Ind. Eng. Chem. Res. 2009, 48, 10877–10883
10877
Gypsum Scale Control by Nitrilotrimethylenephosphonic Acid Marina Prisciandaro,*,† Emilia Olivieri,‡ Amedeo Lancia,‡ and Dino Musmarra§ Dipartimento di Chimica, Ingegneria Chimica e Materiali, UniVersita` dell’Aquila, Piazzale Pontieri 2, Monteluco di Roio, 67040 L’Aquila (AQ), Italy, Dipartimento di Ingegneria Chimica, UniVersita` degli Studi di Napoli “Federico II”, Piazzale Tecchio 80, 80125 Napoli (NA), Italy, and Centro Interdipartimentale di Ricerca in Ingegneria Ambientale, Dipartimento di Ingegneria CiVile, Seconda UniVersita` degli Studi di Napoli, Real Casa dell’Annunziata, Via Roma 29, 81031 AVersa (CE), Italy
In this paper the retardant effect of nitrilotrimethylenephosphonic acid (NTMP) on calcium sulfate dihydrate nucleation kinetics is evaluated by means of an optical technique able to accurately measure the induction period. A laboratory-scale experimental apparatus is used, in which sodium sulfate and calcium chloride are mixed to obtain a supersaturated calcium sulfate dihydrate solution; all experiments are carried out for various values of NTMP concentrations (0.005-0.05 g/L) in solution, while changing the saturation index in the range of 4.04 - 4.82; the temperature was varied in the interval 15-45 °C. Experimentally measured induction times are used to evaluate the interfacial tension (γS) between crystals and mother solution and to estimate the activation energy (Eatt) for precipitation in the presence of NTMP. The measured values of γS and Eatt are compared with those found in the absence of any additive and in the presence of citric acid, showing that NTMP is a very strong retardant for gypsum nucleation. Introduction Calcium sulfate dihydrate (gypsum) is a poorly soluble salt whose precipitation is unwanted in several processes, such as seawater desalination,1 water distillation,2 industrial water recovery in cooling tower technology, and hydrometallurgical operations.3 In such processes, gypsum scale deposition may have several disadvantages: scales offer a resistance to the heat flow when they crystallize on heat-transfer surfaces, and they can accumulate in pipelines, orifices, and other flow passages, seriously impeding the process flow;4 moreover, calcium sulfate scales constitute, together with calcium carbonate scales, the major cause of fouling in reverse osmosis membranes, resulting in a continuous decline in desalted water production and hence reducing the overall efficiency and increasing the operation and maintenance costs.5 Therefore, from the economic point of view, the formation of calcium sulfate mineral scale is an obstacle to the recovery of potable water from sea or brackish water as well as to the industrial utilization of many natural waters.6 Despite the fact that considerable research has been going on during the past decades on the formation of calcium sulfate in aqueous media, there is still a great uncertainty as to the mechanism of formation of this salt because of the widely variable conditions of the solutions in which the salt formation takes place, including temperature, pH, ionic strength, and composition, and the presence of foreign ions and water-soluble compounds.7 However, it is well-known that the precipitation of the calcium sulfate from aqueous solution onto surfaces occurs when an electrolyte solution, containing calcium and sulfate ions, is supersaturated by evaporation, cooling, or heating, etc.; the salts (calcium sulfate anhydrous, hemihydrate or dihydrate), will precipitate according to the concentration of the various ions and to temperature. In particular, the solubility of all calcium * To whom correspondence should be addressed. Tel.: [+39](0862)434255. Fax: [+39](0862)434254. E-mail: marina.prisciandaro@ univaq.it. † Universita` dell’Aquila. ‡ Universita` degli Studi di Napoli “Federico II”. § Seconda Universita` degli Studi di Napoli.
