(1) Department of Geological and Environmental Sciences, Ben-Gurion University of the Negev, P. O. Box 653, Beer-Sheva 84105, Israel.
(2) Institut de Ciències de la Terra “Jaume Almera” (CSIC), Lluís Solé i Sabarís s/n, Barcelona 08028, Catalonia, Spain.
(3) Department of Geology and Geophysics, Yale University, P. O. Box 208109, New Haven, Connecticut 06520-8109, USA.
The kinetics of dissolution of smectite from the Cabo de Gata volcanic deposit was investigated in the present study. Assuming that the sample is composed solely of smectite, the structural formula of the treated smectite was calculated to be
Two types of experiments were carried out: batch experiments to obtain equilibrium data and stirred-flow-through experiments to measure the smectite dissolution rate. All experiments were carried out at a temperature of 80°C and pH of 8.8.
After more than two years smectite was still dissolving in the batch experiments, but at a very slow rate. The slow dissolution rate indicates that the system is reasonably close to equilibrium with respect to smectite dissolution. Therefore, the average ion activity product (5±4x10-53), obtained from the last samples of the batch experiments, is used as a proxy for the equilibrium constant of the smectite dissolution reaction at 80°C given as
In the flow-through experiments at steady state, the average Al/Si (0.33±0.03) and Mg/Si (0.15±0.03) ratios were in a very good agreement with these molar ratios of the whole rock analysis (0.35 and 0.14, respectively). The major achievements and conclusions of the present study are:
* For the first time we present a full stoichiometric dissolution of smectite (i.e., stoichiometric dissolution was observed for Al, Si and Mg), and show that the obtained dissolution rate is a good measure of the smectite dissolution rate.
* Pretreatment of the smectite surfaces is necessary to obtain reliable and stoichiometric kinetic results.
* The dissolution rate of the sample reflects the dissolution rate of the montmorillonitic layers.
* Under the experimental conditions smectite dissolution rate is not inhibited by aluminum.
* The dissolution rate of smectite decreases as a function of the silicon concentration. This observation may be explained both by the effect of deviation from equilibrium on dissolution rate and by silicon inhibition, expressed as
respectively. The current data set cannot be used to differentiate between these two possible reaction mechanisms.
The term smectite is widely used to define a clay 2:1. Many smectitic clays are formed of randomly disposed layers of montmorillonite and illite. In the present study we use a randomly interlayered illite-montmorillonite (I/M) from the Neogene bentonitic deposit of Cabo de Gata, southern Spain.
Smectite-rich bentonites have been recognized as suitable clays to be used as a sealant material in the multibarrier systems designed for storage of high level nuclear waste in burial repositories (Chapman and McKinley, 1989). Due to its osmotic swelling capacity (and consequently its plasticity and impermeability), smectite impedes groundwater interaction with the metal canisters. The cation exchange reactions immobilize undesirable cations from the radioactive waste and retard its leakage from the canisters towards the local groundwater. However, the durability of the smectite itself under confinement conditions is a key data that must also be taken into consideration.
Reactive transport numerical codes are currently used to model the chemical evolution in natural and artificial environments. Several recently developed codes include the kinetics of mineral dissolution/precipitation reactions coupled to the transport equations (see for example Steefel and Lasaga, 1994; Saaltink et al., 1998). The kinetics of smectite dissolution/precipitation reactions, as well as other mineral rate laws, should be included in any such modeling of nuclear waste repositories.
Among the variables controlling the dissolution rate, the degree of saturation deserves special attention. Most of the environmental variables that directly affect the dissolution rate of minerals (i.e., pH, temperature, concentration of dissolved species and ionic strength) affect the degree of saturation as well and as a result indirectly affect the dissolution rate. Therefore, the functional dependence of the rate on the degree of saturation is essential to any attempt to apply experimental kinetic data to natural processes or to processes in nuclear waste repositories (Lasaga et al., 1994).
In the present work, laboratory experiments were conducted to establish the dissolution rate dependence on the degree of saturation of the Neogene Cabo de Gata smectite. This smectite has been selected as a suitable material for the engineering barrier surrounding the nuclear water canister (ENRESA, 1994), and it is being used accordingly in some European field-scale experiments (Cuevas et al., 1997; ENRESA, 1998). We carried out kinetic dissolution experiments using stirred flow-through reaction vessels in which steady-state rates were determined at specific solution saturation states. Possible effects of other variable such as pH and temperature are eliminated by conducting all experiments at constant pH (8.8) and temperature (80±0.2°C). These experimental conditions are relevant for nuclear waste repositories. Our two major goals are: 1) to determine a reliable long-term stoichiometric dissolution rate of smectite, i.e., one that will be based on the release rate of the cations that occupy the octahedral and tetrahedral sites of the smectite; 2) to examine the effect of the degree of saturation on smectite dissolution rate in the framework of kinetic theory.
Only a few studies of smectite dissolution kinetics have been carried out in the last decade. The dissolution rate obtained in all previous studies was based on the realease rate of Si (RSi) and/or Al (RAl). The realeased rate of the other octahedral cations was not measured. Furrer et al. (1993) and Zysset and Schindler (1996) conducted both batch and flow-through dissolution experiments to study the proton-promoted dissolution kinetics of K-montmorillonite. The dissolution experiments were conducted at room temperature in HCl / KCl solutions (pH = 1 to 5 and [KCl] = 0.03 to 1.0 M). Smectite dissolution rate was found to be linearly dependent on the concentration of adsorbed H+ ions. The observed realeased rate ratio, RSi/RAl, depends on both the pH and KCl concentration. Bauer and Berger (1998) conducted batch experiments at 35° and 80ºC in concentrated KOH solutions (0.1 to 4 m) to study the dissolution kinetics of an industrial (Ceca) Na-montmorillonite. They found that under very basic condition (11.5 £ pH £ 13.9) smectite dissolved independently of the aqueous silica or aluminum concentrations. They proposed a non-linear dependency of smectite dissolution rate, . The apparent activation energy was found to be 52 ± 4 kJ/mole.
