Kyanite far from equilibrium dissolution rate at 0-22 °C and pH of 3.5-7.5

Yilun Zhang· Donald J. Rimstidt · Yi Huang · Chen Zhu

Abstract Kyanite is an important and slow-dissolving mineral. Earlier work has measured its dissolution rate at high temperature and acidic pH, but experimental measurements at low temperature and near neutral pH were lacking. The rate equation by Palandri and Kharaka (A compilation of rate parameters of water–mineral interaction kinetics for application to geochemical modeling.US Geological Survey,Open File Report 2004-1068,2004)indicates that the rate of kyanite dissolution at room temperature and near neutral pH is on the order of 10-17 mol m-2 s-1,orders of magnitudes slower than most common silicate minerals such as albite and quartz. This study used an externallystirred mixed-flow reactor,which allows high solid:solution ratios,to measure the dissolution rate of kyanite at 0–22 °C and pH of 3.5–7.5.The measured dissolution rate of kyanite is 4.6–7.6 × 10-13 mol m-2 s-1 at 22 °C,and the apparent activation energy is 73.5 kJ mol-1.This dissolution rate is close to the rate of quartz dissolution and four orders of magnitude faster than the prediction by rate equation of Palandri and Kharaka(2004).Based on our new experimental data,we recommend the following rate equation for modeling the dissolution of kyanite at ambient temperatures.where mol m-2 s-1, and Ea = 73.5 kJ mol-1.Review of literature data(Carroll in The dissolution behavior of corundum, kaolinite, and andalusite: a surface complex reaction model for the dissolution of aluminosilicate minerals in diagenetic and weathering environs. Dissertation, Northwestern University, 1989) led to a recommended rate equation for andalusite as for T = 25 °C and pH = 2–10:where k1 = 4.04 × 10-10 mol m-2 s-1, k2 = 7.95 × 10-10 mol m-2 s-1, k3 = 1.01 × 10-17 mol m-2 s-1, n1 = 1.2 and n3 = - 0.6.

Keywords Kinetics · Kyanite · Reaction rates · Mixedflow reactor

1 Introduction

Kyanite, andalusite, and sillimanite are Al2SiO5polymorphs,which are commonly found in metamorphic rocks.Structurally, kyanite is a nesosilicate, consisting of chains of edge-sharing Al–O octahedrons interlinked by Si–O tetrahedrons and Al–O tetrahedrons. Unlike feldspars,micas and clay minerals, this structure lacks covalent Si–O–Si bonds. As a result, the breaking of Al–O–Al bonds will directly liberate silica directly into solution. The studies of the dissolution kinetics of kyanite, therefore,provides comparison to other silicate minerals with Si–O–Si bonds.

A few studies have evaluated the dissolution rate of kyanite based on field observations and laboratory experiments. Dryden and Dryden (1946) estimated the weathering rates of three Al2SiO5polymorphs from field observations, based on their relative resistance to weathering.Their results showed that,although kyanite dissolved the fastest among the three polymorphs,it was slower than hornblende, whose field weathering rate is on the order of 10-16mol m-2s-1(White et al.1996).Oelkers and Schott(1999) carried out a kyanite dissolution experiment at 100–200 °C and pH ～2. The dissolution rate at their experimental condition was ～10-9to 10-10mol m-2s-1.According to their results, they proposed a rate law (Eq. 1,definitions of the symbols are tabulated in Table 1), where A = 0.2 mol m-2s-1, and Ea= 75 kJ mol-1.

Palandri and Kharaka (2004) adopted the experimental results of Oelkers and Schott (1999) and included kyanite in their kinetic database. Figure 1 illustrates the experimental results of Oelkers and Schott (1999) and the rate equation proposed by Palandri and Kharaka (2004). The extrapolation extends over seven orders of magnitudes from ～150 °C and pH ～2 to 25 °C and pH ～7. Due to the large gap between the experimental condition and the weathering condition in terms of pH and temperature the validity of this extrapolation is questionable. The dissolution rate at low temperature and near-neutral pH calculated from the equation of Palandri and Kharaka (2004)is ～10-17mol m-2s-1(Fig. 1).Such a slow rate at near neutral pH is several orders of magnitudes slower than any known dissolution rate of silicate minerals,even compared to very resistant minerals such as quartz and kaolinite(Palandri and Kharaka 2004;Marini 2006;Brantley 2008).Such slow rates also cannot be measured by the conventional experimental method (Ganor et al. 2007).

