A Thermodynamic Model for the Solubility of Barite and Celestite

Ž .Chemical Geology 153 1999 187–209

A thermodynamic model for the solubility of barite and celestite

in electrolyte solutions and seawater to 2008C and to 1 kbar

Christophe Monnin )

CNRSrUniÕersite Paul Sabatier, Laboratoire de Geochimie, 38 rue des Trente-Six Ponts, 31400 Toulouse, France´ ´

Received 24 December 1997; accepted 17 September 1998

Abstract

This paper describes a model for barite and celestite solubilities in the Na–K–Ca–Mg–Ba–Sr–Cl–SO –H O system to4 2

2008C and to 1 kbar. It is based on Pitzer’s ion interaction model for the thermodynamic properties of the aqueous phase and

on values of the solubility products of the solids revised in this work. It is shown how barite and celestite solubilities in

electrolyte solutions can be accurately predicted as a function of temperature and pressure from previously determinedŽ .Pitzer’s parameters. The equilibrium constant for the BaSO aq ion pair dissociation reaction is calculated from recently4

reported barite solubility in Na SO solutions from 0 to 808C. Pressure corrections are evaluated through partial molal2 4

volume calculations and are partially validated by comparing model predictions to measured barite and celestite solubilities

in pure water to 1 kbar and in NaCl solutions to 500 bars. The model is then used to investigate the tendency of ion pairing

of Ca, Sr and Ba with sulfate in seawater. Finally, the activity coefficient of aqueous barium sulfate in seawater is calculated

for temperature, pressure and salinity values found in the ocean and compared to published values. q 1999 Elsevier Science

B.V. All rights reserved.

Keywords: Aqueous solutions; Barium sulfate; Strontium sulfate; Activity coefficients; Seawater; Thermodynamic properties

1. Introduction

The question of an eventual control of the barium

concentration in seawater by an equilibrium withŽ .solid barium sulfate barite can be addressed through

the calculation of the activity coefficient of aqueous

BaSO as well as the barite solubility product at4

oceanic conditions. This has been done by ChurchŽ .and Wolgemuth 1972 who used an aqueous solu-

tion model based on the ion pairing phenomenology

along with stability constants of aqueous species

available at that time. This water–rock interaction

)

Fax: q33-561520544; E-mail:[email protected]

problem can be reconsidered in light of the recent

development of thermodynamic models of aqueous

electrolyte solutions based on Pitzer’s ion interaction

approach, along with the wealth of data on Ba

distribution in the oceans. Pitzer’s formalism has

allowed the construction of accurate solubility mod-

els for systems including the major species of naturalŽ .waters see Weare, 1987; Pitzer, 1991, for reviews .

Ž .After the landmark paper of Harvie et al. 1984 for

the Na–K–Ca–Mg–H–Cl–SO –HCO –CO –CO –4 3 3 2

H O system at 258C and 1 bar, efforts were made at2

extending such models to elevated temperaturesŽPabalan and Pitzer, 1987; Greenberg and Moller,

. Ž1989, among others and pressures Monnin, 1989,

0009-2541r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved.Ž .PII: S0009-2541 98 00171-5

( )C. MonninrChemical Geology 153 1999 187–209188

.1990 and to other species of geochemical signifi-Ž .cance see Pitzer, 1991 . Pitzer’s ion interaction

approach is semi-empirical, as are most aqueous

solution models of practical interest. It allows the

mathematical representation of the properties of sim-Žple systems binary and ternary with a common ion

.solutions up to high concentrations through the

evaluation of empirical parameters from experimen-

tal data. From this representation the thermodynamic

properties of highly complex solutions like seawater

can be predicted. The accuracy of the calculations is

then established by extensive comparisons between

model predictions and independent experimental dataŽ .Weare, 1987 .

The present paper follows the procedure outlined

above to show that barite and celestite solubilities in

chloride solutions can be accurately predicted in

large temperature and composition ranges using

available Pitzer’s parameters describing interactions

between aqueous Na, K, Ca, Mg, Ba, Sr and chlo-

ride, and those for interactions between aqueous Na,

K, Ca, Mg and sulfate. Interactions between aqueous

barium and sulfate are accounted for by an explicit0Ž .equilibrium between the free ions and the BaSO aq4

ion pair. The enthalpy and entropy of the dissocia-

tion reaction of this aqueous complex is calculatedŽ .from the data of Jiang 1996 on barite solubility in

sodium sulfate solutions. No such data for celestite

solubility in sodium sulfate solutions is available

outside 258C. An evaluation of the ion pairing ten-

dency for alkaline earth sulfates in sulfate rich solu-

tions like seawater nevertheless allows one to esti-0Ž .mate the contribution of the SrSO aq ion pair to4

celestite solubility at temperatures other than 258C.

Pressure effects are evaluated following the methodsŽ .published by Monnin 1989, 1990 . Finally, the pre-

Ž .dicted BaSO aq activity coefficient in seawater is4

compared to values given by Church and WolgemuthŽ . Ž .1972 and by Falkner Kenisson et al. 1993 .

2. Thermodynamic properties of the Na–K–Ca–

Mg–Ba–Sr–Cl–SO –H O system to 2008C and 14 2

kbar

Due to the low solubilities of barite and celestite,

BaSO –H O and SrSO –H O binary solutions can-4 2 4 2

not be studied as a function of Ba or Sr molality.

Ž . Ž .Instead, in order to derive BaSO aq and SrSO aq4 4

thermodynamic properties, one has to use barite and

celestite solubility measurements in more complex

systems, the simplest of which are ternary common

ion systems. Barite and celestite solubility measure-

ments at 258C were compiled and critically evaluatedŽ .by Monnin and Galinier 1988 . Experimental data at

other temperatures and pressures for NaCl, KCl,

CaCl , and MgCl binary aqueous solutions and2 2

Žsome of their mixtures Templeton, 1960; Lucchesi

and Whitney, 1962; Uchameyshvili et al., 1966;

Strubel, 1966; Puchelt, 1967; Strubel, 1967; Mac-¨ ¨Donald and North, 1974; Blount, 1977; Jacques and

Bourland, 1983; Vetter et al., 1983; Reardon and.Amstrong, 1987; Schulien, 1987 have allowed the

development of several high temperature–high pres-Žsure solubility models Blount, 1977; Jacques and

Bourland, 1983; Langmuir and Melchior, 1984;

Reardon and Amstrong, 1987; Moller, 1988; Raju.and Atkinson, 1988, 1989; Yuan and Todd, 1991 .

All of these models are fits of measured solubilities,Žbased either on empirical expressions Jacques and

.Bourland, 1983 , the Debye–Huckel equation for¨Ž .aqueous species activity coefficients Blount, 1977 ,Žor, more recently, Pitzer’s formalism Langmuir and

Melchior, 1984; Reardon and Amstrong, 1987;

Moller, 1988; Raju and Atkinson, 1988, 1989; Yuan.and Todd, 1991 . Several of these models are limited

Žto NaCl solutions Moller, 1988; Raju and Atkinson,.1988, 1989; Yuan and Todd, 1991 . On the contrary,

the present study takes into account the chlorides and

sulfates of the main seawater cations and validates

the model by thorough comparison between model

predictions and measured solubilities.

2.1. Ba–SO and Sr–SO interactions4 4

Ž .Felmy et al. 1990 studied the Na–Ba–SO –H O4 2

and Na–Sr–SO –H O systems at 258C up to 0.014 2

mol Na SO rkg H O. These authors found that2 4 2

celestite solubility in sodium sulfate solutions can be

accurately calculated to moderate sulfate concentra-Ž .tions 0.01 molrkg H O within the standard Pitzer2

Žapproach complete dissociation of the aqueous so-.lutes with Sr–SO interaction parameters assumed4

equal to those for Ca–SO . Conversely, in the Na–4

Ba–SO –H O system, they showed that a solution4 2

( )C. MonninrChemical Geology 153 1999 187–209 189

0Ž .model which includes the BaSO aq ion pair is4

somewhat superior to a strong electrolyte model in

reproducing experimental barite solubilities to 0.01Ž .mol Na SO rkg H O Felmy et al., 1990 .2 4 20Ž . 0Ž .The effect of BaSO aq or SrSO aq ion pair4 4

formation on barite or celestite solubilities can be

illustrated as follows. The dissolution of a solid

alkaline earth sulfate can be written as:

MSO s zM2q aq qSO2y aq 1Ž . Ž . Ž . Ž .4 4

Ž .The equilibrium constant of reaction 1 is the solu-

bility product of the solid. If the model used to

calculate aqueous species activity coefficients is aŽstrong electrolyte model i.e., based on the hypothe-

.sis of complete dissociation of the aqueous solutes ,

then the solubility product is given by:

K sm 2q Pm 2y Pg 2q Pg 2y 2Ž .sp M Žaq . SO Žaq . M Žaq . SO Žaq .4 4

where m is the molality and g the activity coeffi-

cient of the designated aqueous species. In a strong

electrolyte model, activity coefficients can be gener-

ated from numerous models, including the classic

Debye–Huckel theory or Pitzer’s ion interaction ap-¨Ž .proach in its original formulation Pitzer, 1991 .