Lasaga (1995; 1998) proposed a general form of rate law for one mechanism of heterogeneous mineral surface reactions:
where k0 is a constant, Amin is the reactive surface area of the mineral, Eapp is the apparent activation energy of the overall reaction, R is the gas constant, T is the absolute temperature, ai and are the activities in solution of species i and H+, respectively, ni and are the orders of the reaction with respect to these species, g(I) is a function of the ionic strength (I) and f(DGr) is a function of the Gibbs free energy. The much-studied pH dependence of the dissolution/precipitation reactions is represented by the term in equation (1). Terms involving activities of species in solution other than H+, , incorporate other possible catalytic effects on the overall rate. The g(I) term indicates a possible dependence of the rate on the ionic strength in addition to that entering through the activities of a specific ion. The last term, f(DGr), accounts for the important variation of the rate with deviation from equilibrium. Knowing all the variables included in equation (1), e.g., the pH dependency, the apparent activation energy, the function f(DGr), is fundamental to accurately modeling the nuclear waste repository via a coupled reaction-transport model (Cama and Ayora, 1998). Therefore experimental data on smectite dissolution rate dependence on variable environmental conditions are necessary.
The form of the last term in equation (1), f(DGr), for an elementary reaction based on the Transition State Theory (TST) is (Lasaga, 1998):
where R is the gas constant and T is the absolute temperature. The function f(DGr) for overall reactions is difficult to predict a-priori. Equation (2) may be generalized to (Aagaard and Helgeson, 1982):
where s is a coefficient that is not necessarily equal to 1. Near equilibrium, i.e., |DGr| << sRT, the approximation exp(x)=1+x leads to a linear dependence of the rate on DGr
The form of equation (4) can be applied to overall reactions in a few simple cases that are described by Lasaga (1998). In all these cases, defects such as dislocations should not control the dissolution kinetics. Equation (4) was successfully used in studies on the kinetics of dissolution of silica, quartz, kaolinite, K-feldspar, kyanite to describe the observed rate dependence on deviation from equilibrium (Rimstidt and Barnes, 1980; Nagy et al., 1991; Berger et al., 1994; Gautier et al., 1994; Oelkers and Schott, 1994; Devidal et al., 1997; Oelkers and Schott, 1999). In other studies on the dissolution and precipitation kinetics of silica, gibbsite and albite (Nagy and Lasaga, 1992; Burch et al., 1993; Carroll et al., 1998; Nagy et al., 1999) the experimental observations lead to fully nonlinear rate laws, i.e., rate laws in which the rate is not a linear function of the Gibbs free energy even very close to equilibrium. For example, Nagy and Lasaga (1992) described the gibbsite rate dependence using the function
It is important to note that, in contrast to equation (2), equation (5) is not based on a first principle theory, and therefore there is no physical meaning to the values of the coefficients m and n.
Any chemical species in solution may be a potential catalyst or inhibitor, including the reactants and the products of the reaction. As a result, changing the concentration of such species may influence the rate both as a catalyst / inhibitor and by its effect on the degree of saturation. The role of inhibition is not explicitly described in equation (1). Depending on the exact inhibition mechanism, the term ai may represent an inhibitor. However, often this is not the case, and other terms should be introduced into the equation (see for example equations (14) and (43) of Ganor and Lasaga, 1998; equations 7.78 and 7.79 of Lasaga, 1998 ; and equation (44) of Ganor et al., 1999). Ganor and Lasaga (1998) presented a mechanistic model describing the effects of an inhibitor on mineral dissolution rate in the presence of a catalyst. The model is fairly simple and consists of fast adsorption of a catalyst and/or an inhibitor on the mineral surface followed by a slow hydrolysis step. Ganor and Lasaga (1998) proposed two end member mechanisms. In the first mechanism the catalyst and the inhibitor compete with each other, i.e., they have a full mutual (negative) dependence. In the second mechanism the adsorption of the catalyst and the inhibitor are absolutely independent of each other.
The bentonitic smectite used in this study is from Serrata de Níjar, Almería (Spain). This smectite is a product of hydrothermal alteration of volcanic glass (Cuadros and Linares, 1996). Based on X-ray diffraction patterns, the sample is composed of a mixed-layer illite/montmorillonite with about 85-90% montmorillonite, 15-10% illite and minor amounts (3%) of quartz, cristobalite, feldspars. Based on the whole rock composition (Table 1), the molar Al/Si and Mg/Si ratios of this smectite are 0.35 and 0.14 respectively. The specific surface area was measured by the Brunauer-Emmett-Teller (BET) method, using 3-point N2 adsorption isotherms on a Quantachrome unit. Sample degassing lasted 2.6 days at 80°C. The specific surface area was 62 ± 6 m2g-1. Scanning Electron Microscope (SEM) photographs (Fig.1a) show that the surface of the smectite grains is very rough. Each grain is an aggregate of smaller particles.
Smectite was pretreated by the following procedure: Twenty grams of dry raw bentonite plus 447 grams of 0.01 M borax were added to a Teflon bottle. The bottle was placed in a thermostatic bath at 80°C for about 2 months. During this period the bottle was shaken periodically. After this period the borax solution was decanted, the wet smectite was dried at 50°C for three days and was ground to break up the mineral aggregates. The size fraction of the powder ranged between 40 and 100 µm.
