pubs.acs.org/Langmuir © 2010 American Chemical Society
Silica Precipitation in Acidic Solutions: Mechanism, pH Effect, and Salt Effect Elizabeth A. Gorrepati, Pattanapong Wongthahan, Sasanka Raha, and H. Scott Fogler* Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109 Received December 12, 2009. Revised Manuscript Received May 11, 2010 This study is the first to show that silica precipitation under very acidic conditions ([HCl] = 2-8 M) proceeds through two distinct steps. First, the monomeric form of silica is quickly depleted from solution as it polymerizes to form primary particles ∼5 nm in diameter. Second, the primary particles formed then flocculate. A modified Smoluchowski equation that incorporates a geometric population balance accurately describes the exponential growth of silica flocs. Variation of the HCl concentration between 2 and 8 M further showed that polymerization to form primary particles and subsequent particle flocculation become exponentially faster with increasing acid concentration. The effect of salt was also studied by adding 1 M chloride salts to the solutions; it was found that salts accelerated both particle formation and growth rates in the order: AlCl3 > CaCl2 > MgCl2 > NaCl > CsCl > no salt. It was also found that ionic strength, over cation identity, determines silica polymerization and particle flocculation rates. This research reveals that precipitation of silica products from acid dissolution of minerals can be studied apart from the mineral dissolution process. Thus, silica product precipitation from mineral acidization follows a two-step process - formation of 5 nm primary particles followed by particle flocculation - which becomes exponentially faster with increasing HCl concentration and with salts accelerating the process in the above order. This result has implications for any study of acid dissolution of aluminosilicate or silicate material. In particular, the findings are applicable to the process of acidizing oil-containing rock formations, a common practice of the petroleum industry where silica dissolution products encounter a low-pH, salty environment within the oil well.
I. Introduction Silica polymerization and precipitation occurs in a wide variety of environmental and industrial processes: ceramic and catalytic applications, water heater scaling, biomineralization, coating applications to improve adhesion and wetting properties, and so forth, making silica polymerization a much studied subject.1 Recently, silica nanoparticles have also been studied for their potential use in drug delivery, biological imaging, and cancer treatment.2,3 Due to the nature of its applications, silica polymerization and precipitation research concerns polymerization in mildly acidic to basic solutions almost exclusively. Studies of silica precipitation at negative pH conditions are nonexistent. In the past decade, several groups have studied silica nanoparticles in basic solutions in relation to zeolite synthesis. During the early stages of zeolite silicalite-1 synthesis in basic solutions, silica nanoparticles were observed to function as zeolite precursors. Researchers have been using this compositionally simple system as *To whom correspondence should be addressed. E-mail:
[email protected]. (1) Iler, R. K. The Chemistry of Silica: Solubility, Polymerization, Colloid and Surface Properties, and Biochemistry; John Wiley & Sons: New York, 1979. (2) Park, S. J.; Kim, Y. J.; Park, S. J. Langmuir 2008, 24, 12134. (3) Mishra, Y. K.; Mohapatra, S.; Avasthi, D. K.; Kabiraj, D.; Lalla, N, P.; Pivin, J. C.; Sharma, H.; Kar, R.; Singh, N. Nanotechnology 2007, 18, 345606. (4) Provis, J. L.; Gehman, J. D.; White, C. E.; Vlachos, D. G. J. Phys. Chem. C 2008, 112, 14769. (5) Provis, J. L.; Vlachos, D. G. J. Phys. Chem. B 2006, 110, 3098. (6) Nikolakis, V.; Kokkoli, E.; Tirrell, M.; Tsapatsis, M.; Vlachos, D. G. Chem. Mater. 2000, 12, 845. (7) Rimer, J. D.; Trofymluk, O.; Navrotsky, A.; Lobo, R.; Vlachos, D. G. Chem. Mater. 2007, 19, 4189. (8) Fedeyko; Vlachos, D. G.; Lobo, R. F. Langmuir 2005, 21, 5197. (9) Fedeyko, J. M.; Egolf-Fox, H.; Fickel, D. W.; Vlachos, D. G.; Lobo, R. F. Langmuir 2007, 23, 4532. (10) Rimer, J. D.; Trofymluk, O.; Lobo, R. F.; Navrotsky, A.; Vlachos, D. G. J. Phys. Chem. C 2008, 112, 14754. (11) Rimer, J. D.; Lobo, R. F.; Vlachos, D. G. Langmuir 2005, 21, 8960.
