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Desalination 204 (2007) 385402

Presented at EuroMed 2006 conference onDesalination Strategies in South Mediterranean Countries: Cooperation

between Mediterranean Countries of Europe and the Southern Rim of the Mediterranean. Sponsored by the

European Desalination Society and the University of Montpellier II, Montpellier, France, 2125 May 2006.

*Corresponding author.

Scale formation in desalination plants: effect of carbon dioxide

solubility

Khalid Al-Anezi, Nidal Hilal*

Centre for Clean Water Technologies, School of Chemical, Environmental and Mining Engineering,

University of Nottingham, Nottingham, NG7 2RD, United KingdomTel. +44 (115) 9514168; Fax +44 (115) 9514115; email: [email protected]

Received 16 March 2006; accepted 12 April 2006

Abstract

Modeling of the release of CO2

in the multi-stage flash distillers requires knowledge of the CO2solubility in

seawater at the conditions prevailing in the system. The evidence from literature is that measurement of the solubility

of CO2 in pure water has been extensively studied, whereas that in saline solutions has not. Several studies haveinvestigated the solubility of CO2in seawater under different temperatures and pressures, but they have not covered

the conditions that prevailed in the desalination plants, such as low pressures and high temperatures. In the low-

pressure regime (i.e., near atmospheric pressure), the gas solubility can be theoretically estimated by considering

the ionic strength and the salting-out parameter. Gas solubility measurements can be made as a function of the

seawater temperature and salinity. Fouling in the MSF plants occurs as a result of alkaline scale formation and it is

known that the rate of formation of calcium carbonate and magnesium hydroxide in seawater depends on temperature,

pH, concentration of bicarbonate ions, rate of CO2release, concentration of Ca2+ and Mg2+ ions, and total dissolved

solids. This review presents an overview of the CO2solubility in the brine, carbonate equilibria in the seawater and

the various correlations used to characterize the CO2-seawater system. Also, some gas solubility equipment has

been mentioned.

Keywords: CO2 solubility in seawater; Carbonate equilibria; Fouling in the MSF plants; Desalination.

0011-9164/07/$ See front matter 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.desal.2006.04.036


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386 K. Al-Anezi, N. Hilal / Desalination 204 (2007) 385402

1. Introduction

The multi-stage flash (MSF) procedure is the

most common technique for desalination, foundmostly in the Middle East countries. The tech-niques worldwide capacity adds up to about 48%of the total number of bigger plants having a capa-city greater than 4,000 m3/d. Among other evapo-ration techniques, the multi-effect distillation(MED) may be mentioned here, either with ver-tical or horizontal smooth tubes or doubly flutedtubes. The vapour compression course is very pop-ular for remote locations, resort areas, islands, etc.These two techniques, though not widely used,

are promising as far as good water quality, simpleapplication, reliability, and efficiency are con-cerned. Membrane processes, mainly reverseosmosis (RO), are currently the fastest-growingtechniques in water desalination [1,2]. Challenges,however, still exist to produce desalinated waterat affordable costs.

The presence of dissolved non-condensable(NC) gases in process water is a serious problemin thermal desalination of seawater, which can

deteriorate the performance and efficiency of thewhole desalination plant, and hence cause a costincrease in most commercial units. Even low con-centrations of NC gases can significantly reducethe overall heat transfer coefficient and hence theperformance of desalination evaporators. CO

2

dissolves in the condensate and lowers its pHvalue. In the presence of O

2, this may cause corro-

sion of the condenser tubes.Also, the release of CO

2from the evaporating

brine in seawater distillers considerably influences

concentrations of HCO3, CO32, H+ and OH ionsin the carbonate system of the brine and thus playsan important role in alkaline scale formation. Fur-thermore, an accumulation of NC gases may dis-turb the brine flow through the flash chambers ofmulti-stage flash (MSF) distillers. Most often nei-ther a deaerator nor a decarbonator is provided toalleviate the problem of NC gases that is causedby the leakage of ambient air through flanges,man-holes, instrumentation nozzles, etc. into the

parts of the evaporator operating under vacuumand the release of dissolved gases from the eva-porating brine. Molecularly dissolved gases suchas O

2, N

2can be removed by adequate venting. In

contrast to that, CO2chemically reacts in seawater

and is produced during the desalination processitself. Under the alkaline conditions prevailing inseawater only a small proportion of the totalinorganic carbon content in seawater is present asmolecular CO

2, the major proportion is chemically

combined in HCO3and CO

32 ions [37].

