PREDICTION OF VAPOR-LIQUID EQUILIBRIA WITH CHEMICAL REACTION BY ANALYTICAL SOLUTIONS OF GROUPS
Katsumi TOCHIGI, Shigeki MINAMIand Kazuo KOJIMA Department of Industrial Chemistry, Nihon University, Tokyo 101
To discuss prediction of vapor-liquid equilibria with esterification on the basis of the ASOG model, infinite-dilution binary activity coefficients were measured for five systems in the 40°- 100°Crange by an ebulliometric method. The systems measured are methyl acetate-»-heptane, ethyl acetate-ethanol, ethyl acetate-water, acetic acid-w-heptane, and acetic acid-ethyl acetate. The group Wilson parameters for any system made up of CH2, OH, COO, COOHgroups were determined in the 40°-100°C range by infinite-dilution activity coefficients. Vapor-liquid equilib- ria predicted for three quaternary esterification systems and for 26 binary and ternary systems involving alcohols, water, paraffins, esters, and carboxylic acids agreed fairly well with observed values.
Introduction liquid equilibria with esterification by ASOGmodel. Extensive studies of experimental and theoretical madeHere, upthe ofgroupCH2,WilsonOH, COO,parametersCOOHfor groupsany systemwere aspects of vapor-liquid equilibria have been under- determined first in the 40°-100°C range by the ebullio- taken in the past, though mostly on systems in which metric method. Next, by applying the group Wilson no chemical reaction occurs. Apparently, few studies parameters, prediction of vapor-liquid and vapor- of vapor-liquid equilibria of systems in which chemical liquid-liquid equilibria was made for 22 binary reaction occurs in liquid phase, such as esterification, systems constituted by CH2-COO, CH2-OH-COO, have been made. Komatsu, Hirata et al.11~U) ob- CH2-OH-COOH, CH2-COO-COOHgroups and four served vapor-liquid equilibria of quaternary systems, ternary systems constituted by CH2-OH-COOgroups. like acetic acid-alcohols-water-esters, with esterifica- Further prediction of vapor-liquid equilibria with tion and proposed an empirical method for correlat- esterification has been made for the acetic acid- ing vapor-liquid equilibria with esterification by using ethanol-water-ethyl acetate, acetic acid-z-propanol- vapor-liquid equilibrium ratio. Nishi21) observed water-/-propyl acetate and acetic acid-/z-butanol- vapor-liquid equilibria for the acetic acid-z-propanol- water-butyl acetate systems. water-z-propyl acetate system and showed that the data could be correlated satisfactory by the method of 1. Measurement of Infinite Dilution Activity Co- Komatsu, Hirata et aL, Suzuki, Komatsu and Hirata35) effici ents tried to correlate vapor-liquid equilibria with esterifica- GroupWilson parameters necessary for predicting tion on the basis of activity coefficient equations for vapor-liquid equilibria with esterification by using the purpose of developing an empirical method. ASOGare those relating to the six group pairs (made An ASOG(Analytical Solutions of Groups) model up of CH2, OH, COO and COOHgroups) CH2-COO, constitutes a predictive method5>8'36) for obtaining OH-COO, CH2-COOH, OH-COOH, COO-COOH, activity coefficients. It is a widely applicable method CH2-OH. For the sake of simplicity, no distinction is requiring minimumexperimental data and is of prac- made between CH3and CH2groups27 31). tical use in predicting vapor-liquid and liquid-liquid Several attempts30>34'36) have been made for ex- equilibria. Derr and Deal5) suggested application of ASOGto reaction systems. Hardly any studies seems Inperimentallythe previousdeterminingstudy36\ thegroupauthorsWilsondiscussedparameters.the to have been reported, however, for concrete applica- method for determining the parameters by infinite tion of ASOGto reaction systems. dilution activity coefficients measured by using ebullio- The present paper deals with prediction of vapor- meter and determined group Wilson parameters for Received March 10, 1977. Correspondence concerning this article should be addressed to K. Kojima. S. Minami is now with Tsukishima Kikai Co., any system made up of CH2, OH, COgroups in the Ltd., Tokyo 104. 40°-100°C range. The infinite dilution activity co-
