PII S0016-7037(98)00052-0

Amorphous silica precipitation (60 to 120°C):Comparison of laboratory and field rates

SUSAN CARROLL,1 EDWARD MROCZEK,2 MAUREEN ALAI ,1 and MARGARET EBERT1

1Earth Sciences Division, Lawrence Livermore National Laboratory, Livermore, California 94450, USA2Institute of Geological and Nuclear Sciences, Wairakei Research Center, Wairakei, New Zealand

(Received July12, 1996;accepted in revised form January20, 1998)

Abstract—Amorphous silica precipitation behavior was investigated in simple laboratory experiments andmore complex field experiments in the Wairakei, New Zealand, geothermal area. Both the laboratory and fieldprecipitation rates are dependent on reaction affinity for

SiO2(Am.Si.) 1 2H2ON H4SiO4 (AB1)

In simple laboratory solutions supersaturated with respect to amorphous silica by a factor less than 1.3 and inthe absence of chemical impurities, precipitation rates have a first-order dependence on f(DGr)

Rateppt ([Si] m22 s21) 5 kppt exp (2Ea/RT) (12 expDGr/RT) (AB2)

where kppt 5 1021.9 [Si] m22 s21 and Ea 5 616 1 kJ mol21. In more supersaturated and chemically complexfield solutions, amorphous silica precipitation rates have a nonlinear dependence on f(DGr) and may bedescribed by

Rateppt ([Si] m22 s21) 5 10210.0060.06 (expDGr/RT)4.460.3 (AB3)

or

Rateppt ([Si] m22 s21) 5 1029.2960.03 (DGr/RT)1.760.1 (AB4)

The changes in reaction order, form of f(DGr), and chemical impurities suggest that the dominant amorphoussilica precipitation mechanism changes from elementary reaction control in the simple laboratory experimentsto surface defect/surface nucleation control in the complex field experiments.Copyright © 1998 ElsevierScience Ltd

1. INTRODUCTION

Temperature dependent dissolution and precipitation of silicamay greatly affect porosity and permeability in a wide range ofcrustal rocks. Reaction kinetics of silica polymorphs play acritical role in thermally enhanced oil recovery and subsurfacecontaminant remediation, disposal of radioactive waste byburial, and geothermal waste-waters by injection into the sub-surface. Understanding and predicting silica reaction kineticsrequires not only simple laboratory experiments but also anal-ysis of complex field environments. Simple laboratory experi-ments form the basis for geochemical models of silica reactionkinetics, but they may insufficiently describe natural, morecomplex field environments. Thus, silica reaction kineticsshould be compared in laboratory and field settings.

The geochemical understanding of silica polymorph precip-itation kinetics is based on few well-controlled laboratory ex-periments and fewer field studies. Laboratory studies of quartz,cristobalite, and amorphous silica precipitation (Rimstidt andBarnes, 1980; Bird et al., 1986; Renders et al., 1995) assumethat the mechanisms controlling dissolution and precipitationare microscopically reversible and are related to the equilib-rium constants by the principle of detailed balancing (Lasaga,1981). Although these studies cover temperatures ranging from18 to 300°C at conditions near saturation, they have only beenperformed near neutral pH. Laudise (1959), Bohlmann et al.

(1980), Hosaka and Taki (1981a,b), Weres et al. (1981), Flem-ing (1986), and Yokoyama et al. (1989, 1991) have investigatedthe effect of activities of OH2, Na1, and Al31 on silicaprecipitation.

Field studies at elevated temperatures have been conductedalmost exclusively on amorphous silica in geothermal environ-ments. Mroczek (1994) summarized field silica precipitationrates from New Zealand geothermal waters at temperatures lessthan 150°C and moderate to low degrees of silica supersatura-tion. These data are representative of anticipated conditions ata potential radioactive waste repository at Yucca Mountain,Nevada, USA. At these conditions, heterogeneous reactions atthe solid-solution interface are expected to be the dominantprecipitation mechanism. Field silica precipitation rates weredetermined from the buildup of silica scale over time, wherereactive surface area is the most uncertain parameter. Despitethis, the rates calculated from empirical equations of Bohlmannet al. (1980) and Weres et al. (1981) were within an order ofmagnitude of the field rates. In contrast, theoretically basedmodels of precipitation (Rimstidt and Barnes, 1980; Bird et al.,1986; Renders et al., 1995) predict rates that are about threeorders of magnitude slower than the observed field rates.*

*Mroczek (1994) reported that field rates were 7 orders of magnitudegreater than those calculated from Rimstidt and Barnes (1980). Mro-czek has since corrected an error in the reported calculation.

Pergamon

Geochimica et Cosmochimica Acta, Vol. 62, No. 8, pp. 1379–1396, 1998Copyright © 1998 Elsevier Science LtdPrinted in the USA. All rights reserved

0016-7037/98 $19.001 .00

1379

In order to reconcile theoretically based and field-basedprecipitation rates, we have investigated the effect of temper-ature (60 to 120°C), pH, and aqueous silica concentration onamorphous silica precipitation in field and laboratory experi-ments. The field experiments were conducted at the Wairakei,New Zealand, geothermal area.

2. EXPERIMENTAL METHODS

2.1. Starting Materials

Silica gel was used in the laboratory experiments because it provideda large reactive surface area for amorphous silica precipitation. Thestarting material was Mallinckrodt Silicar Silica Gel, 100–200 mesh,with an average pore diameter of 150 Å. The gel was repeatedlycleaned ultrasonically with distilled and deionized water until thesuspension yielded a clear supernatant after 10 min of settling. Thecleaned gel was dried at 40°C for 24 h and then stored in a plasticcontainer at room temperature. Initial total surface area determinedfrom a BET N2 gas adsorption isotherm is 270 m2 g21; final totalsurface areas range from 50 to 280 m2 g21.

A fine-grained (mean diameter 0.02 cm), well-rounded, 99% purequartz sand from Glorit, New Zealand, was used in the field experi-ments. X-ray diffraction analysis showed no indication of other crys-talline material. The initial and final surface areas were calculated to be0.8 and 0.4 m2 g21, respectively, using BET Kr gas adsorption iso-therms. These surface areas are higher than the geometric determina-tion of surface area (1.133 1022 m2 g21) assuming spherical nonpo-rous particles with a density of 2.65 g cm23 (Gregg and Sing, 1982).This discrepancy is consistent with other reported differences betweenBET and geometric surface area determinations of quartz sand (Whiteand Peterson, 1990), and is probably due to significant surface rough-ness and the nonspherical nature of the sand grains. Quartz sand wasused in the field experiments instead of amorphous silica because it wasthe most convenient and cost effective substrate available for thefluidized-bed reactor. The use of quartz should not compromise ourresults, because amorphous silica precipitation rates are comparable fora variety of substrates (Bohlmann et al., 1980).

The composition of the Wairakei geothermal water used in thelaboratory and field experiments is shown in Table 1. Solutions used tocontrol pH in the laboratory experiments are HCl/KHphthalate buffer atpH 3, Na-acetate buffer at pH 5, and NaOH/Na-borate buffer at pH 8and 9 (Table 2). Buffers were needed to control solution pH in thebatch-reactors. In experiment AmSi-1, a simple HCl and NaCl solutionof pH 4 was reacted with amorphous silica. Within 24 h, the solution

pH increased to pH 6.4. With the exception of this initial experiment,the total ionic strength of each buffer was 0.13 M.

2.2. Geochemical Calculations

Solution speciation, pH, and amorphous silica reaction affinity[f(DGr)] were calculated at the experimental temperatures from themeasured solution compositions at room temperature using the React(Bethke, 1994) geochemical code and the SUPCRT92 thermodynamicdata base (Johnson et al., 1992) augmented with o-phthalic acid sta-bility constants at 25°C (Martell and Smith, 1989) and amorphoussilica solubility constants (Fournier and Rowe, 1977; SiO2(Am.Si.) 12H2O N H4SiO4; Keq(80°C) 5 1022.33, Keq (100°C)5 1022.22, andKeq (120°C)5 1022.12).

2.3. Laboratory Experiments

The precipitation experiments were run in Dickson-type, gold bagautoclaves (250 mL) capped with a commercially pure Ti head fittedwith a Ti or Au capillary-lined stainless steel sampling tube thatallowed the experiment to be sampledin situ (Seyfried et al., 1987). Acopper coil around the sampling tube allowed fluids to be quenchedprior to sampling.

