Chemical Engineering Science 60 (2005) 4213–4224

www.elsevier.com/locate/ces

Measurement and prediction of gas hydrate and hydrated salt equilibria inaqueous ethylene glycol and electrolyte solutions

Rahim Masoudia,b, Bahman Tohidia,∗, Ali Danesha, Adrian C. Todda, RossAndersona,RodW. Burgassa, JinhaiYanga

aInstitute of Petroleum Engineering, Heriot-Watt University, Edinburgh, EH14 4AS, UKbNIOC R&D, No. 27, Keshavarz Boulvar, Valiasr Square, Tehran, Iran

Received 5 August 2004; received in revised form 14 February 2005; accepted 21 February 2005Available online 20 April 2005

Abstract

A recently developed method in modelling electrolyte solutions is extended to include phase behaviour of aqueous solutions containinghydrated salts (e.g., calcium chloride) and organic hydrate inhibitors (e.g., ethylene glycol). A novel salt precipitation model applicable tovarious hydrated salts is presented. The precipitation model takes into account various precipitates of hydrated salts over a wide range oftemperature (i.e.,−20–120◦C). Due to lack of the required experimental data in the literature, new experimental data have been generated.These data, which have been used in determining the binary interaction parameters between salts and organic inhibitors, include; freezingpoint depression, boiling point elevation, and salt solubility in the aqueous solutions containing salts and organic inhibitors. The extendedthermodynamic model is capable of predicting complex vapour–liquid–solid equilibria (VLSE) for aqueous electrolytes and/or organicinhibitor solutions over a wide range of pressure, temperature and inhibitor concentration.In addition, in order to establish the effect of a combination of salts and organic inhibitors on the locus of incipient hydrate-liquid

water-vapour (H–LW–V) curve, reliable equilibrium data have been generated for one quaternary system, methane/water/calcium chloride/ethylene glycol at pressures up to 50MPa. These data along with various independent literature data are used to validate the predictivecapabilities of the model for phase behaviour and hydrate equilibria. Good agreement between experimental data and predictions isobserved, demonstrating the reliability of the developed model.� 2005 Elsevier Ltd. All rights reserved.

Keywords:Modelling; Phase equilibria; Thermodynamic; Solutions; Gas hydrates; Electrolytes

1. Introduction

The thermodynamics of electrolyte solutions are of con-siderable importance in a variety of fields of science and en-gineering. Accurate models describing phase behaviour ofthese systems are therefore necessary for analysing, design-ing and optimising processes and equipment in chemical andpetroleum industry. The work presented in this communi-cation is the result of a study on the phase equilibria and

∗ Corresponding author. Institute of Petroleum Engineering, Heriot-Watt University, Edinburgh, EH14 4AS, UK. Tel.: +441314513672; fax:+441314513127.

E-mail address:bahman.tohidi@pet.hw.ac.uk(B. Tohidi).

0009-2509/$ - see front matter� 2005 Elsevier Ltd. All rights reserved.doi:10.1016/j.ces.2005.02.056

gas hydrate inhibition effects of electrolyte and/or organicinhibitor aqueous solutions particularly in relation to subseaoil transmission lines where the proportion of saline watercould be significant.Gas hydrates, or clathrate hydrates, are ice-like crystalline

compounds formed by the inclusion of low molecular diam-eter non-polar or slightly polar molecules (usually gases) in-side cavities formed by water molecules.Although clathrateshave similar properties to ice, they differ in that they mayform at temperatures well above the freezing point of waterat elevated pressure conditions. Gas hydrates are reviewedin depth bySloan (1998).In petroleum exploration and production operations,

clathrates pose a serious economic and safety concern.

4214 R. Masoudi et al. / Chemical Engineering Science 60 (2005) 4213–4224

Hydrates can block pipelines, subsea transfer lines, and, inthe event of a gas kick during drilling, form in the wellbore,risers, BOPs (Blow-Out Preventers) and choke-lines (Barkerand Gomez, 1989).The risk of clathrate formation can be reduced by a num-

ber of methods, including operating outside the hydrate sta-bility region, removing/reducing free water, and/or addingthermodynamic inhibitors (e.g., electrolytes and/or organicinhibitors). Common practice involves the addition of or-ganic inhibitors (or salts and/or organic inhibitors in the caseof drilling fluid) where the salinity of produced water is in-adequate for hydrate prevention. For some deepwater oper-ations, where even saturated saline solutions may be insuffi-cient to prevent hydrate formation, organic inhibitors such asmethanol and ethylene glycol (EG) are generally employed.However, the addition of organic inhibitors may adverselyaffect salt solubility, leading to potential salt precipitation,commonly termed ‘salting-out’ (Amy et al., 2002; Matthewset al., 2002). The deposition of salt may result in flow re-striction due to salt plug formation, as well as increasing therisk of hydrate formation by reducing the chemical preven-tative characteristics of the system.Considering the above issues, accurate knowledge of

the thermodynamic stability of gas hydrates and potentialsalt precipitation, as a function of both electrolyte andorganic inhibitor concentrations, is crucial to the successof any flow assurance strategy. In the light of this, thereis strong industrial interest concerning the measurementand accurate thermodynamic prediction of hydrate phaseequilibria for mixed electrolyte–organic inhibitors aqueousfluids.Several investigations have been carried out to repre-