VOL. 10 NO. 5 1977 349 Table 1 Observed binary activity coefficients at infinite (2).acid (l)-??-heptaneThus (2) and acetic acid (l)-ethyl acetate dilution t [°C] TT - iP/PW - id T/dxOidln PI/dT)}^ (3) System rT 40 60 80 100 r^P/PIW - id T/dx^din pydTm- r},) Methyl acetate (1) 3.63 3.80 3.99 4.19 r? - (d T/dx,)(dln K2/dT)(l - Vl)]X2=Q (4) w-Heptane(2) rT 4.82 5.12 5.37 5.58 Ethyl acetate (1) r? 2.77 2.53 2.25 1.94 where Pf and PI denote, respectively, the vapor Ethanol (2) 3.29 2.82 2.44 2.14 pressures of acetic acid monomer38) and component 2, Ethyl acetate (1) Ti and K2represents the vapor-phase association con- Water (2) r? ll.88 10.40 9.23 8.32 stant of dimerization for acetic acid, calculated on the Acetic acid (1) rT 24.66 18.86 18.ll 17.50 ^-Heptane (2) 10.57 ll.30 12.74 15.14 basis of the data28) obtained from Ritter et al. As Acetic acid (1) rT 1.22 1.40 1.57 1.75 for rju it is the true mole fraction of acetic acid mono- 1.17 1.21 1.25 1.29 mer in vapor phase and is calculated17>38) by applying Ethyl acetate (2) Eq. (5). ?i =(- 1 + )l2K,P (5) efficients for a binary system consisting of acetic acid, Terminal slopes for the T-x curve, (dT/8x^=0, a self-associating component, and water were meas- (dT/dx2)X2=o were evaluated by the Ellis and Jonah ured3^ in the 60°C-1 10°C range. method7}. Vapor pressures for pure materials are In the present study, infinite dilution activity co- efficients have been measured for five binary systems calculated by applying the Antoine equation. Thus made up of CH2, OH, COO, COOHgroups by the dln P°i/dT=2303Bi/(t°C+ Ciy (6) ebulliometric method. The experimental apparatus Table 1 shows the infinite dilution binary activity used is the same as that in the previous paper38}. The coefficients for components 1 and 2 in the 40°-100°C systems measured are methyl acetate-w-heptane (CH2- range by applying Eqs. (1) and (2) for the methyl COO system), ethyl acetate-ethanol, ethyl acetate- acetate-H-heptane, ethyl acetate-ethanol, ethyl acetate- water (CH2-OH-COOsystems), acetic acid-rc-heptane water systems and by applying Eqs. (3) and (4) for the (CH2-COOHsystem), acetic acid-ethyl acetate (CH2- acetic acid-?z-heptane, acetic acid-ethyl acetate sys- COO-COOHsystem). Bubble points were measured tems. for about 15 compositions at 760, 600, 400, 200, 150 mmof Hg and at intervals of about 2mol%in the 2. Determination of GroupWilson Parameters dilute regions (less than 10mol%, greater than On the basis of the ASOG(Analytical Solutions of 90mol%). For a heterogeneous liquid system of Groups) model5>30'36), the activity coefficients are ethyl acetate-water, the bubble points were measured calculated with the help of Eqs. (7) to (9). in a region in which concentration of ethyl acetate is iogri=iogr»?H+iog r»9 (7) rich. The bubble points were not measured in the ethyl acetate-dilute region, because a two-liquid phase iog rfH=iogKH/(j>,VJH)} was formed in the region of less than about 3 mole% ethyl acetate. Infinite dilution activity coefficients +0.434{l -vndtxtf*)} were obtained for water in ethyl acetate alone. Reagents other than water used in the experiments iogr?= 2^«aogr,-iogrii>) were of special grade (Wako Pure Chem. Ind. Ltd.). logrfc=-log Sy(aj!