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a model to better understand the formation, dissolution,4-7 and thermodynamics8-11 of silica nanoparticles in basic solutions. Provis and Vlachos5 showed that the apparent stability of silica nanoparticles over extended periods of time could be explained by a kinetic effect, wherein the system is in a “metastable state” with nanoparticles approximately in equilibrium with monomers. An alternative explanation to silica nanocolloid stability was provided by Rimer et al.,11 who postulated that uniform size of silica nanocolloids is due to a minimum in the free energy as a function of particle size. In contrast, the research in our paper was undertaken to fundamentally understand the kinetics of silica nanoparticle formation and particle growth in very acidic conditions as a function of pH and salt type. This research finds specific application in matrix acidization, a common oil well stimulation technique in which minerals comprising an oil-containing rock formation are dissolved with concentrated acid mixtures. The resulting siliceous reaction products can form silica particles which cause pore blockage, dramatically reducing formation permeability and decreasing oil production.12-14 In mildly acidic to basic conditions, it is known that silica polymerization begins with the condensation of monosilicic acid into cyclic oligomers, which grow to three-dimensional polymer particles.1 These nanoparticles function as nuclei with radii on the order of a few angstroms and may grow larger by Ostwald ripening or monomer addition, or they may remain dispersed until flocculation.1 If the particles or flocculates grow large enough, they will eventually precipitate from solution. (12) Lund, K.; Fogler, H. S.; McCune, C. C. Chem. Eng. Sci. 1973, 28, 691. (13) Crowe, C.; Masmonteil, J.; Touboul, E.; Thomas, R. Oilfield Rev. 1992, 4, 24. (14) Underdown, D. R.; Hickey, J. J.; Kalra, S. K. Proceedings of 65th Annual SPE Technical Coference and Exhibition, New Orleans, LA, 1990.
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The effect of type of salt on nanoparticle formation and flocculation at low pH conditions was also studied. It has been previously established that the rate of silica polymerization increases with increasing ionic strength.15-18 The results from the present study show that silica nanoparticle formation and flocculation in acidic conditions are accelerated by chloride salts in the following order: AlCl3 > CaCl2 > MgCl2 > NaCl > CsCl > no salt Previous researchers have shown the opposite trend for mildly neutral to basic conditions (pH 4-10). Dishon et al.19 found that the amount of cation absorption to a silica surface followed the order Csþ > Kþ > Naþ. Johnson et al.20 similarly found that cation absoption to a silica surface follows the order Csþ > Rbþ > Kþ > Naþ > Liþ with free energy of adsorption following the reverse trend; that is, the lowest free energy of adsorption belonged to the cesium cation. Johnson et al. also found that the greater adsorption of cesium cation on silica translated into faster aggregation rate of silica nanoparticles in the presence of cesium cations compared to the other cations, attributing the faster aggregation rate to the combined effects of ion-ion and ion-surface dispersion interactions and the structure-making or structure-breaking nature of surfaces and ions; the less hydrated and chaotropic cations (Csþ and Rbþ) adsorb more strongly and to a greater extent on the chaotropic silica surface than the more hydrated and kosmotropic cations (Naþ and Liþ) in solutions with a pH above silica’s IEP (pH = 2). The experiments contained in this paper were all carried out below silica’s IEP. In this paper, we investigate the effect of pH and added salts on silica nanoparticle formation and flocculation at extremely low pH, that is, negative pH values. UV-vis is used to follow the consumption of monomeric silica species as silica nanoparticles are formed, and ICP-MS and DLS are used to follow the subsequent flocculation of the nanoparticles. A geometric population balance model for the silica particle flocculation is developed and shows excellent agreement with DLS data.