Literature data regarding solubility of CO2

indifferent solvents and combinations thereof are

rather abundant. However solubility in saline wa-ter at or near conditions prevailing in the thermaldesalinations processes is lacking. Thus, consider-able uncertainty exists in predicting the total CO

2

absorption or release rates in distillers. This studyis essentially aimed at reviewing the solubility ofCO

2in the saline water under the conditions

prevailing in the multi-stage flash evaporators,since the solubility of CO

2in brine is an important

parameter for modelling the behaviour of CO2,

especially on the production of the alkaline scales.

2. Theory: CO2

solubility in seawater and

carbonate equilibria

The carbonate system is a weak acidbase sys-tem which exists in seawater as dissolved carbondioxide, carbonic acid, bicarbonate, carbonate ionsand complexes of these ions. Basically the systemis derived from the dissolution of carbon dioxidegas and carbonate minerals into the water. Addi-

tion of an acid or a base to an aqueous solution ofcarbonate species gives rise to changes in pH andchanges in the concentrations of all the speciesthat constitute the system. A distinguishing featureof the carbonate system is that the gas phase formsan integral part of it. For a system initially in equi-librium, any change in the partial pressure of CO

2

in the gas phase induces a state of non-equilibriumbetween gas and aqueous phases. This causes,with time, an exchange of CO

2between the phases


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K. Al-Anezi, N. Hilal / Desalination 204 (2007) 385402 387

resulting in a shift in pH and the species concen-trations until equilibrium between the phases isre-established. A further feature is the relative in-solubility of many carbonate minerals; the preci-pitation and dissolution of these minerals have asignificant effect on the systems behaviour. As aconsequence of these two features it is often nece-ssary to consider all three phases, aqueous, gasand solid, in order to describe the response of thesystem to external influences [811].

Seawater is an aqueous mixed electrolyte. Itattains its chemical composition through a varietyof chemical reactions and physicochemical pro-

cesses. Among these are: acidbase reactions, gasabsorption and desorption processes, precipitationand dissolution of solids and adsorption processesat interfaces. Characteristic for seawater is the highsalinity that may vary between average limits of7 g/kg (Baltic Sea) and 43 g/kg (Arabian Sea).The pH of seawater is usually in the range from7.7 to 8.3 in surface waters. The pH is bufferedby a set of reactions that take place between CO

2

and water. Table 1 shows the composition of stan-dard seawater with a salinity of 35 g/kg [7, 12

15].

Table 1

The composition of standard seawater with S= 35 g/kg, TA = 2.3103 mol/kg and pH = 8.1 at 25C

ConcentrationSpecies

(g/kg seawater) (mol/kg seawater)

Specific concentration(g/kg)/s

Na+

10.7838 0.46907 0.30811Mg

2+1.2837 0.05282 0.036678

Ca2+

0.4121 0.01028 0.01177

K+

0.3991 0.01021 0.01140Sr

2+0.0079 0.00009 0.000227

Cl

19.3529 0.54588 0.55294SO4

22.4124 0.02824 0.07750

HCO3

0.1070 0.00175 0.00306Br

0.0672 0.00084 0.00192

CO32

0.0161 0.00027 0.000459B(OH

)4 0.0079 0.00010 0.000225

F

0.0013 0.000068 0.000037B(OH)3 0.0193 0.00031 0.000551

Total 35.1707 1.1199 1.004877

Many investigators such as [69,13,14,16,17]have given an overview of the carbonate systemin seawater and they have summarized the fol-lowing: the solubility of CO

2in seawater, the

chemical equilibria, the mechanisms, the ordersand the rates of reactions involved in CO

2release.

Also, they described the effects of temperature,pressure and ionic strength on the solubility, thechemical equilibria and the reaction rates.

The solubility of CO2

in seawater occur as aresult of a number of reactions taking place whencarbon dioxide dissolves in seawater [9,12,15,18].In the presence of gaseousCO

2,The dissolved CO

2

exchanges with CO2 gas can be represented byseries of equilibria. Henrys law describes onlythe physical equilibrium between the phases andmay only be applied to the fraction of the gas thatis molecularly dissolved and not chemically bound[1924]. Henrys law coefficient depends on thetype of the gas and the solvent, the temperature,the total pressure, and in the case of salt solutions,it also depends on the ionic strength of the solu-tion. Gas solubilities in salt or electrolyte solutionsare usually smaller than the gas solubilityK

G,oin

pure water (salting-out effect). The effect of the


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molar salt concentration cs

can be described inthe form of the Setchenow equation [25]. Danck-werts [20] related the Henrys law coefficient inthe salt solution to that in water at the same temp-erature on the basis of a method originally propos-ed by Setchenow [12]. Furthermore, the activitycoefficient of CO

2in seawater can be considered

as the ratio of its solubility in water to the solu-bility in seawater. The application to the solubilityof CO

2in seawater has lead to the formulation of

an empirical correlation which is shown elsewhere[2628].

