CORRELATION OF VAPOR-LIQUID EQUILIBRIA FOR SYSTEMS CONTAINING A POLAR COMPONENT BY THE BWR EQUATION*

Transcription

1 CORRELATION OF VAPOR-LIQUID EQUILIBRIA FOR SYSTEMS CONTAINING A POLAR COMPONENT BY THE BWR EQUATION* JuNicHi NOHKA, Eiji SARASHINA, Yasuhiko ARAI and Shozaburo SAITO Department of Chemical Engineeringy Tohoku University, Sendai, Japan The BWRequation was applied to correlate the vapor-liquid equilibria of the polarnonpolar s. Polar componentsstudied were Freon-22, hydrogen sulfide and ammonia. The vapor-liquid equilibrium data were cited from the literature, except for the Freon-22 mixtures whose data were obtained by a static method in this paper. The BWRconstants also were taken from the literature, but those of Freon-22 were determined from the principle of corresponding states and of ammonia from the P-V-T data. By introducing the interaction parameter into the constant, A 0, the BWRequation was shown to be successful for correlating the vapor-liquid equilibria of the polar-nonpolar s. The characteristics of the parameter were discussed based on the concept of intermolecular potential betweenunlike molecules. Introduction The Benedict-Webb-Rubin (BWR) equation3"6) is being currently used to predict the vapor-liquid equilibria of mixtures1'2'11'15'20'27'30'31'45'46). Although the applicability and limitation of that equation have been reported for nonpolar mixtures18'33'51), atic studies on s containing polar components seem scarce. The present study was undertaken in order to see the usefulness of the BWR equation for predicting or correlating the vapor-liquid equilibria of s containing a polar component. Polar components studied here were chlorodifluoromethane (Freon-22), hydrogen sulfide and ammonia. The vapor-liquid equilibrium data used were cited from the literature except for the s containing Freon Systems Containing Freon-22 The vapor-liquid equilibrium data of the four binary s containing Freon-22 were determined by a static method and the results are shown in Tables 1 to 4. Solute gases were nitrogen, argon, methane and carbon dioxide. The details of the apparatus and the experimental techniques used have been reported in the * Received onjune 19, 1972 Presented at the 37th Annual Meeting of the Soc. of Chem. Engrs., Japan, at Nagoya, April 1972 Table 1 Vapor-liquid equilibria of the nitrogen-freon (10) JOURNAL OF CHEMICAL ENGINEERING OF JAPAN

2 Table 2 Vapor-liquid equilibria of the argon-freon-22 Table 3 Vapor-liquid equilibria of the methane-freon-22 previous papers18'45). The purity of Freon-22 was believed more than 99.9 mole %. To predict the vapor-liquid equilibria by the BWR equation, a set of eight empirical constants is required for each component. However, no set ofbwrconstants for Freon-22 has been published. Therefore, a set of BWRconstants was determined from the correlation Table 4 Vapor-liquid equilibria of the carbon dioxide- Freon-22 Table 5 The constants of BWRequation for Freon-22* Ao Bo Co / x l.0» x(l/r) X 106 X (l/r) x *The set ofconstants is useful at -70 C to 90 G method10'30) by using the critical constants of Freon- 2223) and the saturation pressure data49). The resulting constants are listed in Table 5. Amongthe eight constants, the constant, Cd, was represented as a quadratic function of the reciprocal of absolute temperature. The vapor-liquid equilibria of the above four binary s were calculated by the BWRequation and typical results are shown with dotted lines in Figs. 1 and 2. The BWR constants used for other components were the same as those cited in the previous papers18'45). Slight discrepancies between the experimental results and those calculated by the original BWR equation are shown in the liquid phase. The modification of the BWR equation according to VOL.6 NO (ll) ll

