VAPOR-LIQUID EQUILIBRIUM DATA FOR THE TERNARY SYSTEMS : METHYL ACETATE-2-PROPANOL-BENZENE AND METHYL ACETATE-CHLOROFORM-BENZENE'
ISAMU NAGATA AND HIROMICHI HAYASHIDA** Department of Chemical Engineering, Kanazazva University, Kanazawa
Isobaric vapor-liquid equilibrium data at 76Omm of Hg were determined for the ternary methyl acetate-2-propanol-benzene system and isothermal equilibrium data at 5O°C were obtained for the ternary system methyl acetate-chloroform-benzene and for its binary systems, methyl acetate-chloroform, methyl acetate-benzene, and chloroform-benzene, using a Jones still. The Wilson and NRTLequations were successfully applied for the correlation of the liquid-phase activity coefficient and for the prediction of ternary equilibrium data.
As part of a continuing study of phase equilibria in of the temperature measurements are believed to be nonideal solutions, the purpose of this investigation was within ±0.05°C. Temperature for the isothermal to determine the vapor-liquid equilibria for the following system was controlled at 50°C by adjusting the total binary and ternary systems : methyl acetate-2-propanol- pressure in the still with a Cartesian manostat. Tem- benzene at 760mmof Hg, and methyl acetate-chloro- peratures for isobaric system were corrected to 760mm. form, methyl acetate-benzene, chloroform-benzene, and of mercury2). Pressure effects on equilibrium data were methyl acetate-chloroform-benzene at 50°C, and to considered to be negligible, since barometric pressure comparethe experimental results with data predicted recorded during each experimental run ranged from using the Wilson and nonrandom two-liquid (NRTL) 751.5 to. 760.4mm of Hg. Thecorrections tobemade equations. to barometric reading were added to the measured atmo- spheric pressures2\ Experimental A Shimadzu Pulfrich precision refractometer and a sodium lamp were used to determine the refractive All C.P. grade chemicals were purified for experimental indices of binary and ternary mixtures. The precision use. Methyl acetate was refluxed with anhydrous acetic of the measurements was within ±0.00005. Composi- acid, and then distilled. The distillate was thenshaken tions of ternary mixtures were determined by measuring with anhydrous potassium carbonate and redistilled in their refractive indices and densities. 10cc Ostwald a glass column packed with McMahonpackings. Chloro- pycnometers were used to obtain the densities of the form was distilled in a glass column. Benzene was subjected to repeated recrystallization. 2-Propanol was mixtures. Weighings were made on a Shimadzu balance distilled twice in a packed column after storage over with a precision of O.OOOlg. The refractive index and copper-anhydride. The physical properties of the purified density measurements were made at 25+0.1°C. chemicals are shown in Table 1. A Jones vapor-recirculation still was used to obtain Data Analysis the equilibrium data2). Boiling temperature was meas- ured with a Yokogawa P~7B potentiometer and a The activity coefficient of any component i was calibrated copper-constantan thermocouple. The accuracy calculated by the equation of equilibrium