For aqueous solutes exhibiting strong association,

the complete dissociation hypothesis is no longer

valid. The explicit definition of one or more aqueous

complexes is more efficient for calculating the ther-

modynamic properties of associating electrolytes.Ž . Ž . Ž . ŽPitzer 1991 p. 93 and Weare 1987 p. 148 et

.seq. provide discussions of the limit between strong

and weak electrolytes. When expressed within theŽ . Ž .ion pairing or weak electrolyte formalism, Eq. 2

becomes:

K sm 2q Pm 2y Pg 2q Pg 2ysp M Žaq . ,F SO Žaq . ,F M Žaq . ,F SO Žaq . ,F4 4

3Ž .

where the subscript F designates free ions, i.e., the

part of the total solute concentration not involved in

wany complex or ion pair see Johnson and Pytckow-Ž .icz 1979 , among other authors, for a full descrip-

xtion of this approach . Equilibrium between an ion

pair and an aqueous cation and sulfate can be written

as:

MSO0 aq zM2q aq qSO2y aq 4Ž . Ž . Ž . Ž .4 4

where K stands for the equilibrium constant forip

Ž .reaction 4 :

K ip

m 2q Pm 2y Pg 2q Pg 2yM Žaq . ,F SO Žaq . ,F M Žaq . ,F SO Žaq . ,F4 4s

0 0m PgMSO Žaq . MSO Žaq .4 4

5Ž .

Ž . Ž .Combining Eqs. 3 and 5 leads to:

K 1sp0m s P 6Ž .MSO Žaq .4

0K gip MSO Žaq .4

Ž .Eq. 6 demonstrates that the ion pair concentration

is proportional to the ratio of the mineral solubility

product to the ion pair dissociation constant. Assum-

ing that activity coefficients for neutral species are

close to unity, this ratio can be taken as an estimate

of the ion pair concentration in saturated solutions.

Table 1 compares this ratio for the Ca, Ba and Sr

sulfates, to the solubility of their anhydrous saltsŽ .anhydrite, celestite and barite either in pure water

or in dilute sodium sulfate solution. Aqueous com-

plex stability constants were taken from the literature

and are given in Table 1. It must be emphasized that,

in the present approach, interaction of the element M

in solution with sulfate is accounted for by the0Ž .MSO aq ion pair. Interactions with other aqueous4

anions are accounted for by interaction parameters in

the activity coefficient expressions in Pitzer’s for-

malism. Such an approach has been termed ‘a hybridŽ .model’ by Whitfield 1975 .

Table 1

An estimate of the cation–sulfate ion pair concentration for Ca, Sr and Ba. See text

Salt Log K Log K K rK Solubility in Solubility insp ip sp ip

pure water 0.01 MŽ .molrkg H O Na SO2 2 4

Ž . Ž . Ž . Ž .CaSO anhydrite y4.32 a y1.65 a 0.002 0.015 a 0.010 a4y5 y4Ž . Ž . Ž . Ž .SrSO celestite y6.62 b y1.86 c 1.7=10 0.0012 b 2.0=10 c4y8 y5 y7Ž . Ž . Ž . Ž .BaSO barite y10.05 b y2.72 c 4.7=10 1.0=10 b 1.0=10 c4

Ž . Ž . Ž . Ž . Ž .a Moller 1988 ; b Monnin and Galinier 1988 ; c Felmy et al., 1990.


The data listed in Table 1 indicate that the less

soluble the salt, the stronger the common ion effect.

The addition of 0.01 mol of sulfate to the solution

has almost no effect on anhydrite solubility com-

pared to pure water, but it lowers barite solubility by

two orders of magnitude. Estimates of calcium sul-

fate ion pair formation indicates that this complex

accounts for less than 10% of total dissolved calcium

in pure water or sodium sulfate solutions at equilib-

rium with anhydrite. Consequently, it is possible to

treat this salt at 258C, either as fully dissociatedŽ . ŽHarvie et al., 1984 or as a weak electrolyte Moller,

.1988 , with comparable accuracy. At higher tempera-

tures where ion pairing is enhanced, the inclusion of0Ž . Ž .the CaSO aq complex is necessary Moller, 1988 .4

Strontium sulfate ion pair formation is negligible

in pure water at equilibrium with celestite, but it

accounts for about 10% of total strontium in celestiteŽ .saturated Na SO solutions Table 1 . As shown by2 4

Ž .Felmy et al. 1990 , the thermodynamic properties of

strontium sulfate can be equally well calculated byŽassuming total dissociation ion interaction ap-

. Žproach or assuming aqueous complex formation ion.pairing phenomenology . Reardon and Amstrong

Ž . Ž .1987 and Monnin and Galinier 1988 also calcu-

lated celestite solubilities in seawater assuming total

dissociation which are in close agreement with the

corresponding experimental values reported by Cul-Ž .berson et al. 1978 . Moreover, the Reardon and

Ž .Amstrong 1987 model unambiguously shows that

celestite crystals observed in deep-sea carbonate sed-

iments of DSDP Leg 90 are at equilibrium with poreŽ .waters Baker and Bloomer, 1988 .

Barium sulfate ion pair concentration is negligibleŽ .in barite saturated pure water Table 1 . In 0.01 M

sodium sulfate, however, about 50% of the total0Ž .barium in solution is present as the BaSO aq aque-4

Ž .ous complex, when Felmy et al. 1990 value of the

ion pair stability constant is retained. In this case,

ionic association must be explicitly taken into ac-

count and aqueous barium sulfate has to be treated as

a weak electrolyte.

As can be seen on solubility diagrams reported byŽ . Ž .Harvie et al. 1984 or Monnin and Galinier 1988 ,

there is a marked increase in anhydrite, barite and

celestite solubility with increasing aqueous chlorideŽ .concentration salting-in effect at 258C. As shown

above, ion pair formation is negligible in barite and

celestite saturated pure water. This is also true in

chloride bearing solutions. Consequently, as notedŽ .by Monnin and Galinier 1988 and Reardon and

Ž .Amstrong 1987 at 258C, calculated barite or ce-

lestite solubilities in chloride solutions are insensi-

tive to the Ba–SO or Sr–SO Pitzer interaction4 4

parameters. In models based on the ion pairing phe-

nomenology, calculated barite or celestite solubilities

in chloride solutions are insensitive to the ion pair0Ž . 0Ž .stability constant values for BaSO aq or SrSO aq .4 4

Ž .For example, Moller 1988 calculated barite solubil-

ity in NaCl solutions to 2508C at P 1 by assumingsat0Ž .that the BaSO aq stability constant is equal to that4

0Ž . Ž .for CaSO aq at these temperatures. Moller 19884

showed that the calculated barite solubilities are

sensitive to the Na–Ba interaction parameter. Con-

versely, because calculated barite and celestite solu-

bilities in chloride solutions are insensitive to Pitzer’s

parameters for Ba or Sr interactions with aqueousw 0Ž . 0Ž .sulfate or equivalently to BaSO aq or SrSO aq4 4

xstability constants , these parameters cannot be un-

ambiguously obtained from fits of solubility data in

chloride solutions.

2.2. Binary interaction parameters for aqueous Na,

K, Ca and Mg chlorides and sulfates at high temper-

ature

The full high temperature model of the Na–K–

Ca–Cl–SO –H O system of Greenberg and Moller4 2

Ž .1989 has been adopted in this work. These authors

provide empirical expressions for the temperature

variation of binary interaction parameters for the

aqueous sodium, potassium, and calcium sulfates and

chlorides. Binary interaction parameters for MgCl -2Ž . Ž .aq and MgSO aq were taken from Pabalan and4

Ž . Ž .Pitzer 1987 . Those for SrCl aq were taken from2

Ž . Ž .Phutela et al. 1987 and those for BaCl aq were2

Ž .taken from Monnin 1995 . Alternate ion interaction

models exist for some of these salts. For example,Ž .Holmes et al. 1994 proposed a description of

Ž .CaCl aq thermodynamic properties valid to 526 K2

and 400 bars based on a regression of calorimetric

1P refers to a pressure of 1 bar if temperature is belowsat

1008C, and to pressures corresponding to the liquid vapor–equi-

librium of H O at higher temperatures.2


and volumetric data using Pitzer’s equations. Such

new expressions do extend the range of application

of ion interaction models to higher temperatures,

pressures andror molalities. In the present work, the

internally consistent model of Greenberg and MollerŽ .1989 for the Na–K–Ca–Cl–SO –H O system and4 2

Ž .the MgCl model of Pabalan and Pitzer 1987 were2

sufficient to study the available barite and celestite

solubility data.

2.3. Ternary interaction parameters

Ternary interaction parameters for the Na–K–

Ca–Cl–SO –H O system are from Greenberg and4 2

Ž .Moller 1989 . Note that the Pabalan–Pitzer modelŽfor the Na–K–Mg–Cl–SO –H O system Pabalan4 2

.and Pitzer, 1987 is not compatible with the Green-

berg–Moller model for the Na–K–Ca–Cl–SO –H O4 2

system. It follows that the Greenberg and MollerŽ .1989 model cannot be directly merged with the

Ž .Pabalan and Pitzer 1987 model to build a high

temperature model for concentrated solutions in the

six-ion Na–K–Ca–Mg–Cl–SO –H O system.4 2

Among their differences, they use different expres-

sions to describe the temperature dependence of

Na–Cl and Na–SO interaction parameters. Al-4

though these two expressions are of comparable

accuracies in calculating the thermodynamic proper-

ties and mineral solubilities in the Na SO –H O and2 4 2

NaCl–H O systems to high temperature, they lead to2

different values of ternary Cl–SO and Na–Cl–SO4 4

interaction parameters in the Na–Cl–SO –H O sys-4 2

tem. Inconsistent parameter sets can lead to a signifi-

cant accuracy deterioration in solubility calculationsŽat high concentrations see, for example, Fig. 1 in

Ž .the paper of Greenberg and Moller 1989 or Fig. 2.in the paper of Monnin, 1995 .