3 (1) 0/ I201 * j Methane-Freon-22 Exp^oo Cà"50 C /o/ V 100-BWReqn // \ m=l.à"/ /w \o m=0.95.v /Am \ ^ 80" //// "60- /a /à" f / /à" 50 C P 20^-^ >/ 0 C mole fraction of methane Fig. 1 Vapor-liquid equilibria for the methane-freon : 1 Nitrogen - Freon-22 /^\ E /' \X 5 // x\ loo- y/ I} S Z' /^Exp : 50 C ^ 7/ / BWR eqn 50-/ y^---m=l ' 1 1 i i / ^/^ m=0.90(8=1%) I^-^^ f m=0.90(8=0.01%) 1 fromf-x diagram mole fraction of nitrogen Fig. 2 Vapor-liquid equilibria for the nitrogen-freon-22 Stotler and Benedict48) was then attempted. That is, the combining rule for the constant, Ao, is given by A0 = J] x\aqi + 2 S 2x^jtn^A^A u\ where mis the interaction parameter due to the characteristics of the j-i pair interaction. Eq.(l) has been shown to be successful for several s18'30'33'45'51). The values of m for the Freon-22 mixtures were evaluated by fitting calculated ^-values to those of the experiments, and are shown in Table 6. Figs. 1 and 2 show that the introduction of m not equal to unity is successful in a curve fitting. Among the above four s, the vapor-liquid equilibria of the carbon dioxide-freon-22 were well predicted by letting m be unity, as shown in Fig. 3. Whenthe values ofm presented in Table 6 are used, the K-values of these s can be calculated within an accuracy of 7 to 8%, except for the critical regions. Table 6 Interaction parameter, m, for binary s * Data used were taken from the graphs. ** Large discrepancies were shownfor the heavy component. *** Errors were large at high pressure ranges. **** Errors over 20 % still remained. 2. Systems Containing Hydrogen Sulfide The vapor-liquid equilibrium data of the s containing hydrogen sulfide have been published for many binary s7>9>21>22>24>36>37>40>42). The BWR constants of hydrogen sulfide have been reported by several workers19'28'33'47). Among them, those of 12 (12) JOURNAL OF CHEMICAL ENGINEERING OF JAPAN

4 !001 å, Carbon Dioxide- Freon-22 Exp :o 60 C 80- o 30 C n O 0 C -BWReqn(m=l) o^ j i_j 60- X / // Z 50 r- 'å 1 Hydrogen Sulfide- Propane jg*~-^*< I5O F(66 C) S/* -,''" //''/ 30- //,''' Exp:o9)o21) )/ >'' BWR eqn mole fraction of carbon dioxide Fig. 3 Vapor-liquid equilibria for the carbon dioxide- Freon , Hydrogen Sulfide-n-Butone 80- Exp42)--o 25 F à" 250 F ^ BWR eqn E m= 60- m=0.97^;/ m = mole fraction of hydrogen sulfide Fig. 5 Vapor-liquid equilibria for the hydrogen sulfidepropane B 200 i50^ ^ msy sf' 25O F(I2I C) 100 r-^ "sggg^l?r0f(*> ^) mole fraction of hydrogen sulfide Fig. 4 Vapor-liquid equilibria for the hydrogen sulfide-//- butane Masuda and Yorizane28) seem relatively favorable over wide temperature and pressure ranges, so their constants are used to calculate the vapor-liquid equilibria. Typical comparisons of the calculated results with the literature values are shown in Figs. 4 and 5. In these cases also, the modified combining rule expressed by Eq.(l) was shown to be successful. In the propane-hydrogen sulfide possessing an azeotrope point, different sets of initial ^-values were used to calculate two curves converging on the azeotrope point. The left-hand curve in Fig. 5 was determined, according to the usual procedure14), by letting the initial mole fractions of hydrogen sulfide be nearly zero for liquid and nearly unity for vapor. As the pressure increased, the both lines of dew and bubble points approached closely at about 85 mole% of hydrogen sulfide. The right-hand curve was then calculated by replacing the initial mole fractions of hydrogen sulfide by unity for liquid and 0.85 for vapor. The mole fraction of hydrogensulfide at the azeotrope point was obtained as about On the other hand, it was given as 0.88 from the experiments of Kay and Rambosek21). The values of m for the s containing hydrogen 50 Methane - Ammonia Exp17): BWRe.qn o 0 C m=i m =0.86 Ramaiho etal,35) mole fraction of methane Fig. 6 Vapor liquid equilibria for the methane-ammonia sulfide are listed in Table 6. The BWRconstants given by Benedict et al.b) were used for light paraffins and those by Orye33) for /z-decane. 3. Systems Containing Ammonia The applicability of the BWR equation for the s containing ammonia was examined by using the vapor-liquid equilibrium data already published in the literatures17'29'38*39). Twosets ofbwrconstants for ammoniahave been reported by Ramalho and Frizelle35). One is for the liquid region and the other for the vapor region. As shown in Fig. 6, these two sets could not well represent not only the vapor-liquid equilibria but also the vapor pressure of pure ammonia.therefore, a newset of BWRconstants was determined according to the procedure of Yorizane et al.28>50) by using the P-V-T data of pure ammonia compiled by Groenier and Thodos12). The constants obtained are shown in Table 7. The calculated results from the new con- VOL6 NO (13) 13