sent either experimental data or thermodynamic model onthe solid–liquid equilibria (SLE) in the multi salt systems(Tavares et al., 1999; Farelo et al., 1993; Harvie and Weare,1980). Some studies have been done concerning SLE of sin-gle aqueous electrolyte solutions containing non-electrolyte(Wang et al., 2002; Iliuta et al., 2000; Pinho and Macedo,1996). Most of the existing models are based on activitycoefficient with a number of tuned parameters and empiri-cal equations. As for gas hydrates, several thermodynamichydrate prediction models have been described in the litera-ture (Clarke and Bishnoi, 2002; Vu et al., 2002; Javanmardiet al., 2001), and experimental dissociation data for mixedmethanol and electrolyte solutions have been reportedby several researchers (Jager et al., 2002; Bishnoi andDholabhai, 1999). However, predictions of existing mod-els for salt-methanol solutions can be in error by up to4.5–5.6K (Matthews et al., 2002). To our knowledge, noprevious work available in the literature concerns the simul-taneous representation of vapour–liquid–solid salt equilibria(VLSE) and gas hydrate stability in aqueous multi saltsolutions with or without organic inhibitors.In a recent communication (Masoudi et al., 2004), we

presented a rigorous thermodynamic model developedfor predicting phase equilibria and salt precipitation in

aqueous electrolyte solutions, and this was successfullyapplied to the prediction of hydrate stability for such sys-tems. Here, this model is extended to include calciumchloride and investigate the phase behaviour of aqueoussolutions containing both salts and ethylene glycol. Inaddition, the newly developed salt precipitation model isalso extended to the hydrated salts precipitation such ascalcium chloride. Newly generated experimental data forfreezing point depression, boiling point elevation, and saltsolubility—required for tuning binary interaction parame-ters of thermodynamic model—are reported. In addition,we present novel experimental methane hydrate disso-ciation data for mixed calcium chloride–ethylene glycol(CaCl2–EG) aqueous solutions. The experimental data areused to investigate the hydrate inhibition characteristics ofthese systems, and to validate the developed thermodynamicmodel.

2. Experimental work

Experimental work reported in this paper covers two mainareas, physical property measurements, and hydrate disso-ciation point determinations.

2.1. Freezing point, boiling point and salt solubility

The term ‘physical property data’ here refers to freezingpoint, boiling point and salt solubility data for aqueous so-lutions of salts and organic inhibitors. This data is requiredfor development of the thermodynamic model, and has beengenerated experimentally for systems where no literaturedata is available, or the available data are considered unre-liable.A simple and reliable method for freezing point mea-

surement of liquids has been developed at Heriot-WattUniversity. The method is differential temperature based,relying on detection of the latent heat required to melt icewithin a sample, and has demonstrated good reliability,when the results are compared with the available experi-mental data from International Critical Tables (Washburn,1926–1930). Required boiling point data were determinedusing an approach developed from that ofCottrell (1919).In this method, using a Cottrell Pump, the boiling pointis measured at a location where the boiling liquid andits vapour are in equilibrium, giving reliable results. Foraccurate and reliable measurement of salt solubility, thetechnique selected was that utilised byChiavone-Filho andRasmussen (1993). In this procedure, the solute concentra-tion is accurately determined by gravimetric means follow-ing evaporation of a known mass of the saturated solution inquestion.Measured freezing point and boiling point data for aque-

ous CaCl2–EG solutions are presented inTables 1and2, re-spectively. Experimental CaCl2 solubility data for EG aque-ous solutions is reported inTable 3.

R. Masoudi et al. / Chemical Engineering Science 60 (2005) 4213–4224 4215

Table 1Experimental (this work) and calculated water freezing point temperatures for aqueous CaCl2–EG solutions

Salt Salt conc. (mass%) EG conc. (mass%) Freezing point temperature Abs. dev. (K)

Experimental (K± 0.1) Calculated (K)

CaCl2 3.4 4.1 270.2 270.3 0.16.3 9.0 266.7 266.7 0.011.4 16.7 258.9 258.8 0.113.9 22.3 253.0 253.0 0.0

Table 2Experimental (this work) and calculated water boiling point temperatures for aqueous CaCl2–EG solutions

Salt Salt conc. (mass%) EG conc. (mass%) Boiling point temperature Abs. dev. (K)

Experimental (K± 0.1) Calculated (K)

CaCl2 3.4 4.1 374.1 373.7 0.46.3 9.0 375.2 374.1 1.111.4 16.7 377.1 373.7 3.413.9 22.3 378.7 373.3 5.48.0 37.7 379.9 379.9 0.0

Table 3Experimental (this work) and predicted maximum soluble mass of CaCl2in aqueous ethylene glycol solutions at various temperatures. EG concen-trations are shown on a salt-free basis

Temperature (K± 0.1) EG conc. CaCl2 concentration Abs.(mass%) error%

Experimental Calculated(mass%) (mass%)

273.15 0.00 36.33 37.09 2.0910.00 35.45 35.97 1.4625.00 34.40 33.46 2.7440.00 30.23 30.09 0.48