II. Experimental Methods In this study, two sources of silica were used: a naturally occurring source and a manufactured source. Crystals of the zeolite analcime (Na6.1[(AlO2)16.0(SiO2)32.8] 3 16H2O, from Mount St. Hilaire, Quebec, Canada, bought from Ward Science) were ground and the particles with diameter 0.2 μm < d < 38 μm retained. The manufactured source of silica was sodium metasilicate nonahydrate (SMN) Na2O3Si 3 9H2O from Thermo Sci Acros Organics. Trace metal grade 35-37 wt % HCl solution, NaCl, MgCl2 3 6H2O, CaCl2 3 2H2O, and AlCl3 3 6H2O were supplied by Fisher Chemical, and CsCl was supplied by Sigma-Aldrich. Water was purified by a Milli-Q system to a conductivity of 18 MΩ. A. Analcime Experiments. Analcime was added to HCl or (4 M HCl þ 1 M salt) solution in a jacketed Pyrex reactor connected to a circulating bath. The experimental conditions were a coolant temperature of 5.0 C, a stirring rate of 500 rpm, analcime crystal diameter 0.2 μm < d < 38 μm, and a ratio of
Figure 1. Bulk silicon concentration during dissolution of analcime in 2, 4, 8, and 12 M HCl. mineral to liquid of 2 g:75 mL; under these conditions, it is known that analcime dissolution is reaction-limited.21
B. Sodium Metasilicate Nonahydrate (SMN) Experiments. The experimental conditions were identical to those of analcime experimesnts; however, the order of reactant addition is notable. First, SMN was dissolved in water (solubility in water ∼10 000 ppm) to form a concentrated monosilicic acid solution. Next, a HCl solution was added, initiating monosilicic acid polymerization (monosilicic acid polymerizes rapidly under acidic conditions). For salt experiments, a third, salt-containing solution was immediately added. The additions were designed so that the final solution contained the desired experimental concentrations of silica, acid, and salt. Note the sodium concentration. C. Sample Characterization. Three techniques were used to follow the course of silica polymerization:
1. Measurment of Bulk Silicon Concentration in Solution by Inductively-Coupled Plasma Mass Spectroscopy (ICP-MS). Samples taken from the reactor were passed through polypropylene membrane filters (dpore = 0.2 μm) and immediately diluted to less than 5 ppm Si for ICP-MS analysis (Perkin-Elmer, ELAN9000).
2. Measurement of Silica Particle Growth by Dynamic Light Scattering (DLS). Samples were withdrawn from the reactor and quickly transferred to glass cuvettes for silica particle size measurement. DLS was carried out by a Nano ZS (Malvern) equipped with a 633 nm laser. Temperature control on the Nano ZS allowed reaction solutions to be kept at 5.0 C during measurements. Mean particle diameter was calculated from scattering intensity plots.
3. Measurement of Monosilicic Acid Concentration in Solution by UV-Vis Spectroscopy. Samples were withdrawn and diluted, then molybdate solution was immediately added following the procedure detailed in ASTM D859-05 (molybdenum blue method for silica-in-water analysis). The concentration of the formed blue silicomolybdate complex, which is indicative of monomeric silica concentration, was determined colorimetrically at 640 nm by a Cary100 UV-vis spectrophotometer (Varian).
III. Results and Discussion (15) Icopini, G. A.; Brantley, S. L.; Heaney, P. J. Geochim. Cosmochim. Acta 2005, 69, 293. (16) Fleming, B. A. J. Colloid Interface Sci. 1986, 110, 40. (17) Potapov, V. V.; Serdan, A. A.; Kashpura, V. N.; Gorbach, V. A.; Tyurina, N. A.; Zubakha, S. V. Glass Phys. Chem. 2007, 33, 44. (18) Makrides, A. C.; Turner, M.; Slaughter, J. J. Colloid Interface Sci. 1980, 73, 345. (19) Dishon, M.; Zohar, O.; Sivan, U. Langmuir 2009, 25, 2836. (20) Johnson, A. J. H.; Greenwood, P.; Hagstrom, M.; Abbas, Z.; Wall, S. Langmuir 2008, 24, 12798. (21) Hartman, R. L. Ph.D. Dissertation, University of Michigan, Ann Arbor, MI, 2006.
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A. Experiments on the Effect of pH on Silica Polymerization. The zeolite analcime was dissolved in 2, 4, 8, and 12 M HCl solutions in a temperature-controlled batch reactor, and the bulk silica concentration was measured as a function of time by ICP-MS (Figure 1). The initial rising concentration of silicon occurs as hydrochloric acid partially breaks down the zeolite framework, releasing silicon into solution and leaving behind undissolved siliceous particles. Meanwhile, the silicon released into solution polymerizes and forms growing silica particles; in Langmuir 2010, 26(13), 10467–10474
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and the analcime dissolution ICP results are consistent for 8 M HCl. Consistency is also observed for 4 and 2 M HCl solutions (Figure 4). There is excellent agreement between DLS and ICP data over 2 orders of magnitude, as can be seen in Figure 4. To further investigate the mechanism of silica polymerization after acid dissolution of analcime, the silicomolybdate colorimetric method was employed to investigate the concentration of monomeric silica species during polymerization. The initial polymerization rate of pure monosilicic acid in 8, 4, 6, and 2 M HCl was investigated at various initial concentrations of monosilicic acid using the silicomolybdate technique (ASTM D859-05). The concentration-time data show that the disappearance of monosilicic acid from solution at very low pH is second-order (Figure 5) for all pH solutions studied: Figure 2. Comparison of the silicon profile from analcime dissolution with the silicon profile from sodium metasilicate nonahydrate in 8 M HCl.