At the beginning of each experiment, the Au bag was filled with thereactants, sealed with the Ti head, pressure-tested with an inert gas, andplaced in a pressure vessel filled with distilled and de-ionized water,which served as the pressure medium. Following the removal of excessinert gas in the Au bag as the system was initially pressurized, thesample valve was closed, and the pressure vessel was brought to 200bars and pressure tested for leaks overnight. In the morning, thepressure was reduced to the run value and the pressure vessel wasloaded into the furnace. As temperature was increased slowly, pressurewas bled to maintain the experimental pressure. Throughout the exper-iment, the furnace temperature was controlled by digital proportioningcontrollers, and the internal vessel temperature was monitored withchromel-alumel thermocouples and digital thermometers accurate to61°C.

About 5 g of amorphous silica were reacted with buffer solution orWairakei geothermal water at an elevated temperature until amorphoussilica saturation was achieved. The temperature was then lowered toyield a solution supersaturated with respect to amorphous silica by afactor of about 1.3. One experiment contained only geothermal water todetermine whether silica precipitation occurs via homogeneous nucle-ation in the bulk solution. During sampling, a nominal pressure (35–70bar) was maintained by externally pumping water into the pressurevessel as the sample was taken. The experiments were not rocked tomaintain the sampling port in the upright position, allowing only theaqueous phase to be sampled, and keeping the amorphous silica at thebottom of the Au bag. At the experimental temperatures (80–150°C),precipitation is not limited by aqueous diffusion, so the results shouldnot be compromised with a stationary reactor. The sampling tube wascooled prior to sampling to prevent boiling and subsequent silicaprecipitation. About 5 mL of solution were taken during each samplingperiod. All samples were extracted from the sample port with plasticsyringes. After 1 mL was extracted to clear the sampling line, 1 mL wastaken to measure pH at room temperature, and two 1 mL samples weretaken through a 0.2mm filter into a syringe for total and molybdate-active Si analyses. Molybdate-active Si analysis was conducted within30 min of sampling to avoid Si polymerization. For total Si analysis,the syringe contained 1024 m NaOH to prevent Si precipitation at roomtemperature. At the completion of the experiment, the amorphous silicawas removed, rinsed in distilled and deionized water five times, anddried at 40°C overnight.

2.4. Field Experiments

Silica precipitation was measured in the field with a fluidized-bedreactor (FBR) constructed at the Wairakei geothermal energy plant inNew Zealand (Fig. 1, Axtmann and Grant-Taylor, 1986). Geothermalwaters from Flash Plant 10 at 130°C and 2 bars were passed throughsteam-grade iron pipe to a heat exchanger. A 100 mesh (0.25 mm3 0.25 mm) stainless steel filter upstream of the heat exchangerremoved fines from the fluid. Temperature and flow of the fluid through

Table 1. Chemical composition of geothermal waters from FlashPlant 10, Wairakei, New Zealand.

Total Concentration

pH (25°C) 8.4 (Field)7.8 (Lab)

ppm

Na 1308Li 12.74K 210Ca 18.22Mg 0.08Rb 2.76Cs 2.58S 10.96B 26.77Si 234F 8.45As 4.84Al 0.60Fe 0.13Cl 2247

1380 S. Carroll et al.

the FBR were controlled by valves on the bypass line and upstream tothe FBR inlet, respectively. The FBR consists of three sections: (1) a10-cm-long stainless steel flow-straightening cone and a 30 and a 100mesh stainless steel filter; (2) 2 or 3 m of flanged 50 mm (ID) stainlesssteel pipe; and (3) a 30-cm-long stainless steel disengaging cone.Within the disengaging cone, flow rate is reduced sufficiently to allowsuspended particles to remain in the bed. The unit was insulated with50 mm thick fiberglass covered with aluminum foil to minimize con-ductive heat loss. For experiments at temperatures greater than 100°C,we inserted a small heat exchanger at the outlet of the disengagingcone. Flow rate was measured at the effluent stream. Inlet and outletsampling points were located at the bypass line and at the top of thereactor column just below the disengaging cone, respectively.

At the beginning of a run, the FBR was loaded with 4.5 or 6 kg ofsand (about 60% of the reactor volume), temperature and flow rate wereset, and sand was reacted with the geothermal waters for at least 48 hto obtain a coating of amorphous silica. Sampling was delayed for 2–4h after each adjustment of temperature or flow rate to ensure steady-state condition within the FBR (fluid residence times are only 3–5 min).Inlet and outlet samples were collected, preserved with HCl to avoidpolymerization, and analyzed for molybdate-active silica within 30min. Filtered samples (0.2mm pore size) were analyzed for total silicaat a later time. After each run (2 runs about 15 days each), the bed wasdismantled, the sand was washed into a bucket, and subsequently driedand weighed.

2.5. Analytical Techniques

All aqueous samples were analyzed by inductively coupled plasma-atomic emission spectrometry (ICP-AES) or atomic absorption spec-trometry (AA) for total dissolved silica. In addition, ICP-AES was usedto analyze Al, B, Ca, Fe, K, Li, Mg, Na, Rb, and S concentrations;inductively coupled plasma-mass spectrometry (ICP-MS) was used to

analyze total As, Cs, and Rb; and ion chromatography (IC) was used toanalyze Cl2, F2, and SO4

22 concentrations in the initial geothermalwaters. Samples were pretreated to remove Cl2 to quantitatively ana-lyze F2 and SO4

22 by IC. Reproducibility of each of these analyticaltechniques is better than 2% and analyte concentrations are a least oneorder of magnitude greater than the detection limits of the analyticaltechnique. Standards were made in background electrolyte solutionsidentical to the diluted composition for the buffered experiments todirectly correct for matrix effects, and in distilled and deionized waterfor analyses of the geothermal water.

Molybdate-active silica was measured using a UV photospectrom-eter and the yellow-b silicomolybdate method (Iler, 1979). Analyseswere performed after 10 min of reaction between the reagent and thesample. A calibration curve with five standards was run prior to sampleanalysis. Two standards were run with the samples to measure thedeviation from the calibration curve. This method has a detection limitof about 1 ppm and an error typically less than 6%.

Under the conditions of our experiments, most of the molybdate-active silica is monomeric, although we cannot entirely rule out thepresence of low molecular weight polysilicic acids (oligomers). Trimer,tetramer, and pentamer species do not react rapidly with molybdic acidunder similar conditions as used in our method (Makrides et al., 1980),and must depolymerize to form the silicomolybdate complex. Whenthis occurs, UV absorbance of the molybdate complex increases slowlywith time. We did not observe this effect in any of our analyses.

Starting materials and run products were analyzed by powder X-raydiffraction (XRD), scanning electron microscopy (SEM), energy dis-persive spectroscopy (EDS), and BET gas adsorption to check forchanges in crystalinity, morphology, chemical composition, and sur-face area, respectively. Krypton and nitrogen were the gas adsorbentsused to determine the surface area of the solids in the field andlaboratory experiments, respectively.

Table 2. Laboratory amorphous silica precipitation results. Ti is the initial temperature at which the starting materials were saturated with respectto amorphous silica, Tppt is the precipitation run temperature, kppt is the precipitation rate constant, and SA is BET surface area at the end of theexperiment.

EXPT Solution Composition Ti°C Tppt°C pH (T) kppt SA (m2 g21)

AmSi1 0.1 M NaCl (unbuffered) 120 100 6.4 1.73 10211 11861 3 10212

AmSi2 0.1 M NaCl1 0.013 M HCl1 0.03M KHphthalate

120 100 5.0 1.33 10211 168

61 3 10212

AmSi3 0.1 M NaCl1 0.03 M Na Acetate10.02 M Acetic Acid

120 100 3.0 2.63 10212 260

63 3 10213

AmSi5 0.13 M NaCl (unbuffered) 100 80 6.5 7.73 10212 13561 3 10212

AmSi6 0.1 M NaCl1 0.013 M HCl1 0.03M KHphthalate

100 80 3.0 9.83 10212 280

64 3 10213

AmSi7 0.1 M NaCl1 0.03 M Na Acetate10.02 M Acetic Acid

100 80 4.9 2.73 10212 209

64 3 10213

AmSi8 0.13 M NaCl (unbuffered) 150 120 7.2 3.73 10211 5367 3 10212

AmSi10 Geothermal Water (Table 1) 100 80 7.3 1.23 10211 13562 3 10212

AmSi11 Geothermal Water (Table 1) 120 100 7.2AmSi12 Geothermal Water (Table 1) 150 120 7.1 1.03 10210 66

61 3 10211

AmSi13 Geothermal Water (Table 1) 120 100 7.2 3.43 10211 10865 3 10212

AmSi14 0.121 M NaCl1 0.009 M NaOH10.05 M Boric Acid

120 100 7.9 3.03 10211 107

68 3 10212

AmSi15 0.094 M NaCl1 0.036 M NaOH10.05 M Boric Acid

120 100 8.7 5.43 10211 99

62 3 10212

1381Precipitation kinetics of amorphous silica

3. GENERAL RATE EQUATION

For amorphous silica precipitation, the reaction of interest is

dd precipitation

SiO2(Am.Si.) 1 2H2ON H4SiO4 (1)

dissolutionff

where the Gibbs free energy of reaction,DGr,

DGr5RT ln Q/Keq (2)

and solution saturation is equal to the ratio of the aqueous ion activityquotient, Q, to amorphous silica solubility constant,Keq, assumingideal unit activity of the solid phase.

