Experimental study of K-feldspar dissolution rates as a function of chemical affinity at 150°C and pH 9

Acta,Vol.58,No. 21,pp. 4549-4560,1994 Copyright0 1994 Elwier Science Ltd Printedin the USA. All rights reserved

Gecchimica et Cosmochimica

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Experimental study of K-feldspar dissolution rates as a function of chemical affinity at 150°C and pH 9 JEAN-MARIEGAUTIER, ERIC H. OELKERS,and JACQUESSCHOTT Laboratoire de Gtochimie, CNRS-Universitt Paul Sabatier, 38 rue des Trente-six Ponts, 3 1400 Toulouse, France (Received February 28, 1994; accepted in revisedform August 8,

1994)

Abstract-Steady state dissolution rates of a K-rich feldspar (~.s,N~.lsB~.o~Al,.~~Si2.9608) were measured as a function of chemical affinity and aqueous Si and Al concentration in solutions containing 5 X 10e3 m total K using a titanium mixed flow reactor at a temperature of 150°C and pH of 9.0. All dissolution experiments exhibited stoichiometric dissolution with respect to Al and Si. The concentration of aqueous silica and Al ranged from 1 X 10 -6 to 5 X 10 -4 mol/ kg and 4 X 10 -’ to 5 X 10 -4 mol/ kg, respectively, corresponding to K-feldspar chemical affinities ranging from -90 to - 5 kJ/mol. Logarithms of measured dissolution rates are an inverse linear function of aqueous aluminum concentration, but independent of aqueous silica concentration at all chemical affinities greater than -20 kJ/mol. These rates become increasingly controlled by chemical affinity as equilibrium is approached. This variation of steady state dissolution rates is consistent with their control by the decomposition of silica rich/aluminum deficient surface precursor complex. Taking account of transition state theory and the identity of reactions to form this precursor complex, an equation was derived to describe the steady state dissolution rates over the full range of chemical affinity. A simplified but less general version of this equation, which can be used to describe the steady state rates (r) obtained in the present study can be expressed as r = k+ ( n.\,~o~li(l~+)“3( 1 - ew(-A/3RT)), where k+ stands for a rate constant equal to 1.7 X lo-” mol/cm2/s, a”+ and CI~,(~~)~designate the activities of H+ and Al(O respectively, A refers to the chemical affinity of the overall reaction, R signifies the gas constant, and T denotes the temperature in K. Corresponding experiments performed in a batch-type reactor illustrate the consistency between dissolution rates generated in open and closed systems. an equation to describe these rates as a function of chemical affinity and aqueous Al and Si concentration.

INTRODUCTION THE GOAL OF THISWORKis the better understanding of feldspar dissolution rates as a function of chemical saturation state. The characterization of these rates is essential for the accurate description of numerous geochemical processes such as chemical weathering, diagenesis, metamorphism, and ore formation. Although the bulk of these processes occur at near to equilibrium conditions, most experimental investigations of feldspar dissolution rates have been performed at far from equilibrium conditions ( LAGACHE, 1976; BUSENBERGand CLEMENCY,1976; HELGESONet al., 1984; CHOU and WOLLAST, 1984, 1985; HOLDRENand SPEYER, 1985; BALESand MORGAN, 1985; KNAUSSand WOLERY, 1986; MURPHY and HELGESON,1987; AMRHEINand SUAREZ, 1988,1992; MURPHY, 1989; ROSE, 1991; HELLMANN, 1994). The extrapolation of these data to near to equilibrium conditions is complicated by the fact that the dissolution rates of aluminosilicate minerals apparently do not follow simple transition state derived rate equations (NAGY et al., 199 1; SCHOTTet al., 199 1; NAGY and LASAGA, 1990, 1993; DEVIDAL et al., 1992; OELKERS and SCHOTT, 1992, 1994a; BURCH et al., 1993; DEVIDAL, 1994). In an attempt to quantify the variation of the rates for K-rich feldspars, the steady state dissolution rates of a natural sample were measured as a function of solution composition at 150°C and pH = 9. The purpose ofthis paper is to present the results of these experiments and to generate

THEORETICAL CONSIDERATIONS The dissolution of K-feldspar at 15O’C and pH = 9 can be represented by the reaction KAlSi30s + 2H20 w K+ + Al(OH);

+ 3SiOz(aq)

(1)

for which the law of mass action can be written K& 3

KkspXkspXksp

=

a,tI(OH)i&+U&(aq),

(2)

where Kk~p refers to the equilibrium constant for a pure Kfeldspar, ai designates the activity of the subscripted species, and xksm xksp, and K;, stand for the mole fraction, activity coefficient, and effective equilibrium constant for a natural K-rich feldspar which may have a non-endmember composition. The chemical affinity for this reaction (A) can thus be expressed by K&l

A = RTln (

uAI(OH)~"K+~S.i~(aq)

(3) IT

where R corresponds to the gas constant and T refers to absolute temperature. The standard state adopted in this study is that of unit activity for pure minerals and HZ0 at any temperature and pressure. For aqueous species other than 4549

J-M. Gautier, E. H. Oelkers. and J. Schott

4550

H20. the standard state is unit activity of the species in a hypothetical 1 molal solution referenced to infinite dilution at any temperature and pressure. In accord with transition state theory as applied to minerals, the overall rate of a mineral hydrolysis reaction per unit surface area (Y) can be described using ( AAGAARD and HELGESON. 1977. 1982; LASAGA, 198 I)

r = r+( I - exp(-A/crR7‘)),

(4)

where v+ refers to the forward dissolution rate per unit surface area, and c stands for Temkin’s average stoichiometric number equal to the ratio of the rate of destruction of the activated or precursor complex relative to the overall dissolution rate. As emphasized by WIELAND et al. (1988), the forward reaction rate can be assumed to be proportional to the concentration of a precursor species P’ according to r+ = k/P{ P’},