Yasunishi and Yoshida [29] determined the

solubility of CO2 in aqueous solutions of 16 elec-trolytes and found that the empirical Setchenowequation was not applicable to some electrolytesystems. But [2628] presented an empiricalmodel for the prediction of gas solubilities in elec-trolyte solutions which described the data withgreater accuracy, the observed influence of thesalt type on the gas specific part of the Setchenowconstant was considered in their model. The modelpresented by Schumpe [27] has a simple structureand is consistent when applied to mixed electrolyte

solutions. The parameter values evaluated for thismodel allowed estimation of the effects of 20 cationsand 19 anions on the solubilities of 15 gases in-cluding CO

2, further work was carried out by

Weisenberger and Schumpe [28] to study the effectof temperature on the model and they extendedthe model to the temperature range of 273363 K,and assumed that the gas-specific constant to belinear function of the temperature. This model wasused to evaluate the Setchenow constants for dif-

ferent gas/salt/temperature combinations in therange of 273363 K, and they observed lineardecrease of the Setchenow constant with tempera-ture in most cases.

The ionic strength can be related to salinity Sand, as it is know, NaCl is the main constituent ofseawater and it accounts for 73% of seawater ionicstrength, the ion specific parameters of Na+ andClare the only considered parameters.

Teng et al. [22] presented a theory of CO2-gas

solubility in seawater, and in their paper theyinvestigated the CO

2water binary system and

CO2

-gas solubility in seawater. They carried outa complete mathematical derivation of the CO

2

water binary system and CO2-gas solubility in sea-

water and they have obtained an expression to cal-culate the solubility coefficient for the CO

2water

binary system and CO2-gas solubility in seawater

similar to that obtained by Weiss [30]. The solu-bility of CO

2in seawater was measured in [30

33]. The latter work of Weiss [30] supported theaccuracy of the measurements of Li and Tsui [31]and led to the formulation that is used to calculate

Henrys law constant,Ko for seawater as a func-tion of salinity (S) and temperature (T, K). Thisequation is derived from the integrated vant Hoffequation and the logarithmic Setchenow salinitydependence, and has the form given by Weiss [30]:

( )

( ) [

( ) ( )

0ln 60.2409 93.4517 100/

23.3585ln /100 0.023517

0.023656 /100 0.0047036 /100

K T

T S

T T

= +

+ +

+

(1)

All of these measurements were made on acidi-fied seawater equilibrated with pure CO

2, and with

a certain temperature range and salinity range (T

= 040oC and S = 040). The extrapolation of

Eq. (1) for higher temperatures and salinities doesnot give reliable results. The more recent measure-ments of Roy et al. [34] indicate that theK

omea-

surements by Weiss [30] are consistent with theirK

oK

1measurements to 0.0003 in logK

o.

Since the extrapolation of Eq. (1) for higher

temperatures and salinities does not give reliableresults, many researchers such as Glade and Gen-thner [5] determined Henrys law coefficient ofCO

2in the brine by using Eq. (5) and using the

correlation for Henrys law coefficient in purewater given by Plummer and Busenberg [35]which is valid up to 334oC:

,0

2

ln 108.3865 0.01985076

6919.53 40.45154 log 669365/

GK T

T T T

= +

+(2)


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However, Duan and Sun [36] proposed a morerecent thermodynamic model for the solubility ofcarbon dioxide in pure water and in aqueous NaClsolutions for temperatures from 273 to 533 K, forpressures from 0 to 2000 bar. Their CO

2solubility

model was based on the equation of state (EOS)of Duan et al. [37] and the theory of Pitzer [38,39].Duan and Suns [36] model was able to predictCO

2solubility in seawater-type brine and was

compared to experimental data obtained byMurray and Riley [32] with great accuracy (only3% deviation from the experimental data). But,this model relies on a complex virial EOS that

needs to be solved iteratively.Solubility of gases in the seawater is a function

of their molecular weight, temperature and sali-nity, Table 2 [6,15] shows the concentrations ofthe gases dissolved in seawater with a salinity of35 g/kg in equilibrium with the atmosphere at25C and from this table we can see that CO

2is

more soluble than O2, N

2and Ar. The Henrys law

coefficient of CO2decreases with increasing temp-

erature passes through a minimum at 170C andincreases again. The Henrys law coefficient also

decreases with increasing salinity. The effect ofsalinity is less pronounced at high temperatures.