Table I Physical properties of pure compounds Boiling point, °C Density at 25°C Refractive index at 25°C O Compound Obs. Lit. Obs. Lit. bs. Lit. 56.86) 0. 9269 0. 92736) 1.3587 1.35896) Methyl acetate 56. 8 56.913) Chloroform 61. 2 61.2615) 1. 4784 1.47873) 1.4430 1.44303) Benzene 80. 1 80.ln 0. 8737 0. 87371) 1. 4980 1.4979° 2-Propanol 82. 4 82.415) 1. 3749 1. 374715) 0. 7809 0. 7809515)
Received on September 24, 1969 Idemitsu Petrochemical Co., Tokuyama
VOL.3 NO.2 1970 161 ViLP Table 2 Equilibrium data for the methyl (PiyiP = yiXifi L exp-^- (1) acetate (l) -chloroform(2) system at 5O°C Activity Fugacity where Table 3 Equilibrium data for the methyl acetate (l) -benzene(2) system at 5O°C //i = ^P/exp(- ^^) (4) Activ ity Fugacity where Pi is the saturation pressure of the pure liquid Press. coeffic ien t coefficient i and 0.693 0.824 424.0 0.981 0.895 0.979 0.977 N 0.746 0.863 437.6 0.984 0.869 0.978 0.976 0.833 0.922 467.7 1.004 0.803 0.977 0.975 J] xizijGij 0.868 0.942 478.2 1.006 0.772 0.976 0.974 N 0.946 0.980 499.8 1.003 0.679 0.975 0.973 k=l 2 GkjXk 0.951 0.983 501.6 1.004 0.639 0.975 0.973 (5) 162 0JOURNAL OF CHEMICAL ENGINEERING OF JAPAN Table 5 Equilibrium data for the ternary methyl acetate (I)-chloroform (2)-benzene (3) system at 5O°C Liquid mole fraction Vapor mole fraction Press. Liquid activity coefficient Vapor fugacity coefficient Vi V2 ys mm of Hg Ti li Tz 0.103 0.076 0.821 0.219 0.091 0.690 326.0 1.192 0.764 1.014 0.982 0.984 0.981 0. 120 0.073 0.807 0.252 0.082 0.666 332.7 1.200 0.731 1.016 0.982 0.984 0.981 0.163 0.068 0.769 0.313 0.074 0.613 348.4 1. 147 0.741 1.027 0.980 0.983 0.980 0.257 0.073 0.670 0.438 0.057 0.495 385.9 1. 124 0.690 1.053 0.977 0.981 0.979 0.588 0.050 0.362 0.740 0.031 0.229 486.3 1.036 0.585 1. 134 0.968 0.976 0.977 0.820 0.018 0.162 0.892 0.010 0.098 553.8 1.014 0.595 1.234 0.963 0.974 0.977 0.054 0.164 0.782 0. 105 0.220 0.675 315.2 1.055 0.828 1.008 0.984 0.985 0.981 0.077 0.169 0.754 0. 149 0.215 0.636 324.3 1.079 0.807 1.013 0.983 0.984 0.981 0.125 0.162 0.713 0.231 0.192 0.577 341.4 1.083 0.791 1.022 0.981 0.983 0.980 0.200 0. 153 0.647 0.339 0. 160 0.501 368.4 1.069 0.752 1.054 0.978 0.982 0.979 0.299 0.139 0.562 0.471 0. 125 0.404 401.2 1.078 0.703 1.065 0.975 0.980 0.979 0.422 0. 119 0.459 0.605 0.088 0.307 447.0 1.089 0.642 1.102 0.971 0.978 0.978 0.667 0.073 0.260 0.793 0.039 0. 168 510.3 1.025 0.528 1.215 0.966 0.975 0.977 0.062 0.244 0.694 0.108 0.318 0.574 330.8 0.990 0.843 1.013 0.982 0.984 0.981 0.093 0.240 0.667 0. 162 0.301 0.537 341.3 1.020 0.837 1.016 0.981 0.983 0.980 0.211 0.219 0.570 0.338 0.229 0.433 378.8 1.038 0.772 1.063 0.977 0.981 0.979 0.338 0. 198 0.464 0.495 0.174 0.331 412.9 1.030 0.706 1.087 0.974 0.979 0.979 0.687 0.102 0.211 0.800 0.052 0. 138 513.8 1.011 0.605 1.239 0.966 0.975 0.978 0.883 0.038 0.079 0.931 0.020 0.049 562.6 0.998 0.573 1.287 0.962 0.974 0.978 0.867 0.044 0.089 0.919 0.024 0.057 563.8 1.005 0.595 1.331 0.962 0.974 0.978 0.066 0.338 0.596 0. 