(SiOz.nHsO)’

CJ + %Al(OH)4

{ H113A11,3SiOX,3j + i (SiOz.nH20)‘}

= S,

(8)

where ( H1,3AlI,XSiOR,I ) and { ( SiOz * nH20)‘] denote the concentration of the indicated surface species per unit surface area. Combining Eqn. 8 with Eqn. 7 and the assumption that the activities of H,,3Al,,XSi08,J and ( SiOZ - nH*O)‘are equal to their concentration* gives

{

(SiOz+nHzO)‘}

=

(9)

which can be further combined

with Eqn. 5 to yield

(5)

where kp- refers to a rate constant consistent with the P’ precursor species and {P’} stands for the concentration of the precursor complex per unit surface area. Equations 4 and 5 can be used to describe the dissolution/precipitation rates of K-rich feldspars by characterizing the identity and concentration of the precursor complex as a function of solution composition. The identity and concentration of P’ can be determined by considering the various steps involved in the dissolution of an alkali feldspar. In accord with OELKERS et al. ( 1994) and OELKERS and SCHOTT ( 1994a), the dissolution of alkali feldspars can be considered to be a three step process as outlined in Fig. I. The first of these steps is the relatively rapid equilibration between hydrogen and alkali ions on the mineral surface (Fig. la). Although it is still unclear if this exchange is reversible (MURPHY and HELGESON, 1989; CHOU and WOLLAST, 1989; WOLLAST and CHOU, 1992), the removal of alkali cations can lead to an alkali deficient surface layer several unit cells deep into the surface (CASEY et al., 1988. 1989; HELLMANN et al.. 1990; NESBITT et al., 1991). The second step, illustrated in Fig. 1b, is the reversible exchange of hydrogen with Al on this surface involving the breaking of AI-O-B groups and producing Al-deficient surface precursor complexes ( OELKERS et al., 1994). At basic conditions this reaction is consistent with H1,3A11,3SiOs,3 + (% + n)H20

suming that S is equal to the total number of sites available per unit surface area for reaction 6 to occur one can write

+ %H+,

(6)

where H1,3All ,3Si08,3 designates a hydrogenated feldspar normalized to one Si atom, ( SiOl - nHl0)’ stands for the silica rich/aluminum deficient surface precursor complex, and n refers to the number of moles of Hz0 contained in each mole of precursor complex. The final step of the dissolution is the detachment of this precursor complex by the irreversible hydrolysis of Si-0-Si groups (Fig. lc). The law of mass action for reaction 6 can be expressed by

where a, refers to the activity of the subscripted species and K’ designates the equilibrium constant for reaction 6. As-

/“Al(OhjiuH+)“3 r+=

+ k

(10) ’ +

“(

&,,(‘,ij,&?,,+)“3

’

where k, - k,>.K’S.

( lOa)

Substituting Eqn. 10 into Eqn. 4, and taking account the fact that the dissolution of one mole of K-feldspar requires the removal of three moles of Si-rich precursor complexes (c = 3 ), yields a general rate expression for the dissolution of K-feldspar given by

X (I - exp(-.4/3RT)).

(11)

Equation 1 1 implies that the variation of K-feldspar dissolution rates exhibits three distinct behaviors depending on the saturation state: ( 1) the rates are independent of chemical affinity and Al concentration at extremely far-from-equilibrium conditions, where the mineral surface is saturated with precursor complexes ( { HAlSi301( } G { ( Si02 - nHz0)‘) ), (2) the rates are controlled by aqueous aluminum concentration, but independent of chemical affinity in an intermediate region where few precursor complexes are present at the mineral surface ( { HAlSi 30s } $ { ( SiOZ - nH*O)‘} ), and ( 3 ) the rates are dominated by the effects of chemical affinity in the near-to-equilibrium region. Note that when the surface has relatively few precursor complexes ( { HA1Si308 } ti { ( SiOz * nH,O)' } ) Eqn. 1 1 reduces to

’ = k+ ( ‘?*llo;,;&+)“3

(1 - exp(-A/3RT)),

(12)

* Note the activities of surface sites may be complex functions of solute concentration at certain conditions ( WOLLAST and CHOU, 1985; STUMM, 1992; DEVIDAL. 1994).

4551

Study of K-feldspar dissolution rates

(C)

FIG. 1. Schematic illustration depicting the three major steps in the dissolution of a K-rich feldspar. (a) The exchange of hydrogen and alkali ions in the feldspar structure. (b) Reaction among aqueous hydrogen ions and aluminum in the feldspar framework leading to the formation of aluminum deficient surface precursor complexes. (c) The irreversible detachment of the precursor complex.

EXPERIMENTAL

which implies that (13)

Natural K-rich feldspar crystals having an average size of -0.5 cm were obtained from Wards Natural Science. These crystals were handoicked. then around with an aeate mortar and nestle. and sub. sequently sieved. The size fraction between 50 and iO0 pm was ultrasonically cleaned using acetone to remove fine particles, rinsed repeatedly with distilled water, and dried overnight at 80°C. The specific surface area of the cleaned powder was 1116 + 10% cm2/ gm as measured by krypton absorption using the B.E.T. method. I

when exp(-A/3RT) 4 1. The degree to which these equations can be used to describe the dissolution rates of a K-rich feldspar can be assessed by measuring its dissolution rate as a function of chemical affinity and solution composition.

METHODS

_

4552

J-M. Gamier.