/i Distilled water was used after ion exchange. Measurement of infinite dilution binary activity +0.434[l - I] {A'iai/,/(2Jrmai/m)}] coefficients from T-x data for the three binary systems Xk=ZXiVnlExtHvki constituted by ethyl acetate (l)-^-heptane (2), ethyl i=l i=\ acetate (l)-ethanol (2), ethyl acetate (l)-water (2) is based on calculations using Eqs. (1) and (2)10)16). where v\H represents the number of atoms (other than the hydrogen atoms) in the molecular species i, and r^ iP/PW l - id T/dx^dln PI/dT)}^ (1) vki is the number of interaction groups of kind k in r~= (P/P°){ l - (d T/dx2)(dln PydT)}X2=0 (2) molecule /. The entities Fk and Xk represent, respec- Assuming that the formation of higher aggregates tively, the group activity coefficient and the group than dimer for acetic acid is negligible in the vapor fraction of group k. As for ak/h aVk, these are group phase, Eqs. (3) and (4) below, derived earlier38), were Wilson parameters. Activity coefficients are calcu- applied for computing the infinite dilution activity lated by substituting known values of ak/u ai/k in coefficients for two binary systems containing acetic Eqs. (7) to (9). acid (which is a self-associating component): acetic As for the method of determining the group Wilson
350 JOURNAL OF CHEMICAL ENGINEERING OF JAPAN Table 2 Constants mm and nm in Eq. (10) (40°-100°C) / CH2 OH COO COOH k mk/i nk/i mk/i nk/t mk/i nk/i mk/i nk/i
CH2 0 0 -0.4962 -ll.2 -0.1209 18.1 -0.3307 150.6 OH 0.6007 -767.1 0 0 0.1616 -286.1 0.7907 -418.6 COO -0.3730 41.5 -0.0615 52.5 0 0 1.2470 -363.1 COOH 0. 1364 -265.6 -0.5256 223.3 -2.2885 690.0 0 0 parameters on the basis of infinite dilution activity coefficients, this consists of calculation of twelve group Wilson parameters madeup of the six group pairs CH2-COO, OH-COO, CH2-COOH, OH- COOH, COO-COOH, CH2-OH under the condition of constant temperature as follows: First the group Wilson parameters for CH2-COOsystem are deter- mined on the basis of the infinite dilution activity coefficients of methyl acetate-^-heptane. The number ^coo of COOgroups in methyl acetate used in the calculation is 3, i.e. vc00=3. This value is the same as that used by Derr and Deal5). The group Wilson parameters for OH-COOsystem are calculated on the basis of the infinite dilution activity coefficients of ethyl acetate-ethanol and ethyl acetate-water by using known values of ^Ch2/oh? 0oh/ch2 obtained in the previous paper36\ The water molecule is treated36} as 1.6 interaction hydroxyl groups. The group Wilson parameters for CH2-COOHsystem are calculated on the basis of the infinite dilution activity coefficients of acetic acid-/z-heptane. The number %0Hof COOH groups in acetic acid used in the calculation is 3, i.e. vC00H=3. The group Wilson parameters for COO- COOH system are calculated on the basis of the Fig. 1 Variation of group Wilson parameters with infinite dilution activity coefficients of acetic acid- temperature ethyl acetate by using known values of <2Ch2/cooh> Prediction on vapor-liquid equilibria with esterifica- 0cooh/ch2- The group Wilson parameters for OH- tion has been preceded by that on vapor-liquid equilib- COOHsystem are calculated by using knownvalues ria using the group Wilson parameters for 22 isobaric °f ^CH2/OH? flOH/CH2J ^CH2/COOH? ^COOH/CH2 On the baSIS binary systems (Table 3) constituted by CH2-COO, of the infinite dilution activity coefficients of acetic CH2-OH-COO, CH2-OH-COOH, CH2-COO-COOH acid-water given in the previous paper38). groups and four isobaric ternary systems (Table 4) Figure 1 shows group Wilson parameters (deter- constituted by CH2-OH-COOgroups. The systems mined at 40°, 60°, 80° and 100°C) plotted against the discussed include those with two liquid phases, namely temperature. As is evident from the figure, the ethyl acetate-water, water-propyl acetate (Nos. 12, 13 logarithms of group Wilson parameters are inversely in Table 3), rc-propanol-propyl propionate-water, proportional to the absolute temperature in the tem- methyl acetate-methanol-water (Nos. 3, 4 in Table 4), perature range in this work. Therefore and nine binary systems (Nos. 14-22 in Table 3) con- logak/i=mk/i+nk/i/T (10) taining acetic and propionic acids, both of which are self-associating components in vapor phase. Thus, where mk/i and nk/i are constants with respect to calculation for the vapor-liquid equilibria is carried group pairs. Table 2 shows the constants mk/i and out on the basis of Eqs. (ll) to (13), derived with a nk/i for any system made up of CH2, OH, COO, view to applying them to ordinary and heterogeneous COOH groups. In Table 2, the constants for the liquid systems25}, as well as to systems with a self- CH2-OHsystem obtained in the previous paper36} associating componentin vapor phase. are also shown. v^ rlPUl/P^VPUV/P (l i) 3. Prediction of Vapor-Liquid Equilibria for Binary Vi+Vi2+tvi=h Vi2=K2P7}l (12) and Ternary Systems