Ž .Reardon and Amstrong 1987 calculated ternary

mixing parameters u and c from emfNa,Sr Na,Sr,Cl

Ž .data Lanier, 1965 for the Na–Sr–Cl–H O system2

Ž .at 258C. Monnin 1995 studied the solubility of

solid BaCl P2H O in NaCl, KCl, and CaCl solu-2 2 2

tions, to generate the corresponding Pitzer’s ternary

mixing parameters involving the interaction of aque-

ous Ba with either Na, K or Ca.

A large number of ternary mixing parameters are

still unknown. Calculated activity coefficients are

likely insensitive to mixing parameters representing

M–Ba–SO , Ba–SO –X, M–Sr–SO or Sr–SO –X4 4 4 4

Ž .interactions M being a cation and X an anion due

to the limitation of barium or strontium concentra-

tions to low values. Missing parameters are set to

zero in the present work, although in some instancesŽ .see, for example, BaSO in KCl solutions they can4

be adjusted to the data in order to correct for the

discrepancies between calculated and experimental

solubilities. Such corrections are sensitive only for

concentrations above 1 M or so and, in many cases,

they lead to meaningless parameter values that can-

not be recommended. As such the present model is

limited to moderately concentrated solutions and is

suited for seawater, but should be used with caution

for brines.

2.4. Pressure effects

The effect of pressure on aqueous activity coeffi-

cients can be obtained through calculation of partialŽmolal volumes within Pitzer’s formalism Monnin,

.1989, 1990 . Expressions for the partial molal vol-

umes and compressibilities of aqueous solutes inŽ .complex mixtures are given by Monnin 1989, 1990

along with expressions of the corresponding Debye–

Huckel slopes. Compressibility has only a second¨order effect which is negligible at moderate pres-

Ž .sures Millero, 1979; Monnin, 1990 . Because no

compressibility data is available for BaCl solutions,2

no estimate of compressibility effects have been

included in this work. One can refer to MonninŽ .1990 for a discussion of the contribution of com-

pressibility to the thermodynamic properties of aque-

ous electrolytes.

First derivatives of Pitzer’s interaction parameters

with respect to pressure are given by Phutela et al.Ž . Ž . Ž . 21987 for SrCl aq and by Monnin 1990 for2

Ž . Ž . Ž .NaCl aq , Na SO aq and CaCl aq . Puchalska and2 4 2

Ž .Atkinson 1991 give the temperature variation ofŽ .the standard molal volume of BaCl aq while tem-2

perature and pressure dependent expressions of the

BaCl interaction parameters are reported by2

Ž .Manohar et al. 1994 .

2Note that the a parameter in Table 1 in the paper of Monnin1

Ž . q2 y21990 should be 8.525003=10 instead of 8.525003=10 .


3. Barite and celestite solubility products

The variation of the solubility product with pres-

sure is given by:

0D VrlnK T ,P s lnK T ,P y PyPŽ . Ž . Ž .sp sp 0 0

RT

7Ž .

0where D V stands for the standard molal volume ofr

the dissolution reaction.Ž .The solubility product, K T ,P at temperaturesp 0

T and reference pressure P can be obtained from0

the standard heat capacity of the dissolution reaction.

When this heat capacity is constant over the investi-Ž .gated temperature range, then K T ,P is given by:sp 0

ClnK T ,P sAqB lnTq 8Ž . Ž .sp 0

T

with

D S0 D C 0r r pw xAs y 1q lnT0

R R0D Cr p

9Ž .BsR

0 0D H T D Cr 0 r pCsy q

R R

where D S0, D H 0 and D C 0 respectively refer tor r r p

the standard entropy, enthalpy and heat capacity of

the dissolution reaction. R is the gas constant and T0Ž .the reference temperature 298.15 K .

3.1. Celestite

The celestite solubility product was determined byŽ .Reardon and Amstrong 1987 from their own pure

water celestite solubility measurements from 10 to

908C. Their 258C value is in close agreement withŽ .those of Monnin and Galinier 1988 and Felmy et

Ž . Ž .al. 1990 . Reardon and Amstrong 1987 repre-

sented K values as a function of temperature usingsp

four- and five-parameter expressions which both im-

ply a temperature dependent heat capacity of the

dissolution reaction. Their K values can be fittedsp

with the same accuracy using the three-parameterŽ .Eq. 8

lnK T ,P s224.069y35.9422 lnTŽ .sp 0

y10302.32rT 10Ž .

Žsuggesting that the original interpretation Reardon.and Amstrong, 1987 was an overfit. Such overfits

may lead to poor values to the solubility products

when extrapolated outside the range of the fittedŽ . Ž . 0data. Eqs. 9 and 10 lead to D S sy138.5"0.5r

Jrmol, D H 0sy3.44"0.12 kJrmol and D C 0sr r p

y298.8"0.3 Jrmol Ky1.

The standard molal volume of the celestite disso-

lution reaction is:

0 0 0D V sV SrSO ,aq yV SrSO ,s 11Ž . Ž . Ž .r 4 4

0Ž .The standard volume of celestite V SrSO ,s is43 Ž46.25 cm rmol at 258C and 1 bar Robie et al.,

.1979 and is considered to be constant over the

temperature and pressure ranges investigated in this

study. The standard molal volume of aqueous stron-

tium sulfate is calculated at T and P from those ofsat

Ž .sodium sulfate and sodium chloride Monnin, 1990Ž .and of strontium chloride Phutela et al., 1987 at the

same temperature and pressure using the additivity

rule which is expressed by:

0 0 0V SrSO ,aq sV SrCl ,aq qV Na SO ,aqŽ . Ž . Ž .4 2 2 4

0y2V NaCl,aq 12Ž . Ž .0where V is the standard molal volume of the

designated aqueous electrolyte.

3.2. Barite

The barite solubility product at P is calculatedsat

from pure water barite solubilities measured byŽ .Blount 1977 to 2508C and fit to the following

equation:

15806.30lnK T ,P s275.053y43.014 lnTyŽ .sp sat

T

13Ž .

from which the following thermodynamic quantities

are retrieved: D S0sy108.5"1.5 Jrmol, D H 0r r

s24.755"0.35 kJrmol and D C 0sy357.2"0.8r p

Jrmol Ky1. The uncertainties attached to these val-

ues are based on an uncertainty on K of 1% atsp

298.15 K and of 10% at other temperatures.


The standard volume of the barite dissolution

reaction can be calculated from:

0 0 0DV sV BaCl ,aq qV Na SO ,aqŽ . Ž .r 2 2 4

0 0y2V NaCl,aq yV BaSO ,s 14Ž . Ž . Ž .4

0 3Ž . Žwhere V BaSO ,s s52.1 cm rmol Robie et al.,4

.1979 . The standard molal volume of aqueous bar-

ium chloride is given by Puchalska and AtkinsonŽ .1991 .

4. Calculated barite and celestite solubilities in

electrolyte solutions versus experimental data

4.1. Barite and celestite solubilities in pure water at

high pressure

Pure water celestite solubilities were measured at

2, 22 and 358C to 1000 bars by MacDonald andŽ . Ž .North 1974 . Blount 1977 reported pure water

barite solubility to 2508C and to 1 kbar. A close

agreement between the predicted and measured val-

ues can be seen in Fig. 1. It must be emphasized that

the only data used in model construction is pure

water barite solubility at P to get the barite solubil-sat

ity product. The curves in Fig. 1 are model predic-

tions. Keeping in mind that no Ba–SO or Sr–SO4 4

interaction parameters or association constants are

included in the model, Pitzer’s expression for the

activity coefficient reduces to a simple Debye–

Huckel term. The close correspondence between the¨symbols and the curves in Fig. 1 demonstrates that

this simple Debye–Huckel term is sufficient to accu-¨rately calculate pure water barite and celestite solu-

bilities. These results confirm the analysis that was

carried out above from the results reported in Table

1.

4.2. The Na SO –BaSO –H O system2 4 4 2

Barite solubility in sodium sulfate solutions to

0.008 mol SO rkg H O is reported by Felmy et al.4 2

Ž . Ž .1990 at 258C and Jiang 1996 from 0 to 808C.Ž .Unfortunately, Felmy et al. 1990 reported their data

only as plots. Fig. 2 compares measured barite solu-Ž . Ž .bilities black squares of Jiang 1996 at 0, 40 and

808C, to those calculated when only Na–SO interac-4

Fig. 1. The solubility of barite and celestite vs. pressure at variousŽ .temperatures. The experimental data for celestite filled circles is

Ž .from MacDonald and North 1974 . The calculated and experi-

mental celestite solubilities at 22 and 358C are vertically offset by

0.001 molrkg H O for clarity. The experimental data for barite2

Ž . Ž .filled squares is from Blount 1977 . The experimental barite

solubility at 248C is represented by open squares and the calcu-

lated solubility at this temperature by a dashed curve to avoid

overlap with the results at 1898C.