E. H. Oelkers. and J. Schott

Table 1: Elemental analysis of the K-rich Feldspar used in the present study obtained from electroprobe analysis. Element Si Al K Na Ba 0 Others

1 Atom Percent 22.75 I 8.04 6.35 1.17 0.23 61.53 0.03

The chemical composition of the feldspar was determined by electron microprobe. The results of this analysis, given in Table 1, indicate that the mineral is comprised of approximately 80% K-feldspar and contains appreciable amounts of Na and Ba. Analysis of the feldspar was performed by X-ray diffraction (XRD). The distribution of the resulting diffraction peaks, their interpretation using the “three peak method” of WRIGHT ( 1968), and the bulk composition ofthe feldspar as given in Table 1 indicate that this feldspar exhibits a small degree of exsolution consisting of -95% intermediate microcline ([K]/[Na] = 8. I, Al occupancy in the T,, + Ti, sites = 0.7) and -5% albite. This composition corresponds to an equilibrium assemblage at a temperature of -450°C (see SMITH and BROWN, 1988). XRD analyses of reacted feldspar indicate that there was no compositional or structural change during the experiments. The effects ofthe presence of albite are assumed to be negligible on the steady state dissolution rates measured in the present study as the relative amount of albite in the feldspar is small, the dissolution rates of albite are approximately equal to that of K-feldspar ( HELGESON et al., 1984), and the XRD analysis shows albite to be present following the experiments. Images of the mineral surfaces were performed using a scanning electron microscope. Photomicrographs of the mineral surfaces prior to and following experiments can be seen in Fig. 2. As seen in this figure no fine particles are evident on these mineral surfaces prior to the experiments and no secondary minerals are evident on these surfaces following reaction. In addition, the photomicrograph of the feldspar grain following dissolution illustrates the presence ofetch pits resulting from the dissolution process. The location of these etch pits may be related to the presence of feldspar exsolution. Dissolution experiments were carried out in fluids comprised of demineralized/degassed HzO. Merck reagent grade KCI, KOH, and AICI,, and H4Si04 obtained by the dissolution of amorphous silica for one week at 90°C. The relative amounts of KC1 and KOH were chosen so that the pH of the input solution would be equal to 9.0 at 150°C and the total concentration of aqueous K would be equal to 5 x 10e3 mol/kg. The quantity of these salts required to obtain an input solution with a pH of 9.0 at 150°C was computed with the aid of the EQ3NR software package ( WOLERY, 1983); the pH of these input solutions ranged from I 1.5 to I 1.6 at 25°C. Thermodynamic calculations indicate that, at these conditions, congruent dissolution of alkali feldspars is possible at chemical affinities approaching 0. The compositions of each of the input solutions used in the present study are listed in Table 2. Note that input solution B is slightly supersaturated with respect to gibbsite at 25°C but undersaturated with respect to all stable solid phases at 150°C. No evidence of the precipitation of any mineral phase was observed during the experiments. In addition, as neither the concentration of aqueous K nor the ionic strength of the input solution was varied significantly, the results generated in the present study cannot be used to quantify the effect of these factors on K-feldspar dissolution rates. The open-system experiments were carried out in a titanium mixed flow reactor system illustrated in Fig. 3. As the application of this reactor to perform mineral dissolution experiments has already been described in detail by BERGER et al. ( 1994). only a brief description is provided below. The input fluid for these experiments is stored in a sealed polyethylene container to prevent the dissolution of CO?

into the fluid. The fluid passes through a 10 Grn filter and enters the reactor via a Waters 5 10 high pressure liquid chromatography pump allowing flow rates ranging from 0. I to 10 gm/min. The flow passes into a 2 15 ml. Parr pressurized reactor vessel, which is stirred at a constant rate with a Parr magnetically driven stirrer and kept at a temperature of 150” -+ 1“C by a Parr controlled furnace. The fluid leaves the reactor through a 10 pm titanium filter whereupon it is quenched before passing through a back pressure regulator that maintained a constant pressure of 40 bars throughout the system. All parts in contact with the high temperature reactive fluid are made of Ti. No corrosion of the reactor or the connecting fluid lines was observed during the experiments. This reactor system is ideally suited to investigate the reaction rates of water/mineral interaction. The saturation state and composition of the fluid can be regulated by either changing the flow rate or the composition of the input solution without dismantling the reactor and/or changing the amount of mineral present during the experiment. A steady state dissolution rate, as indicated by a constant output concentration of AI and Si. was obtained after an elapsed time ranging from 2 h to 4 days, depending on the flow rate. Closedsystem experiments were performed in a sealed Ti rocking reactor with a volume of 400 cm’. Samples were obtained through a 0. I pm

0) FIG. 2. Photomicrographs showing the surfaces of the K-rich feldspar used in the present study: (a) Before dissolution experiment: (b) Post-Experiment A.

Study of K-feldspar dissolution rates

4553

Magneti Stirrer

I

HPLC Pump

FIG. 3. Schematic ilius~ation of the experimental apparatus used in the present study to perform open-system experiments (see text).

