Chemical Geology, 71 (1988) 283-296 Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands

283

[1]

THE SOLUBILITY OF CELESTITE AND BARITE IN ELECTROLYTE SOLUTIONS AND NATURAL WATERS AT 25 °C: A THERMODYNAMIC STUDY C H R I S T O P H E MONNIN and C O L E T T E GALINIER Laboratoire de Min~ralogie et de Cristallographie, F-31062 Toulouse Cddex (France) (Received January 21, 1988; revised and accepted June 22, 1988 )

Abstract Monnin, Chr. and Galinier, C., 1988. The solubility of celestite and barite in electrolyte solutions and natural waters at 25°C: A thermodynamic study. Chem. Geol., 71: 283-296. The solubility data of barite and celestite in NaCI, KC1, CaC12, MgC12and Na2S04 aqueous solutions at 25 ° C have been evaluated using Pitzer's ion interaction model. From the examples of BaS04 and SrS04 the limited influence of the binary interaction parameters for slightly soluble salts is demonstrated. Even when most of the mixing parameters are omitted the model still accurately predicts barite and celestite solubilities in various ionic media, except for the case of barite in seawater. The analysis of the role of these various parameters shows that the activity coefficients of trace elements in natural waters can be calculated by Pitzer's model using only a small number of parameters. In the case of barite solubility in seawater, the discrepancy between the calculated and measured values can be explained by the formation of a (Ba,Sr) S04 solid solution during the experiments performed by reaching equilibrium by precipitation {supersaturation). This phase controls the Ba content of the solution which may then be higher than pure barite solubility as calculated by the model.

1. I n t r o d u c t i o n

The study of the solubility of solid phases in the system Na-K-Ca-Mg-H-C1-SO4-HCO3CO3-CO2-H20 at 25 ° C has been completed recently by Harvie et al. (1984). Based on Pitzer's (1979) ion interaction formalism, this approach, along with other similar modelling efforts (see Pitzer, 1987; Weare, 1987, for reviews), has proven very effective in understanding the evolution of brines and mineral assemblages in various natural environments at low temperature (e.g., Brantley et al., 1984; Monnin and Schott, 1984; Felmy and Weare, 1986). In the light of such a success, the challenge is now to extend this model to high tem0009-2541/88/$03.50

peratures (MoUer, 1987; Pabalan and Pitzer, 1987) and pressures, and to include minor and trace elements. Among the latter, Ba and Sr are of great importance. Their content in natural waters is likely to be controlled by the limited solubility of their sulfates: barite and celestite, which can form solid solutions, the study of which is under progress in our laboratory (Galinier, 1988). During this work we have found the need to accurately calculate the solubility of the pure end-members BaSO4 and SrSO4 in various aqueous electrolyte solutions. This, of course, requires the calculation of the activity coefficients of BaS04 (aq) and SrS04 (aq)Previous workers have shown that Pitzer's interaction parameters for CaS04 (aq) (Harvie et

© 1988 Elsevier Science Publishers B.V.

284 al., 1984) can be used as an approximation for the interaction parameters for the chemically similar species BaS04 (,q) or SrS04 (~q) (Rogers, 1981; Langmuir and Melchior, 1985; Reardon and Amstrong, 1987), although in an older paper, Whitfield (1975) has found that it does not account well for the barium sulfate interactions. In this paper we investigate the influence of the various adjustable parameters contained in Pitzer's equation for the activity coefficient by an analysis of literature solubility data of BaS04 (~) and SrSO4 (s) in aqueous electrolyte solutions, and the bearing this has for the other trace elements. 2. T h e m o d e l The activity coefficient of MSO4 (aq) (with M = Ba or Sr) in an aqueous solution of NC1, (with N = N a , K, Ca or Mg) is given by the following expression (Pitzer, 1979): In ~'MSO4: 4f ~'+ mso, (BMso4 + ZCMso4 )

(2) with A , = 0.392 at 25 ° C (Ananthaswamy and Atkinson, 1984 ) and b = 1.2 at all temperatures. I=Zmlz~/2 is the ionic strength of the solution. The quantity Z is:

Z= ~ mcZc=2mM +ZNmN c

in which ZN is the charge of the cation N. The second virial coefficient BMX is a function of the ionic strength:

BMx _oo(o) (1) g(O/x ~ ) -- ~/J MX + flMX

(3) and its first derivative with respect to I is:

B'MX = ( OBMx/OI)T.p=

fl(1) ., ~t-¢l ,.~, Xf~) l l T fl(MZ)xg,( ol2~/~) / i MX~I

+ mcl (BMcI + Z C M c I -~- Oclso 4 )

(4)

+ mM (BMso4 "[- Z C M s o 4 )

with

-]- DIN (BNso4 -~-Z e N s o 4 -~- 0MN )

g(x) =2x-211 - ( l + x ) e x p ( - x ) ]

+ rrtMmc1 (4B ~¢IC1"4- 2CMc1 ) + mMmso, [4B'MSO4

and

+ ½(4CMso4 + ~MSO4CI)]

g' ( x ) = - 2 x - 2 1 1 - ( l + x + ½x2)exp(-x)]

+mN mcl (4B ~c1 + 2CNcl)

a(1) R(2)(and CMx paramf MX~ ]JMX~ l t-MX o are adjustable ) eters specific to each solute. Ozjand ~0h are parameters related to the excess free energy on mixing two ions of the same sign. The ~ok's are constant.

+ mN mso, [4B ~so~

d- ½(4CNso4 + ~¢NSO4C1"[- UffMNSO4) ] +rrtMmN( ½ ~bCMNS04-[-40~N)

0~= so~ + EO~(I) +mclmso, (½ g]MC,SO4+40~1so4) (1) and The m's are the molalities of the ions. f ~ is the Debye-Hfickel function:

O~j= ( OEOij(I) /Ol)T,p

285

s0ij is an adjustable parameter. EOij(I) and are complex functions of the ionic strength and the charges of the ions i andj. They take into account the effect of asymmetrical mixing (Pitzer, 1975). In order to calculate them we have used the method proposed by Harvie (1982). In these equations, all the interaction parameters which do not involve the ion M (i.e. Ba or St) are already known from previous studies. Most of them are taken from Harvie et al. (1984). The binary parameters for BaC12 and SrC12 are from Pitzer (1979). The binary interaction parameters a(o) PMSO4, O t'MSOna(1),PMSO~a(~)and CMso4 can in principle be determined from the properties of a binary solution of MSO4 measured as a function of the MSO4 molality. For insoluble salts, such a measurement is impossible. An alternative is to consider the ternary systems with a common ion (e.g., BaSOn-Na,_,SO4-H20). From the properties (activity and osmotic coefficients, solubility data) of such a system, one can calculate the fl's and C ~', but also 0MN and ~gMNX (e.g., 0B~N~and ~N~SO4). 0N~Sr and ~NaS~Clare from Reardon and Amstrong (1987). The other parameters for the ternary systems with a common ion like S r - C a C1-H~O (i.e. (~SrCa and ~'SrC,Cl) are still unknown. They can be determined from the properties of ternary solutions with a common ion at high concentration. An illustration of their influence at high ionic strength is given by Monnin and Schott (1984). However, we will show that they are not needed for the study of the solubility of barite and celestite. The available data for BaSO4 (s) and SrSO 4 (s) solubility in aqueous solutions of various electrolytes (see Section 3) give the order of magnitude of the sulfate and Ba or Sr concentration of the solution at equilibrium with the solid. For barite solubility, mso~ and mBa are around 10 -4 mol/kg H20, while for celestite solubility, msr and mso~ are ~ 10 -~-10 -2 mol/kg H20. Then, if the interaction parameters for BaS04 (~q)and E 0,~(I) i

SrS04 (aq) are of the order of magnitude of those for other 2-2 salts (Pitzer, 1979) like CaS04 (aq) as suggested by previous studies (Rogers, 1981; Moller, 1987; Reardon and Amstrong, 1987), (0) then flMSO4 --~0.2; f4(1) t'MSO4--~2; t~(2) ~MSO4--~ -- 40. It can be checked that with such estimates anytime these parameters are multiplied by mso4, msr or rnBa in eq. 1, their contribution to the value of In YMSO4is always lower t h a n 0.01 (i.e. < 1% of the activity coefficient). In their study of the solubility of celestite, Reardon and Amstrong (1987) have already noted that the calculated solubility product of celestite does not depend on the value of the flSrSO~parameters. They have chosen to equate these parameters to those for CaSO4 (aq)- Instead, because of their limited influence, we propose to set them equal to zero. The 0MN and {gMNSO~parameters have not yet been determined. We will show that they are not required in the analysis of the available data. Eq. 1 then reduces to: i n 7MSO4 : 4f )'+ mcl (BMc1 -]- ZCMc1 ~- 0ciso4 )

