Ind. Eng. Chem. Res. 2003, 42, 6647-6652
6647
GENERAL RESEARCH The Retarding Effect of Citric Acid on Calcium Sulfate Nucleation Kinetics Marina Prisciandaro,† Amedeo Lancia,*,‡ and Dino Musmarra§ Dipartimento di Chimica, Ingegneria Chimica e Materiali, Universita` dell’Aquila, Monteluco di Roio, 67040 L’Aquila (AQ), Italy, Dipartimento di Ingegneria Chimica, Universita` degli Studi di Napoli, Federico II, P.le Tecchio 80, 80125 Napoli (NA), Italy, and Dipartimento di Ingegneria Civile, Seconda Universita` degli Studi di Napoli, Real Casa dell’Annunziata, Via Roma 29, 81031 Aversa (CE), Italy
Measurements of the induction period for gypsum nucleation, when citric acid is added in solution as an additive to retard calcium sulfate nucleation, are reported in the present paper. The supersaturation ratio was varied in the interval 4-5; the concentration of citric acid was varied from 0.01 to 0.30 g/L; and, finally, different temperature levels were explored in the range 1545 °C. The induction period values were compared to those previously obtained by using the same experimental technique in the absence of foreign ions in the mother liquor, showing that the citric acid has a strong retarding effect toward gypsum nucleation. Eventually, several values for the interfacial tension and activation energy have been estimated as a function of citric acid concentration and of temperature. Introduction The precipitation of calcium sulfate from aqueous solution onto surfaces occurs when an electrolyte solution containing calcium and sulfate ions is supersaturated by evaporation, cooling, heating, etc.; the salts (calcium sulfate anhydrous, hemihydrate or dihydrate) will precipitate according to the concentrations of the various ions and the temperature. In particular, the solubility of all calcium sulfate forms decreases with increasing temperature starting from 40 °C1, a fact that is responsible for the formation of scale mostly constituted by a mixture of calcium sulfate dihydrate (gypsum) and calcium sulfate anhydrous (anhydrite). The comprehension of nucleation and crystal growth mechanisms that regulate calcium sulfate precipitation is thus of interest in all those processes in which gypsum formation is unwanted. Seawater desalination,2 water distillation,3 industrial water recovery in cooling tower technology, and hydrometallurgical operations4 are all examples of processes in which gypsum scale formation usually occurs. An accounted technique to hinder or delay gypsum scale formation is the addition of additives in solution which retard calcium sulfate formation, i.e., which slows down the nucleation mechanism. Many substances, organic as well as inorganic, have been tested as additives for their capability of retarding the unwanted gypsum precipitation process; among organic additives, citric acid seems to be one of the most effective.5 * To whom correspondence should be addressed. Tel.: [+39](81)7682243. Fax: [+39](81)5936936. E-mail:
[email protected]. † Universita ` dell’Aquila. ‡ Dipartimento di Ingegneria Chimica, Universita ` degli Studi di Napoli. § Dipartimento di Ingegneria Civile, Seconda Universita ` degli Studi di Napoli.
Study of the effect of an additive on gypsum nucleation can be carried out by evaluating the induction period, defined as the time that elapses between the onset of supersaturation and the formation of critical nuclei, or embryos. This time primarily depends on solution supersaturation and temperature and it is the sum of two components: the nucleation time (tn), related to the appearance of the critical nuclei, and the growth time (tg), connected to the growth process which leads from critical nuclei to measurable crystals. Depending on the relative values of these two time periods, the induction time can be influenced by nucleation alone (tn . tg, nucleation-controlled induction period), by both mechanisms (tn ≈ tg, nucleation- and growth-controlled induction period), or by growth alone (tn , tg, growthcontrolled induction period).6,7 Although tg can be estimated from a kinetic growth expression, tn is more difficult to quantify. Nevertheless, it is possible to discriminate whether the appearance of the new solid phase is controlled by nucleation or by growth or both, on the basis of the dependence of tind on supersaturation. In particular, if the process which takes place is truly homogeneous nucleation, i.e., it occurs in a clear solution under the effect of supersaturation alone, tind is inversely proportional to the nucleation rate, defined as the number of nuclei formed in solution per unit time and volume. In this case, as shown by Mullin8 and So¨hnel and Garside,7 it is possible to use the experimental knowledge of the induction period to estimate the activation energy (Eact) for nucleation from the dependence of tind on temperature. Moreover, tind dependence on supersaturation allows determination of the interfacial tension (γs) among crystals and the surrounding solution. Actually, depending on the prevailing mechanismsnucleation or growthsthe dependence of the induction time on supersaturation ratio (σ)
10.1021/ie020996h CCC: $25.00 © 2003 American Chemical Society Published on Web 11/12/2003
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Figure 1. Schematic diagram of the experimental apparatus.