5 Table 7 The constants of BWRequation for ammonia Ao Bo Co a b c a r Data points used: 7V^358 Temp.: Tr^5 Press.: Pr^10 g i=l (zexp._zcalc.)2}/ar=0< Table 8 Values of m for binary s Temp. H2-N2 H2- N2- H2-NH3 N2-NH3 CH4- [ C] GH443) CH448) NH3 " å I Nitrogen -Ammonia 300- /f X I 3 // I/ H 200-// / I? J/ 100/ ^^^^^ I--- Exp39:' o 220 F (!04 C) 1 å å å å å 1 BWR eqn m= I m = _j O.I mole fraction of nitrogen Fig. 7 Vapor-liquid equilibria for the nitrogen-ammonia s Table 9 Comparison of predicted and experimental A-values for ternary and quarternay s containing ammonia* Experiment8'25) Errors in prediction** [%] Temp. [ G] Press, [atm] K^ Km Kcm #nh. K^ #n2 Ken* #nh Press (70)*** 7 (25) 12 (130) 23 (68) (87) 7 (25) 8 (104) 26 (73) (110) 8 (28) 0.2 (56) 36 (80) (130) 8 (32) 9 (34) 46 (86) (137) 9 (33) ll (28) 48 (88) (44) 4 (21) 2 (59) 0 (44) (76) 9 (25) 6 (53) 0.2 (49) (90) 9 (25) 10 (27) 8 (57) (92) 9 (26) 19 (26) 25 (67) (98) 13 (28) ll (33) 48 (72) 50.0 å (47) 10 (22) 2 (21) 0.6 (19) (44) 13 (23) 34 (55) 2 (24) (48) 12 (21) 48 (51) 20 (24) (45) 0.3 (9) 66 (104) 137 (24) (31) 21 (27) 54 (58) 15 (8) (27) 50 (25) 95 (69) 23 (10) (17) 26 (31) 125 (130) 58(20) (5) - 34 (36) 0.8 (3.9) 3 (30) (5) - 25 (27) 0.3 (36) 6 (34) (23) - 9 (15) 2 (18) 7 (41) (27) - 5 (10) 8 (23) 12 (44) (13) 20 (37) 7 (19) 10 (4) 15 (21) (24) 16 (47) 0.6 (10) 8 (12) 19 (26) (16) 6 (14) 8 (24) 6 (1) 38 (0) (ll) 22 (40) ll (22) 13 (2) 19 (18) (ll) 9 (30) 0.8 (8) ll (16) 16 (23) (12) 97 (156) 6 (13) 4 (9) 33 (22). * K-values were predicted at given temperature and liquid compositions. ** Exp. - Calc. /Exp. X 100 [%] *** Values in parentheses were obtained from the original BWRequation. stants were compared with the literature values in Figs. 6 and 7. The discrepancy can be readily removed by introducing m into the constant, Ao. The values of mfor the s containing ammoniare summarized in Table 6. As for the nitrogen-ammonia and the hydrogen-ammonia s, discrepancies still remain at the high temperature range (121 G) which is close to the critical temperature of pure ammonia (133 C). The vapor-liquid equilibria of multicomponent s containing ammonia are important in the ammoniasynthesis process. The BWRequation was then applied to predict K-values of multicomponen s containing ammonia by using the interactioi parameter, m, of each binary. The value ofma given temperature for each binary was de termined approximately by interpolating or extra polating the values in Table 6 and is listed in Table 8 The value ofm between nonpolar molecules was taker from the literatures for the hydrogen-methane43} anc the nitrogen-methane48) s,, and for the hydrogen nitrogen s it was determined here by using th< vapor-liquid equilibrium data of Yorizane et al52) 14 (14) JOURNAL OF CHEMICAL ENGINEERING OF JAPAN

