A good description of liquid-liquid equilibrium is important to design extraction separation processes. Equilibrium data are normally needed as distribution coefficients for each individual component. In this paper we have combined activity coefficient models with Hand?s equation for tie lines to calculate distribution coefficients in ternary systems. The proposed method gives betterdistribution coefficients than those calculated using only activity coefficient models. Besides, the proposed method could be employed to extrapolate experimental information when liquid-liquid equilibrium data are few.Fil: Mandagaran, Beatriz Adriana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: Campanella, Enrique Angel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentin

Campanella, Enrique Angel

Mandagaran, Beatriz Adriana

English

LAReferencia - Red Federada de Repositorios Institucionales de Publicaciones Científicas Latinoamericanas

DISTRIBUTION COEFFICIENT CALCULATIONIN TERNARY LIQUID-LIQUID SYSTEMSB.A. Mandagaran and E.A. Campanella#INTEC (CONICET – UNL), Güemes 3450, 3000 Santa Fe, Argentinae-mail: tquique@ceride.gov.arKeywords: Liquid-liquid equilibrium, UNIQUAC, UNIFAC, HandAbstractA good description of liquid-liquid equilibrium is important to design extraction separationprocesses. Equilibrium data are normally needed as distribution coefficients for each individualcomponent. In this paper we have combined activity coefficient models with Hand’s equation fortie lines to calculate distribution coefficients in ternary systems. The proposed method gives betterdistribution coefficients than those calculated using only activity coefficient models. Besides, theproposed method could be employed to extrapolate experimental information when liquid-liquidequilibrium data are few.                                                          # Author to whom correspondence should be addressed.1. IntroductionPrediction and/or correlation of ternaryliquid-liquid equilibrium is of importance inchemical engineering applications such asextraction and, when combined with vapor-liquid equilibrium data, in heterogeneousazeotropic distillation. In the literaturevarious methods have been used to correlateand to predict the compositions ofequilibrium phases for ternary liquid-liquidsystems. A series of recent articles (Sorensenet al. 1979a, 1979b; Magnussen et al. 1980)have presented an excellent review ofexperimental data sources, correlationmodels and prediction methods. Basically,there are two approaches to correlate data.One of them uses the equality of activitieswith a model for the activity coefficient, theother correlate data with equations such thatof Hand (Treybal, 1963). Furthermore, forpractical utilization of the equilibrium data inseparation processes calculation it isconvenient to describe the equilibrium interms of the distribution coefficients for eachcomponent. As those distribution coefficientsare system composition dependent, it isconvenient to represent them as polynomials(Rod, 1976).This paper presents a calculation schemethat combines the activity approach with theequation approach. The proposed methodwill improve coefficient distributionscalculations in a way that is suitable for itscorrelation with polynomials.2. Models and Method2.1 Thermodynamics ModelsA well-known empirical correlation fortie lines in liquid-liquid equilibrium is Hand’smethod (Treybal, 1963). Using molar fractionand natural logarithm, Hand’s equation isgiven by:ln y2/y1 = k ln x2/x3 + C (1)where component 2 is  the solute, yi is thecomposition of component i in the phase richin component 1, xi is the composition ofcomponent i in the phase rich in component3, and k, C are ternary system dependentconstants.Other way to calculate liquid-liquidequilibrium is using the equality of chemicalpotential for each component in both phases.Normally the equality is rewritten in terms ofactivities.  Using a model  for the activityTable 1. Ternary Systems and Models PerformanceSystem Type Temperature(K) Reference m2 Calculation Performance1)Toluene(1)2-Propanone(2)Water(3)I 283.15 Sorensen and Arlt,1980,Vol. 5/2,pág.497.UNIQUAC spec.par.+HandUNIQUAC spec.par.UNIFAC+HandUNIFACToluene(1)2-Propanone(2)Water(3)I 293.15 Sorensen and Arlt,1980,Vol. 5/2,pág.498.UNIQUAC spec.par.