Ž .tions are taken into account dashed curves , i.e.,

when Ba–SO interactions are neglected. The calcu-4

lated solubilities are lower that the measured values,Ž .indicating that the calculated BaSO aq activity co-4

efficient is overestimated. As ion association tends to0Ž .lower activity coefficients, a BaSO aq ion pair4

may account for the difference between calculated

and measured barite solubilities. The difference be-


Fig. 2. Barite solubility in sodium sulfate solutions. The experi-Ž . Ž .mental data filled squares is from Jiang 1996 . The dashed

curve is calculated without the barium sulfate ion pair and the

plain curve includes this aqueous complex.

tween calculated and measured barium concentration

in sodium sulfate solutions is reported in Fig. 3 for a

temperature of 808C. One can see in Fig. 3 that, inŽ .accordance with Eq. 6 , this difference is constant

for sodium concentrations above 0.0025 molrkg

H O. Therefore, it provides an estimate of the20Ž . 0Ž .BaSO aq ion pair concentration. If the BaSO aq4 4

0Ž .activity coefficient is taken equal to unity, BaSO aq4

ion pair dissociation constant values can be calcu-Ž .lated from Eq. 6 and the experimental data of Jiang

Ž .1996 . These values are reported in Fig. 4 and fit to:

383.6770lnK sy6.5032q 15Ž .BaSO4 T

The enthalpy and entropy of the BaSO0 ion pair4

dissociation reaction are D H 0sy3.190"0.039r

kJrmol and D S0sy54.07"0.13 Jrmol. Ther0Ž .decimal logarithm of the BaSO aq stability con-4

Ž .stant calculated from Eq. 15 is y2.26 at 258C,

Fig. 3. Difference between measured barite solubility in sodium

sulfate solutions at 808C and solubility calculated without the0Ž .BaSO aq ion pair vs. the sodium molality.4

which falls within the range of literature valuesŽ .compiled by Felmy et al. 1990 . Felmy et al.’s value

0Ž .for the BaSO aq stability constant lead to a degree4

Ž .of BaSO association of 50% at 258C Table 14

while it is only about 15% with the value determined

in the present work. It only slightly increases to0Ž .about 20% at 808C. Adjusting the BaSO aq aque-4

ous complex stability constant to the data is enough

to bring calculated barite solubilities in good agree-Ž .ment with the measurements plain curves in Fig. 2

Ž .of Jiang 1996 . Note that, with this new value of the0Ž .BaSO aq stability constant, the logarithms of the4

0Ž .Fig. 4. The decimal logarithm of the BaSO aq ion pair dissocia-4

tion constant vs. temperature.


Ž .Fig. 5. pK values for the dissociation constants of MSO aq ion4

Ž .pairs with MsCa, Ba, Sr vs. the solubility products of theŽcorresponding anhydrous solids i.e., anhydrite, barite and ce-

.lestite . Plotted values are those given in Table 1 except that for0Ž .BaSO aq . The value determined in this work has been used.4

barite, celestite and anhydrite solubility products at

258C are linearly correlated to the logarithms of the0Ž . 0Ž . 0Ž .CaSO aq , SrSO aq and BaSO aq dissociation4 4 4

Ž .constants Fig. 5 . This may reflect the fact that the

more stable the aqueous complex, the more soluble

the mineral.

The correlation exhibited in Fig. 5 does not hold0Ž .if the values for the SrSO aq dissociation constant4

Ž .of Reardon and Amstrong 1987 are retained. These

values have been determined in pure SrSO solutions4

Ž .by Reardon 1983 using conductimetric and ionw 0Ž .xexchange techniques. His pK SrSO aq value at4

258C is 2.29, compared to the value of 1.86 of FelmyŽ . 0Ž .et al. 1990 . As said above, the SrSO aq dissocia-4

tion constant would be best determined from ce-

lestite solubility in sodium sulfate solutions at vari-

ous temperatures. For now, in light of the discrep-

ancy between various sources, it is impossible to0Ž .recommend any value of the SrSO aq dissociation4

constant. An estimate can be obtained using theŽ .value of Felmy et al. 1990 at 258C and the enthalpy

Fig. 6. The solubility of celestite in sodium chloride solutions at 80 and 1208C and at 1 and 400 bars. Plain curves: predicted values; filledŽ . Ž .squares: experimental data from Schulien 1987 ; open squares: experimental data from Strubel 1966 .¨


Ž . 0Ž .of Reardon 1983 for the SrSO aq dissociation4

Ž .reaction 8.7 kJrmol at 258C .

4.3. The NaCl–SrSO –H O system4 2

There is a large body of data for this system.Ž .Reardon and Amstrong 1987 studied celestite solu-

bility in sodium chloride solutions from 10 to 908C

using their own experimental data and those ofŽ .Strubel 1966 . The measurements of Jacques and¨Ž .Bourland 1983 are consistent with these data in the

region of overlap. Celestite solubilities predicted by

the present model are in close agreement with the

experimental values, as well as with the calculationsŽ .of Reardon and Amstrong 1987 . We here illustrate

results for some data not used by Reardon andŽ .Amstrong 1987 .

Celestite solubility measurements reported byŽ .Schulien 1987 in solutions up to 2 M NaCl at 80

and 1208 and at 1 and 400 bars are shown in Fig. 6.

It is assumed in this study that Schulien reported his

data using the molality scale. Adoption of this as-

sumption renders these data consistent with the dataŽ . Žof Strubel 1966 in the region of overlap 808C; Fig.¨

.6 . Our predicted solubilities are in good agreementŽ .with the measured solubilities of Strubel 1966 and¨

Ž . Ž .Schulien 1987 Fig. 6 as well as with other data,Ž .reported by Jacques and Bourland 1983 at pres-

sures up to 200 bars and temperatures to 1498C that

are not included in Fig. 6.Ž .Vetter et al. 1983 reported a large body of

celestite solubility data in NaCl, CaCl and MgCl2 2

solutions and their mixtures at 25, 75, 95 and 1258C.

Solubility was measured using a radioactive tracer

technique using90Sr. Some of the results were

cross-checked using35S instead of

90Sr, but the two

methods lead to solubility values differing by as

much as 30%. Our calculations are in agreement

with the35S measurements, which is consistent with

Ž .the results of Monnin and Galinier 1988 at 258C.Ž .Lucchesi and Whitney 1962 reported solubility

data at 08C. Similar to the 258C results of MonninŽ .and Galinier 1988 , calculated solubilities at 08C are

higher than the measured values by a factor of aboutŽthree for the highest NaCl concentration 5.6 molrkg

.H O . Despite the fact that measurements below2

258C are of great importance for oceanographic stud-

ies, these data are not given further consideration in

this work.

Note that celestite solubility can be accurately

calculated assuming that mixing parameters involv-Žing Na–Sr and Na–Sr–Cl interactions at 258C Re-

.ardon and Amstrong, 1987 do not vary with temper-

ature and can be used up to 1508C.

4.4. The MgCl –SrSO –H O system2 4 2

Data for this system is reported by Vetter et al.Ž .1983 at 75, 95 and 1258C at P and magnesiumsat

Ž .chloride concentrations up to 0.5 M Fig. 7 . Note

the discrepancy between the celestite solubility mea-

sured with35S and that obtained with

90Sr.

Fig. 7. The solubility of celestite in magnesium chloride solutions

at 75, 95 and 1258C and 1 bar or water vapor saturation pressure.35 Ž .Open squares: measured values using S Vetter et al., 1983 ;90 Ž .filled squares: measured values using Sr Vetter et al., 1983 ;

plain curves: solubility calculated using u and cCl ,SO Mg,Cl,SO4 4

Ž .from Pabalan and Pitzer 1987 ; dashed curves: solubility calcu-Ž .lated using u and c from Moller 1988 .Cl ,SO Mg,Cl,SO4 4


The aqueous solution model for this system is

built from the binary interaction parameters ofŽ .Phutela et al. 1987 for SrCl and of Pabalan and2

Ž .Pitzer 1987 for MgCl and MgSO . To maintain2 4

model consistency, Pitzer’s mixing parameters in-

volving Cl–SO and Mg–Cl–SO interactions4 4

Ž .u and c are also taken from PabalanClSO MgClSO4 4

Ž .and Pitzer 1987 . Ternary interaction parameters

involving Sr are set to zero. As seen in Fig. 7,

predicted solubility agrees closely with the35S ex-

perimental data at 758C, but departs increasingly

from the measured values as temperature increases.

Solubility calculated using u and c takenClSO MgClSO4 4

Ž .from Moller 1988 are also plotted in Fig. 7. These

results deviate from those obtained with the Pa-

balan–Pitzer ternary parameters; the difference in-

creases with increasing magnesium chloride concen-

tration. This difference is as large as the data scatter

at 0.5 M MgCl . This result demonstrates the need2

to maintain model consistency. As emphasized above

it is not possible to build a high temperature Na–K–

Ca–Mg–Cl–SO –H O model for concentrated solu-4 2

tions by combining Moller’s and Pitzer and Pabalan’s

models without refitting some parameters. Celestite

solubility in moderately concentrated magnesium

chloride solutions can nevertheless be satisfactorily

calculated up to 1008C by setting u and cMg,Sr Mg,Sr,Cl

equal to zero.