283.15 0.00 38.46 38.56 0.26

288.15 0.00 40.00 39.88 0.3010.00 40.18 40.42 0.6025.00 39.11 38.88 0.5840.00 39.16 36.82 5.96

293.15 0.00 41.49 41.20 0.70

303.15 0.00 48.84 48.48 0.7410.00 48.43 45.97 5.0825.00 47.04 45.18 3.9540.00 44.20 45.36 2.61

313.15 0.00 52.14 53.26 2.15318.15 0.00 55.37 56.56 2.15323.15 0.00 56.20 56.35 0.27333.15 0.00 56.58 57.46 1.56

2.2. Hydrate equilibria

For many electrolytes and organic inhibitors (and theircombinations), hydrate dissociation data is insufficient, un-available, or unreliable. Therefore, it is vital to generate high-quality experimental data for such compounds, allowing theinvestigation of inhibitor characteristics, and the validationof predictive models.In this work, hydrate dissociation point measurements

were made by a method known as step-heating. In the step-heating technique, the system temperature is raised in steps,with sufficient time being given following each step time forequilibrium to be achieved. Only equilibrium (stable pres-sure) data are used to determine dissociation conditions. Thereliability and repeatability of this method has been previ-ously demonstrated as being considerably more reliable andrepeatable than conventional continuous-heating and/or vi-sual techniques (Tohidi et al., 2000).Methane hydrate dissociation conditions have been mea-

sured for aqueous solutions of CaCl2–EG of different con-centrations at pressures up to 50MPa. Data are presented inTable 4.

3. Thermodynamic modelling

We detail here the extension of a recently developedthermodynamic model for electrolyte solutions to the inclu-sion of a new salt (i.e., calcium chloride) and the predictionof equilibria involving hydrated salts and/or organic hydrateinhibitors. A comprehensive description of the model isgiven elsewhere (Masoudi et al., 2004). In summary, the

4216 R. Masoudi et al. / Chemical Engineering Science 60 (2005) 4213–4224

Table 4Experimental (this work) methane hydrate dissociation conditions in thepresence of CaCl2–EG aqueous solutions

Salt Salt conc. EG conc. Dissociation point(mass%) (mass%)

Temperature Pressure(K ± 0.1) (MPa± 0.008)

CaCl2 15.0 21.3 269.4 4.027277.6 10.756283.1 22.918287.8 43.864

15.3 13.4 265.1 3.971272.7 9.804279.5 25.090283.6 45.436

18.0 14.0 261.5 3.907268.9 9.404275.2 22.994279.6 44.843

14.0 26.0 261.6 4.675268.1 9.942273.5 22.801277.9 43.347

thermodynamics model uses the Valderrama modification ofthe Patel and Teja equation of state (VPT EoS) for fugacitycalculations in all fluid phases (Valderrama, 1990). Non-density dependent (NDD) mixing rules are applied to modelpolar–nonpolar and polar–polar interaction (Avlonitis et al.,1994). Salts are considered as entity pseudo-components ina modified VPT EoS by defining their critical properties andacentric factors (Masoudi et al., 2004). The hydrate phaseis modelled by using the solid solution theory ofVan derWaals and Platteeuw (1959), as implemented byParrish andPrausnitz (1972). The Kihara model for spherical moleculesis applied to calculate the potential functions for compoundsforming the hydrate phase (Kihara, 1953).The VPT EoS has been chosen based onDanesh et al.

(1991)evaluation of 10 equations of state with classical mix-ing rules for predicting the phase behaviour and volumetricproperties of hydrocarbon fluids, with particular relevanceto the North Sea gas injection systems. They concluded thatthe VPT EoS was superior to other equations of state, par-ticularly without using any binary interaction parameter.However, the classical mixing rule is not satisfactory for

polar–nonpolar liquidmixtures and amore complicatedmix-ing rule is necessary.Avlonitis et al. (1994)proposed a NDDmixing rule and showed its superiority to density dependent(DD) mixing rules in representing the phase behaviour ofmulti component mixtures containing polar and non-polarcomponents.As mentioned earlier, in this model, salts are treated as

pseudo components that enables the model to simultane-

Table 5Optimised critical properties and acentric factor of CaCl2

TC (K) 3900PC (MPa) 48.32VC (cm3/mol) 212.61ZC 0.3168� 0.40

ously predict gas hydrate formation and salt precipitation,addressing the main shortcoming of the most of the previ-ously published models in the literature.Calcium chloride is a hydrated salt as it absorbs several

water molecules, mainly depending on temperature. The ex-tension of the recently developed model to including cal-cium chloride is detailed in the following section.