In this study, we endeavored to fill the data gap and measure the dissolution rate of kyanite at low temperature and near-neutral pH. As the rate is potentially slow, an externally-stirred column reactor, which is capable of holding a large solid to solution ratio, was used. This enables the measurement of the slow dissolution rate of kyanite at room temperature and near-neutral pH.

Fig. 1 Dissolution rates of kyanite measured by Oelkers and Schott(1999) at high temperature and acidic pH (shaded area), and the extrapolated dissolution rate by Palandri and Kharaka(2004)to room temperature(blue curve).The extrapolation was over a wide range of pH and temperature

Table 1 Experimental conditions and solution chemistry of the effluent for all experiments

2 Method

2.1 Materials

A crushed kyanite sample (in 200 mesh size, from Buckingham, VA) was purchased from Virginia Kyanite. The powder was sieved to obtain a 53–74 μm portion(200–270 mesh). XRD analysis showed the samples contain 90%kyanite, 9% quartz, and 1% rutile. The initial specific surface area of the kyanite powder was characterized with N2-BET measurements, yielding an initial BET surface area of 0.461 m2g-1. The sieved powder was first ultrasonicated and rinsed with ethanol three times for 10 min per treatment to remove submicron-to-micron sized particles. Next, the ultra-sonicated powder was rinsed with ethanol ～10 times until the supernatant was clear, and then air-dried overnight.

To further reduce the ‘‘highly-reactive sites’’ on the surface, the cleaned powder was immersed in DI water in HDPE bottles. The bottles were maintained at 80 °C in a water bath for 6 weeks.After that, the water was decanted and the powder was rinsed with ethanol three times to remove the residue water. The pre-treated kyanite powder was air-dried overnight and kept in a desiccator for the experiment. The pre-treated kyanite samples were also characterized by SEM analysis. The result shows that the samples were nearly free of ultrafine particles and the crystal surfaces were mostly fresh (Fig. 2).

2.2 Externally-stirred mixed flow reactor

An externally-stirred column reactor was used for this experiment (Rimstidt et al. 2016, see Fig. 3). This reactor uses a densely-packed column made of PVC instead of a continuously stirred tank, and it uses a fast and turbulent flow to ensure efficient mixing.The packed-column design allows for a very large solid to solution ratio(～1 g/L mL in this experiment), compared to the common tank reactor(usually ＜1 g/10 mL). As a result, the externally-stirred column reactor is better suited for running kinetic experiments involving minerals with very slow reaction rates.Two cotton balls were placed at the ends of the column,to prevent the particles from being flushed out. The column was sealed by two rubber stoppers and epoxy resin. Continuous fast mixing was achieved via a recycle pump that purged the solution through the column at a high flow rate,which reduced the concentration gradient inside the column. A gas wash bottle was installed before the influent storage tank to prevent the atmospheric CO2from decreasing the pH of the influent.

For this kyanite experiment, the column was 10 cm in length, 1.5 cm in diameter, and it held ～20 g of pretreated kyanite. The flow rate of the feeding pump was adjusted to 0.5–10 mL h-1, according to the reaction rate of kyanite at the experimental conditions. The recycle pump ran at a much higher flow rate(＞100 mL h-1).The influent solution was 1 mM NaNO3solution.The initial pH of the influent was adjusted within the range of 3–11,using with concentrated HNO3and NaOH solutions. No pH buffers were used in this experiment. The experiments were carried out at room temperature (22 °C) and 0 °C(temperature controlled by an ice bath).