4.5. The CaCl –SrSO –H O system2 4 2

Ž .Vetter et al. 1983 give data for this system at

75, 95 and 1258C at P . It can be seen in Fig. 8 thatsat

celestite solubility is satisfactorily predicted by set-

ting the mixing parameters u and c equalCa,Sr Ca,Sr,Cl

to zero. When the calcium concentration of celestite

saturated solutions increases, the solid calcium sul-

fate stability field is reached. At 258C, gypsum can

form in solutions having a calcium molality aboveŽ .0.75 molrkg H O Monnin and Galinier, 1988 . At2

higher temperatures, anhydrite is the stable solid

calcium sulfate phase. Its solubility decreases with

temperature. We find that anhydrite is saturated in

celestite saturated solutions when the calcium con-

centration is equal to 0.5 molrkg H O at 758C, 0.242

molrkg H O at 958C, and 0.06 molrkg H O at2 2

Ž .1258C Fig. 8 .

Ž .Fig. 8. The solubility of celestite expressed as strontium molality

in calcium chloride solutions at 75, 95 and 1258C and 1 bar or

water vapor saturation pressure. Open squares: measured values35 Ž .using S Vetter et al., 1983 ; filled squares: measured values90 Ž .using Sr Vetter et al., 1983 ; plain curves: celestite solubility

calculated taking into account anhydrite precipitation; dashed

curves: celestite solubility calculated for the sole equilibrium with

celestite.

When anhydrite precipitates, the calcium and the

sulfate concentrations are lowered, which increases

the strontium content of the solution. It can be seen

in Fig. 8 that calculated solubilities closely match the

experimental data when anhydrite formation is not

taken into account. This suggests that anhydrite did

not precipitate in the experiments of Vetter et al.Ž .1983 , although its stability field was reached.

4.6. The NaCl–MgCl –SrSO –H O, NaCl–CaCl –2 4 2 2

SrSO –H O, CaCl –MgCl –SrSO –H O and4 2 2 2 4 2

NaCl–CaCl –MgCl –SrSO –H O systems2 2 4 2

Data for these complex systems are from Vetter etŽ .al. 1983 . In general our calculated celestite solubili-


Fig. 9. Barite solubility in sodium chloride solutions at 50, 80 and

1008C. The curves represent calculated values. Experimental data:Ž . Ž .open squares: Templeton 1960 ; filled squares: Schulien 1987 ;

Ž . Ž .filled circles: Strubel 1967 ; open diamonds: Blount 1977 : open¨Ž . Ž .circles: Uchameyshvili et al. 1966 ; plusses: Puchelt 1967 .

ties agree with the35S data, but are about 25%

higher than the90Sr data, as found for other simpler

systems. In addition, data for calcium containing

systems were found to be supersaturated with respect

to anhydrite at 1258C.

4.7. The Nacl–BaSO –H O system4 2

Numerous experimental solubility data are avail-

able in this system. Barite solubility has been mea-Ž .sured at 1 bar by Strubel 1967 at 108C intervals¨

from 20 to 1008C in solutions containing up to 2 MŽ .NaCl. Puchelt 1967 reports barite solubilities at

508C as a function of NaCl concentration up to haliteŽ .saturation. Templeton 1960 reports smoothed solu-

Ž .bility data to 958C and to 5 M NaCl. Schulien 1987

measured barite solubility in solutions containing up

to 2 M NaCl at 80, 100, and 1208C and at pressuresŽ .of 1, 200, and 400 bars. Blount 1977 reports data

up to 2508C, 500 bars and 4 M NaCl. UchameyshviliŽ .et al. 1966 give barite solubilities up to 3708C at

P and sodium chloride concentrations up to 2 M.sat

Ž .Strubel 1967 reports data for a single 2 M NaCl¨solution, but to 6008C.

It can be seen in Fig. 9 that the data of TempletonŽ . Ž . Ž .1960 , Puchelt 1967 and Strubel 1967 at 508C¨are consistent, and predicted barite solubilities are

within experimental uncertainty. Model predictions

are in full agreement with Templeton’s data at 808C,

but are up to 10% higher than the experimentalŽ . Ž .values of Blount 1977 and Strubel 1967 in the 1¨

to 3 M NaCl concentration range at 1008C. It can

Fig. 10. Barite solubility in sodium chloride solutions at 150, 200

and 2508C and water vapor saturation pressure. The dashed curves

represent solubility values calculated with u s0.0. The plainNa,Ba

curves are calculated with u equal to 0.02 at 1508C, 0.05 atNa,Ba

2008C and 0.12 at 2508C. Experimental data: filled circles: Strubel¨Ž . Ž .1967 ; open diamonds: Blount 1977 : filled squares:

Ž .Uchameyshvili et al. 1966 .


also be seen in Fig. 9 that the data of SchulienŽ .1987 is inconsistent with Templeton’s results at

808C and with other reported solubilities at 1008C.

We also found that calculated barite solubilities are

systematically higher than Schulien’s measurements

at 80, 100 and 1208C and at 1, 200 and 400 bars.

Experimental data reported for temperatures above

1008C and at P are shown in Fig. 10. Data re-sat

Ž .ported by Blount 1977 and by Uchameyshvili et al.Ž .1966 are in agreement in the region of overlap.

Strubel’s datum agrees with these data at 1508C, but¨not at 2008C and 2508C. Barite solubilities calculated

with u equal to zero and c equal toNa,Ba Na,Ba,Cl

Ž .0.0128 Monnin, 1995 , which are depicted by the

dashed curve in Fig. 10, are higher than the experi-

mental data, with a discrepancy increasing with tem-Ž .perature. As shown by Moller 1988 , calculated

solubilities can be brought into agreement with the

experimental data by adjusting only u . ThisNa,Ba

leads to u values equal to 0.02 at 1508C, to 0.05Na,Ba

at 2008C and 0.12 at 2508C. These values are large

relative to characteristic Pitzer’s mixing parameter

values describing interaction between univalent andŽ .divalent cations Pitzer, 1991 . Consequently they

should only be used for interpolating between these

experimental data. Note that the model with uNa,BaŽ .s0 and c s0.0128 Monnin, 1995 can ac-Na,Ba,Cl

curately predict barite solubility to moderate NaCl

concentrations even at 2508C, despite the fact that

these parameters are based on regression of low

temperature data.

Barite solubilities in NaCl bearing solutions atŽ .500 bars up to 2508C reported by Blount 1977 are

depicted in Fig. 11. Barite solubilities at 1508C and

500 bars calculated using a 1 bar barium sulfate

activity coefficient are substantially above Blount’sŽ .data. The pressure effect on BaSO aq activity coef-4

ficient can be calculated by integration of its partial

molal volume that can be obtained by additivity fromŽ . Ž . Ž .the NaCl aq , Na SO aq , and BaCl aq partial2 4 2

Žmolal volumes. All the needed parameters first

derivatives of Pitzer’s parameters with respect to

Fig. 11. Barite solubility in sodium chloride solutions at 150, 200 and 2508C and 500 bars. The dashed curve labeled A is calculated with

the barium sulfate activity coefficient calculated at water vapor saturation pressure instead of 500 bars. The dashed curve labeled C isŽ .calculated with Pitzer’s parameters for the volumetric properties of BaCl given by Manohar et al. 1994 . The dashed curves labeled B are2

Ž .calculated with Pitzer’s parameters for the volumetric properties of BaCl equal to those for CaCl Monnin, 1990 at the same temperature.2 2

Ž .The plain curves are calculated with the values of u adjusted to the experimental data at P see Fig. 10 and text . The filled squaresNa,Ba sat

Ž .are the experimental data of Blount 1977 .


. Ž .pressure are taken from Monnin 1990 except thoseŽ .for BaCl which are from Manohar et al. 1994 .2

The barite solubility calculated assuming u s0Na,Ba

is in close agreement with the experimental data up

to 3 M NaCl, but deviates at higher NaCl molalities.

It must be kept in mind that the BaCl volumetric2

Ž .parameters of Manohar et al. 1994 have been deter-

mined from density measurements up to 1408C and

that the results depicted in Fig. 11 already represent

extrapolations outside the range of validity of these

parameters. When the same calculation is carried outŽ .using CaCl volume parameters Monnin, 1990 in2

place of those for BaCl , the discrepancy at high2

NaCl molalities disappears and barite solubility is

predicted at 1508 and 500 bars with the same accu-

racy as at 1508C and P . When u is set tosat Na,Ba

0.02, the agreement between predicted and measured

values is very good. It thus appears that the pressure

effect on barium sulfate activity coefficients at ele-Ž .vated temperatures above 1508C can be accounted

for by using CaCl volumetric properties as a proxy2

for those of BaCl . The plain curves at 200 and2

2508C and 500 bars in Fig. 11 are calculated assum-

ing this pressure correction and by adopting uNa,Bavalues determined from the P data. It can again besat

seen that barite solubility is accurately predicted at

2508C and 500 bars up to 3 M NaCl.