fact, the drop in silicon concentration will be shown, later in this section, to correspond to when these particles grow to 0.2 μm in diameter. The undissolved siliceous analcime particles, which coexist with growing silica particles in these solutions, hinder study of the silica polymerization process. Therefore, sodium metasilicate nonahydrate (SMN), which becomes monosilicic acid in neutral to basic solutions,22 was tested as a silica source to mimic the silica from analcime dissolution. A neutral solution of monosilicic acid was acidified such that the final concentration of silicon equaled the concentration of silicon at the plateau during analcime dissolution (Figure 2). The silicon concentration-time trajectory of the pure monosilicic acid was similar to those from analcime dissolution; consequently, it is concluded that the processes of analcime dissolution and the subsequent silica precipitation are independent of each other (i.e., they are decoupled). Because of their similarity in behavior to silicon dissolved from analcime, pure monosilicic acid solutions were used to further investigate the polymerization of silica, which occurs after analcime dissolution. First, silica particle growth in solutions of pure monosilicic acid was monitored by DLS. The intensity distribution of the growing silica particles’ sizes followed a log-normal distribution, from which the intensity-average particle diameter was calculated (Figure 3). The growth of the intensity-average particle diameter was found to be approximately exponential and was fit to the equation D ¼ Aexpðk g tÞ
ð1Þ
Modeling of particle growth is discussed later in section III.B. Because analcime dissolution and silica precipitation are decoupled, the pure monosilicic acid DLS results show that silica nanoparticles have formed and are growing larger during the silica plateau observed by ICP during analcime dissolution. When the particles grow to 200 nm in diameter, they are filtered out of solution by the 0.2 μm filters used before ICP analysis, resulting in a drop in measured silica concentration, thus ending the plateau region. DLS data for 8 M HCl show that silica particle size reaches 200 nm at 142 min (Figure 3); ICP data for 8 M HCl show that the drop in silicon concentration occurs around 140 min (Figure 1), revealing that the pure monosilicic acid DLS results (22) Halasz, I.; Agarwal, M; Li, R.; Miller, N. Catal. Lett. 2007, 117, 34.
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d½SiðOHÞ4 ¼ - kd ½SiðOHÞ4 2 dt
ð2Þ
½SiðOHÞ4 0 - 1 ¼ ½SiðOHÞ4 0 kd t ½SiðOHÞ4
ð3Þ
Integrating
where kd is the dimerization rate constant, [Si(OH)4] is monosilicic acid concentration, and [Si(OH)4]0 is initial monosilicic acid concentration. The initial polymerization rate of monosilicic acid is a strong function of HCl concentration and a weak function of initial monosilicic acid concentration, as shown in Figure 6. The monomer consumption will be discussed further in section III.B. Previous studies on monosilicic acid polymeriation at pH values above the IEP of pH 2 have reported conflicting reaction orders. For example, Icopini et al.15 reported a fourth-order reaction from pH 3 to pH 11, whereas Alexander23 reported a third-order reaction at pH 4, and Goto24 reported a third-order reaction from pH 7 to pH 10. However, Rothbaum and Rohde25 showed that a second-order reaction is consistent with their data taken at pH 7 to pH 8; our data are also best fit by a second-order reaction at pH 0 and below. B. Modeling of Silica Particle Growth. The silica particle growth observed by DLS could be hypothesized to occur via two mechanisms: (1) particle growth by addition of monomer, (2) particle growth by flocculation. To gain insight into the mechanism of particle growth, we compare UV-vis and DLS data for our 8 M HCl solution (Figure 7). UV-vis data show that monosilicic acid is virtually depleted from solution after 15 min, while DLS shows rapid silica particle growth up to 160 min in the same solution. Thus, monomer addition is ruled out. That is, silica particle growth in acidic solutions takes place via flocculation, which is consistent with the work of Drews and Tsapatsis26 on aggregation of silica nanoparticles during zeolite formation in basic solutions. Modeling of the silica particle aggregation was undertaken, with the basic Smoluchowski equation27 as the starting point: k-1 ¥ X dNk 1 i ¼X Ki, j Ni Nj - Nk Ki, k Ni ¼ 2 j¼k-i dt i¼1
ð4Þ
i¼1
(23) (24) (25) (26) (27)
Alexander, G. B. J. Am. Chem. Soc. 1954, 76, 2094. Goto, K. J. Phys. Chem. 1956, 60, 1007. Rothbaum, H. P.; Rohde, A. G. J. Colloid Interface Sci. 1979, 71, 533. Drews, T. O.; Tsapatsis, M. Microporous Mesoporous Mater. 2007, 101, 97. Von Smoluchowski, M. Z. Phys. Chem. 1917, 92, 129.