The dissociation of H2CO

3in water, the disso-

ciation of water obeys the equilibrium conditionsand are important parts of carbonic acid equilibria[9,12,15,18], where the equilibrium conditions arequantified by the dissociation or acidity constants:

+

1 3 2 3[H ][HCO ] /[H CO ]K

= (3)

and

+ 2

2 3 3[H ][CO ]/[HCO ]K

= (4)

+ +

2H O H OH , where [H ][OH ]WK

+ = (5)

The carbonate system in seawater is charac-terised by the interaction of major cations (Na+,Mg2+, Ca2+ and K+) and major anions (Cl, SO

42,

HCO3 and CO

32). These interactions can be de-

scribed in terms of an ion association formalismand, more recently, in terms of a specific interac-tion theory [6,12,13,15,40].

+ 2

3 3

2+ +

3 3

2+ +

Na CO NaCO ,

Ca HCO CaHCO ,

Mg OH MgOH

+

+

+

(6)

+ 2 +

4 4H SO HSO , H F HF

+ + (7)

Additionally insoluble calcium carbonate andmagnesium hydroxide can be formed [41,42].Fig. 1was presented by Al-Rawajfeh [12] and it shows

a schematic representation of the carbonate systemin gas, liquid and solid phases.

The dissociation constant of water, the stoi-chiometric equilibrium constant of water in sea-waterK

wsw can be expressed as:

( )+ +H OH/ [H ] [OH ]sw sw sw sw sw

w wK K

= = (8)

Culberson and Pytkowicz, Dickson and Riley,Hansson and Mehrbach et al. [4346] measured

Table 2

Solubility data of the gases dissolved in seawater with S= 35 g/kg in equilibrium with the atmosphere at 25C

Concentration in seawaterGas Partial pressure inatmosphere (bar)

Henrys law coefficient(mol/(m

3bar))

(mol/kg SW) (mg/kg SW)

CO2 0.00033 29.3 9.45 0.4N2 0.7808 0.5 383.4 10.7O2 0.2095 1.0 206.3 6.6Ar 0.00934 1.1 10.11 0.4


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Fig. 1. Schematic representation of the carbonate system.

the equilibrium constant of water in seawater fortemperatures up to 35C and salinities up to 44 g/kg.Another correlation to calculate the equilibriumconstant of water in seawaterK

wsw can be found in

another reference [44].Basically all values of the solubilities and dis-

sociation constants are temperature dependent.However, theKvalues also depend on the soluteconcentrations, because the formation of ion com-plexes between the carbonic ions and moleculesand ions in the solution hinder the dissolved car-bonic molecules and ions to take part in the ther-modynamic equilibrium reactions. Therefore, inthe thermodynamic equation, the concentrationshave to be replaced by their activities that are smal-ler than the concentrations. The thermodynamicsolubilityconstant is:

22 3 CO[H CO ]/o aK P= (9)

where, in general, the activity coefficients >1(= 1 for an ideal solution, i.e. with zero soluteconcentrations or zero ionic strength).

In the non-ideal solutions of seawater andbrackish water it is more practical to describe therelation between the real, measurable concen-trations by the apparent solubility constant. Fulldetails of the correlations to calculate the solu-

bilities and dissociation constants can sited else-where [6,9,11,17,47].

For practical reasons the values of the dissocia-tion constants are generally given as: pK= 10log

KorK= 10pK. Many investigators as in [34,4446,4851] presented various correlations of thedissociation constants K

1sw and K

2swof carbonic

acid in seawater. Millero [7], Lueker et al. [47],Millero et al. [52] investigated the parameters usedto study the carbonate system such as pH, totalalkalinity (TA), f

CO2(fugacity) and T

CO2, since a

combination of at least two of these parameters isneeded to characterise the carbonate system. Millero[7] suggested two correlations for calculating thestoichiometric dissociation constantsK

1swandK

2sw

and these correlations are based on the experi-mental data of [34,49]:

( )1

0.5

1.5

ln 2.18867 2275.036/

1.468591ln 0.138681 9.33291/

0.0726483 0.00574938

swK T

T T S

S S

=

+

+

(10)

( ) (

)

2

0.5

1.5

ln 0.84226 3741.1288/

1.437139ln 0.128417

24.41239 / 0.1195308

0.00912840

swK T

T

T S S

S

=

+

+

(11)


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where K1

sw and K2

sw are on the basis mol/kg

seawater, Tis in K and Sis in g/kg.