The dissolution rate was calculated by measuring the change in effluent concentration through Eq. (2) at steady state. Since the concentration of Al could be decreased by Al hydroxide precipitation and cause interference on rate determination,Si was used as the reaction progress variable for estimating the dissolution rate of kyanite according to the following formula:

2.3 Sample collection and analysis

Fig. 2 a SEM micrographs of treated kyanite samples, b is a zoom-in view of the kyanite sample surface

10 mL of samples were collected each day for each experiment. At the start and end of the collection process,the time was recorded and the mass of the collectors was measured. The flow rate of the feeding pump was then calculated as the ratio of the change in collector mass to the change in time. The collected samples were subsequently separated into two portions: one for pH and Si concentration analysis and the other for Al analysis. The Al portion was then immediately acidified with concentrated HCl to avoid Al precipitation. In the the pH/Si portion, pH was also measured immediately after sample collection (an exception was made in the case of experiments at 0 °C,for which pH was measured when the solution had equilibrated to room temperature). Each experiment ran until steadystate was achieved.In this study,the steady state is defined as three to five consecutive samples whose Si concentrations varied by less than 10% (Yang and Steefel 2008;Gudbrandsson et al. 2014).

Total concentrations of dissolved Si in solution were analyzed with a Perkin Elmer Lambda 2S UV–visible spectrophotometer, using the molybdate blue method(Govett 1961). The uncertainty in measured Si was less than ± 5%for concentrations above 4 μM.Total[Al]were analyzed via ICP-MS with a measurement uncertainty of ± 5%.The detection limit of this method is estimated to be 5 ppb (～0.2 μM). In this study, we define the uncertainty as the 95% confidence interval.

2.4 Thermodynamic properties and calculations

Standard state thermodynamic properties for most endmember minerals were taken from Holland and Powell(2011). For allophane and imogolite, the thermodynamic properties were re-calculated based on the recommendations of Su and Harsh (1994, 1998) and Stefansson and G?′slason(2001),in order to ensure that they were internally consistent with the rest of SUPCRTBL database (Zimmer et al. 2016). For Al-bearing aqueous species, the thermodynamic properties were taken from Tagirov and Schott(2001);for SiO2o(aq),they were taken from Rimstidt(1997)and Apps and Spycher (2004); for the rest of the aqueous species,they were taken from Shock and Helgeson(1988),Shock et al. (1989, 1997), and Sverjensky et al. (1997).When applicable, the T and P dependencies of the thermodynamic properties for aqueous species were predicted using the parameters of the revised HKF equations of state for aqueous species (Helgeson et al. 1981; Tanger and Helgeson 1988; Shock et al. 1992).

The equilibrium constants of relevant reactions were calculated through SUPCRTBL (Zimmer et al. 2016),using the heat capacity function of Holland and Powell(2011) for minerals. Speciation and solubility calculations were performed by PHREEQC 3.4 (Parkhurst and Appelo 2013).A customized database compatible with PHREEQC at 0.01–90 °C and 1 bar using the above-mentioned equilibrium constants was constructed specifically for this modeling study. Activity coefficients for the charged aqueous species were calculated from B-dot equation fitted to mean salt NaCl activity coefficients (Helgeson et al.1978; Oelkers and Helgeson 1990). Activity coefficients for neutral or uncharged aqueous species were calculated from the Setche′now equation with a coefficient of 0.1(PHREEQC).

In evaluating the aqueous speciation and mineral saturation states at experimental conditions, we used the pH and total analytical concentrations of the constituents measured at ambient conditions (i.e. ～22 °C and 1 bar)as inputs for the modeling codes and then ‘‘re-heated’’ the solution to experimental T and P. This method calculates the in situ pH at the experimental conditions by taking account of the effects of T and P on the distribution of aqueous species (Zhu et al. 2010).

3 Results

3.1 Al:Si stoichiometry

The experimental conditions and solution chemistry of the effluent in all the experiments are tabulated in Table 1.The typical temporal evolution curves of the effluent Si concentration and pH are shown in Fig. 4. Since there is no buffer in the influent solution, the pH of the effluent was shifted over time as the kyanite dissolution reaction consumed or released H+(Fig. 4b), depending on the solution pH (Eqs. 3–7).

