pure CaSO4 are lower thanthose in the literature (Marshall & Slusher, 1968). Thedi/erence can be due to the method of solution prepa-ration and analysis; in this study, all CaCO3 and CaSO4solutions were obtained by mixing CaCl2, NaHCO3 andNa2SO4 solutions while the previous researchers de-termined the Ksp from pure crystals. In the followingdiscussion, the measured values are used to compare thesolubility constants in mixtures with those in pure saltsto ensure consistency; however, this would not have anye/ect on the trends obtained even if the literature valueswere to be used.The results show that the solubility product of CaCO3

in the co-precipitation process is greatly a/ected by thepresence of CaSO4. For example, by introducing 0:002 MSO24 into the solution at 70

C the Ksp value for CaCO3increased to 1:943 108, by about 500% from the Ksp(3:00109) for pure salt. TheKsp 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 pureCaCO3. The Ksp for CaSO4 was also calculated for all theruns with sulfate. The Ksp for pure CaSO4 at 70

C was1:760105 while in a mixed solution with minor amountof sulfate (0:002 M) the Ksp had dropped by about 75% to4:308106. While for the solutions with higher concen-trations of sulfate (0.008 and 0:01 M), the Ksp in mixedsolutions were very close (between 1% and 10%) to ofthose in pure calcium sulfate solution. Fig. 5 shows agraphical representation of the trend between the Ksps at60C for each salt in the mixed solution in comparisonto those of pure salts. The same trends were observed atother temperatures. It is very clear that the solubility con-stant of the dominant calcium carbonate is greatly a/ectedby presence of calcium sulfate and the e/ect levels-o/ asthe concentration of the non-dominant anion increases.

T. H. Chong, R. Sheikholeslami / Chemical Engineering Science 56 (2001) 53915400 5397

As seen in previous discussion, the equilibrium concen-tration of both Ca2+ and CO23 ions has increased in pres-ence of sulfate. The e/ect on the non-dominant ion ismuch less though cannot be neglected at some ratios ofnon-dominant to dominant ions. This means the Ksp val-ues for the pure salts are not suitable to be used when pre-dicting the equilibrium established in a co-precipitatingsystem.The e/ect of presence of foreign coprecipitating ionic

species upon the thermodynamic solubility constant ofpure salt could be explained from the thermodynamicaspect. The formation of pure CaCO3 from Ca

2+ andCO23 proceeds according to the reaction below

Ca2+ + CO23 CaCO3 (s): (6)

At equilibrium, the Gibbs free energy of reaction (RrG)is zero. Therefore based on Eq. (7), at equilibrium thethermodynamic solubility constant will be related to thestandard molar Gibbs free energy of reaction (RrG)according to Eq. (8)

RrG=RrG + RT ln(aCa2+ aCO23

aCaCO3

); (7)

RT ln(Ksp)=RrG: (8)a is the activity of ions or salt, R is the universal gasconstant and T is temperature in Kelvin. By de=nition,RrG is the di/erence between the total standard Gibbsfree energy of formation of products RfG(products)and the reactants RfG(reactants). For the formation ofCaCO3, the following equation can be written:

RrG =RfG(CaCO3) {RfG(Ca2+)+RfG(CO

23 )}: (9)

In the coprecipitation process, the product di/ers fromthat of single salt precipitation. This is supported by thescale morphology of salt forms from mixture where theneedle-shaped CaSO4 grows in the hexagonal-shapedCaCO3. For the sake of reference, the product inco-precipitation is denoted by an asterisk (CaCO3).Since the standard Gibbs free energy of formation ofthat mixed salt RfG(CaCO

3) is di/erent from that of

the pure salt RfG(CaCO3), hence the thermodynamicequilibrium constant of the coprecipitation is di/erentfrom that of single salt precipitation.The solubility product of salts for all solutions de-

creased with increasing temperature, as both salts are ofinverse solubility characteristic. For the pure CaCO3, theKsp determined from the experimental data was 4:011 109 and decreased by 25% and 52% for 70C and 80C,respectively. As mentioned previously, the di/erence inthe measured and literature values for pure salts are ex-pected to be due to the e/ect of sample preparations.The solubility constants for both salts were =tted to

vant Ho/ equation (Atkins, 1995) to obtain correlations

Fig. 5. Comparison of Ksp for both salts in pure and mixed solutions.