The sodium concentration of the pretreated smectite increased by more than a factor of two as a result of the treatment with borax (Table 1), probably due to ion exchange and adsorption. Other than that, the chemical composition of the smectite was not affected by the pretreatment. Assuming that the bentonite is composed solely of smectite, the structural formula of the treated smectite was calculated according to the procedure given by Ross and Hendricks (1945)
Smectite samples after most of the experiments, as well as the raw and the treated smectite, were examined by X-ray diffraction and by SEM (Fig.1). Neither method revealed a change in smectite following the treatment and the experiments.
After the pretreatment, the specific surface area of the smectite decreased to 23±2.3 m2g-1. A further change in surface area was observed in the smectite retrieved from most of the flow-through experiments (Table 2).
Two types of experiments were carried out; flow-through experiments to measure the smectite dissolution rate, and batch experiments to obtain equilibrium data.
The flow-through experiments allow us to measure the dissolution rate under fixed saturation state conditions by modifying flow rate, initial powder mass and Si input concentrations. Experiments were carried out using stirred-flow Lexan reactors (30-45 ml in volume) which were fully immersed in a water bath held at constant temperature of 80±0.2°C (Fig. 2a). Smectite reacted with a through-flowing fluid of fixed input composition. The flow rates were controlled by a peristaltic pump and ranged from 0.019 to 0.37 ml min-1 yielding residence times within the cell of about 4 to 40 hours. Stirring of smectite and fluid was controlled by a stirring plate placed directly beneath the bath. Two different types of cells were used. In the first type (Fig. 2b), a Teflon-coated stir bar was mounted on a Lexan pin to avoid possible grinding of the smectite (details of the design are given in Nagy et al., 1990; Nagy et al., 1991). In the second cell type (Fig. 2c), the sample powder and the stir bar were separated by a fine nylon mesh (5 mm pore size) in order to avoid any contact of the sample with the stir bar. Two experiments with similar initial conditions (CS-88-9 and CS-88-1) were conducted in order to compare the results obtained in the two different types of cells. The dissolution rates in these two experiments are the same within error.
In any one run, the flow rate and the input pH were held constant for a long enough time so that steady-state conditions were closely achieved. Achievement of steady-state was verified by a series of constant Si and Al output concentrations, where constancy was defined as output concentrations that differed by less than 5%. After steady-state conditions were reached, dissolution rates were evaluated. Some experiments consisted of one stage, i.e., the experiment was stopped after steady state was approached. Other experiments consisted of two or three stages, in each of which Si input concentrations and/or the flow rate were changed. After the end of the last stage the cell was dismantled and the final surface area was measured using the BET method. The error in the surface area measurement was generally ±10%. Calculated total dissolved material throughout the experiments was less than 12% of the starting mass of smectite.
Batch experiments were carried out in Teflon bottles under controlled temperature conditions (80±0.2°C). In the first experiment (BSB) the material consisted of pretreated smectite whereas in the second experiment (BSC) untreated smectite was used. Water/rock ratios were roughly 140:1 and 70:1 in experiments BSB and BSC, respectively. The batch solutions (0.01 M borax) were shaken once every two days for the first year. After this period the batch solutions were shaken between once every two days and once a month. Sampling consisted of the extraction of 20 ml of solution. In experiment BSB, after 550 hours and 890 hours, 40 ml of the fresh borax solution were added to the bottle, after sampling, to avoid drying of the solution. As a result, there was a slight dilution and the concentration of Al and Si decreased in the next sampling. Total Al and Si concentrations and pH were analyzed for all samples, whereas Ca, Mg, Fe, and K concentrations were only analyzed for the final samples (Table 3).
Input solutions (0.01 M borax) were prepared by diluting Na2B4O7 (AR, Mallinckrodt) and variable amount of silicon source solution with distilled, de-ionized water. The silicon source solution was of dissolved Na2SiO3 . 9H2O. All output solutions were analyzed for Al, Si, and pH. Mg, Ca, Fe, Na and K concentrations were measured in some of the output solutions (see text below). Total Al and Si were analyzed colorimetrically with a UV-visible spectrophotometer, using the catechol violet method (Dougan and Wilson, 1974) and molybdate blue method (Koroleff, 1976), respectively. The uncertainty in measured Al and Si was ± 3% and the detection limit 0.5mM. Na, Mg, Ca and Fe were determined by Inductively Coupled Plasma (ICP). The uncertainty in the measurements was ±5%. K was analyzed by flame atomic adsorption spectrometer with an uncertainty of ±5%. pH of input and output solutions was measured at 80 °C on an unstirred aliquot of solution using a Ross combination electrode with a reported accuracy of ± 0.02 pH units (± 4.5% in H+ activities). The pH electrode was standardized against NBS buffers (Bates, 1954) prepared from reagent grade salts.
The overall dissolution reaction of the pretreated Cabo de Gata smectite under alkaline pH conditions can be expressed as:
Based on a simple mass balance equation, the dissolution rate (mole m-2 s-1), R, in a well-mixed flow-through experiment is obtained from the expression
where Cj,inp and Cj,out are the concentrations of component j in the input and the output solutions, respectively (mole m-3), nj is the stoichiometry coefficient of j in the dissolution reaction, t is time (s), A is the reactive surface area (m2), V is the volume of the cell (m3) and q is the fluid volume flux through the system (m3 s-1). Note that in our formalism, the rate is defined to be negative for dissolution and positive for precipitation. The dissolution rate in such an experiment may be readily obtained if steady state is reached, i.e., if the composition of the output solution reaches a constant value. In this case, the dissolution rate is balanced by the difference between input and output solutions
The error in the calculated rate (DR) is estimated using the Gaussian error propagation method (Barrante, 1974) from the equation:
For most of the experiments, the error in the calculated rate ranged from 11% to 16 % and is dominated by the uncertainty of the BET surface area measurement (±10%). For experiments in which the input concentration is similar to the output concentration the error in the obtained dissolution rate is dominated by the uncertainty of the input and output concentrations and may become as high as ±3600% , as will be commented below (Table 2).