Fig. 4 An example of the temporal evolution of Si concentration(a) and pH (b) in a kyanite dissolution experiment at 22 °C (KY1).The influent pH in this experiment is 5.52(denoted as a dashed line).Shaded area denotes the steady state observed in this experiment. Al concentration in the KY1 experiment was below the detection limit and thus not shown. Error bars stand for the 95% confidence interval(± 5% for Si concentration and ± 0.1 for pH measurement)

As Table 1 shows,a number of experiments had low Al concentrations and several were below the detection limit,especially at near-neutral pH (Fig. 5). The dissolution of kyanite was congruent when the pH was low, but the dissolution was incongruent near neutral pH (Fig. 6). The Al:Si ratio was far less than the theoretical stoichiometric ratio of 2 in the near-neutral pH range.An exception to this trend was the KYHT2 experiment in which the Al concentration never achieved a steady state (and thus was not shown in Fig. 6). Figure 5 shows the solubility of gibbsite at various temperatures and pH levels. At near-neutral pH,Al concentration was below the detection limits and could be regulated by gibbsite solubility (Fig. 5).

Fig. 5 Aluminum solubility at different pH values, assuming dissolved Al is at equilibrium with gibbsite. The dashed line is the common detection limit of Al concentrations by an ICP-MS. Solid symbols represent the Al concentrations measured in the experiments;cross symbols represent the sample pH but without measurable Al concentrations. Red notation stands for the 22 °C experiments, and blue notation stands for the 0 °C experiments. The red box denotes the experiments where Al concentrations are below detection limits.The KYHT2 experiment is not shown on this figure because steady state effluent concentration for Al was not achieved during the experiment

Fig. 6 The Al:Si ratios in the effluent. Symbols represent the steady state Al:Si ratio in each experiment (0 °C experiments denoted as blue circles and 22 °C experiments denoted as red squares. Solid symbols represent ICP-MS measurements, cross symbols represent ratios calculated with assumed [Al] concentrations that is at equilibrium with gibbsite. The dashed line is the theoretical stoichiometric ratio in kyanite.The KYHT2 experiment is not shown on this figure because steady state effluent concentration for Al was not achieved during the experiment

3.2 Saturation indices of the effluent

Saturation indices (SI) for kyanite and common secondary phases were calculated for the steady-state effluent of each experiment (Table 2). For those experiments in which the Al concentration was below detection, Al concentration was assumed to be at equilibrium with gibbsite.

The calculated SI for kyanite was mostly much less than- 2.1, within the range defined as far from equilibrium(Rimstidt 2014). The calculated SIs for kaolinite showed that the effluent was undersaturated with respect to kaolinite for 0 °C experiments, and slightly supersaturated for 22 °C experiments.With respect to allophane and other intermediate secondary phases (e.g., imogolite and halloysite), the effluent was undersaturated in every experiment. (In the interest of brevity, the SI calculation of the other intermediate secondary phases are not presented in this paper.)

3.3 Kyanite dissolution rate

The dissolution rates were calculated using Eq. (2) based on Si concentrations,and are tabulated in Table 3.At room temperature, the measured dissolution rate of kyanite was 5–8×10-13mol m-2s-1. This rate is similar to that of quartz, slightly slower than feldspars, and much slower than pyroxene and olivine (Fig. 7). This result agrees with the field observation that kyanite is resistant to weathering(Dryden and Dryden 1946;Velbel 1999).Furthermore,the dissolution of kyanite showed little dependence on the solution pH. This is in contrast with the strong pH dependence of dissolution rates for most silicate minerals(Fig. 7).

Figure 8 shows the dissolution rates measured in experiments as a function of pH. Unlike most aluminosilicates, whose dissolution rates are strongly correlated with pH, kyanite’s dissolution rate is approximately constant over a wide range of pH.This trend has also been observed for andalusite(Carroll 1989),whose dissolution rate is also almost constant over the pH range of 2–10. To our knowledge, this phenomenon is unusual for silicate minerals, and it might be attributed to the mineral structure of the Al2SiO5polymorphs.

The activation energy of the kyanite dissolution reaction was estimated by comparing the dissolution rate at temperatures of 0 °C and 22 °C using the Arrhenius equation(Eq. 8). The calculated activation energy in this study was 73.5 kJ mol-1, close to the activation energy of 75 kJ mol-1proposed by Oelkers and Schott(1999)based on the rate differences between 111 and 150 °C. The activation energy measured in this experiment falls within the range for most silicate minerals (Palandri and Kharaka 2004; Brantley 2008).