4.8. The KCl–BaSO –H O system4 2

Barite solubilities in this system are reported byŽ .Puchelt 1967 at 508C up to 5 mol KClrkg H O. It2

can be seen in Fig. 12 that these data are consistent

with a u parameter value of 0.04, but use ofK,Ba

u s0 leads to a discrepancy no greater thanK,Ba

about 15% at the highest KCl concentration. Fitting

u to the barite solubility data lead to meaninglessK,Ba

parameters, especially if one keeps in mind that itŽ .was found Monnin, 1995 that the solubility of

BaCl P2H O in potassium chloride solutions below2 2

1008C can be accurately calculated with u s0.K,Ba

Moreover, barite solubilities calculated assuming

u s0 have been found in rough agreement withK,Ba

the scattered data reported by Uchameyshvili et al.Ž .1966 for a solution containing 0.25 mol KClrkg

H O between 100 and 2508C.2

Fig. 12. Barite solubility in potassium chloride solutions at 508C.Ž .The filled squares represent measurements of Puchelt 1967 . The

dashed curve is calculated with u equal to zero and the plainK,Ba

curve with u s0.04.K,Ba

4.9. The MgCl –BaSO –H O system2 4 2

Barite solubilities in MgCl solutions were mea-2

Ž .sured by Puchelt 1967 at 508C. Similar results are

found for 508C as were found for 258C by MonninŽ .and Galinier 1988 : the calculated value is in close

agreement with the experimental data up to 0.5 mol

MgCl rkg H O, but lower at higher concentrations.2 2

Ž .Data reported by Uchameyshvili et al. 1966 for

a 0.083 mol MgCl rkg H O solution up to 2308C2 2

show that barite solubility increases with tempera-

ture. The present model predicts this tendency, but

the agreement between measured and calculated val-

ues is only rough.

4.10. The CaCl –BaSO –H O system2 4 2

Barite solubilities calculated at 508C are in closeŽ .agreement with the data of Puchelt 1967 at concen-

trations up to about 1 molrkg H O, but depart for2

experimental data at higher concentrations, similarlyŽto what was observed for KCl solutions see Fig.

.11 .Ž .Uchameyshvili et al. 1966 measured barite solu-

bility in solutions containing 0.165 and 0.5 mol

CaCl rkg H O to 2408C. They observed anhydrite2 2

formation at temperatures above 2308C. As can be


seen in Fig. 13, calculated barite solubilities are

higher than measured values by a factor of 2 at

1008C and by about 25% at 2008C. The anhydrite

stability field is reached when temperature increasesŽ .at constant calcium molality Fig. 13 or when the

calcium content of the solution is increased at con-

stant temperature. It can be seen in Fig. 13 that the

aqueous phase becomes anhydrite-saturated at about

2108C for a solution containing 0.165 mol CaCl rkg2

H O and at 1658C for a solution containing 0.5 mol2

CaCl rkg H O. At 2308C when anhydrite precipi-2 2

tates from barite saturated solutions, aqueous sulfate

content decreases and barium concentration in-

creases. This has been experimentally observed byŽ .Uchameyshvili et al. 1966 . The dashed curves in

Fig. 13 represent calculated barium molality for equi-Žlibrium with barite alone anhydrite is prevented

Fig. 13. Barite solubility in calcium chloride solutions vs. temper-Ž .ature. The experimental data filled squares is from Uchameyshvili

Ž .et al. 1966 . The plain curves are calculated allowing anhydrite to

form. The dashed curves are calculated for equilibrium with bariteŽ .alone anhydrite remains supersaturated .

.from precipitating , while the upper part of the plain

curves is calculated for a solution at equilibrium with

both barite and anhydrite. Note that the calculations

at 2308C require extrapolation of some model param-

eters, including the interaction parameters for bariumŽchloride beyond their 2008C validity limit Monnin,

.1995 . It is nevertheless evident in Fig. 13 that

calculated values are in better agreement with exper-

imental data if the absence of anhydrite is assumed.

This type of agreement was also found for celestiteŽ .see Fig. 10 .

5. Discussion

The experimental data reported in Figs. 1–13

show that the solubility of barite and celestite in

aqueous solutions containing alkali and alkaline earth

chlorides increases with the chloride content of the

solution, at least to 2508C. This salting-in effect is

due to a lowering of the aqueous barium or strontium

activity coefficient when the ionic strength of theŽ . Ž .solution increases. BaSO aq and SrSO aq activity4 4

coefficients in chloride solutions can be calculated

by taking into account the sole binary interactions

between aqueous barium or strontium, chloride and

the other cations. The interactions between aqueousŽ . Žstrontium or barium and aqueous sulfate which are

usually taken into account either as interaction pa-

rameters in Pitzer’s formalism or as ion pair stability.constants can be neglected in this case. In the

present work, Ba–SO interactions have been evalu-4

ated from barite solubility data in sodium sulfate

solutions by determining the aqueous barium sulfate

ion pair stability constant as a function of tempera-

ture. The determination of the variation of this stabil-

ity constant with respect to pressure requires new

experimental data. It is nevertheless very likely that

this variation, which is neglected in the present

model, has only a minor effect on calculated barite

solubilities at high pressure in sulfate-rich systems.

The present model treats aqueous barium sulfate as a

weakly associated electrolyte in solution and its de-Ž .gree of association less than 20% up to 808C , only

slightly varies with temperature. The results reported

in Table 1 indicate that aqueous strontium sulfate is

an even stronger electrolyte than barium sulfate. Due

to the lack of celestite solubility data in sodium

sulfate solutions at various temperatures, the stability


Table2

Calculatedmeanactivitycoefficientsofaqueousbariumsulfateinseawateratvarioussalinitiesandthebaritesolubilityproductasafunctionoftemperatureandpressure

ŽŽ

.Ž

.Temperature

Pressure

Salinity

Banmolr

gBaSO

LogK

Barite

4sp

Ž.

Ž.

Ž.

.8C

bars

‰kgHO2

Ž.

Ž.

Falkneretal.1992

Thiswork

Falkneretal.1992

Thiswork

51

22

102

0.156

0.165

y10.36

y10.38

90

6

510

22

105

0.158

0.165

y10.34

y10.37

36

7

520

22

108

0.157

0.165

y10.33

y10.36

89

6

71

22

114

0.157

0.165

y10.31

y10.34

23

1

710

22

118

0.156

0.165

y10.30

y10.33

36

2

720

22

121

0.156

0.165

y10.29

y10.32

29

1

91

22

128

0.157

0.165

y10.26

y10.29

22

7

9100

22

162

0.156

0.168

y10.16

y10.19

79

9

9200

22

201

0.156

0.171

y10.07

y10.09

13

9

20

122

226

0.150

0.163

y10.05

y10.08

63

6

20

10

22

231

0.150

0.163

y10.04

y10.07

76

8

20

20

22

236

0.150

0.163

y10.03

y10.06

88

9

25

118

204

0.191

0.179

y9.96

y10.00

50

8

Ž.

Ž.

ChurchandWolgemuth1972

Thiswork

ChurchandWolgemuth1972

Thiswork

25

135

260

0.121

0.127

y9.96

y10.00

61

8

11

35

180

0.103

0.128

y10.27

y10.482

10

1500

35

360

0.121

0.144

y9.82

y9.957

82


constant of the SrSO0 ion pair cannot be determined40Ž .as accurately as that of BaSO aq . Provisional val-4

ues can be obtained using the value of Felmy et al.Ž . Ž .1990 at 258C and the enthalpy of Reardon 1983

0Ž .for the SrSO aq dissociation reaction.4

Only a few Pitzer’s mixing parameters involving

interactions between aqueous barium or strontium

and other cations are available for now. Missing

parameters are best determined from data on ternary

systems that do not exist at present. As such the

present model is limited to moderately concentrated

solutions, although it is difficult to give a quantita-

tive meaning to ‘moderately’. For example, barite

solubility in NaCl solutions can be accurately pre-

dicted to high concentrations at temperatures belowŽ .1008C Fig. 9 , but not above without fitting addi-

Ž .tional parameters Figs. 10 and 11 .

Pressure effects on the thermodynamic properties

of aqueous strontium and barium can be calculated

using the equations for the volumetric properties ofŽ . Ž . Ž .SrCl aq Phutela et al., 1987 and of BaCl aq2 2

Ž .Manohar et al., 1994 along with those for otherŽ .salts Monnin, 1990 in order to compute partial

molal volumes. The derived pressure effect brings

calculated celestite and barite solubilities either inŽ .pure water to 1 kbar Fig. 1 or in NaCl solutions to

Ž .500 bars Figs. 6 and 11 in good agreement with

measured values.

In the present model, due to the fact that most of

the mixing parameters are taken equal to zero, the

barite and celestite solubilities are almost exclusively

calculated from Pitzer’s binary parameters for simple

salts like NaCl, BaCl , SrCl , etc. Expressions giv-2 2

ing these binary parameters as a function of tempera-

ture have been shown to be valid to 08C, allowing

calculations to be carried out for oceanic conditions.

These expressions are summarized in Appendix A.

