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Prediction of BaSO4 Precipitation in the Presence and Absence of a Polymeric Inhibitor: Phosphino-polycarboxylic Acid Jianjun (Alan) Xiao Cognigen Corporation, 395 Youngs Road, Williamsville, New York 14221
A. T. Kan* and M. B. Tomson Department of Environmental Science and Engineering, MS-519, Rice University, Houston, Texas 77005 Received December 8, 2000. In Final Form: April 30, 2001 The induction periods of BaSO4 nucleation from supersaturated solutions have been measured over a wide range of conditions in the presence and absence of phosphino-polycarboxylic acid (PPCA). The inhibition of Barite nucleation in the presence of PPCA was correlated to the solution chemistry over a wide range of conditions. Only the dissociated fraction and the metal-complexed fraction of PPCA are effective to inhibit BaSO4 nucleation, while the protonated fraction has a poor inhibitory effect toward Barite nucleation. Ca2+ enhances the overall efficiency of PPCA through forming Ca-PPCA complexes and decreasing the fraction of protonated PPCA. Temperature does not strongly affect the Barite nucleation inhibition by PPCA. A set of equations has been proposed to model Barite nucleation time in the presence and absence of PPCA.
Introduction Barium sulfate, BaSO4, is a scale commonly found in oil and gas wells and the various industrial water treatment systems. It is problematic since BaSO4 is difficult to remove once it is formed. Furthermore, it is often enriched with radium due to coprecipitation. Therefore, the study of precipitation of BaSO4 from supersaturated solution is of both scientific and practical importance.1-5 Besides barium and sulfate, other components in the solution, such as noncrystalline metal ions and organic inhibitors, can influence Barite nucleation and crystal growth in many different ways. For example, divalent metal ions can replace the crystalline cation in the crystal lattice to form a solid solution or influence the crystal nucleation and growth by adsorption to the nuclei.6 Some organic inhibitors have profound effects in inhibiting nucleation/crystal growth.7-10 The inhibition is presumably caused by adsorption on growth sites or by incorporation into the lattice thereby distorting the crystal lattice.11 Since organic inhibitors are usually weak polyacids, their speciation in solution is sensitive to temper* Corresponding author. E-mail:
[email protected]. (1) He, S.; Oddo, J. E.; Tomson, M. B. J. Colloid Interface Sci. 1995, 174, 319-326. (2) Wojciechowski, K.; Kibalczyc, W. J. Cryst. Growth 1986, 76, 379382. (3) Hartman, P.; Strom, C. S. J. Cryst. Growth 1989, 97, 502-512. (4) Allan, N. L.; Rohl, A. L.; Gay, D. H.; Catlow, C. R.; Davey, R. J.; Mackrodt, W. C. Faraday Discuss. 1993, 95, 273-280. (5) Liu, S. T.; Nancollas, G. H. J. Cryst. Growth 1976, 33, 11-20. (6) Ready, M. M.; Wang, K. K. J. Cryst. Growth 1980, 50, 470-480. (7) Fernandez-Diaz, L.; Putnis, A.; Cumberbatch, T. J. Eur. J. Mineral. 1990, 2, 495-501. (8) Benton, W. J.; Collins, I. R.; Grimsey, I. M.; Parkinson, G. M.; Rodger, S. A. Faraday Discuss. 1993, 95, 281-297. (9) Black, S. N.; Bromley, L. A.; Cottier, D.; Davey, R. J.; Dobbs, B.; Rout, J. E. J. Chem. Soc., Faraday Trans. 1991, 87, 3409-3414. (10) Boak, L. S.; Graham, G. M.; Sorbie, K. S. SPE 50771 1999. (11) Nancollas, G. H.; Zawack, S. J. Inhibitors of Crystallization and Dissolution. In Industrial Crystallization 84; Elsevier: Amsterdam, 1984.