sulfate forms decreases with increasing temperature starting from 40 °C, a fact that is responsible for the formation of scale mostly made up of a mixture of calcium sulfate dihydrate (gypsum) and calcium sulfate anhydrous (anhydrite).8 An accounted technique to hinder or delay gypsum scale formation is the addition of additives in solution, which retards calcium sulfate formation. The additives commonly employed for gypsum scale control are some organic and inorganic substances capable of altering the surface properties of the crystals, affecting the nucleation and growth rate, and modifying the shape of formed crystals and their agglomeration/dispersion behavior.9 A number of investigations have reported that the precipitation of calcium sulfate is significantly reduced in the presence of water-soluble additives such as special types of polymers and copolymers with carboxyl groups7 (e.g., polyacrilic acid (PAA) and copolymer of PAA with polystyrene sulfonic acid (PSA)), organophosphorus compounds derivative of phosphonic acid10 (phosphonates such as nitrilotrimethylenephosphonic acid (NTMP), 1-hydroxyethane-1,1-diphosphonic acid (HEDP), and others11), organic phosphate esters,4 citric acid,12 anionic and cationic surfactants,13 and some metal ions,14 while among organic additives, the NTMP is used as a cost-effective gypsum scale inhibitor in circulating cooling water treatment, industrial boilers, and heat exchangers.10 A well-documented state of the art on the NTMP effects on gypsum precipitation is reported in a previously published paper.15 The 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 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
10.1021/ie900253f CCC: $40.75 2009 American Chemical Society Published on Web 10/15/2009
10878
Ind. Eng. Chem. Res., Vol. 48, No. 24, 2009
Figure 1. Sketch of the experimental apparatus.
growth-controlled induction period), or by growth alone (tn , tg, growth-controlled induction period).16 While 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 and/or by growth, 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 Mullin17 and So¨hnel and Garside,18 it is possible to use the experimental knowledge of the induction period to estimate the activation energy (Eatt) for nucleation from the dependence of tind on temperature. Moreover, tind dependence on supersaturation allows one to determine the interfacial tension (γS) among crystals and the surrounding solution. Actually, depending on the prevailing mechanism, nucleation or growth, the dependence of the induction time on saturation index (SI) has different shapes, and, namely, if tn . tg or tn = tg, a linear relationship between log(tind) and (log SI)-2 does exist, with a different value of the regression slope; on the contrary, when tn , tg, the correlation is between log(tind) and (log SI)-1. This paper mainly focuses on the measurement of the induction period for gypsum nucleation when NTMP is added to solutions as an additive at various temperatures, by using a well-assessed laser light scattering technique previously devised for the measurement of tind.19 The measured induction period values are used to estimate the values for the interfacial tension between gypsum crystals and the mother solution for each NTMP 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 liquor19 and in the presence of citric acid.12 Experimental Apparatus and Procedure The experimental apparatus consists of a stirred reactor with a related optical device and is schematically shown in Figure 1. The reactor is 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 is surrounded by a water jacket for temperature control; stirring is 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, allows one to remove samples of the suspension; the position of the tube has been chosen to ensure that the content of the exit stream is the same as the content of the reactor.20 The stream removed by the off-take tube is sent, by a peristaltic pump, to an analysis flow-through cell and then is
conveyed again to the crystallizer. The cell, made of quartz, is 0.07 m long, with a square section of 0.01 m2 and 0.0025 m thickness. A 10 mW He-Ne laser beam (I0 ) 632.8 nm) is focused on the cell, orthogonal to its walls; the beam, whose diameter is 2 mm, is vertically polarized. On the path of the laser beam, placed at 45° with respect to its direction, a beam splitter is provided in order to divide the laser beam into two parts: one is used to light the measure cell, while the other, collected by a photodiode, allows one to check the stability and the intensity of laser beam (I0). The signal of the scattered light (Isca) is collected by two lenses of focal lengths 120 and 50 mm, at 90° with respect to the laser beam; this signal is sent, through a quartz optical fiber which ends 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) is