assumes different shapes, and namely, if tn . tg or tn ≈ tg, a linear relationship between log(tind) and (logσ)-2 does exist, with a different value of the regression slope; on the contrary, when tn , tg, the correlation is between log(tind) and (logσ)-1. The main object of the present paper is measurement of the induction period for gypsum nucleation when citric acid is added in solutions as an additive, by using a well-assessed laser light scattering technique for the measurement of tind previously devised.9 The measured induction period values are used to estimate the values for the interfacial tension between gypsum crystals and the mother solution for each citric acid concentration level and for different temperature levels, together with the activation energy for gypsum nucleation. The obtained values are then compared to those estimated in the absence of additives in the mother liquor.9 Experimental Section Apparatus and Procedure. The experimental apparatus consisted of a stirred reactor with a related optical device and is schematically shown in Figure 1. The reactor was a batch cylindrical crystallizer, made of glass, with a working volume of 1.1 × 10-3 m3 and a diameter of 0.09 m. The crystallizer was surrounded by a water jacket for temperature control; stirring was provided by a two-blade polypropylene stirrer, with rotation rate ranging between 1 and 10 s-1. An off-take tube, placed at half of the working height of the vessel, allowed removal of samples of the suspension; the position of the tube was chosen to ensure that the content of the exit stream was the same as the content of the reactor.10 The stream removed by the off-take tube was sent, by a peristaltic pump, to an analysis flow-through cell, and then conveyed again to the crystallizer. The cell, made of quartz, was 0.07 m long, with a square section of 0.01 m2, and 0.0025 m thickness. A 10-mW He-Ne laser beam (Io ) 632.8 nm) was focused on the cell, orthogonal to its walls; the beam, diameter 2 mm, was vertically polarized. On the path of the laser beam, placed at 45° with respect to its direction, a beam splitter was provided to divide the laser beam into two parts: one used to illuminate the measuring cell, and
the other, collected by a photodiode, used to check the stability and intensity of the laser beam (Io). The signal of the scattered light (Isca) was collected by two lenses of focal length 120 and 50 mm, at 90° with respect to the laser beam. This signal was sent, through a quartz optical fiber ending on an interferential filter, to a photomultiplier tube, connected to a power supply with voltage variable in the range of 0-1000 V. The signal of the transmitted light (Itrans) was collected by a photodiode located beyond the cell, at 0° with respect to the laser beam. A recorder device collected the two analogue signals of scattered and transmitted light, together with Io. Supersaturated solutions of calcium sulfate were prepared by using two clear aqueous solutions of reagent grade CaCl2‚2H2O and Na2SO4 in bidistilled water. The dissolved Ca2+ ion concentration was measured by EDTA titration using Murexide (Carlo Erba) as an indicator, whereas SO42- ion concentration was measured by means of turbidity measurements carried out in a spectrophotometer (Hach, 2010). After their preparation the two solutions were filtered, by using a 0.45µm filter (Millipore, HVLP 4700) and a vacuum pump (Vacuubrand, MZ4C), to eliminate all foreign material inevitably present in the solution, and then mixed directly into the reactor. The concentration of Ca2+, added as CaCl2‚2H2O, and Na2SO4 in solution varied between 110 and 145 and 220-290 mol/m3, respectively. Citric acid aqueous solution was added to the Na2SO4 solution and then fed to the reactor, so that citric acid concentration (cCA) in the reactor varied in the interval 0.01-0.30 g/L (0.052-1.560 mol/m3). The supersaturation ratio was calculated considering the liquid-solid equilibrium between Ca2+ and SO42ions and solid CaSO4‚2H2O, as described by the following equation:
Ca2+ + SO42- + 2H2O ) CaSO4‚2H2O
(1)
so that it is:
σ)
aCa2+aSO42-a2H2O Kps
(2)
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Figure 2. Intensities of the transmitted (Itrans/Io) light, as a function of time for different values of supersaturation ratio with and without citric acid; σ ) 4.16, T ) 25 °C.