-~-rrt N (BNso4

-]-ZCNso4 )

+ mM mc, (4B hc, + 2CMcl) + mN mcl (4B ~cl + 2CNcl) + mN mso4 [4B'N S O 4 H- 1 ( 4 C N s o 4 _}_~NCISO, ) ] t

-~-4mM mN 0~1N "Jr-4mc1 mso40clso~ (5) All the parameters in eq. 5 are already known from previous studies (Pitzer, 1979; Harvie et al., 1984). This equation shows that, beside the Debye-Hiickel term, the activity coefficient of g s o 4 mainly depends on the interaction of the major cation N with the minor anion SO4, and on the interaction of the major anion C1 with the minor cation M. It neglects the interaction between the minor species M and SO4. We will now test the validity of these approximations by analysing solubility data for celestite and barite in various electrolyte solutions.

286

3. R e v i e w o f celestite and barite solubility data in aqueous e l e c t r o l y t e solutions at 250C

IC

O MULLER. g60 O LUCCMES~~.D W.,'*4EY,19~2 • STRUBEL.lga7 eROWER AND RENAUL?Ig71 DA~IS AND COLLINS,1971 • CULIIEflSON lET At ,11~78 • VETTER ET AL.tTDe3 O RE*ROON AND A~Msr~oNG.I~SZ

1 0.0

O

O

A survey of the literature indicates that the solubilities of celestite and barite at 25 ° C have already been measured in aqueous solutions of NaC1, KC1, CaC12, MgC12, Na2SO4 and various complex media, sometimes by several authors (e.g., we found 8 data sets for SrSO4 in NaC1 and 4 for BaSO4 in NaC1). After adequate conversion of molarities into molalities with the use of density data (Monnin, 1988), the experimental solubilities have been reported in solubility diagrams (Figs. 1-10), where mMso4 is plotted vs. the molality of the other salt. Despite the distortion induced by the log-log plots of Figs. 1 and 6, one can see the net decrease of barite and celestite solubilities in Na2SO4 solutions due to the common-ion effect. Figs. 2-5 and 7-10 show that an increasing chloride concentration produces a net saltingin effect: the solubility of celestite and barite

%

1

-

T

I

o O

o2

o

©

0

l

I

I

J

l

1

2

3

4

5

mNaCI

Fig. 2. Celestite solubility in NaC1 solutions (solid c u r v e = calculated solubility).

15

,

I

~, BROWER AND RENAULT,1971 • DAVIS AND COLLINS,1971 Ul VETTER ET AL.,1983

i

I

E~ -

z5

K

5

I

O LUCCNES; AND WNITNEY, 1962 • LIESER, 1965 A BROWER A N D RENAULT,1971

I 0

i

0.5

1,0

1.5

m MgCI2

i L

Fig. 3. Celestite solubility in MgCI~ solutions c u r v e = calculated solubility).

(solid

"~ 0.5 E

i

i

-

A BROWER AND RENAULT, 1971 • DAVIS AND COLLINS,1971 "(~\

II /

\\0.

\

g'i'--

// x

°

E -3

I -2

1 -1 log

I 0

tuna

Fig. 1. Celestite solubility in N a 2 S Q solutions ( s o l i d c u r v e = solubility predicted with fls,so, =0; d a s h e d c u r v e = calculated solubility with fls~so~ fitted to the data).

0

l

/

0.5

1.0 mKC

1.5

I

Fig. 4. Celestite solubility in KC1 solutions c u r v e = calculated solubility ).