ature, ionic strength, pH, and ionic composition of the solution. Similarly, these factors also have a strong influence on the inhibition efficiency of common scale inhibitors.10,12,13 Therefore, the efficiency of inhibitors has to be related to solution chemistry. Phosphonates and polycarboxylic acids are good inhibitors of mineral nucleation and are widely used in industries. The solution chemistry of phosphonates has been better understood than that of the polycarboxylic acids.14-16 Recently, the authors have made significant progress toward the understanding of the solution chemistry of a specific polymeric inhibitor, phosphino-polycarboxylic acid (PPCA).17 Equations based upon the electrostatic theory of macromolecules18 have been developed to estimate PPCA’s solution speciation as a function of temperature, ionic strength, pH, and Ca concentration. The objective of this study is to develop a quantitative relationship between the inhibition of Barite nucleation by PPCA and PPCA’s solution properties. In this study, induction period monitored at various solution conditions was used as an index to evaluate BaSO4 nucleation kinetics. Barite induction periods at various supersaturation, ionic strength, temperature, pH, and calcium ion concentrations are determined in the absence and presence of PPCA. Equations developed by Xiao et al.17 are used to determine PPCA solution properties under various conditions. Finally, PPCA solution properties are correlated to (12) He, S. L.; Kan, A. T.; Tomson, M. B. Langmuir 1996, 12, 19011905. (13) Collins, I. J. Colloid Interface Sci. 1999, 212, 535-544. (14) Nikitina, L. V.; Grigor’ev, A. I.; Dyatlova, N. M. J. Gen. Chem. USSR 1974, 44, 1568-1571. (15) Tikhonova, L. I. Russ. J. Inorg. Chem. 1968, 13, 1384-1388. (16) Tomson, M. B.; Kan, A. T.; Oddo, J. E. Langmuir 1994, 10, 14421449. (17) Xiao, J.; Kan, A. T.; Tomson, M. B. Langmuir 2001, 17, 4661. (18) Tanford, C. Physical Chemistry of Macromolecules; John Wiley & Sons: New York, 1967.
10.1021/la001721e CCC: $20.00 © 2001 American Chemical Society Published on Web 06/16/2001
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its inhibitory effect on the Barite induction period in a quantitative manner based upon the So¨hnel and Mullin19 nucleation model. Semiempirical Inhibition Model. According to So¨hnel and Mullin,19 the induction period (t0ind, s) can be determined from eq 1 when the induction period is influenced by both the nucleation time for a critical nuclei to form and the time for the critical nuclei to grow to detectable size (as was done in this study):
log(t0ind) ) a +
βσ3Vm2NA 2
3
2
2/3 β′σ2V4/3 m NA
+
4ν (2.303RT) (SI)
{
(
0.25 -0.32 + log10
V5/3 m
r2 ) 0.999 (4)
4ν(2.303RT) (SI) (1)
)
4 0.5 N8/3 A D Ksp
}
Ω + log10 (Ω - 1)2
where β and β′ are geometric shape factors, σ is the crystal/ solution interfacial energy, Vm is the molar volume of the crystals, NA is Avogadro’s number, R is the gas constant, ν is number of ions in a molecular unit, SI is the saturation index (which is the logarithm of the ratio of ion activity products divided by the thermodynamic solubility product of Barite (SI ) log {Ba2+}{SO42-}/Ksp)), D is the diffusion coefficient in a solution, and Ω is the supersaturation (Ω ) {Ba2+}{SO42-}/Ksp). In eq 1, the second term is related to the nucleation and/or diffusional growth, either of which cannot be distinguished, and the third term is related to polynuclear growth or other unidentified growth mechanisms. On the basis of the previous research on BaSO4 nucleation and inhibition,12 a semimechanistic model is proposed as below. 0 log10(tPPCA ind ) ) log10(tind) + (fuθu + fMθM)Cp
(2)
(s) is the induction period in the presence of where tPPCA ind PPCA, t0ind (s) is the induction period in the absence of PPCA, θu is the fractional concentration of the deprotonated fraction, and θM is the fractional concentration of PPCA that forms ion-pairs with metal ions. fu and fM are empirical functions of SI and temperature. Cp is PPCA concentration (mg/L). For any solution condition, the protonated fraction (θH), the deprotonated fraction (θu), and the metal complexed fraction (θM) can be calculated from an electrostatic polymer model, similar to those in Tanford,18 developed by Xiao et al.17 for PPCA under a wide range of ionic strength and temperature conditions. Briefly, θu can be calculated from eq 3 below (eq 3 is reproduced from eq 17 of Xiao et al.17).