The degree of saturation of the solution with respect to smectite dissolution (equation (7)) is calculated in terms of the Gibbs free energy of reaction DGr
where R is the gas constant, T is the absolute temperature, and IAP and Keq are actual and equilibrium ion activity products of the solution, respectively. Assuming that the activity of water is very close to 1, the ion activity product for the smectite dissolution reaction is given by
where a, g, and C are the activity, activity coefficient and concentration of each component, respectively.
Using the measured pH, Al, Mg, Ca, Fe, K, Si, and Na total concentrations, the activity coefficients and the concentrations of the different species in equation (12) were calculated using the EQ3NR code (Wolery, 1992).
Errors (DP) in the above calculated parameters (P), i.e., IAP, DGr and stoichiometric ratio, were estimated according to the Gaussian error propagation equation (Barrante, 1974):
where Dxi is the estimated uncertainty of the measurements of the quantity xi.
The change in Al, Si, K, Ca, Fe and Mg concentrations with time in the batch experiments BSB and BSC are given in Table 3. As shown in Fig. 3, both experiments demonstrate a highly non-stoichiometric dissolution, even though a pre-equilibrated smectite was used in experiment BSB, and an untreated sample in BSC. For example, the Al/Si ratios during the last year of experiments BSB and BSC are 0.005 and 0.007, respectively, whereas the Al /Si ratio of the whole rock is 0.35. The release rate of both Si and Al in the first 100 hours of the experiment was much faster than in the following few hundred hours as is demonstrated by the change in the slope of concentration versus time (Fig. 3a and c). Fig. 3b and d show the change of Al and Si concentrations versus time during the entire span of experimental time. After about 2000 hours the aluminum concentrations reach a maximum value and thereafter start to decrease. In contrast, the silicon concentrations continue to slowly increase even after more than two years.
The variation of input and output Al, Si and Mg concentrations in three of the flow-through experiments as a function of time are shown in Fig. 4 as representative ones of the experimental set. The experimental conditions of all the experiments are shown in Table 2, in which the experiments are sorted according to flow rates. High Al and Si concentrations are observed at the onset of most of the experiments. Afterwards, Al and Si concentrations decrease until a steady state is approached (Fig. 4). Dissolution rates were calculated based on Al, Si, and Mg steady-state concentrations using eq. (9).
Mg, Ca, Fe, Na and K concentrations were measured in some of the output solutions. In all of these samples Na concentration was 0.02 M, equal within error to the input. Ca concentration ranges between 0.03 and 0.4 mM, K ranges between 0.7 and 2.7 mM and Fe concentration was below the detection limit (0.9 mM).
Nonstoichiometric dissolution may reflect chemical zonation or the presence of non-homogenous defects or impurities, such that the stoichiometry of the dissolved surface is different from the average composition of the mineral. Nonstoichiometric dissolution may also be the result of precipitation of other phases. To ascertain that the dissolution rate obtained is reliable, and may be used to model the long-term dissolution rate of smectite, it is important to show that the rate reflects the destruction of the whole crystallographic framework of the smectite.
Smectite dissolution rates were obtained based on the release of silicon (RSi), aluminum (RAl) and magnesium (RMg) at steady state, for each of the flow-through experiments (Table 2). Fig. 5 plots the dissolution rates evaluated based on the release of Al and Mg versus those obtained based on the release of Si. The solid line in Fig. 5 is the 1/1 diagonal. The stoichiometric ratio between two components (SRi/j) is defined as the ratio between the release of i and the release of j at steady state:
where Ci,inp and Ci,out are the concentrations of component i in the input and the output solution, respectively. Taking into account the appropriate errors, Fig. 5 shows a good agreement between the different estimates of smectite dissolution rate. For most experiments, the Al/Si ratio ranges between 0.27 and 0.42 (Table 2). The exceptions are experiments CS-88-16, CS-88-18, and CS-88-19, which were conducted under near-equilibrium conditions. In these experiments the silicon-input concentration was very high and similar to the output concentration, and therefore the rate was obtained from the small difference between two rather large numbers. As a result the error on the calculated rates (Table 2) and on the stoichiometric ratio is very high. With the exception of the three experiments mentioned above, the average Al/Si ratio is 0.33±0.03. This ratio is in very good agreement with the Al/Si molar ratio of 0.35 of the whole rock analysis of the smectite. The Mg/Si ratio at steady state ranges between 0.08 and 0.20 and the average Mg/Si ratio is 0.15±0.03, in agreement with the whole rock ratio of 0.14.
In all experiments, iron concentration is below detection limit (0.9 mM). Assuming stoichiometric dissolution, the expected Fe concentration in most of the flow-through experiments is below the detection limit and ranges between 0.9 and 2.9 mM in the other samples. The observation that the iron concentration is below detection limit in all samples indicates that either the release rate of iron is less than the stoichiometric release or that the iron is re-precipitated in another phase. Taking into account the low solubility of iron in basic solution, the latter explanation seems to be very probable. For example, the expected total iron concentration in equilibrium with amorphous Fe(OH)3 at pH 8.8 was calculated using EQ3NR code (Wolery, 1992) to be 0.6 mM, less than the detection limit of iron. Since, as we show above, the release of Mg and Al, the major octahedral cations, is stoichiometric we assume that the release of Fe is stoichiometric as well.