collected by a photodiode located beyond the cell, at 0° with respect to the laser beam. The two analogue signals of scattered and transmitted light, together with I0, are collected by a recorder device. Supersaturated solutions of calcium sulfate are prepared by mixing clear aqueous solutions of reagent-grade CaCl2 · 2H2O, Na2SO4 (Applichem, Darmstadt, Germany), and N(CH2PO3H2)3 (Acros Organics, Geef, Belgium) in bidistilled water. The dissolved Ca2+ ion concentration is measured by ethylenediaminetetraacetic acid titration using Murexide (Applichem, Darmstadt, Germany) as an indicator, while the SO42- ion concentration is measured by means of turbidity measurements carried out in a spectrophotometer (Hach model 2010). The NTMP concentration is determined by converting it into the orthophosphate form with potassium persulfate and a UV lamp and analyzing the free orthophosphate by means of a spectrophotometer (Hach model 2010). The complete conversion of phosphonate into orthophosphate is verified with total organic carbon (TOC) analysis (TOC-V CSH Shimadzu) carried out on several samples. Once prepared the two solutions are filtered, by using a 0.45 µm filter (Millipore, HVLP 4700) and a vacuum pump (Vacuubrand, MZ4C), in order to eliminate all foreign material inevitably present in the solution, and then mixed directly into the reactor. A NTMP aqueous solution is added to the Na2SO4 solution and then fed to the reactor. The equimolar concentrations of CaCl2 · 2H2O and Na2SO4 in the reactor vary between 108.7 and 139.3 mol/m3, while NTMP concentration (cNTMP) varies in the interval 0.005-0.05 g/L (1.7 × 10-2 to 1.7 × 10-1 mol/m3). With regard to the tind calculations, three NTMP levels are explored, namely, cNTMP ) 0.005 g/L, cNTMP ) 0.01 g/L, and cNTMP )0.05 g/L, and the relative pH values are 4.1, 3.8, and 3.1. The lower level (cNTMP ) 0.005 g/L) has been selected by considering the dosage range of NTMP typically used as a scale inhibitor in process equipment.21 The saturation index has been calculated considering the liquid-solid equilibrium between Ca2+ and SO42- ions and solid CaSO4 · 2H2O, as described by the following equation: Ca2+ + SO24 + 2H2O ) CaSO4 · 2H2O
(1)
so that it is SI )
(aCa2+)(aSO42-)(aH2O)2 Kps
(2)
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
Ind. Eng. Chem. Res., Vol. 48, No. 24, 2009
Figure 2. Intensities of the transmitted light (Itrans/I0, upper curves) and scattered light (Isca/I0, lower curves) as a function of time for different NTMP concentrations. SI ) 4.32; T ) 15 °C.
of gypsum. The value of Kps is calculated as a function of temperature by means of the following relationship:8 ln(Kps) ) 390.96 - 152.62 log T - 12545.62/T + 0.08T (3) The concentration values of the J species are calculated by solving a numerical model based on the equilibria that take place in the aqueous solution and, namely, the protonation equilibria of NTMP,22 the complexation equilibria between NTMP and Ca2+,22 the protonation equilibrium of SO42-, and the water ionic product. The activity coefficients in the supersaturated solution are calculated by using Bromley’s method23 and are reported in detail elsewhere.12 All experiments have been carried out for various values of NTMP concentrations (0.005-0.05 g/L) while changing the saturation index in the range of 4.04-4.82. The temperature varies in the interval of 15-45 °C. The induction period is evaluated by measuring the intensity of scattered and transmitted light signals as a function of time. Such signals are processed to evaluate tind by adopting two parallel procedures, a graphic procedure and a numerical one. These procedures, described in detail elsewhere,19 have given quite similar ((10%) results. Gypsum crystals grown at T ) 35 °C at fixed supersaturation (SI ) 4.83) in the presence of 0.05 g/L of NTMP are analyzed by scanning electron microscope (Philips SEM XL30) and then compared to those grown in solution without any additive. Results and Discussion In Figure 2 the smoothed curves of Itrans/I0 and Isca/I0 are reported as a function of time for SI ) 4.32, in the presence of different NTMP concentrations added to the solution (cNTMP ) 0.005, 0.01, and 0.05 g/L), at the temperature of 15 °C. The figure shows that the system optical properties remain unchanged until nucleation occurs in solution: then, signals of transmitted light change, in particular, Itrans/I0 starts declining while Isca/I0 begins to grow. This change in system optical properties, which is a measure of the induction period, is clearly affected by the presence of NTMP in solution; as a matter of fact it is clear, by comparing the curves, that when increasing NTMP concentra-
10879
Figure 3. Induction period as a function of saturation index for different temperatures (cNTMP ) 0.005 g/L): O, T ) 15 °C; 0, T ) 25 °C; ∆, T ) 35 °C; ×, T ) 45 °C.