where aJ represents the activity of the J species (J ) Ca2+, SO42-, and water) expressed as the product of the molality (mJ) and the activity coefficient (γJ), and Kps is the solubility product of gypsum. The value of Kps was calculated as a function of temperature by means of the following relationship1:
ln(Kps) ) 390.96 - 152.62 log T - 12545.62/T + 0.08 T (3) The activity coefficient calculations in the supersaturated solution have been carried out by using Bromley’s method11 and are reported in detail elsewhere.9 All experiments have been carried out for various values of citric acid concentrations, while changing the supersaturation ratio in the range 4-5. The temperature was varied in the range 15-45 °C to ensure that the only species present in solution was the calcium sulfate dihydrate.12 The induction period was evaluated by measuring the intensity of scattered and transmitted light signals as a function of time. Such signals have been processed to evaluate tind by adopting two parallel procedures: one graphical and the other one numerical. These procedures, described in detail elsewhere,9 gave quite similar ((10%) results. Results and Discussion In Figure 2 the smoothed curves of Itrans/Io are reported as a function of time for a supersaturation ratio σ ) 4.16, in the absence of citric acid (cCA ) 0) and in the presence of different citric acid concentrations added in solution (cCA ) 0.01, 0.05, 0.10, and 0.30 g/L), at the temperature of 25 °C. The figure shows that system optical properties remain unchanged until nucleation occurs in solution; at that time, signals of transmitted light register a modification, in particular, Itrans/Io starts to decline. This change in system optical properties, which is a measure of the induction period, is evidently affected by the presence of citric acid in solution; as a matter of fact it is clear, from the comparison among curves, that when citric acid is present in solution, induction time increases, thus gypsum nucleation is retarded with respect to the case of cCA ) 0.9
Figure 3. Induction period as a function of supersaturation ratio for different temperatures: open symbols, cCA ) 0.05 g/L; filled symbols, cCA ) 0.10 g/L; (O-) T ) 15 °C; (0--) T ) 25 °C; (4-‚-‚-‚) T ) 35 °C; (]‚‚‚‚) T ) 45 °C.
Figure 3 shows, for fixed citric acid concentrations, and namely cCA ) 0.10 g/L and cCA ) 0.05 g/L, the dependence of induction period on supersaturation ratio; tind experimental results are reported for the temperatures of 15, 25, 35, and 45 °C. Figure 3 shows that, as expected, the induction period for gypsum nucleation continuously decreases with increasing supersaturation,9 and that the effect of temperature is opposite to that of citric acid, as T enhances the nucleation of gypsum crystals by reducing the induction time. Again, all experimental points obtained with the higher citric acid concentration (cCA ) 0.10 g/L) lay above the corresponding points obtained at the lower cCA (cCA ) 0.05 g/L). Moreover, the figure shows that the retarding effect of citric acid on induction time is stronger at low temperature (see 15 °C) than at higher temperature levels (see 45 °C). As indicated by the literature, the dependence of tind on supersaturation allows discrimination of whether the appearance of the new solid phase is controlled by nucleation and/or by growth and to distinguish between homogeneous and heterogeneous nucleation phenomena.6,7 This is noteworthy in the estimation of some characteristic parameters of primary nucleation, such as the interfacial tension. Because it is not possible to distinguish a priori which of possible mechanisms controls the induction period, experimental data have been interpreted according to the different relationships, valid when tn . tg, tn = tg and tn , tg; the so-estimated values of the interfacial tensions, compared with wellassessed literature values, allowed us to choose the most probable among the mechanisms cited above.13 This a posteriori analysis permitted us to establish that in the present experimental conditions, the most likely mechanism is the nucleation governing mechanism, taking place when tn . tg. Consequently, the following equation derived from homogeneous nucleation equations when nucleation is controlling, was considered:6,14
log(tind) ) C +
D T (log σ)2 3
(4)
where C is an empirical constant and D is given by
6650 Ind. Eng. Chem. Res., Vol. 42, No. 25, 2003
D)
βγ3SVm2NAf(φ) (2.3R)3ν2
(5)
