Pergamon Calphad Vol. 21, NO. 4, pp. 521-534, 1997

Q 1998 Published by Elsevier Science Ltd Printed in Great Britain. All rights reserved

0364-5916198 $19.00 + 0.00

PII SO364-5916(98) 00009-I

MODELLING OF MULTICOMPONENT SALT SYSTEMS

Application to sea water and brines

I. Derivation of the model

Roger Cohen-Adad*, Dalila Ben Hassen-Chehimi**, L.&i Zayani***, Marie-The&e Cohen-Adad*, Malika Trabelsi-Ayedi **, Najia Kbir-Ariguib***

* Labor-at&e de Physicochimie-Min6rale 2, Universid Claude Bernard Lyon I 43 Boulevard du 11 Novembre 1918, F-69622 Villeurbanne Cedex , France

** Laboratoire de Physicochimie-Minerale, Faculte des Sciences de Bizerte 7021 Zarzouna, Bizerte, Tunisie

***L.aboratoire de GEnie des Pmc6d6s Institut National de la Recherche Scientifique et Technique B.P.95 Hammam-Lif, Tunisie

(Presented at CALPHAD XXV, Erice, Sicily, Italy, May 1996)

ABSTRACT

The solubiiity of a salt in saturated solution is described in terms of heterogeneous reaction between solid and liquid and an equation of the solubility field is established for each solid phase (limiting or intermediate phase) of a multicomponent aqueous salt system.

The model supposes that solid phases are stoichiometric and that the solution is a strong electrolyte. It includes all sub-systems and the procedure used for the calculation of coefficients is described.

The equations allow the critical evaluation of solubiiity data, the calculation of phase diagrams and the determination of equilibrium (proportion and nature of phases) under any conditions of temperature and composition.

The application to the sub-systems involved in sea water and natural brines will be developed in forthcoming publications.

Key words : Multicomponent, salt, sea water, brine, critical evaluation, mode&g

This work is a contribution to a large project developped in Tunisia to find the possibilities of exploitation of brines from “Sebkhats” and “Chotts” (salt lakes). The main tar solubility fields involved in the quinary system Na +, K+, 9

et of the overall project is the modeling of all Mg + I Cl-, SO42- I/ Hz0 in order to derive, in a

further stage, the treatment of bitterns and in particular an extraction process of potassium salts.

The present paper is focused on the derivation of an adapted model. The application to critical evaluation of solubility data and to a computer assisted representation of the systems involved in the treatment of sea water and natural brines will be presented in forthcoming publications. At last the application to an industrial process will be studied.

Original version received on 26 August 1997, Revised version on 28 October 1997

521

522 Ft. COHEN-ADAD et al.

Similar projects are developed around the world, and particularly in the frame of IWAC where a critical evaluation of solubility data concernin g sea water systems has been undertaken (commission V.8, Solubility Data Series) [ 11, and of European Community [2]. Our task is complementary to the work performed in these groups and limited to the data involved in the treatment of brines. A compilation on sea water systems had already been performed around 1930 by D’Ans [3], but the data had to be updated and more readable graphical representations than that of Liiwenhertz [4], used in most cases by D’Ans, had to be employed.

The main difficulties of modelling are co~ected to the complexity of the sea-water system [5] : about 70 elements are contained in the brine, but there are seven major ions, Na, K, Mg, Ca, Cl, sulphate, carbonate involved in a crystalbzation sequence. The others (minor and trace elements) remain, in prmciple, in the bittern. Their concentration in creases during an evaporation process and they can induce a significant modification of the ionic strength of the medium. Calcium ions disappear almost in totality during the first stages of crystallization as CaCO3, CaS04 or CaSO42H20 so that investi reciprocal system Na+, K+, Mg2’ // Cl-, f

ations on sea water can be reduced to the study of a fifth order SO4 - - Hz0 (type 3/2 in the Radischev classification [6]) and the

quinary system involves 20 aqueous sub-systems (table I) :

TABLE I

Sub-systems of the Quinary System Na+, K+t l&2+// Cl-,SO42- - Hz0

Number Systems

Binary 6 NaCl - Hfl NazSO4 - Hz0 KCl - Hz0 K2SO4 - H20 Mgc12 - H20 MgS04 - H20

Ternary 9 NaCl - KC1 - Hz0 NaCl - MgCl2 - Hfi KCl - MgCl2 - Hz0 NaCl - Na2SO4 - Hfl KCl - K2SO4 - Hfi MgCl2 - MgS04 - Hz0