102 0.433 0.465 348.4 0.924 0.872 1.005 0.980 0.983 0.980 0.106 0.314 0.580 0.173 0.391 0.436 354.6 0.992 0.862 0.986 0.980 0.983 0.980 0.140 0.303 0.551 0.227 0.350 0.423 369.5 0.983 0.833 1.048 0.978 0.982 0.979 0.234 0.294 0.472 0.345 0.302 0.353 388.6 0.979 0.778 1.073 0.976 0.981 0.979 0.346 0.259 0.395 0.485 0.230 0.285 415.9 0.993 0.719 1.108 0.974 0.979 0.979 0.498 0.212 0.290 0.641 0.160 0.199 459.5 1.003 0.673 1.163 0.970 0.977 0.978 0.701 0. 127 0. 172 0.808 0.080 0.112 513.6 1.000 0.627 1.233 0.966 0.976 0.978 0.856 0.062 0.082 0.915 0.034 0.051 556.6 1.001 0.591 1.277 0.963 0.974 0.978 0.071 0.420 0.509 0.096 0.527 0.377 364.8 0.845 0.893 0.998 0.979 0.982 0.979 0.107 0.403 0.490 0.151 0.487 0.362 368.9 0.891 0.870 1.007 0.978 0.982 0.979 0.158 0.374 0.468 0.221 0.431 0.348 382.7 0.915 0.860 1.051 0.977 0.981 0.979 0.291 0.344 0.365 0.394 0.338 0.268 407.9 0.941 0.780 1. 106 0.975 0.980 0.979 0.368 0.315 0.317 0.475 0.290 0.235 422.6 0.929 0.757 1.156 0.973 0.979 0.979 0.486 0.258 0.256 0.621 0.202 0. 177 456.9 0.991 0.695 1. 166 0.970 0.978 0.978 0.679 0.170 0. 151 0.791 0. 110 0.099 514.6 1.012 0.645 1.244 0.966 0.976 0.978 0.886 0.062 0.052 0.934 0.033 0.033 565.8 1.003 0.583 1.324 0.962 0.974 0.978 0.076 0.506 0.418 0.096 0.619 0.285 384.7 0.831 0.917 0.968 0.977 0.981 0.979 0.120 0.479 0.401 0. 128 0.571 0.301 386.4 0.705 0.898 1.071 0.977 0.981 0.979 0.173 0.465 0.362 0.215 0.527 0.258 392.0 0.832 0.866 1.032 0.976 0.980 0.979 0.264 0.427 0.309 0.338 0.436 0.226 410. 1 0.895 0.815 1.107 0.974 0.980 0.979 0.367 0.376 0.257 0.467 0.348 0. 185 430.3 0.931 0.774 1. 143 0.973 0.979 0.979 0.506 0.300 0. 194 0.628 0.234 0.138 463. 1 0.975 0.701 1.216 0.970 0.977 0.978 0.886 0.074 0.040 0.935 0.038 0.027 563.7 1.001 0.560 1.404 0.962 0.974 0.979 0.078 0.601 0.321 0.083 0.716 0.201 408.0 0.741 0.946 0.942 0.976 0.980 0.978 0.184 0.545 0.271 0.204 0.608 0.188 405.7 0.767 0.881 1.039 0.975 0.980 0.978 0.270 0.496 0.234 0.318 0.518 0.164 420.1 0.843 0.853 1.087 0.974 0.979 0.978 0.376 0.435 0.189 0.453 0.410 0.137 434.7 0.890 0.797 1.163 0.972 0.978 0.979 0.518 0.343 0. 139 0.625 0.277 0.098 459.6 0.941 0.721 1.196 0.970 0.978 0.979 0.670 0.239 0.091 0.775 0. 163 0.062 509.7 0.996 0.674 1.281 0.966 0.976 0.978 0.890 0.082 0.028 0.938 0.046 0.016 561.7 0.996 0.610 1.184 0.963 0.974 0.979 0.092 0.241 0.087 0.768 0.145 428.9 0.691 0.961 0.951 0.974 0.979 0.977 0.140 0.216 0.136 0.729 0.135 427. 1 0.707 0.940 0.984 0.974 0.979 0.979 0.191 0.181 0.189 0.694 0. 117 424.2 0.715 0.912 1.011 0.974 0.979 0.978 0.279 0.183 0.312 0.560 0.128 424.8 0.809 0.860 1.096 0.973 0.979 0.978 0.383 0. 127 0.442 0.468 0.090 436.9 0.857 0.811 1. 143 0.972 0.978 0.979 0.517 0.080 0.605 0.338 0.057 462.0 0.917 0.753 1.216 0.970 0.978 0.979 0.701 0.060 0.800 0.160 0.040 506.6 0.977 0.658 1.247 0.966 0.976 0.979 0.865 0.022 0.922 0.064 0.014 553.2 0.993 0.606 1.299 0.963 0.975 0.979 0.090 0.112 0.069 0.874 0.057 463.4 0.604 0.985 0.868 0.971 0.977 0.975 0.145 0.107 0.120 0.819 0.061 453.0 0.637 0.963 0.951 0.972 0.977 0.976 0.208 0.102 0.190 0.746 0.064 444.2 0.690 0.933 1.027 0.972 0.978 0.977 0.288 0.081 0.294 0.657 0.049 442.2 0.767 0.895 0.987 0.972 0.978 0.978 0.396 0.060 0.431 0.526 0.043 448.4 0.829 0.842 1.186 0.971 0.978 0.979 0.522 0.046 0.602 0.367 0.031 466.5 0.912 0.770 1. 161 0.969 0.977 0.979 0.984 0.697 1. 