in which β is a shape factor, γS is the surface energy, NA is the Avogadro number, R is the gas constant, Vm the molar volume, ν is the number of ions in which the molecule is dissociated, and f(φ) is a correction factor which takes into account for the heterogeneous nucleation. In particular, according to So¨hnel and Mullin,6 when purely homogeneous nucleation takes place it is f(φ) ) 1, whereas when heterogeneous nucleation occurs it is f(φ) < 1. Therefore, a change in the slope of the linearization of experimental results according to eq 4 may indicate a transition from homogeneous to heterogeneous nucleation mechanisms. In a previous work,13 the distinction between homogeneous and heterogeneous nucleation mechanisms has been already carried out for cCA ) 0.01 g/L, by plotting experimental data of tind as a function of numerous σ values, at a fixed temperature of 25 °C. In particular, a transition zone between the two nucleation mechanisms has been individuated, and the data belonging to the homogeneous region have been used to estimate the interfacial tension values. In this paper, this distinction between the two nucleation regions has been carried out for all tind experimental data, selecting among them the ones belonging to the homogeneous nucleation region; particularly, it is worth noting that all the experimental results obtained for cCA ) 0.30 g/L have been not considered, as they belong to the heterogeneous nucleation region. Figure 4 shows the distinction among homogeneous and heterogeneous nucleation data carried out for the citric acid concentration cCA ) 0.10 g/L, at the temperature T ) 15 °C. Figure 5 reports the linearization of selected experimental data for cCA ) 0.10 g/L and cCA ) 0.05 g/L at the temperatures of T ) 15, 35, and 45 °C, respectively. In particular, from the slopes of the straight lines reported in Figure 5 and in an analogous plot for cCA ) 0.01 g/L, the values reported in Table 1 have been obtained (in eq 5 it was considered β ) 16π/3, assuming a spherical particle, and Vm ) 74.69 cm3/mol). As already found,13 the interfacial tension slightly varies with citric acid concentrations, if compared with the γS value obtained in the absence of any additive at T ) 25 °C (γS ) 31.9 mJ/m2);9 this circumstance may be explained by considering that the action of the additive, in the specific case of citric acid, is of retarding nucleation kinetic, but not of modifying the relative crystalsolution properties. A possible explanation of this specific additive behavior can be found in the work by Sarig and Mullin,15 who found that foreign substances added in precipitating solution may enhance or suppress nucleation, depending on whether the ion builds into the crystal lattice or it is adsorbed on surface. In the first case, the rate of homogeneous nucleation can be strongly influenced, whereas in the opposite case the solid phase does not exhibit any influence. Probably the marked retarding effect of citric acid on the homogeneous nucleation of gypsum is due to its setting into lattice; it is likely that the additive molecules enter the structure, and hence disrupt the formation of the critical nucleus and/or the formation of nuclei to the detectable crystal size.16 However, the surviving stable nuclei do not show any modification of their surface properties, as for example the interfacial tension values.
Figure 4. Distinction between homogeneous and heterogeneous nucleation data: T ) 15 °C; cCA ) 0.10 g/L.
Figure 5. Estimation of interfacial tension: open symbols, cCA ) 0.05 g/L; filled symbols, cCA) 0.10 g/L. Table 1. Estimated Interfacial Tension Values for Calcium Sulfate Dihydrate in Aqueous Solutions
a
T (°C)
cCA (g/L)
γS (mJ/m2)
15 15 15 25 25 25 35 35 35 45 45 45
0.01 0.05 0.10 0.01 0.05 0.10 0.01 0.05 0.10 0.01 0.05 0.10
40.7 41.3 38.1 37.0a 41.0 43.8 38.1 38.0 41.9 34.8 46.3 44.2
See ref 13.
Moreover, for a fixed citric acid level the effect of temperature is almost insignificant, according to the fact that, as reported in detail elsewhere,13 a good agreement has not been found among researchers mostly for what concerns the dependency of γS on temperature. Once the distinction between homogeneous and heterogeneous nucleation data has been carried out, the
Ind. Eng. Chem. Res., Vol. 42, No. 25, 2003 6651
technique, for a supersaturation ratio ranging from 4 to 5, at temperatures in the range 15-45 °C, and with citric acid added in solution as an additive, in concentrations ranging from 0.01 to 0.30 g/L. These values have been compared with those previously estimated in the absence of additives, showing that the citric acid has a strong inhibiting effect on gypsum nucleation kinetic. Various interfacial tension values between crystals and solution have been calculated as a function of temperature and by exploring different citric acid concentrations, in the case of nucleation controlled induction period; results indicate that the average interfacial tensions slightly vary in the citric acid interval explored. Moreover, the activation energy for gypsum nucleation has been estimated, confirming a previous result, obtained in the absence of any additive. Notation
Figure 6. Estimation of activation energy for gypsum nucleation: (a) cCA ) 0.05 g/L; (b) cCA ) 0.10 g/L.