Na2SO4 - K2SO4 - H20 Na2SO4 - MgS04 - H@ K2SO4 - MgS04 - Hfl

Simple

Reciprocal

NaCl - KC1 - MgC12 - Hz0 NqS04 - K2SO4 - MgS04 - H20 Na+v K+ N Cl-,SO42- - Hfi Na+* Mg2’// Cl-,SO42+ - Hz0 K+, Mg2+// Cl-,SO42- - Hz0

EXPRESSION OF COMPOSITION

The use of molalities is not convenient for exIme.ssion of composition because, in a study of phase diagram, the data are considered in all extents of composition and a symmetrical representation is necessary. Furthermore the charge of ions must be taken in account for reciprocal systems, so that the composition of a mixture in the quinary system is expressed in solute mole f?actons by mole of cations or anions (Jtiecke coordinates, relations 1)

X,,, =n,/D xK =%cD XM -hP YC = ncP Ys = 2n s/D ZH =nH/D with D=nN+nK+2nM=nc+2ns and X,+X,+X, =Yc+Ys -1

(1)

The quantities nN,nK,nM,nc,ns,nB are the amounts of Na+, K+, Mgz+, Cl-, SO42-, Hz0 and D expresses the electric neutrality of the solution.

The samples are always prepared from salts and the composition must also be expressed in mole fraction of saltsx,:

x, =n,/E with Q'nNC,nKC,nMC,nNS,nKS,nMS,nH and E=xn,, (2) Q

MODELLING OF MULTICOMPONENT SALT SYSTEMS 523

A conversion between Jtiecke coordinates and mole fractions of salts is necessary and relations 1 become :

& = hw +2niv, J/F x, = cx KC + 2xKS )/F

x&f ‘bwc +xhfs p 2, =x,/F (3)

‘C =(‘NC +XKC +2xMC)/F ‘S = 2(xNS +‘KS +‘MS )/F

With F=l+xMC +XNS +XKS +XMS -XH

In relations (2) and (3) n N=, n KC,n MC, n NS, nKs, n MS, n H are the basic components NaCl, KCI, MgC12, NazS04, K2,SO4, MgSO4, H20.

It is also very useful to express the composition in actual water or ionic mole fractions, i.e. mole fractions based on the composition expressed in terms of individual ions :

YN =(.TNc+~~N& YK=(XKC+~KS)/G

Y M =bm+xm)/G Y H =xH/G (4)

Yc=(XNC+XKC+~MC)/G Ys=(X~s+Xus +XYS)/G

with G=2+x MC +xNS +XKS -xH

REPRESENTATION OF THE PHASE DIAGRAM

At constant tempetature and pressure the variance of a quinary system is four, so that the representation of the phase diagram requires the use of two projections in three dimensional spaces, one for salts, one for the content in waterThe salts composition is located in a prism (figure 1) where apices correspond to NaCl (NC), KC1 (KC), Mgclz (MC), Na2SO4 (MS), K2SO.t (KS), IWO4 (MS).

WO,

FIG. 1

Representation of quinary system Na+, K+, Mg2’ fJ Cl-, SO42- - Hz0 Soiubility field of NaCl

524 R. COHEN-ADAD et al.

The content of water can be presented in a planar projection, or preferably in a space projection as function of

xK andXy.

FIG. 2

Quirnuy system Na+, K+, Mg2’ I! Cl-, SO42- - Hz0 JZnecke mole fraction of water

During the treatment of a brine the solution is always saturated in NaCl, so that the representation of the quinary phase diagram can be limited, in a first stage, to the solubility field of NaCl under isobaric-isothermal conditions. Twenty nine compounds can be observed in the phase diagram (table JI), but as shown in figure 1 the solubility field of NaCl is a volume limited at 25°C by 12 faces corresponding to the coprecipitation of NaCl and other compounds ; 36 edges related to the coprecipitation of three compounds (for example the line fm corresponds to the coprecipitation of sodium chloride, potassium chloride and glaserite), 25 apices related to the coprecipitation of four solid phases (invariant isothermal-isobaric equilibria). The right angle of the figure has been expanded in order to show the crystallization range of bischoffite.