The steady-state Ca/Si ratio ranges between 0.0007 and 0.01. This range is much lower than the stoichiometric ratios in the whole rock analysis of the smectite (0.025). The non-stoichiometric behavior of the Ca may indicate that the composition of the interlayer exchangeable cations was modified during the experiment as a result of the high sodium content of the input solution. The K/Si ratios are very variable too. Few of the samples have ratios similar or slightly lower than the whole rock ratio (0.024), whereas the rest of the samples demonstrate significantly higher ratios of up to 0.083. We do not have a good explanation for the non-stoichiometric release of the K. The input concentration of sodium (0.02 M) was very high, and therefore, it is impossible to detect any change in Na concentration in solution resulting from mineral dissolution.
As we showed above, all cations belonging to the octahedral and tetrahedral layers of the smectite, except Fe, which probably re-precipitates as iron hydroxide, displayed stoichiometric dissolution. Therefore, we conclude that the smectite dissolved stoichiometrically, and that the dissolution rate calculated based on the release rate of Si, Al and Mg is a good measure of the smectite dissolution rate. The stoichiometric release of structural smectite ions rules out precipitation of secondary phases, as well as significant smectite-to-illite transformation during the experiments. Production of illitic layers would involve decrease in K concentration and a change in the Si/Al/Mg ratios.
Two preliminary flow-through experiments were conducted using untreated smectite. The first experiment lasted 300 hours and the second 625 hours. The average Al/Si ratios in these experiments were 0.1 and 0.25, respectively, significantly different than the Al/Si ratio of the whole rock (0.35). For kaolinite, Nagy et al. (1991) found that pretreatment of the mineral surfaces is necessary to obtain reliable and stoichiometric kinetic results. Following Nagy et al. (1991), the smectite sample was pre-equilibrated with borax solution at 80°C for two months. As was discussed in the previous section, the pre-treated smectite dissolved stoichiometrically in our flow-through experiments. As for kaolinite (Nagy et al., 1991) the bulk properties of the smectite e.g., its XRD pattern and whole rock composition (Table 1) were not significantly influenced by the pretreatment of the sample. The achievement of stoichiometric dissolution may be explained either by dissolution of fast dissolving minor phases such as amorphous silica or by changes in the Al/Si ratio of the reactive surface of the mineral. We do not have a good explanation for the decrease in BET surface area following the pretreatment. A further discussion of the effect of mineral pretreatment can be found in Nagy et al. (1991).
A significant variation between the initial and final BET surface area measurements of the smectite was observed in most of the experiments (Table 2). Changes in measured surface area are commonly observed in mineral dissolution experiments (Nagy et al., 1991; Amrhein and Suarez, 1992; Nagy and Lasaga, 1992; Ganor et al., 1995; Stillings and Brantley, 1995; Metz and Ganor, 1998; Ganor et al., 1999). In the present study, we observed both increase and decrease of the BET surface area during the experiments. Experiment CS-88-A, D and G illustrates that the change in reactive surface area did not occur between the different stages (Fig. 4c). This experiment was composed of three stages. The experimental conditions during the first stage (A) and the last stage (G) were similar and different from the intermediate stage (D). Regardless of the changes occurring during the intermediate stage, the aluminum, magnesium and silicon concentrations in the first and the last stage were similar. Whereas the change between the initial and the final BET surface area in this experiment was 90%, the observed changes in RSi, RAl and RMg were 13%, 15% and 21%, respectively. Therefore, we conclude that most of the change in surface area occurs either before the first steady state or after the last steady state. Following Nagy and Lasaga (1992), Ganor et al. (1995) and Ganor et al. (1999), we normalize the dissolution rate to the final surface area, assuming that the changes in surface area occurred early in the experiment, before the first steady state was approached. Fig. 6 compares the dissolution rate obtained by normalizing the rate to the final surface area to that obtained using the initial surface area. For most of the experiments, the differences between these two estimates are somewhat larger than the analytical uncertainty. For the rest of the experiments, the dissolution rate based on the initial surface area may be a factor of 3 faster than those estimated based on final surface area. In other words, if our assumption that the change in surface area occurs before the first steady state is wrong and the change occurred after the last steady state, then the calculated dissolution rates would be faster than the 'real' rates by up to a factor of 3.
A more severe problem arises from our inability to correctly define the reactive surface area of the smectite. By substituting the BET surface area as the reactive surface area in equation (9) to calculate the dissolution rate, we make the assumption that the BET surface area is a good measure of the reactive surface area. However, for smectite the BET surface area represents the area of the external surface of dry aggregates of smectite layers, and there is no guarantee that it reflects the surface area of smectite exposed to aqueous solution. In addition, different surface sites may have different reactivity, and therefore, their rate of dissolution may be different. For example, for single biotite crystals, Turpault and Trotignon (1994) estimated that the dissolution rate of the edges is 250 times faster than that of the external basal planes. Until we can independently estimate the edge surface area, it seems to us that the external surface area is the best available proxy for the reactive surface area.