We can compare predicted activity coefficients ofŽ .BaSO aq in seawater to the results of Church and4

Ž .Wolgemuth 1972 and of Falkner Kenisson et al.Ž . Ž1993 . In Table 2 we report the total or stochiomet-

.ric mean activity coefficient of aqueous barium

sulfate calculated from the distribution of species

and the activity coefficients of the free ions with the

following relationship:

m 2q Pm 2y Pg 2Ba Žaq . ,t SO Žaq . ,t BaSO Žaq . ,t4 4

sm 2q Pm 2y Pg 2Ba Žaq . ,F SO Žaq . ,F BaSO Žaq . ,F4 4

ŽThe subscript t indicates the total concentration or.activity coefficient of the designated species. One

Ž .can see Table 2 that our results for the barite

solubility product are close to those of FalknerŽ .Kenisson et al. 1993 , but our values of the

Ž .BaSO aq activity coefficient are higher by about4

6% than those of Falkner et al. In agreement with

Falkner et al., we find that the variation of the

barium sulfate activity coefficient in seawater in the

moderate temperature and pressure range considered

here is slight, but that a salinity change from 18 to

22‰ has a noticeable effect. Although our value at

258C and 1 bar is close to that of Church andŽ .Wolgemuth 1972 , it is markedly different for 18C,

1 bar and for 18C, 500 bars. We also find that the

barite solubility product determined in this work is in

close agreement with values given by Falkner Kenis-Ž .son et al. 1993 at all temperatures and pressures

where comparison is possible. It is within 10% of

Church and Wolgemuth value at 258C and 1 bar, but

our value is smaller by almost a factor 2 at 18C, 1

bar and by about 40% at 18C, 500 bars. We have

used the present model to calculate the barite satura-

tion state of the world’s ocean. The results areŽ .presented elsewhere Monnin et al., submitted .

Acknowledgements

I am grateful to Roberto Pabalan and an anony-

mous reviewer for their careful and insightful re-

views of the present paper.

Appendix A

The MX activity coefficient and its partial molal

volume at T and P are obtained by calculatingsat

Pitzer’s interaction parameters and the Debye–

Huckel slopes at these conditions. The expressions of¨the various thermodynamic properties of aqueous

Žsolutions activity coefficients, partial molal vol-.umes, activity of water, etc. for simple systems and

for multicomponent mixtures within Pitzer’s formal-Žism are given in many papers see Harvie et al.,


Table 3Ž Ž ..Values of the fitting constants Eq. A1 for the binary interaction parameters for aqueous electrolytes

a a a a a1 2 3 4 5

a a a a a6 7 8 9 10

FA 3.36901531Ey01 y6.32100430Ey04 9.14252359E00 y1.35143986Ey02 2.26089488Ey03Ž .a 1.92118597Ey06 4.52586464Eq01 0.0 0.0 0.0

Ž0.NaCl b 1.43783204Eq01 5.60767406Ey03 y4.22185236Eq02 y2.51226677Eq00 0.0Ž .a y2.61718135Ey06 4.43854508Eq00 y1.70502337Eq00 0.0 0.0

Ž1.b y4.83060685Ey01 1.40677479Ey03 1.19311989Eq02 0.0 0.0

0.0 0.0 y4.23433299Eq00 0.0 0.0FC y1.00588714Ey01 y1.80529413Ey05 8.61185543Eq00 1.24880954Ey02 0.0

3.41172108Ey08 6.83040995Ey02 2.93922611Ey01 0.0 0.0

Ž0.Na SO b 8.16920027Eq01 3.01104957Ey02 y2.32193726Eq03 y1.43780207Eq01 y6.66496111Ey012 4

Ž .a y1.03923656Ey05 0.0 0.0 0.0 0.0Ž1.b 1.00463018Eq03 5.77453682Ey01 y2.18434467Eq04 y1.89110656Eq02 y2.03550488Ey01

y3.23949532Ey04 1.46772243Eq03 0.0 0.0 0.0FC y8.07816886Eq01 y3.54521126Ey02 2.02438830Eq03 1.46197730Eq01 y9.16974740Ey02

1.43946005Ey05 y2.42272049Eq00 0.0 0.0 0.0

KCl b Ž0. 2.67375563Eq01 1.00721050Ey02 y7.58485453Eq02 y4.70624175Eq00 0.0Ž .b y3.75994338Ey06 0.0 0.0 0.0 0.0

Ž1.b y7.41559626Eq00 0.0 3.22892989Eq02 1.16438557Eq00 0.0

0.0 0.0 y5.94578140Eq00 0.0 0.0FC y3.30531334Eq00 y1.29807848Ey03 9.12712100Eq01 5.86450181Ey01 0.0

4.95713573Ey07 0.0 0.0 0.0 0.0

Ž0.K SO b 4.07908797Eq01 8.26906675Ey03 y1.41842998Eq03 y6.74728848Eq00 0.02 4

Ž .b 0.0 0.0 0.0 0.0 0.0Ž1.b y1.31669651Eq01 2.35793239Ey02 2.06712594Eq03 0.0 0.0

0.0 0.0 0.0 0.0 0.0FC y1.88000000Ey02 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0

Ž0.CaCl b y9.41895832Eq01 y4.04750026Ey02 2.34550368Eq03 1.70912300Eq01 y9.22885841Ey012

Ž .a 1.51488122Ey05 y1.39082000Eq00 0.0 0.0 0.0Ž1.b 3.47870000Eq00 y1.54170000Ey02 0.0 0.0 0.0

3.17910000Ey05 0.0 0.0 0.0 0.0FC 1.93056024Eq01 9.77090932Ey03 y4.28383748Eq02 y3.57996343Eq00 8.82068538Ey02

y4.62270238Ey06 9.91113465Eq00 0.0 0.0 0.0

Ž0. Ž .CaSO b 0.15 f 0.0 0.0 0.0 0.04

Ž .a 0.0 0.0 0.0 0.0 0.0Ž1.b 3.00000000Eq00 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0Ž2.b y1.29399287Eq02 4.00431027Ey01 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0FC 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0

Ž0.MgCl b 5.76066000Ey01 y9.31654000Ey04 0.0 0.0 0.02

Ž .c 5.93915000Ey07 0.0 0.0 0.0 0.0Ž1.b 2.60135000Eq00 y1.09438000Ey02 0.0 0.0 0.0

2.60169000Ey05 0.0 0.0 0.0 0.0FC 5.95320000Ey02 y2.49949000Ey04 0.0 0.0 0.0

2.41831000Ey07 0.0 0.0 0.0 0.0


Ž .Table 3 continued

a a a a a1 2 3 4 5

a a a a a6 7 8 9 10

Ž0.MgSO b 9.39251515Eq01 y5.14100000Ey01 y6.84801984Eq03 0.0 0.04

Ž .c 1.41316667Ey03 0.0 0.0 y1.94722500Ey06 1.07875000Ey09Ž1.b 5.28624842Eq02 y1.47980000Ey01 y5.78048532Eq03 0.0 0.0

1.57606667Ey04 0.0 0.0 0.0 0.0Ž2.b 1.06150006Eq03 y6.88200000Eq00 y6.78768888Eq04 0.0 0.0

2.02016667Ey02 0.0 0.0 y2.30350000Ey05 0.0FC y3.71761334Eq01 2.10820004Ey01 2.62610734Eq03 0.0 0.0

y5.95440002Ey04 0.0 0.0 8.36666686Ey07 y4.6872000Ey10

Ž0.SrCl b 4.42847700Eq00 y1.09557500Ey02 y5.12215000Eq02 0.0 0.02

Ž .d 9.44275000Ey06 0.0 0.0 0.0 0.0Ž1.b 1.14437700Eq01 y3.36065000Ey02 y1.06459300Eq03 0.0 0.0

4.24357000Ey05 0.0 0.0 0.0 0.0FC y1.54490900Ey02 0.0 4.51223000Eq00 0.0 0.0

0.0 0.0 0.0 0.0 0.0

Ž0.BaCl b 3.43831400Eq01 6.37500000Ey04 y1.33653000Eq03 y5.30213100Eq00 0.02

Ž .e 4.60872500Ey06 0.0 0.0 0.0 0.0Ž1.b y1.04230500Eq02 3.22500000Ey03 4.37411000Eq03 1.58751700Eq01 0.0

y6.77403000Ey06 0.0 0.0 0.0 0.0FC y2.41201200Eq01 y1.53700000Ey04 7.87197800Eq02 3.90395300Eq00 0.0

y1.10262000Ey05 0.0 0.0 8.76150800Ey09 0.0

Ž . Ž . Ž . Ž . Ž . Ž . Ž . Ž . Ž . Ž . Ž .a Moller 1988 ; b Greenberg and Moller 1989 ; c Pabalan and Pitzer 1987 ; d Phutela et al. 1987 ; e Monnin 1995 ; f note thatŽ0.Ž . Ž .the b CaSO parameter is reported as 0.015 by Greenberg and Moller 1989 . This seems to be an error although these authors refer to4

Ž . Ž .the paper of Moller 1988 . When used instead of 0.15, this value 0.015 leads to noticeable discrepancies in the calculation of the

thermodynamic properties of aqueous calcium ion.

1984; Pabalan and Pitzer, 1987; Weare, 1987; Moller,

1988; Greenberg and Moller, 1989; Monnin, 1989,.1990; Pitzer, 1991, among others . Pabalan and Pitzer

Ž . Ž . Ž .1987 , Phutela et al. 1987 , Moller 1988 , Green-Ž . Ž .berg and Moller 1989 and Monnin 1995 have

used different empirical functions describing the

variation of Pitzer’s parameters with respect to tem-

perature. For computational ease, these functions can

be recast into the following ten parameter expression

using simple algebraic transformations:

a a3 5 2X T sa qa Tq qa lnTq qa TŽ . 1 2 4 6T Ty263

a a7 8 3 4q q qa T qa T9 10680yT Ty227

A1Ž .

