Dissolution kinetics of natural calcite minerals in CO2-water systems approaching calcite equilibrium

Chemical Geology, 100 ( 1 9 9 2 ) 129-145 Elsevier Science Publishers B.V., A m s t e r d a m

129

[NA]

Dissolution kinetics of natural calcite minerals in CO2-water systems approaching calcite equilibrium U. Svensson and W. Dreybrodt Institut J~r Experimentelle Physik, Universitdt Bremen, W-2800 Bremen 33, Federal Republic of Germany (Received December 16, 1991; revised and accepted May 2, 1992 )

ABSTRACT Svensson, U. and Dreybrodt, W., 1992. Dissolution kinetics of natural calcite minerals in CO2-water systems approaching calcite equilibrium. Chem. Geol., 100: 129-145. We have measured dissolution rates of various natural calcite samples, e.g marbles, limestones and marine pelagic sediments, in CO2-H20 solutions of fixed Pco2 and temperature during their approach to equilibrium with respect to calcite. The runs have been carried out as batch experiments using the free-drift technique (Pco2:5.10-3atm; T: 20°C), where size fractioned particles of 100/~m were kept in suspension by turbulently stirring the solution. In each experiment three natural specimens and for reference one of synthetic NBS Calcite (SRM 915) have been investigated. The dissolution rates observed for all natural samples can be represented by an empirical rate law given as R =a~ ( 1 - C / C s ) n' at Ca 2+ concentrations C
REMp(C)m(1-O)Rpwp;

C=[O/(1-O)]fexp[-(Uo+Uo'O)/kBT]

where Rpwp is the rate predicted by the PWP model; and ( 1 - O) gives the amount of surface sites still active to dissolution, which is represented by the Fowler-Frumkin isotherm. Our results show that the binding enthalpy Uo is a property of the pure calcite surface, whereas Uo' is dependent on the origin of the materials. Using this rate equation we have examined a variety of calcite dissolution data published in the literature and, in all cases, have found them to obey closely the suggested rate law. Especially the earlier published data on inhibition of calcite dissolution by heavy-metal ions, e.g. Cu 2+ and Sc 3+, fit well into our model. It reconciles with many apparently conflicting results and explains the dissolution rates from the chemical reactions proposed by L.N. Plummer and coworkers and adsorption processes of the solute, both acting simultaneously.

1. Introduction

The dissolution and precipitation of calcite Correspondence to: U. Svensson, Institut far Experimentelle Physik, Universit~it Bremen, W-2800 B r e m e n 33, Federal Republic o f G e r m a n y .

from aqueous solutions plays a major part in various geological environments, e.g., formation of karst landscapes (Dreybrodt, 1987, 1988, 1989, 1990, 1992), early diagenesis in marine sediments (Sj/Sberg, 1978; Berner, 1980; Murray et al., 1980; Keir, 1982; Morse, 1983; Sayles, 1985; Boudreau, 1987), or the

0 0 0 9 - 2 5 4 1 / 9 2 / $ 0 5 . 0 0 © 1992 Elsevier Science Publishers B.V. All rights reserved.

130

U. SVENSSON AND W. DREYBRODT

evolution of downstream water chemistry in rivers (Suarez, 1983; Herman and Lorah, 1987; Dreybrodt et al., 1992). It is a characteristic of many geochemical environments that solutions are close to equilibrium with respect to calcite. Therefore, exact knowledge about the kinetics of dissolution and precipitation processes is required when modeling time-space relationships of these environments. Boudreau (1987) has shown that consideration of the CaCO3 dissolution kinetics is very critical in modeling chemical profiles of pore waters in pelagic sediments (pH, HCO~- ). This is also valid for the evolution of cave conduits in limestone areas, which is critically influenced by the dissolution kinetics of CaCO3 close to equilibrium (Dreybrodt, 1989, 1990, 1992). Although an extensive literature has been published in the past, related to the dissolution kinetics of CaCO3 far from equilibrium, only little data exist dealing with the region close to equilibrium, i.e. C>_,0.9Cs ( C is the actual concentration of the Ca 2+ ion and Cs that at saturation with respect to calcite). The most comprehensive studies of surface-controlled calcite dissolution have been published by Plummer et al. (1978). As a condensed result of their investigations, they derived the nowadays widely accepted mechanistic reaction model (PWP model), which describes the disssolution rates on the heterogeneous surface as a function of the surface activities of the species Ca 2+, H +, HCO~- and H2CO ° (Plummer et al., 1978, 1979; Reddy et al., 1981; Inskeep and Bloom, 1985; Busenberg and Plummer, 1986). In accordance, Plummer et al. have formulated a rate equation of the form: R p w p --/¢1 a n + + / ¢ 2 a H 2 C O $ "Jr-K'3 a H 2 0 - - K4 a c a 2+ aHCO ~-

(1)

where K1, l('2 and l(3 are forward rate constants dependent on temperature; x4 describes the rate of the backward reaction and is a function of both temperature and Pc02; and ai's denote the activities. This rate equation comprises

three elementary chemical reactions that occur simultaneously at the calcite surface: CaCO3 + H + ~ C a 2+ + H C O ;

(I)

CaCO3 +H2CO3 ~ C a 2+ + 2 H C O ;

(II)

CaCO 3 + H : O ~ C a 2 + + C O 2 + H 2 0 ~ Ca 2+ + H C O ; + O H -

(III)

These mechanisms have also been verified on aragonite, and analogous ones on witherite and magnesite by Chou et al. ( 1989 ), who suggest a slightly modified rate equation that reads:

R=x'~ all+ + X~aH,CO~ "+'K'3aH20 --t¢'_3aca:+aco ~-

(2)

where all constants ~c~ do depend only on temperature. This equation is valid for p H > 6 , since above pH 6, reaction (III) is rate determining ( P l u m m e r et al., 1978). The fact that eq. 2 is generally valid for alkaline-earth carbonates of Ca a+, Mg 2+ and Ba 2+ supports confidence that reactions ( I ) - (III) correctly describe the chemistry of calcite as well as of aragonite in the system CaCO3-COe-H:O. Far from equilibrium, rates predicted by the PWP model agree within a factor of ~ 2 to those obtained experimentally. Close to equilibrium, however, experimental rates are distinctly lower than those calculated by use of eq. 1 (Plummer et al., 1979). Herman (1982) performed rotating-disc experiments for measuring dissolution rates of a calcite single crystal (Pco2:1 atm, T: 25°C). In all runs she observed that dissolution rates became undetectably small at concentrations of already ~ 50% of the corresponding Ca :+ concentration at equilibrium. Palmer ( 1991 ) evaluated the experimental data of P l u m m e r et al. ( 1978 ) with the result that all examined experimental rates could be described by empirical rate equations of the type:

REMp=OLI( I--C/Cs) nl

for

C~xC~ (3a)