+HandUNIFAC+HandUNIQUAC spec.par.UNIFACToluene(1)2-Propanone(2)Water(3)I 303.15 Sorensen and Arlt,1980,Vol. 5/2,pág.499.UNIQUAC spec.par.+HandUNIQUAC spec.par.UNIFAC+HandUNIFAC1-Butanol(1)Succinic Acid(2)Water(3)I 283.15 Sorensen and Arlt,1980,Vol. 5/3,pág.11.UNIQUAC spec.par.+HandUNIQUAC spec.par.UNIFAC+HandUNIFAC1-Butanol(1)Succinic Acid(2)Water(3)I 303.15 Sorensen and Arlt,1980,Vol. 5/3,pág.14.UNIQUAC spec.par.+HandUNIQUAC spec.par.UNIFAC+HandUNIFACPropanoic Acid,EthylEster(1)2-Propanone(2)Water(3)I 303.15 Sorensen and Arlt,1980,Vol. 5/2,pág.474.UNIQUAC spec.par.UNIQUAC spec.par.+HandUNIFAC+HandUNIFACBenzene(1)1,4-Dioxane(2)Water(3)I 298.15 Sorensen and Arlt,1980,Vol. 5/3,pág.72.UNIQUAC spec.par.+HandUNIQUAC spec.par.UNIQUAC com.par.+HandUNIQUAC com.par.Heptane(1)Cyclohexane(2)Aniline(3)II 298.15 Sorensen and Arlt,1980,Vol. 5/3,pág.304.UNIFAC+HandUNIQUAC com.par.+HandUNIFACButane,2,2-Dimethyl(1)Cyclopentane(2)Aniline(3)II 288.15 Sorensen and Arlt,1980,Vol. 5/3,pág.248.UNIQUAC spec.par.UNIQUAC spec.par.+HandUNIFAC+HandUNIFACAcetic Acid,Ethyl Ester(1)1-Propanol(2)Water(3)I 293.15 Sorensen and Arlt,1980,Vol. 5/2,pág.550.UNIQUAC spec.par.+HandUNIQUAC spec.par.UNIFAC+HandUNIFACToluene(1)Acetaldehyde(2)Water(3)I 290.15 Sorensen and Arlt,1980,Vol. 5/2,pág.215.UNIFAC+HandUNIFAC1) m2 = distribution coefficient of component 2 = y2/x20 20 10040 80606040200MOL PER CENT OF (3)MOL PER CENT OF (2)TOLUENE(1) - 2 PROPANONE(2) - WATER(3)Fig.1a. Comparison of calculated binodal curve withexperimental data:  !Experimental,   UNIFAC, – – –UNIQUAC (“specific”),  ο ο ο UNIQUAC (“common”).coefficients one can carry out calculations toobtain liquid-liquid compositions (Sorensenet al., 1979b). We used two models in ourcalculations: UNIQUAC and UNIFAC. Wetook data, equations, parameters andprograms from Sorensen and Arlt (1980) andMagnussen et al. (1981).2.2 Proposed MethodWe combined Hand’s equation andactivity coefficient models in the followingway: 1) We got  k and C constants of Hand'sequation (Eqn. 1) using experimental liquid-liquid ternary equilibrium data, 2) weobtained the binodal curve of the ternarysystem under study using an activitycoefficient model,  3) we got x1 and x3 fromthe binodal curve of step 2 after choosing aDISTRIBUTION COEFFICIENT OF (2), m20 10 20 30TOLUENE(1) - 2 PROPANONE(2) - WATER(3)3,52,03,02,5 Fig.2a. Comparison of calculated distributioncoefficient with experimental data: ! Experimental, UNIFAC + Hand, ο ο ο UNIQUAC(“specific”) +Hand, – – –UNIQUAC (“common”) + Hand.TOLUENE(1) - 2 PROPANONE(2) - WATER(3)MOL PER CENT OF (2)60402000 20 10040 8060MOL PER CENT OF (3) Fig.1b. Comparison of calculated tie lines withexperimental data: ! ! Experimental, ο – – – οUNIFAC, !!!! UNIQUAC (“specific”).value for x2, 4) with x2/x3 , k and C fromprevious steps and using Eqn.1 we got y2/y1,5) from the binodal curve and y2/y1 wecalculated y1,y2 and y3, 6) we computed mi,where mi = yi / xi .3. Results and DiscussionsTable 1 contains the systems we did inthis study. Experimental reference, temp-erature, and type of mixture are written downin the table. The sample of systems understudy encompasses ternary mixtures with andwithout water, with one and two inmisciblebinaries,  and  some mixtures  at   differentTOLUENE(1) - 2 PROPANONE(2) - WATER(3)0 10 20 3054321DISTRIBUTION COEFFICIENT OF (2), m2MOL PER CENT OF (2) IN PHASE RICH IN (3), 100 X2Fig.2b. Comparison of calculated distributioncoefficient with experimental data: !Experimental,   UNIFAC + Hand,   – – –UNIFAC, οο ο UNIQUAC (“specific”).0 10 20 30TOLUENE(1) - 2 PROPANONE(2) - WATER(3)MOL PER CENT OF (2) IN PHASE RICH IN (3), 100 X2400102030405060MOL PER CENT OF (2) IN PHASE RICH IN (1), 100 Y2 Fig.3. Comparison of calculated solute distributionwith experimental data: ! Experimental,   UNIFAC,– – –UNIQUAC (“specific”), ο ο ο  UNIQUAC(“specific”) + Hand.temperatures. Table 1 and Figs. 1 to 9compare and display results from thecalculations described in item 2: Models andMethod. Table 1 shows in its last columncalculated distribution coefficient for thesolute, component 2, in a qualitative way. Inthat last column an order is written reflectingthe agreement of the model/method with theexperimental information.The model named first in the list is theone that presents the best agreement. Thepicture of the agreement results of threerepresentative systems could be appreciatedfrom Fig.1 to 9. As expected, correlation ofdata (UNIQUAC) is better than pre-diction (UNIFAC) for phase envelope and tie1 BUTANOL(1) - SUCCINIC ACID(2) - WATER(3)30 9050 7001284MOL PER CENT OF (3)MOL PER CENT OF (2) Fig.4a. Comparison of calculated binodal curve withexperimental  data: !  