{ (
θu + (CCaθu102belecθu) KCa,int 1 +
pKH,int ) 4.856 - 0.984I1/2 + 0.253I - 198.7/T
2
where
a)
assumed for the PPCA used in this study. For example, a PPCA concentration of 2.63 × 10-7 m (∼1 mg/L PPCA) is equivalent to CA ) 1.37 × 10-5 m. pKH,int, pKCa,int, and belec are the intrinsic proton dissociation constant, intrinsic Ca complex stability constant, and the electrostatic slope function, respectively. Xiao et al.17 have proposed the following equations (eqs 4-6) to correlate pKH,int, pKCa,int, and belec to ionic strength and temperature.
)}
θu102belecθuCA 2KCa,int
-1
+
θu10-pH10belecθu ) 1 (3) KH,int
where CCa is the Ca concentration (m) and CA is the PPCA concentration as the acrylic acid monomer (m). To calculate PPCA concentration as monomer (CA), the molecular weight of 3800 and 52 monomer units/molecule are (19) So¨hnel, O.; Mullin, J. W. J. Colloid Interface Sci. 1988, 123, 43-50.
belec ) 2.778 - 1.081I1/2 + 0.226I
r2 ) 0.998 (5)
pKCa,int ) 3.969 - 2.671I1/2 + 0.750I - 1102.3/T r2 ) 0.998 (6) For a given set of pH, I, T, CCa, and CA values, the equilibrium speciation of the PPCA species can be calculated. First, the values of pKH,int, belec, and pKCa,int can be calculated from eqs 4, 5, and 6, respectively, at a given I and T. Equation 3 is a function of only θu and known experimental values and can be readily solved by most root-finder routines, such as Microsoft Excel Goal Seek. Once θu is calculated from eq 3, the values for θCa and θH can easily be calculated as the second and third terms, respectively, of the left-hand side of eq 3. In the following, Barite induction period is correlated to the proposed model (eq 3) via a statistics program (SAS). In the SI calculation, the activity coefficients of Ba2+ and SO42- are calculated with Pitzer equations and ionic interaction parameters. Experimental Section Chemicals. BaCl2‚2H2O (granular, AR), Na2SO4 (granular, AR), NaCl (crystal, reagent), and CaCl2‚2H2O (granular, reagent) were from Fisher Scientific Inc. Phosphino-polycarboxylic acid (PPCA) is the active component of Bellasol S29 (FMC), which was used as received. PPCA, H-{{CH2CH(COOH)}x-PO(OH){CH2CH(COOH)}y}z-H, is a poly(acrylic acid) with about 1% phosphino groups imbedded in the structure to facilitate analytical determination. Bellasol S29 contains 50% PPCA. The average molecular weight is 3800, and it is composed of about 52 monomer units. All solutions were prepared with deionized water and filtered through a 0.1 µm microfilter. Analytical Techniques. First, PPCA was separated and concentrated by the solid-phase separation. Samples containing PPCA were acidified with HCl to pH 2. A C18 cartridge (Waters Corp.) was conditioned with methanol, water, and 0.01 N HCl in sequence. An acidified sample was then injected dropwise through the preconditioned C18 cartridge by a syringe, followed by about 5 mL of deionized water. The cartridge was then backward eluted dropwise with a 0.01 m Borax solution (pH 9.18). This eluate was collected and neutralized to pH 5. Then, the solution was oxidized by UV radiation in the presence of potassium persulfate (0.1 g c.a.). After UV oxidation, the solution was cooled to room temperature, and phosphorus was analyzed by the ascorbic acid method.20 The total PPCA concentration in the product Bellasol S29 was determined by measuring the carbon content via the COD method.20 Calcium concentrations were analyzed by either EDTA titration or ICP analysis.21 Barium concentrations were analyzed by ICP. BaSO4 Nucleation Kinetic Experiments. In Table 1 is listed the range of various experimental conditions used in this study. A total of 150 experiments were done at different PPCA (20) Chemical Procedures Explained; Hach Chemical Co.: Loveland, CO, 1986. (21) Greenberg, A. E.; Clesceri, L. S.; Eaton, A. D. Standard Methods for the Examination of Water and Wastewater, 18th ed.; American Public Health Association: Washington, DC, 1992.