TABLE II

Main Observed Compounds at 25°C

Symbol

k

NC2

E MC6 NS NS7 NSlO KS KS1 MS

Name

Elite

Sylvinite

Bischoffite Thenardite

Mimbilite Arcanite

Formula

H20 NaCl

E1*2H20 MgcIz MgClr 6H20 Na2SO4 Na2SOe 7H20 Na2SOe 1 OH20 K2S04

KzS04 Hz0 MgSO4

NaCl+Salt

bfmnpqe

al& shcg

MODELLING OF MULTICOMPONENT SALT SYSTEMS 525

-Symbol

MS1 MS1 MS4 MS7 KMC6 1.5KMC2 N3KS NMS NMS2.5 NMs4 3NMs KMS2 KMS4 KMS6 K2MS KMCQ 3NC9NMS

TABLE II (continuation)

Name Formula NaCl+Salt

Sakeite Kieseaite Leonhardite Epsomite

Camallite

Loeweite AstmlGkte Vrilrthoffite

Leo&? Schonite Langbeinite Kainite D’Ansite

MgSO‘t.HzO MgSOqH20 MgSO~4H20 MgSOK 7H20 KCl. MgClr 6H20 lSKCl.MgCl~2H20 NazSOq 3K#O4 Na2SOK MgSO4 Na2SO~MgSO4-2.5HzO N&IO‘+. MgSOe4HzO 3Na2SOcMgSO4 K2S04’ MgSOK 2H20 K2SOe MgSOK 4H20 K2S04’ MgSOe 6H2O K2~&2@~4 KCl. MgSOF 3Hfl 3NaCI9Na#Oc MgSO4

YUb vijxw

esrdx

fgstm

ihstuv

unpwv tumn

The amount of water, along the solubility field of NaCl, is represented by a volume (figure II) and a single

value2; is associated to each set (Xi, XL, Yi ). As long as Z, > Z$ the brine is not saturated in sodium

chloride.

ATMENT OF DATA

The modelling of sea water phase diagram requires an accurate knowledge of the solubility field of all solid phases involved in a crystalkation process, in the range of temperature concerned by industrial treatments, i.e. *C to 120°C and there is an enormous amount of data concerning the various solubility domains (for example more than 130 references and 2OOO solubility data are found in literature for the quaternary simple sub-system Na+ K+ Mg2’ // Cl- - H20). * 1

The raw solubility data collected in publications are generally expressed in various units and must be converted to mass % , mole fraction and/or ionic mole fraction of anions or cations. There are frequently great discrepancks between the results of the different authors, even when they are presented with the same precision. A critical evaluation of raw data.must consequently be performed. It is based on appropriate models and contains always adjustable coefficients, whatever the model.

Several models have been proposed in the literature for the calculation of salt stems and, for example, the Piker model based on the calculation of ion interaction parameters in solution [7, sy ] describes successfully the isothermal sections of multicomponent salt systems and has been extended to equilibria at various temperatures.

The model developed in this paper is especially adapted to the critical evaluation of solubiity data over a large range of tempemture and composition [9-l l] and to a computer-assisted treatment of brines. It involves the representation of each solubility domain of the system, using all experimental data (solubility or thermodynamic variables), whatever the composition and temperahue.

The basic theory for calculation of solubility of a salt in sammted solution is well known [ 121 and is usually described in terms of heterogeneous reaction between solid and liquid An analytical equation of the solubility field is deduced from the thermodynamic condition of phase equilibrium by equating the chemical potentials. For example the dissolution of camallite KCl.MgClz 6H2O in water cormsponds to the reaction :

KCl.MgC1,.6H,O * K’ +Mg2’ +3Cl- +6Ha0 (5)

526 R. COHEN-ADAD et al.

and the condition of phase equilibrium in the soltiity domain is :

The model supposes that brines are strong electrolytes and that the observed solid phases (ice, salts, hydrates) are stoichiomebic. As seen further the validity of these assumptions can be checked a posteriori, by correlation between experimental and calculated phase change enthalpy at the congruent melting point of the considered species [ 131, but as such they are sufficient for modelling the soltiility fields of the sea water system. The model may also be applied to stoichiometric phases of non-electrolytes or extended to systems involving associated solutions [ 141.