3.1. Critical properties of calcium chloride

There are very limited reported studies in the open liter-ature on the critical properties of salts (Carlson et al., 1960;Kirshenbaum et al., 1962; Pitzer, 1984). In all cases, criticalproperties of salts were estimated based on extrapolating ex-perimental liquid and vapour density data of each salt to hightemperature conditions. Therefore, the scatter observed inthe reported critical properties of salts in the literature is dueto differences in estimating approaches for critical points.As mentioned earlier, in this work salts are treated as

pseudo-components by optimising their critical propertiesand acentric factor using reliable initial guesses through anoptimisation process. For the modelling of CaCl2, there isno physical property data reported in the literature to beused as initial guess in the optimisation process. Therefore,the following relationships have been proposed and used toestimate initial values for the critical properties (TC, VC, PC)

of CaCl2, using NaCl as a reference salt:

TC(Salt) = Tb(Salt) ∗ TC(NaCl)/Tb(NaCl), (1)

VC(Salt) = v(Salt) ∗ VC(NaCl)/v(NaCl), (2)

PC(Salt) = ZC(Salt)RTC(Salt)/VC(Salt)

(with an initial value ofZC = 0.31). (3)

WhereTb and v are the boiling point and molar volumeof salt, respectively. After substituting the optimised criticalvalues for NaCl (Masoudi et al., 2004) into the above equa-tions, the initial estimates for CaCl2 critical properties are:TC = 3765K,VC = 366 cm3/mol, andPC = 26.54MPa.These initial estimates are further refined and tuned during

the optimisation process to match the VLS equilibria datausing experimental data on freezing point depression andboiling point elevation of aqueous electrolyte solutions. Allbinary interaction parameters between water and salt are setto zero at this stage.Table 5presents the critical properties(TC, PC, VC, ZC) and acentric factor (�) for CaCl2.

R. Masoudi et al. / Chemical Engineering Science 60 (2005) 4213–4224 4217

3.2. Solid–liquid equilibria (SLE)

In order to predict salt deposition in the liquid phase, itis necessary to examine solid–liquid equilibria (SLE). Mod-elling salting-out in aqueous electrolyte solutions is very im-portant as salts have significant effects on the solubility ofone another. Prediction of crystallisation of inorganic saltsfrom aqueous brines requires reliable solubility data and nu-merical modelling. Available predictive models in calculat-ing salt precipitation in multi electrolyte solutions as well asin aqueous solutions of salt and hydrate organic inhibitorsare very scarce with a large deviation from limited reportedexperimental data. For most multi-component systems theavailable solubility data are scarce and with significant dis-agreement. The majority of the available experimental dataand predictive electrolyte models are limited to systems at298.15K. At higher and lower temperatures, the number ofpredictive models decreases with a decrease in the availabil-ity of experimental data. Below, the recently developed saltprecipitation model, which is based on the equality of thefugacities of salt in the salt phase and the aqueous phase, isextended to the hydrated salts.In isothermal systems the equality of chemical potentials

can be expressed as

f̂ li = f̂ s

i (all i), (4)

wheref̂ li andf̂ s

i are the fugacities of speciesi in liquid andsolid phases, respectively. When the solvent does not enterthe solid phase, the fugacity of the solid phase, salt, remainsthat of the pure solid.The ratio of fugacity of pure solid at subcooled condition

to that of solid at the same temperature, considering theeffect of pressure and assuming that the volume change onmelting is independent of pressure, is expressed as

��i

RT= ln

f li

f si

= �hfi

RT

(1− T

Tm

)+ 1

RT

∫ T

Tm

�CpdT

− 1

R

∫ T

Tm

�CpT

dT + �Vfi

RT(P − PTm), (5)

where�Vfi and PTm are volume change on melting and

pressure at the melting point (normally equal to 1 bar), re-spectively. Eq. (5) shows the relationship between the fu-gacities of pure subcooled liquid and that of solid state.The reported heat capacity of liquid and solid calcium

chloride is the same up toT = 700K but they are differentat higher temperatures (Chase, 1985). Consequently, two�Cp equations have been correlated and used in numericalmodelling. They are:

�Cp(

J

molK

)= 0.0, T /K <700 (6)

�Cp(

J

molK

)= 19.4054403+ 0.0240587T

− 2.67∗ 10−5 ∗ T 2

700�T/K �1045, (7)

where�Cp= CplCaCl2 − CpsCaCl2. It should be noted thatpressure does not have a significant effect in Eq. (5) and sothe last term is ignored.The above solubility relations are valid for pure CaCl2

precipitation. However, calcium chloride generally precipi-tates as a hydrated salt with a number of water molecules(SaltnH2O) depending on temperature. Clearly, the SLE ofa hydrated salt is different from the pure salt, so it is neces-sary to develop suitable SLE relationship for hydrated salts(saltnH2O).In the case of a hydrated salt (SaltnH2O), the same ap-

proach asKashchiev and Firoozabadi (2002)for chemicalpotential of solid gas hydrate has been taken for the chemi-cal potential of hydrated salts. At the precipitation point fora hydrated salt (SaltnH2O), we have the following equilib-rium reaction:

Salt+ nH2O⇔ SaltnH2O. (8)

This relationship shows the salt and H2O as separate com-ponents in the fluid phase although not in the solid phase,so the solid–liquid equilibrium condition is

�fluidSalt + n�fluidH2O = �solidSaltnH2O, (9)

where�i is the chemical potential of speciesi. Eq. (9) can berewritten in the fugacity form (considering�i = RTLnf i):

ln f fluidSalt + n ln f fluid

H2O = ln f solidSaltnH2O. (10)

Moreover, Eq. (5), assuming the heat capacity terms can beneglected, is rewritten for hydrated salt as

(�PureSalt + n�PureH2O) − �SolidSaltnH2O

RT= ln

f PureSalt ∗ (f Pure

H2O)n

f SolidSaltnH2O

= �hf

R

(1

T− 1

Tm

). (11)