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Table 1. Range of Barite Nucleation Kinetic Conditions Studied in This Paper parameters studied PPCA
Ca
concn range (mg/L)
no. of obs
0 1-10 11-50
104 24 22
concn range (m) 0 0.003-0.2
temperature no. of obs
range (°C)
121 29
25 26-83
ionic strength
no. of obs
range (m)
no. of obs
range
pH no. of obs
range
SI no. of obs
73 77
0-0.5 0.5-6
9 141
3-5 5-6 6-7 7-8
4 7 131 8
0.5-1 1-2 2-3 3-4
4 50 66 92
concentration, pH, Ca concentration, ionic strength, temperature, and SI. The induction period (tind) of BaSO4 nucleation is defined as the time elapsing between the mixing of two solutions and the onset of an increase in the turbidity reading. In each experiment, cationic and anionic solutions were prepared separately, one with crystallizing cations Ba2+ and another with crystallizing anions SO42-. The Ba2+ and SO42- concentrations were systematically varied from 0.28 to 16.38 mm to yield a SI variation of 0.5-4.0 SI unit. Both solutions contained the same amount of NaCl. If Ca2+ and/or PPCA were added to the solution, Ca2+ was added to the cationic solution and inhibitor was added to the anionic solution. The pH levels of the cationic, anionic solutions were adjusted with 0.01 m NaOH solution to the desired pH. No buffer was used to avoid any interference of the foreign molecules to nucleation reaction. These two solutions were filtered through a 0.1 µm microfilter (Osmonics, DDR01T2550) and preheated to the set temperature. The two solutions (10 or 25 mL each) were then rapidly added into a turbidity cell (30-50 mL) and mixed under continuous stirring at 350 rpm by a Teflon-coated magnetic stirring bar. No systematic variation in induction time can be attributed to the variation in sample volume in this study. The cell was kept at the set temperature by circulating water from a heated water bath through a stainless steel coil. The turbidity of the solution was tracked by a ratio/XR turbidimeter (Hach Co.), and the data acquisition was accomplished via a digital multimeter (Radio Shack) connected to a PC for data logging. At the end of the experiments, the mixed solution pH was determined with a pH meter. Once the data were collected, the turbidity reading versus time (seconds) was plotted on a semilogarithmic chart. The logarithmic induction time at the onset of turbidity changes was determined from the chart. The induction time determined in this way eliminates the ambiguity regarding the onset of turbidity increases at slow nucleation rates. A number of experiments were done in duplicate or triplicate. The relative error in logarithmic induction time (seconds) of these duplicated and triplicated experiments is generally within 20% when the nucleation rate is fast (tind < 15 s). The relative error in logarithmic induction time (seconds) of the experiments with long nucleation time (tind is between 6 and 30 min) is about 2% or less.
Results and Discussion Influence of PPCA to Barite Nucleation and Precipitation. In Table 2 are listed a representative set of experimental conditions and results that demonstrate how PPCA influences the induction period of Barite precipitation at various supersaturation, pH, Ca, temperature, and inhibitor concentrations. In Table 2, T is the temperature in °C, CCa is the concentration in molality, CBa and CSO4 are Ba2+ and SO42- concentrations in millimolal, Cp is PPCA concentration in mg/L, tind is the observed induction period in units of seconds, and log10(tind) is the base-10 logarithm of the observed induction period. In Table 2 are also listed PPCA solution speciation results (θu, θH, θCa). In section A of Table 2 and Figure 1, the influence of PPCA concentration on the Barite induction period is reported. These experiments were run at a Barite SI ) 2.77. These data are consistent with the proposed model (eq 2) that the logarithmic induction period is proportional to the inhibitor concentration (R2 ) 0.98). In section B of Table 2 is listed the influence of pH on PPCA inhibition. These experiments were run at two supersaturation levels and two inhibitor concentrations.