(solid

287 T R E N A U L T , '1 9 7 1 is I •~,• BROWER c~.,,s'oAND ........... D A V I S AND C O L L I N S , l g T T

,, C~

'

%

I

I

1

2

10

=<

d tn

"I

E

0

O ~

-~ /

* / CaSQ ,2H~O 1

•

~

15--

~e ................ . /%r| , ob ~ / SrS0._ | /

E

T

1

O TEMPLETON1960 O PUCHELT,19B7 BROWER AND m~NA~LT,IgT1 • DAVIS AND COLLtNS,t971

/

¢o E

F

¢

3

0

mci

1

2

3

4

5

mKCI

Fig. 5. Celestite solubility in CaCl2 solutions ( s o l i d c u r v e = c a l c u l a t e d Sr molality; d a s h e d c u r v e = c a l c u l a t e d sulfate molality; the two curves are the same below gypsum saturation for mcl-~ 1.5 ).

Fig.

8. Barite

solubility in

KC1 solutions

20 . . . .

7. . . .

/

i

l

•

LIESER, 1965

15 I.

•

i

=2

2

\

•

~~

I

•

(solid

c u r v e = calculated solubility).

-.

x

E

~

/

o-,

4

5 NEUMANN,1933 PUCHELT,1967 D & V I S AND COLLIN$,1971

•

lP

0-4

@••

I

I

L

I

I

I

-3

-2

-1

0

-1

log m

0

i

I

i

i

20

I

[

I

%

2.5

Fig. 9. Barite solubility in MgCle solutions ( s o l i d c u r v e = calculated solubility).

OI

0

•

0I 15

E

ZO

Na

20

x

1

m MgCI 2

Fig. 6. Barite solubility in Na2SO4 solutions ( s o l i d c u r v e = solubility predicted with flB~so, = 0; d a s h e d c u r v e = calculated solubility with fls~so, fitted to the data).

151

0.5

•

•

••

×

-/

d

m

lO

E~

O TEMPLIETON 1 9 e 0

:

• PUCMELT,19eT • STmUOEL,19e7

5

•

~vts

AND COLL NS 97

• PUCHELT,~967 •

0

I

I

1

2

[

t

L

3

4

5

mNacI

Fig. 7. Barite solubility in NaC1 solutions c u r v e = calculated solubility ).

0

0.5

1.0

1.5

D&VIS AND COLLINS 1971

2.0

2.5

mcacI7

(solid

Fig. 10. Barite solubility in CaC12 solutions ( s o l i d c u r v e = calculated solubility).

288 increases with the salt content of the solution. A similar effect occurs in the CaSO4-NaC1-H20 system (Harvie et al., 1984). Figs. 1-10 also provide a picture of the dispersion of the measurements. 3.I. Celestite The solubility equilibria in the common-ion system N a - S r - S O 4 - H 2 0 have been determined by three authors (Lucchesi and Whitney, 1962; Lieser, 1965; Brower and Renault, 1971). These data are reported in Fig. 1 in a log-log plot. Lieser's data are for 20 ° C and agree reasonably well with Lucchesi and Whitney's results at 25°C. The solubility of celestite in NaC1 solutions has recently been determined by Reardon and Amstrong ( 1987 ) who also reviewed older data which have been reported in Fig. 2 along with more recent ones. Reardon and Amstrong's data are a little bit lower t h a n the results of Vetter et al. (1983). Striibel's (1966) data have been interpolated between his values at 20 ° and 30 ° C. These data sets agree reasonably well over the whole NaC1 concentration range. For the solubility of celestite in MgC12 solutions (Fig. 3), the three data sets (Brower and Renault, 1971; Davis and Collins, 1971; Vetter et al., 1983 ) are in good agreement. For KC1 solutions (Fig. 4), the data exhibit a larger scatter. The system SrSQ-CaC12-H20 (Fig. 5) is a very special case that will be discussed in Section 4. 3.2. Barite Barite solubility in Na2SO4 solutions has been measured only by Lieser (1965) at 20 °C and is shown in Fig. 6. The very low Ba concentrations have been measured using a radioactive tracer. Lieser presented his results only in a graph from which the data have been read,

which may add some error. The data that we found for the solubility of barite in NaC1 (Fig. 7) and KC1 (Fig. 8) solutions are in rather good agreement. Again, Strfibel's ( 1967 ) data are interpolated between his values at 20 ° and 30°C. For MgC12 and CaC12 solutions (Figs. 9 and 10, respec.), there is a very large discrepancy between the two main data sources, those of Puchelt (1967) and Davis and Collins (1971).

