1212
Ind. Eng. Chem. Res. 1992, 31, 1212-1216
Thermodynamic Property Predictions for Refrigerant Mixtures Ming-Jer Lee* and Hsueh-Cheng S u n Department of Chemical Engineering, National Taiwan Institute of Technology, Taipei, 106, Taiwan
The vapor-liquid equilibrium data of various refrigerant mixtures are correlated by the Soave, Patel-Teja, and Iwai-Margerum-Lu equations of state, respectively, with one adjustable binary interaction constant, ka12. The Patel-Teja equation is slightly better than others. A generalized equation for ka12is, then, developed that enables the Patel-Teja equation to predict the equilibrium-phase properties for such mixtures within reasonable accuracy. With the aid of this model, the bubble and dew pressures are predicted for 55 binary non-chlorofluorocarbon (non-CFC) refrigerant mixtures containing HCFC-22, HFC-32, HCFC-123, HCFC-124, HFC-125, HFC-l34a, HCFC-l42b, HFC-l43a, HFC-l52a, HFC-1243, and dimethyl ether at temperatures from 233.15 to 363.15.K over the entire composition range. The prediction shows that the mixtures of HCFC124/HCFC-l42b as well as HFC-l34a/dimethyl ether could work as near-azeotropic refrigerants. Introduction Because the commonly used CFCs (chlorofluorocarbons) should be phased out before 2000 according to the Montreal Protocol, it is urgently necessary to find new CFC alternatives. Currently HCFC (hydrochlorofluorocarbon) -22, HCFC-123, HFC (hydrofluorocarbon) -125, HFC-134a, and the “Suva” blended (HFCF-22/HFC-152a/HCFC-124) are becoming commercially available for replacing the CFC refrigerants. However, the above tentative pure CFC substitutes (HCFC-22, HCFC-123, HFC-125, and HFC134a) may have one or more thermophysical shortcomings such as unsatisfactory cycle efficiency, high specific compressor displacement, high minimum superheat of vapor, subatmospheric vapor pressure, poor heat-transfer capability, or poor oil compatibility as indicated by Spauschus (1990),Lee and Chao (1992), etc. Moreover, Lee and Chao (1992) reported that HFC-1243 and HFC-143a have comparable thermophysical performances to the CFC refrigerants, but the fluids are flammable and may be poor in material compatibility. These problems could be partially overcome, if we are able to find the refrigerant mixtures whose individual drawbacks of the components can be compensated by each other. Basically, the blended refrigerants are preferable to pure working fluids on account of energy saving and the flexibility of operation (Watanabe, 1987, 1990). The extension of the exploration of CFC alternatives to mixture area, consequently, could be of interest. A reliable thermodynamic model is required for evaluating the performances of a given refrigerant mixture in a refrigeration cycle. As we know, some cubic equations of state can be successfully applied to the mixtures containing nonpolar or slightly polar fluids (Anderko, 1990). The Soave (1972, 1979) and the Peng-Robinson (1976) equations of state have been used previously to correlate the vapor-liquid equilibrium (VLE) data of refrigerant mixtures, for example, by Aaselineau et al. (1978), Connon and Drew (1983), Camporese et al. (1985), Valtz et al. (1986), and Maezawa et al. (1991). Zheng et al. (1990) improved the performance of the Soave equation by means of a density-dependent local-composition mixing rule with two adjustable binary interaction constants. Moat recently, Abu-Eishah (1991) made the phase equilibrium calculations for the fluorocarbon/fluorocarbon and gas/fluorocarbon mixtures by using the Peng-Robinson equation and stated that the binary interaction parameter might not always be correlated easily by one single general equation
* Author to whom correspondence should
be addressed.