6 (vc2lvg) 148 arm 140 atm Nitrogen 50 C - Freon-22 BWReqn (m=0.90) 120 atm ^S. Nitrogen / I \ / / X^-x/ {0) o 86O'-/ " ' 50 C 120atm it '- BWR eqn.(m=0.90) o 18.0\ à"2 \ Freon-22 /^^N \ / \(b) r-i \^y \ mole fraction of nitrogen.0.65, å ;, i2 Equilibrium ^ Compositions y^^ / (c) 86- Z 1 55" /r 2 å ' / 'Nitrogen o E '50"-Freon-22 O45I mole fraction of nitrogen I Liquid] Fig. 8 Graphical determination of the equilibrium compositions The calculated results are compared with the literature values in Table 9 for two ternary8'25) and a quarternary25) s. The computation procedure for multicomponent s is the same as that described in the previous paper43). Table 9 shows that the calculated lvalues ofmulticomponent s can be improved by introducing the interaction parameter, m. 4. Discussions 4. 1 Tolerance in the iterative computation near the critical point Someproblems occur when the BWRequation is applied near the critical point. In the critical region, the calculated results of vapor-liquid equilibria are dependent on the tolerance, d, in the iterative computation. In Fig. 2 the chained lines and full lines were obtained by letting d be 1% and 0.01%, respectively. The chained lines are different from the full lines at the critical region over 130 atm. To see the reason for this disagreement, the equilibrium compositions were obtained directly by a graphical analysis and they were comparedwith the results of the iterative computation. Fig. 8(a) and (b) show the fugacity-composition diagrams of both components at given temperature and pressure. The various sets of compositions having equal fugacities can be obtained on the graphs for nitrogen and Freon-22. They are plotted on Fig.8(c). The limitation in theoretical prediction of m even for nonm12 oc {1 + (Wci)1/3}< mole fraction of nitrogen Fig. 9 Fugacity-composition diagrams near the critical pressure vapor-liquid equilibrium compositions were determined by finding the intersection point of the both curves. The results from the above procedure agreed with those from the iterative computation by letting 3 be 0.01%. This suggests that the tolerance, d, should be reduced in the critical region because the fugacitycomposition curve becomesflat as the pressure approaches the critical pressure, as shown in Fig Features of interaction parameter As shownabove, the BWRequation was successful in correlating the vapor-liquid equilibria of the containing a polar molecule. However, to predict the vapor-liquid equilibria from the knowledge of pure component only, the successful value of m has to be estimated. Then some features of interaction parameter were discussed briefly below. The well-known London formula41} shows for nonpolar mixtures that the ratio of the critical volumes is more effective on the value of m*. Namely,from the study on various binary mixtures33), it has been shown that the interaction parameter, m, is required when the ratio of the critical volumes is greater than three (vc2/vcl >3). For instance, the interaction parameter was required for the methane-^-heptane (vc2jvcl> 4.3) and the methane-/z-decane (yc2/ycl>6.1). However, the values evaluated from the London formula was not necessarily successful for correlating the vapor-liquid equilibria. Although both components are nonpolar and the values of their critical volumes are similar, the carbon dioxide and light hydrocarbon mixtures required the interaction parameter,. m18»33»51). The unusual interaction between carbon dioxide and light hydrocarbons has been already pointed Out13'16'18'32'33'51). Now^ there is a VOL.6 NO (15) 15

7 Light Gas-Ammonia Mixtures S* o _ E -8~ ^^ }^ // Carbon Dioxide-n-Butane 340 F (l7i C) o Exp44) BWR eqn m=i m= mole fraction of carbon dioxide Fig. 10 Second virial coefficient for the carbon dioxide-//- butane polar mixtures. However,the values of the interaction parameter, m, may be estimated by using other thermodynamic properties of mixtures besides vapor-liquid equilibria. In this study, the second virial coefficient was taken. For example, as for the carbon dioxidepropane and the carbon dioxide-ra-butane, the value of m was successfully obtained by fitting the second virial coefficient in the BWRequation (BO-AOI RT-Cq/RT3) to the experimental data, as shown in Fig, 10. The value of m evaluated from the second virial coefficient agree well with those obtained from vapor-liquid equilibria. Unfortunately, sufficient reliable data of the second virial coefficients for the other s are scarce, so that the application to the other s could not be undertaken. On the other hand, it is more difficult to predict the values ofm in nonpolar-polar mixtures. On the basis of the induced dipole-dipole interaction expressed by Prigogine et al.43\ the interaction parameter in the nonpolar-polar mixtures maybe shown as where m12 = [2V/i/a /(A + 4)](^018^023/gQ aifi22<le02le01 X Jt = ^/Ve*r*35(2) 5 = a/r*3 and f== A:r/ * e* and <j* are the coordinates of the minimumof intermolecular potential energy, fi and a are dipole moment and polarizability, respectively. 0 and a0 are the nonpolar parts of the potential parameter. Eq.(2) suggests that the interaction parameter in the nonpolar-polar mixtures is dependent on temperature and increases with temperature. The temperature dependency of m is noticeable in the ammoniamixtures, L^\^/^ Hydrogen 0e- ^^^^^ W trogen -a?5^^^ ^ a Argon Methane 0.4 L-' ' ' 1 ' 1 l_ temperature C CJ Fig. ll Relationship between m and temperature for the light gas and ammoniamixtures as shown in Fig. ll, and m increases almost linearly with temperature. This temperature dependency agrees with Eq.(2), qualitatively. Nevertheless, the value of min the Freon-22 mixtures are almost independent of temperature, though they contain the same gases as those contained in the ammonia mixtures and the dipole moment of Freon-22 is close to that of ammonia. This fact contradicts Eq. (2). As discussed above, the successful value of m can hardly be obtained from theoretical treatment. Especially, an exact treatment of the polar effect is very difficult because one can no longer assume random mixing of molecules in a polar solution. That is, the properties of mixtures containing polar components cannot be given well by the simple combining rule with mole fraction. Conclu sion The BWR equation is shown to be successful in correlating the vapor-liquid equilibria of the s containing a polar component by using the interaction parameter, m. However,at least one experimental data point ofa binary is required in order to find the successful value of m. The theoretical or semiempirical method of evaluating the interaction parameter is still to be studied. Nomenclature 16 (16) JOURNAL OF CHEMICAL ENGINEERING OF JAPAN

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