A generalized equation describing surface-reaction controlled pre-cipitation rate, as a function of reaction affinity, [12 exp (DGr/RT)],may be written as

Rateppt 5 2d[Si]/dt 5 2kppt [1 2 n exp (DGr/RT)]m (3)

where kppt is a rate constant that may be dependent on temperature,pressure, total reactive surface area, surface defect density, and anyunidentified effect of the solution composition (such as the activities ofOH2, Na1, Al31) and n and m are empirical constants. The form of theGibbs free energy function, f(DGr),

f(DGr) 5 [1 2 n exp (DGr/RT)] (4)

and its reaction order (i.e., m) are used to infer the rate controllingmechanism from theoretical considerations.

If amorphous silica precipitation rates are controlled by one or moreelementary reactions at steady-state, then irreversible thermodynamicsmay be applied to complex solid-solution reactions, and Rateppt will belinearly dependent on f(DGr) (Nagy et al., 1991; Nagy and Lasaga,1992). If precipitation involves a series of elementary reactions, wherethe rate is controlled by the slowest elementary reaction, then Eqn. 3simplifies to

Rateppt 5 2kppt [1 2 exp (DGr/RT)] (5)

where n and m equal 1. If the reaction rate is controlled by more thanone elementary reaction at steady-state, then Eqn. 3 may be expressedby

Rateppt 5 2kppt [1 2 n exp (DGr/RT)] (6)

where n is a constant not equal to 1 and m equals 1. The reader isreferred to Lasaga (1981), Aagaard and Helgeson (1982) and Stummand Wieland (1990) for a more complete discussion of the applicationof transition state and surface complexion theories to mineral kinetics.

Mineral precipitation rates controlled by other surface reactionmechanisms, such as structural and chemical defects and surface nu-cleation have a nonlinear dependence on f(DGr):

Rateppt 5 2kppt f (DGr)m (7)

where f(DGr) may be a different form of the one in Eqn. 4 (Burton etal., 1951, Ohara and Reid, 1973). Although several surface nucleationand surface defect precipitation models have been proposed, it is

Fig. 1. Schematic of the fluidized bed reactor used in the amorphous silica precipitation field experiments.

1382 S. Carroll et al.

difficult to distinguish between surface defect and surface nucleationmechanisms, because the form of f(DGr) and the reaction order effec-tively mask several important, yet nonmeasurable parameters, such asdensity, size, and geometry of nucleation clusters, edge or step freeenergy, and absorption frequency (Zhang and Nancollas, 1990). Forthis reason, we do not distinguish between these mechanisms.

Precipitation rates controlled by aqueous diffusion to the mineral-solution interface also are linearly dependent on f(DGr) and are similarin form to Eqn. 5 (Casey, 1987). Aqueous diffusion maybe describedby

J5 2KeqD/d[1 2 exp (DGr/RT)] (8)

where J (mol cm22 s21) is the flux, D (cm2 s21) is the diffusion

coefficient, and d (cm) is the thickness of the boundary layer betweenthe bulk solution and the mineral surface. Equation 8 is an endmembercase in which the dissolved silica concentration at the mineral solutioninterface is equal to the equilibrium silica concentration.

4. RESULTS AND DISCUSSION

4.1. Laboratory Experiments

Amorphous silica precipitation rates are dependent on reac-tion affinity, pH, and temperature (Fig. 2–4, 4 App. A–B). To

Fig. 2. Amorphous silica precipitation plotted as [Si] m22 vs. Days and as Rateppt ([Si] m22 d21) vs. [12 exp (DGr/RT)]at (a) 80° (A–H), (b) 100° (I–T), and (c) 120°C (U–X).

1383Precipitation kinetics of amorphous silica

calculate these rates from the laboratory experiments, curvesare fit to the exponential decrease in aqueous silica concentra-tions normalized to surface area as a function of time (Fig. 2).The precipitation rate at any point along the curve is equal tod[Si]m22/dt. Only data from the first 10 days of precipitationare used in the exponential curve fit to minimize potentialartifacts of increasing relative surface area as aqueous samplesare extracted from the reaction vessel over time. We assumethat the reactive surface area available for precipitation isproportional to the BET surface areas of amorphous silica at theend of each experiment, which range from 50 to 280 m2 g21

(Table 2). We assume that most surface area reduction occurs

at elevated temperature prior to decreasing the temperature forthe precipitation run. These assumptions are warranted, be-cause the solutions have reached amorphous silica saturation atelevated temperature and because BET surface area systemat-ically decreases with increasing pH and temperature. Iler(1979) also observed a similar pH trend with synthesized silicagels. Because no changes in surface morphology are observedin SEM images of initial and final solids, the reduction insurface area must be due a reduction in internal porosity. Nocrystalline phases were detected in the solid phases with XRD.

Amorphous silica precipitation rates are best modeled withthe following form of the general rate Eqn. 3:

Fig. 2. (Continued)

1384 S. Carroll et al.

Rateppt 5 2d[Si]m22/dt 5 2kppt(pH, T)(12 expDGr/RT)(9)

where n5 m 5 1 and kppt ([Si]m22 s21) is dependent on pHand temperature. For each experiment, there is a linear rela-tionship between Rateppt and f(DGr) with a slope proportionalto kppt (Fig. 2). Precipitation rates approach zero as solutionsapproach equilibrium. In experiments at pH. 6, precipitationrates approach zero in slightly undersaturated solutions, corre-sponding toDGr about2200 J mol21, which limits the accu-racy of Eq. 9 as equilibrium is approached. One experiment,containing measurable polymeric silica at pH 8.7 and 100°C,approaches zero rate atDGr at 2700 J mol21.

The pH dependence of amorphous silica precipitation isshown in Fig. 3. At 80 and 100°C, kppt is proportional to{H 1} 20.2 from pH 3 to 8.7. The pH dependence of kppt isslight, but statistically different from zero. Uncertainty in kppt

calculated from each experiment ranges from 3 to 20%, withthe exception of experiments AmSi-6 (44%) and AmSi-12(33%). The pH dependence is about 20 times greater than thecalculated uncertainty in kppt. At 120°C, there are not enoughdata to establish a pH dependence of kppt. These results agreewith lower-temperature experiments in which rates increasefrom pH 4 to 8 at 25°C (Fleming, 1986). Our results alsoqualitatively agree with aqueous silica polymerization, which

Fig. 2. (Continued)

1385Precipitation kinetics of amorphous silica

occurs within a few hours at acid pH and within a few ofminutes at pH. 7 (Iler, 1979). There is the possibility kppt isindependent of pH, if lower kppt at pH 3 is due to K1 in thebuffer solution and if higher kppt at pH 8.7 is due to polymericprecipitation.

Dissolved components in the chemically complex Wairakeigeothermal water do not significantly affect amorphous silicaprecipitation rates in batch reactor experiments (Fig. 3). At 80and 100°C, kppt determined from experiments with Wairakeigeothermal water agrees with kppt determined from experi-ments with simple buffer solutions. At 120°C and about pH 7,kppt determined from the experiments with geothermal water isabout three times higher than kppt determined from the exper-iment with NaCl solution.

Temperature dependence of amorphous silica precipitationrates is evaluated in an Arrhenius plot of log kppt vs. 1/T(Fig. 4), where activation energy, Ea,

Ea 5 22.303R (d log kppt/d(1/T)) (10)

Calculated Ea 5 61 6 1 (kJ mol21) from Wairakei geothermalwaters (about pH 7.2) also fits the pH 3, 5, and 6.5 data. Thisvalue is consistent with rates controlled by reactions at thesolid-solution interface, and with other values (30 to 150 kJmol21) determined for a variety of silica polymorphs at tem-peratures between 20 and 500°C (Table 3).