Figs. 26 show the solubility constants (=

solubilities in M/L.atm) and stoichiometric

dissociation constantsK1swandK

2sw for CO

2in

freshwater, seawater and brackish water as a func-

tion of temperature and salinities.

3. Fouling, alkaline scale formation and

solubility product of calcium carbonate

Fouling is the accumulation of undesired solid

materials at the phase interfaces. Build-up of

fouling film leads to an increase in resistance anddeteriorates the performance of process equipment

such as membranes and heat exchangers and is

costing industries billions of dollars annually. One

Fig. 2. The solubility constants (= solubilities in M/L.atm) for CO2

in freshwater, seawater and brackish water as a

function of temperature at salinities of 0, 5, 15, 25, and 35 (= g of salt per kg of water) (upper graph) and as a function

of salinity at 20C (lower graph). All values are according to [7, 88], at higher salinities similar to [30] [Eq. (7)]; the

values for freshwater are similar to those in [89].

of the major fouling phenomena encountered in

the aqueous systems is scale formation due to

precipitation of salts present in the water. Alkaline

scale formation in seawater distillation begets

from the decomposition hydrolysis of seawater

bicarbonate ion as process temperature is increas-

ed [53]. In real-life situations, scale deposits are

formed mainly through thermal effects. In fact,

heating of the water has the consequence that car-

bon dioxide solubility decreases, pH increases and

finally calcium carbonate precipitates.

Multi-stage flash (MSF) plants usually operate

at temperatures as high as 120C, and multiple

effect evaporation (MED) plants operate at temp-eratures lower than 70C. Consequently, the major

risk of scaling is for minerals whose solubility

decreases with increasing temperature. The mostly


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observed scales that occur in MSF distillers are

found to be either CaCO3

or Mg(OH)2. The two

are commonly referred to as alkaline scale. The

formation of the alkaline scales CaCO3

and

Mg(OH)2

strongly depends on temperature, pH,

the release rate of CO2

as well as the concentra-

tions of HCO3, CO

32, Ca2+, and Mg2+ ions. Lots of

metals and anions exist naturally in the water;

among them, CaCO3

and CaSO4

are major fouling

contributors [2,4,5461].

Al-Sofi [4] made an attempt based primarily

upon visual and reported observations of fouling

in various parts along the flow path of brine

solutions in MSF distillers and proposed a certain

sequence of scale forming reaction steps, and also

suggested certain experiments that could verify

the validity of his proposed reaction mechanism.

Meanwhile, the presence of hydroxyl ions will

Fig. 3. The acidity constants for the first dissociation of carbonic acid in freshwater and seawater as a function of the

water temperature at salinities of 0, 5, 15, 25, and 35. The values are according to [7,88]. The freshwater values are

equal to those in [89], the marine values are in good agreement with those reported in [46] as discussed in [48].

be short lived primarily due to Mg(OH)2

precipi-

tation. The proposed steps support CaCO3precipi-

tation ahead of Mg(OH)2. The abundance of mag-

nesium ions and the extreme low solubility of

magnesium hydroxide will then rapidly lead to

its formation. However, scale precipitation inside

tubes is not only from the initial scale formation

under pressure inside the tubes but also due to

nucleates recirculation from flash chambers back

into heat gain exchanger tubes because of brine

recycling. Recent analysis of variation in colora-

tion of water boxes came as a strong support to

this hypothesis. It is worth to note that the end

results of various reaction mechanisms are almost

the same in the cited ones also the same to the

proposed overall reaction.

A number of studies done by Al-Rawajfeh [3,

12] Shams El Din and Mohammed [42], Al-


9/18


Fig. 4. The acidity constants for the second dissociation of carbonic acid in freshwater and seawater as a function of the

water temperature at salinities of 0, 5, 15, 25, and 35. The values are according to [88]. The freshwater values are equal

to those in [89], the marine values are in good agreement with those reported in [46] as reported in [48].