filter from this closed reactor during the experiment resulting in a small decrease in the fluid volume over time. The silica composition of the output fluids from both types of experiments was determined using the molybdate blue method f K~ROLEFF,1976). The Al com-

position of these fluids was determined by the pyrocatechol violet method ( DOUGAN and WILSON, 1974) if the fluids contained more than 75 ppb Al, or by flameless atomic absorption in a graphite furnace (Perkin Elmer Zeeman 5000) if the fluids were more dilute. The pH of the output fluids were measured immediately after sampling. To prevent the pH of the output samples from drifting due to the dissolution of atmospheric CO*, the output samples for all the experiments other than Experiment A were taken under nitrogen gas. The pH values for output fluids obtained from Experiment A differed by as much as 0.25 from the input value, whereas all other output pH values were within 0. I of the corresoondina innut values. The surfaces of both fresh and reacted fildspar samples were analyzed using a VG ESCALAB MkII X-ray Photoelectric Soectrophotometer-( XPS) with non-monochro&atic Al-X-rays (kl Kot = 1486.6 eV). A review of the application of XPS to the analysis of mineral surfaces is given by CARLSON ( 1975) and HOCHELLA( 1988). Sample preparation and analysis were identical to those previously described in SCHOTTet al. ( 1981). The relative abundances of elements near the mineral surfaces were obtained from measured peak areas and Scofield sensivity factors (SCOFIELD,1976) for Silp, Alzs, K2p3, and 0,s. RESULTS AND DISCUSSION

Open-System Experiments Open-system experiments were carried out using the three different fluid input compositions listed in Table 2. For each input fluid composition and flow rate, the reaction was allowed to proceed until the composition of the output fluid attained a constant value. One example of the evolution of output fluid composition during an experiment is depicted in Fig. 4. The symbols in this figure depict the measured silica concentration as a function of time during experiment

B-6. It can be seen in this figure that the output solution a constant concentration of -8.9 X lo-’ molfkg after -20 h of reaction. As an additional test of the attainment of steady state, a steady state dissolution rate measurement was replicated at least once for each input solution. In each case a close correspondence was found between the original and replicated result. Measured steady state iluid compositions, flow rates, computed steady state dissolution rates, and chemical affinities are listed in Table 3. Steady state dissolution rates (r) given in this table were computed from the measured solution compositions using

attained

y_

AmiF

(14)

ViS ’

where Ami refers to the concentration difference between the input and output of the ith element in solution, F designated the fluid flow rate, vi represents the stoichiometric number of moles of the ith element in one mole of the feldspar, and s refers to the total mineral surface area present in the reactor. The chemical affinity values listed in Table 3 were calculated using Eqn. 3 together with solute activities computed with the EQ3NR computer program ( WOLERY, l983), an effective equilibrium constant for reaction 1 obtained by regression of closed-system experimental data obtained in the present study (log K&, = -16.1, see below) and equilibrium constants for the formation of aluminum hydroxide complexes taken from CASTET et al. ( 1993). The stoichiometry of these open-system dissolution experiments at steady state can be assessed with the aid of Fig. 5, where the difference in the measured input and output silica concentration is plotted as a function of the corre-

Table 2. Compostion of input solutions used in the present study. Experiment A,E,F,G, Closed Sys. B C

KCI (mollkg) 2.18803 9.8OE-04 2.03E-03

KOH (mollkg) 2.83E-03 4.02E-03 2.978-03

SiOz (mollki) 0 0 3.01 E-04

AIC13 (moi/kg) 0 3.5‘1E-04 0

PH (20” C) ‘1 ii.48 11.58 II.54

J-M. Gautier, E. H. Oelkers, and J. Schott

4554 12 steattystatec,oncentration

I

Experiment 06 0

B-6 1

800

400 Elapsed

1200

1600

Time,minutes

FIG. 4. Con~ent~tjon of aqueous silica in the output solution of Experiment B-6 as a function of time. The symbols in the figure

correspond to the measured silica concentration, whereas the line denotes the steady state concentration. sponding change in Al concentration. The linear curve in this figure has a slope of 2.8 1, which represents the Si to Al ratio of the dissolving K-rich feldspar. The close agreement between this curve and the symbols illustrates the stoichiometric nature of the mineral dissolution during these experiments at steady state. Corresponding analysis of the stoichiometry ofthese reactions prior to the attainment ofsteady

t I

state was not performed. In addition, because the output concentration of K was negligibly different from its input concentration, the relative release rate of this element could not be unambiguously determined. The variation of the steady-state rates obtained in experiments A, B. and C on Al and Si concentration can be seen in Fig. 6a and b. It can be seen in Fig. 6a that the experiments carried out with a Si-rich input solution resulted in similar steady-state dissolution rates as those experiments performed in a Si- and Al-free input solution. The dashed line in this figure corresponds to a slope of -%, which is consistent with the variation of rates with aqueous Al concentration implied by Eqn. 13. In contrast, as illustmted in Fig. 6b, at constant silica concentration the steady-state dissolution rates obtained From experiments performed in a Al-rich input solution are -0.4 log units less than those obtained from experiments performed in an Al/%-free input solution which themselves are -0.2 log units less than those obtained from experiments obtained in a Si-rich input solution. These same data are depicted by symbols plotted as a function of the chemical affinity for the K-feldspar dissolution reaction in Fig. 7a. It can be seen in this figure that these steady state dissolution rates of the K-rich feldspar apparently depend on ( 1) the

Table 3. Summary of experimental data obtained in the present study ixperiment A-

Zxperimen number

A-8 A-Q A-10 A-11 A-12 A-13 A-14 A-15 A-16 A-17

F‘low

B-16

4465 cm2

Surface Area = Output Si 1 Output Al

1

1.95 1.46 3.80 6.02 9.46 1.10 3.00 0.24 0.63 1.92

Rate Si

WAAI

(mol/cm2/sec) 2.32E-04 l.lOE-04 8.61 E-05 5.61 E-05 2.53E-04 1.24E-04 5.oOE-04 3.05E-04