Fig. 6. Solubility constants for both salts.

with respect to temperature and also to obtain the heat ofprecipitation (RHR) based on the following relationship:d ln(Ksp)d(1=T )

= RHRR

: (10)

The plot of ln(Ksp) vs. 1=T should yield a straight linewith a slope equal to RHR=R, where R is the universalgas constant. Fig. 6 shows the plots for both CaCO3 andCaSO4. The correlations showing the e/ect of tempera-ture are given in Table 4.As seen in Fig. 6(a), the slope of the curves for

pure measured and literature (Bott, 1995) values ofCaCO3 were very similar though the Ksp values wereslightly higher. This indicates comparable heats ofprecipitation. In addition, Table 4 shows that the heats

5398 T. H. Chong, R. Sheikholeslami / Chemical Engineering Science 56 (2001) 53915400

Table 4Equations of Ksp for CaCO3 and CaSO4 (CaCO3 Dominant)

Solution composition Ksp (CaCO3) Ksp (CaSO4)

CaSO4 CaCO3

0:000 M 0:030 M ln(Ksp)= 4:353 103=T + 32:370:002 M 0:028 M ln(Ksp)= 7:858 102=T + 20:09 ln(Ksp)= 1:966 103=T + 18:090:008 M 0:022 M ln(Ksp)= 1:195 103=T + 20:35 ln(Ksp)= 7:036 102=T + 12:980:010 M 0:020 M ln(Ksp)= 1:252 103=T + 20:67 ln(Ksp)= 6:175 102=T + 12:64

of precipitation for both CaCO3 in solutions with 0.008and 0:01 M CaSO4 were almost the same. Likewise,the heats of precipitations for CaSO4 in these solutionswere almost the same. These were the solutions thatexhibited almost the same Ksp values at given temper-atures. So, one hypothesis might be that the presenceof a co-precipitating salt with a common cation some-what a/ects the heat of precipitation and therefore theextent of precipitation and this as discussed before canbe explained from the standard Gibbs free energy of thesubstance produced.

4.6. Rate of precipitation for CaCO3

Fig. 2 shows that there was a sharp decline in the con-centration of Ca2+ initially right after the solutions weremixed; for example in Run BT8, Ca2+ in the solutiondropped to 0:0212 M and 29% of initial Ca2+ precipitatedin less than 2 min. The decline in Ca2+ becamemore grad-ual as the time progressed. Runs (BT1, BT2, BT7, BT8,BT9 and BT12) with high levels (0.03 and 0:028 M) ofCaCO3 showed a rapid decrease in the =rst 50 h beforeapproaching equilibrium. To study CaCO3 precipitationprocess under the inJuence of CaSO4 and temperature,the rate constant associated with each run was calcu-lated. The initial attempt was to use the integral approachand to =t the data to 2nd order reaction that had beensuggested (Nancollas & Reddy, 1971) for pure calciumcarbonate. Therefore, according to a second-order reac-tion (Eq. 12) between Ca2+ and CO23 (Eq. 11), the plotof log(d[Ca2+]=dt) vs. log({[Ca2+][CO23 ]K sp})should yield a straight line with the slope of 1 and theintercept of log(kr).Ca2+ + CO23

krCaCO3 (s); (11)

d[Ca2+]

dt= kr{[Ca2+][CO23 ] K sp}: (12)

K sp in Eq. (12) is the concentration product of Ca2+ and

CO23 at equilibrium. The experimental data shown inFig. 7 (a) indicated that there was a region, known asinitial surge growth, where the crystallisation rate couldnot be predicted by Eq. (12). This initial surge was alsonoted by Nancollas and Reddy (1971) who thus sug-gested applying Eq. (12) to the rate of crystallization but

Fig. 7. Assessment of rate of precipitation for calcium carbonate (at 60C, at 70C, and 4 at 80C).

excluding the initial surge period and through this ob-tained linear relationship with slope of unity. Therefore,the same approach of excluding the initial surge periodwas used (as shown in Fig. 7(b)); however, the slopesof the plots were greatly di/erent from unity. This wouldmean that the crystallisation rate of calcium carbonate inpresence of calcium sulfate could not simply be modelledas a second order reaction. This suggests that using therate equations suggested for a single salt crystallizationto crystallization of mixed salts might as well be ques-tionable. Controlled experiments and possibly continu-ous monitoring of calcium concentration (e.g. by calciumelectrode) is necessary to provide more precise measure-ments for kinetic analysis during the very early stagesand hence determining the rate and order of reaction.