VOL 10 NO. 5 1977 351 Table 3 Deviations of predicted values from observed vapor-liquid equilibria for binary systems System No. of Absolute arithmetic No. Press. data deviations in Ref. Component (1) Component (2) [mmHg] points Vi X lOOO / [°C] Group CH2+COO 1 Methyl formate «-Hexane 10 1.57 23 2 Ethyl acetate Butyl acetate 0.49 32 Group CH2+OH+COO 7 6 14 1.31 Methanol Methyl acetate 1 Methanol Ethyl acetate 19 ll 0.99 Ethyl acetate Ethanol 12 6 0.47 15 Ethyl acetate #-Propan ol 14 18 1.00 20 Ethyl acetate «-Butanol 16 16 1.47 32 Propyl acetate «-Propanol ll 7 0.45 26 «-Butanol Butyl acetate 24 8 0.52 3 Propyl formate w-Prop anol 6 36 18 «-Propanol Propyl propionate 7 26 1.79 Ethyl acetate Water 22 49 1.80 15 Water Propyl acetate 7 49 2.37 33 Group CH2+OH+COOH Acetic acid Water 760 16 10 1.18 14 Propionic acid Water 9 21 0.96 2 Acetic acid Methanol 706 20 21 1.23 29 Acetic acid Ethanol 16 27 1.91 Acetic acid «-Propanol 14 27 2.60 Acetic acid n-Butanol 18 30 2.28 Group CH2+COO+COOH 9 20 Acetic acid Ethyl acetate 21 Acetic acid Propyl acetate 23 22 Acetic acid Butyl acetate 15 * heterogeneous liquid system Table 4 Deviations of predicted values from observed vapor-liquid equilibria for ternary systems (760 mmof Hg) System No. of No. data Absolute arithmetic deviations in Ref. Component(1) Component (2) Component (3) points yxx1000 v2x1000 /[°C] Group CH2+OH+COO Ethyl acetate Ethanol 77 23 12 0.38 32 Ethyl acetate Ethanol 8819 6534 30ll 1.021.05 19 «-Propanol Propyl propionate 32 43 23 2.27 4 Methyl acetate Methanol Buthyl acetate «-Butanol Water Water * heterogeneous liquid system
acid, 5712=0, 7]i=yi and rjj=yj. Activity coefficients are predicted by applying Eqs. (7) to (10) on the basis i=2 of the ASOGmodel. In the above equations it has been assumed that the Prediction of vapor-liquid equilibria has been made formation of higher aggregates than dimer for an on the basis of an ASOGmodel for 22 isobaric binary associating component is negligible in vapor phase. systems. Table 3 shows the deviations between pre- dicted and observed vapor compositions and bubble Also, x\ and x}1 are, respectively, the mole fraction of points. As indicated in Table 3, the results agree component i in the two liquid phases I and II in fairly well with observed values. Figures 2 to 5 com- equilibrium and are evaluated22>37) from the conditions pare predicted and observed vapor compositions for of liquid-liquid equilibria by a modified Newton- the ethyl acetate-ethanol, acetic acid-water, acetic Raphson method. It naturally follows that in the region where a system becomesone constituted by a acid-methanol and ethyl acetate-water systems. single liquid phase x1i=x]I=xi, fi=fil=ji. In the Prediction of vapor-liquid equilibria was made for equations % represents true mole fraction in the four isobaric ternary systems. A comparison of vapor phase and subscripts 1 and 12 denote, respec- predicted and observed vapor compositions and tively, an associating component monomerand a bubble points appears in Table 4. dimer. When applied to a system not containing 4. Prediction of Quaternary Vapor-Liquid Equilibria associating components like acetic acid or propionic with Esterification
352 JOURNAL OF CHEMICAL ENGINEERING OF JAPAN Fig. 2 Vapor-liquid equilibria for ethyl acetate (1)- Fig. 4 Vapor-liquid equilibria for acetic acid (1)- ethanol (2) system at 760 mmof Hg methanol (2) system at 706 mmof Hg
Fig. 3 Vapor-liquid equilibria for acetic acid (1)- Fig. 5 Vapor-liquid equilibria for ethyl acetate (1)- water (2) system at 760 mmof Hg water (2) system at 760 mmof Hg