7.01E-05 3.28G05 2.57G05 1.71 E-05 7.71 E-OS 3.79E-05 1.52E-04 9.33E-05

1.45E-04 1 4.53E-05 1

:hemical Affinitp

3.95E-13 4.22E-13 520E-13 6.45E-13 6.60E-13 3.46E-13 4.64E-13 1.49E-13 2.37&13

3.29 3.31 3.35 3.34 3.27 3.28 3.28 3.28 3.27

22.54 17.57 28.13 31.56 37.51 16.33 26.33 6.74 13.70

3.47E-13

3.20

24.04

Initial Si = Initial Al =

:hemicai

Output A

Experiment 1Flow Rate B-6 B-7 B-8 B-Q B-IO B-11 B-12 B-13 B-14 B-15

0 mol/kg

Initial Al =

(gm/min)

Experiment B-

number

0 mollkg

initial Si =

1 (gm/min) 1 2.34

Affinity

0.21 0.92 0.69 1.48 5.62 7.09 8.09 9.47 0.42

4.07E-04 1.88E-04 2.23E-04 1.33E”04 4.00E-05 3.8OE-05 3.60E-05 3.1 OE-05 2.9iE-04

5.07E-04 4.16G04 4.36E-04 4.01E-04 3.62E-04 3.65E.-04 3.63G04 3.63E-04 4.61 E-04

2.39

8.QOE-05 1 3.85E-04 1

7.09E-14 1.44B13 1.27E-13 1.63E-13 2.14E-13 2.24E-13 2.42E-13 2.44E-13 i.OlE-13 1.76E-13

1

2.61 2.89 2.62 2.66 4.18 2.71 3.00 2.58 2.65

21.78 4.68 73.53 11.56 17.31 28.87 30.86 31.45 33.02 8.56

2.62

21.69

4555

Study of K-feldspar dissolution rates Table 3. (Continued) 3.13E-04 molkg

Initial Si = Initial Al =

!xperimen! C-

0 mot/kg 1674 cm=

Surface Area =

Experiment .low number

:gm/mini

C-8 c-7 C-8 c-9 c-10 c-11 c-12 C-l 3 c-14 c-15 C-18

2.80 1.47 0.44 0.87 1 .oo 4.30 5.80 7.50 9.35 0.27 2.70

3qerimenl number E-03 E-04 E-05 E-08 E-07 E-08 E-09

E-l 0 E-11 E-12 E-l 3

:low (gm/min) 2.31 4.92 1.20 3.19 9.88 1.83 3.95 8.85 2.33 9.85 7.85

Output Output

Rate Al

(moWi) (moW)

mol/cm%ec)

3.84E-04 1.9iE-05 5.32E-13 4.08E-04 5.28E-04 4.89E-04 4.28E-04 3.48E-04 3.40E-04 3.34E-04 3.30E-04 5.37G04 3.57G04

(moM3) (moWI

5.35E-13 5.19E-13 5.38E-13 5.59E-13 2.12E-13 4.30G13

Rate Si :mol/cm%ec;

7.39E052.60G05 4.19E-05 l.l2E-04 5.51 E-05 2.43G05 8.49E-05 4.30E-05 2.85E-05 5.84E-05 1.98E-05 2.20E-05

1.37E-05 4.2OE-05 1.88G05 7.49E-08 2.95E-05 1.41 E-05 7.81 E-08 1.99E-05 5.70E-08 8.98E-08

chemical affinity for dissolution reaction and (2) the Si to Al ratio of the reacting fluid. Experiments E, F, and G were performed in Al/Si-free input solutions to determine the existence of a chemical affinity beyond which the steady state dissolution rates appear to be independent of mineral saturation state. The results of these experiments are represented by symbols as a function of chemical affinity in Fig. 7b. The distribution of points in Fig. 7b show that these steady state dissolution rates are an apparent+ function of mineral saturation state at chemical affinities to at least -90 kJ/mol ([Al] = 5 X lo-’ mol/ kg). This result is in contrast with the interpretation of albite dissolution experiments results obtained at 8O’C and pH = 9 reported by BURCHet al. ( 1993). Based on the distribution of three steady-state dissolution rates obtained at chemical affinities between 40 and 43 kJ/mol, BURCH et al. ( 1993) concluded that the dissolution rates of albite were independent of chemical affinity (and thus the + The word apparent is used in this context because a dependence of these dissolution rates on either aqueous Si or Al concentration would lead to the appearance in Fig. 7b that the rates depend on chemical affinity.

2.67

4.84E-13 3.32/Z-1 3 3.74E-13 4.04E-13

3.31 E-05 7.88E-05 5.81 E-05 4.08E-05 1.25E-05 9.30E-08 7.2OE-08 e.ooE-08 7.87E-05 1.80E-05

Output Output

r&ii

7.08E-13 8.55E-13 5.80E-13 7.29E-13 9.74E-13 5.74E-13 7.04G13 7.5lE-13 5.84C13 7.94E-13 7.18E-33

4

2.87 2.78 2.78 2.82 2.80 2.90 2.92 2.83 2.85 2.75

WAAI 2.84 3.05 2.88 2.98 3.24 2.88 3.08 3.39 2.94 3.48 3.17

:hemical Affinitp 17.39 14.25 8.82 10.93 13.01 19.38 20.84 21.73 22.50 8.31 18.22

:hemical AffiljitF 33.14 41.37 27.02 37.40 49.28 31.23 41 .Ol 48.20 38.58 52.34 50.53

concentration of aqueous aluminum and silica) when A > 40 kJ/mol. The degree to which Eqns. 11 to 13 can be used to describe these data can be assessed in Fig. 7a and b. As the lack of an observed rate maxima with affinity makes it impossible t0 unambiguously characterize the parameter K’, Eqn. 12 was used for the regression of the experimental data in the present study rather than the more general Eqn. 11. The curves depicted in these figures were computed with Eqn. 12 together with a value of k, = 1.7 X 10-l’ mol/cm*/s. This value of k, resulted from a regression of all of the data depicted in Fig. 7a and b. The close correspondence between the curves and the experimental data represented by symbols in Fig. 7a and b demonstrates consistency with Eqn. 12 and supports the hypothesis that these rates are controlled by Si-rich, Aldeficient surface precursor complexes. Note that it would be theoretically predicted by the general rate expression (Eqn. 1 I ) that these reaction rates will reach some maximum value at low Al concentrations. Such a maxima has been observed in the kaolinite dissolution rates reported by DEVIDAL( 1994). Although some of the steady-state dissolution data obtained in silica-rich input solutions appear to suggest that these rates