As we show above, both the Al/Si ratio and the Mg/Si ratio in the output solutions at steady state are within error equal to the whole rock ratio. If the dissolution rate of the illitic layers is independent of that of the montmorillonitic layers, then the Al/Si and Mg/Si ratios depend on the actual composition of the two layers, on the relative proportion of these layers, and on the ratio between their dissolution rate:
where Ratej and Wtj are the dissolution rate (mole g-1 sec-1) and the mass (g) of the j layer, respectively, nSi_j and nAl_j are the stoichiometry coefficients of Si and Al in the j layer, respectively, and the subscript I and M refer to the illitic and the montmorillonitic layers, respectively. We calculate the chemical formula of the montmorillonitic layers to be
The calculations are based on the assumptions that the whole rock sample is composed solely of I/M layers, that the composition of the illitic layers is KAl2(AlSi3)O10(OH)2 and that all the K in the smectite is in the illitic layers. According to these calculations 8.7 wt. % of the smectite are illitic layers. Using the above illite and montmorillonite compositions we calculate the expected Al/Si and Mg/Si ratios for different dissolution rate ratios (RateI/RateM). The results of the calculation are shown in Table 4. Table 4 shows that depending on the relative dissolution rate of the illitic and the montmorillonitic layers the Al/Si ratio would vary between 1 and 0.31 and the Mg/Si ratio between 0 and 0.15. The observed average Al/Si (0.33±0.03) and Mg/Si (0.15±0.03) ratios indicate that there is no preferential dissolution of the illitic layers (I) over the montmorillonitic ones (M) in the mixed-layer I/M structure. The dissolution rate of the illitic layers is either similar or slower than that of the montmorillonitic layers. Within error, the dissolution rate of the smectite reflects the dissolution rate of the montmorillonitic layers.
Knowledge of the equilibrium constant is required to determine the effect of the degree of saturation on smectite dissolution. May et al. (1986) tried to determine the solubilities of five smectites. After more than three years of equilibration the system did not approach equilibrium, and solution composition was controlled by the formation of aluminum hydroxide. The final conclusion was that reliable equilibrium solubility of smectite could not be rigorously determined by conventional experimental procedure. Taking this into account, we use our batch experiments to determine an apparent equilibrium constant as a proxy for the required constant.
The fast increase in Al and Si concentrations during the first few thousands hours of the batch experiments (Fig. 3a and b) mainly indicates smectite dissolution. Thereafter, the changes in concentration with time are relatively small. During the last year of the batch experiments, aluminum concentrations decrease by about one mM/year, whereas Si concentrations increase by 60 and 100 mM/year in experiments BSB and BSC, respectively. The increase in Si concentration reflects slow dissolution of a silicate phase, whereas the decrease in Al reflects precipitation of aluminum or aluminum silicate phases. The final solid samples from BSB batch experiment were examined by XRD and SEM. Calcite was the only new phase that was observed, but amorphous or small amounts of other crystalline phases cannot be ruled out. In order to examine the possible precipitation of other phases the saturation index (SI=log (IAP/Keq) of the last samples of the batch experiments were calculated (Table 5). Calculations using the EQ3NR code (Wolery, 1992) show that the saturation index with respect to gibbsite is less than –0.4 and thus gibbsite could not precipitate in the batch experiments. Lower undersaturation is expected for amorphous aluminum hydroxides. Therefore, the precipitated phase might be an aluminum silicate phase. The solution is highly supersaturated with respect to mesolite and muscovite, and close to equilibrium with respect to several aluminum silicate phases such as K-feldspar, microcline, laumontite, analcime, albite and paragonite. Among these silicates, those with Al/Si ratio higher than 0.35 (muscovite, paragonite, mesolite, analcime and laumontite) are the only ones suitable for depletion of Al from the solution, allowing the Si to increase as smectite dissolves.
The solution in the batch experiments is close to equilibrium with respect to a Na-montmorillonite (Na0.33Mg0.33Al1.67Si4O10). However, the equilibrium constant with respect to the Cabo de Gata smectite used in the present study is unknown. The main objective of the batch experiments is to obtain the equilibrium constant of this smectite. The slow release of Si to solution during the second year of the batch experiments indicates that at least one phase, probably the smectite, is dissolving. Ion activity product (IAP) with respect to the smectite dissolution reaction (equation (7)) was calculated using equation (12), and is shown in Fig. 7. The IAP of samples collected during the first few thousand hours of each experiment are not shown in the figures. The estimated total uncertainty in the IAP calculations is 26% (± 0.2 log units). The IAP values of most of the samples are the same within error. Log IAP values in both experiments lie in the range of –52.9 < log IAP < -51.9 (shaded area in Fig. 7). The slow release of silicon with time shows that smectite is slowly dissolving. Therefore, the constancy of IAP with time does not reflect equilibrium. This constant IAP probably results from a balance between smectite dissolution and precipitation of another phase. However, the slow dissolution rate indicates that the system is reasonably close to equilibrium. Therefore, the IAP obtained from the batch experiments will be used as an approximation for the equilibrium constant for the smectite dissolution reaction at 80°C. Such approximation may be based either on the average IAP (5±4x10-53) or on the maximum (and therefore closer to equilibrium) calculated IAP value (1x10-52). In the present paper, the first value is used as the approximation for the equilibrium constant of smectite dissolution reaction and will be refer to as K*eq. As pointed out by Burch et al. (1993) it should be noted that substituting K*eq for Keq in equation (11) would shift the values of the Gibbs free energy without affecting the functional dependence of rate on the degree of saturation.
To calculate the ion activity product, IAP, (Table 6) with respect to the smectite dissolution reaction, we used average measured steady-state Mg, Al and Si concentrations. Ca and K were measured only in some of the experiments. In these experiments, Ca concentration ranges between 0.03 and 0.4 mM and K ranges between 0.7 and 2.7 mM. There is no correlation between the output concentration of K and Ca to the output concentration of the structural cations. Therefore, we used the average Ca (0.13 mM) and K (1.63 mM) concentration values of the measured experiments in order to calculate the IAP for the rest of the experiments. In all experiments, iron concentration is below detection limit (0.9 mM). As we suggested above, the iron probably re-precipitated in an iron hydroxide phase. Therefore, we used the expected total iron concentration in equilibrium with amorphous Fe(OH)3 (0.6 mM). It is important to note that the contribution of Fe, Ca and K to the calculated IAP value is minor, and therefore, even if all the above assumptions were wrong, the error in the calculated IAP would be less than 0.4 log units. Table 6 shows the activity values used to calculate IAP. Values in italics are estimated values.