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Figure 3. Intensity-average silica particle diameter in monosilicic acid solutions. [Si(OH)4]0 = 135 mmol/L for 8 M HCl, 190 mmol/L for 4 M HCl, 240 mmol/L for 2 M HCl.
Figure 6. Monosilicic acid dimerization rate constant normalized by initial monosilicic acid concentration versus HCl molarity. Figure 4. Time for growing silica particles to reach 200 nm as measured by DLS and ICP.
Figure 7. Comparison of silica monomer disappearance and silica particle growth; 8 M HCl, [Si]0 = 135 mmol/L.
Figure 5. Normalized inverse concentration of monosilicic acid versus time showing a second-order consumption; t = 0 in this figure corresponds to t = 0 in Figures 2 and 3.
where i, j, and k represent the number of primary units in the aggregate, Nk is the number density of kth aggregates, and Ki,j is the collision kernel for aggregation of ith aggregates with jth aggregates. However, using the original Smoluchowski equation to model experimental data is computationally expensive;as noted in Table 1, the number of ODEs which must be simultaneously solved to predict growth from a nanoparticle size to a final micrometer size is 106 when fractal dimension is 2 and 1012 when fractal dimension is 3, requiring months of computational time. To reduce the number of required differential equations, a geometric population balance is incorporated into the original 10470 DOI: 10.1021/la904685x
Smoluchowski equation in a model first developed by Batterham et al.28 and later modified by Hounslow et al.29 In the Hounslow et al. model,29 species are placed into geometric bins (Figure 8) and population balance equations are written for each bin rather than each species, exponentially reducing the number of required ODEs to 28 when fractal dimension is 2 and 41 when fractal dimension is 3 (see Table 1). Though the original Hounslow et al. model partitioned species into volume-based bins, mass conservation is violated for fractal aggregates, so we instead used massbased bins, which fulfills mass conservation. In other words, the ith bin includes aggregates of 2i-1 to 2i primary particles. In this model, particles can aggregate into a given bin only if one of the particles, prior to forming the aggregate, was in the bin (28) Batterham, R. J.; Hall, J. S.; Barton G. Third International Symposium on Agglomeration, Nurnberg, 1981, pp A136-A150. (29) Hounslow, M. J.; Ryall, R. L.; Marshall, V. R. AIChE J. 1988, 34, 1821.
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Article Table 1. Comparison of Number of ODEs Required with and without a Geometric Population Balance Diameter, m
Number of ODEs
case
primary unit, dp
largest aggregate, da
Df
na
Smoluchowski
geometric (R = 2)
1 2
1 10-9 1 10-9
1 10-5 1 10-6
3 2
1.0 1012 1.0 106
1.0 1012 1.0 106
41 28
Figure 8. Geometric binning process used to reduce number of ODEs. Table 2. Binary Interaction Mechanisms for Aggregation in the Geometric Population Balance Model (Adapted from Table 1 in Hounslow et al.29) mechanism
formation or depletion in bin i
1
formation
(i - 1)
1 f (i - 2)
2
formation
(i - 1)
(i - 1)
3
depletion
i
1 f (i - 1)
4 depletion Represents largest bin in model.