EOUATION OF SOLUBILITY FIELDS

The thermodynamic condition of equilibrium along the solubility field of a compound is :

dpso, = j&b or d(tL,D)=~vid(~ib’) (7) i

where CL_,, , pi and Vi are respectively the chemical potentials of the solid compound, the chemical potential in the liquid phase of a constituent i (ion or water) present simultaneously in solid and liquid and the stoichiomet& coefficient of i in the reaction involved in solubility process Equation (7) is applied to all solubility fields of the system.

The calculation of salt solubilities in electrolyte solutions is usually performed through the determination of i) standard-state chemical potentials of solids and of aqueous species at the temperature of interest and ii) activity coefficients of aqueous species as functions of composition, temperature and pressure [12]. The main differences of our approach concern the choice of a particular reference state for activities and the expansion in series of the bulk activity coefficient in a sohtbility domain.

After development of the chemical potentials according to :

cli -flg +RTlnai

equation (7) can be written :

(8)

x vid lnai = M/(RT’)dT i

(9)

ai is the activity of i, AH is the reaction enthalpy , i.e the enthalpy of fusion and dissociation of the compound in

standard state at temperature T .

The equation of the solubility field is obtained by integmtion of (9), taking for limit the congruent melting point T,, of the pure compound in a stable or metastable state. This poinf is also taken as a particular reference state for evaluation of activities along the considered solubility surface so that the equation becomes :

(10)

After separation of the activity coefficients, equation (10) can be written, along the solubility field of the compound :

u-u0 =v -v” -In&/To) (11)

MODELLING OF MULTICOMPONENT SALT SYSTEMS 527

U represents the solubility product logarithm of the speck in equilibrium with liquid and Uo is the same quantity considered at stoichiomeby :

U=CVilnXi U” =xvilnxP with Xp =vi Cvj i i I i

(12)

it is reduced to ln(x i/x: ) if the solubility surface concerns a molecular compound (water).

V is obtained by integration of the enthalpic term of equation (10). The reaction enthalpy AH’ can be developped in a series and may be written :

AH = AH’ +AC”(T -To)+... (13)

where AH o and AC’ are respectively the enthalpy and heat capacity of phase change at the reference temperature

and composition. By substitution of AH in the second member of (lo), V - V" can be written :

V -V” =a IT +b InT +c +dT +....

with a = --( AH0 - ACOT, )/R

b = AC0 /R

c-(AH”/To -AC’[l+lnT,])/R

(14)

(15)

The phase change enthalpies and heat capacities AHo , AC’ are known only for ice and for the most usual

salts involved in sea-water system, so that in general a ,b , c ,d . . . must be considered as adjustable parameters.

The third term of relation (11) expresses the deviation Ram ideality and includes the interactions in solution :

ln( I/T” ) = F vi In@, /ff )

and the activity coefficients fi and f p are for saturated solution, in the solubility field

. . Develooment of Bulk Actlvltv Cm

There is in the literature a very great number of data concerning the values of mean activity coefficients of dilute electrolyte solutions at 25OC, but much less for concentrated complex mixtures of electrolytes and very few at high or low temperature. Usually the bulk activity coefficient of the solutes is found by integration of the activity coefficient of water using the Gibbs-D&em equation and its value at mom temperature in dilute sohrtion is extrapolated in composition and temperature to saturation, using models ]8,15-281.

We had used this pmcedure in a previous publication [29] where the modeEng of water activity coefficient along the liquidus curve of ice had been performed in binary systems MCI-Hfl (M= Li, Na, K, Rb, Cs, NIQ).

For most solubility fields in the quinary system this method cannot be applied because i) the osmotic properties of solution are often unknown, ii) the expression of activity coefficient depends directly of the assumptions made for the modelling of the electrolyte solution, iii) modelhng of the bulk activity coefficient in a solubility field requires an extrapolation in composition and temperature tiom dilute to concentrated solutions. The isothermal variation with composition of the bulk activity coefficient is not very important in the solubility domain of salts, since the ionic strength of such media is high and its relative change with composition is small, but an extrapulation from dilute solution is hazardous due to the anomaly of strong electrolytes 130-321. The variation of activity coefficients with temperature is much more significant.