140 0.966 0.6670.6440.628 0.028 0.773 0.210 0.017 508.4 0.976 0.979 0.6750.5380.490 0.4030.2390.113 0.7980.748 0.6900.631 0.5440.4320.297 0.153 0.236 0.611 0.254 0.269 0.477 356.6 1.014 0.794 1.029 0.979 0.982 0.980 VOL.31970 NO.2 163 Table 6 Experimental equilibrium data for the ternary methyl acetate (I)-2-propanol (2)-benzene (3) system at 76Omm of Hg Temp. Liquid mole fraction Vapor mole fraction Liquid activity coefficient Vapor fugacity coefficient yi yi y* 0.400 0.2621.045 1.532 0.338 66.4 0.283 0.323 0.394 1.330 0.962 66.6 0.285 0. 167 0.548 0.179 2.009 1.168 0.099 0.963 0.113 67.6 0.279 0.073 0.648 0.161 2.436 1.097 0.964 65.9 0.350 0.097 0.553 0.281 2.251 1.139 0.962 0.349 64.8 0.383 0.177 0.440 0.260 1.843 1.230 0.961 0.206 0.150 0.416 65.3 0.346 0.416 0.238 0.478 1.338 1.477 0.400 66.6 0.297 0.546 0.157 0.331 1.196 1.674 64.0 0.429 0.417 0. 154 0.218 1.307 1.556 0.170 63.7 0.444 0.304 0.252 0.142 1.441 1.398 0.207 .958 0.959 0.959 0.959 0.971 0.969 0.959 0.960 0.968 63.7 0.459 0.177 0.364 0, 267 1,802.960 .960 0.960 0.961 0.969 0.971 - 1.246 62.8 0.538 0.100 0.362 0.093 2.059 0.959 62.6 0.528 0.310 0.162 0.198 1.426 0.958 63.0 0.510 0.420 0.070 0.246 1.284 0.958 61.5 0.631 0.202 0.167 0.138 1.602 0.958 60.2 0.724 0.102 0.174 0.075 1.829 0.957 60.4 0.709 0.149 0.142 0.791 0.111 0.098 1.836 0.957 58.5 0.858 0.109 0.033 0.905 0.073 0.022 1.801 0.955 where Binary parameters of Eqs. (8) and (9) were determined ?ji - (Qji ~ gu)/RT (6) with experimental data using a nonlinear least square Gji = pjiexp(- ajiTji) (7) fitting program. The program minimizes the sum of (gji-gu) is a binary energy parameter to be determined squares of deviations in the vapor-phase mole fraction with experimental data. The Wilson and the NRTL plus the sum of squares of relative deviations in pressure equations are obtained by giving the following values for all data points. The method seeks a minimumof to p, q, pij, and the deviations on one parameter at a time by variation Equation P q pij aij i-aji) of one parameter, the other parameter being held con- Wilson 0 1 vi/vj 1 stant, then fixed parameter is altered with a parameter NRTL 1 0 1 OCi j increment set by a programmer and the next another The values of an in the NRTLequation are taken to minimum seeking iteration starts. The procedure is be 0.47 for the benzene-2-propanol and to be 0.30 repeated until the improvement is negligible. The for all other binary systems according to the rules given search starts with one parameter increment less than by Renon and Prausnitz12). the first one at a time. The search ends when impro- For a binary mixture Eq. (5) reduces to vement cannot be obtained by change of parameter in any direction. Physical constants for the pure com- ]nTi=q Xi + X2G21 ponents used for calculations are available8'10'11'10. xiG\i Figs. 1 and 2 compare calculated and experimental X2 + X1G12 --lnGci + X2G21) vapor compositions and total pressures against liquid 2lG"21 ri2(_X12 Ui + ^2G2i)2 compositions. Both the Wilson and the NRTLequa- (X2 + tions give a good representation of these data. For InJ2=q all binary data used in this investigation obtained param- X2 + XlGl2 eters and root-mean-square deviations in the vapor-phase X\Gi\ mole fraction and root-mean square relative deviations \n(x2 + X1G12) Xi + X2G21 in pressure are given in Table 7. The magnitude of n2G122 4- deviations of the calculated values from the experimental +pxi (X2 + XlGl2)2 (xi + X2G21)2 results are comparable to the results obtained by Renon 164 JOURNAL OF0 0 CHEMICAL ENGINEERING OF JAPAN Fig. I x-y diagram Fig. 2 Pressure vs. composition diagram Table 7 Parameters and root-mean-square deviations for binary systems System Parameters[cal/mole] rms Deviation in* rms Deviation in** Component 1 Component 2 WilsonCondition NRTL{Qu~Q22) vapor(qi2~Q22) mole fraction X1000relative pressureX1000 (02i-0n) (02i-0n) ais Wilson NRTL Wilson NRTL Ref. Benzene -. 1056 895 A An c a Q n (z-\ 2-Propanol 1 atm 121 245 0 A7 5 6 8 7 (5) Chloroform nn°r - 116 - 153 n QA Q . . r- TU. , Benzene 50 C -24 21 0' 30 3 4 4 5 This work Methyl acetate rAor 100 318 A Oa a n c ^ to.- å i Benzene 50 C 126 -73 °' 30 6 7 5 4 This work 1atm "Ho "^ 0.30 8 10 9 5 (6) Methyl acetate rAor -505 -704 A QA A . . . TU. , Chloroform 50 C 130 412 0 ' 30 4 4 4 4 Thls work Methyl acetate - 301 387 A q0 o « å 7 r r^ 2-Propanol X atm 207 112 °' 308875(5) * {E (>alc-^exPtl)ViV}1/2. ** Ci:{(Pealc-PeXptl)/Pexptl}2/iV]1/2 Table 8 Comparison of prediction of ternary vapor-liquid equilibria with Wilson and NRTLequations No. of Deviation in vapor mole fraction* Relative deviation in pressure** Absolute deviation in pressure*** System data X 1000 X 1000 mmof Hg points Arithmetic Root-mean-square Arithmetic Root-mean-square Arithmetic Root-mean-square Wilson NRTL Wilson NRTL Wilson NRTL Wilson NRTL Wilson NRTL Wilson NRTL Methyl acetate 5 7 6 9 2-Propanol 32 - 3 - 3 5 7 4 5 8 9 3 4 6 7 Benzene - 2 - 4 6 7 Methyl acetate 3 2 6 5 Chloroform 66 -2 - 1 3 3 -3 -7 7 10 - 1 -3 3 4 Benzene - 1 - 1 4 4 *å ^=>alc-^exptl. ** ^rel= (Fcalc-iWl)APexptl. *** ^PabB=Pcalc"PexptL ofandpredictionPrausnitz forforthemanyternarybinarydatadata12).and the Theabilityclosenessof Acknowledament the equations with two parameters per binary system The authors are grateful to the Data Processing Center, Kyoto andå 1 no. . ternary-i constant . are1 summarized1 in Table 8 by University,use of theirand facilities.the Computer Center, Osaka University, for obtaining the mean arithmetic and root-mean-square deviations of the predicted vapor compositions and pressure from the experimental data. VOL.3 NO.2 1970 165 sity, College Station, Tex. (1964) Nomenclature 2) Hala, E., Pick, J., Fried, V. and Vilim, O. : Vapour-Liquid Equilibrium", 2nd ed., Pergamon, Oxford (1967) Bu, Bjj, Bij = second virial coefficients [m//mol] 3) Karr, A. E.,Bowes,W. M. andScheibel, E. G. : Anal. Chem., = fugacity of pure component i [atm] 23, 459 (1951) = energies of interaction between an i-j pair 4) Lyckman, E., Eckert, C.A. and Prausnitz, J.N.: Chem. of molecules [cal/mol] Eng. Sci., 20, 685 (1965) Gjt = coefficient as defined by Gji=pji exp(-ajiTji) 5) Nagata, I.: Can. J. Chem. Eng., 41, 21(1963), ibid., 42, P = coefficient (0 or l) 32 (1964) Pis 6) Nagata, I.: J. Chem. Eng. Data, 7, 360 (1962) P = saturation pressure