tions are added to the solution, induction time increases and gypsum nucleation is retarded. Figure 3 shows the dependence of induction period on saturation index for four temperature levels, and, namely, T ) 15, 25, 35, and 45 °C, respectively. It can be observed that the induction period for gypsum nucleation continuously decreases with increasing supersaturation.19 By using the following semiempirical correlation to fit experimental data24 tind )
K SIr
(4)
where K and r are empirical constants, the curves sketched in Figure 3 are obtained. Moreover, Figure 3 shows that the effect of temperature is opposite to that of NTMP, since T enhances the nucleation of gypsum crystals by reducing the induction time; however, the figure shows that experimental points at T ) 45 °C and T ) 35 °C are inverted; i.e., induction period values obtained at the highest temperature (T ) 45 °C) lay above the corresponding values at T ) 35 °C: this circumstance could be explained by considering that, above 40 °C, the solubility of all calcium sulfate forms decreases;8,25 probably, at T ) 45 °C, a mixture of calcium sulfate dihydrate and calcium sulfate anhydrous is precipitated in solution. This behavior is confirmed even at the other tested NTMP concentrations (i.e., cNTMP ) 0.01 and 0.05 g/L). Therefore, data obtained at T ) 45 °C have not been taken into account for the parameter estimation carried out in the following. Parts a and b of Figure 4 show the decreasing trend of induction time with supersaturation for the three selected temperature levels (T ) 15, 25, and 35 °C) at the other two studied additive concentrations studied (0.01 and 0.05 g/L, respectively). The decreasing trend of induction time with supersaturation is confirmed, together with the strong retardant effect of NTMP, fluctuating on a tind percentage increase of about 40% while passing from cNTMP ) 0.01 g/L to cNTMP ) 0.05 g/L for a fixed SI and T; with regard to, for example, SI ) 4.82 and T ) 35 °C, tind increases by 45%; moreover, this figure reports also the comparison between NTMP and citric acid, previously studied.12 At the same additive concentration, experimental points in the presence of NTMP lay always above the corresponding results obtained in the
10880
Ind. Eng. Chem. Res., Vol. 48, No. 24, 2009 Table 1. Estimated Interfacial Tension Values for Calcium Sulfate Dihydrate in Aqueous Solutions in the Presence Of NTMP T (°C)
cNTMP (g/L)
γS (mJ/m2)
T (°C)
cNTMP (g/L)
γS (mJ/m2)
15 15 15 25 25
0.005 0.01 0.05 0.005 0.01
51.7 47.1 47.6 41.2a 46.5a
25 35 35 35
0.05 0.005 0.01 0.05
54.0a 39.6 36.2 52.2
a
Reference 15.
Figure 4. Induction period as a function of saturation index for different temperatures at two additive concentrations: (a) cadditive ) 0.01 g/L; (b) cadditive ) 0.05 g/L. Symbols: open, experiment with NTMP; filled, experiments with citric acid; O, b, T ) 15 °C; 0,9, T ) 25 °C; ∆, 2, T ) 35 °C.
Figure 5. Induction period as a function of saturation index: (a) T ) 15 °C; (b) T ) 35 °C. Symbols: O, cNTMP ) 0.005 g/L; 0, cNTMP ) 0.01 g/L; ∆, cNTMP ) 0.05 g/L.
presence of citric acid at the same temperature, a result already observed for T ) 25 °C.15 As indicated in the literature, the dependence of tind on supersaturation allows one to discriminate 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.16,17 This is noteworthy in the estimation of some characteristic parameters of primary nucleation, such as the interfacial tension. Since it is not possible
Figure 6. Induction period as a function of the inverse of temperature: (a) cNTMP ) 0.005 g/L; (b) cNTMP ) 0.01 g/L; (c) cNTMP ) 0.05 g/L. Symbols: O, SI ) 4.16; 0, SI ) 4.32; ∆, SI ) 4.66; ×, SI ) 4.83; --, no additive, SI ) 2.16.
to identify a priori the mechanism controlling the induction period, experimental data have been interpreted according to the different relationships, valid when tn . tg, tn = tg, and tn , tg; interfacial tension values estimated in this way have been compared with well-assessed literature values, thus allowing one to identify the most likely mechanism among those mentioned above.16 This a posteriori analysis permits one to establish that, in the present experimental conditions, the most likely mechanism is the nucleation governing mechanism, taking place when t n . t g.
Ind. Eng. Chem. Res., Vol. 48, No. 24, 2009
10881
Figure 7. SEM images of gypsum precipitates in the absence and in the presence of NTMP (SI ) 4.83; T ) 35 °C): (a) no additive; (b) cNTMP ) 0.05 g/L.