DISSOLUTION KINETICS OF NATURAL CALCITE MINERALS IN CO2-WATER SYSTEMS

REMP~-OL2(1--C/Cs) n2

for

C>xCs (3b)

with values for n~ in the range from 1.5 up to 2.2 depending on Pco2, n2~4.0 and x ~ 0 . 8 , where C denotes the Ca 2+ concentration in the solution and Cs the equilibrium concentration of Ca 2+ with respect to calcite. The o~ denote rate constants. This kind of dissolution behaviour had already been observed by Plummer and Wigley ( 1976 ) and was later confirmed by Herman ( 1982 ) in dissolution experiments on large single crystals. There has been much discussion about the reasons of inhibited calcite dissolution close to equilibrium. The switch in reaction order as given in eqs. 3 has been attributed to a change of the chemical mechanisms at the surface of the calcite mineral. In view of the consistency of the chemical reactions in the PWP model, however, it is difficult to envisage such a change and moreover explain it reasonably from the point of view of physical chemistry. A more plausible argument was proposed by Berner and Morse (1974), who observed strong inhibition of dissolution on calcite in artificial seawater when they added orthophosphate. They suggested adsorption of phosphate ions at the surface, acting as inhibitors by blocking surface sites active to dissolution. Terjesen et al. ( 1961 ) also noticed inhibition of calcite dissolution when metal ions, e.g. Cu 2+ and Sc 3+, were added to the solution. All dissolution experiments so far discussed have been performed on pure, natural calcite crystals (Iceland spar), either as single crystals or broken down to particle sizes in the order of 300 /tm. One could well ask the question whether impurities present in these specimens might act as inhibitors too. The latter is of considerable interest, because it would explain the drastically reduced rates observed on these samples in pure CO2-H20 solutions, compared to those predicted by eq. 1. Dissolution experiments on natural limestone samples that have been carried out by Rauch and White

]3 1

(1977) in C O 2 - H 2 0 systems (Pco2:1 arm, T: 23 °C ) seem to indicate that a chemical regime of strong inhibition is present for C > 0.6C~, apparently even valid for very pure limestone. Dissolution experiments on synthetic calcites and biogenic calcium carbonates have also been performed in seawater at saturation states in the range o f ~ = 0.5-0.9 (g2= IAP/Kc, where IAP=aca2+aco]- and Kc is the equilibrium constant) by Keir (1980), as well as by Walter and Morse (1985). These authors observed a rate dependence of the form (Ohara and Reid, 1973):

(4) with values for n varying from 2.7 to 4.3. For synthetic calcites in artificial seawater Keir found n = 4 , whereas Walter and Morse observed a value n = 3 in Gulf Stream seawater. This is undoubtedly a strong hint to the fact that components of seawater likely interact with the calcite surface, :inducing inhibited dissolution. This is further corroborated by the observation of Morse and Berner ( 1979 ), who found that the empirical reaction order n critically depends on the concentration of phosphate in the solution. Increasing PO43- concentrations from 0.1 to 10/~M, led to variations of n in the range from 3 to 17. In view of these difficulties it seems to be inappropriate to apply the PWP equation in modeling geochemical systems, where inhibiting ions might be present in the aqueous solution a n d / o r where natural minerals such as calcites or calcareous marine sediments are involved in dissolution processes. Accordingly, we have performed experiments studying the dissolution of pure synthetic NBS Calcite (SRM 915) and also natural materials such as limestones, marbles and marine pelagic sediments under identical experimental conditions. As will be discussed later (p. 134) our results demonstrate that by use of eq. 1, the PWP model is applicable in predicting sufficiently accurate rates for NBS Calcite, even close to equilibrium. In contrast, however, the

132

U. SVENSSON A N D W. D R E Y B R O D T

system evolved towards equilibrium with respect to calcite. Fig. 1 schematically shows the experimental set-up. The experimental design allowed the simultaneous investigation of four samples during one experimental course. Three natural samples and one sample of standard calcite powder (NBS Calcite) were measured each time whereby NBS Calcite was used for reference. In addition, we have performed experiments on highly purified deionized water (MILLI-Q Organex ® system: resistivity >~1 MI2) and found that equilibrium with respect to CO2, was achieved within 30 min. Since the average time duration for dissolution experiments amounted to > 100 hr, equilibrium of the solution with respect to CO2 was always warranted. The ratio of the volume of the solution to the geometric surface of the solid exceeded 0.1 cm

PWP model fails in accurately predicting rates for natural materials in the very near-equilibrium region, i.e. C >/ 0.95Cs, where dissolution rates drop down significantly by at least one order of magnitude compared to those displayed by NBS Calcite.

2. Experimental 2.1. Methods

All runs have been carried out as batch experiments using the free-drift technique, where size fractioned particles of natural material and NBS Calcite were kept in suspension by turbulently stirring them in solutions of fixed Pco2 (open system). We measured the time dependence of [Ca 2+ ] by monitoring the specific conductance of the solution, while the

&']

19

18

l

,°0

17

7

6

5

~\

3

2

4

4

2

3

8

\ '\

9

\ I

10

1?

\, ]G

14

11

//

~5

/ 13

Fig. 1. Experimental set-up [ / = T e f l o n ® vessels ( 4 X ) ; 2=Teflon ® stirrer ( 4 X ) ; 3=conductivity electrode ( 4 X ) ; 4=capillary for extraction of solution ( 4 × ) ; 5 - o u t e r vacuum-tight vessel to establish defined Pco2; 6-8, 1721=components of thermostating; 10, 14, 15, 22, 23=system for evacuating outer vessel (5); 16, 24, 25=system for filling outer vessel with defined Pco2; lO-13=system to record conductivity].

DISSOLUTION KINETICS OF NATURAL CALCITE MINERALS IN CO2-WATER SYSTEMS

in all experiments. This ensures that the dissolution rates are limited by the surface reactions ( I )- ( III ) and not by slow CO2 hydration (Buhmann and Dreybrodt, 1985 ). Solution volumes of 150 ml each were contained in 4 Teflon ® vessels (Fig. 1, 1), equipped with Teflon ® stirrers (2) and conductivity electrodes (3) (Radiometer ® PP1042) suitable for solutions with low conductivities of about several hundred #S cm - 1. To achieve equilibrium of the solution with respect to a given CO2 pressure (5-10 - 3 arm have been employed in most of the runs), the Teflon ® vessels were m o u n t e d into a thermostated, large evacuable stainless-steel container (5), which could be flushed with commercial N2-CO2 mixtures. Approximately 1800 mg per vessel of natural calcite particles (the 100-#m fraction was preferred in most of our experiments) and 500 mg of NBS Calcite were used for an average run. After filling the 4 Teflon ® beakers with deionized water, sample materials were added and the container was evacuated within 1 min down to at least 20 mbar. In a next step, the generated vacuum was leveled out by the N2CO2 gas mixture to normal atmospheric pressure and finally the stirrers were switched on. The temperature of the experimental system was accurately controlled, warranting a temperature stability within an accuracy of +_0.02 °C. Conductivity of each sample solution was recorded in suitable time intervals (between 1 min initially and 10 min close to equilibrium) and stored on a harddisk. To take the gauge of the measured conductivity of the actual calcium concentrations [Ca2+], aliquots of 4 ml were extracted periodically during the runs by use of capillaries (4) and analyzed for Ca and Mg by inductively coupled plasma mass spectrometry (ICP). Additionally, at the end of each experiment the pH was measured, and the concentrations Ca 2+ , Mg 2+ and HCO 3 were determined by applying standard titration methods. All samples were filtered across 0.45-/~m filters.