Table 5 Deviations of predicted values from observed vapor-liquid equilibria for quaternary systems with esterification (760 mmof Hg) System No. of Absolute arithmetic deviations in No. Component Component Component Component data yt x 1000 t [°C] Ref. (1) (2) (3) (4) points j! y2 yz y, 1 Acetic acid Ethanol Water Ethyl acetate 270 12 ll 21 21 1.47 12 2 Acetic acid /-Propanol Water /-Propyl acetate 243 12 26 28 33 1.52 21 3 Aceticacid w-Butanol Water Butyl acetate 143 22 14 34 19 2.16 ll
Prediction of vapor-liquid equilibria with esterifica- three esterification systems. The observed values tion was made on the basis of an ASOGmodel for employedfor comparison with the predicted ones are three isobaric quaternary systems, acetic acid- those obtained by Komatsu, Hirata et al.lljl2) for the ethanol-water-ethyl acetate, acetic acid-z'-propanol- acetic acid-ethanol-water-ethyl acetate and acetic water-z-propyl acetate, and acetic acid-w-butanol- acid-w-butanol-water-butyl acetate systems and by water-butyl acetate. It has been pointed outn>12'21) Nishi21) (values evaluated by correlation12>) for the that these esterification systems have two liquid acetic acid-/-propanol-water-/-propyl acetate system. phase regions within a range of approximately 70°- Conclusion 100°C. Further, they contain acetic acid, an associat- ing component in vapor phase. Therefore, calculation To discuss prediction of vapor-liquid equilibria for vapor-liquid equilibria is carried out on the basis with esterification on the basis of the ASOGmodel, of Eqs. (ll) to (13), which appeared earlier and which the group Wilson parameters for any system madeup are applicable to systems having two liquid phases of CH2, OH, COO, COOHgroups were determined and a vapor associating component. Activity co- in the 40°-100°C range by an ebulliometric method. efficients are calculated on the basis of ASOGfrom By using the parameters so determined, vapor-liquid Eqs. (7) to (10) using the constants shown in Table 2. equilibria predicted for three quaternary esterification Table 5 shows the deviations between predicted and systems and 26 binary and ternary systems involving observed vapor compositions and bubble points for alcohols, water, paraffins, esters and carboxylic acids
VOL. 10 NO. 5 1977 353 10) Gautreaux, M. F. and J. Coates: AIChEJ., 1, 476 (1955). agreed well with observed values. ll) Hirata, M. and H. Komatsu: KagakuKogaku,30, 129 (1966). Nomenclature 12) Hirata, M. and H. Komatsu: ibid., 30, 989 (1966). a = group Wilson parameter [-] 13) Hirata, M., H. Komatsu and Y. Misaki: ibid., 31, 1184 B, C = constants of Antoine equation [-] (1967). K2 = vapor-phase association constant of 14) Ito, T. and F. Yoshida: /. Chem. Eng. Data, 8, 315 (1963). dimer [mmHg- 1] 15) Kato, M. H. Konishi and M. Hirata: ibid., 15, 435 (1970). m, n = constants in Eq. (10) [-] 16) Kojima, K. and M. Kato: Kagaku Kogaku, 33, 769 (1969). P° [mmHg] 17) Marek, J. and G. Standard: Collect. Czech. Chem. Com- vapor pressure man., 19, 1074 (1954). P total pressure [mmHg] T absolute temperature [°K] 18) Mozzhukhin, A. S., V. A. Mitropolskaya, L. A. Serafinov, t temperature [°C] A. I. Torubarov and T. C. Rudakovskaya: Zh. Fiz. Khim., X group fraction [-] 41, 227 (1967). x mole fraction in liquid phase [-] 19) Mozzhukhin, A. S., L. A. Serafinov, V. A. Mitropolskaya y stoichiometric mole fraction in vapor and L. M. Sankina: ibid., 41, 1687 (1967). phase [-] 20) Murti, P. S. and M. Van Winkle: /. Chem. Eng. Data, 3, 72 (1958). group activity coefficient [-] 21) Nishi, Y.: Kagaku Kogaku, 35, 1257 (1971). activity coefficient [-] 22) Null, H. R.: "Phase Equilibrium in Process Design", p. = true mole fraction in vapor phase [-] 21 1 , Wiley-Interscience (1970). = number of groups [-] 23) Ogorodnikov, S. K., V. B. Kogan and M. S. Nemtsov: Zh. Prikl. Khim., 34, 5S1 (1961).
354 JOURNAL OF CHEMICAL ENGINEERING OF JAPAN