of pure component i [atm] 7) ibid., 14, 418 (1969) q = total pressure [atm] R = coefficient (0 or 1) 8) O'Connell, J. P. and Prausnitz, J. M.: Ind. Eng. Chem. T = gas constant Process Design and Develop., 6, 245 (1967) = absolute temperature [°K] 9) Pitzer, K.S. and Curl, R.F.: J. Am. Chem. Soc,79, 2369 = partial molar liquid volume of component i (1957) [mZ/mol] 10) Prausnitz, J. M., Eckert, C. A., Orye, R. V. and O'Connell, = molar liquid volume of pure component i J. P. : "Computer Calculations for Multicomponent Vapor- [mZ/mol] Liquid Equilibria", Prentice Hall, Englewood Cliffs, N. J. = molar volume of vapor mixture [m//mol] (1967) = liquid-phase mole fraction of component i ll) Reid, R. C. and Sherwood, T. K. : "ThePropertiesofGases - vapor-phase mole fraction of component i and Liquids", 2nd ed., McGraw Hill, New York (1966) 12) Renon, H. and Prausnitz, J.M. : A. I. Ch. E. Journal,14, Greek(Xij Letters nonrandomness constant for binary i-j 135 (1968) interactions 13) Timmermans, J. : "Physico-Chemical Constants of Pure activity coefficient of component i Organic Compounds", Vol. II, Elsevier, New York (1964) Pij coeffic ient 14) Timmermans, J. : "The Physico-Chemical Constants of coefficient as defined by rji= (gji-gu) /RT Binary Systems in Concentrated Solutions", Vol. 2, Inter- fugacity coefficient of pure component i science, New York (1959) fugacity coefficient of component i 15) Weissberger, A., Proskauer, E. S., Riddick, J. A. and Toops, E. (1955)E. Jr. : "Organic Solvents", 2nd ed., Interscience, New York Literature cited l) Am. Petrol. Inst. Research Project 44, TexasA& MUniver- EDDY VISCOSITY AND UNIVERSAL VELOCITY PROFILE IN TURBULENT FLOW IN A STRAIGHT PIPE* TOKURO MIZUSHINA AND FUMIMARU OGINO Department of Chemical Engineering, Kyoto University, Kyoto Simple but systematic expressions for eddy viscosity based on the available experimental results are presented and the universal velocity profile is obtained from the eddy viscosity distribution. The present analysis takes account of the Reynolds number effect on the eddy viscosity. The friction factor based on the universal velocity profile was in good agreement with the Blasius formula, which was derived from the (Ifl)-power law of the velocity profile, and was sepresented precisely by the Prandtls universal law of friction. Introduction -=*y (1) Chemical engineers are often concerned with the eddy and constant shear stress, viscosity in a turbulent liquid flow in theoretical predic- t - Tw(const. ) (2) tions of rates of heat or mass transfer. Hinze5) derived the logarithmic velocity distribution as Numerousformulas have been proposed to describe the eddy viscosity distribution in pipe flow. Assuming U+ =-j\ny+ + C (3) the eddy viscosity proportional to the distance from The same velocity profile has been deduced from the wall, different assumptions by Prandtl12), von Karman7) and others. Different values of /c and C are used by Received on November 29, 1969 Presented at the 35th Annual Meeting of the Soc. Chem. different investigators, but a:-0.4 and C=5.5 are often Eng., Japan, April, 1970. accepted. 166 JOURNAL OF CHEMICAL ENGINEERING OF JAPAN