133

2.2. Materials A total of 16 marble and 19 limestone samples (low Mg-calcites) from separate locations with molar M g / C a ratios between 0.002 and 0.06 were broken down and sized by wet-sieving with deionized water to fractions of 100 #m, respectively, while NBS Calcite was used as delivered. As determined by visual inspection by use of a microscope the average size of the crystals was 10 #m. Samples were treated with diluted HC1 (0.01 M) for ~ 10 s, again rinsed with deionized water and finally with acetone. Then they were dried and stored for further use. NBS Calcite was only washed with deionized water and dried without further treatment. The starting material for each run was always new unreacted material. In addition, we examined samples of a calcareous deep-sea m u d (foraminiferal ooze) primarily consisting of assemblages of foraminiferal shells and tiny fragments of bivalves. The material was treated analogously by wetsieving with deionized water to a mean particle fraction of 80/zm, then dried and stored at room temperature for further use. 3. Results

Fig. 2 typically shows the time evolution of the Ca :+ concentrations during a dissolution run (Pco2: 5- 10 - 3 atm; T: 20°C). The uppermost line displays NBS Calcite quickly achieving equilibrium exponentially in contrast to the natural calcites (lower curves), which exhibit a drastically slower approach ( M = m a r b l e , L = l i m e s t o n e ) . Fig. 3 gives the dissolution rates calculated by numerical differentiation from three successive data points by use of a central difference formula (Plummer and Wigley, 1976). Since the determination of the surface areas by geometrical calculation yields large errors of about a factor of 2, we have scaled the rates to those predicted by eq. 1 for a given Pco2 and temperature at the C a 2+ c o n c e n t r a t i o n of 0.2Cs, i.e. 20% of the saturation

134

U. SVENSSON A N D W. D R E Y B R O D T

:SE 0 0 5

o

12E 005

i

c: 9 0E 004 '!1~ =D .% t~ ] E

()04

RUN # 2 ~ 2C',°C P ,~, ~ 1 0 3arm Ca "ec 1 4 . 1 0 mnqol~cm NBS 1 0 p r o M # 1 , M~,~4, L ~ 2 0 : 1 0 0 p m ,

1> , F rln4

I I i

/ ~(;

~'~

60

(~)

80

I O0

120

Fig. 2. Time evolution of Ca 2+ concentration for NBS Calcite ( u p p e r m o s t curve) a n d three natural samples (lower curves). Particle size of NBS Calcite is ~ 10 gm, that of natural samples is ~ 100 gm.

2.0E -007 l

? 1 6E -007

RUN # 2 3 2 0 2+ ° O'P c o 2 : 5 * 1 0- 3- ~ a t m -3 Ca e q : l 4 . 1 0 mmol*cm

J \

0 1 2E 007 ~

\ " ~

-~ 8.0E-008 .l .'D 40E 008 3 0 u3 oo O.OE+O00 ~3 O.OE+O0~O5.0E-004

10E-O05

Ca~+ c o n c e n t r a t T o n

1.5E-003

2.0E-~03

(mmol*cm

)

Fig. 3. Dissolution rates as a f~'nction of Ca 2+ concentrations for Pco,.: 5"10 -3 atm ( o p e n system) at 20°C and [ Ca 2+ ] ~q= 1.4 m m o l c m - 3; solid line = rate calculated by the P W P equation ( 1 ); open squares=experimental data on synthetic NBS Calcite; solid circles= experimental data on Marble No. 4, containing 1.3 mole% Mg. Note that experimental data are scaled to eq. 1 at C=0.2Cs!

concentration. This is reasonable since it is known that far from equilibrium ( P l u m m e r et al., 1979; B u h m a n n and Dreybrodt, 1985; Busenberg and Plummer, 1986; Dreybrodt, 1988) the PWP model works sufficiently accurate, even for natural limestone (Rauch and White, 1977). In our runs the surface area of the sized material was calculated by assuming each particle to be a r h o m b o h e d r o n of width equal to the mean size. By this assumption we

obtained rates at 0.2Cs, comparable to those predicted within + 50%. As a further method for surface estimation we have carried out runs on marble plates exposing a defined area of 36 cm 2 to the turbulently stirred solution ( B u h m a n n and Dreybrodt, 1985 ). The evaluation of these experiments yielded rates at C=0.2Cs, lower by a factor of 2, in comparison with those predicted. An additional reason for the inaccuracy of the observed rates of the natural samples may be caused by material strain in which surface dislocations are created. Schott et al. (1989) have observed rate enhancements of ~ 2-3 times for dislocation densities varying from 106 to 109 cm -2. The PWP rates (eq. 1 ) were calculated by use of a computer program (Dreybrodt, 1988 ), which uses Pco2, [Ca 2+ ] and temperature as input parameters to compute the activities of H +, H C O ; , CO 2- and Ca 2+ for open-system conditions. These are then used to obtain the dissolution rates from eq. 1. The full line in Fig. 3 shows the rates thus calculated from eq. 1 as a function of the Ca 2+ concentration in the solution. The straight upper line with data points (open squares) represents the rates measured on NBS Calcite and exhibits a linear dissolution behaviour, quite close to the theoretical rates. The lower curve (full circles) shows the rates measured on Marble No. 4 (M4). Close to equilibrium a drastic reduction of rates in comparison to NBS Calcite and the predicted rates by eq. 1 becomes quite evident. This behaviour was observed at all natural calcite samples investigated. The difference between synthetic NBS Calcite and natural samples becomes even more obvious by plotting logarithmically the rates vs. ( 1 - C / C ~ ) , as illustrated in Fig. 4, where squares represent the data points of NBS Calcite. The slope of this line is n~ = 1. Natural specimens show slopes of nl ~ 2 far from equilibrium with a switch to a steeper slope n2 ~ 4 at concentrations C > 0.7Cs, a behaviour also observed by other authors and formulated by eqs. 3. The values of n~ and n2 for various sam-

DISSOLUTION KINETICS OF NATURAL CALCITE MINERALS IN CO2-WATER SYSTEMS

* £

~ ~

~

!'3 °C P'-o : 5 . 1 0 aatrn ,,o e q : , ~ - , ! 0 mnqo!*cm

NBS slope n = l . 0

*.