The lack of silica precipitation in the absence of amorphoussilica seed material implies that amorphous silica precipitationis controlled by reactions at the solid-solution interface, ratherthan homogeneous nucleation (Fig. 5a). Wairakei geothermalwaters are slightly supersaturated with respect to amorphoussilica at 120°C. In the presence of amorphous silica, aqueoussilica decreases to amorphous silica saturation at 100°C within24 h after the drop in temperature. In the absence of amorphoussilica, there is no measurable decrease in silica concentrationsup to three days after the temperature is decreased from 120 to100°C. In experiments where both total and molybdate-activesilica were measured, dissolved silica is present as molybdate-active silica, except in one experiment at pH 8.7 and 100°C(Fig. 5b). Silica polymerization kinetics are rapid at pH. 7(Iler, 1979). The presence of polymeric silica in this experiment

may be an artifact of sampling procedure, in which polymer-ization occurs prior to analysis at room temperature.

According to the principle of detailed balancing, the rateconstants for precipitation, kppt, and dissolution, kdiss, are re-lated to each other through the equilibrium constant. Thus, kppt

and kdiss must have the same dependence on f(DGr) and pH.Rates of amorphous silica precipitation (this study) and disso-lution (Rimstidt and Barnes, 1980) have the same form off(DGr):

f(DGr) 5 (1 2 expDGr/RT) (11)

but kdiss was determined only at one pH in distilled and de-ionized water. Our study shows that amorphous silica precip-itation rate equations can be extrapolated to acid and alkalinepH solutions, using the principle of detailed balancing and thepH dependence of kppt. However, at conditions far from equi-librium, the principle of detailed balancing may not adequatelymodel mineral dissolution and precipitation reactions. Nagyand Lasaga (1992) showed that the principle of detailed bal-ancing describes gibbsite dissolution and precipitation kineticsat 80°C and pH 3 in solutions close to equilibrium,20.8, DGr

, 0.8 (kJ/mol), but not at greater degrees of undersaturation.Burch et al. (1993) and Nagy and Lasaga (1993) showed thatthis principle may not apply to more complex mineral phases,even near equilibrium.

4.2. Field Experiments

The amorphous silica precipitation rates determined fromWairakei, New Zealand, geothermal area are summarized inTable 4 and Figures 6 and 7. The steady-state precipitation rate([Si] m22 s21) from the FBR experiments may be calculated asfollows

Rateppt 5n3D@Si#

SA(12)

where n (Kg s21) is the flow rate,D[Si] (mol Kg21) is thechange between inlet and outlet Si concentration, andSA (m2)is the total surface area. Equation 12 is valid only if the FBRbehaves as a continuously stirred reactor, such that the flow rate

Fig. 3. pH-dependence of amorphous silica precipitation rates plottedas log kppt ([Si] m22 s21) vs. pH at 80, 100, and 120°C. GW refers toamorphous silica precipitation from Wairakei, New Zealand geother-mal water.

Fig. 4. Temperature dependence of amorphous silica precipitationrates plotted as log kppt ([Si] m22 s21) vs. 1/T(K). GW refers toamorphous silica precipitation from Wairakei, New Zealand geother-mal water.

1386 S. Carroll et al.

approximates the settling rate of the particles (Posey-Dowty etal., 1986). The use of Eqn. 12 to calculate amorphous silicaprecipitation rates is supported by the linear decrease inD[Si]/SA as a function of increasing flow rate over limited temper-ature intervals (Fig. 6).

Amorphous silica precipitation rates increase with decreas-ing temperature (Fig. 7), because the geothermal waters aremore supersaturated at lower temperature (for near constantsilica input). The uncertainty inRateppt is due to the uncer-tainty of D[Si], which varies from 1 to 8 mol% of the totaldissolved silica. Uncertainty attributed to changing surface areais thought to be negligible because the measured rates arereproducible at the beginning and the end of a run. Uncertaintyin [1 2 exp (DGr/RT)] is calculated from the uncertainty in themeasured silica concentrations in the outlet solutions.

In these experiments, we assume that amorphous silica rap-idly coats the sand grains, and therefore that steady-state valuesof D[Si] are controlled by precipitation at the amorphous silica-solution interface. Bohlmann et al. (1980) and Axtmann andGrant-Taylor (1986) have shown that rutile and quartz grainsare quickly coated with amorphous silica. Homogeneous nu-cleation of amorphous silica from the bulk solution is mini-mized by the short residence time (3–5 min) of the solutions inthe FBR. Typical induction times observed prior to the onset ofsilica polymerization are 0.5 h at 70°C and 2 h at 100°C(Rothbaum and Rhode, 1979). Our calculated inlet and outletpolymeric silica concentrations were typically within analyticaluncertainty of the measured total and molybdate-active silicaconcentrations, and showed no systematic dependence on tem-perature (Fig. 8).

Silica precipitation on the sand substrate is seen in SEMimages of the unreacted and reacted sand (Fig. 9). The reactedsand is covered with hemispherical silica precipitates with 1 to2 wt% Al. No Al was detected in the unreacted sand. Thepresence of significant surface roughness in both the reactedand unreacted sand supports the use of BET-determined surfaceareas in the precipitation rate calculations. Silica precipitationwas also observed on the reactor wall as a very thin, hard,translucent layer, and as a much softer material in the mesh

filters at the base of the reactor (estimated to be 0.01% of thetotal silica removed from solution).

Extrapolation of microscopic reaction mechanisms frommacroscopic rates is ambiguous because data from complexnatural systems may be interpreted in several ways. We con-clude, by a process of elimination, that amorphous silica pre-

Fig. 5. (A) Molybdate-active silica (UV photospectrometry) vs. timein Wairakei, New Zealand geothermal water in the absence (opensquares) and presence (solid squares) of amorphous silica seed mate-rial. (B) Molybdate-active silica vs. total silica (ICP).

Table 3. Summary of silica polymorph precipitation experiments.

Phase T°C Ea (kJ/mol) Q/KeqSolution

composition Reference

Amorphous Silica 18–300 49.8 1.7 distilled water Rimstidt and Barnes, 1980Amorphous Silica 60–120 0 4 pH 5–8 Bohlmann et al., 1980

1 N NaClAmorphous Silica 25–50 54.8 10 pH 4–8 Fleming, 1985

0.1–1 m NaClAmorphous Silica 80–120 61 ,1.3 pH 3–7 this study

I 0.13 Mgeothermal waters

Amorphous Silica 60–117 50 1 to 2 pH 7–8 this studygeothermal waters

a-cristobalite 18–300 49.8 1.7 distilled water Rimstidt and Barnes, 1980a-cristobalite 150–300 52.9 2 Renders et al., 1995b-cristobalite 18–300 49.8 1.7 distilled water Rimstidt and Barnes, 1980Quartz 300–420 57–164 — 0.5 m NaCl Laudise, 1958Quartz 18–300 49.8 1.7 distilled water Rimstidt and Barnes, 1980Quartz 300–500 88–159 — 0.1–1 m NaCl Hosaka and Taki, 1981aQuartz 300–500 29.3–33.5 — 0.1–1 m KCl Hosaka and Taki, 1981bQuartz 120–255 34 2 Bird et al., 1986

1387Precipitation kinetics of amorphous silica

cipitation in our field study is controlled by surface defect/surface nucleation processes and not by aqueous diffusion orelementary reactions at the solid-solution interface. Amorphoussilica precipitation is not controlled by aqueous diffusion. Dif-fusion boundary layers calculated from Eqn. 8 using the fieldprecipitation rates, solution compositions and temperatures,and D5 1025 cm2 s21 (Cussler, 1984) range between 2 and10 m thick. Clearly this is not reasonable for our experiments

with reactor dimensions of 50 mm in diameter and 2 to 3 m inlength, residence times of 3 to 5 min, and significant surfacearea.

Amorphous silica precipitation in the field experiment doesnot appear to be controlled by rate-limiting elementary reac-tions at the solid-solution interface, as it does in the laboratoryexperiments. Figure 10 compares the measured field rates withcalculated rates using field solution chemistry and the labora-

Table 4. Amorphous silica precipitation rates determined in the field using a FBR and geothermal waters from Wairakei, New Zealand.