To predict the solubility of any hydrated salt (SaltnH2O) inwater, Eqs. (10) and (11) must be solved together. In anideal case, enthalpy change of melting at the solid meltingpoint (�hf ) and the melting point temperature (Tm), canbe obtained from experimental measurements for the solidphase. However, such data are usually not available for mostsalt hydrates (or even various anhydrous crystalline forms),therefore, it will be necessary to consider them as adjustableparameters, determined by matching the SLE data.For CaCl2, there are three main hydrate crystals, which

have different number of water molecules (CaCl2.6H2O,CaCl2.4H2O and CaCl2.2H2O), depending on temperature.In the literature, transition temperatures have been reported

4218 R. Masoudi et al. / Chemical Engineering Science 60 (2005) 4213–4224

Table 6Optimised�hf andTm for different precipitates of CaCl2 crystal

�hf (kJ/mol) Tm (K)

CaCl2·6H2OT �303.15K 434.31 398.35

CaCl2·4H2O303.15< T �318.15K 418.55 395.02

CaCl2·2H2O318.15< T (K) 362.57 396.10

210

230

250

270

290

310

330

350

0 10 20 30 40 50 60 70 80

CaCl2 / mass%

T /

K

Liquid

Liquid + Ice

Ice + CaCl2.6H2O

Liquid +

CaCl2.6H2O

CaCl2.6H2O

CaC

l 2.6H

2O

CaC

l 2.4H

2O

CaC

l 2.2H

2O

+CaCl2.4H2O

CaCl2.4H2O

CaCl2.4H2O

CaCl2.2H2O

+CaCl2.2H2O

Liquid + Liquid +

Fig. 1. Phase diagram of binary CaCl2–H2O. Freezing point experimentaldata(�): CRC (1989) and salt solubility data (©): This work; Stephenand Stephen (1963), Potter and Clynne (1978), Breton (1967).

as follows:

CaCl2 · 6H2O⇔ CaCl2 · 4H2O+ 2H2O,

30.1± 0.2◦C (Linke, 1965) & 30.08

± 0.05◦C (Potter and Clynne, 1978).

CaCl2 · 4H2O⇔ CaCl2 · 2H2O+ 2H2O,

45.1± 0.2◦C (Linke,1965) & 45.13

± 0.05◦C (Potter and Clynne, 1978).

Therefore, SLE experimental data could be used in the op-timisation process to tune�hf andTm of each CaCl2 pre-cipitate in the temperature range indicated above.Table 6presents the optimised�hf andTm for different precipitatesof CaCl2 crystal. Finally, salt precipitation can be predictedusing Eqs. (10) and (11). The quality of the optimisationprocess results has been presented inFig. 1 in salt solubilitylines for various CaCl2 precipitates.

-100

102030405060708090

100110120

0 10 20 30 40 50 60 70

CaCl2 / mass%

P /

kPa

Exp. data: Washburn (1926-30)

Predictions

273.15 K

313.15 K

343.15 K

363.15 K

373.15 K393.15 K

403.15 K

Fig. 2. Experimental and predicted water vapour pressure lowering in thepresence of CaCl2 at different temperatures.

266.15

267.15

268.15

269.15

270.15

271.15

272.15

273.15

0 8 10 12

(NaCl + CaCl2) / mass%

T /

KExp. data: Gibbard & Fong (1975)Prediction

NaCl/(NaCl+CaCl2)=0.51

2 4 6

Fig. 3. Experimental and predicted water freezing point temperatures inthe presence of NaCl and CaCl2.

4. Results and discussions

4.1. Modelling electrolyte solutions

Experimental data on the phase behaviour of water-saltsystems have been used in the optimisation of binary in-teraction parameters (BIPs) between water and salts. Thesedata include freezing point depression (CRC Hand Book ofChemistry and Physics, 1989) and boiling point elevation(Washburn, 1926–1930) data for electrolyte aqueous solu-tions. Fig. 1 presents the entire binary phase diagram ofCaCl2–H2O including the experimental data and model cal-culations.Fig. 2shows the vapour pressure lowering exper-imental data (Washburn, 1926–1930) together with modelpredictions of CaCl2 aqueous solutions at various tempera-tures. Experimental (Gibbard and Fong, 1975) and predictedwater freezing point temperatures in the presence of NaCland CaCl2 at 0.51 NaCl mass fraction [NaCl/(NaCl+CaCl2)]are depicted inFig. 3. Fig. 4 shows experimental (Shiah

R. Masoudi et al. / Chemical Engineering Science 60 (2005) 4213–4224 4219

0

5

10

15

20

25

30

295 300 305 310 315 320 325 330 335 340 345 350

T / K

P /

kPa

5.31 mass% NaCl / 5.81 mass% CaCl2Prediction7.60 mass% NaCl / 7.72 mass% CaCl2Prediction

Exp. data: Shiah & Tseng (1996)

Fig. 4. Experimental and predicted vapour pressure of NaCl and CaCl2aqueous solutions.