The Gibbs free energy of reaction for each of the flow-through experiment calculated using equation (11) is shown in Table 6. Fig. 8 plots the variation of smectite dissolution rate (RSi) as a function of the degree of saturation calculated in terms of the Gibbs free energy of reaction, DGr. The dissolution rate increases as a function of the Gibbs free energy all over the experimental range (-3> DGr > -31 kcal mole-1). To correctly interpret this observation, one should separate the possible effect of saturation state on dissolution kinetics from other possible catalytic or inhibitory effects of variables such as Si and Al concentrations, which vary between the experiments. Fig. 9a plots the smectite dissolution rate as a function of the Gibbs free energies using different markers for different ranges of aluminum concentration. Fig. 9a shows that the dissolution rate in experiments with similar aluminum concentration changes as a function of the degree of saturation, whereas the dissolution rate in experiments with similar DGr is similar, regardless of the aluminum concentration. Therefore, we conclude that under the experimental conditions the reaction is neither inhibited nor catalyzed by the presence of aluminum. For silicon (Fig. 9b), it is impossible to differentiate between Si inhibition and DGr effect using the data set of the present study, since DGr was mainly varied by changing silicon concentration. Below, we present possible kinetic mechanisms that may explain the rate dependency shown in Fig. 9b.
In the following discussion we assume that Si does not inhibit the smectite dissolution rate, and that the observed change in rate is solely a function of the degree of saturation. As for albite (Burch et al., 1993) and gibbsite (Nagy and Lasaga, 1992) the dissolution rate of smectite is a non-linear function of the Gibbs free energy. However, in contrast to these studies the dissolution rate continues to increase under far from equilibrium conditions. In other words, in our experiments we did not approach the dissolution plateau even at DGr of -31 kcal mole-1. Following Nagy and Lasaga (1992) we described the smectite rate dependency on the degree of saturation by fitting the experimental data to equation (5). In all our experiments the temperature, the pH and the ionic strength are constant. If the DGr function given in equation (5) is substituted into equation (1), it follows that under constant temperature, pH, and ionic strength, and in the absence of catalysts and inhibitors, the dissolution rate normalized to the surface area is
The coefficients: k, m and n were calculated from a non-linear regression of equation (17) using least squares. The regression coefficient R2=0.93 and the resulting coefficients are: k= -8.1x10-12 mole m-2 sec-1, m=-6x10-10 and n=6. Substituting the resulting coefficients in equation (17) gives,
Comparison of the prediction of equation (18) with the experimental data is shown by the solid line in Fig. 8. The best-fit curve adequately describes the experimental data. However, it is important to note that different combinations of the three coefficients yield other curves that adequately describe the experimental data. For example the dashed line in Fig. 8 was obtained by forcing the coefficient k to be equal to -1x10-10 mole m-2 sec-1. The regression coefficient R2=0.91, and the other coefficients are m=-9x10-7 and n=3. In other words, the best-fit plot obtained by the regression (equation (18)) is not unique, and therefore, the value of the coefficients should be refined using additional experimental data not available at present.
In the following discussion we assume that most of the experiments were conducted under far from equilibrium conditions, and the dramatic increase in dissolution rate as a function of the Gibbs free energy is caused by silicon inhibition. Fig. 10 plots the logarithm of the smectite dissolution rate as a function of the logarithm of total Si in solution. A simple rate law for the Si dependence of the rate may be calculated by linear regression (solid line in Fig. 10) to be,
This best-fit regression curve adequately describes the experimental data. However, equation (19) is not derived from a mechanistic model. Following the competition model and the independent adsorption model of Ganor and Lasaga (1998), we propose that the hydroxyl-promoted smectite dissolution reactions under basic conditions might be inhibited by silicon as a result of adsorption of a silicon species (the inhibitor) near or at the same site in which the hydroxyls (the catalyst) are adsorbed. The predictions of the competition model and the independent adsorption model were examined by a nonlinear regression of equations (14) and (43) of Ganor and Lasaga (1998) using least squares. The best-fit equations are described by,
The same regression line (dotted line in Fig. 10) describes the prediction of both equation (20) and equation (21) because, as will be shown below, both equations reduce to the same simple rate law under the experimental conditions. Substituting the average activity of OH- in the experiments (1.85x10-4) into equations (20) and (21) gives,
The minimum silicon concentration in our experiments is 5x10-6 M and therefore, both 7x109xCSi>>1 and 4.3x1017xCSi>>1. As a result, both equations (20) and (21) reduce under the experimental conditions to the same simple rate law:
As the experimental results can be described by simple rate laws such as that in equations (19) and (24), it is important to note that different combinations of the parameters in the rate laws of equations (20) and (21), as well as rate laws obtained from other models, may fit the experimental data.
As we show above, the decrease of smectite dissolution rate as a function of the silicon concentration may be explained both by the effect of deviation from equilibrium on dissolution rate and by silicon inhibition. To differentiate between these two alternatives additional dissolution experiments in which the degree of saturation is varied by changing aluminum concentrations are needed.