for the mixtures. Nevertheless, the generalizations of interaction parameters of the Pew-Robinson equation have been reported by Kato et al. (19811, Oba et al. (1985), and Nishiumi et al. (1988) for the mixtures composed of normal fluids. Applying similar approach to the other advanced cubic equations of state, we attempt to develop a generalized ka12correlation for refrigerant mixtures. In this work, we compare the performances of three notable cubic equations of state including Soave (1972, 19791, Patel-Teja (1982), and Iwai-Margerum-Lu (1988) for refrigerant mixtures. The comparison shows the Patel-Teja equation is slightly better. Using the acentric factors and the critical compressibility factors as variables, we propose an equation to estimate the cross parameter (ka12)of the Patel-Teja equation for such mixtures. This generalized Patel-Teja model predicts the equilibrium phase properties reasonably well. Consequently, we use it to calculate the bubble and dew pressures for a wide variety of non-CFC binary refrigerant mixtures. Two types of mixtures, azeotropic and nonazeotropic systems, are categorized on the basis of the predictions. Equilibrium Phase Property Calculations Lee and Chao (1991) has shown that the Patel-Teja (1982) and the Iwai-Margerum-Lu (1988) equations of state are able to reproduce well the thermodynamic properties for the pure halogenated refrigerants. In this section, we extend the comparison of the applicabilities of three cubic equations of state including Soave, PatelTeja, and Iwai-Margerum-Lu to refrigerant mixtures. The one-fluid mixing rule of van der Waals is applied to the calculations of mixture constants a, b,, and c,, and only a single adjustable binary interaction constant, k,,,,is used in the combining rule for aij, that is a, =
Cxixj(1 - k , , ) ( a i ~ j ) ’ . ~
i = l j=1
(3)
where ci = -biui for the Iwai-Margerum-Lu equation. The following vapor-liquid equilibrium calculations include vaporized equilibrium ratio (Ki = yi/xi)computations for the mixtures having P-T-xl-yi data and bubble and/or dew pressure calculations for the mixtures having P-T-xi and/or P-T-yi data. The optimal k,,, for each binary
0SSS-5885/92/2631-1212~03.00/0 0 1992 American Chemical Society
Ind. Eng. Chem. Res., Vol. 31, No. 4, 1992 1213 Table I. VLE Calculations from the Soave, Patel-Teja, and Iwai-Margerum-Lu Equations of State with Generalized Substance Parameters Patel-Teja Iwai-Margerum-Lu Soave mixture. 1 + 2 CFC-11 + CFC-12 CFC-11 + HCFC-22 CFC-11 HFC-23 CFC-12 CFC-13 CFC-12 Halon-1301 CFC-12 HCFC-22 CFC-12 + CFC-114 CFC-12 HFC-152a CFC-13 CFC-14 CFC-13 HFC-23 CFC-13 CFC-113 Halon-1301 HCFC-22 Halon-1301 HFC-152a CFC-14 + HFC-23 HCFC-22 CFC-113 HCFC-22 CFC-114 HCFC-22 + HCFC-142b HCFC-22 + HFC-152a HFC-23 + CFC-113 CFC-113 + HFC-152a CFC-114 HFC-152a
+ + + + + + + +
+ +
+ +
+
M 65 29 11 17 35 5 25 17 10 65 47 79 16 80 10 44 12 66 14 10 38
k,,." 0.0141 0.0455 0.1351 0.0266 -0.0023 0.0569 0.0168 0.0723 0.0273 0.1060 0.0190 0.0125 0.0843 0.1061 0.0428 0.0521 -0.0489 -0.0243 0.1196 0.0830 0.0503
AAD," % K1 K2 P 6.2
1.7 1.0 2.1
7.3 5.0 10.4 2.7 7.5 6.4 3.6
2.2 2.5 3.2 4.7 2.9 1.5 2.7
1.3 2.6 1.1 5.5
1.5 5.1
1.8
5.3
1.5 2.2 3.3 1.5 2.0 4.1
AAD," % ka3* 0.0150 0.0421 0.1319 0.0285 -0.0032 0.0568 0.0179 0.0709 0.0290 0.1001 0.0203 0.0359 0.0810 0.1010 0.0421 0.0501 -0.0207 -0.0236 0.1113 0.0828 0.0814
K,
Kz
5.1
1.3
P 1.6 1.5
7.5 5.2 10.8 2.8 7.6 5.4 3.7
2.5 2.4 3.0 4.7 3.0 1.4 2.5 1.4 1.2
1.0 5.4
1.4 4.7
2.0
4.5
0.1 1.1 1.6 1.4 1.7 3.0
k... 0.0100 0.0497 0.1360 0.0294 0.0019 0.0534 0.0111 0.0644 0.0323 0.0923 0.0313 0.0359 0.0720 0.0995 0.0418 0.0500 -0.0572 -0.0138 0.1198 0.0837 0.1002