0c:

u~u" -90

~.~u ~J~°

/ , /

-~-

1

nL20 ~ / ~'~ ~ ~

n

-t

n;~_~i~ ~ ,m

n==4.2

tn 100t ...... ,','' . . . . . . . . . . . . .

:6

C~-110 o 20

s'99

-1.6

-1.2

e~ ,

=2. 4

....... i ....

-0.8

-0.4

,,, 0.0

log(1 -C/Cs) o'97o'95 o'90 0% &o-So c/cs

Fig. 4. Logarithm of dissolution rates calculated from Fig. 2 vs. log( 1 - C/C~). NBS Calcite exhibits a linear behaviour with slope n = 1.0. The limestone (L 20) and the marble ( M 4) exhibit a change in reaction order as given at the curves by n~ and n2. The lowerabscissa displays C/

pies investigated are listed in Table 1. To elucidate the reasons for the different solution behaviour of synthetic calcite and natural materials, one could guess that inhibition on dissolution of natural materials might originate from surface impurities which have been incorporated during their genesis. Therefore, we investigated the dissolution behaviour of synthetic calcite in a CO2-H20 solution containing 10 # M PO43- added a s K-H2PO 4 as an inhibitor (Morse and Berner, 1979). This is shown in Fig. 5. The upper straight line (open squares) gives the rates for NBS Calcite, whereas the lower curve (solid circles) illustrates inhibition of dissolution in the presence of orthophosphate. Qualitatively, this curve is very similar to those of the natural samples as depicted in Fig. 3, although inhibition is much stronger close to equilibrium. During a repetition of this experiment on natural specimens (Limestone No. 20) the observed reduction of rates upon the addition of 10 # M PO 34- was only small, as illustrated in Fig. 6. This behaviour might be explained by assuming that phosphate is chemisorbed to surface sites on the crystal surface of synthetic cal-

135

cite. When dissolution proceeds the crystal surface is exposed to C a 2+ ions in solution. Some of these Ca 2+ ions may adsorb onto a crystal surface site that is closely associated with one of the phosphate-poisoned sites. This adsorption of a Ca 2+ ion onto the surface is due to interaction between the adsorbed phosphate ion and the adsorbing Ca 2÷ ion. The adsorption of Ca 2÷ onto surface sites effectively reduces the number of sites from which dissolution may occur. Thus the dissolution rate is governed by the adsorption isotherm of Ca 2+ ions to sites that were previously active dissolution sites. If this model is valid, then we expect a rate law of the form: REMP = (1 - O)Rpwv

(5)

where O is the fraction of sites having adsorbed Ca 2+ ions and are consequently unavailable for further dissolution. The rate, given by eq. 1 is multiplied by the portion of sites, ( 1 - O ) , still active to dissolution (Zhang and Nanchollas, 1990 ). As the numbers of surface sites that are poisoned by PO43- ions increases, the Ca 2+ ions might adsorb more effectively and dissolution rates would be further reduced. To explain the small inhibiting effect of PO43- on the rate of dissolution of natural limestone samples, we assume that most surface sites are already poisoned by unknown inhibitors. These unknown inhitors are similar to phosphate, i.e. attracting Ca z+ ions to nearby surface sites and thus decreasing the dissolution rate. This results in a similar rate law. The presence of these unknown inhibitors on the surface of natural samples is inferred as occuring during formation. Since most surface sites are already occupied by an inhibitor, an only limited adsorption of PO34- occurs and as a consequence no further significant inhibition of the dissolution rate is observed when natural calcites are exposed to PO 34- -containing solution. Applying this model we now develop a tool to analyze the experimental data. The iso-

136

U. SVENSSONAND W. DREYBRODT

TABLE 1 Values of n l and n2 determined to the empirical rate equation REMp = O~1( 1 -- C~ Cs )" and parameters A and B for fitted isotherm Sample No.

Rate constant, ce~ ( 10 -v mmol cm -2 s-~ )

Slope n~

Slope n2

x

A

B

fl

2.1 1.7 1.7 1.9 2.1 2.0 1.7 1.4 2.0 1.9 2.2 1.6 2.0

9 3.0 4,9 3.8 3,1 3.1 4.1 2.6 ? 2.8 9 2.7 3.3

9 0.78 0.89 0.75 0.80 0.82 0.81 0.77 9 0.71 9 0.80 0.64

5.82 5.65 5.23 5.59 5.74 5.60 5.34 5.56 5.76 5.76 5.73 5.56 5.76

2.52 2.44 3.07 2.77 2.73 2.94 3.13 2.61 2.71 2.88 2.77 2.97 2.86

0.77 0.65 0.62 0.73 0.78 0.79 0.73 0.68 0.80 0.82 0.80 0.80 0.81

! .7 1.7 2.0 1.7 2.3 1.7 1.9 2.0 1.8 2.2 1.7 2.0 1.6 2.5 1.5 2.3

3.8 2.8 3.1 2.8 3.9 3.0 2.8 2.8 3.9 3.3 2.5 2.8 2.6 4,1 3.0 3.9

0.78 0.80 0.72 0.75 0.70 0.75 0.72 0,73 0.71 0.70 0.65 0.66 0.63 0.60 0.68 0.65

5.58 5.61 5.50 5.48 5.54 5.55 5.56 5.75 5.70 5.85 5.82 5.78 5.54 5.73 5.57 5.72

2.88 2.81 3.29 3.01 3.36 3.01 3.06 2.89 2.61 2.70 2.72 2.74 3.02 3.14 2.96 3,05

0.77 0.77 0.85 0.80 0.85 0.81 0.81 0.84 0,74 0.80 0.80 0.80 0.80 0.84 0.78 0.82

1.7 1.7 1.2

4.2 3.0 3.6

0.86 0.84 0.86

5.43 5.53 5.25

2.71 2.71 2.91

0.62 0.62 0.60

2.0 2.1

11.1 16.7

0.74 0.73

5.4I 5.39

3.12 3.22

0.68 0.70

Limestone specimens: L1-092 I_1-113 1,1-162 L1-343 L2-103 L2-114 L5-172 L6-084 L6-094 L6-104 L6-124 L9-322 L20-302

2.0 1.3 2.0 1.6 1.8 1.8 1.8 1.6 2.1 2.1 2.2 1.6 1.8

Marble specimens: M 1,072 M 1-202 M 1,212 M1-222 M 1-232 M4-073 M4-203 M4-213 M4-223 M4-233 M5-204 M5-214 M5-224 M5-234 M6-074 M16-303

1.6 1.9 2,0 1.9 1.8 1.8 1.6 1.6 1.5 1.6 1.3 2.0 1.8 2.0 1.6 2.0

Calcareous deep,sea sediment: F1-1203 F2-1203 F3-1209

1.4 1,4 1,0

Synthetic Mg-calcites: SMGCI SMGC2

1.8 2.0

? = determination not possible.