Along the solubility surfaces the activity tent has therefore been determined from solubility data through an expansion in series. The same kind of development as for the entipic term (relation 14) has been used since the

528 R. COHEN-ADAD et al.

quantity LW” -RT’C Vi InO;) represents th e molar enthalpy of phase change m and is closely related to I

the reaction enthalpy at the melting point, andthe general equation of a solubility field can be written :

U=A IT +BlnT +C+DT+... (17)

DEPENDENCE OF COEFFICIENTS ON COMPOSITION

In order to take in account the variation of solubility of a species with composition, the coefficients A , B , c, D . . . have been expanded in series and the same kind of series has been used for all coefficients. Under isobaric conditions, the variance in a solubility field is v = c - 1 and consequently the adjustable coefficients are chosen to be independent of composition in a binary sub-system.

The development of adjustable coefficients must comply with some constraints i) It must fit with the quinary system and with any simple or reciprocal sub-system as well. ii) The solubility and the activity coefficients depend on the nature of solutes as shown in figure 3 where the solubility of ice in solutions of alkali halides is given as a function of temperature [29].Ice is involved in six binary sub-systems (NaCl-H20, KCl-H20, MgQ-H20, Na2S04-H20, K2S04-H20, MgS04-H20) and the adjustable coefficients of ice must be different in each of these systems.

_” 0 0,oz O,O‘l 0.06

FIG. 3

Solubility of Ice in Alkali Halide solutions

Several empirical expressions have been tried and compared. They give a very good simulation when limited to a single system [34-361, but most of them are unable to fultil all constraints. Actually two polynomial series are proposed which till almost all criteria of selection.

The first has been tested with simple systems such as NaCI-KCI-H20, MgClz-KCI-Hz0 and MgClz-KCl- MgClz-Hz0 [37, 381 and gives a good description of the solubility surfaces, but its application to reciprocal systems and to the solubility range of ternary or more complex salts is not easy. The coefficients along the solubility domain of a compound are :

MODELLING OF MULTICOMPONENT SALT SYSTEMS 529

(18)

vi, xi are respectively the stoichiometric coefficient and the mole fraction of constituent i (salt or water) in the

compound, LI ii , a ‘jk are adjustable coefficients; j, k, . . . are different from i.

The second is more convenient for reciprocal systems. The ions are separated as cations N , K , M and anions

C , s . The general equation of the solubility field of a compound in the quinary system is written :

A(U)= C EXiYj

i J

where A ((T) is an adjustable coefficient of the solid phase o solubility field (for example H, NC or NC2 in the

binary system NC-H20) Xi and Yj represent respectively the composition variables of cations and anions in

the considered system, U, V, and W are also composition variables of anions or cations (X or Y) with the

conditionsthatk+i,j ;Z+i,j,k ;m +i,j,k,l. X) isthecompositionvariableofconstitnentimisedto power n,

The former relation includes the solubility fields of all sub-systems. a “( 6) is the coefficient of species u in

the binary system (i,j)-H20. a”(o) = 0 when i and j are not constituents of u except for the solubihty field of

ice where a”(H) f 0 for all binary sub-systems. afk (0) is the coefficient of U; in the ternary system (i, j,

k)-H20, en:. For example the solubility domain of NaCl is observed in seven sub-systems, one binary, 3 ternary,

3 quaternary and the development in series of A (NC) contains one parameter uNC (NC) related to the binary

system NaCl-H20, n parameters for each ternary sub-system (u:~‘(NC),U~~“~ (NC),UfCS (NC)), np

parameters such as u$” (NC) f or each simple or reciprocaJ quaternary system , npq parameters for the quinary system.

The numbers of terms, n, np, npq are chosen in order to get the best adjustment of the isothermal solubility curve and in many cases they can be reduced to 1 or 2.

For a ternary salt (two cations-one anion or one cation-two anions), hydrated or not :

uk((o)XiYjUk +I: UT(U)+ CWiUg”(O)

P 4 (20)

INSTABLE COEFFICIENTS

The procedure used for calculation of adjustable coefficients is described in the present paper but the application to concrete systems will be developped latter. The detmmination of the coefficients in equation (19) is performed step by step, starting from the simplest sub-systems.

If we consider, for example, the solubility field of NaCl in the quinary sea-water system, the coefficients of the fitting equation for the soltiility field of NaCl are demrmined successively in one binary system (NaCl-Hfl), in three ternary systems (NaCLKCLH20, NaCLMgCl2-Hfl, NaCl-Na#O&-Hfl), in one quaternary simple system (NaCl-KCl-MgCl2-HZO), in two reciprocal quaternary systems (Na+, K+//Cl-SO$-=HzO, Na+, Mg2+//CPSO$-=Hfl and then in the quinary system.