Table 7Experimental and predicted water vapour pressures in the presence ofKCl and CaCl2 at 298.15K

KCl CaCl2 P (kPa) P (kPa) Abs. error(mass%) (mass%) (experimental) (predicted) (%)

62842 3.5611 3.0144 3.0327 0.6152084 4.5748 3.0134 3.0316 0.61120979 4.3174 2.8837 2.9101 0.9192732 6.7083 2.8827 2.9141 1.0966275 8.8261 2.8827 2.9171 1.20

and Tseng, 1996) and predicted vapour pressure of NaCland CaCl2 aqueous solutions.Table 7depicts experimen-tal (Robinson and Bower, 1965) and predicted water vapourpressure lowering in the presence of KCl and CaCl2. It isimportant to note that the data presented inFigs. 2–4 andTable 7have not been used in the optimisation process, sothey are independent data and can justifiably be used for thevalidation of the model. The agreement between experimen-tal data and model predictions is good. It should be notedthe term “predicted” means that the experimental data havenot been used in the optimisation of the interaction parame-ters, whereas the term “calculated” means that the data havebeen used for tuning the required model parameters.

4.2. Gas solubility in electrolyte solutions

Available literature data for gas solubility in aqueous elec-trolyte solutions are used to optimise gas–salt binary interac-tion parameters. Since salts are polar and gases are non-polarmolecules, asymmetric mixing is applied for non-densitydependent mixing rules when modelling these systems. Asdetailed in a previous publication (Masoudi et al., 2004),for non-density dependent mixing rules, three parametersrequire optimisation: one classical, and two asymmetric bi-nary interaction parameters. All these binary interaction pa-

0.0005

0.001

0.0015

0.002

0.0025

0.003

0 10 20 30 40 50 60 70P / MPa

Con

cent

ratio

n of

CH

4 / m

ole

frac

tion

298.15 K

324.65 K

344.15 K

Predictions

Exp. data: Blanco & Smith (1978)

Fig. 5. Experimental and calculated methane solubility in 10.22 mass%CaCl2 aqueous solutions at three different temperatures.

0

0.005

0.01

0.015

0.02

0.025

0 10 20 30 40 50 60 70

P / MPa

Con

cent

ratio

n of

CO

2 / m

ole

frac

tion 10.1 mass% CaCl2

20.2 mass% CaCl230.2 mass% CaCl2Predictions

Exp. data: Prutton & Savage (1945)

Fig. 6. Experimental and calculated CO2 solubility in CaCl2 aqueoussolutions at 349.15K.

rameters have been presented in tabulated form inTable 8for the components investigated in this work.Fig. 5presents the experimental data (Blanco and Smith,

1978) and the model calculations for methane solubility in10.22 wt% of CaCl2 aqueous solutions at 298.15, 324.65,and 344.15K.Fig. 6 shows the experimental data (Pruttonand Savage, 1945) and the model calculations for carbondioxide solubility in 10.1, 20.2, and 30.2 mass% of CaCl2aqueous solutions at 349.15K.

4.3. Aqueous solutions of salts and organic inhibitors

Salts and organic inhibitors can be used in avoiding gashydrate problems in natural gas and oil production and trans-portation. For some ultra-deep waters, a combination of saltsand organic inhibitors is generally required to prevent gashydrate formation. However, the introduction of organic in-hibitors (e.g., methanol, ethanol, ethylene glycol, triethy-lene glycol, etc.) may adversely affect the salt solubility and

4220 R. Masoudi et al. / Chemical Engineering Science 60 (2005) 4213–4224

Table 8Binary interaction parameters for the VPT EoS and the NDD mixing rules

kij H2O CH4 CO2 EG NaCl KCl CaCl2

H2O 0 0.5058 0.2659 −0.0965 −0.2049 −0.2139 −0.4775CH4 0.5058 0 0 0.3762 1.13 0.9835 −1.665CO2 0.2659 0 0 0.0973 −0.2275 −0.5324 −0.3079EG −0.0965 0.3762 0.0973 0 −0.325 −0.0275 −5.9145NaCl −0.1793 1.13 −0.2275 −0.243 0 −0.3416 −0.8240KCl −0.1856 0.9835 −0.5324 −0.0466 −0.3872 0 −1.4453CaCl2 −0.4241 −1.665 −0.3079 1.4752 −2.3788 −2.7824 0

l0ij

H2O 0 1.818 0.81386 −0.004 −0.0484 −0.1044 1.439EG −0.0092 0.6614 0.0335 0 −0.432 0.2006 −0.6517NaCl 0.4425 52.88 −14.835 −0.1528 0 −1.9144 2.4967KCl 0.3694 −24.131 −38.254 −0.179 −2.3508 0 2.671CaCl2 5.563 370.466 522.33 8.3366 1.7435 0.2307 0

l1ij

∗ 1E + 4

H2O 0 49 18.3228 3.5392 −2.5 3.08 130.671EG 3.0836 22.147 12.139 0 −20.774 24.148 1814.699NaCl 46.47 7638.77 1624.81 73.266 0 173.703 −313.7401KCl 17.156 2347.553 4413.794 −4.984 8.2241 0 −380.7788CaCl2 673.718 112000 70185.959 −4836.8461 179.9688 9.1866 0

0

5

10

15

20

25

30

0 5 10 15 20 25 30 35 40 45 50

CaCl2 / mass%

NaC

l / m

ass%

Exp. data: 298.15 K, D'Ans (1933) & Linke (1965)