Rawajfeh et al. [62] to analyze scale formation in

seawater distillers which is mainly caused by

crystallization of the inversely soluble salts cal-

cium carbonate, magnesium hydroxide, and cal-

cium sulphate. The release of CO2from the evapo-

rating brine shifts the pH to higher values and con-

siderably influences the concentrations of HCO3

and CO32 ions in the brine. Thus, it plays an im-

portant role in alkaline scale formation. CO2 re-lease and alkaline scale formation in seawater

distillers are closely related to the carbonate sys-

tem in the brine. Al-Rawajfeh [3] proved that the

model developed by Al-Rawajfeh [3,12,18,58,62]

is very useful to calculate the CO2

release rates

and the HCO3, CO

32, CO

2, H+ and OHconcentra-

tions in the brine on its flow path through multiple-

effect distillers.

A simple and easy programmed code is pro-

posed by Al-Shammiri et al. [63] for estimating

the scaling potential for different scaling species

that expected to be precipitated in an RO system,

as calcium carbonate, calcium sulfate, barium

sulfate, calcium fluoride and strontium sulfate

scaling. Azaroual et al. [64] presented a thermo-

kinetic geochemical calculation program

(SCALE2000) based on Pitzers ion interaction

model, which can take into account the fluid floweffect using a specific approach based on a scheme

of serially connected homogeneous reactors.

According to the authors [64,65] SCALE2000 is

well adapted to perform scaling risk prediction

applied to industrial desalination facilities and the

authors tested the reliability of the SCALE2000

results against measurements of individual mine-

ral solubility and kinetics data derived from the

literature.


10/18


Fig. 5. Values for the first and second dissociation constants of dissolved carbonic acid as a function of the salinity. The

values are valid for a water temperature of 20C. Values for the first and second dissociation constants of dissolved

carbonic acid as a function of the salinity [7,88].

Fig. 6. Distribution of the carbonic acid fractions as a percentage of the total carbon content, CT. The values are calculated

at temperatures of 5 and 25C and for salinities of 0 and 35 as a function of the pH. Seawater has pH values around 8.2.

However, the carbon distributions are shown for an (unrealistic) wider range of pH values, to illustrate the dependence of

the carbon distribution on salinity [7,88,90].


11/18


Calcium carbonate CaCO3dissolves according

to the following equation:

2+ 23( ) 3CaCO Ca COS

+ (12)

The solubility product of calcium carbonate is

given by

( )2+ 23

2+ 2

3Ca CO/ [Ca ] [CO ]sw sw sw sw swsp spK K

= =

(13)

whereKsp

is the thermodynamic solubility product

and [i]sw and i

sw are the concentration and the

activity coefficients of the component i, respec-tively.

Kspsw of calcite and aragonite, respectively, can

be calculated from correlations reported by Dick-

son and Millero [48], Sheikholeslami and Ong

[61], Azaroual et al. [64], Mucci [66], Zuddas and

Mucci [67] for a salinity between 5 and 45 g/kg

and a temperature between 5 and 40C at 1 atm

total pressure.Kspsw values increase with pressure

and salinity but decrease with temperature. At T

= 30C, S= 60 g/kg andp = 10 bar, the values of

K1sw,K

2sw andK

wsw differ from the values at 1 bar by

1%, 0.3% and 0.3%, respectively [8]. Kspswdiffers

from the values at 1 bar by 0.3%. Thus, for small

and moderate pressures, the pressure dependence

of the equilibrium constants can be neglected.

The activity coefficients in reality are complex

functions of the composition of the aqueous

solution. In electrolyte solutions, the activity

coefficients are influenced mainly by electrical

interactions. Much of their behaviour can be

correlated in terms of the ionic strength defined

by:

212 i iI z m= (14)

In general, model equations which express the

dependence of activity coefficients on solution

composition only in terms of the ionic strength

are restricted in applicability to dilute solutions.

Al-Rawajfeh, [12] has summarised the theoretical

expressions for the activity coefficients in Table 3

[6,8,19,25,6872].