4. Data analysis There are two ways to test our hypothesis about the activity coefficients. One can either use a chemical equilibrium model to calculate the solubilities and then compare the calculated values to the experimental data, or follow the procedure described below that we used in a previous work on sodium carbonates (Monnin and Schott, 1984). If the calculated activity coefficients at saturation are sufficiently accurate, then the ion product of the solid at equilibrium with the aqueous phase must be a thermodynamic constant. In other words, it must depend only on temperature and pressure, and not on the solution concentration. So, when plotted vs. the ionic strength of the solution, the calculated ion products must lie on a horizontal line with a constant value equal to the solubility product.

4.1. Celestite

In Fig. 11, one can see that the calculated ion products msrmso47~rso4 are constant when plotted vs. the ionic strength of the chloride solutions, which shows that our hypothesis concerning the calculation of activity coefficients holds for SrSO4 (aq). The value of the solubility product of celestite, calculated from the solubility in NaC1 solutions:

289 k

t

I

I

(a)

25

oo

i ~

0

• u

u

n

• D

[]

0

L 1

i 2

I 3

I 4

I 5

!

I

I

I

I

&

(b)

% &

~

0

•

A

.... .-x

F

I 0.5

I

1

1.0

l 1.5

L 2,0

I

I

I

I 2.5 "'1

(c)

% N

0

z5 ~ $ - - -

0

t'

•

I 0.5 l

A

I 1.0

I 1.5

I 2.0

I 2.5

I

I

I

I

(d)

5,0

%

3.0

• L

2.@ %

0

LL •

8

I ~5

•

i. tO

-~

I 13

l 2D

I 2~

3~

!

Fig. 11. Calculated celestite solubility product vs, the ionic strength of solutions of: (a) NaCl; (b) KC1; (c) MgCl~; and (d) CaCl2 (symbols as for Figs. 2-6).

290

Ksp ( S r S 0 4 ) =

(2.41 _0.21)-10 -7

or

log Ksp

(celestite)

=

--

6.618

is in good agreement with the recently established value of Reardon and Amstrong (1987) who found 10-6G32 In order to maintain full consistency between the activity coefficients at saturation and the solubility product, the Ksp calculated above is to be used with eq. 1 or eq. 5. A different method of calculating the activity coefficients may lead to a different value of the thermodynamic constants. One can see in Fig. 2 that the data for concentrations below 1 M NaC1 are consistent, but the corresponding calculated solubility products (Fig. 11a) show some scatter (this is even more obvious for the BaSO4-NaC1-H20 system; see Figs. 7 and 12a). This is due to the fact that a difference of 5.0"10 -4 mol/kg H20 between two experimental solubilities at the same NaC1 molality implies a 10% discrepancy in the value of the ion product at 3 M NaC1 while it rises to 100% at 0.01 M NaC1. We have used our value of the standard chemical potential of celestite to calculate its solubility in the various media. One can see in Figs. 2-5 that the agreement between the experimental and calculated values is generally very good. The SrSO4-CaC12-H20 system shows a peculiarity (Fig. 5). Celestite solubility increases with the CaC12 concentration up to a point where S r S Q becomes more soluble t h a n gyp_ sum which is then the phase that controls the sulfate content of the solution. In other words, the dissolution of celestite in Ca-rich solutions leads to the formation of CaSO4" 2H20 as a secondary phase. We have calculated the solubility of celestite in sodium sulfate solutions with the solubility product determined above and with the flSrSO~ parameters set equal to zero. As indicated by the plain curve in Fig. 1, the agreement with the

experimental data is only qualitatively good. Fitting the interaction parameters to the data leads to a much better agreement (dashed curve in Fig. 1 ) and to the following values: (o)

flsrso4 = - 0.43 ~(i)

SrS04 ----5 . 7 (2)

flsrso~ = - 94.2 C ~rSO4 ~- ~bCNaSrSO4~---0

(with ~NaSrgiven by Reardon and Amstrong, 1987). One can note that the definition of an SrS04 (~q) ion pair is not required to reproduce the data. The parameter fl(2) is often considered to be indicative of the tendency of a salt to form an ion pair. W h e n it is negative and larger in absolute value than 200, then it is more convenient to explicitly include an ion pair (see Weare, 1987 for a discussion). Our value for (2) flSrSO4 indicates that this salt has a stronger tendency to form an ion pair t h a n CaS04 ( f l ( 2 ) - - - 5 4 ) . It is nevertheless difficult to firmly establish such a conclusion from the sole value of the fl(2) parameters obtained from an analysis of solubility data, as shown by the discussion for BaS04 (see below). We checked that the inclusion of the above values of the fl parameters has no effect on the calculated solubility of celestite in chloride solutions. 4.2. Barite