Experimental,      UNIFAC,ο ο ο UNIQUAC (“specific”).1 BUTANOL(1) - SUCCINIC ACID(2) - WATER(3)MOL PER CENT OF (2) IN PHASE RICH IN (3), 100 X2MOL PER CENT OF (2) IN PHASE RICH IN (1), 100 Y20 2 4 6 1081086420Fig.6. Comparison of calculated solute distributionwith experimental data: ! Experimental,   UNIFAC,– – –UNIQUAC (“specific”), ο ο ο UNIQUAC(“specific”) + Hand.lines determination. Those facts that are notwritten in Table 1 could be seen in Figs.1, 4and 7. In Table 1 it is also possible to seeunder its last heading that the calculationmethods that combine a thermodynamics  model(UNIQUAC or UNIFAC) with the Handcorrelation give better coefficient distributionthan the one calculated using thethermodynamics model itself. In some casesthe combination UNIFAC plus Hand is evenbetter than correlation of data usingUNIQUAC. Figure 1 presents phaseenvelope (Fig.1a) and tie lines (Fig.1b) forToluene(1)-2 Propanone(2)-Water(3). Figure1a shows  experimental, UNIQUAC, andUNIFAC results. Results from UNIQUACbelong to two  different  sets  of  parameters(Sorensen and Arlt, 1980). The parameters1 BUTANOL(1) - SUCCINIC ACID(2) - WATER(3)30 9050 70MOL PER CENT OF (3)01284MOL PER CENT OF (2)Fig.4b. Comparison of calculated tie lines withexperimental data: ! ! Experimental, ο!!οUNIFAC, !– ⋅ ⋅ –!  UNIQUAC (“specific”).1 BUTANOL(1) - SUCCINIC ACID(2) - WATER(3)MOL PER CENT OF (2) IN PHASE RICH IN (3), 100 X20,0 1,0 2,0 3,0 5,04,01,02,03,04,0DISTRIBUTION COEFFICIENT OF (2), m2Fig.5a. Comparison of calculated distributioncoefficient with experimental data: ! Experimental, UNIFAC + Hand, !! UNIQUAC (“specific”) +Hand.are “specific” when they are fitted to oneparticular system. The parameters are“common” when they are determined bysimultaneous correlation of experimental datafrom different systems. Figure 1b shows afew tie lines near plait point and another fewat low concentration of the distributedcomponent. The tie lines are fromexperimental data, UNIQUAC with specificparameters and UNIFAC. The objective ofFig.1 is to show the fact that UNIQUAC/UNIFAC represent better the binodal curveof liquid-liquid equilibrium in ternarymixtures than theirs corresponding tie lines.The association of Hand with UNIQUAC/UNIFAC proposed in this paper is built inthat fact. Figure 2 presents the distributioncoefficient of 2-Propanone. The coefficientis calculated dividing the concentration ofHEPTANE(1) - CYCLOHEXANE(2) - ANILINE(3)MOL PER CENT OF (3)0 20 40 60 10080MOL PER CENT OF (2)020406080100 Fig.7a. Comparison of calculated binodal curvewith experimental data: ! Experimental, UNIFAC, ο ο ο UNIQUAC  (“common”).MOL PER CENT OF (2) IN PHASE RICH IN (3), 100 X20,0 1,0 2,0 3,0 5,04,01 BUTANOL(1) - SUCCINIC ACID(2) - WATER(3)0,023,04,0DISTRIBUTION COEFFICIENT OF (2), m21,0Fig.5b. Comparison of calculated distributioncoefficient with experimental data: ! Experimental, UNIFAC + Hand, – – –UNIFAC, !! UNIQUAC(“specific”).2-Propanone in the Toluene rich phase by theconcentration of  2-Propanone in the Waterrich phase. Figure 2 is split in Fig.2a and 2bto facilitate the visualization of results. Thedistribution coefficient belonging to thecombination Hand with UNIFAC was drawnin both figures ( Fig.2a and  Fig.2b) as areference for comparison. Examination ofFig.2 indicates that the use of Handcorrelation improves the description ofdistribution coefficient. Any model incombination with Hand’s equation(UNIQUAC with specific or commonparameters, or UNIFAC) gives a betterdistribution coefficient than the use of anymodel alone. Figure 3 displaying 2-Propanoneconcentration in both phases shows the sameresult than Fig.2: combination of model withHand gives better results.Figures 4 and 5 display identical resultsthan Figs.1 and 2 for 1-Butanol(1)- SucccinicHEPTANE(1) - CYCLOHEXANE(2) - ANILINE(3)MOL PER CENT OF (3)0 20 40 60 10080MOL PER CENT OF (2)020406080100Fig.7b. Comparison of calculated tie lines withexperimental data: ! ! Experimental, ο— —οUNIFAC, !!!! UNIQUAC (“common”).HEPTANE(1) - CYCLOHEXANE(2) - ANILINE(3)MOL PER CENT OF (2) IN PHASE RICH IN (3), 100 X20 5 10 15261014DISTRIBUTION COEFFICIENT OF (2), m2 Fig.8a. Comparison of calculated distributioncoefficient with experimental data: ! Experimental, UNIFAC + Hand, – – –UNIFAC, ο ο ο  UNIQUAC(“common”).Acid(2)-Water(3). Figure 6 shows solute(Succinic Acid) distribution in both phases.Figures 7 , 8 and 9 displays the same form ofbehavior for the Heptane(1)-Cyclohexane(2)-Aniline(3) system than the other two earliersystems . This last ternary system is a type IImixture, meaning that two binaries areinmiscibles: Heptane-Aniline, and Cyclohexane-Aniline. The previous two systems are type Imixtures with only one binary showinginmiscibility. In Figs.7 and 8 the numbers forthe UNIQUAC with specific parameters aremissing because the parameters were notavailable from the data source (Sorensen  andArlt, 1980). Distribution coefficients for theother two components of the ternary systemsshow the same behavior than  distributionMOL PER CENT OF (2) IN PHASE RICH IN (3), 100 X20 40HEPTANE(1) - CYCLOHEXANE(2) - ANILINE(3)20 60 80806040200MOL PER CENT OF (2) IN PHASE RICH IN (1), 100 Y2Fig.9.Comparison of calculated solute distributionwith experimental data: ! Experimental,   UNIFAC+ Hand.261014DISTRIBUTION COEFFICIENT OF (2), m2HEPTANE(1) - CYCLOHEXANE(2) - ANILINE(3)MOL PER CENT OF (2) IN PHASE RICH IN (3), 100 X20 5 10 15Fig.8b. Comparison of calculated distributioncoefficient  with  experimental data: !  Experimental,  UNIFAC + Hand, – – –UNIQUAC (“common”) +Hand.coefficient for component 2 in all the ternarymixtures under study.The proposed combination seems towork because it uses the best of each of theapproaches cited earlier in this work. Theorientation of the tie lines is set by Hand’sequation and the binodal curve is set byUNIQUAC/UNIFAC. We could guess thatthe proposed method is going to work betterin cases were tie line's differences betweenUNIQUAC and experiments are larger. Thecombination works even when the availableexperimental information is little allowingfor extrapolation of data. The minimunexperimental information required for thecombination to work is two tie lines that areneeded to obtain Hand’s parameter k and Cof Eqn. 1. Then, it is possible to use theproposed combination to get a table ofextrapolated distribution coefficients that arefitted with polynomials as recommended inthe literature (Rod, 1976). Additionalundertaking is necessary to evaluatecompletely the proposed calculation method.Two things will be done: a) a systematicstudy of many more systems; b) an analysisof how to assemble Hand’s equation withUNIQUAC/UNIFAC at the very lowcomposition of the distributed componentand at the plait point.4. ConclusionsThis paper presents a method tocalculate coefficient distributions for  liquid -liquid ternary systems. The proposed methodcombines Hand’s equation with UNIQUACor UNIFAC model. The combination givesdistribution coefficients that agree withexperimental ones better than the coefficientscalculated using the models alone. Inaddition, the proposed method could be usedto extrapolate scare experimental information.AcknowledgmentsThe authors are thankful for the financialaid received from CONICET, UNL,ANPCyT and Fundación ANDES.ReferencesMagnussen T., P. Rasmussen and A.Fredenslund, “UNIFAC Parameter Tablefor Prediction of Liquid - LiquidEquilibria”, Ind. Eng. Chem. ProcessDes. Dev. 20, 331-339 (1981).Magnussen T., J.M. Sorensen, P. Rasmussenand A. Fredenslund, “Liquid - LiquidEquilibrium Data: Their Retrieval,Correlation and Prediction, Part III:Prediction”, Fluid Phase Equilibria 4,151-163 (1980).Rod V.,”Correlation of Equilibrium Data inTernary Liquid - Liquid Systems”, TheChemical Engineering Journal 11,105-110 (1976).Sorensen J.M., T. Magnussen, P. Rasmussenand A. Fredenslund, “Liquid - LiquidEquilibrium Data: Their Retrieval,Correlation and Prediction, Part I:Retrieval”, Fluid Phase Equilibria 2,297-309 (1979).Sorensen J.M., T. Magnussen, P. Rasmussenand A. Fredenslund, “Liquid - LiquidEquilibrium Data: Their Retrieval,Correlation and Prediction, Part II:Correlation”, Fluid Phase Equilibria 3,47-82 (1979).Sorensen J.M. and W. Arlt, Liquid-LiquidEquilibrium Data Collection, Dechema(1980).Treybal R., Liquid Extraction, 2nd Edn., McGraw Hill, New York (1963).