530 R. COHEN-ADAD et al.

Binarv Svstem NaCI-H?o,

The procedure has been described in previous publications ]9- 111. The first member of the aeneml equation (17) canbewritten:

U = In(y Ny c)= ln(XNYc)+ 2ln(F/G)

in which X, = Yc = 1 and the first member of equation (23) is reduced to :

u =21n(k/(l+k))

The melting point of NaCl (T, = 1073.8k 1 K [38]) isintroduced in equation (17) which becomes ::

=A,,(lP -lPo I+& ln(T/T,)+D,,(T --To >+...

(21)

(22)

(23)

The determination of the fitting equation and the critical evaluation of data are performed simultaneously : i) The raw data of solubility are converted in mole fractions and a graphical selection is performed in order to delete the obviously aberrant values of solubility. ii) A set of coefficients of the fitting equation is then determined by linear regression, and the equation is used to recalculate all experimental dataiii) Relative deviations between calculated values and experience are determined. Limits are fixed to relative deviations in order to select 80% at least of the initial data and these data are used to recalculate the coefficients. iv) The treatment is repeated until two successive iterations give the same set of coefficients.

Te best results were obtained with four coefficients (table IIl) 191. The coefficients of the binary system are then introduced in the calculation of more complex systems.

TABLE IU

Binary system NaCLH20 C!oefficients of fitting equation, Solidus of Nail [9]

COeffici~tS Conditions Rangen<

A= 99.14456 K melting point of NaCl, peritectic point 273 - 1073 B = - 1.53935 deviations : c = 7.24959 l&SK-’ lax/x (calc)l co.01 if t < 1looC D= 2.86411 l#x (talc)] ~0.25 if t > 1 WC

Higher-order svstems

In the experimental methods of determination of multi-component salt systems, isothermal sections of the diagram are usually determined first. The same procedure has been used for the calculation of coefficients of the fitting equation.

The expressions of coefficients in relations (19) are reported in equation ( 17) and the terms are grouped together in order to explicit the composition variables. After substitution the equation becomes for the soiubility field of NaCl (relation 24) :

MODELLING OF MULTICOMPONENT SALT SYSTEMS 531

where the coefficients m are constant under isothermal conditions In the ternary system NaCl-KCl-H20, taken as example, relation 24 is reduced to :

m, NKC := #KC n b +brKC ln(T)+c~KC +dfKCT

I \

(25)

(26)

(27)

The determination of coefficients m is made according to the same procedure : i) A graphic selection of the data located on each isothermal section of the diagram is performed and the abarant data are set aside. ii) The values of

coefficients m ,“” are determined from eq. 25 and 27 by linear regression, for all isothermal sections of the

diagramiii) thecoefficients afKC,b~KC,cfKC,dfKC are calculakd by a second linear regression, using the NKC variation of m R . . . with temperature (relation 26) iv) once determined, the adjustable coefficients are used for

recalculation of ail experimental solubiity da@ including the values not located on isothermal sections or not taken in account in the first determination, v) deviations are adjusted in order to eliminate aberrant values and to select a new set of data (about 80% if initial data), vi) the same procedure is repeated until two successive iterations give

thesamesetofcoefficientsa~KC,b~KC...

As for binary sub-systems the critical evaluation of data and the determination of fitting equation are performed simultaneously. Then calculated coefficients for ternary systems are introduced in equation 24 and the coefficients of higher order system are cakulated.

The knowledge of the fitting equations allows the calculation of solubility under any conditions of composition or temperature, and a rational study of extraction processes. All stages of a crystallization sequence can be foreseen and calculated but an experimental control of the results is always necessary, due to the fact that brines and sea-water system are more complex than the quinary system considered for simulation.

EVALUATlON D

Several different equations have been tested for the representation of solubiity fields and most of them are able to fit correctly with experimental data, even if they are empirical or if the assumptions made for the derivation of equation are not good. The comparison of calculated and measured phase change enthalpy at the congruent melting point. gives a good evaluation of the validity of the assumptions made for the derivation of equation and allows to

improve the model.

TABLElV

Bii system NaCLH20 PhaseChangeenthalpies [13]

Species PC Phase change enthalpy kJfm;$ CA.