AAD," % K2 P
K, 5.6
sourceb 1 2 3 4
1.8 0.9 1.6
8.0 4.5 10.7 3.3 7.0 3.3 3.3
2.6 2.8 2.7 4.1 2.9 1.4 2.7
5
6 5 7 8 9 10 11 12 13 14 5 15 16 17 17 18
1.1 1.3
1.0 5.6
2.0 5.4
2.1
5.7
0.6 6.5 1.6 3.5 2.2 3.5
"AAD(%) = 100[~$l(~Xidc - Xyptl/Xi()IPt)j]/M,where Xi represents K1,K 2 ,and P, respectively. b(l)Loi (1983). (2) Meskel-Lesavre et al. (1982a). (3) Chareton et al. (1990). (4) Mollerup and Fredenslund (1976). (5) Kubota et al. (1990). (6) Whipple (1952). (7) Pennington and Reid (1950). (8)Proust and Stein (1979). (9) Stein and Proust (1971). (10) Meskel-Lesavre et al. (1982b). (11)Hongo et al. (1990). (12) Connon and Drew (1983). (13) Piacentini and Stein (1967). (14) Valtz et al. (1986). (15) Kumagai et al. (1991). (16) Maezawa et al. (1991). (17) Valtz et al. (1987); (18) Yada et al. (1988). Table 11. VLE Calculations from the Patel-Teja Equation of State with kalz= 0 and Predicted kalz AAD, % AAD,%, at kaI2= 0 mixture, 1 + 2 K1 K2 P pred k,,, Kl K2 CFC-11 + CFC-12 6.4 4.7 0.0220 5.4 2.6 10.3 0.0413 CFC-11 + HCFC-22 27.6 0.0596 CFC-11 + HFC-23 0.0244 7.1 3.2 9.7 6.4 CFC-12 + CFC-13 0.0264 6.0 7.8 5.1 2.6 CFC-12 Halon-1301 0.0479 8.6 6.4 22.2 13.5 CFC-12 + HCFC-22 0.0137 3.3 4.3 6.3 5.4 CFC-12 + CFC-114 0.0778 3.8 8.0 21.9 21.0 CFC-12 + HFC-152a 0.0219 6.5 2.4 9.9 9.6 CFC-13 + CFC-14 0.0579 13.2 9.6 23.7 19.9 CFC-13 HFC-23 4.8 0.0012 CFC-13 + CFC-113 3.5 0.0294 Halon-1301 + HCFC-22 0.0646 2.7 5.1 13.4 20.0 Halon-1301 + HFC-152a 0.0520 18.4 10.0 17.2 31.0 CFC-14 + HFC-23 10.5 0.0288 HCFC-22 + CFC-113 0.0398 3.2 5.8 14.0 10.4 HCFC-22 + CFC-114 2.7 0.0752 HCFC-22 + HCFC-142b 3.0 0.0522 HCFC-22 + HFC-152a 19.4 0.0716 HFC-23 + CFC-113 18.3 0.0540 CFC-113 + HFC-152a 4.9 0.0907 CFC-114 + HFC-152a
P 1.7 15.4
+ +
mixture is determined by the minimization of the following objective function, either eq 4 or eq 5. M
2
j=1
i=l
Obj, = {E[(C(Kicalc- KFPtl/KFpt)/21j)/M
(4)
for the equilibrium ratio calculations and (5) j=1
for the bubble and/or dew pressure calculations. Table I presents the results that were calculated from the models Soave (1972), Patel-Teja (1982) and IwaiMargerum-Lu (1988) with the generalized substance parameters. We see that all three models correlate the phase equilibrium data satisfactorily and the Pate-Teja equation appears to be slightly better than two other equations. The
4.6 1.3 3.5 9.4 3.0 10.2 6.7 3.1
same VLE data were also correlated by the Soave (1979), Patel-Teja (1982), and Iwai-Margerum-Lu (1988) equations with the substance-specific pure component parameters (rather than generalized parameters). The optimal values of the substance parameters for the fluids were taken from the previous work of Lee and Chao (1991). As shown later in Table 111,the improvement is minor when the individual substance parameters were used. Although the optimal values of k,,, reported in Table I are small (usually lower than 0.1 except for the systems containing HF'C-23), the deviations of the VLE calculations could increase significantly if we set k,,, to zero as given in Table 11. It appears that the use of the binary interaction constant is generally essential to obtain accurate results. However, the optimal value of kalpfor a given binary mixture should be determined from ita measured data. Unfortunately, the available data for refrigerant
1214 Ind. Eng. Chem. Res., Vol. 31, No. 4, 1992 6.0
1
I
I
T = 255.35 K
21 .o
19.0
17.0
0
0.0 0.0
0.2
0.4
0.6
0.8
’‘a
1.0
5’0
00 0 00
:
X1
Figure 1. Comparison of phase equilibrium calculations for the Halon-1301 (l)/HFC-I52a (2) system.