Consequently, the following equation, derived from homogeneous nucleation equations when nucleation is the control mechanism, has been considered:16 log(tind) ) C +
D T3(log SI)2
(5)
where C is an empirical constant and D is given by D)
βγS3Vm2NAf(φ) (2.3R)3ν2
(6)
in which β is a shape factor, γS is the surface energy, NA is the Avogadro number, R is the gas constant, Vm is 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 the heterogeneous nucleation; in particular, according to So¨hnel and Mullin,16 when purely homogeneous nucleation takes place, it is f(φ) ) 1, while when heterogeneous nucleation occurs, it is f(φ) < 1. Therefore, a change in the slope of the linearization of experimental results according to eq 5 may indicate a transition from homogeneous to heterogeneous nucleation mechanisms. In a previous work,15 the distinction between homogeneous and heterogeneous nucleation mechanisms has already been carried out for cNTMP ) 0.005, 0.01, and 0.05 g/L, by plotting experimental data of tind as a function of numerous σ values, at the fixed temperature of 25 °C. In particular, a transition zone between the two nucleation mechanisms has been identified, and the data belonging to the homogeneous region have been used to estimate the interfacial tension values at T ) 25 °C. In this paper, this distinction between the two nucleation regions has been carried out for all tind experimental data at the different temperature levels explored (T ) 15 and 35 °C), selecting among them the ones belonging to the homogeneous nucleation region. Parts a and b of Figure 5 report the linearization of selected experimental data for all cNTMP levels explored (cNTMP ) 0.005, 0.01, and 0.05 g/L) at the temperatures of T ) 15 and 35 °C, respectively. In particular, from the slopes of the straight lines reported in Figure 5a,b, the following average values are obtained: γS ) 48.8 mJ/m2 at T ) 15 °C; γS ) 42.6 mJ/m2 at T ) 35 °C (in eq 6 β ) 16π/3, assuming spherical particle, and Vm ) 74.69 cm3/ mol are considered). Table 1 reports the punctual γS values, as a function of temperature (15, 25, and 35 °C) and NTMP concentration. The analysis of the table reveals that, for a fixed additive concentration, interfacial tension values exhibit a slight variation with temperature, with a decreasing trend as temperature increases. However, a good agreement has not been found
among researchers, especially as far as the dependence of γS on temperature is concerned. Moreover, for a fixed temperature level the effect of NTMP is more interesting, even if not very strong and rather variable. As a matter of fact, in agreement with experimental observations by Hasson and co-workers,26 the presence of an antiscalant could be expected to enhance the crystallization surface energy. In the case of NTMP, this is particularly true for the temperature of 35 °C: when passing from cNTMP ) 0.005 to cNTMP ) 0.05 g/L, the surface energy increases by about 25%. This dependence of γS on additive concentration could be explained by considering that the action of the additive, NTMP in this case, is retarding nucleation kinetics, modifying the relative crystal-solution properties.17 Probably, the marked retarding effect of NTMP on the homogeneous nucleation of gypsum is due to its setting into lattice; it is likely that the additive molecules enter the structure, disrupting the lattice structure and creating a higher surface energy that prevents the formation of other nuclei and the growth of nuclei into larger crystals. On the contrary, in the case of citric acid,12 the surviving stable nuclei do not show any modification of their surface properties, such as the interfacial tension values.27 Once the distinction between homogeneous and heterogeneous nucleation data has been carried out, the 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 NTMP level. The following empirical relationship, derived from the classical nucleation theory,28 was used to correlate data of tind versus T: tind ) τ exp
( ) Eatt RT
(7)