5. Concluding remarks

The e/ect of water quality is of great importance oninduction 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) 53915400 5399

particulate matter plays a signi=cant role in promotingprecipitation of a salt solution due to the aGnity thatthe salt has to precipitate on other particulate matter inpreference to, say, the heat transfer surface. The specieswill tend to do this long before homogeneous nucleationbecomes a viable option. Nevertheless work has mainlybeen in the absence of other precipitating species andcorrelations have been established where nucleation hasbeen achieved homogeneously.In this study, the e/ect of co-precipitation of calcium

carbonate and calcium sulfate in a solution having CaCO3as the dominant salt was investigated at 60, 70 and 80C.In presence of CaSO4, the CaCO3 scale which is usu-ally very adherent and tenacious loses its strength andbecomes less adherent and more freely moving. Also,presence of SO24 in solution increases the equilibriumconcentration of both Ca2+ and CO23 and therefore thesolubility constant for CaCO3. The thermodynamic solu-bility constant of pure salt precipitation is di/erent fromthat of the co-precipitation due to the fact that the prod-uct of co-precipitation di/ers from that of single saltprecipitation; based on thermodynamic principles, it ishypothesized that this is related to the change in stan-dard molar Gibbs free energy of reaction RrG. Thisis evident from the structure of the product of mixedcalcium carbonate and sulfate solution that showed thegrowth of needle-shaped CaSO4 in the hexagonal-shapedCaCO3.The solubility constant for CaCO3 increases with in-

crease in sulfate ion but there seems to be a limit to thee/ect of CaSO4 on CaCO3 precipitation. This is evidentfrom the experimental runs with 0.008 and 0:01 M CaSO4where the e/ect of SO24 had levelled-o/. Presence ofCaCO3 had a di/erent e/ect on CaSO4 solubility. In so-lutions with minute amounts of sulfate (0:002 M), theCaSO4 solubility product in the mixture was much lessthan that of pure salt. However, further increases in thesulfate concentration to 0:01 M, has increased the CaSO4solubility constant in the mixture to that of pure salt.Therefore, these suggest that the thermodynamic data forpure salts are not extendable to co-precipitation; also itseems that the e/ect depends on the dominance as well.Experimental measurements are necessary until theoret-ical studies will address the co-precipitation issue. Alsoadditional tests are necessary to verify the existence ofcritical composition range where Ksps are una/ected bycomposition.The solubility product of pure CaCO3 determined ex-

perimentally was slightly higher than those reported byBott (1995) while that of pure CaSO4 was slightly lowerthan those reported by Marshall and Slusher (1968). Thisdi/erence could be due to the e/ect of sample prepa-ration; in this study, all CaCO3 and CaSO4 solutionswere obtained by mixing CaCl2; NaHCO3 and Na2SO4solutions while the previous researchers determined theKsp from pure crystals of calcium carbonate and calcium

sulfate. This suggests that there are two di/erent con-stants for dissociation and association of salt.Solubility products for both salts were correlated with

temperature using vant Ho/ relationship (Atkins, 1995).Heat of reaction was similar for solutions with 0.008 and0:01 M of CaSO4 that exhibited similar solubility con-stants. This again may suggest and reinforce the hypoth-esis that presence of non-dominant ion a/ects the heat ofprecipitation.Kinetic data for calcium carbonate did not correspond

to a second-order reaction as suggested in the literature(Nancollas & Reddy, 1971). But from the concentrationpro=le of the species, it was shown that there was aninitial surge followed by an exponential decrease beforereaching equilibrium. It is possible that the extent of su-persaturation had caused this. It is highly recommendedto study the change in [Ca2+] and [CO23 ] at the initialstage of crystallisation to examine what is the extent ofthe surging process. Also the applicability of 2nd orderreaction rate should be examined with either less super-saturated solutions or with Ca2+ monitoring with electro-chemical method that would permit more accurate mea-surements during initial periods.

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