Distribution Coefficient Calculation in Ternary Liquid-Liquid Systems

CONICET Digital

DISTRIBUTION COEFFICIENT CALCULATIONIN TERNARY LIQUID-LIQUID SYSTEMSB.A. Mandagaran and E.A. Campanella#INTEC (CONICET – UNL), Güemes 3450, 3000 Santa Fe, Argentinae-mail: tquique@ceride.gov.arKeywords: Liquid-liquid equilibrium, UNIQUAC, UNIFAC, HandAbstractA good description of liquid-liquid equilibrium is important to design extraction separationprocesses. Equilibrium data are normally needed as distribution coefficients for each individualcomponent. In this paper we have combined activity coefficient models with Hand’s equation fortie lines to calculate distribution coefficients in ternary systems. The proposed method gives betterdistribution coefficients than those calculated using only activity coefficient models. Besides, theproposed method could be employed to extrapolate experimental information when liquid-liquidequilibrium data are few.                                                          # Author to whom correspondence should be addressed.1. IntroductionPrediction and/or correlation of ternaryliquid-liquid equilibrium is of importance inchemical engineering applications such asextraction and, when combined with vapor-liquid equilibrium data, in heterogeneousazeotropic distillation. In the literaturevarious methods have been used to correlateand to predict the compositions ofequilibrium phases for ternary liquid-liquidsystems. A series of recent articles (Sorensenet al. 1979a, 1979b; Magnussen et al. 1980)have presented an excellent review ofexperimental data sources, correlationmodels and prediction methods. Basically,there are two approaches to correlate data.One of them uses the equality of activitieswith a model for the activity coefficient, theother correlate data with equations such thatof Hand (Treybal, 1963). Furthermore, forpractical utilization of the equilibrium data inseparation processes calculation it isconvenient to describe the equilibrium interms of the distribution coefficients for eachcomponent. As those distribution coefficientsare system composition dependent, it isconvenient to represent them as polynomials(Rod, 1976).This paper presents a calculation schemethat combines the activity approach with theequation approach. The proposed methodwill improve coefficient distributionscalculations in a way that is suitable for itscorrelation with polynomials.2. Models and Method2.1 Thermodynamics ModelsA well-known empirical correlation fortie lines in liquid-liquid equilibrium is Hand’smethod (Treybal, 1963). Using molar fractionand natural logarithm, Hand’s equation isgiven by:ln y2/y1 = k ln x2/x3 + C (1)where component 2 is  the solute, yi is thecomposition of component i in the phase richin component 1, xi is the composition ofcomponent i in the phase rich in component3, and k, C are ternary system dependentconstants.Other way to calculate liquid-liquidequilibrium is using the equality of chemicalpotential for each component in both phases.Normally the equality is rewritten in terms ofactivities.  Using a model  for the activityTable 1. Ternary Systems and Models PerformanceSystem Type Temperature(K) Reference m2 Calculation Performance1)Toluene(1)2-Propanone(2)Water(3)I 283.15 Sorensen and Arlt,1980,Vol. 5/2,pág.497.UNIQUAC spec.par.+HandUNIQUAC spec.par.UNIFAC+HandUNIFACToluene(1)2-Propanone(2)Water(3)I 293.15 Sorensen and Arlt,1980,Vol. 5/2,pág.498.UNIQUAC spec.par.+HandUNIFAC+HandUNIQUAC spec.par.UNIFACToluene(1)2-Propanone(2)Water(3)I 303.15 Sorensen and Arlt,1980,Vol. 5/2,pág.499.UNIQUAC spec.par.+HandUNIQUAC spec.par.UNIFAC+HandUNIFAC1-Butanol(1)Succinic Acid(2)Water(3)I 283.15 Sorensen and Arlt,1980,Vol. 5/3,pág.11.UNIQUAC spec.par.+HandUNIQUAC spec.par.UNIFAC+HandUNIFAC1-Butanol(1)Succinic Acid(2)Water(3)I 303.15 Sorensen and Arlt,1980,Vol. 5/3,pág.14.UNIQUAC spec.par.+HandUNIQUAC spec.par.UNIFAC+HandUNIFACPropanoic Acid,EthylEster(1)2-Propanone(2)Water(3)I 303.15 Sorensen and Arlt,1980,Vol. 5/2,pág.474.UNIQUAC spec.par.UNIQUAC spec.par.+HandUNIFAC+HandUNIFACBenzene(1)1,4-Dioxane(2)Water(3)I 298.15 Sorensen and Arlt,1980,Vol. 5/3,pág.72.UNIQUAC spec.par.