where τ is a constant, Eatt is the activation energy for the process, and R is the gas constant. In particular eq 7 is reported as continuous lines in Figure 6a-c, and from the slopes of these straight lines the values of 30.3 kJ/mol (cNTMP ) 0.005 g/L), 29.3 kJ/mol (cNTMP ) 0.01 g/L), and 17.1 kJ/mol (cNTMP ) 0.05 g/L) are determined for the activation energy. This decreasing trend of activation energy with increasing NTMP concentration could be explained by considering that, during the induction period, an increase in antiscalant concentration into crystal lattice poisons most of the active growing sites. However, some of the growth sites of lower energy may still be free to grow, and the reaction proceeds at a very slow rate since the additive has disrupted the lattice ordinate structure, thus reducing the activation energy necessary to create new nuclei.29 However, the activation energy average value is 25.6 kJ/mol, comparable with those previously found in the absence of any
10882
Ind. Eng. Chem. Res., Vol. 48, No. 24, 2009
additives (Eatt ) 30 kJ/mol),19 and in the presence of citric acid (Eatt ) 29 kJ/mol).12,30 Finally, parts a and b of Figure 7 show two SEM photographs of the formed precipitates at T ) 35 °C without any additive (Figure 7a) and in the presence of 0.05 g/L NTMP (Figure 7b), at the same supersaturation level SI ) 4.83; the comparison between the two images confirms that NTMP affects the shape and size of gypsum crystals. According to a previous work,15 it can be observed that crystals formed without NTMP exhibit the long, needle-shaped structure which is typical of gypsum, while in the presence of NTMP the shape changes to a less elongated, platelike type with a regular shape. The change may be explained in terms of adsorption of the NTMP onto the crystalline growth site of gypsum, as reported in the literature.31 Conclusions Experimental results presented in this paper have shown that commercially employed concentrations of nitrilotrimethylenephosphonic 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 technique, for a saturation index in the range of 4.04-4.82, at temperature in the interval of 15-35 °C, and, with NTMP added in solution as an additive, in concentration varying from 0.005 to 0.05 g/L. These values have been compared with those previously estimated in the absence of any additives, and in the presence of citric acid, showing that the NTMP has a marked inhibiting effect on gypsum nucleation kinetic, stronger than that of citric acid. Various interfacial tension values between crystals and solution have been calculated as a function of temperature and by exploring different NTMP concentrations, in the case of nucleation controlled induction period; results indicate that the average interfacial tensions slightly vary in the NTMP interval explored. Moreover, the activation energy for gypsum nucleation has been estimated, confirming a previous result, obtained in the absence of any additive and in the presence of citric acid. Notation a ) activity, mol/m3 c ) concentration, mol/m3 C ) constant in eq 5, dimensionless D ) constant in eq 5, K3 Eatt ) activation energy, kJ/mol f(φ) ) correction factor in eq 6, 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) SI ) saturation index, dimensionless t ) time, s tind ) induction period, s T ) absolute temperature, K Vm ) molar volume, m3/mol
Greek Letters β ) shape factor, dimensionless γ ) activity coefficient, dimensionless γS ) surface energy, J/m2 λ0 ) wavelength, m ν ) number of ions, dimensionless τ ) constant in eq 7, s Subscripts J ) chemical species sca ) scattered trans ) transmitted w ) water 0 ) relative to incident light
Literature Cited (1) Stumm, W., Morgan J. J. Aquatic Chemistry, 3rd ed.; John Wiley & Sons: New York, 1996. (2) Betz. Handbook of Industrial Water Conditioning, 8th ed.; Betz Laboratory Inc.: Trevose, PA, 1982. (3) Adams, J. F.; Papangelakis, V. G. Gypsum scale formation in continuous neutralization reactors. Can. Met. Q. 2000, 39, 421–432. (4) El Dahan, H. A.; Hegazy, H. S. Gyspum scale control by phosphate ester. Desalination 2000, 127, 111–118. (5) Sheikholeslami, R.; Ong, H. W. K. Kinetics and thermodynamics of calcium carbonate and calcium sulfate at salinities up to 1.5 M. Desalination 2003, 157, 217–234. (6) Hamdona, S. K.; Al