i
i f iMAXa
a
collisions between particles in bins
rate of formation or depletion iP -2
2j - i þ 1 Ki - 1, j Nj j¼1 Ki - 1, i - 1 2 Ni - 1 2 iP -1 -Ni 2j - i Ki, j Nj j¼1 imax P
Ni - 1
-Ni
j¼i
Ki, j Nj
immediately smaller than the bin of interest.29 Furthermore, an aggregate formed by particles from the same bin will always be counted in the next bin29 (Figure 8). For the above binning process, there are four mechanisms by which an aggregate in bin i may be formed or depleted, as shown in Table 2. The resulting differential equation for this model is the sum of mechanisms 1, 2, 3, and 4 (cf. Hounslow et al.29): i-2 X dNi 1 ¼ Ni - 1 2j - iþ1 Ki - 1, j Nj þ Ki - 1, i - i Ni2- 1 2 dt j¼1
- Ni
i-1 X
2j - i Ki, j Nj - Ni
j¼1
imax X
Ki, j Nj
ð5Þ
j¼i
where i and j now represent bin numbers, Ni is the number density of the aggregates in the ith bin, and Ki,j is the collision kernel for aggregation of aggregates in the ith bin with aggregates in the jth bin. Please see Supporting Information for a detailed derivation. A reaction-limited collision kernel developed by Ball et al.30 is used because exponential silica particle growth observed by DLS (Figure 3) is consistent with reaction-limited flocculation:31 Ki:j ¼
2 Rg T ðdi þdj Þ2 β ¼ Cðdi þdj Þ2 3 ηDp 2
ð6Þ
where Rg is the universal gas constant, T is absolute temperature, Dp is primary particle diameter, di is the diameter of the ith aggregate, η is kinematic viscosity of the medium, and β is collision efficiency. Assumptions made by our model are (i) silica aggregates are fractal with Df = 2.1, in accordance with fractal dimension (30) Ball, R. C.; Weitz, D. A.; Witten, T. A.; Leyvraz, F. Phys. Rev. Lett. 1987, 58, 274. (31) Sandk€uhler, P.; Lattuada, M.; Sefcik, J.; Morbidelli, M. Adv. Colloid Interface Sci. 2005, 113, 65. (32) Martin, J. E.; Wilcoxon, D. S.; Odinek, J. Phys. Rev. A 1990, 41, 4379.
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Figure 9. Comparison of experimental and simulated evolution of silica particle growth.
observed in reaction-limited systems;32,33 (ii) nucleation produces primary particles with uniform diameter; and (iii) aggregation is irreversible. The system of differential equations given by eq 5 were solved using Matlab 2008a ode23. Thirty equations were solved simultaneously, with the largest bin containing aggregates consisting of 229 to 230 primary particles (or equivalently, particles from 72 to 100 μm in diameter). The primary particle diameter used was 5 nm, which was estimated from the DLS data (see Figure 3) and is consistent with the 5 nm size found for silica precuror nanoparticles in basic solutions by Davis et al.34 The collision efficiency parameter β was the only fitting parameter in our model. The model predicts the particle size distributions, from which the intensity-mean aggregate diameter is calculated. The mean particle diameter predicted by the geometric population balance model agrees well with the mean particle diameter measured by DLS (Figure 9). (33) Burns, J. L.; Yan, Y.; Jameson, G. J.; Biggs, S. Langmuir 1997, 13, 6413. (34) Davis, T. M.; Drews, T. O.; Ramanan, H.; He, C.; Dong, J.; Schnablegger, H.; Katsoulakis, M. A.; Kokkoli, E.; McCormick, A. V.; Penn, R. L.; Tsapatsis, M. Nat. Mater. 2006, 5, 400.
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Figure 10. (a) Particle intensity distribution from geometrically modified Smoluchowski equations for 8 M HCl solutions. (b) Particle intensity distribution from DLS measurements on 8 M HCl solutions.
Figure 11. Plot of collision efficiency versus HCl concentration.