DateT

(°C)n

(kg/d21)

D[Si]mol/kg3 1024

[Si]mol/kg3 1023 pH (T) 1 2 exp (DGr/RT)

Rate(ppt)

(mol m22 s21)

3 July 95 89 786.2 4.496 0.12 8.213 7.86 20.469 1.143 1029

4 July 95 88 1814.4 1.006 0.24 8.538 7.86 20.549 5.833 10210

5 July 95 74 1226.9 3.506 0.35 8.163 7.95 20.784 1.383 1029

10 July 95 58 820.8 6.496 0.12 7.947 8.08 21.193 1.713 1029

11 July 95 97 1071.4 1.666 0.12 8.530 7.82 20.383 5.733 10210

12 July 95 71 1417.0 3.666 0.12 8.163 7.98 20.859 1.673 1029

13 July 95 97 838.1 2.416 0.12 8.480 7.82 20.375 6.53 10210

28 Sept 95 79 1166.4 4.836 0.47 8.138 7.92 20.660 1.183 1029

28 Sept 95 79 1252.8 5.086 0.35 8.155 7.92 20.663 1.333 1029

28 Sept 95 80 1408.3 4.246 0.12 8.205 7.91 20.651 1.253 1029

28 Sept 95 78 976.3 6.166 0.24 8.039 7.93 20.662 1.263 1029

29 Sept 95 96 2315.5 7.496 0.12 8.638 7.82 20.418 3.983 10210

29 Sept 95 84 829.4 4.166 0.24 8.255 7.89 20.578 7.933 10210

29 Sept 95 69 717.1 8.406 0.35 7.623 7.99 20.790 1.383 1029

2 Oct 95 92 985.0 2.006 0.24 8.605 7.84 20.485 4.523 10210

2 Oct 95 75 924.5 6.076 0.12 7.997 7.95 20.722 1.293 1029

2 Oct 95 61 829.4 9.076 0.12 7.256 8.05 20.913 1.733 1029

3 Oct 95 93 1158.0 1.756 0.12 8.646 7.84 20.472 4.653 10210

3 Oct 95 100 1062.7 1.756 0.24 8.688 7.80 20.345 4.263 10210

3 Oct 95 83 1028.2 3.916 0.12 8.363 7.89 20.619 9.233 10210

4 Oct 95 76 1114.6 5.416 0.24 8.055 7.94 20.711 1.383 1029

4 Oct 95 70 1088.6 6.076 0.12 7.964 7.98 20.841 1.523 1029

5 Oct 95 61 1140.5 7.326 0.24 7.623 8.05 21.010 1.923 1029

5 Oct 95 67 1123.2 6.246 0.12 7.964 8.01 20.925 1.613 1029

6 Oct 95 112 846.7 0.926 0.12 8.679 7.75 20.183 1.783 10210

6 Oct 95 115 846.7 0.926 0.12 8.696 7.74 20.145 1.783 10210

6 Oct 95 104 794.9 1.256 0.24 8.704 7.78 20.298 2.283 10210

9 Oct 95 102 1149.1 0.926 0.24 8.654 7.79 20.320 2.423 10210

9 Oct 95 117 1088.6 0.756 0.12 8.704 7.73 20.121 1.873 10210

9 Oct 95 107 1019.5 1.176 0.12 8.679 7.77 20.251 2.733 10210

10 Oct 95 101 1036.8 1.006 0.24 8.654 7.80 20.336 2.383 10210

10 Oct 95 106 1036.8 0.836 0.24 8.721 7.77 20.271 1.983 10210

Fig. 6. Amorphous silica precipitation from Wairakei, New Zealand,FBR experiments shown asD[Si] m22 and flow rate over discreettemperature intervals (61, 696 1, 75 6 1, 79 6 1, 86 6 2, 95 6 2,103 6 2, and 1136 2°C).

Fig. 7. Precipitation rates determined from Wairakei, New Zealand,FBR experiments plotted as a function of T°C (open diamonds) and[1 2 exp (DGr/RT)] (solid circles).

1388 S. Carroll et al.

tory rate equation for amorphous silica precipitation as a func-tion of temperature at pH 7.2:

Rateppt 5 21021.89 exp (2Ea/RT)({H1}/1027.2)20.2

z(1 2 exp (DGr/RT)) (13)

where Ea 5 61.1 (kJ mol21) and ({H1}/1027.2)20.2 accountsfor pH dependence of Rateppt from pH 7 to 8.1. In slightlysupersaturated solutions [f(DGr) . 20.4] at 100 and 117°C,rates predicted using Eqn. 13 are only 15 to 30 times slowerthan field rates. However, at lower temperatures and in moresupersaturated solutions, field rates may be as much as 400times greater than rates predicted with Eqn. 13. Changes inreactive surface or the precipitation of quartz cannot accountfor the more than two order of magnitude discrepancy at lowertemperature in the more supersaturated solutions. The finalsurface area of the reacted sand, which reflects precipitationfrom a highly supersaturated solution at ambient temperaturesas the FBR was dismantled, is only a factor of two higher thaninitial surface area. If quartz precipitated at the sand-solutioninterface, then the calculated field precipitation rate wouldincrease by only one order of magnitude. Quartz probably didnot precipitate based on the high aluminum content of reactedsand surface.

Amorphous silica appears to be controlled by surface defect/surface nucleation reactions in our field experiment. Amor-phous silica precipitation has a non-linear dependence onf(DGr) and may be described by either of the following equa-tions (Fig. 11):

Rateppt 5 10210.0060.06 (expDGr/RT)4.460.3 (14)

or

Rateppt 5 1029.2960.03 (DGr/RT)1.760.1 (15)

Temperature dependence is accounted for in f(DGr) and theoverall rate has an Ea 5 506 3 kJ mol21. The role of chemicalimpurities, such as Al precipitation, in amorphous silica pre-cipitation is unclear. Aluminum has been shown to increase anddecrease growth of silica polymers (Yokoyama et al., 1989;1991; Weres et al., 1981). Qualitiatively, Al has been shown to

decrease silica solubility (summarized in Dove, 1995), whichwould impact reaction affinity rate equations. In the field ex-periments the FBR design allows for continual preferentialremoval of the aluminum and silica as high volumes of fluidflow through the reactor. The Al concentration in the reactedsand surfaces (1–2 wt%) four orders of magnitude higher thanin the geothermal water (,1 ppm). No significant effects of thegeothermal water on amorphous silica precipitation were ob-served in our laboratory experiments, because total dissolvedaluminum available for precipitation is limited by the volumeof the reaction vessel.

It is important to remember that Eqns. 14 and 15 are empir-ical, because both the form of f(DGr) and the reaction order arenot unique. Microscopic studies of amorphous silica precipita-tion are needed to determine rate controlling mechanisms andto bridge the gap between mechanistic theories and macro-scopic observations. For example, the application of atomic

Fig. 8. Percentage of non-molybdate-active silica calculated as thedifference between total dissolved silica by atomic absorption andmolybdate-active silica by UV photospectrometry. Dashed lines repre-sent uncertainty inherent in the UV photospectrometric analysis.

Fig. 9. SEM photomicrocraphs of (A) reacted sand and (B) unreactedsand used in Wairakei, New Zealand, FBR experiments.

1389Precipitation kinetics of amorphous silica

force microscopy to amorphous silica precipitation would pro-vide in-situ observations of growth by surface processes suchas the formation and growth of surface nuclei, movement ofsteps along dislocations, and the impact of chemical impuritieson growth.

Further investigations into the role of the low molecularspecies in deposition of amorphous silica are needed. We

cannot categorically prove that monomeric silica is the onlydepositing species; however, the experimental design, analyti-cal results, and other silica polymerization studies suggest thatlow molecular polysilicic acids are negligible. In our experi-ments, a geothermal fluid undersaturated with respect to amor-phous silica is cooled in a heat exchanger and immediatelyintroduced into the reactor. Dissolved silica in the geothermalfluid is supersaturated with respect to amorphous silica on entryand exit from the reactor. Rapid color development of thesilicomolybdate complex, agreement between total and molyb-date-active silica of the inlet and outlet fluids, and significantsurface area suggest monomeric deposition over polymericdeposition. If polymeric deposition occurs, then polymeric spe-cies form more readily at the mineral-solution interface thanthey do in the bulk solution. Rothbaum and Rhode (1979)analyzed for dimers, trimers, and low molecular weight poly-mers during silica polymerization by silylation. The dimerconcentration at the maximum rate of polymerization was only7% at 30°C, 5% at 90°C, and 3.5% at 120°C; concentrations ofthe higher species were negligible. Weres et al. (1980) used thisdata to estimate 0.7% dimer at 90°C at equilibrium, rising to1.5% dimer in solutions 1.5 times saturation. Makrides et al.(1980) and Crerar et al. (1981) found monomer silica to be intemporary equilibrium with high molecular weight specieswithout intervening oligomers during polymerization.