Ž . Ž0.with X T being either Pitzer’s parameters b ,

b Ž1., b Ž2., CF, Q orC or their first derivatives with

respect to pressure noted b Ž0.,v, b Ž1.,v, b Ž2.,v, CF ,v,

v v Ž .Q orC . The a constants in Eq. A1 are given ini

Table 3 for Pitzer’s interaction parameters for pure

electrolytes and in Table 4 for the ternary parame-

ters. These constants for the standard partial molal

volumes of the aqueous solutes and for the interac-

tion parameters for their volumetric properties are

reported in Table 5.Ž .Moller 1988 established the following expres-

sion for the variation with temperature of AF, the

Debye–Huckel slope for the activity coefficient:¨

AFs3.36901531=10y1y6.32100430=10y4T

q9.14252359rTy1.35143986

=10y2 lnTq2.26089488=10y3r Ty263Ž .

q1.92118597=10y6T 2q4.52586464

=101r 680yTŽ .


Table4

ŽŽ

..FittingconstantsEq.A1forPitzer’sternaryinteractionparameters

aa

aa

aa

12

34

56

Ž.

Ž.

uCl,SO

25–150a

0.07

0.0

0.0

0.0

0.0

0.0

4

Ž.

Ž.

uCl,SO

150–250a

5.67983244Eq1

y1.63021206Ey1

y1.8747982Eq4

5.70511185

8.900099309Eq2

9.2144343Ey5

4

Ž.

Ž.

cNa,Cl,SO

25–150a

y0.009

0.0

0.0

0.0

0.0

0.0

4

Ž.

Ž.

cNa,Cl,SO

150–250a

y3.29811409Eq2

y4.42410302Ey2

1.62957351Eq4

5.16258079Eq1

y3.53341751Eq2

0.0

4

Ž.Ž.

cK,Cl,SO

ay2.12481475Ey1

2.4869833Ey4

3.7561961Eq1

0.0

0.0

0.0

4

Ž.Ž.

cCa,Cl,SO

ay0.018

0.0

0.0

0.0

0.0

0.0

4

Ž.Ž.

cMg,Cl,SO

by1.174Ey1

0.0

32.63

0.0

0.0

0.0

4

Ž.Ž.

uNa,K

ay5.02312111Ey2

0.0

1.40213141Eq1

0.0

0.0

0.0

Ž.Ž.

cNa,K,Cla

1.34211308Ey2

0.0

y5.10212917

0.0

0.0

0.0

Ž.

Ž.

cNa,K,SO

0–150Ca

3.4811517Ey2

0.0

y8.21656777

0.0

0.0

0.0

4

Ž.

Ž.

cNa,K,SO

150–250Ca

6.56482122y2

0.0

y2.12621122Eq1

0.0

0.0

0.0

4

Ž.Ž.

uNa,Caa

0.05

0.0

0.0

0.0

0.0

0.0

Ž.Ž.

cNa,Ca,Cla

y0.003

0.0

0.0

0.0

0.0

0.0

Ž.Ž.

cNa,Ca,SO

ay0.012

0.0

0.0

0.0

0.0

0.0

4

Ž.Ž.

uNa,Mgb

0.07

0.0

0.0

0.0

0.0

0.0

Ž.Ž.

cNa,Mg,Clb

1.99Ey2

0.0

y9.51

0.0

0.0

0.0

Ž.Ž.

uNa,Src

0.051

0.0

0.0

0.0

0.0

0.0

Ž.Ž.

cNa,Sr,Clc

y0.0021

0.0

0.0

0.0

0.0

0.0

Ž.Ž.

cNa,Ba,Cld

0.0128

0.0

0.0

0.0

0.0

0.0

Ž.Ž.

uK,Caa

0.1156

0.0

0.0

0.0

0.0

0.0

Ž.Ž.

cK,Ca,Cla

4.76278977Ey2

0.0

y2.70770507Eq1

0.0

0.0

0.0

Ž.Ž.

cK,Ca,SO

a0.0

0.0

0.0

0.0

0.0

0.0

4

Ž.Ž.

uK,Mgb

0.0

0.0

0.0

0.0

0.0

0.0

Ž.Ž.

cK,Mg,Clb

2.586Ey2

0.0

y14.27

0.0

0.0

0.0

Ž.

Ž.Ž.

Ž.Ž.

Ž.Ž.

Ž.

aGreenbergandMoller1989;bPabalanandPitzer1987;cReardonandAmstrong1987;dMonnin1995.Allotherparametersareequaltozero.


Table 5

Fitting coefficients for the interaction parameters for the partial molal volumes and for the standard partial molal volumes of aqueousŽ Ž ..electrolytes Eq. A1

a a a a a1 2 3 4 5

a a a a a6 7 8 9 10

0Ž .NaCl a V 8.520003Ey02 y3.581619 y7.515469Eq04 0.0 0.0

7.234513Ey03 0.0 y3.007338Eq02 y5.839699Ey06 0.0Ž0.,vb 5.3699517Ey05 y2.6538013Ey07 0.0 0.0 0.0

8.6255554Ey10 y2.682931Ey02 2.2020163Ey03 0.0 0.0Ž1.,vb 3.200188Ey3 y1.092875Ey06 y8.373935Ey01 0.0 0.0

y7.1016610Ey9 0.0 4.901041Ey02 0.0 0.0F ,vC 1.145144Ey05 y4.527545Ey08 0.0 0.0 0.0

4.34633Ey11 2.595239Ey04 y2.165713Ey04 0.0 0.0

0Ž .Na SO b V 1.281259Eq03 y3.292342 y1.231424Eq05 0.0 0.02 4

4.267199Ey03 y9.132116Eq04 1.067946Eq3 0.0 0.0Ž0.,vb 5.3088Ey05 4.33707Ey6 1.42266Ey01 y2.70953Ey04 0.0

y3.262413Ey09 0.0 4.51986Ey03 0.0 0.0Ž1.,vb 3.200188Ey03 y1.092875Ey06 y8.373935Ey01 0.0 0.0

y7.1016610Ey09 0.0 4.901041Ey02 0.0 0.0F ,vC y2.7186409Ey04 1.84544081Ey6 7.1598902Ey02 0.0 0.0

y7.10166104Ey09 0.0 y4.1886382Ey03 0.0 0.0

0Ž .CaCl b V 4.175000Eq01 4.121094Ey01 0.0 0.0 0.02

y2.841949Ey4 y4.35200Eq04 y5.54500Eq02 0.0 0.0Ž0.,vb y9.949027Ey05 4.549863Ey7 0.0 0.0 0.0

y3.008955Ey10 y1.201352Ey2 2.501298Ey3 0.0 0.0F ,vC 2.34138Ey5 y1.405386Ey7 0.0 0.0 0.0

2.97171Ey10 0.0 y1.7478264Ey4 y2.146539Ey13 0.0

0Ž .MgCl c V y1.798135Eq03 1.719652Eq01 0.0 0.0 0.02

y5.421483Ey02 0.0 0.0 5.6747Ey05 0.0Ž0.,vb y5.4648Ey04 2.6088Ey06 0.0 0.0 0.0

y3.2424Ey09 0.0 5.116Ey03 0.0 0.0F ,vC 2.2968216Ey05 7.121304Ey080.0 0.0 0.0 0.0

1.8013521Ey07 0.0 y2.131572Ey04 0.0 0.0

0Ž .SrCl d V y1.22812Eq03 4.2668 1.19602Eq5 0.0 0.02

y4.80302Ey03 0.0 0.0 0.0 0.0Ž0.,vb y2.14925Ey04 0.0 7.65753Ey02 0.0 0.0

0.0 0.0 0.0 0.0 0.0Ž1.,vb y7.54375Ey05 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0F ,vC 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0

0 Ž .BaCl V e y1.553467Eq02 6.3836Ey01 0.0 0.0 0.02

y1.7000Ey02 0.0 0.0 0.0 0.0Ž0.,v Ž .b f 8.670239Ey5 y4.977946Ey7 0.0 0.0 0.0

5.583802Ey10 0.0 2.154935Ey3 0.0 0.0Ž1.,v Ž .b f 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0F ,v Ž .C f y8.240557Ey5 2.433938Ey7 0.0 0.0 0.0

0.0 0.0 7.142877Ey4 0.0 0.0

Ž . Ž . Ž . Ž . Ž . Ž . Ž . Ž . Ž . Ž . Ž .a Rogers and Pitzer 1982 ; b Monnin 1990 ; c Monnin 1989 ; d Phutela et al. 1987 ; e Puchalska and Atkinson 1991 ; fŽ .Manohar et al. 1994 . Note that the CaCl parameters can be used in place of these. See text.2


The Debye–Huckel slope for the partial molal¨v Ž .volume, A , is given by Monnin 1990 as a function

of temperature: from 0 to 1008C,

Avs8.106377y1.256008=101Tq7.760276

=10y4T 2y2.098163=10y6T 3q2.25777

=10y9T 4

from 100 to 3008C:

Avs3.849971=102y6.982754Tq3.877068

=10y2T 2y1.11381=10y4T 3q1.589736

=10y7T 4y9.395266=10y11T 5q6.469241

=10q4r 680yTŽ .

When necessary, concentration scale conversions

have been carried out using the VOPO programŽ .Monnin, 1994 .

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A Thermodynamic Model for the Solubility of Barite and Celestite

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