NaCl 8008 KC1 771’ 2:9 5 6 LiCl 610 20:5

28 26:; 19.8

LiChH20 123.12* 2.4 * meta&ble

R. COHEN-ADAD et al.

For example the melting enthalpy has been calculated for alkali chlorides and compared to experimental data (table IV). The results show a good agreement between calculated and measured melting enthalpies for KC1 or LiCl and the model seems satisfactory, but there is a great difference for NaCl ; the equation gives a very good representation of the liquidus curve of NaCl below 1 1oOC and must be considered as a very good fitting equation. The observed discrepancy may be due to the model itself or, more probably, to the fact that the solubility range of NaCl is very extended (between 273 and 1073 K) with inaccurate data above 383 K (high pressure measurements)

CONCLUSION

The main target of the overall project is the modelling of all solubility fields involved in the quinary system Na+, K+, Mg2’ // Cl-, S042- - Hz0 to derive, in a further stage, a treatment of brines and bitterns in order to recover potassium and eventually magnesium salts. In the present paper the procedure used for derivation of a model adapted to the calculation of solubility fields and to the critical evaluation of data is developed:

- the solubility of a salt is described in terms of heterogeneous reaction between liquid and solid, - a fitting equation is deduced from the condition of phase equilibria for each solubility surface of the system, assuming that the aqueous solution is a strong electrolyte and that all solid phases are stoichiometric, - after their conversion in convenient units, the raw &la are used to calculate the coefficient of fitting equations, - for binary sub-systems the coefficients are chosen to be independent of composition and the influence of composition under isothermal conditions is taken in account by a plynomial development in series for more complex systems.

ACKNOWLEDGEMENTS

We had the opportunity to have a discussion with prof. J. W. Lorimer on the modelling of sea-water system and we wish to thank him for his useful comments and for his thorough review of the manuscript.

r11 PI

[31

[41

PI

161

[71

WI

PI

WI

WI

iI31

u41

WI

UFERENCES

IUPAC Solubihty Data Series, Volumes 1-53 Pergamon Press ; Volumes 54-65 Oxford University Press

European Community, Utilization of the sea-salt production and of the waste brine, connected with the

minbni.zatiott of the Black Sea envitxmrnental damage, Contract IClS-Cl%-0747,

J. D’Ans, Die Usungsgkichgewichte der System der Sake oseanischer Sakabkgerungen 2 Vol.,

Verlagsges. fiir Ackerbau M.B.H. Berlin. (1933).

R. Z., Liiwenhertz , Z Phys. Chem, 13,459,( 1894)

S.L. Clegg and M. Whifield in K.S. Pi&r, Activity Coe@kients in Electrolyte Solutions, 2nd edition,

CRC Press, Boca Raton, (1991) p. 282

V.P. Radischev, IN. Sectora Fit ZUtim An&z, 2 3,46, (1953)

KS. Pitzer, J. Phys. Chem,7 7,268-77 , (1973)

K.S. Pitzer Activity Gejkients in Electrolyte Solution s, 2nd ed, CRC Press, Boca Raton, (1991), ch.. 3

R. Cohen-Ark& J.W. Lorimer, ZUPACSolubility Data Series., Alkali Metal and Anunomuan Chlorides in

Water and Heavy Water (Binary Systems), Pergamon Press, Oxford, (1991), ~0147

R. Cohen-A&d, J.W. Lorimer, S.L. Phillips, M. Salomon J. Chem Znfo. Comp. Sci, 35,675-696

(1995) [1 l] Cohen-A&d, R. ; Pure Apple Chem 5 7,255-62, (1985)

R. T. Palaban, K.S.Pitxer, in K.S. Pitzer Activity CIqJicients in Ekctrolyte solution s, 2nd edition,

CRC Press, Boca Raton, (MN), ch. 7

M.-T. Cohen-Adad, R. Cohen-A&d Entqrie No 160,47-55, (1991)

M. Ferriol, M. Giudice, MTh. Cohen-Adad, M. Foulon, N. Lebrun, M. Muller, J. Bureau, T. El Witadi,

FluidPhaseEquili., 86,187-200, (1993)

G. Scat&@ Chem Rev., 19,309-27, (1936)

MODELLING OF MULTICOMPONENT SALT SYSTEMS 533

WI U71

WI

1191

WI

WI

1221

1231

v41

L-1

WI

t271

WI

1291

1301

[311

1321

1331

[341

[351

1361

r371

t381

[391

J.G.. Kirkwood, J.C. Poirier J. Phys. Chem, S&591-596, (1954)