5. CONCLUSIONS

The results of this study confirm the need for complementarylaboratory and field experiments to determine the factors thatcontrol mineral-water interactions in the earth’s crust. Weinvestigated the effects of dissolved silica concentration, pH,and temperature on amorphous silica precipitation in field andlaboratory experiments. The most important parameter may bethe incorporation of Al in the precipitating phase, resulting insurface defect/surface nucleation controlled precipitation in thefield study. This conclusion is supported by the nonlineardependence of field precipitation rates on f(DGr) and the 1–2wt% Al in the reacted sand. In the absence of significantchemical impurities, amorphous silica precipitation rates maybe controlled by elementary reactions at steady-state in solu-tions supersaturated by a factor,1.3. This conclusion is sup-ported by the linear dependence of the precipitation rate onf(DGr) in laboratory experiments. The rates determined in ourlaboratory study have a fractional dependence on solution pHproportional to {H1} 20.2. Activated energies calculated fromthe laboratory experiments at pH 7.2 equal 616 1 kJ mol21

and from the field study equal 506 3 kJ mol21.

Acknowledgments—We thank K. Brown, W. Bourcier, C. Bruton,R. D. Parker, and D. Rimstidt for critical review of an earlier draft ofthis manuscript. We thank the Electricity Corporation of New Zealandfor access to the Wairakei geothermal field, G. McDowell for con-structing the fluidized bed reactor, and T. Duewer for analysis of theaqueous solutions. This work was performed under the auspices of theU.S. Department of Energy by Lawrence Livermore National Labora-tory under Contract W-7405-Eng-48. Prepared by Yucca Mountain SiteCharacterization Project (YMSCP) participants as part of the CivilianRadioactive Waste Management Program. YMSCP is managed by the

Fig. 10. Comparison of field rates calculated directly from Wairakei,New Zealand, FBR experiments using Eqn. 12 (Rateppt Field) and fromrate equation and constants derived from the laboratory amorphoussilica precipitation experiments (Eqn. 15) and the outlet silica concen-tration (RatepptLab).

Fig. 11. Wairakei, New Zealand, FBR experiments. Amorphoussilica precipitation plotted as (A) rate vs. exp (DGr/RT) and (B) rate vs.DGr/RT.

1390 S. Carroll et al.

Yucca Mountain Site Characterization Project Office of the U.S. Dept.of Energy, Las Vegas, Nevada, USA.

Editorial handling: M. A. McKibben

Accepted in revised form:G. Faure

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1391Precipitation kinetics of amorphous silica

APPENDIX A: UNCERTAINTY ANALYSIS AND ERRORPROPOGATION (BEVINGTON AND ROBINSON, 1992).

Calculated precipitation rate and reaction affinity uncertainties arepropagated from the uncertainty of the dissolved silica measurements.Precipitation rates are calculated from the derivative of exponential fitof [Si] m22 vs. time. The fit to data is

@Si#m22 5 ~a 6 sa! exp @~2b6sb!t# 1 ~c 6 sc! (A1)

The calculated precipitation rate is

R 5@Si#m22

dt5 ab exp ~2bt! (A2)

Uncertainty from the precipitation rate,sR, is

sR2 5 sa

2~­R/­a!2 1 sb2~­R/­b!2 (A3)

where

­R/­a 5 b exp ~2bt! (A4)

and

­R/­b 5 a@exp ~2bt!#~12bt! (A5)

Uncertainty from reaction affinity,s12exp(DGr/RT), is calculated fromthe saturation index,

s12exp~DGr/RT!2 5 sQ

2 ~­SI/­Q!2 1 sK2~­SI/­K!2 (A6)

where

SI 5Q

K(A7)

sQ is equal to measure silica uncertainty andsK is estimated from thedifference in amorphous silica solubility reported by Fournier andRowe (1977) and Walther and Helgeson (1977)

­SI

­Q5

1

K, (A8)

and

­SI

­K5 2Q. (A9)

Uncertainty in precipitation rate constant,skppt, is calculated from alinear regression ofR vs. [1 2 exp (DGr/RT)].

1392 S. Carroll et al.

Appendix B: Laboratory amorphous silica precipitation results. Precipitation rates are calculated for the first 10 hours of reaction. Amorphous silicasolubility (K) is based on Fournier and Rowe (1977).

TimeDays

SiMolal 6s[Si] 1 2 Q/K 6s(12Q/K)

