Modeling electrolyte solutions with the Extended UNIQUAC model

Modeling electrolyte solutionswith the Extended UNIQUACmodelKaj ThomsenIVC-SEP, Department of ChemicalEngineering, Technical University ofDenmark, DK-2800 Lyngby, Denmark.E-mail: kth@kt.dtu.dk26-07-2004 11 th ISSP, Aveiro

Models for electrolytes• Debye-Hückel electrostatic term– Pitzer– Electrolyte NRTL– Extended UNIQUAC• MSA electrostatic term– Equation of state for electrolytes• Debye-Hückel / MSA26-07-2004 11 th ISSP, Aveiro

Standard states• Water is the solvent RT ln( x ); 10w w w w w x w1• Ions, non-electrolytes, gases aresolutes* * * RT ln( x ); 1i i i i i xi0i26-07-2004 11 th ISSP, Aveiro

Relative permittivity90Relative permittivity of aqueous solutionsRelative permittivity .80706050403020NaCl, Hasted et al, 1948Ethanol, Åkerlöf, 19321000 10 20 30 40 50 60 70 80 90 100Mass26-07-2004 11 th % soluteISSP, Aveiro

Extended UNIQUAC• Excess gibbs energy function– Debye-Hückel term– Standard UNIQUAC term• Activity coefficients and thermalproperties are derived by standardmethods known from classicalthermodynamics26-07-2004 11 th ISSP, Aveiro

Model parameters• Standard UNIQUAC parameters– Volume parameter for each species– Surface area parameter for each species– Interaction energy parameter for eachpair of species• Temperature dependence of interactionenergy parameter• Number of parameters:• eUNIQUAC ~ eNRTL

Databank• Over 100,000 experimental data– Activity coefficient– Enthalpy of mixing– Heat capacity– Degree of dissociation– Gas solubility– Salt solubility– Liquid-liquid equilibrium– Vapor-liquid equilibrium26-07-2004 11 th ISSP, Aveiro

Parameter estimation• Critical review of data• Non-linear least squares optimization– Differences between experimental andcalculated values are minimized– The calculation of the differencedepends on the type of data– All data of same type weighted equally26-07-2004 11 th ISSP, Aveiro

Anchoring of parameters• No binary solution of one ion inwater• Parameters of ions are relative toeach other• The hydrogen ion is used as anchor– Parameters for the hydrogen ion aregiven fixed values26-07-2004 11 th ISSP, Aveiro

Thermal properties• Excess enthalpy is calculated from thetemperature derivative of activitycoefficients.• By using thermal properties in theparameter estimation a bettertemperature dependency of activitycoefficients is achieved• Clear distinction between temperaturedependency and concentrationdependency26-07-2004 11 th ISSP, Aveiro

Parameters• H + , Na + , K + , NH 4+, Ca 2+ , Mg 2+ , Mn 2+ , Fe 2+ ,Co 2+ , Ni 2+ , Cu 2+ , Zn 2+ , Ba 2+ , Sr 2+• F - , Cl - , Br - , NO 3-, SO 42-, HSO 4-, OH - , CO 32-,HCO 3-, S 2O 82-, SO 32-, HSO 3- , HPO 4- , H 2 PO 4-• H 2 O, CO 2 , NH 3 , SO 2 , C 12 H 22 O 11 , CH 3 OH,C 2 H 5 OH, n-C 3 H 7 OH, i-C 3 H 7 OH, n-C 4 H 9 OH,i-C 4 H 9 OH, s-C 4 H 9 OH, t-C 4 H 9 OH26-07-2004 11 th ISSP, Aveiro

Equilibrium calculations• Speciation equilibrium• +• Solid-liquid equilibrium• Vapor-liquid equilibrium• Liquid-liquid equilibrium26-07-2004 11 th ISSP, Aveiro

Speciation equilibriaNH 3 (aq)+H 2 O NH 4+ (aq)+OH - (aq)Equilibrium condition: NH H O NH OH3 2 4 - -a a- lnRT a a* * * 0 * *NH OH NH H O NH OH- -4 3 24-*NHH O3 226-07-2004 11 th ISSP, Aveiro