DISSOLUTION

KINETICS OF NATURAL

CALCITE MINERALS

IN CO~-WATER

10-

~2.0E-007

1.6E-007

RUN #34 3 20.~C;Pco2:5.1 Q- arm . Ca eq:1.4.10 mmol cm

••,.~ ,',, ,, ,,u 0.8

(J

c -5 20 2+o C'Pco-,o*IO atm ' -~

Co

eq:l.~*lO

.

m m o l * c m -a

'~p".~ u

I

tz ~0.6 02

"'el

1.2E-007

"*~~',&

E

•

oj

[~0.4

-~ 8.0E-008 L

*-

%

0.2

L~ 4 . 0 E - 0 0 8

NBS with ~ 1 KH2P04

o {n

t~

0.0

O.OE+O00 5.0E-004 2+

Co

1.0E-005 -

concentration

1.SE-O03

2.0.E3-~003

L'~" 2.0E-007

'.~ (J

V,

g

4.0E-008

O o3

O.OE+O00

,111

fl[llll~llllll

5.0E-004

i flltlllllll[lllltll

1.0E-003

Ca 2÷ c o n c e n t r a t i o n

1.5E-003

2.0E-003

( m m o l * c m -3)

Fig.

7. Experimentally observed isotherms (1 -O)=REMr,-Rp-wlp in comparison with the fitted Fowler-Frumkin isotherms (dotted lines): (a) NBS Calcite: A= 5.9, B=0; (b) NBS Calcite in solution containing l0 #M KH2PO4 (cf. Fig. 3 ): A = 5.9, B = 3.4; and (c) marble

strongly indicate one common mechanism of inhibition, which might be described by some type of theoretical isotherm. For synthetic NBS Calcite the linear behaviour of ( 1 - O ) suggests a Langmuir isotherm (Ponec et al., 1974) given as:

1.2E-007 .

o 8.0E-008 L,

-

C a 2 + e q : 1 . 4 * 1 0 - ~ m m o l * c m -~

O

E

u

(M 4):A=5.8, B=2.7

#34 20 *C;Pco~:5*I0- atm RUN

1.6E-007 •

o"

',"

0.0E+000

(mmol*cm-)

Fig. 5. Dissolution rates of pure NBS Calcite (open squares) compared to the rates when dissolution of NBS proceeds with 10 #M KH2PO4 (solid circles).

..fo b '~M."~

NBS without

~ddition

addition O.OE4-O00

~

137

SYSTEMS

'::,?,.

L•20 with ~ ' , KH2P04 ~-addition , ~

L#20

without

addition

,,,,,,,,,t,,,,,,,,,i,~,,,,,',l'''''''''

O.OE+O00 5.0E--004 1.OE-O03 1.5E-003 2.0E-003 2+ " --3 CG concentrotlon (mmol*cm

Fig. 6. Dissolution rates of limestone (L #20) in a 10 #M KI-IePO4 solution compared to the rates in the absence of phosphate. Only little inhibition is observed.

therm which describes O as a function of [Ca 2÷ ] in the solution can be obtained from the experimental data by plotting the observed rate REMP divided by the theoretically predicted rate Rewe vs. Ca 2+ concentration by eq. 5. As a result we obtain a straight line for NBS Calcite (Fig. 7, a ), which includes also the data for Marble No. 4 (Fig. 7, c), and NBS Calcite exposed to a solution containing 10/J31 PO 43(Fig. 7, b). The natural sample displays a steep decrease in surface sites still remaining active to dissolution (REMpRpwp-'= 1 --O), whereby the latter is valid for all natural materials investigated. Furthermore plots of (b) and (c)

C- 1_~fexp(- k~ )

(6)

where C denotes the concentration of the adsorbing ion, Uo the adsorption enthalpy, ka the Boltzmann constant and T the temperature in kelvins, and the factor f i s related to partition sums of the system. This type of isotherm shows a linear behaviour for sufficiently low concentrations C. The isotherm ( 1 - O ) for Marble No. 4 shows a steep decrease compared to NBS Calcite. Such a decrease can be caused by increasing adsorption enthalpy Uo, due to the presence of adsorbing inhibitors, e.g., orthophosphate or heavy-metal ions (Terjesen et al., 1961 ). In this case a much steeper Langmuir isotherm would be expected, which does not exhibit a S-shaped curve. S-shaped isotherms result in the case when the adsorption enthalpy increases by Uo' O with the degree of coverage

138

U. SVENSSON AND W. DREYBRODT

O by adsorbing ions. This can be formulated as;

U(0) =

Uo+ U~,O

(7)

This behaviour could originate from an attractive interaction of the inhibitors with the adsorbing Ca 2+ ions. In this case one obtains an isotherm, called the Fowler-Frumkin isotherm (Ponecet al., 1974; Sposito, 1990)given by: C = f ~ 0- e x p ( "

U°+u°O)kB

(8a,

Formally, this expression resembles that of a Langmuir isotherm written as:

l_o-Cfexp

=K'(O)C

[ C a 2 + ] _ 1 --REMp/Rpw p

REMp/RpwP -B

1 Rpwp/_j

(9a)

The parameters A and B are respectively given as:

exp ( - A ) = f e x p ( -

[Ca2 + ] _

(1 --REMp/Rpwp)fl 1 -- (1 --REMp/Rpwp)fl

(8b)

with a mass action constant K' dependent on O. In order to verify our findings, we have tried to fit our experimental data to an expression derived by use of eqs. 5 and 8b:

×exp(-A)exp

unacceptable since for a value of 0 = 0 it is required that C = 0. This reveals the problem that one does not know Oi at Ci. However, if we arbitrarily choose some value O~ for G, then the real value of Oi is given by Orea~=flOi. The scaling constant fl is chosen in such a way that the extrapolated value of (1-OEMPfl)=0 for C--,oc. In other words: the empirical value of O is not scaled correctly. Because of this problem, eq. 9a is not appropriate to fit the experimental data and it has to be corrected by introducing the scaling factor fl as a third fit constant to obtain the form:

U,,/kBT)

and

B= UI,/kBT Eq. 9a also represents a Langmuir isotherm in the case of B=0. To carry out the fit, however, one has to consider that in evaluating R E M p R p w P -1 from the experimental data, we have scaled the experimental rates to the predicted ones at some arbitrary value of C~, far from equilibrium (usually the first point where the rates could be measured, i.e. Ci ~ 3"10 -4 mol 1-1). This yields a value of 1 - O i = l at C # 0 , which is