E. A. Guggenheim; J.C. Turgeon, li’rwrs. Farad Sot., 5 1, 747-61, (1955)

R. Haaae Angew. Chem, 7 7, 5 17-529, (1965)

E. Hala, J. Pick; V. Frjed, 0. Vilim, Vupour-liquid Equilibrium Pergamon Press, Oxford, 2nd ed.,

144-155, (1967)

M.H. Lietzke, R. W. Stroughton, R.M. FUOSS, Proc. Nut. Acao! Sci., 59, 39-45, (1968)

E. Gluekauf, Proc. R Sot. London, A310,449-462, (1969)

R. A. Robinson, R.H. Stokes EkctrolyteSolutions, Butterworths, 2nd ed., London, 222-60, (1970)

L.A. Bromley, J. Am Chem Eng. , l&294-298, (1972)

HP. Meissner, C.L. Kusik, Znd Eng. Chem Prows. Des. Develop. , l&205-208, (1973)

R.H. Stokes, R. A. Robinson, .Z. solution Chem, 2,173-191,(1973)

E. Vega, J.H. Vera, Can J. Chem Eng., 54,245-248, (1976)

J.L. Cruz, H. Renon, C. R Acad Sci. Paris ,2 82,477-480, (1976)

J.L,. Cruz, Revue de 1’Znstitut Fran&s du P&ok,, 32 (3), 393, (1977)

R. Cohen-A&d; J.W. Lorimer Alkali Metal and Ammonium Chloride in Water and Heavy Water

IUPAC Solubility Data Series Vo147, pp. xvi ,67, (1991)

H. Falkenhagen Electrolytes, traduction frarqaise, Alcan, Faris p. 77,.( 193)

W.J. Moore Physicul Chemistry, Prentice Hall N.Y. 1957, traduction franqaise, Dunod, p. 565, (1957)

G.:N. Lewis, M. Randall, rev. K. S. pitzer and L. BrewerThennodyMmics, 2nd edition, McGraw Hill, ,

pp. 284,326, (1961)

R. Cohen-A&d, ; M.-Th. Saugier, J. Said, , Rev. Chim Min , 10,631, (1973)

R. Cohen-A&d, M.-Th.Saugier-Cohen Adad, R. Ouaini, Pure Appl Chem. ,62 (11, l-7,.( 1990)

R. Cohen-Adad, M.-Th. Saugier-Cohen A&d, R. Ouatii, F. W. J. Getzen, Chim Phys. 8 7, 1441-55,

(1!)90)

M.-T. Cohen-Adad, R. Cohen-Adad, D. Ben Hassen-Chehimi, JEEP XZX Barcelona , M.A. Cuevas-

Diarte, L.Li Tamarit, E. Estop edit_, ISBN 84-604-5729-X, p.1 (1993)

D. Ben Haasen-Chehimi 2%&e, Bizerte (Tunisia), (1997)

J.A.N.A.F. Thenxochemic~ Tabks NSRDS-NBS , 37, (1971)

Berkeley, Earl of, Trans. R Sot. London , A 203,189, (1904)

534 R. COHEN-ADAD et a/.

A ,B,C,D ,... a,b ,c,d . . .

ai

D

E

;

G

AH@

iii?

i

ni

R

T

To sol

u

V

U,V,W

XNrXK,XY

Gc ,Ys

yHtYNC--*

ZH

r

Pi

“i

0

PJOTA’I’ION

m Adjustable coefficients

Activity of i

Total amount of positive or negative charges of solution

Total amount of constituents (salts and water)

Relative amount of salts in solution

Activity coefficient of constituent i

Sum of the actual amounts of water and ions

Enthalpy of phase change in reference state (not specified)

Molar enthalpy of phase change

Constituent of the system (ion or molecule)

Amount of constituent i (ions or molecules)

Gas constant

l%ermodynamic temperature/K

Stable or met&able melting point of a solid

Logarithm of the solubility constant of a solid

Bmhalpic team in the fitting equation

J&recke (solute) mole fraction of anion or cation

J&necke mole fractions of cations

Mole fraction of salt or water

J&s&e mole fractions of anions

Actual mole iiaction of water, NaCl...

JZnecke mole fraction of water

Bulk activity coefficient

Chemical potential of censtituent i (ion or molecule)

Stoichiometric coefficient of constituent i in a salt

Solid phase in equilibrium with liquid