RateMol m22 s21 6sRate

AmSi10.00 7.223 1023 2.173 1024 22.463 1021 3.313 1022 4.343 10212 1.063 10212

0.78 6.703 1023 1.343 1024 21.573 1021 2.053 1022 3.353 10212 6.183 10213

1.04 6.603 1023 1.983 1024 21.383 1021 3.023 1022 3.073 10212 5.043 10213

1.79 6.333 1023 1.273 1024 29.553 1022 1.933 1022 2.403 10212 2.583 10213

2.01 6.253 1023 1.253 1024 28.073 1022 1.913 1022 2.233 10212 2.053 10213

2.78 6.093 1023 1.833 1024 25.293 1022 2.793 1022 1.733 10212 8.323 10214

3.00 6.003 1023 1.203 1024 23.593 1022 1.833 1022 1.603 10212 7.103 10214

4.12 5.953 1023 1.193 1024 22.713 1022 1.823 1022 1.103 10212 1.103 10213

6.02 5.893 1023 1.183 1024 21.623 1022 1.803 1022 5.893 10213 1.443 10213

7.02 5.863 1023 1.173 1024 21.203 1022 1.793 1022 4.223 10213 1.373 10213

8.03 5.753 1023 1.153 1024 7.113 1023 1.763 1022 3.023 10213 1.223 10213

8.80 5.713 1023 1.143 1024 1.443 1022 1.753 1022 2.343 10213 1.103 10213

9.83 5.613 1023 1.123 1024 3.173 1022 1.713 1022 1.663 10213 9.103 10214

AmSi20.00 7.673 1023 1.533 1024 22.673 1021 2.313 1022 4.233 10212 5.723 10213

0.25 7.553 1023 1.513 1024 22.473 1021 6.553 1023 3.843 10212 4.743 10213

0.99 7.193 1023 7.193 1025 21.883 1021 6.553 1023 2.883 10212 2.593 10213

1.35 6.903 1023 6.903 1025 21.403 1021 6.553 1023 2.503 10212 1.863 10213

2.01 6.503 1023 6.503 1025 27.313 1022 6.553 1023 1.943 10212 9.843 10214

2.20 6.483 1023 6.483 1025 27.103 1022 6.553 1023 1.803 10212 8.343 10214

2.98 6.183 1023 6.183 1025 22.103 1022 6.553 1023 1.333 10212 6.273 10214

3.24 6.523 1023 6.523 1025 27.653 1022 6.553 1023 1.203 10212 6.493 10214

4.02 6.143 1023 6.143 1025 21.383 1022 6.553 1023 8.853 10213 7.463 10214

4.30 6.143 1023 6.143 1025 21.513 1022 6.553 1023 7.973 10213 7.663 10214

5.43 6.043 1023 1.213 1024 1.473 1023 6.553 1023 5.123 10213 7.643 10214

6.13 5.823 1023 5.823 1025 3.883 1022 6.553 1023 3.913 10213 7.143 10214

7.15 6.033 1023 6.033 1025 3.863 1023 6.553 1023 2.633 10213 6.123 10214

8.24 6.453 1023 1.943 1024 26.623 1022 6.553 1023 1.723 10213 4.923 10214

9.28 5.973 1023 1.793 1024 1.433 1022 6.553 1023 1.143 10213 3.873 10214

10.28 5.823 1023 1.743 1024 3.923 1022 6.553 1023

11.20 6.533 1023 6.533 1025 27.893 1022 6.553 1023

14.25 5.723 1023 1.723 1024 5.463 1022 6.553 1023

15.21 5.863 1023 1.763 1024 3.273 1022 6.553 1023

16.23 5.963 1023 1.193 1024 1.533 1022 6.553 1023

17.23 5.813 1023 1.163 1024 3.973 1022 6.553 1023

18.23 5.943 1023 5.943 1025 1.833 1022 6.553 1023

21.53 1.313 1022 1.313 1024 21.16 6.553 1023

AmSi30.00 8.273 1023 1.653 1024 23.493 1021 2.503 1022 1.233 10212 3.703 10213

0.18 7.863 1023 1.573 1024 22.853 1021 2.383 1022 1.193 10212 3.483 10213

0.93 7.623 1023 3.813 1024 22.503 1021 5.773 1022 1.043 10212 2.693 10213

1.18 8.033 1023 6.423 1024 23.123 1021 9.723 1022 9.963 10213 2.463 10213

2.04 7.793 1023 3.893 1024 22.763 1021 5.903 1022 8.513 10213 1.793 10213

2.25 7.223 1023 6.503 1024 21.863 1021 9.833 1022 8.203 10213 1.663 10213

3.08 6.923 1023 4.153 1024 21.383 1021 6.293 1022 7.053 10213 1.203 10213

3.20 7.153 1023 6.433 1024 21.753 1021 9.743 1022 6.903 10213 1.153 10213

3.96 7.093 1023 7.803 1024 21.673 1021 1.183 1021 6.013 10213 8.563 10214

4.20 6.423 1023 2.573 1024 25.933 1022 3.893 1022 5.763 10213 7.843 10214

5.03 6.333 1023 6.333 1025 24.473 1022 9.593 1023 4.953 10213 6.023 10214

6.14 6.243 1023 1.253 1024 23.043 1022 1.893 1022 4.043 10213 5.003 10214

7.04 6.443 1023 6.443 1025 26.173 1022 9.753 1023 3.433 10213 4.873 10214

8.01 6.573 1023 2.633 1024 28.393 1022 3.983 1022 2.883 10213 4.983 10214

9.11 6.053 1023 1.213 1024 21.003 1024 1.833 1022 2.363 10213 5.103 10214

10.22 6.333 1023 2.533 1024 24.473 1022 3.833 1022

11.28 6.203 1023 1.243 1024 22.333 1022 1.883 1022

14.16 6.323 1023 6.323 1025 24.233 1022 9.563 1023

15.16 6.323 1023 1.263 1024 24.233 1022 1.913 1022

16.32 6.493 1023 6.493 1025 27.153 1022 9.823 1023

17.28 6.393 1023 6.393 1025 25.443 1022 9.683 1023

18.25 6.293 1023 6.293 1025 23.753 1022 9.523 1023

21.24 8.323 1023 8.323 1025 23.583 1021 1.263 1022

22.98 6.033 1023 6.033 1025 2.303 1023 9.133 1023

1393Precipitation kinetics of amorphous silica

Appendix B (Continued)

TimeDays

SiMolal 6s[Si] 1 2 Q/K 6s(12Q/K)

RateMol M22 s21 6sRate

AmSi50.00 5.523 1023 1.663 1024 23.093 1021 3.073 1022 2.813 10212 5.503 10213

0.83 5.143 1023 5.143 1025 22.173 1021 9.523 1023 2.253 10212 3.543 10213

1.13 5.253 1023 1.053 1024 22.473 1021 1.953 1022 2.073 10212 2.993 10213

1.79 4.813 1023 4.813 1025 21.433 1021 8.923 1023 1.733 10212 2.003 10213

2.07 5.273 1023 5.273 1025 22.563 1021 9.773 1023 1.603 10212 1.683 10213

2.74 4.653 1023 4.653 1025 21.053 1021 8.613 1023 1.343 10212 1.103 10213

3.07 4.553 1023 9.113 1025 27.843 1022 1.693 1022 1.223 10212 9.013 10214

3.75 4.623 1023 9.243 1025 29.523 1022 1.713 1022 1.023 10212 6.833 10214

4.04 4.723 1023 4.723 1025 21.223 1021 8.753 1023 9.413 10213 6.523 10214

4.78 4.363 1023 8.733 1025 23.493 1022 1.623 1022 7.693 10213 6.663 10214

4.92 4.293 1023 4.293 1025 21.793 1022 7.963 1023 7.393 10213 6.753 10214

5.96 4.213 1023 4.213 1025 22.543 1023 7.803 1023 5.583 10213 7.383 10214

6.73 4.163 1023 8.313 1025 1.103 1022 1.543 1022 4.533 10213 7.543 10214

7.78 4.453 1023 4.453 1025 25.713 1022 8.243 1023 3.413 10213 7.343 10214

9.02 4.313 1023 4.313 1025 22.573 1022 7.993 1023 2.433 10213 6.693 10214

9.75 4.573 1023 1.373 1024 28.723 1022 2.543 1022 2.003 10213 6.203 10214

10.76 4.463 1023 8.923 1025 26.073 1022 1.653 1022

13.77 4.393 1023 1.763 1024 24.403 1022 3.263 1022

14.76 4.323 1023 4.323 1025 22.683 1022 8.013 1023

15.79 4.193 1023 8.373 1025 9.213 1024 1.553 1022

16.97 4.093 1023 4.093 1025 2.553 1022 7.593 1023

17.78 4.153 1023 8.303 1025 1.103 1022 1.543 1022

21.79 4.103 1023 8.203 1025 29.093 1022 1.523 1022

AmSi60.00 5.933 1023 5.933 1025 23.523 1021 1.103 1022 2.393 10212 2.093 10212

0.83 6.763 1023 6.763 1025 25.423 1021 1.253 1022 1.763 10212 1.143 10212

1.08 1.023 1022 1.023 1024 21.33 1.893 1022 1.613 10212 9.403 10213

1.82 6.113 1023 6.113 1025 23.933 1021 1.133 1022 1.223 10212 5.103 10213

2.06 5.313 1023 1.063 1024 22.113 1021 1.973 1022 1.123 10212 4.223 10213

2.83 5.023 1023 1.513 1024 21.463 1021 2.793 1022 8.433 10213 2.723 10213

3.12 2.523 1023 1.013 1024 4.263 1021 1.873 1022 7.573 10213 2.603 10213

3.89 3.863 1023 7.723 1025 1.193 1021 1.433 1022 5.693 10213 2.723 10213

4.19 5.403 1023 1.083 1024 22.303 1021 2.003 1022 5.093 10213 2.793 10213

4.92 4.823 1023 9.653 1025 29.903 1022 1.793 1022 3.893 10213 2.873 10213

5.06 4.743 1023 9.493 1025 28.143 1022 1.763 1022 3.693 10213 2.863 10213

7.94 4.843 1023 1.943 1024 21.043 1021 3.593 1022 1.283 10213 2.053 10213

8.91 4.793 1023 2.393 1024 29.143 1022 4.443 1022 8.923 10214 1.683 10213

9.90 4.813 1023 1.923 1024 29.653 1022 3.563 1022 6.203 10214 1.353 10213

12.08 5.073 1023 2.533 1024 21.563 1021 4.703 1022

14.94 4.753 1023 2.373 1024 28.393 1022 4.403 1022

16.89 4.773 1023 1.433 1024 28.893 1022 2.653 1022

19.07 4.543 1023 1.363 1024 23.513 1022 2.533 1022

22.39 4.823 1023 4.823 1025 29.903 1022 8.933 1023

23.86 4.623 1023 4.623 1025 25.443 1022 8.563 1023

25.90 4.673 1023 4.673 1025 26.413 1022 8.663 1023

AmSi70.00 5.643 1023 1.693 1024 23.653 1021 1.533 1021 1.753 10212 4.823 10213

0.35 6.033 1023 1.813 1024 25.173 1021 1.633 1021 1.593 10212 4.033 10213

1.02 5.773 1023 2.893 1024 24.163 1021 2.603 1021 1.323 10212 2.793 10213

1.33 5.943 1023 1.193 1024 24.833 1021 1.073 1021 1.213 10212 2.353 10213

2.10 5.393 1023 3.233 1024 22.713 1021 2.913 1021 9.783 10213 1.503 10213

2.31 5.033 1023 1.013 1024 21.383 1021 9.063 1022 9.223 10213 1.323 10213

3.02 5.103 1023 1.533 1024 21.643 1021 1.383 1021 7.583 10213 8.923 10214

3.23 4.983 1023 9.963 1025 21.193 1021 8.973 1022 7.153 10213 8.103 10214

4.00 4.803 1023 1.443 1024 29.143 1022 1.303 1021 5.773 10213 6.543 10214

4.30 5.093 1023 5.093 1025 21.593 1021 4.593 1022 5.313 10213 6.383 10214

7.02 4.713 1023 9.433 1025 22.333 1022 8.503 1022 2.503 10213 6.573 10214

9.06 4.743 1023 9.483 1025 23.513 1022 8.543 1022 1.423 10213 5.653 10214

10.00 4.583 1023 4.583 1025 2.053 1022 4.123 1022 1.103 10213 5.053 10214

11.34 4.623 1023 9.243 1025 6.883 1023 8.333 1022

14.07 4.573 1023 4.573 1025 2.503 1022 4.123 1022

16.04 4.723 1023 4.723 1025 22.803 1022 4.253 1022

18.07 4.443 1023 4.443 1025 6.893 1022 4.003 1022

21.13 4.713 1023 4.713 1025 22.333 1022 4.243 1022

23.05 4.483 1023 4.483 1025 5.383 1022 4.043 1022

25.03 5.253 1023 5.253 1025 22.193 1021 4.743 1022

28.20 4.843 1023 4.843 1025 26.913 1022 4.363 1022

1394 S. Carroll et al.

Appendix B (Continued)

TimeDays

SiMolar 6s[Si] 1 2 Q/K 6s(12Q/K)