Figure 1. Plot of the logarithmic induction time versus PPCA concentration. The data were from expts 1-6 of Table 2, where the experiments were done at 25 °C, with 1 m NaCl and 0.1 m CaCl2‚2H2O as background electrolyte. The Ba and SO4 concentrations are 2.79 mm.
Figure 2. Plot of the logarithmic induction time (s) versus deprotonated fraction of PPCA, θu, at two SI values. The data are listed in Table 2, expts 7-10 (data set a, SI ) 2.92/2.93) and expts 11-13 (data set b, SI ) 2.13). The experiments were done at 25 °C, with 1 m NaCl as background electrolyte.
The reported pH is the measured solution pH at the end of the nucleation study. As the data show, PPCA is more effective at higher pH than at lower pH. In Figure 2 is plotted the logarithmic induction period versus θu, where data sets a and b are data from expts 7-10 (SI ) 2.92/ 2.93) and expts 11-13 (SI ) 2.13) and the corresponding linear fit equations, respectively. Interestingly, the pH effect can be interpreted with molecular level understanding of PPCA speciation. PPCA is a more effective inhibitor when it becomes deprotonated and the logarithmic induction period is linearly related to the concentrations of the deprotonated PPCA. Note that the deprotonated fraction increases from 39% to 83% between pH 4 and 5.76 and is equal to 100% at pH 8.41 (see Table 2). Therefore, the predominant pH effect is observed at the lower pH range. Over 83% of PPCA is in the deprotonated form when pH > 5.76. Therefore, it is expected that the efficiency of PPCA is less pH dependent when the solution pH > 6.
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Table 2. Representative Barite Nucleation Kinetic Experimental Conditions and Observations expt no.
T (°C)
I (m)
CCa (m)
1 2 3 4 5 6
25 25 25 25 25 25
1.01 1.31 1.31 1.31 1.31 1.31
0.10 0.10 0.10 0.10 0.10 0.10
7 8 9 10 11 12 13
25 25 25 25 25 25 25
1.01 1.01 1.01 1.01 1.00 1.00 1.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00
14 15 16 17 18 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41
25 25 25 25 25 25 25 45 45 45 66 66 66 83 83 83 25 25 25 25 25 25 25 25 25 25 25
1.00 1.00 1.00 1.06 1.15 1.30 1.60 1.00 1.00 1.30 1.01 1.00 1.30 1.01 1.00 1.30 1.01 1.31 1.01 1.02 1.07 1.07 1.16 1.16 1.25 1.31 1.31
CBa & CSO4 (mm)
CP (mg/L)
pH
SI
θu
θH
θCa
log10(tind) (s)
2.77 2.77 2.77 2.77 2.77 2.77
0.00 0.67 0.67 0.67 0.67 0.66
0.00 0.01 0.01 0.02 0.02 0.05
0.00 0.32 0.32 0.31 0.31 0.29
1.30 1.78 2.70 3.00 4.70 4.70
B. Variables Are PPCA Concentration and pH 2.79 26.85 4.00 2.93 2.79 27.00 5.76 2.93 2.79 27.00 5.82 2.92 2.79 27.00 8.41 2.93 1.16 1.08 4.75 2.13 1.16 1.08 6.31 2.13 1.16 1.08 7.80 2.13
0.39 0.83 0.85 1.00 0.59 0.75 0.92
0.61 0.17 0.15 0.00 0.41 0.03 0.08
0.00 0.00 0.00 0.00 0.00 0.22 0.00
2.58 3.70 3.70 3.78 2.18 2.63 2.85