Exp. data: 288.71 K, Parrish (2000)

Predictions

Halite

Fig. 7. Salt solubilities in common-ion chloride ternary NaCl–CaCl2–H2Osystem at different temperature.

some salt may precipitate (salting-out), causing salt deposi-tion and reducing the hydrate preventive characteristics ofthe systems.New experimental data on physical properties (freezing

point, boiling point and salt solubility) of aqueous EG–saltsolutions (generated in this work) have been used to opti-mise salt–EG binary interaction parameters. Since ethyleneglycol and salt are both considered to be polar molecules,asymmetric mixing is applied for non-density dependentmixing rules whenmodelling these systems. For non-densitydependent mixing rules, three parameters require optimisa-tion: one classical, and two asymmetric binary interactionparameters.

The calculated freezing points of aqueous EG–CaCl2 so-lutions are compared with the experimental data inTable 1.Table 2presents the experimental data and the model calcu-lations for boiling point of EG–CaCl2 aqueous solutions.In the case of CaCl2 solubility in EG aqueous solutions,

the precipitation behaviour is different from that in pure wa-ter.As it is understood from generated experimental data, thiscould be due to a change in the number of water moleculesin the CaCl2nH2O precipitated crystals and/or the tempera-ture dependency of CaCl2 crystallisation process. Here, thesolubility of CaCl2 in EG aqueous solution has been pre-dicted based on pure CaCl2 precipitation not hydrated CaCl2as the precise nature of hydrated salt precipitations in thepresence of hydrate organic inhibitors (e.g., EG) is not cur-rently well known. Calculated CaCl2 solubility on ethyleneglycol concentration in aqueous solutions at various tem-peratures is also presented inTable 3. This table essentiallyshows the maximum concentrations of CaCl2 that can existwith EG in aqueous solution without any salt precipitation.

4.4. SLE in the ternary system NaCl–CaCl2–H2O

In the case of salt precipitation in the mixed electrolytesolutions,Harvie and Weare (1980)employed the literaturedata and investigated the mineral solubility in natural water.The authors showed that in the system NaCl–CaCl2–H2O,during precipitation, there is an initial precipitate region,which is halite (NaCl). Therefore, at any mole fraction ofNaCl (or CaCl2), the solid phase initially precipitated is onlyNaCl.

R. Masoudi et al. / Chemical Engineering Science 60 (2005) 4213–4224 4221

0

5

10

15

20

25

30

0 5 10 15 20 25 30 35 40 45

CaCl2 / mass%

KC

l / m

ass%

Exp. data: 298.15 K, D'Ans (1933) & Linke (1965)

Predictions

Sylvite

Fig. 8. Salt solubilities in common-ion chloride ternary KCl–CaCl2–H2Osystem at 298.15K.

Considering the above,Fig. 7 presents the calcu-lated mineral solubilities in common-ion chloride ternaryNaCl–CaCl2–H2O system compared to the experimentaldata at 298.15 (D’Ans, 1933; Linke, 1965) and 288.7K(Parrish, 2000). It is important to note that the data at288.7K has not been used in the optimisation process.

4.5. SLE in the ternary system KCl–CaCl2–H2O

In the event of precipitation in the ternary KCl–CaCl2–H2Osystem,Harvie and Weare (1980)showed there is just oneinitial precipitate region, which is sylvite (KCl). Therefore,at any mole fraction of KCl (or CaCl2), the solid phaseis initially KCl. Considering this fact;Fig. 8 shows calcu-lated mineral solubilities in common-ion chloride ternaryKCl–CaCl2–H2O system compared to experimental data at298.15K (D’Ans, 1933; Linke, 1965).

4.6. Validation of the model

A large number of experimental data covering a widerange of salt concentrations and temperatures have been usedin the validation of the model. A few are presented in thispaper. None of the above data have been used in optimisa-tion process. In the following sections, the model has beenvalidated for another two independent calculations (i.e., gashydrate phase boundaries in the presence of electrolyte andorganic inhibitor and SLE in the multi salts systems and inthe presence of non-electrolyte).

4.6.1. Gas hydrate stability zone predictionsIn this section the extended model is validated against the

independent literature and newly generated experimentaldata for gas hydrate inhibition effect of aqueous solutionscontaining salts and ethylene glycol.Fig. 9 shows exper-imental (Dholabhai et al., 1991) and predicted methanehydrate dissociation conditions for aqueous solutions

1000

10000

100000

266 268 270 272 274 276 278 280 282 284 286

T / K

P /

kPa

3 mass% NaCl / 3 mass% CaCl23 mass% NaCl / 10 mass% CaCl26 mass% NaCl / 10 mass% CaCl2distilled water

Predictions

Exp. data: Dholabhai et al. (1991)

Fig. 9. Experimental and predicted methane hydrate dissociation condi-tions in the presence of different concentrations of NaCl and CaCl2.