+HandUNIQUAC spec.par.UNIQUAC com.par.+HandUNIQUAC com.par.Heptane(1)Cyclohexane(2)Aniline(3)II 298.15 Sorensen and Arlt,1980,Vol. 5/3,pág.304.UNIFAC+HandUNIQUAC com.par.+HandUNIFACButane,2,2-Dimethyl(1)Cyclopentane(2)Aniline(3)II 288.15 Sorensen and Arlt,1980,Vol. 5/3,pág.248.UNIQUAC spec.par.UNIQUAC spec.par.+HandUNIFAC+HandUNIFACAcetic Acid,Ethyl Ester(1)1-Propanol(2)Water(3)I 293.15 Sorensen and Arlt,1980,Vol. 5/2,pág.550.UNIQUAC spec.par.+HandUNIQUAC spec.par.UNIFAC+HandUNIFACToluene(1)Acetaldehyde(2)Water(3)I 290.15 Sorensen and Arlt,1980,Vol. 5/2,pág.215.UNIFAC+HandUNIFAC1) m2 = distribution coefficient of component 2 = y2/x20 20 10040 80606040200MOL PER CENT OF (3)MOL PER CENT OF (2)TOLUENE(1) - 2 PROPANONE(2) - WATER(3)Fig.1a. Comparison of calculated binodal curve withexperimental data:  !Experimental,  UNIFAC, – – –UNIQUAC (“specific”),  ο ο ο UNIQUAC (“common”).coefficients one can carry out calculations toobtain liquid-liquid compositions (Sorensenet al., 1979b). We used two models in ourcalculations: UNIQUAC and UNIFAC. Wetook data, equations, parameters andprograms from Sorensen and Arlt (1980) andMagnussen et al. (1981).2.2 Proposed MethodWe combined Hand’s equation andactivity coefficient models in the followingway: 1) We got  k and C constants of Hand'sequation (Eqn. 1) using experimental liquid-liquid ternary equilibrium data, 2) weobtained the binodal curve of the ternarysystem under study using an activitycoefficient model,  3) we got x1 and x3 fromthe binodal curve of step 2 after choosing aDISTRIBUTION COEFFICIENT OF (2), m20 10 20 30TOLUENE(1) - 2 PROPANONE(2) - WATER(3)3,52,03,02,5 Fig.2a. Comparison of calculated distributioncoefficient with experimental data: ! Experimental,UNIFAC + Hand, ο ο ο UNIQUAC(“specific”) +Hand, – – –UNIQUAC (“common”) + Hand.TOLUENE(1) - 2 PROPANONE(2) - WATER(3)MOL PER CENT OF (2)60402000 20 10040 8060MOL PER CENT OF (3) Fig.1b. Comparison of calculated tie lines withexperimental data: !! Experimental, ο – – – οUNIFAC, !!!! UNIQUAC (“specific”).value for x2, 4) with x2/x3 , k and C fromprevious steps and using Eqn.1 we got y2/y1,5) from the binodal curve and y2/y1 wecalculated y1,y2 and y3, 6) we computed mi,where mi = yi / xi .3. Results and DiscussionsTable 1 contains the systems we did inthis study. Experimental reference, temp-erature, and type of mixture are written downin the table. The sample of systems understudy encompasses ternary mixtures with andwithout water, with one and two inmisciblebinaries,  and  some mixtures  at   differentTOLUENE(1) - 2 PROPANONE(2) - WATER(3)0 10 20 3054321DISTRIBUTION COEFFICIENT OF (2), m2MOL PER CENT OF (2) IN PHASE RICH IN (3), 100 X2Fig.2b. Comparison of calculated distributioncoefficient with experimental data: !Experimental,  UNIFAC + Hand,   – – –UNIFAC, οο ο UNIQUAC (“specific”).0 10 20 30TOLUENE(1) - 2 PROPANONE(2) - WATER(3)MOL PER CENT OF (2) IN PHASE RICH IN (3), 100 X2400102030405060MOL PER CENT OF (2) IN PHASE RICH IN (1), 100 Y2 Fig.3. Comparison of calculated solute distributionwith experimental data: ! Experimental,  UNIFAC,– – –UNIQUAC (“specific”), ο ο ο  UNIQUAC(“specific”) + Hand.temperatures. Table 1 and Figs. 1 to 9compare and display results from thecalculations described in item 2: Models andMethod. Table 1 shows in its last columncalculated distribution coefficient for thesolute, component 2, in a qualitative way. Inthat last column an order is written reflectingthe agreement of the model/method with theexperimental information.The model named first in the list is theone that presents the best agreement. Thepicture of the agreement results of threerepresentative systems could be appreciatedfrom Fig.1 to 9. As expected, correlation ofdata (UNIQUAC) is better than pre-diction (UNIFAC) for phase envelope and tie1 BUTANOL(1) - SUCCINIC ACID(2) - WATER(3)30 9050 7001284MOL PER CENT OF (3)MOL PER CENT OF (2) Fig.4a. Comparison of calculated binodal curve withexperimental  data: !  