4556

J-M. Gautier, E. H. Oelkers, and J. Schott Table 3. (Continued)

!xperiment F-

Initial Si = Initial Al =

0 mol/kg 0 mol/kg

Surface Area = Experimenl number

Output

-low Rate (gmlmin)

F-02 F-03 F-04 F-05 F-08 F-07 F-08 F-09 F-IO F-12

Output Al

Rate Si (moUcmz/sec~

m%

2.04 9.82 1.14 5.00 1.44

8.70E-08 3.88E-05 l.l8E-05 2.70E-05 1.58E-05 7.81 E-08 2.01 E-05 l.l2E-05 8.70E-08

2.97 8.88 2.07 3.98 9.85

Ixperiment G-

223 cm2

(mopkg) 8.54E-08 2.25E-08 1.37E-05 3.57E-08 9.83E-08

Initial Si =

-

0 mol/kg 0 mol/kg

Surface Area =

G-02 G-03 G-04 G-05 G-08 G-07 G-08 G-09 G-10

52.97 87.08 42.73 59.44 47.17 54.98 84.42 51.59 80.03 87.40

2.97 2.89 3.31 2.75 3.00 2.80 2.95 3.10 3.27

Initial Al =

Experiment number

Affinitya

2.73

9.07E-13 1.80E-12 1.05E-12 1.47E-12 9.89E-13 l.l7E-12 1.33E-12 l.O3E-12 l.lOE-12 1.81E-12

5.28E-08 3.01 E-08 8.80E-08 3.80G08 2.05E-08

:hemica

MIdAl

35 cm2

I Flow Rate1 Outwt Si 1Outrwt Al 1 (gmlmin)

1

2.02 1.14 9.88 3.98 1.80 8.79 3.05 2.05 8.00

(m&/kg)

Rate Si (mol/cmVsec)

(m&g)

5.61 1.84E-08 8.89E-06 2.41E-08 1.84E-08 5.11 E-07 2.81 E-08 8.87E-07 5.38E-08 1.79E-08 2.14E-08 8.02E-07 3.31E-08 l.lOE-08 4.42E-08 1.48E-08 12.31E-08 I8.90E-07

1.8lE-12 1.28E-12 2.53E-12 1.79E-12 1.37E-12 2.33E-12

1.82E-12 1.45E-12 222E-12

2.85 3.20 3.17 2.99 3.55 3.01 2.99 3.34

1

88.53 87.15 79.52 70.23 83.75 77.01 72.93 82.47

a) kJ/mol

maximize with chemical affinity, the steady-state rate data obtained from Al- and %-free input solutions continue to increase with increasing chemical affinity to at least 90 kJ/ mol. The absence of a maximum K-feldspar dissolution rate even at Al concentrations as low as 5 X lo-’ molal, suggests that relative abundance of silica-rich precursor complexes is

0.00018

)

I

K-Feldspar

150 C, pH=9.0

.

CI) 0.00012 r z E g

0.00006

a Stoichiometric 0

0.00025 ~5 Si,

Dissolution

0.0005

mollkg

FIG. 5. Difference in the input and output Si concentrations plotted as a function of the corresponding difference in the input and output Al concentrations for all of the open-system experiments at steady state. The linear curve has a slope equal to 2.8 I, the ratio of Si to AI in the dissolving K-rich feldspar.

low and therefore the equilibrium constant, K',for reaction 6 is small (K'< 10m6,'). Within the theoretical framework described above the surface complexes are assumed to be in equilibrium with the solution. Thus, the observed low equilibrium constant for reaction 6 suggests that aqueous Al has a strong tendency to reattach itself to the feldspar surface, thereby condensing and dehydrating the silica-rich surface precursors. This destruction, or “poisoning,” of the surface precursor results in a lower overall rate. As already emphasized by CASEY et al. ( 1988) it is likely that other solutes can also inhibit or catalyze feldspar dissolution by adding or removing cross links to the silicate framework by either destroying or forming surface precursor complexes. The reaction mechanism presented above is also consistent with the results of XPS surface analyses performed on this feldspar. Chemical analyses of the surface of unreacted feldspar as well as the feldspar reacted during experiment A are listed in Table 4. A comparison of the results of these two analyses indicates that the reacted K-feldspar is depleted in Al, but enriched in K relative to the unreacted material. The Al depletion observed on the surface strongly supports the control of K-feldspar dissolution by %-rich precursor complexes. A similar depletion of Al has also been observed following the dissolution of albite at 150°C and pH = 9 ( OELK-

4551

Study of K-feldspar dissolution rates

T=lW,

pH = 9

-12.4

$4

.

-42.8

l

-13.2

UN

1T=190” C, pH = 9.0 .5 -5 4.5 4 logWI I (moW 1)

Chemical Affinity, KJlmol

K-Feldspar

.

-12.4

.

.

8

lS. l

.

.

s* l

50’C, pH=9.0 -4.2

.

a

t-feldspar -13.2 -4.6

A .A

.

.

-12.8

1

T=190’, pH = 9.0

*.

..