4 Discussion

4.1 Al inhibition effect and the Palandri and Kharaka rate at 25 °C

Prior to this study, kyanite dissolution rates had not been measured at low temperatures and non-acidic pH. Palandri and Kharaka (2004) extrapolated the rate constant for kyanite from high temperature to low temperature and acidic pH to near neutral pH based on the experimental data of Oelkers and Schott (1999). Their extrapolated rate constant for the neutral mechanism (kH2Oat 25 °C) is 10-17.44mol m-2s-1,which is ～5 orders of magnitudes lower than the dissolution rate of kyanite that we measured at room temperature and near neutral pH. This huge discrepancy appears to be the result of their improper assumption of a constant Al concentration while applying the Al inhibition model of Oelkers and Schott (1999). At near-neutral pH, the Al concentration is most likely regulated by the solubility of gibbsite or other Al-bearing phases (Fig. 5). Therefore, the assumption that Alconcentration over a wide pH range is constant was not appropriate.

Table 2 The saturation indices of kyanite and kaolinite in the effluent of all the experiments

Table 3 Calculated dissolution rates for kyanite

Fig. 7 Comparison of the dissolution rates of kyanite and andalusite with other minerals at 25 °C.Blue circles represent the measured dissolution rates of kyanite from this study at 22 °C,and red squares represent the andalusite dissolution rate from Carroll (1989) at 25 °C.The dissolution rates of other minerals were calculated following Brantley (2008)

4.2 Proposed rate equations for kyanite and andalusite dissolution

We recommend a rate equation to replace the rate equation proposed by Palandri and Kharaka (2004) because of the errors in their extrapolation of rates from acidic to neutral pH range. This rate equation works for the pH range of 3.5–7.5 and T = 0–22 °C, and is written as

where k = 5.08 × 10-13mol m-2s-1, and Ea= 73.5 kJ mol-1.

The rate equation for andalusite at 25 °C and for the pH range of 2–10 is based on the experimental data from Carroll (1989), and is given by

Fig. 8 Kyanite dissolution rates at various pH and temperatures(solid symbols). Andalusite dissolution rates from Carroll (1989) at various pH at 25 °C and 80 °C (open symbols) were also plotted for comparison

where k1= 4.04 × 10-10mol m-2s-1, k2= 7.95 × 10-10mol m-2s-1, k3= 1.01 × 10-17mol m-2s-1, n1= 1.2 and n3= - 0.6.

5 Conclusions

In this study,mixed reactor experiments were carried out to measure kyanite dissolution rates at low temperatures(0–22 °C) and pH of 3.5–7.5, at far-from-equilibrium conditions. Dissolution is nearly stoichiometric in acidic conditions (pH ＜4.5), but becomes non-stoichiometric at higher pH (pH ＞4.5), probably due to the precipitation of Al-hydroxide phases. The dissolution rate of kyanite at room temperature is 5–8 × 10-13mol m-2s-1at pH =3.5–7.5,which is much slower than most common silicate minerals and is similar to quartz. The activation energy of kyanite dissolution reaction is 73.5 kJ mol-1. The dissolution rate of kyanite at room temperature is also slower than the rate of andalusite in Carroll(1989),contrary to the prediction in Dryden and Dryden (1946).

We propose a new rate equation for kyanite based on our experimental data to replace the dissolution rate equation for kyanite proposed by Palandri and Kharaka (2004). The latter is the result of an extrapolation from acidic pH to neutral pH under the improper assumption of constant total Al concentration. These extrapolated rates are five orders of magnitude slower than those which we observed in our experiments. We also propose a new rate equation for andalusite based on experimental data found in the literature.

These new rate equations were programmed into Basic language scripts that are suitable to be used in the United State Geological Survey geochemical modeling software PHREEQC (Parkhurst and Appelo 2013) and can be downloaded from the website of www.indiana.edu/～hydrogeo.

AcknowledgementsFinancial support of this research was provided by the U.S. NSF Grant EAR-1225733 to Dr. Chen Zhu, and Indiana University.