RateMol m22 s21 6sRate

AmSi80.23 9.343 1023 9.343 1025 22.933 1021 1.153 1022 1.293 10211 2.333 10212

0.91 8.513 1023 8.513 1025 21.473 1021 1.043 1022 1.023 10211 1.473 10212

1.19 8.323 1023 8.323 1025 21.293 1021 1.023 1022 9.373 10212 1.213 10212

1.91 7.913 1023 7.913 1025 26.073 1022 9.713 1023 7.363 10212 7.003 10213

2.17 7.793 1023 7.793 1025 25.203 1022 9.563 1023 6.753 10212 5.753 10213

2.90 7.643 1023 7.643 1025 21.983 1022 9.373 1023 5.313 10212 3.693 10213

3.19 8.533 1023 8.533 1025 21.533 1021 1.053 1022 4.813 10212 3.383 10213

3.91 7.803 1023 7.803 1025 26.273 1022 9.583 1023 3.793 10212 3.343 10213

4.15 7.573 1023 7.573 1025 22.403 1022 9.293 1023 3.493 10212 3.423 10213

7.06 7.433 1023 7.433 1025 5.053 1023 9.123 1023 1.323 10212 3.353 10213

7.92 7.083 1023 7.083 1025 3.883 1022 8.693 1023 9.943 10213 3.013 10213

8.88 6.833 1023 6.833 1025 7.573 1022 8.383 1023 7.203 10213 2.593 10213

9.91 7.613 1023 7.613 1025 22.473 1022 9.343 1023 5.113 10213 2.153 10213

10.88 7.503 1023 7.503 1025 21.063 1022 9.213 1023

AmSi100.00 6.283 1023 6.283 1025 25.143 1021 1.163 1022 4.833 10212 1.413 10212

0.11 5.823 1023 5.823 1025 24.003 1021 1.083 1022 4.583 10212 1.273 10212

0.27 6.083 1023 6.083 1025 24.673 1021 1.133 1022 4.253 10212 1.103 10212

0.42 6.343 1023 6.343 1025 25.353 1021 1.173 1022 3.963 10212 9.533 10213

1.04 5.393 1023 5.393 1025 23.103 1021 1.003 1022 2.973 10212 5.013 10213

1.29 5.843 1023 5.843 1025 24.193 1021 1.083 1022 2.643 10212 3.753 10213

2.04 5.793 1023 5.793 1025 24.013 1021 1.073 1022 1.863 10212 1.693 10213

2.34 5.283 1023 5.283 1025 22.783 1021 9.793 1023 1.623 10212 1.513 10213

3.04 4.673 1023 4.673 1025 21.263 1021 8.663 1023 1.173 10212 1.723 10213

3.25 5.173 1023 5.173 1025 22.583 1021 9.583 1023 1.053 10212 1.803 10213

6.04 5.253 1023 5.253 1025 22.613 1021 9.723 1023 2.863 10213 1.473 10213

7.22 5.003 1023 5.003 1025 22.173 1021 9.283 1023 1.653 10213 1.103 10213

8.23 5.163 1023 5.163 1025 22.463 1021 9.573 1023 1.033 10213 8.193 10214

9.21 4.803 1023 4.803 1025 2.523 1022 8.893 1023 6.493 10214 5.993 10214

10.22 5.153 1023 5.153 1025 22.423 1021 9.553 1023

13.22 5.033 1023 5.033 1025 22.313 1021 9.333 1023

15.24 5.633 1023 5.633 1025 23.583 1021 1.043 1022

AmSi120.00 9.673 1023 9.673 1025 22.983 1021 1.193 1022 3.283 10211 4.453 10212

0.28 9.263 1023 9.263 1025 22.383 1021 1.143 1022 2.543 10211 2.783 10212

1.01 8.403 1023 8.403 1025 21.253 1021 1.033 1022 1.293 10211 8.463 10213

1.12 8.253 1023 8.253 1025 21.223 1021 1.013 1022 1.163 10211 7.613 10213

1.25 8.143 1023 8.143 1025 29.403 1022 9.993 1023 1.033 10211 7.013 10213

2.06 7.813 1023 7.813 1025 21.373 1022 9.593 1023 4.853 10212 6.133 10213

2.27 7.663 1023 7.663 1025 22.613 1022 9.403 1023 4.003 10212 5.8613 10213

6.08 7.343 1023 7.343 1025 3.173 1022 9.013 1023 1.173 10213 6.503 10214

7.03 8.123 1023 8.123 1025 26.813 1022 9.973 1023 4.863 10214 3.203 10214

9.08 7.423 1023 7.423 1025 1.943 1022 9.113 1023 7.303 10215 6.443 10215

AmSi130.00 7.913 1023 7.913 1025 23.183 1021 1.213 1022 1.013 10211 2.893 10212

0.34 7.033 1023 1.413 1024 21.943 1021 2.153 1022 8.133 10212 1.913 10212

1.06 6.973 1023 6.973 1025 21.803 1021 1.063 1022 5.113 10212 7.103 10213

1.32 6.333 1023 6.333 1025 26.563 1022 9.673 1023 4.343 10212 5.103 10213

2.05 6.683 1023 6.683 1025 29.823 1022 1.023 1022 2.703 10212 3.763 10213

2.26 6.563 1023 6.563 1025 29.883 1022 1.003 1022 2.363 10212 3.853 10213

5.06 6.253 1023 6.253 1025 21.183 1022 9.553 1023 3.923 10213 2.373 10213

6.05 6.263 1023 6.263 1025 26.663 1022 9.563 1023 2.083 10213 1.603 10213

7.06 6.233 1023 6.233 1025 22.003 1022 9.523 1023 1.083 10213 1.023 10213

8.05 5.913 1023 5.913 1025 2.733 1022 9.023 1023 5.733 10214 6.363 10214

1395Precipitation kinetics of amorphous silica

Appendix B (Continued)

TimeDays

SiMolar 6s[Si] 1 2 Q/K 6s(12Q/K)

RateMol m22 s21 6sRate

AmSi140.00 8.573 1023 8.573 1025 21.753 1021 1.313 1022 9.803 10212 3.513 10212

0.30 8.343 1023 8.343 1025 21.433 1021 1.273 1022 8.103 10212 2.443 10212

0.99 7.723 1023 7.723 1025 25.443 1022 1.183 1022 5.203 10212 9.743 10213

1.24 7.583 1023 7.583 1025 23.513 1022 1.163 1022 4.433 10212 7.043 10213

2.00 7.873 1023 7.873 1025 27.653 1022 1.203 1022 2.723 10212 4.653 10213

2.26 7.063 1023 7.063 1025 3.843 1022 1.083 1022 2.313 10212 4.733 10213

3.05 6.863 1023 6.863 1025 6.673 1022 1.053 1022 1.393 10212 4.773 10213

6.01 7.913 1023 1.583 1024 27.893 1022 2.423 1022 2.083 10213 1.963 10213

8.01 7.183 1023 7.183 1025 2.053 1022 1.103 1022 5.753 10214 7.843 10214

10.02 6.583 1023 6.583 1025 1.053 1021 1.003 1022 1.583 10214 2.833 10214

13.20 6.583 1023 6.583 1025 1.053 1021 1.003 1022

AmSi150.00 1.473 1022 1.473 1024 29.653 1022 2.253 1022 1.583 10211 1.633 10212

0.04 1.473 1022 1.473 1024 29.653 1022 2.243 1022 1.543 10211 1.563 10212

0.16 1.433 1022 1.433 1024 25.933 1022 2.183 1022 1.453 10211 1.393 10212

0.29 1.393 1022 1.393 1024 22.333 1022 2.123 1022 1.353 10211 1.223 10212

0.98 1.323 1022 1.323 1024 4.283 1022 2.013 1022 9.453 10212 5.713 10213

1.31 1.293 1022 1.293 1024 6.893 1022 1.983 1022 7.953 10212 3.883 10213

1.97 1.263 1022 1.263 1024 9.643 1022 1.923 1022 5.633 10212 2.163 10213

2.27 1.253 1022 1.253 1024 1.073 1021 1.903 1022 4.823 10212 2.033 10213

2.98 1.223 1022 1.223 1024 1.333 1021 1.863 1022 3.333 10212 2.183 10213

5.95 1.153 1022 1.153 1024 1.953 1021 1.763 1022 7.073 10213 1.453 10213

7.96 1.153 1022 1.153 1024 1.953 1021 1.763 1022 2.473 10213 7.533 10214

9.97 1.133 1022 1.133 1024 2.133 1021 1.733 1022 8.663 10214 3.503 10214

13.06 1.143 1022 1.143 1024 2.043 1021 1.733 1022

1396 S. Carroll et al.