Experimental,     UNIFAC,ο ο ο UNIQUAC (“specific”).1 BUTANOL(1) - SUCCINIC ACID(2) - WATER(3)MOL PER CENT OF (2) IN PHASE RICH IN (3), 100 X2MOL PER CENT OF (2) IN PHASE RICH IN (1), 100 Y20 2 4 6 1081086420Fig.6. Comparison of calculated solute distributionwith experimental data: ! Experimental,  UNIFAC,– – –UNIQUAC (“specific”), ο ο ο UNIQUAC(“specific”) + Hand.lines determination. Those facts that are notwritten in Table 1 could be seen in Figs.1, 4and 7. In Table 1 it is also possible to seeunder its last heading that the calculationmethods that combine a thermodynamics  model(UNIQUAC or UNIFAC) with the Handcorrelation give better coefficient distributionthan the one calculated using thethermodynamics model itself. In some casesthe combination UNIFAC plus Hand is evenbetter than correlation of data usingUNIQUAC. Figure 1 presents phaseenvelope (Fig.1a) and tie lines (Fig.1b) forToluene(1)-2 Propanone(2)-Water(3). Figure1a shows  experimental, UNIQUAC, andUNIFAC results. Results from UNIQUACbelong to two  different  sets  of  parameters(Sorensen and Arlt, 1980). The parameters1 BUTANOL(1) - SUCCINIC ACID(2) - WATER(3)30 9050 70MOL PER CENT OF (3)01284MOL PER CENT OF (2)Fig.4b. Comparison of calculated tie lines withexperimental data: !! Experimental, ο!!οUNIFAC, !– ⋅ ⋅ –!  UNIQUAC (“specific”).1 BUTANOL(1) - SUCCINIC ACID(2) - WATER(3)MOL PER CENT OF (2) IN PHASE RICH IN (3), 100 X20,0 1,0 2,0 3,0 5,04,01,02,03,04,0DISTRIBUTION COEFFICIENT OF (2), m2Fig.5a. Comparison of calculated distributioncoefficient with experimental data: ! Experimental,UNIFAC + Hand, !! UNIQUAC (“specific”) +Hand.are “specific” when they are fitted to oneparticular system. The parameters are“common” when they are determined bysimultaneous correlation of experimental datafrom different systems. Figure 1b shows afew tie lines near plait point and another fewat low concentration of the distributedcomponent. The tie lines are fromexperimental data, UNIQUAC with specificparameters and UNIFAC. The objective ofFig.1 is to show the fact that UNIQUAC/UNIFAC represent better the binodal curveof liquid-liquid equilibrium in ternarymixtures than theirs corresponding tie lines.The association of Hand with UNIQUAC/UNIFAC proposed in this paper is built inthat fact. Figure 2 presents the distributioncoefficient of 2-Propanone. The coefficientis calculated dividing the concentration ofHEPTANE(1) - CYCLOHEXANE(2) - ANILINE(3)MOL PER CENT OF (3)0 20 40 60 10080MOL PER CENT OF (2)020406080100 Fig.7a. Comparison of calculated binodal curvewith experimental data: ! Experimental,UNIFAC, ο ο ο UNIQUAC  (“common”).MOL PER CENT OF (2) IN PHASE RICH IN (3), 100 X20,0 1,0 2,0 3,0 5,04,01 BUTANOL(1) - SUCCINIC ACID(2) - WATER(3)0,023,04,0DISTRIBUTION COEFFICIENT OF (2), m21,0Fig.5b. Comparison of calculated distributioncoefficient with experimental data: ! Experimental,UNIFAC + Hand, – – –UNIFAC, !! UNIQUAC(“specific”).2-Propanone in the Toluene rich phase by theconcentration of  2-Propanone in the Waterrich phase. Figure 2 is split in Fig.2a and 2bto facilitate the visualization of results. Thedistribution coefficient belonging to thecombination Hand with UNIFAC was drawnin both figures ( Fig.2a and  Fig.2b) as areference for comparison. Examination ofFig.2 indicates that the use of Handcorrelation improves the description ofdistribution coefficient. Any model incombination with Hand’s equation(UNIQUAC with specific or commonparameters, or UNIFAC) gives a betterdistribution coefficient than the use of anymodel alone. Figure 3 displaying 2-Propanoneconcentration in both phases shows the sameresult than Fig.2: combination of model withHand gives better results.Figures 4 and 5 display identical resultsthan Figs.1 and 2 for 1-Butanol(1)- SucccinicHEPTANE(1) - CYCLOHEXANE(2) - ANILINE(3)MOL PER CENT OF (3)0 20 40 60 10080MOL PER CENT OF (2)020406080100Fig.7b. Comparison of calculated tie lines withexperimental data: !! Experimental, ο— —οUNIFAC, !!!! UNIQUAC (“common”).HEPTANE(1) - CYCLOHEXANE(2) - ANILINE(3)MOL PER CENT OF (2) IN PHASE RICH IN (3), 100 X20 5 10 15261014DISTRIBUTION COEFFICIENT OF (2), m2 Fig.8a. Comparison of calculated distributioncoefficient with experimental data: ! Experimental,UNIFAC + Hand, – – –UNIFAC, ο ο ο  UNIQUAC(“common”).Acid(2)-Water(3). Figure 6 shows solute(Succinic Acid) distribution