Hadad, O. A. Influence of additives on the precipitation of gypsum in sodium chloride solutions. Desalination 2008, 228, 277–286. (7) Lioliou, M. G.; Paraskeva, C. A.; Koutsoukos, P. G.; Payatakes, A. C. Calcium sulfate precipitation in the presence of water-soluble polymers. J. Colloid Interface Sci. 2006, 303, 164–170. (8) Marshall, W. L.; Slusher, R. Thermodynamics of calcium sulfate dihydrate in aqueous sodium chloride solutions 0-110°. J. Phys. Chem. 1966, 70, 4015–4027. (9) El Shall, H.; Rashad, M. M.; Abdel-Aal, E. A. Effect of phosphonate additive on crystallization of gypsum in phosphoric and sulfuric acid medium. Cryst. Res. Technol. 2002, 37, 1264–1273. (10) Klepetsanis, P. G.; Koutsoukos, P. G. Kinetics of calcium sulphate formation in aqueous media: effect of organophosphorus compounds. J. Cryst. Growth 1998, 193, 156–163. (11) Liu, S. T.; Nancollas, G. H. The crystal growth of calcium sulfate dihydrate in the presence of additives. J. Colloid Interface Sci. 1973, 44 (3), 422–429. (12) Prisciandaro, M.; Lancia, A.; Musmarra, D. The retarding effect of citric acid on calcium sulfate nucleation kinetics. Ind. Eng. Chem. Res. 2003, 42, 6647–6652. (13) Mahmoud, M. M. H.; Rashad, M. M.; Ibrahim, I. A.; Abdel-Aal, E. A. Crystal modification of calcium sulfate dehydrate in the presence of some surface-active agents. J. Colloid Interface Sci. 2004, 270, 99–105. (14) Hamdona, S. K.; Al Hadad, U. A. Crystallization of calcium sulfate dihydrate in the presence of some metal ions. J. Cryst. Growth 2007, 299, 146–151. (15) Prisciandaro, M.; Olivieri, E.; Lancia, A.; Musmarra, D. Gypsum precipitation from an aqueous solution in the presence of nitrilotrimethylenephosphonic acid. Ind. Eng. Chem. Res. 2006, 45, 2070–2076. (16) So¨hnel, O.; Mullin, J. W. Interpretation of crystallization induction periods. J. Colloid Interface Sci. 1988, 123, 43–50. (17) Mullin, J. W., Crystallization, 3rd ed.; Butterworth-Heinemann: Oxford, U.K., 1993. (18) So¨hnel, O.; Garside, J. Precipitation; Butterworth-Heinemann: Oxford, U.K., 1992. (19) Lancia, A.; Musmarra, D.; Prisciandaro, M. Measurement of the induction period for calcium sulfate dihydrate precipitation. AIChE J. 1999, 45, 390–397. (20) Zacek, S.; Nyvlt, J.; Garside, J.; Nienow, A. W. A stirred tank for continuous crystallization studies. Chem. Eng. J. 1982, 23, 111–113. (21) Screening Information Data Set (SIDS) for High Volume Chemicals, http://www.chem.unep.ch/irptc/sids/OECDSIDS/6419198.pdf, 1993. (22) Deluchat, V.; Bollinger, J. C.; Serpaud, B.; Caullet, C. Divalent cations speciation with three phosphonate ligands in the pH-range of natural waters. Talanta 1997, 44, 897–907.
Ind. Eng. Chem. Res., Vol. 48, No. 24, 2009 (23) Bromley, L. A. Thermodynamic properties of strong electrolytes in aqueous solutions. AIChE J. 1973, 19, 313–320. (24) Packter, A. The precipitation of calcium sulfate dihydrate from aqueous solutionsInduction period, crystal numbers and final size. J. Cryst. Growth 1974, 21, 191–194. (25) Lancia, A.; Musmarra D.; Prisciandaro, M. Calcium sulfate. Contribution on Kirk-Othmer Encyclopedia of Chemical Technology, 4th ed.; John Wiley & Sons: New York, 2002. (26) Hasson, D.; Drak, A.; Semiat, R. Induction times induced in an RO system by antiscalants delaying CaSO4 precipitation. Desalination 2003, 157, 193–207. (27) Sarig, S.; Mullin, J. W. Effect of impurities on calcium sulphate precipitation. J. Chem. Technol. Biotechnol. 1982, 32, 525–531. (28) Wu, W.; Nancollas, G. H. Determination of interfacial tension from crystallization and dissolution data: a comparison with other methods. AdV. Colloid Interface Sci. 1999, 79, 229–279.
10883
(29) 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, 593–601. (30) Prisciandaro, M.; Santucci, A.; Lancia, A.; Musmarra, D. Role of citric acid in delaying gypsum precipitation. Can. J. Chem. Eng. 2005, 83, 586–592. (31) Amathieu, L.; Boistelle, R. Improvement of the mechanical properties of set plasters by mean of four organic additives inducing {101} faces. J. Cryst. Growth 1986, 79, 169–177.
ReceiVed for reView February 16, 2009 ReVised manuscript receiVed August 1, 2009 Accepted September 21, 2009 IE900253F