The Cabo de Gata smectite dissolution rates obtained in the present study allow one to make some considerations about the implication of using this smectite as a backfilling material in waste nuclear repositories. The kinetics of dissolution of smectite in contact with ground water circulating through the host rock becomes a key factor affecting the porosity and permeability of the clayey barrier. The smectite sealing the canister can undergo temperatures of about 80ºC during the first 1000 years (ENRESA, 1998). The chemical composition of the ground water is influenced by interactions between the ground water and the smectite. Using the outcomes of the present study, Cama and Ayora (1998) presented some preliminary modeling results of the stability of the Cabo de Gata smectite backfilling, examining the development of the system both at pH 9 and 12. Ground-water pH around 9 represents conditions similar to those of the Grimsel granite host rock (Switzerland), whereas highly basic (~12) pH is typical to ground water that passes through a concrete plug made of portlandite (ENRESA, 1998). The calculations of Cama and Ayora (1998) showed that the obtained results strongly depend on the function that is used to calculate the effect of saturation state on dissolution rate. Moreover, the smectite dissolution rate obtained in the present study is slower than those of many common silicates. As a result, small amounts of albite and muscovite may increase the expected porosity of the backfill.
The dissolution rates of the Cabo de Gata smectite were examined using well-mixed flow-through reactors. The experiments were conducted at 80°C, pH of 8.8 and variable degree of saturation state. The average Al/Si (0.33±0.03) and Mg/Si (0.15±0.03) ratios are in a very good agreement with these molar ratios of the whole rock analysis (0.35 and 0.14, respectively). In the present study, for the first time, all cations belonging to the octahedral and tetrahedral layers of the smectite, except Fe that probably re-precipitates as iron hydroxide, displayed stoichiometric dissolution. This stoichiometric dissolution indicates that the rate calculated based on the release of Si, Al and Mg is a good measure of the smectite dissolution rate, and is not affected by dissolution or precipitation of any other phase. The stoichiometric dissolution of smectite was obtained in samples that were pre-equilibrated with borax solution at 80°C for two months. We suggest that, as for kaolinite (Nagy et al., 1991), pretreatment of the smectite surfaces is necessary to obtain reliable and stoichiometric kinetic results.
The agreement between the average Al/Si and Mg/Si ratios in the flow-through experiments with those of the whole rock indicates that there is no preferential dissolution of the illitic layers (I) over the montmorillonitic ones (M) in the mixed-layer I/M structure. The dissolution rate of the illitic layers is either similar or slower than that of the montmorillonitic layers. Within error, the dissolution rate of the smectite reflects the dissolution rate of the montmorillonitic layers.
The smectite dissolution rate increases as a function of the Gibbs free energy all over the experimental range (-3> DGr > -31 kcal mole-1). Catalytic/inhibitory effects caused by aluminum can be excluded. The degree of saturation was mainly varied by changing the silicon concentration. Therefore, it is impossible to use our data set to differentiate between a possible effect of silicon inhibition and that of the degree of saturation. We showed that experimental data might be fitted to several rate laws suggested by Nagy and Lasaga (1992) and Ganor and Lasaga (1998). Therefore, different models and reaction mechanisms adequately explain the experimental results. The fact that the models are not unique, and several possible models cannot be ruled out is to be expected and, in fact, forms the basis for guiding future research.
Fruitful commentaries during the course of the study from I. MacInnis, J. L. Mogollón, V. Metz, K. Nagy, G. Kacandes and J. Cuadros are greatly appreciated. The smectite sample from Cabo de Gata was selected and supplied by J. Linares. Analytical support from E. Pelfort, S. Matas, R. Fontarnau and X. Alcover of Serveis Científico-Tècnics of Barcelona University and technical assistance of T. Vujic, S. Riney, and A. Goodhue from Yale University are also gratefully acknowledged. We also would like to acknowledge Susan Carroll, Paul Wersin and an anonymous reviewer for their constructive comments that increased the quality of the paper. JC and CA wish to thank the support of ENRESA (Spanish Nuclear Waste Management Company) and the Spanish Government CICYT AMB96-1101-C02-02 research contract. JG wishes to thank the Ministry of National Infrastructures grant # 97-17-010 and the Belfer Foundation for Energy and Environmental Research for financial support.
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Fig. 1 SEM microphotographs of untreated (a) and treated (b) smectite. The smectite has a rough surface and it consists of clusters of smaller particles. There are no significant differences in surface morphology between the untreated and the treated smectite.
Fig. 2 General experimental set-up and detailed view of the reaction cells used in the present study; a) Schematic illustration of the flow-through system; b) a cell with a Teflon-coated stir bar mounted on a Lexan pin; c) a cell with a fine nylon mesh that separates the sample powder and the stir bar.
Fig. 3 Variation in the Al and Si concentration as a function of time in batch experiments BSB (a and b) and BSC (c and d). Figures (a) and (c) show the first few thousands hours and Figures (b) and (d) show the entire span of the experiments.
Fig. 4 Variation in the Si input concentration and the output concentration of Al, Si and Mg as a function of time in flow-through experiments. The vertical lines represent changes in experimental conditions between the different stages.
Fig. 5 Comparison of the smectite dissolution rates that were obtained based on the release of aluminum (a) and magnesium (b) to that obtained based on the release of silicon. The figure shows good agreement between the different estimates of smectite dissolution rate.
Fig. 8 Effect of the degree of saturation on smectite dissolution rate. The solid and the dashed lines are two possible fittings of the f(DGr) function of equation (17) to the experimental data.
Fig. 9 Effect of Si and Al concentrations on the smectite dissolution rate dependence on the Gibbs free energy. The different markers denote different ranges of Al concentration in Fig. 9a and different ranges of Si concentration in Fig. 9b.
Fig. 10 Effect of silicon inhibition on smectite dissolution rate. The solid line is a best fit regression line of the simple rate law of equation (19) and the dotted line is a fitting of two possible mechanistic models for inhibition - see text for explanation.