We have calculated the solubility product of barite (Fig. 12) from its solubility in NaC1 solutions (Fig. 7). Because of the scatter in the calculated ionic products at low concentration (Fig. 12a), we have calculated the average of the points above 1 M NaC1. This leads to: K~p (BaSO4)= (9.81 --+0.88)"10 - u or

log Ksp (barite)= -- 10.008 Fig. 12 again provides a check on the activity coefficient calculations for BaSO4 (~q).Again the agreement between the experimental and cal-

291 I

i

I

!

I

(a)

2O o It

@ 10

I-

O o

o •

0

00-

A

0

o

w

1 1 I

(b)

2O o

CA

~_ 10

• Q

e

•

• &

o

}, 1

1 2

I 3

!

I

I

L

I 5

1

1

4

(c)

20 o

,ex

0 10

0

I

l

J

I

l

2

4

6

8

10

f

1

I

T

I

(d)

2O o O0

0

QQ

•

10

A A

0

I

L

~,

t

i

2

4

6

8

10

I

Fig. 12. Calculated barite solubility product vs. the ionic strength of the solutions of: (a) NaC1; (b) KCl; (c) MgCI~; and (d) CaCL, (symbolsare the same as in the corresponding solubility diagrams, Figs. 7-10).

292

culated solubilities in sodium or potassium chloride solutions (Figs. 7 and 8) is very good. For the BaSO4-MgCle-H20 and BaSO4CaCI~-H20 systems (Figs. 9 and 10), the two main data sources (Puchelt, 1967; Davis and Collins, 1971 ) show very large discrepancies, as already noted above. If we calculate the solubility of barite in such systems with the solubility product that we have determined, the results almost perfectly fit Davis and Collins' data for MgC12 (Fig. 9), but the fit is poor for CaC12 (Fig. 10). These latter data suggest gypsum formation as postulated by Davis and Collins and as found for the SrSO4-CaC12-H20 system. But because barite solubility is an order of magnitude lower t h a n that of celestite, the sulfate content of the solution is never high enough to allow gypsum to precipitate. Puchelt's (1967) data lie above the calculated curves in both cases (Figs. 9 and 10). T h e y also fail either to give a constant ionic product (Fig. 12c ), or to lead to the same value as determined above in the case when it is constant (Fig. 12d). Further experimental data are needed to elucidate the solubility of barite in CaC12 solutions. The solubility of barite in Na2SO4 solutions is reported in Fig. 6. The plain curve is calculated without the flBaSO4 parameters. The agreement may be considered fair in the low concentration range, but is bad at high sulfate content. Adjusting the fl's leads to a much better agreement (dashed curve) and to: fiB(0) ~so~ = - - 1 . 0 )~(1)

BaSO4= 12.6

flg~a~O~= -- 153.4 C ~aS()4 = 0NaBa = ~/NaBaSO4 = 0

It must be noted that if the solubility product of barite is adjusted to these data (which are for 20°C), the )if(z) is reduced to ~- - 5 0 , but the new value of the solubility product is not consistent with the one determined above. Strong ion pairing (here indicated by a large and negative value of fl(2) ) stabilizes the aqueous phase,

which results in an increased solubility of the solid. In Fig. 6, the plain curve calculated for fl(2)= 0 should then lie below the experimental data, so that it is shifted to higher solubilities when a negative fl(2) is included. However, the contrary is in fact observed, which casts some doubt on the physical significancy of fl(2). The negative value of fl(2) is certainly an artefact of the least-squares fit due to the strong correlation between the flparameters. Any further discussion of this point must first await confirmation of Lieser's data which involve very low Ba contents. Meanwhile setting the flBaSO4 parameters to zero is a very satisfactory approximation. 5. P r e d i c t i o n o f c e l e s t i t e a n d b a r i t e solubilities in seawater and mixed brines - tests of the model