Solid-liquid equilibrium• At equilibrium, the chemical potentialof the pure crystalline salt(hydrate)equals the sum of the chemicalpotentials of the salts components insolution• It is required that other salts are notsupersaturated.26-07-2004 11 th ISSP, Aveiro

Vapor-liquid equilibrium• Equality of chemical potential in gasphase and in liquid phase (Gamma-phimethod)• Gas phase fugacities are calculatedwith the Soave-Redlich-Kwongequation of stateCO ( g) CO ( aq)2 2 ˆ ln RT ln y P RT x 0, g* *CO CO CO CO CO CO2 2 2 2 2 226-07-2004 11 th ISSP, Aveiro

Liquid-liquid equilibrium• Equilibrium between component i inphase I and phase IIIi RT ln( x ) RT ln( x )* * I * * IIi i i i i i• Here the activity product of salts ratherthan the activities of the individual ionsions are comparedIIi( x) ( x)* I * IIi i i i26-07-2004 11 th ISSP, Aveiro

Standard state properties• The numerical values of standard statechemical potentials are needed beforeequilibrium calculations can be made• Such values for most solutes and manysalts are found in the NBS tables• Those not found have to be fitted toexperimental data• Temperature dependence calculated withclassical thermodynamic method26-07-2004 11 th ISSP, Aveiro

908070Extended UNIQUAC modelExperimental data--60Temperature °C50403020100-10IceMn(NO 3 ) 2·6H 2 OMn(NO 3 ) 2·4H 2 OMn(NO 3 ) 2·2H 2 OMn(NO 3 ) 2·H 2 O-200 10 20 30 40 50 60 70 80 90 100Mass percent Mn(NO 3 ) 226-07-2004 11 th ISSP, Aveiro

120100Ca(OH) 2Temperature °C80604020CalculatedExperimental00 0.05 0.1 0.15 0.2Mass percent Ca(OH) 226-07-2004 11 th ISSP, Aveiro

K2CO3 salt fractionNa2CO310.90.80.70.60.50.40.30.20.10IceNa 2 CO 3·10H 2 ONaKCO 3·6H 2 ONa 2 CO 3·7H 2 OK 2 CO 3·½H 2 OExtended UNIQUAC modelExperimental dataNa 2 CO 3·H 2 ONa 2 CO 3·K 2 CO 3Na 2 CO 3-40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 110Temperature, °C26-07-2004 11 th ISSP, Aveiro

9080Extended UNIQUAC modelExperimental data__5.9 molal NH 380°CCO2 partial pressure, bar70605040300.6 m1 m6.8 molal NH 32 molal 4.1 mNH 39 molal NH 312 molal NH 3201000 2 4 6 8 10CO 2 mol kg -126-07-2004 11 th ISSP, Aveiro

9010010010090H 2 O15°C2080807025°C307050°C406060504075°C6050504070303080Thompson and Vener (1948)20Armstrong and Eyre (1910)90Gerardin (1865)Schiff (1861)10KNO 3Extended UNIQUAC model100Series20Series30 10 20 30 Series4 40 50 60 70 80 90 100C 2 H 5 OH2010026-07-2004 11 th ISSP, Aveiro

100.0090.0080.0070.0060.0050.0040.0030.0020.00K 2 CO 310010.009080706050403010100H 2 O0 10 20 30 40 50 60 70 80 90 10026-07-2004 11 th ISSP, Aveiroiso-propanol0.00Iino et al. (1971)Do & Park (1974)Extended UNIQUACSeries2Series330 °C Series4Series72009080706050403020100

xy - diagram for iso-propanol - water, 1 bar10.90.8y iso-propanol0.70.60.50.40.30.20.10Extended UNIQUAC modelMarzal et al. (1996)Saturation with K2CO30 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x iso-propanol26-07-2004 11 th ISSP, Aveiro

Concluding remarks• The Extended UNIQUAC model is avery simpel model, with only binaryparameters, yet it is able to describethe phase behavior of electrolytesolutions within the experimentalaccuracy• Modeling of electrolytes under highpressure will be presented by AdaVilafafila Garcia on her poster26-07-2004 11 th ISSP, Aveiro