in both phases.Figures 7 , 8 and 9 displays the same form ofbehavior for the Heptane(1)-Cyclohexane(2)-Aniline(3) system than the other two earliersystems . This last ternary system is a type IImixture, meaning that two binaries areinmiscibles: Heptane-Aniline, and Cyclohexane-Aniline. The previous two systems are type Imixtures with only one binary showinginmiscibility. In Figs.7 and 8 the numbers forthe UNIQUAC with specific parameters aremissing because the parameters were notavailable from the data source (Sorensen  andArlt, 1980). Distribution coefficients for theother two components of the ternary systemsshow the same behavior than  distributionMOL PER CENT OF (2) IN PHASE RICH IN (3), 100 X20 40HEPTANE(1) - CYCLOHEXANE(2) - ANILINE(3)20 60 80806040200MOL PER CENT OF (2) IN PHASE RICH IN (1), 100 Y2Fig.9.Comparison of calculated solute distributionwith experimental data: ! Experimental,  UNIFAC+ Hand.261014DISTRIBUTION COEFFICIENT OF (2), m2HEPTANE(1) - CYCLOHEXANE(2) - ANILINE(3)MOL PER CENT OF (2) IN PHASE RICH IN (3), 100 X20 5 10 15Fig.8b. Comparison of calculated distributioncoefficient  with  experimental data: !  Experimental, UNIFAC + Hand, – – –UNIQUAC (“common”) +Hand.coefficient for component 2 in all the ternarymixtures under study.The proposed combination seems towork because it uses the best of each of theapproaches cited earlier in this work. Theorientation of the tie lines is set by Hand’sequation and the binodal curve is set byUNIQUAC/UNIFAC. We could guess thatthe proposed method is going to work betterin cases were tie line's differences betweenUNIQUAC and experiments are larger. Thecombination works even when the availableexperimental information is little allowingfor extrapolation of data. The minimunexperimental information required for thecombination to work is two tie lines that areneeded to obtain Hand’s parameter k and Cof Eqn. 1. Then, it is possible to use theproposed combination to get a table ofextrapolated distribution coefficients that arefitted with polynomials as recommended inthe literature (Rod, 1976). Additionalundertaking is necessary to evaluatecompletely the proposed calculation method.Two things will be done: a) a systematicstudy of many more systems; b) an analysisof how to assemble Hand’s equation withUNIQUAC/UNIFAC at the very lowcomposition of the distributed componentand at the plait point.4. ConclusionsThis paper presents a method tocalculate coefficient distributions for  liquid -liquid ternary systems. The proposed methodcombines Hand’s equation with UNIQUACor UNIFAC model. The combination givesdistribution coefficients that agree withexperimental ones better than the coefficientscalculated using the models alone. Inaddition, the proposed method could be usedto extrapolate scare experimental information.AcknowledgmentsThe authors are thankful for the financialaid received from CONICET, UNL,ANPCyT and Fundación ANDES.ReferencesMagnussen T., P. Rasmussen and A.Fredenslund, “UNIFAC Parameter Tablefor Prediction of Liquid - LiquidEquilibria”, Ind. Eng. Chem. ProcessDes. Dev. 20, 331-339 (1981).Magnussen T., J.M. Sorensen, P. Rasmussenand A. Fredenslund, “Liquid - LiquidEquilibrium Data: Their Retrieval,Correlation and Prediction, Part III:Prediction”, Fluid Phase Equilibria 4,151-163 (1980).Rod V.,”Correlation of Equilibrium Data inTernary Liquid - Liquid Systems”, TheChemical Engineering Journal 11,105-110 (1976).Sorensen J.M., T. Magnussen, P. Rasmussenand A. Fredenslund, “Liquid - LiquidEquilibrium Data: Their Retrieval,Correlation and Prediction, Part I:Retrieval”, Fluid Phase Equilibria 2,297-309 (1979).Sorensen J.M., T. Magnussen, P. Rasmussenand A. Fredenslund, “Liquid - LiquidEquilibrium Data: Their Retrieval,Correlation and Prediction, Part II:Correlation”, Fluid Phase Equilibria 3,47-82 (1979).Sorensen J.M. and W. Arlt, Liquid-LiquidEquilibrium Data Collection, Dechema(1980).Treybal R., Liquid Extraction, 2nd Edn., McGraw Hill, New York (1963).

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Distribution Coefficient Calculation in Ternary Liquid-Liquid Systems

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