5.1. Celestite

Rogers (1981) and Reardon and Amstrong (1987) have already successfully used Pitzer's model to predict the solubility of celestite in seawater (measured by Culberson et al., 1978) and in NaCl-dominated mixed brines (measured by Davis and Collins, 1971). Our results are a little bit higher than Reardon and Amstrong's, but only by a few percent. Vetter et al. (1983) have also measured the solubility of celestite in complex solutions containing NaC1, CaCle and MgC12 up to high concentrations. We have calculated the saturation indices of these solutions with respect to celestite. We found an average value of 1.12 _+0.25, which is consistent with Fig. 2 in which our calculated solubilities are lower t h a n Vetter et al.'s data. We noticed that the saturation indices of the most concentrated multicomponent solutions (ionic s t r e n g t h > 7 ) t e n d to increase (up to 1.6). This can certainly be attributed to an increasing influence of the mixing parameters 0 and ~. At lower concentrations, the agreement between the model and the experimental data is quite good.

293

5.2. Barite Davis and Collins (1971) have measured the solubility of barite in the same complex chloride brines in which they have measured celestite solubility. It can be seen in their paper that the table and the figure in which they report their results are not consistent. Our calculations agree with their figure (within the uncertainty of the reading), but not with their table which is apparently misprinted. This problem has already been noted and discussed by Whitfield (1975). Barite solubility in standard natural seawater (salinity 35%c) has been measured by Puchelt (1967) and Burton et al. (1968) for a temperature of 20 ° C. Their results are in rather good agreement: 89 pg BaS04/1 for Puchelt and 82/~g BaS04/1 for Burton et al., which gives an average value of 3.7.10 -7 mol/kg H20 for the molality of Ba in seawater at equilibrium with barite. Whitfield (1975) reports an apparent barite solubility product of 10 -s°5 from a personal communication from J.D. Burton, which leads to tuba = 3.17.10-7 mol/kg H20 for a temperature of 25 ° C. We have calculated barite solubility in seawater with three different sets of flUaSO4parameters. The results are reported in Table I. First one can see the limited influence of the flBaSO4values. All the calculated solubilities are within + 10% of each other. With the fl's for BaS04 equal to those for CaSO4 and a barite solubility TABLE I Comparison of experimental barite solubility in seawater with those calculated using various BaSO4 interaction p a r a m e t e r s Calculated

Measured (Puchelt, 1967; B u r t o n et al., 1967 )

]:~t~aS( } t = 0

] • B a=S~/]CaS04 04

fl(B%O, = -- 1.0 fl~l~so, = 12.6 fl~B2~SO,= -- 153.6

2.10"10 7

2.02' 10 7

1.87.10 -7

product of 1.1" 10- lo, Rogers ( 1981 ) has calculated a Ba concentration at saturation of 2.09-10 -7 m. All these calculated results are nevertheless lower t h a n the measured value by a factor of ~ 2. Considering the usual ability of Pitzer's model to accurately predict the solubility of minerals in multicomponent electrolyte solutions, as amply demonstrated by numerous papers in the literature and shown here once again for SrSO4, we are rather confident in the model predictions. Chow and Goldberg (1960) have already calculated the solubility of barite in seawater. T h e y used a value of 0.1 for the activity coefficients of 2-2 salts in seawater. This is low when compared to our values for YBaSO4 (0.127), YSrSO4 (0.137) and 7CaSO4 (0.141), which results in a calculated barite solubility higher than ours. Church and Wolgem u t h (1972) calculated a Ba concentration in barite-saturated seawater of 3 5 + 7 /lg/kg (2.6-10 -7 mol/kg) which they accepted as close enough to the experimental value of Burton et al. The difference between their results and ours mainly comes from a difference in the solubility product of barite. Burton et al. (1968) do not indicate from what side (undersaturation or supersaturation) a steady Ba concentration has been reached during their experiments. On the contrary, Puchelt (1967) has measured barite solubility from the supersaturated side. The natural seawater as well as standard seawater, that he used, the composition of which is given for example by Whitfield (1979) contains 9-10 -5 tool Sr/kg H20. It is thus likely that the solid which has formed during this experiment is a (Ba,Sr)SO4 solid solution, the solubility of which controls the Ba content of the solution. If we define the B a / S r partition coefficient between the aqueous phase and the solid solution taken as ideal, as:

( aBa/ aSr ) aq.sol. K D - (XBa/XSr)sol.sol" Ksp

3.7-10 7

gsp

(barite)

(celestite)

--

10-33s2

294

where x is the Ba mole fraction in the solid solution, we can calculate the composition of the solid solution which can form from the aqueous solution from the following values of the parameters: mB~ =3.7" 10 -7 mol/kg H 2 0 ,

~Ba =0.151

msr = 9 " 1 0 -5 mol/kg H20,

YSr =0.175

We find that xBa -~ 0.90. This is, of course, only a tentative value in the sense that it depends on the kinetics of precipitation [in Puchelt's (1967) experiments the degree of saturation at the beginning of the run is ~ 6700 ] and also on the solid solution model that is used in the calculation. It nevertheless shows that the incorporation of 10 mole% Sr in barite can alter its solubility by a factor of almost 2, provided that we rely on our calculated pure barite solubility. We are presently undertaking experiments to measure the solubility of barite in artificial standard seawaters with and without Sr (C. Monnin and J.L. Dandurand, in prep. ). It is also apparent from the data of Dehairs et al. (1980) on suspended barite particles in the open ocean, that Ba distribution in seawater and the mechanisms of its regulation cannot be fully understood without a clear knowledge of the solubility behavior of (Ba,Sr) SO4 solid solutions.

6. Concluding remarks Pitzer's model has been parameterized for the Na-K-Ca-Mg-H-C1-SO4-OH-HCO~-CO3CO2-H20 system by Harvie et al. (1984). Anytime another ion or new species is included in this chemical system, as it is desirable to incorporate minor species in a model of wide generality, a large number of interactions parameters must then be determined from experimental data which are often unavailable. It is thus interesting to investigate the means to reduce the number of parameters in the model. In order to include trace components into a seawater model, Whitfield (1975) has proposed a "hybrid" model which combines the ion in-

teraction and the ion association approaches: where the interaction parameters for Pitzer's equations are not available the interaction between a trace element and a major component can be adequately characterized by the inclusion of an ion pair whose formation constant can be found in the extensive data base of the ion association models. It has been shown (Pitzer, 1987; Weare, 1987) that in Pitzer's formalism, the coefficient m2) ~MX is related to the constant KMXfor the formation of an M X ion pair. The trap in Whitfield's approach is that the necessary consistency between these parameters may be lost if no care is taken in their choice. Such a trap has been avoided by Whitfield who set the Sr-SO4 and the Ba-SO4 interaction parameters to zero but included ion pairs like BaSO ° (aq) and SrSO ° (aq)- Our results are in full agreement with his. His value for the conventional total activity coefficient of Ba in seawater (0.151) is the same as we have calculated, but in a simpler manner due to a smaller number of parameters. Because we have not included most of the mixing parameters 0 and ~] involving Sr or Ba, it is likely that the model fails for highly concentrated waters like the MgSO4-dominated brines produced in the latest stages of the evaporation of seawater, where the influence of parameters such as ~BaMgbecomes important. For concentrations lower than those at such extreme conditions, the accuracy with which barite and celestite solubilities can be calculated is certainly better than _+10%. Finally, it seems that the determination of Pitzer's parameters for the interaction between trace metals like Pb, Zn, Cu, Ni, etc., and the two major cations sulfate and chloride may be sufficient to allow accurate modelling of the behavior of such elements in the majority of natural waters over a large range of concentrations and compositions.

Acknowledgements A part of this work has been accomplished during two stays of one of us (C.M.) in the lab-

295 oratory of Professor John Weare at the University of California at San Diego. We would like to express our gratitude to John Weare, Jerry Greenberg and Nancy Moller for many suggest i o n s a n d for s h a r i n g t h e i r p o w e r f u l e q u i l i b rium and curve-fitting computer codes. We t h a n k J e a n - L o u i s D a n d u r a n d f o r h i s h e l p in discussing the role of solid solution formation during barite dissolution, Jacques Schott for continuous interest and support to this work, and David Crerar for his detailed review of the manuscript. All ideas and concepts contained in t h i s p a p e r a r e t h e r e s p o n s i b i l i t y o f t h e a u thors. Funding of this study has been made available through the CNRS-NSF cooperation g r a n t N o . 920123.

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