100

100000

264 266 268 270 272 274 276 278

T / K

P /

kPa

5 mass% CaCl2 / 20 mass% EG

5 mass% CaCl2 / 5 mass% NaCl / 15 mass% EG

distilled water

Predictions

Exp. data: Dholabhai et al. (1997)

Fig. 10. Experimental and predicted methane (80 mole%)+carbon dioxide(20 mole%) hydrate dissociation conditions in the presence of CaCl2,NaCl, and EG.

of sodium chloride and calcium chloride. Experimental(Dholabhai et al., 1997) and predicted 80 mole% methane +20 mole% carbon dioxide hydrate phase boundaries in thepresence of calcium chloride, sodium chloride and ethyleneglycol is depicted inFig. 10. Methane hydrate dissociationdata for various aqueous solutions of calcium chloride andethylene glycol measured as part of this work are comparedwith model predictions inFig. 11. Predictions show a goodagreement in all cases, demonstrating the reliability of thedeveloped model.

4.6.2. SLE in the quaternary systemNaCl–CaCl2–EG–H2OTo our knowledge, there is still no predictive model in

the open literature capable of predicting salt precipitationbehaviour in the aqueous multi-salt systems containingnon-electrolytes. In addition, very few experimental dataare available in the literature on the salt precipitation inaqueous multi-salt systems containing non-electrolytes.Fig. 12 presents independent experimental data (Parrish,2000) and model predictions for salt precipitation behaviour

4222 R. Masoudi et al. / Chemical Engineering Science 60 (2005) 4213–4224

1000

10000

100000

250 260 270 280 290 300

T / K

P /

kPa

10.0 mass% CaCl / 15.0 mass% EG15.3 mass% CaCl / 13.4 mass% EG18.0 mass% CaCl / 14.0 mass% EG14.0 mass% CaCl / 26.0 mass% EGdistilled waterPredictions

Fig. 11. Experimental (this work) and predicted methane hydrate disso-ciation conditions in the presence of CaCl2 and EG. Experimental datafor CH4-distilled water are fromDeaton and Frost (1946), McLoed andCampbell (1961), Jhaveri and Robinson (1965).

0

5

10

15

20

25

30

0 5 10 15 20 25 30 35 40 45CaCl2 / mass%

NaC

l / m

ass%

0 mass% EG

10 mass% EG

25 mass% EG

Predictions

Halite

Exp. data: Parrish (2000)

Fig. 12. Experimental and predicted salt solubility in quaternaryNaCl–CaCl2–EG–H2O system at 288.71K and various concentrations ofEG.

in the NaCl–CaCl2–EG–H2O quaternary systems at var-ious concentrations of EG. An acceptable agreement isobserved. It should be mentioned that, as experimental dataand model predictions show, in this system, same as theNaCl–CaCl2–H2O ternary system, the precipitation regionis initially halite. The predictions presented in this figureshow the reliability of the developed model.

5. Conclusions

Novel freezing point, boiling point and salt solubility datahave been measured for CaCl2–EG aqueous solutions. Thedata have been used in the optimisation of binary interac-tion parameters between salts and ethylene glycol in orderto extend a recently developed thermodynamic model to in-clude the phase equilibria involving combinations of saltsand organic inhibitors.

Recently developed model has been extended to includehydrated salts (e.g., CaCl2) and organic inhibitors. Themodel is capable of predicting complex VLSE for aqueouselectrolytes and/or organic inhibitor solutions over a widerange of pressure, temperature and salt concentrations.The salt precipitation model has been extended to include

hydrated salts with various precipitates. The model is basedon the equality of the fugacities of salt in the salt phaseand the aqueous phase, which are calculated from an EoS.The model has been successfully employed in modelling saltprecipitation in multi electrolyte solutions with or withoutorganic inhibitors.Reliable hydrate dissociation data for one quaternary

system—CH4–H2O–CaCl2–EG-has been measured at pres-sures up to 50MPa. These data have been used to validatethe predictive capabilities of the model for hydrate equilib-ria. Good agreement between model predictions and inde-pendent experimental data on; water freezing point depres-sion, vapour pressure lowering, salt solubility, and hydratestability zone, is observed, demonstrating the reliability androbustness of the developed model.

Notation

�Cp heat capacity change between liquidand solid states (J/(mol K))

f̂ li , f̂

si fugacity of speciesi in liquid and solid

phasesf l

i , fsi fugacity of pure speciesi as a liquid

and solid at T and P of the mixture�h

fi enthalpy change of melting at solid’s

melting point (J/mol)PTm pressure at solid’s melting point (bar)R ideal gas constant (= 8.314 J/(mol K))T temperature (K)Tb normal boiling point (K)TC, PC, VC, ZC critical propertiesTm melting point (K)v molar volume of salt (cm3)�V

fi volume change on melting at solid’s

melting point (cm3/mol)

Greek letters

�i chemical potential of speciesi (J/mol)��i chemical potential change between

liquid and solid states (J/mol)� acentric factor

Acknowledgements

This study was funded through a Joint Industry Projectat Heriot-Watt University, Inistitute of Petroleum Engineer-ing, sponsored by ABB, Petrobras, Shell, TOTAL and the

R. Masoudi et al. / Chemical Engineering Science 60 (2005) 4213–4224 4223

DTI, which is gratefully acknowledged. Mr Rahim Masoudiwishes to thank the National Iranian Oil Company (NIOC)for financial support. The authors wish to thank Dr. AndrzejAnderko for his invaluable and constructive comments andsuggestions.

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