_________
I
Expt. Hongo et ol., 1990) optimal kOl2) Calc. predicted ka12)
. - Calc. 13.0 1
Table 111. Comparison of Grand AAD of the VLE Calculations from Different Treatments substance grand AAD, % equation of state Soave Iwai-Margerum-Lu Patel-Teja Soave Iwai-Margerum-Lu Patel-Teja Patel-Teja Patel-Teja
param generalized generalized generalized individual individual individual generalized generalized
ka,,
optimal optimal optimal optimal optimal optimal 0 predicted
K1 4.7 4.5 4.6 4.7 4.2 4.0 16.1 9.1
KZ
P
3.4 3.5 3.1 3.4 3.5 3.1 12.8 6.7
2.5 1.9 1.6 2.5 1.9 1.6 6.6 3.7
mixtures are rather limited, especially for non-CFC systems. To predict the thermodynamic properties for the lack-of-data mixtures, we need to estimate the values of k,, via an appropriate method. a n the basis of the tabulated k, ,values for the PatelTeja equation in Table I, we correlated them by using an empirical function in terms of the absolute difference between the acentric factors of the components and the critical compressibility-factor ratio (SI),Le.
k,,, = 0.6858 + 0.002713(01-
0.6842(Z,i/z,J
(6)
The above correlation enables the Patel-Teja equation to be a predictive model for mixture property calculations. Table I1 shows that this predictive model reproduces the VLE behavior for most selected mixtures reasonably well and is much better than the Patel-Teja equation with setting k, ,to zero. As an example, Figure 1compares the calculated bubble pressures from the Patel-Teja equation using the optimal k,, and the predicted k,,, with the literature values for Hdon-1301/HFC-l52a mixtures. Another illustration for the mixtures of HCFC-22/CFC-115 is given in Figure 2 indicating that the models predict the azeotropes quite well. For comparison purposes, the grand averages of the calculated deviations from the previous different treatments are summarized in Table 111. In addition, the average absolute deviations (AAD) of the saturated liquid mixture’s molar volumes from the Patel-Teja equation with each of three different values of k,,, are listed in Table IV. It is shown that all the treatments are quite acceptable and the accuracy of the volumetric property computations is much less sensitive to the value of cross-interaction constant being used than that of the VLE calculations. On the basis of the previous comparison, it appears that the Patel-Teja equation together with the generalization of k,,, could be applicable to the refrigerant mixtures and
3
X1
Figure 2. Comparison of phase equilibrium calculations for the HCFC-22 (I)/CFC-115 (2) system (optimal k,,, = 0.0564, predicted k,,, = 0.0336). Table IV. Saturated Liquid Volumes Calculated from the Patel-Teja Equation of State AAD,” % mixture, 1 + 2 Ib 11‘ IIId CFC-11 + HCFC-22 2.9 2.9 2.3 CFC-11 + HFC-23 2.7 1.6 2.0 CFC-13 + CFC-113 3.1 3.2 3.2 HCFC-22 + CFC-113 4.4 4.2 4.0 HFC-23 + CFC-113 3.5 2.3 1.9 CFC-113 + HFC-152a 3.8 3.3 2.5 a AAD(%) = 100[~$l(Iudc - u ~ ~ P ~ ~ / u ~ ~Patel-Teja ~ ~ ) ~ ] equation with optimal k,,,. Patel-Teja equation with predicted k,,,. dPatel-Teja equation with k,,, = 0.