Examining the particle size distributions from the model, it is seen that the geometric population balance model gives the same qualitative PSD change with time that is observed with DLS (Figure 10). However, the DLS data show a somewhat higher standard deviation than the geometrically modified Smoluchowski population balance model data, resulting in shorter, broader peaks for the DLS data as compared to the Smoluchowski model data. The collision efficiency calculated from the model increases exponentially with increasing hydrochloric acid concentration. Furthermore, the collision efficiency was found to vary by orders of magnitude (10-9∼10-12) as the Hþ concentration increases from 2 to 8 M (Figure 11). C. Effect of Salts on Silica Polymerization. The effect of added salt on silica precipitation in acidic solutions was also studied. One molar concentrations of CsCl, NaCl, MgCl2, CaCl2, or AlCl3 were added to solutions of monosilicic acid in 4 M HCl. Silica polymerization in these solutions was studied using the same techniques previously dicussed: UV-vis, DLS, and ICP. Similarly, the geometric population balance modeling was used to model the DLS results. Comparison of mean silica floc diameter measured from DLS and calculated using geometric population modeling for these salt solutions is shown in Figure 12, where one notes excellent aggreement. Note that ICP data and DLS results for salt solutions (35) Gorrepati, E. A. Silica Precipitation from Analcime Dissolution. Ph.D. Dissertation, University of Michigan, Ann Arbor, MI, 2009.
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Figure 12. Comparison of experimental and simulated evolution of silica particle growth in acidic solutions with 1 M salts added; [Si]0 = 170 mmol/L.
are also consistent in regard to time for aggregates to reach 200 nm in diameter.35 Again, the geometrically modified Smoluchowski population balance model describes well the evolution of silica particle size. The salts added to 4 M HCl (pH -0.6) accelerated the formation of silica flocs in the following order: AlCl3 > CaCl2 > MgCl2 > NaCl > CsCl > pure 4 M HCl. The order of salts partially agrees with that found by Crerar et al.36 who studied silica polymerization at pH 7. In their study they found salts affected silica polymerization in the order CaCl2 > MgCl2 > NaCl. However, other researchers have found the opposite trend in mildly acidic to basic conditions, as mentioned in the Introduction. Ion pairing may be a factor in the observed salt order and is an area for further study. UV-vis data for these salt solutions showed the same trend for monosilicic acid disappearance. That is, AlCl3 promoted the disappearance of monosilicic acid the most, while CsCl promoted the disappearance the least. To evaluate the relationship between ionic strength and rate constants for silica, a model for activity coefficients based on the (36) Crerar, D. A.; Axtmann, E. V.; Axtmann, R. C. Geochim. Cosmochim. Acta 1981, 45, 1259.
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Figure 13. Silica particle growth rate constant, collision efficiency, and monosilicic acid disappearnce rate in 4 M HCl solutions with 1 M chloride salts added. Rates and ionic strength were nomalized to rates for 4 M HCl with no salt added. The value of b was set to 1.2, in acccordance with Harvie and Weare.37
semi-empirical Pitzer model and formulated by Harvie and Weare37 is used. The Debye-Huckel terms in the Harvie and Weare model37 is shown below: " pffiffi # pffiffiffi I 2 pffiffi þ lnð1 þ b I Þ ln k ¼ A 1þb I b
ð7Þ
where I is ionic strength, k is a polymerization rate constant, and A and b are empirical constants. Equation 7 was applied to our low pH systems with added salt. The particle growth rate (kg, eq 1), collision efficiency (β, eq 6), and monosilicic acid disappearance rate (kd, eq 2) dependence on ionic strength are shown in Figure 13. All rate constants were normalized to base case values of rate constants for 4 M HCl and no salt. The ionic strength function in the brackets on the righthand side of eq 7 was also normalized to the base case, which had an ionic strength function value of 2.63. The normalized rate constants (Figure 13) show that particle growth rate constant collision efficiency and disappearance rate constant increase exponentially with respect to the ionic strength function; however, Figure 13 reveals that there is a specific salt effect as shown by the scatter in the normalized rate constants. In the colloidal science literature, the interaction between charged colloidal particles in a liquid medium has been explained in terms of classical DLVO forces, that is, an attractive van der Waals force and a repulsive electrical double layer force. In this framework, as ionic strength of the medium increases, the screening length and electrical double layer force decrease, resulting in the coagulation of particles above a critical coagulation concentration (ccc) of salt. However, in our high ionic strength systems well above the ccc, the screening length is calculated to be only ∼0.5 A˚, which is small enough that any double layer repulsive forces should not have an effect on silica flocculation. That is, flocculation should depend only on the attractive van der Waals forces. However, our results show that salt identity has an effect on the silica flocculation rate, and consequently, classical DLVO theory does not completely describe the interaction of silica particles in our system. The method by which salt is affecting particle flocculation rate may be through a controversial, additional short-range repulsive force, which was previously reported for silica particles. Several researchers believe that the silica colloidal particle is strongly (37) Harvie, C, E.; Weare, J. H. Geochim. Cosmochim. Acta 1980, 44, 981.