Xexp(-A)exp -B

1 RpwpJ J

The factor fl has no physical meaning and depends only on the value given to O~ at C~. The fits have been performed, applying a FORTRAN IV version of the CERN library called MINUITL (James, 1972). It contains three different minimizing subroutines SEEK, SIMPLX and MIGRADfor the search of a local minimum of the corresponding Zz function. The dashed lines in Fig. 7 represent the fits through the experimental data. NBS Calcite clearly exhibits a Langmuir isotherm with A = 5.8, whereas Marble No. 4 follows a Fowler-Frumkin isotherm with A = 5.8 and B=2.7, indicating quite clearly that the presence of adsorbed inhibitor interacts with the adsorbing Ca 2+, thus increasing the adsorption enthalpy. Fig. 7 also shows the isotherm for NBS Calcite dissolved in a solution of 10 /tM PO43- as obtained from the data of Fig. 5. The adsorption isotherm for the phosphate exposed NBS Calcite exhibits values of A = 5 . 9 and B = 3.4. It should be mentioned here that increasing B lowers the value of [Ca 2+ ] where the system attains an apparent equilibrium, i.e. the concentration where the isotherm approaches the value of zero. For Marble No. 4

DISSOLUTION KINETICS OF N A T U R A L CALCITE MINERALS IN CO,-WATER SYSTEMS

this is the case at C ~ 1.3- 1 0 - 3 mol 1-i, while the corresponding value for the PO 3- exposed NBS Calcite is at C ~ 9.10 - 4 mol 1-l. We have fitted the experimental data of all samples investigated and always found a Fowler-Frumkin isotherm with similar values of A and B and the same quality of the fits as depicted from Fig. 7. Table 1 summarizes these results. Our data on the dissolution of two calcareous deep-sea sediments ( > 99% pure CaCO3 ) may be particularly interesting. Fig. 8 shows the corresponding dissolution isotherms. The fit through the experimental data is given by the dashed line. The values of A = 5.6 and B = 2.8 are close to those obtained for the limestones and marbles, indicating that incorporation of inhibitors might take place during early diagenesis. Further experiments conducted on marine sediments are necessary to confirm this assumption. For an additional test to verify our adsorption model we have performed the following experimental sequence: a limestone, marble and NBS Calcite were reacted to their apparent equilibria and their [ C a 2 + ] ( t ) courses were recorded. Then the sample solutions were diluted by a factor of 3, resulting in a correspondingly lower Ca 2+ concentration and 1o

]

j RUN # 3 8 '',7, 2 0 2+ °C'Pco' ~ : 5 . 1-03- a a t m -3 "..',. Ca e q : 1 . 4 , 1 0 mmol*cm o'-..'-~

0.8.

6...,.

7 Q_

"bC, ".,,\

METEOR CRUISE 1 2 / 1

%,,,\

~0.6 05_ [3~ 0-4

°%~'~~ 12o9/1 0.2

12o3/£~

0.0 O.OE + 0 0 0

5.0E-004

1.0E-003

1.5E-003

2.0E-003

Ca 2÷ concentration (mmol*cm -~) Fig. 8. Experimentally observed isotherms in comparison with the fitted isotherms for two different marine pelagic sediments:1209/l: A=5.3, B=2.7; and 1203/2: A=5.5, B=2.9

139

again for all three samples the rates were measured. It turned out that the approach to equilibrium was reproducible compared to the first data set and the rates in their dependence on [Ca 2÷ ] were correspondingly identical for both runs. This shows that both adsorption and desorption reactions occur simultaneously and that the adsorption process is reversible. In summary, we can state that the dissolution rates on natural calcite minerals can be described by the PWP model modified by an adsorption isotherm, assuming that Ca 2+ ions are adsorbed at solutionally active sites on the surface and subsequently prevent further dissolution at this site. In case of NBS Calcite the isotherm is a Langmuir isotherm. It should be pointed out that Langmuir isotherms also have similarly been observed by Busenberg and Plummer (1986) for pure calcite at saturation states of 12=0.0-0.6. For natural samples the isotherm is changed by adsorbed impurities, e.g. phosphate or heavy-metal ions, yielding a linear increase in adsorption enthalpy of Ca 2+ with coverage O, but leaving the initial adsorption energy at O= 0 unchanged with respect to the pure crystal.

4. Comparison with previous work The first experiments concerning the inhibiting effect of Cu 2+ and Sc 3+ ions on calcite dissolution were, to our knowledge, reported by Erga and Terjesen (1956) and Terjesen et al. ( 1961 ). These authors measured the time course of [Ca 2+ ] in batch experiments similar to ours. They employed nat',aral calcites of high purity in pure CO2-H20 solutions (Pco2:1 atm; T: 25°C), where Cu 2+ or Sc 3+ were added in concentrations from 10 - 6 t o 1 0 - 3 mol 1-1. The obtained results are very similar to ours. For solutions without inhibiting ions the dissolution rates varied linearly with concentration and equilibrium was reached. With increasing amount of inhibitors the rates decreased approaching zero at concentrations far below the true equilibrium at an apparent

140

U. SVENSSON

equilibrium concentration Capp, which decreased with increasing concentration of the metal ions. We have analyzed the data of Terjesen et al. (1961 ) in the way described in the previous section. The results are shown in Fig. 9. Here we have plotted the ratio REMpRpw P -1 for Cu 2+ concentrations of l0 -3, l0 -4 and 10 -5 mol l-1. The dashed lines represent the fits by eq. 9b, TERJESEN et a1.(1961) 0.8

" ",k"~. ~" ", ", ,

"~ 0=~0.6 ~[3::5

~

25°C;Pc0:1.0 Legend:

0.4

atrn

i ~ . i ~ -Ua m o l , ~UU 2 +/.I, -4 2+

,,,, ',

2-.10

'', 1, ; ', '', "',', "' ",

3 ~ 1 0 -5 reel 4 ~ 1 0 -5 r n o I

mol Cu /I Cu 2+ / So 3+ / I

-

02

*',

o o [,

,

",

".

k- 4", J. " t ""

"~'

3 ".. • "'-"

r,,,,,,, ,,,,,,,,,ijljT,,,,,i, O.OE+O00 2 . 0 E - 0 0 3 4.0E-003

Ca 2+ c o n c e n t r o t i o n

"-.o ""

""

2"'~""

W. DREYBRODT

with values of A = 4 . 8 , 4.9 and 4.6. They are only slightly dependent on the concentrations of the inhibiting ions. However, the values of B = 3.0, 2.1 and 1.8 increase with increasing Cu 2+ concentrations, indicating that the coverage-dependent adsorption enthalpies must be due to the adsorbed Cu 2+ ions. Similarly, we obtain a fit to the inhibition curve of a Sc 3+ concentration of 10-5 tool 1-' with values of A = 4 . 7 and B = 2.6, as is also illustrated in Fig. 9. To investigate the influence of calcite dissolution kinetics on the evolution of karst landscapes Palmer (1991) analyzed the experimental data of free-drift runs performed on Iceland spar by P l u m m e r et al. ( 1978 ). All the rates could be fitted to an empirical rate law of the form:

1.0

~, I!.,,,.