Many researchers such as Al-Rawajfeh [12]

and Mucci [65] have used the Davies equation to

Table 3

Expressions for activity coefficients withzias the charge of the ion,A as the DebyeHckel parameter which depends on

the dielectric constant of the solvent and on the temperature; for water at 25CA = 0.509 kg1/2 mol1/2;B as temperature-

dependent parameter; aiand b

ias ion specific parameters

Approximation Equation Applicability

DebyeHckel 2logi i

Az I = I< 0.005 mol/kg

Extended DebyeHckel

2

log 1i i

i

I

Az Ba I = + I< 0.1 mol/kg

WATEQDebyeHckel2

log1

i i i

i

IAz b

Ba II = +

+ I< 1 mol/kg

Davies2

log 0.21

i i

IAz I

I =

+

I< 0.5 mol/kg

Gntelberg2

log1

IAz

i i I =

+

I< 0.1 mol/kg

useful for mixed electrolytes


12/18


describe the concentration dependence of activity

coefficients:

( )( )2log / 1 0.2i iA z I I I = + (15)

It should be noted that many other workers

have replaced the value of 0.2 with 0.3 value. The

Davies equation is normally only used for temp-

eratures close to 25C. It is only accurate up to

ionic strengths of a few tenths molal in most solu-

tions. Withzias the charge of the ion Helgeson

and Kirkham [73] presented an interpolation

formula to calculate the DebyeHckel constantA:

0.4819 0.0011A T= + (15a)

where Tis the temperature in C, which is valid

forI< 0.5 mol/kg, has the advantage that it needs

no adjustable ion size parameter.

Davies Eq. (15) is used in many of the chem-

ical equilibrium systems because of its simplicity.

In this version of DebyeHckel equation a simple

term, linear inI, was added at the end of the equa-

tion. This term improves the empirical fit to higherionic strength but it has no theoretical justification

[12,65,72,74,75]. The activity coefficients for

seawater (I= 0.72 mol/kg) are for monovalent

ions i= 0.69, for divalent ions

i= 0.23 and for

trivalent ions i= 0.04 (Table 4). Loewenthal and

Marais [11] concluded that these values are realis-

tic even though seawater ionic strength is outside

the valid range of this equation.

4. Carbonate system and chemical kineticsThe carbonate system in seawater have been

described in [6,7,9,51,52,58,7678] by the follow-

ing six quantities:

1. Concentration of dissolved CO2

[CO2].

2. Concentration of bicarbonate ions [HCO3].

3. Concentration of carbonate ions [CO32].

4. pH value or concentration of H+ ions [H+] or

concentration of OHions [OH]. For seawater

samples, three pH scales have been proposed

Table 4

Activity coefficients for some species in seawater (S=

35 g/kg) at 25C

Activity coefficient in seawater

(I= 0.72 mol/kg)

Species

Loewenthal and Marais Davies equation

Na+

0.693 0.69

Ca2+

0.248 0.23

HCO3

0.669 0.69

Cl

0.649 0.69

CO32

0.203 0.23

CO2 1.171.167

(seawater scale, total proton scale, and free

proton scale [7981]).

5. Total carbon dioxide content, TC:

2

3 3 2 3TC [HCO ] [CO ] [H CO ]

= + + (16)

6. Total alkalinity, TA.

The alkalinity is a practical quantity, following

from the conservation of electroneutrality in solu-

tions where the metal ion concentrations (Na, Ca,Mg) and pH are constant, the concentration of all

bases that can accept a proton when seawater is

titrated to the pH end point of carbonic acid:

2 +

3 3TA [HCO ] 2 [CO ] [OH ] [H ]

+ [other weak acid atoms]

= + +

(17)

in which concentrations of other weak acids may

be included in the interest of high precision, such

as humic acids in freshwater or borate, [B(OH)4],

in seawater. Alkalinity and total carbon dioxideare both conservative properties (i.e. salinity is

conservative).

Stumm and Morgan [40] related the total

alkalinity TA to chlorinity, Cl, and it is known

that TA and TC vary as a result of any changes in

salinity due to mixing, evaporation or dilution,

so, to remove these variations Millero et al. [17]

presented the normalized values NTA and NTC

which are defined as follows:


13/18


( )NTA TA 35/X S= (18)

and

( )NTC TC 35/X S= (19)

with NTA, NTC, TA and TC in mol/kg and Sin

g/kg.

Many authors [6,8,33,8284] have described

the reaction mechanisms and reaction ratesof the

hydration and dehydration of CO2

in aqueous

bicarbonatecarbonate solutions. They have pre-

sented parallel reaction mechanisms and presented

many correlations to calculate the reaction rate

constant and reaction time. In our study of thesolubility of CO

2in seawater we will be using

these reaction mechanisms to determine the reac-

tion rates, reaction time and the rate constants

since it is known that the reaction rate depends

on the temperature, the pressure and the ionic

strength.

5. Vaporliquid equilibrium and gas solubility

apparatus previously used

Many researchers have tested different types

of experimental equipment to measure the gas

solubility in alkaline and saline solutions under

different experimental conditions.