C. Variables Are Ca and PPCA Concentration and Temperature 0.00 1.16 0.00 6.10 2.13 0.00 0.00 1.16 1.08 6.31 2.13 0.92 0.00 1.16 1.08 7.80 2.13 0.92 0.02 1.16 1.08 6.27 2.10 0.70 0.05 1.16 1.08 6.14 2.05 0.67 0.10 1.16 1.08 6.11 1.98 0.67 0.20 1.16 1.08 6.21 1.89 0.65 0.00 1.16 0.00 7.00 1.85 0.00 0.00 1.16 1.08 6.21 1.85 0.97 0.10 1.16 1.08 6.24 1.76 0.60 0.00 1.16 0.00 7.00 1.64 0.00 0.00 1.16 1.08 6.98 1.64 0.99 0.10 1.16 1.08 6.90 1.55 0.56 0.00 1.16 0.00 7.00 1.51 0.00 0.00 1.16 1.08 7.26 1.51 1.00 0.10 1.16 1.08 6.04 1.43 0.57 0.00 2.79 0.00 6.00 2.93 0.00 0.10 2.79 0.00 6.00 2.77 0.00 0.00 2.79 27.00 5.82 2.92 0.85 0.003 2.79 27.00 6.15 2.92 0.84 0.02 2.79 26.85 5.86 2.89 0.74 0.02 2.79 27.00 5.86 2.89 0.74 0.05 2.79 27.00 5.76 2.84 0.69 0.05 2.79 26.83 6.10 2.84 0.70 0.08 2.79 27.00 5.84 2.80 0.67 0.10 2.79 27.00 5.75 2.77 0.66 0.10 2.79 26.84 6.08 2.77 0.67
0.00 0.08 0.08 0.03 0.02 0.02 0.01 0.00 0.03 0.00 0.00 0.02 0.02 0.00 0.00 0.01 0.00 0.00 0.15 0.07 0.07 0.07 0.06 0.03 0.04 0.05 0.02
0.00 0.00 0.00 0.27 0.31 0.31 0.33 0.00 0.00 0.40 0.00 0.00 0.42 0.00 0.00 0.42 0.00 0.00 0.00 0.09 0.19 0.19 0.25 0.27 0.28 0.29 0.31
1.95 2.63 2.85 3.30 3.60 3.70 3.95 1.82 3.18 3.43 1.82 3.18 3.30 1.85 3.18 3.30 1.30 1.30 3.70 3.81 3.84 3.85 4.23 4.30 4.54 4.70 4.70
A. Variable Is Inhibitor Concentration 2.79 0.00 6.00 2.79 2.68 6.44 2.79 7.16 6.48 2.79 14.22 6.28 2.79 26.84 6.08 2.79 27.00 5.75
Calcium ion (Ca2+) is the predominant divalent metal ion in most waters including brines from the oil field and in cooling towers. Previously, several reports have indicated that Ca2+ has a strong effect on inhibition of Barite by common inhibitors.7,10,13 The nucleation kinetic experiments at varying Ca, PPCA, and temperature are compared in section C of Table 2. Collins13 has previously observed a clear change in crystal habit between Barite growth in the absence of Ca and crystal growth in the presence of Ca. In this study, we observed that Ca significantly enhances the inhibitor efficiency (see expts 14-21, Table 2). However, the effect of Ca on Barite nucleation time in the absence of PPCA inhibitor is undetectable (see expts 31-32). In Figure 3 is plotted the observed turbidity change versus time for expts 31 and 32. Even though the supersaturation state for expt 32 (SI ) 2.77) is slightly lower than the supersaturation state for expt 31 (SI ) 2.93) because of ion pair formation between Ca and SO4, yet negligible difference in the turbidity formation is observed for these two experiments. According to eq 1, the expected induction times are 11 and 16 s for expts 31 and 32, respectively. We observed an induction time of 20 s for these experiments, which is within the expected experimental error for these two experiments. In expts 14-30 and expts 33-41, the effect of Ca on PPCA inhibition efficiency is compared. In Figure 4 is
Figure 3. Plot of the turbidity versus time for two induction experiments in the presence and absence of 0.1 m Ca. The experimental conditions are listed in Table 2, expts 31 and 32. The experiments were done at 25 °C, with 1 m NaCl as background electrolyte.