$5 Q l

3

-12 l

s ; f

0 -3.5

0 3.8

-3.4

0 3

100

60

60

40

20

0

log WI 1 (~W))

Chemical Affinity, KJlmol

FIG. 6. Measured steady-state dissolution rates of the K-rich feldspar at 150°C and pH = 9 obtained from experiments A, B, and C as a function of (a) total aqueous Al concentration and (b) total aqueous Si concentration. The triangles, circles and squares correspond to results of experiments carried out in Sikh, Al-rich, and %/Al-free input solutions (see Table 2).

FIG. 7. Measured steady-state dissolution rates of the K-rich feldspar at 150°C and pH = 9 as a function of chemical affinity for (a) experiments A, B, and C, and (b) experiments A, E, F, and G. The triangles, circles and squares correspond to results of experiments carried out in Sikh, Al-rich, and Si/Al-free input solutions (see Table 2), but the curves represent a fit of these data to Eqn. 12, assuming k, = 1.7 X IO-” mol/cm2/s and log K;O, = -16.1.

ERS and SCHOTT, 1994a). The K enrichment may stem from reequilibration of the mineral surfaces with the K-rich reactive fluids; the unreactive mineral surfaces having been depleted in K due to repeated rinsing in distilled water. This latter

equal to the logarithm of the labeled value. These solid curves were generated from Eqn. I2 and k, = 1.7 X 10mt7 mol/

observation appears to support the possibility that the exchange of alkalis for hydrogen on feldspar surfaces is a reversible process. The variation of these rates with chemical affinity and solute concentration can also be illustrated by means of isotach plots. An isotach plot illustrating contours of equal K-feldspar steady state dissolution rates (isorate contours) for the conditions adopted in the present study, depicted as functions of aqueous aluminum and silica activity, is given in Fig. 8. The location of the symbols in this figure denotes the activities of aqueous silica and Al for which steady-state dissolution rates were obtained. The corresponding reaction rate is indicated by the shape of the symbols. The bold dashed lines in Fig. 8 illustrate the Al and Si concentrations corresponding to the constant chemical affinity values listed on the lines. The solid curves are isorate contours depicting the Al and Si concentrations which have the steady-state dissolution rates

cm2/s. The close correspondence between the change of symbol type and the curves in Fig. 8 again confirms that Eqn.

I2 yields an excellent description of these data. As emphasized by BURCH et al. ( 1993 ) , isotach plots allow for identification

of regions of reaction space where differing rate controlling parameters dominate. Isorate contours parallel to the dashed iso-affinity lines denote that the rates are controlled by chemical affinity; isorate contours parallel to the ordinate imply that the rates are controlled by aqueous silica concentration; and isorate contours parallel to the abscissa suggest the rates are controlled by aqueous aluminum concentration. The distribution of the various experimental data points in Fig. 8 confirms the control of K-feldspar steady-state dissolution rates solely by aqueous Al at concentrations where A > 20 kJ/mol. In addition, the shape of the computed curves in this figure indicates that these rates tend to become controlled by chemical affinity as equilibrium is approached.

Table 4. Surface composition, obtained using XPS, of the unreacted K-feldspar and this same mineral following its reaction in AVSi free input solutions for 170 hours. All atomic ratios are normalized to Si.

Unreacted K-feldspar Reacted K-feldspar

Si I 1

Al

0.38 0.34

K 0.17 0.25

0 i .a8 i .a9

4558

J-M. Gautier, E. hi. Oelkers, and J. Schott

“”

0

50

la0

150

Eiapssdlime, hours FIG. 8. Isotach plot depicting the steady-state K-feldspar rates obtained from the open-system ex~~ments ~rformed in the present study contoured as a function of the activities af aqueous Al and silica. The solid curves are isorate contours generated from Eqn. 12 and k, = 1.7 X lO-‘7 moi/cm*/s, depicting the AI and Si concentrations which would have the steady state dissolution rates equal to the logarithm of the labeled value. The bold dashed lines illustrate the AI and Si concentrations corresponding to chemical affinities equal to the labeled values in kJ/mol. The location of the symbols denote the activities of aqueous silica and aluminum for which steadystate dissociation rates were obtained. The corresponding reaction rate is indicated by the shape of the symbols: lO-“.6 > r r 10-‘* by filled squares, lOWi > r 1 tO~‘*.3by the symbol X, iO_“.’ > r > 10-r2.6 by open triangles. t11m126 > r > tOer3 bp tilled triangles, and r < tOmi by stars.

ClosedSystem Experiments The evolutions of both fluid com~sition and chemical allinity during the closed-system experiment are listed as a function of time in Table 5. The data in this table indicate that the concentrations of Si and Al in the fluid phase increase continuously with time. Note, however, that the Si/Al ratio of the fluid ranges from -3.4 to -4.2 over the duration af the experiment differing somewhat from the Si/AI ratio of 2.81 in the mineral. The origin of this difference is dilhcult to ascertain. Although it could be the result of the precipitation of a small quantity of an Al-rich solid phase in the reactor, none was observed in the analysis of the solids following the experiment, nor was any evidence of the precipitation of an Al-rich phase in any of the open-system experiments which all exhibited stoichiomet~c dissolution with respect to Al and Si. The variation of chemical affinity in this experiment is depicted as a function of time in Fig. 9. The chemical affinity values depicted in this figure were calculated from the experimental data listed in Table 5 using Eqn. 3 together with solute activities computed with the EQ3NR computer program ( W~LERY, I983 ) , equilibrium constants for the formation of Al-hydroxide complexes taken from fable 5. Measured ~ncentrations

Fit;. 9. Vacation of the chemical affinity of the cfosed-system experiment as a function of time The symbols ~o~~~nd to the results ofthe closed-system experiment, and the solid curve to an independent prediction ofthis chemical affinity generated with Eqn, I2, assuming li, = I.7 *: IO-‘? mol/cm”/s and log q,, = - 16. I. The dashed line in this figure corresponds to equilibrium.