AND

REMP=a~(1--C/Cs) n' for C<~xC~ °'"%

, 6.0E-003

,,j 8.0E-003

(mmol,crn

R E M I , = a 2 ( 1 - - C / C s ) n2 for

-3)

C>xC,

(3a) (3b)

It turned out that a], a 2 and x are dependent on temperature and Pco2 in equilibrium with the solution. Table 2 lists the values derived by those from Palmer ( 1991 ). We have used these

Fig. 9. Isotherms taken from the dissolution rates observed by Terjesen et al. ( 1961, figs. 2 a n d 3), c o m p a r e d to the fitted isotherms: ( 1 ) A = 4 . 8 , B = 3 . 0 ; ( 2 ) A = 4 . 9 , B - 2 . 1 : ( 3 ) . 4 = 4 . 6 , B = 1.8; a n d ( 4 ) A = 4 . 7 , B = 2 . 6

TABLE 2 Same as for Table 1, values derived by those of Palmer ( 1991 ) (data analyzed after Plummer et al., 1978) Temperature (°C)

Pco2 ( 1 0 - 2 atm)

Rate constant, a~*~ ( 1 0 - 7 m m o l c m - 2 s -1 )

Slope n~

Slope x n2 (_+0.4)

A (_+0.1)

B (_+0.1)

0.3 3 30 100

1.6 2.2 4.5 13

2.2 1.7 1.6 1.5

4.0 4.0 4.0 4.0

0.60 0.60 0.65 0.80

5.8 4.9 4.0 3.6

2.7 2.7 2.9 2.6

0.78 0.75 0.79 0.75

15

0.3 3 30 100

1.5 2.0 5.0 14

2.2 1.7 1.6 1.5

4.0 4.0 4.0 4.0

0.70 0.70 0.70 0.85

5.9 5.0 4.1 3.8

2.7 2.8 3.0 2.5

0.78 0.78 0.79 0.75

25

0.3 3 30 100

1.9 2.1 5.6 18

2.2 1.7 1.6 1.5

4.0 4.0 4.0 4.0

0.80 0.80 0.80 0.90

6.0 5.1 4.2 3.9

2.8 2.9 2.9 2.6

0.78 0.78 0.79 0.75

*These values deviate slightly from those by Palmer due to the procedure of scaling to the PWP rates by eq. 1.

DISSOLUTIONKINETICSOF NATURALCALCITEMINERALSIN CO2-WATERSYSTEMS 1.0 "~"

PALMER (1991) data

",, "~,~.

0.8

#1,2,3,5 analyzed

,,, m,~,

after PLUMMER et ol,

~,..~ (1978)

~_0.6 L't/ *o_

", 4 ~

~o.4

"~, % , ", ~", ', \ ',

'!

',,, o ',,,

ii~ 0.2

'*.ko

1~ z'~

0.0

' '~'

O.OE4-000

HERMAN (1982) #4 experimental by rotating disc

' '~

3"" .

.

u ',¶

~4 .

3.2E-003

"*'"~'"~-..5 .

6.4E-003

Co 2+ concentrcltion

9.6E-003

(mmol*cm -~)

Fig. 10. Fowler-Frumkin isotherms calculated from Palmer's ( 1991 ) analysis, by eqs. 3a and 3b with the values of cq, n~, n2 and x taken from Table 2 (data points), in comparison with the fitted isotherms (dotted lines) at T=25°C: ( I ) Pco2=3.10 -3 atm, A=6.0, B=2.8; (2) P c o : = 3 - 1 0 -2 atm, A=5.1, B=2.9; (3) Pco2=3-10 -~ atm, A =4.2, B=2.9; (5) Pco:= 1.0 atm, A = 3.9, B=2.6; (4) experimental data of Herman ( 1982 ): P c o : = 1.0 atm,

A=3.8, B=3.1.

~o ~[

-=~o "='-" o.8 ~ '"~::~::.

:y

Synthetic Mg-calcites 7.4 mole°/o Mg (circles) 10.7 mole*/o Mg (_£ubes) 20 °C;PC02:5.10 ~atm

~o.6 !

• a,'i,

°i 0.0

,,rll,

2.0E-004

,I[,~,T,

5.6E-004

,lIT

\

,illiCit

9.2E-004

Co ~+ concentration

I

1.3E-003

(mmol*cm -s)

Fig. 11. Experimental isotherms of synthetic Mg-calcites in comparison with the fitted isotherms: 7.5 mole% Mg: ,4=5.4, B=3.1, fl=0.68 (open circles); and 10.7 mole% Mg: A =5.4, B = 3.2,fl=0.70 (open squares).

empirical relations to calculate rates at given concentrations of Ca 2+ and have constructed from them the isotherm (1 O) =REMpR-1 as illustrated in Fig. 10, where the points are the calculated data. The dashed lines represent the fits to the F o w l e r - F r u m k i m isotherm. The --

PWP

| 41

numbers on the curves ( 1, 2, 3, 5 ) refer to the Pco2 in equilibrium with the solution during a free-drift run (cf. figure caption ). The full line with No. 4 furthermore represents a fit to the experimental data obtained by Herman ( 1982 ) in a free-drift run (Pco2:1 atm; T: 25°C) performed by use of rotating-disc technique on a large calcite single crystal. Table 2 also displays the fit parameters A and B obtained for this set of data. These data of the PWP freedrift experiments are comparable to each other, since they relate to the same material. There is a clear dependence of A on Pco2. From the decreasing values of A with increasing Pco2, we conclude that the coverage-independent part of the adsorption enthalpy Uo increases with increasing Pco2. In contrast, the value of B representing the part of enthalpy Uo' @ dependent on coverage, remains constant. This observation also indicates to the fact that B is mainly determined by the impurities at the surface of the mineral. The data for the single crystal of Herman (1982), included in Fig. 10, show a value ofA = 3.8, close to the value ofA = 3.9 in the comparable free-drift run of Plummer et al. (1978). The value of B = 3.1 turns out to be higher, thus causing a lower apparent equilibrium. Our experiments have been performed at P c o 2 : 5" 10 - 3 atm and T: 20°C on 16 different marble and 19 limestone samples. For the marbles we have obtained values of A=5.64+_0.12 and B = 2 . 9 5 + 0 . 2 0 . The limestone specimens showed values of A=5.6_+0.16 and B = 2 . 7 8 + 0 . 1 9 . At a/'co=: 5-10 -3 atm the value of A lies between those of the data of Plummer at Pco2:3.10- 3-3- 10- 2 atm. The statistical error is in the order of + 3%. For B we find a statistical error of ~ + 10%, which again indicates the varying properties of the mineral surface with respect to inhibiting impurities. To give further support on these findings we have carried out freedrift dissolution experiments on synthetic highMg calcites containing 7.53 and 10.68 mole% Mg. These samples were kindly delivered by