plotted the logarithmic induction period versus Ca concentration for expts 15-21 and expts 33-41. PPCA prolongs Barite induction periods of these supersaturated solutions by 1-2 orders of magnitude. However, the induction period of BaSO4 nucleation was further prolonged when Ca is added to the solution. Note that the
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Langmuir, Vol. 17, No. 15, 2001
Figure 4. Plot of the logarithmic induction time (s) versus Ca concentrations for three sets of experiments containing various concentrations of Ca and PPCA. Details of experimental conditions are listed in Table 2 (expts 14-22, expts 28-30, and expts 33-41).
addition of Ca reduces the solution supersaturation state slightly. However, such small changes in SI cannot account for the large change in the induction time observed when Ca is present in the solution. From PPCA speciation results, it is observed that the presence of Ca changes a portion of the deprotonated PPCA to the Ca-PPCA ion pair. Collins13 has observed a similar effect of Ca with polyaspartate as a Barite inhibitor. He attributed the enhanced efficiency to the reduction of net negative charge of the polyion due to complexation of the polyaspartate with divalent cations, but he gave no quantitative correlation(s). Figure 5 shows BaSO4 crystal morphology under different conditions. In the absence of PPCA and Ca2+ (Figure 5a,b), BaSO4 forms the typical orthorhombic crystals. The slight differences between the morphologies observed in Figure 5a,b are most likely due to the differences in growth
Xiao et al.
conditions.22 In the presence of PPCA or PPCA/Ca2+, BaSO4 solids are not in any regular morphology. This might be due to the linearity and flexibility of the PPCA backbone, which makes PPCA easily adjust to “match” different lattices on different surfaces.7-9,13,23-24 PPCA also tends to result in chained/agglomerated amorphous BaSO4 solids or fiberlike crystals (Figure 5c-e). The fiberlike crystals form at high SI in the presence of PPCA and in the absence of Ca2+. The fiberlike crystals were also observed in the presence of maleic acid homopolymer by Benton et al.8 and in the presence of poly(ethylene glycol)block-poly(methacrylic acid)-monophosphonic acid (PEGb-PMAA-PO3H2) by Qi et al.25 A Model of Barite Nucleation in the Presence and Absence of PPCA. The induction period data were fitted to eq 7, below, by assuming that the Barite induction period in the absence of PPCA is related to SI and T in a functional form similar to So¨hnel and Mullin’s nucleation equation (eq 1) with some simplification. The inhibition by PPCA is governed by PPCA solution chemistry. 0 log10(tPPCA ind , s) ) log10(tind, s) + (fuθu + fCaθCa)Cp (mg/L) r ) 0.95 (7)
log10(t0ind, s) ) [1087 - 0.30T]3 0.12 T2SI T3SI2 (7.1) 1.03 4.84 745 + + (7.2) fu ) -3.31 + SI T SI2
-2.24 +
[1087 - 0.30T]2
fCa )
0.52 SI2
(7.3)
The respective standard deviations are 0.30, 58, 0.22, 0.01,
Figure 5. Morphology of Barite crystals formed in the presence and absence of PPCA. The solution also contains 1 m NaCl as background electrolyte at pH 6.
Prediction of BaSO4 Precipitation
Figure 6. Plot of the predicted logarithmic induction time using the proposed model (eq 7) versus the observed logarithmic induction time (s) for all Barite nucleation experiments reported in this study. The circles are the Barite nucleation experiments in the absence of PPCA, and the crosses are the Barite nucleation experiments in the presence of PPCA. The lines are the 1:1 quality line and 95% confidence interval of the data.