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bound to water molecules and the additional repulsive force is a “hydration force”38,39 arising from the disruption of the ordered water layer necessary for particles to approach each other and form aggregates. In the framework of this “hydration force”, various salts may disrupt the ordered water layer to different extents, depending on the kosmotropic or chaotropic properties of the specific salt. Other researchers hypothesize that the repulsive force is a steric force arising from the existence of “silica hairs” protruding from the silica surface.40,41 These hairs, which are silanol (Si-OH) or silicilic acid (Si-O-) groups, may lie down at higher ionic strength, offering less steric resistance.42 Futher studies are needed to investigate this short-range repulsive force in order to allow better understanding of the overall interaction of silica particles. A third mechanism by which salt may be affecting the silica particle flocculation rate may be the influence of specific ionic effects on the chemical bonding between aggregating particles. That is, the irreversible aggregation of silica and the rate formation of silanol bonds between the particles may be influenced by specific ion effects. These three hypothesis are all areas for further research.
IV. Conclusions This research shows that silica particle formation and growth in negative pH solutions occur in two distinct steps. UV-vis measurements show that, first, monosilicic acid disappears rapidly via a second-order dimerization reaction, forming nanoparticles 5 nm in diameter. These primary particles flocculate, and mean floc diameter increases exponentially in time as measured by dynamic light scattering. Both the rate of monomer disappearance and flocculation rate increase by 2 orders of magnitude as HCl concentration is increased from 2 to 8M. A modified Smoluchowski equation that incorporates a geometric population balance was developed and used to simulate the flocculation. Particle diameter evolution predicted by the model shows excellent agreement with the exponential increase in diameter measured by DLS. Five different chloride salts were added to 4 M HCl solutions, and it is found that the salts accelerate both the monosilicic acid disappearance and the flocculation of primary particles in the following order: AlCl3 > CaCl2 > MgCl2 > NaCl > CsCl > no salt. Results show that silica polymerization rates increases exponentially with increasing ionic strength, but there is also a secondary specific ion effect, which is very likely related to a shortrange repulsive force that occurs between silica particles. Further investigation of this short-range repulsive force to establish whether it arises from a “hydration force” or “silica hairs” is necessary for development of a comprehensive model for silica polymerization in low pH. It is observed that silica dissolved from the zeolite analcime behaves identically to pure monosilicic acid solutions. Thus, siliceous mineral dissolution products also polymerize in two steps;formation of primary particles followed by flocculation; with their polymerization rate increasing exponentially with increasing acid concentration and with salts accelerating polymerization in the same order given above. The deeper implication is that acid dissolution of a mineral is not necessary to study the polymerization of its siliceous dissolution products. Instead, a model monosilicic acid solution can be used to study the (38) Yotsumoto, H.; Yoon, R. H. J. Colloid Interface Sci. 1993, 157, 434. (39) Horn, R. G.; Smith, D. T.; Haller, W. Chem. Phys. Lett. 1989, 162, 404. (40) Vigil, G.; Xu, Z. H.; Steinberg, S.; Israelachvili, J. J. Colloid Interface Sci. 1994, 165, 367. (41) Israelachvili, J. N.; Wennerstr€om, H. Nature 1996, 379, 219. (42) Yokoyama, A.; Srinivasan, K. R.; Fogler, H. S. Langmuir 1989, 5, 534.
DOI: 10.1021/la904685x
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polymerization process, which is a particularly useful result given the complexity of naturally occurring minerals and diversity of reservoir compositions. Acknowledgment. We thank the following members of the Industrial Affiliates Program on Flow and Reaction in Porous Media at the University of Michigan for support: Chevron Corporation, ConocoPhillips Company, Nalco, Schlumberger Oilfield Chemical Products, Shell International
10474 DOI: 10.1021/la904685x
Gorrepati et al.
Exploration & Production, StatOil ASA and Total. Further, we acknowledge Tom Yavaraski at the University of Michigan Civil and Environmental Engineering Department for kindly assisting with ICP-MS measurements. Supporting Information Available: Detailed derivation of the geometric population balance equation (eq 5), as derived in Hounslow et al.29 This material is available free of charge via the Internet at http://pubs.acs.org.
Langmuir 2010, 26(13), 10467–10474
