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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: nidal.hilal@nottingham.ac.uk
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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388 K. Al-Anezi, N. Hilal / Desalination 204 (2007) 385402
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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K. Al-Anezi, N. Hilal / Desalination 204 (2007) 385402 389
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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390 K. Al-Anezi, N. Hilal / Desalination 204 (2007) 385402
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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K. Al-Anezi, N. Hilal / Desalination 204 (2007) 385402 391
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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392 K. Al-Anezi, N. Hilal / Desalination 204 (2007) 385402
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-
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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.
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394 K. Al-Anezi, N. Hilal / Desalination 204 (2007) 385402
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].
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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
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396 K. Al-Anezi, N. Hilal / Desalination 204 (2007) 385402
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:
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K. Al-Anezi, N. Hilal / Desalination 204 (2007) 385402 397
( )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
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398 K. Al-Anezi, N. Hilal / Desalination 204 (2007) 385402
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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