58, and 0.22 for the coefficients in eq 7.1. Similarly, the respective standard deviations are 0.31, 0.11, 0.48, and 69 for the coefficients in eq 7.2 and 0.11 for the coefficient in eq 7.3. The large relative standard deviation for the coefficient of T in eq 7.1 and that for 1/SI2 in eq 7.3 are possibly because of few data points available to be fit and the relatively weak effect of T and 1/SI2. In Figure 6 is plotted the calculated logarithmic induction period (seconds) using eqs 7 versus the observed logarithmic induction period (seconds). The data were separated into two groups: (1) induction period measured in the absence of PPCA and (2) induction period measured in the presence of PPCA. Considering the difficulty in nucleation studies and the range of conditions studied, such agreement for the predicted and observed induction periods in the absence and presence of PPCA is quite good. Equations 7.2 and 7.3 demonstrate the contribution of the deprotonated and Ca-complexed PPCA to inhibition. As discussed before, protonated PPCA does not have a significant inhibitory effect and the pH effect is implicitly included in the speciation calculation (eq 3). Temperature has a small effect on PPCA’s inhibition efficiency. Both fu and fCa diminish at high SI, and fu reduces as temperature increases. This would imply that the PPCA inhibitory effect diminishes at higher SI or temperature. At suf(22) Dunn, K.; Daniel, E.; Shuler, P. J.; Chen, H. J.; Tang, Y.; Yen, T. F. J. Colloid Interface Sci. 1999, 214, 427-437. (23) Davey, R. J.; Black, S. N.; Bromley, L. A.; Cottier, D.; Dobbs, B.; Rout, J. E. Nature 1991, 353, 549-550. (24) Rohl, A. L.; Gay, D. H.; Davey, R. J.; Cotlow, C. R. A. J. Am. Chem. Soc. 1996, 118, 642-648. (25) Qi, L.; Colfen, H.; Antonietti, M. Chem. Mater. 2000, 12, 23922403.
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ficiently high SI or temperature, PPCA might accelerate the nucleation of Barite, and this is consistent with observations by Fernandez-Diaz et al.7 However, one should be cautious when interpreting eq 7 for conditions that are beyond the range of data used to develop it. (See Table 1.) Note that the effect of the phosphino group in PPCA has not been specifically addressed in this research (the phosphino group was deprotonated in the range of pH used in this study). The effect of the phosphino group is assumed to be negligible since the acid/base chemistry and inhibition efficiency26 were not significantly different from those of the corresponding poly(acrylic acid) (PAA) of similar molecular weight. When we compare eq 7.1 with So¨hnel and Mullin’s equation (eq 1) using the parameters ν ) 2, Vm ) 0.0000521 m3/mol (for BaSO4), and β ) 16π/3, eq 7.1 leads to the following equation for apparent BaSO4 interface energy:
σ (J/m2) ) 0.087 - 2.36 × 10-5T (K)
(8)
This interface energy is the apparent BaSO4-H2O interface energy in the absence of polymer inhibitors. The value of the apparent interface energy at 25 °C is about 79.5 mJ/m2. This value is consistent with the literature1reported interface energy of 38-150 mJ/m2 and with that of 79.2 mJ/m2 predicted by He et al.1 Conclusions A semiempirical model has been presented to predict the induction period of Barite in the presence and absence of a representative polymeric scale inhibitor, PPCA. The method utilizes a novel approach to predict nucleation time by both the nucleation theory of So¨hnel and Mullin and the electrostatic theory based PPCA solution speciation equations. First, PPCA solution species distribution is calculated from ionic strength, temperature, pH, and Ca and PPCA concentrations. Second, the induction period in the presence of PPCA is correlated to the deprotonated and Ca-complexed PPCA concentrations, temperature, and degree of supersaturation. The model provides a good fit of a large number of laboratory observed induction period data over a wide range of conditions. Acknowledgment. The financial support of Rice University Energy and Environmental Systems Institute and Brine Chemistry Consortium of companiessAramco, B.J. Services, Baker-Petrolyte, Champion Technologies, Inc., Chevron Petroleum Technologies, Inc., Conoco, Inc., Texaco, Inc., British Petroleum, Nalco Exxon, and Solutias to this research is greatly appreciated. LA001721E (26) He, L.; Kan, A. T.; Tomson, M. B. Inhibition of Mineral Scale Precipitation by Polymers. In Water Soluble Polymers: Solution Properties and Applications; Amjad, Z., Ed.; Plenum: New York, 1997.