CASTETet al. ( 1993), and a value ofthe effective equilibrium constant for reaction I obtained from the regression ofthese experimental data. The symbols in Fig. 9 designate experimentally deduced chemical affinity values, but the curve represents a prediction of the change of chemical allinity with time computed by first nume~cally integrating Eqn. I2 and subsequently combining the results with Eqn. 3, This calculation was performed using k, = 1.7 X lo-l7 mol/cm’/s between and log K;,, = - 16. I. The cfose correspondence the curve and the symbols illustrates the consistency between the results of the closed and apen system experiments, confirming the value adopted for the effective hydrolysis constant for K-feldspar used in the present study. It also follows that the extraction of dissolution rate constants from batch reactor type experiments requires knowledge of the exact mechanism which controls the dissolution. EXPERIMENTAL AND COMPUTATIONAL UNCERTAINTIES Un~~inties associated with the steady state rate constants generated above stem from a number of sources, including the measu~m~nt of aqueous solution ~ncentrations and mineral surface areas. The uncertainties in the measured values of the total fluid concentrations of Al and Si are on the order of &4% or less. Computational and experimental uncertainty in the pH of these solutions are on the order of +O. 1 pH units. In contrast, the uncertainties associated with the measurement of the surface area of the solid powder is +I@%. Moreover, as the total mass of mineral powder

of aqueous Al and Si as a function of time in the cfosed system experiment

4559

Study of K-feldspar dissolution rates changed over the duration of the experiment, so too did the mineral surface area. To assess the temporal effects of changing mineral surface areas on the resulting steady state dissolution rates one of the final fluid flow rates for each mineral sample of a single fluid composition was set approximately equal to the first. The difference in the resulting fluid concentrations were on the order of 10% or less. Because the uncertainties associated with the resulting steady state mineral dissolution rates are directly proportional to the uncertainties in the fluid concentrations and the mineral surface areas, the overall uncertainties in these rates are on the order of - + 15%. The uncertainties in the computed chemical affinities reported in Tables 3 and 5 are difficult to assess owing to the large number of equilibrium constants upon which they depend, and due to the fact that the natural K-rich feldspar used in the present study contained quantities of Na and Ba. In addition, the presence of these impurities renders it difficult to perform the definitive reversed equilibrium experiments to completely constrain the effective equilibrium constant for reaction 1. Nevertheless, it is believed that the effective equilibrium constant adopted for reaction 1 in the present study ( IO -16.’) permits a better representation of the stability of this natural K-rich feldspar than possible by adopting an independent value from a thermodynamic database. As emphasized by BURCH et al. ( 1993)) changes in the equilibrium constants will shift only the origin (A = 0) without affecting the functional dependence of rate on chemical affinity. For example, if the value for the equilibrium constant of reaction 1was taken to be equal to 10-‘5.24,which is the value obtained for pure K-feldspar at 150°C and 40 bars from SUPCRT92 (JOHNSONet al., 1992), each chemical affinity listed in Tables 3 and 5 would increase by a value of 7 KJ/mol. CONCLUSIONS Values of the steady state dissolution rates of a natural Krich feldspar have been measured in an open-system mixed flow reactor as a function of chemical affinity and solution composition at a temperature of 150°C and pH = 9. Corresponding results generated from closed-system experiments demonstrate the consistency between rates obtained in open and closed systems. These rates were found to be an inverse function of aqueous Al concentration at concentrations as low as [ AlToT] = 5 X IO-’ molal. Similarly, the dissolution rates of albite (OELKERS et al., 1994; OELKERS and SCHOTT, 1994a) and kaolinite ( DEVIDAL et al., 1992; DEVIDAL, 1994) have also been observed to be strong inverse functions of aqueous Al concentration. The fact that the dissolution rates of K-feldspar depend on aqueous Al concentration leads to the appearance that these rates are functions of mineral saturation state at chemical affinities to at least -90 kJ/mol. The variation of these rates with chemical affinity and Al/Si ratio can nevertheless be described using a relatively simple mathematical expression based on the concept that they are controlled by the decomposition of a %-rich, Al-deficient precursor complex. Further, it seems likely that the effect on these rates of various organic and inorganic complexing agents can be accurately predicted with this mathematical expression by first computing the relative activities of Al and hydrogen in solution ( OELKERS et al., 1994). Note, however, that the

dissolution rates of Al-rich feldspars (e.g., anorthite) do not require the breaking of Si-0-Si groups to dissolve and do not depend on aqueous aluminum concentration at far from equilibrium conditions ( OELKERS and SCHOTT, 1994b). Consequently, further experimental work is required before the rate expression generated above can be confidently applied to more aluminous feldspars. Acknowledgments-This manuscript is contribution number 706 of the Dynamique et Bilan de la Terre (DBT) program of the CNRS. We would like to thank Jean-Louis Dandurand, Robert Gout, Gilles Berger, Eric Cadore, Christophe Monnin, Sigurdur Gislason, and Jean-Luc Devidal for helpful discussions during the course of this study. We are grateful to Nicholas M. Rose, Kevin Knauss, and Rolland Hellmann for their helpful reviews. We are indebted to Jocelyne Escalier, Jean Claude Harrichoury, Claude Lurde, and Michel Thibaut for technical assistance. Support from the NATO/NSF postdoctoral fellowship program (award NSF-9 I8055 to EHO) and the CNRS is gratefully acknowledged. Editorial handling: J. D. Rimstidt

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