142

Dr. L.N. Plummer. Procedures of preparation and analysis are given in detail by Busenberg and Plummer ( 1989 ). With respect to the natural low-Mg calcites, we would expect changed values for B, because the high content of Mg should give rise to the formation of inhibiting impurities at the surface. Since the lattice constant of the material changes with increasing Mg content (Mackenzie et al., 1983) changes in values of A with respect to low-Mg calcites are also probable and indeed this is observed. Fig. 11 illustrates the isotherm fitted to the experimental data. The resulting values for A = 5.4 and B = 3.2 are different from the values of the natural samples (A=5.6; B = 2 . 8 ) . Especially, note the comparatively large variation in B. 5. Discussion

With the comparatively large set of data represented here, one can speculate on the mechanisms of inhibition: ( 1 ) In case of a pure synthetic calcite we have a crystal surface to which either Ca 2+ or HCO7 ions from the solution can be physisorbed, thus stopping dissolution at the sites of adsorption. These sites may be kinks which are favourable for dissolution. From our data we cannot tell, whether Ca 2+ or HCO~- or both are absorbed, since in our experiments 2 [Ca 2+ ] = [HCOs ]. The fact that we obtain a Langmuir isotherm indicates that no interaction takes place between the physisorbed particles, thus rendering B = 0. (2) If inhibitors are present these could increase the binding energy of the physisorbed Ca 2+ ions by attractive interaction, thus forming a distribution of physisorbed Ca 2+ ions around them. We can assume that the binding energies are low, such that the physisorbed ions can be assumed as mobile on the crystal surface. With increasing O there will be a higher probability of finding physisorbed ions close to the inhibitors and correspondingly the binding energy will increase. Furthermore, the total in-

U. SVENSSON AND W. DREYBRODT

crease in binding energy at 69= 1 will also depend on the number of inhibitors on the surface. This explains, why the value of B increases with increasing concentration of the inhibiting metal ions in the experiment of Terjesen et al. ( 1961 ). Similarly Berner and Morse (1974) have shown that the inhibiting effect of orthophosphate on calcite dissolution in seawater increases with increasing phosphate concentration. These are first explanations which are highly speculative. To gain more insight, further experiments are necessary: (a) To elucidate the kind of physisorbing ions, dissolution experiments have to be performed in CaCO3-CaCI2-CO2-H20 and CaCO3-NaHCO3-CO2-H20 solutions. It should be noted that all experiments were performed in dilute solutions [Ca 2+ ] ~< 1.6.10 -3 mmol cm -3. At very large concentrations of Ca 2+ or HCO~- in CaC12-H20 or K2HCO3H20 solutions Busenberg and Plummer (1986) found little effect on the dissolution rates far from equilibrium. Therefore, for the time being our model is limited to dilute solutions. Improvements are necessary to include also dissolution rates in concentrated solutions. (b) The dependence of the fit parameter B on the concentrations of inhibiting ions, e.g. Cu-7+ . Sc3+ and PO 3- , has to be investigated in detail. (c) Terjesen et al. (1961) have performed experiments on natural calcites, where the inhibiting effect was eliminated by a sample pretreatment with a solution containing 4.10 -5 mol 1-~ of the complexing agent EDTA (ethylene diamine tetraacetate). Such experiments with complexing agent might be a suitable tool to investigate the character of the inhibiting surface impurities. (d) Within the limits of error no temperature dependence of the values A and B could be detected from the data in Table 2. A change of A by +0.2, when altering Tfrom 25 ° to 5°C, would correspond to a binding energy Uo 3kT at room temperature. Contrary to this the

DISSOLUTION KINETICS OF NATURAL CALCITE MINERALS IN CO2-WATER SYSTEMS

data from Table 2 show a negative change of A. Therefore, we conclude that only a slight temperature dependence of A and B exists. This indicates low physisorption energies or low contributions to the binding energy, which are mainly entropic. To elucidate these questions very accurate measurements of temperature dependence are required. (e) To understand the influence of Pco2 on the constant A, further measurements at various Pco2 are necessary. This is a quite large program, since all experiments have to be carried out on a great variety of synthetic and natural samples.

6. Conclusions We have measured the dissolution rates of a variety of C a C O 3 specimens in aqueous CO2 solutions (synthetic NBS Calcite, marbles, limestones, calcareous deep-sea sediments) in free-drift experiments under open-system conditions with respect to CO2. The results show that the dissolution rates of all natural materials are lower than those of synthetic pure calcite with increasing deviations between the rates when thermodynamic equilibrium is approached. The experimental data are compared to the rates predicted by the mechanistic model of P l u m m e r et al. ( 1978 ). For synthetic material the experimental rates are in acceptable agreement to those predicted, whereas for natural samples the deviations are dramatic. Especially close to equilibrium, the rate of dissolution of natural specimens is beyond the limit of detection. This behaviour has raised the question, whether there might be a change of reaction mechanism close to equilibrium and has been subject of conflicting debates. The analysis of our data shows that all experimental data observed by us and a variety of data taken from the previous and current literature can be described by a combination of the PWP model with an adsorption isotherm, which describes adsorption of Ca 2+ to the mineral surface. If one assumes that all sites

143

where dissolution reactions proceed can be inactivated by physisorption of Ca 2+, the observed rates are given by: REMP = ( 1 -- O)Rpwp

(5)

The experimental data display clear evidence that 6) is given by a Fowler-Frumkin isotherm for natural calcites. This isotherm results from the interaction of Ca 2+ ions physisorbed to the mineral surface with fixed impurities, thus increasing the binding energy of Ca 2+ with increasing surface coverage. There is evidence that the binding energy at zero coverage depends only on the properties of the pure C a C O 3 - H 2 0 - C O 2 system, whereas increasing binding energy with coverage results from the impurities in natural materials. Our findings reconciles with many apparently contradictory results and explain the dissolution rates as two mechanisms acting simultaneously, which are both clear cut from aspects of physical chemistry. The new model will allow concepts for further investigations of calcite dissolution rates in more complex systems, such as dissolution of biogenic calcite in seawater, which is of utmost relevance in modeling diagenetic processes.

Acknowledgements We want to thank Dr. L.N. Plummer for kindly supplying the synthetic Mg-calcites to us and we also are indebted to Dr. A.N. Palmer for submitting to us his data prior to publication. This paper represents publication No. 43 of Special Research Project SFB 261. Financial support was kindly provided by the "Deutsche Forschungsgemeinschaft".

References Berner, R.A., 1980. Early Diagenesis: A Theoretical Approach. Princeton University Press, Princeton, N.J., 241 pp. Berner, R.A. and Morse, J.W., 1974. Dissolution kinetics of calcium carbonate in seawater, IV. Theory of calcite dissolution. Am. J. Sci., 274:108-134.

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U. SVENSSON AND W. DREYBRODT

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