estimation of the activation energy for gypsum primary nucleation and interfacial tension between gypsum crystals and surrounding aqueous solution can be easily performed for each citric acid level. The following empirical relationship, proposed by Liu and Nancollas,17 was used to correlate data of tind versus T:
( )
tind ) τexp
Eact RT
(6)
where τ is a constant, Eact is the activation energy for the process, and R is the gas constant. In particular eq 6 was reported as continuous lines in Figure 6a and b, and from the slopes of these straight lines the values of 30.7 kJ/mol (cCA ) 0.01 g/L), 26.9 kJ/mol (cCA ) 0.05 g/L), and 29.0 kJ/mol (cCA ) 0.10 g/L) were determined for the activation energy. These values, whose average is 28.9 kJ/mol, are comparable with respect to that previously found in the absence of any additives (Eact ) 30 kJ/mol9). Conclusions Experimental results have shown that very low concentrations of citric acid are capable of retarding calcium sulfate nucleation. Interfacial tensions between gypsum crystals and aqueous solution and activation energy for gypsum nucleation have been calculated by means of the experimental measurements of induction time. In particular, the induction period for gypsum nucleation has been experimentally measured by using an optical
a ) activity, mol/m3 c ) concentration, mol/m3 C ) constant in eq 4, dimensionless D ) constant in eq 4, K3 Eact ) activation energy, kJ/mol f(φ) ) correction factor in eq 5, dimensionless I ) intensity of light, W/m2 Kps ) solubility product, mol4/kg4 m ) molality, mol/kg NA ) Avogadro number, 1/mol R ) gas constant, J/mol K t ) time, s tind ) induction period, s T ) absolute temperature, K Vm ) molar volume, m3/mol z ) electric charge, dimensionless Greek Letters β ) shape factor, dimensionless γ ) activity coefficient, dimensionless γS ) surface energy, J/m2 λo ) wavelength, m ν ) number of ions, dimensionless σ ) supersaturation ratio, dimensionless τ ) constant in eq 6, s Subscripts CA ) citric acid J ) chemical species sca ) scattering trans ) transmitted w ) water 0 ) relative to incident light
Literature Cited (1) Marshall, W. L.; Slusher, R. Thermodynamics of calcium sulfate dihydrate in aqueous sodium chloride solutions, 0-110°. J. Phys. Chem. 1966, 70, 4015. (2) Stumm, W.; Morgan, J. J. Aquatic Chemistry, 3rd ed.; Wiley & Sons: New York, 1996. (3) Betz Handbook of Industrial Water Conditioning, 8th ed.; Betz Lab, Inc.: Trevose, PA, 1982. (4) Adams, J. F.; Papangelakis, V. G. Gypsum scale formation in continuous neutralization reactors. Can. Metal. Quart. 2000, 39, 421. (5) Badens, E.; Veesler, S.; Boistelle, R. Crystallization of gypsum from hemihydrate in the presence of additives. J. Cryst. Growth 1999, 198/199, 704. (6) So¨hnel, O.; Mullin, J. W. Interpretation of crystallization induction periods. J. Colloid Interface Sci. 1988, 123, 43.
6652 Ind. Eng. Chem. Res., Vol. 42, No. 25, 2003 (7) So¨hnel, O.; Garside, J. Precipitation. Butterworth-Heinemann Ltd.: Oxford, 1992. (8) Mullin, J. W., Crystallization, 3rd ed.; Butterworth-Heinemann Ltd.: Oxford, 1993. (9) Lancia, A.; Musmarra, D.; Prisciandaro, M. Measurement of the induction period for calcium sulfate dihydrate precipitation. AIChE J. 1999, 45, 390. (10) Zacek, S.; Nyvlt, J.; Garside, J.; Nienow, A. W. A stirred tank for continuous crystallization studies. Chem. Eng. J. 1982, 23, 111. (11) Bromley, L. A., Thermodynamic properties of strong electrolytes in aqueous solutions. AIChE J. 1973, 19, 313. (12) Lancia, A.; Musmarra, D.; Prisciandaro, M. Calcium sulfate. Contribution in Kirk-Othmer Encyclopedia of Chemical Technology, 4th ed.; John Wiley: New York, 2002. (13) Prisciandaro, M.; Lancia, A.; Musmarra, D. Citric acid retarding effect on gypsum crystallization. Chem. Eng. Trans. Ser. 2002, 1, 677.
(14) He, S.; Oddo, J. E.; Tomson, M. B. The nucleation kinetics of calcium sulfate dihydrate in NaCl Solutions up to 6 m and 90 °C. J. Colloid Interface Sci. 1994, 162, 297. (15) Sarig, S.; e Mullin, J. W., Effect of impurities on calcium sulphate precipitation. J. Chem. Technol. Biotechnol. 1982, 32, 525. (16) Chen, B. D.; Garside, J. Crystallization of tetracosane from dodecane solutions with homologous additives., J. Cryst. Growth 1996, 166, 1094. (17) Liu, S. T.; Nancollas, G. H. A kinetic and morphological study of the seeded growth of calcium sulfate dihydrate in the presence of additives. J. Colloid Interface Sci. 1975, 52, 593.
Received for review December 9, 2002 Revised manuscript received September 4, 2003 Accepted September 5, 2003 IE020996H