Yasunishi and Yoshida [29] and Tokunaga [85]

used an apparatus that was comprised of an ab-

sorption chamber, gas burettes, manometer and a

stirrer of magnet coated with glass in it. They

determined the solubility of CO2in aqueous solu-

tions of 16 electrolytes by using the gas volumetric

method at 1 atm and temperatures of 15, 25, and35C. They evaluated the CO

2solubilities by the

Ostwald coefficient,L and concluded that the em-

pirical Setschenowequation was not applicable

to some systems. The data of those systems were

correlated by a two-parameterequation within a

deviation of 2%. A bubble column reactor has been

designed by Shorter et al. [86] to study the uptake

of gas in liquid, and they concluded that this tech-

nique had an applicability wider than the deter-

mination of solubilities and simple reaction rates.

The device, for example, has a unique utility in

studying interactions at the gasliquid interface.

Researchers such as Lueker et al. [47] designed

an apparatus that consisted of an equilibrator and

vacuum extraction system to achieve complete

and stable thermodynamic equilibrium of CO2

between the gas and solution phases in a closed

system and to provide for sampling of the gas and

solution without disturbing the equilibrium. The

partial pressure of carbon dioxide in the oceans

surface waters, precisely expressed as the fugacity

fCO2

is determined from dissolved inorganic carbon

DIC and total alkalinity TA.A PVT apparatus was designed by Nighs-

wander et al. [87] where they employed a tech-

nique for liquid sample withdrawal, which was

shown to provide accurate and reproducible gas

solubility measurements at temperatures up to

200C and pressure up to 10 MPa. They found

that CO2

solubility is slightly lower in a 1 wt %

NaCl solution than in pure water due to the salting-

out effect.

It is clear from the previous studies conducted

on the CO2 solubility in alkaline solutions thatthere are many more different designs of gas

solubility equipments that have been used for the

measurement of CO2

absorption in alkaline and

saline solutions. If a study of CO2

solubility is to

be carried out for conditions similar to those in

MSF plants, careful consideration should be taken

into account for the effect of temperature, pressure,

salinity, and pH.

4. Conclusions

The resulting survey of the literature has shown

that there are different models to measure the solu-

bility of CO2

in seawater under different condi-

tions, and many workers have suggested certain

reaction mechanisms trying to better understand

the reaction kinetics that takes place in these con-

ditions. Generally, the solubility of a gas in water

decreases as the water warms, and it is known


14/18


that high temperature conditions are usually en-

countered in desalination plants. Due to high tem-

peratures encountered in the desalination plants,

pH rise caused by the carbon dioxide loss involves

calcium carbonate precipitation.

In MSF desalination plants fouling occurs as

a result of CO2release and alkaline scale formation

in seawater distillers. Therefore, there is a need

for in-depth knowledge of solubility of CO2

in

seawater.

Acknowledgements

We would like to thank The Public Authorityof Applied Education in Kuwait (PAAET) for

funding this work.

Symbols

A DebyeHckel constantaq Dissolved phase

ci

Concentration of the ion i, kmol/m3

Cl Chlorinity, g/kg

g Gaseous phaseh Summation of ion specific parame-

ters of the positive ions (h+), negative

ions (h) and the gas specific para-

meter (hG)

hi

Ion-specific parameter, m3/kmol

hG

Gas-specific parameter, m3/kmol

HG

Gas-specific part of the Setchenow

constant, m3/kmolI Ionic strength, mol/kg

K1

First dissociation or acidity con-

stantsK

2 Second dissociation or acidity con-

stants

KW

Thermodynamic equilibrium con-

stant of water

Kw

sw Stoichiometric equilibrium constant

of water in seawater, mol/kg seawater

Ko, K

G Gas solubility coefficient in salt solu-

tion, mol L1atm1 or moles kg1atm1

KG,o

Gas solubility in water, moles kg1

atm1

KG,o

/KG

Ratioof the gas solubility in water

to that in a salt solutionmi Molality of ion i

ni= c

i/ c

s Index of ion i

PCO2

Atmospheric CO2

partial pressure,

PCO2

, atm

S Salinity of the seawater, g/kg

T System temperature, C or K

TA Total alkalinity, mol/kg

TC Total carbon dioxide content

zi

Charge of ion i

[i]sw

Concentration of the component i[H

2CO

3] Dissolved CO

2concentration in

mol/kg of water

Greek

swCO2

Activity coefficient of carbon di-

oxide

isw Activity coefficient of the compo-

nent i that is free or involved in ion

pairing

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