could be tentatively employed to predict the thermodynamic properties of the refrigerant mixtures whose experimental data are currently unavailable. Thermodynamic Property Predictions In this section we attempt to predict the thermodynamic behavior of some refrigerant mixtures of interest with the aid of the above predictive method. The bubble and dew pressures of 55 binary non-CFC refrigerant mixtures composed of HCFC-22, HFC-32, HCFC-123, HCFC-124, HFC-125, HFC-R134a, HFCF-l42b, HFC-l43a, HFC-l52a, HFC-1243, and dimethyl ether were predicted at temperatures from 233.15 to 363.15 K over the entire composition range. Several mixtures may form azeotropes according to the prediction. It is indicated that the azeotropic compositions of the HFCF-124/HCFC-l42b system are almost irrelevant to temperature; that is, the mixture blended at the azeotropic composition behaves nearly as a pure refrigerant in a refrigeration system. Additionally the azeotrope-insensitive mixtures such as HFC-l34a/dimethyl ether are capable of working as near-azeotropic refrigeranta. This type of refrigerant could be utilized in existing refrigeration systems after minor revamping.
/ ~ .
Ind. Eng. Chem. Res., Vol. 31, No. 4, 1992 1215
Conclusion This study shows that the Patel-Teja equation of state correlates the equilibrium phase data of the refrigerant mixtures quite satisfactorily. The generalization of k,,, developed in this work makes the Patel-Teja equation to be a predictive model for the refrigerant mixtures, and the model reproduces the thermodynamic properties within reasonable accuracy. On the basis of the predictions, we found that the mixtures of HCFC-124/HCFC-l42b and HFC-134aldimethyl ether behave as near-azeotropic refrigerants. Moreover, it is suggested that the predictive model could be tentatively applied to estimate the thermodynamic properties of the new refrigerant mixture for qualitatively evaluating their performances in a cyclic system. Acknowledgment Financial support from the Union Chemical Laboratories, ITRI, ROC, is gratefully acknowledged.
Nomenclature a , b, c = constants in the equations of state k,, = binary interaction constant K = vaporization equilibrium ratio ( = y i / x i ) M = number of data points P = pressure (bar) R = gas constant (bar cm3 mol-l K-l) T = temperature (K) u = substance parameter in the Iwai-Margerum-Lu equation u = molar volume (cm3mol-') x = mole fraction in liquid phase y = mole fraction in vapor phase 2 = compressibility factor Greek Symbol w =
acentric factor
Superscripts
calc = calculated value expt = experimental value Subscripts 1 = for component 1 2 = for component 2 c = critical property
i = for component i j = for component j m = for mixture Registry NO.HCFC 22,75-45-6; HFC 32,75-10-5; HCFC 123, 306-83-2; HCFC 124, 2837-89-0; HFC 125, 354-33-6; HFC 134a, 811-97-2; HCFC 142b, 75-68-3; HFC 143a, 420-46-2; HFC 152a, 75-37-6.
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Hongo, M.; Kusunoki, M.; Matsuyama, H.; Takagi, T.; Mishima, K.; Arai, Y. Bubble Point Pressures for Binary Mixtures of Bromotrifluoromethane (R13bl) and Chloropentafluoroethane (R115) with Chlorodifluoromethane(R22). J. Chem. Eng. Data 1990,35, 414-417. Iwai, Y.; Margerum, M. R.; Lu, B. C.-Y. A New Three-Parameter Cubic Equation of State for Polar Fluids and Fluid Mixtures. Fluid Phase Equilib. 1988,42, 21-41. Kato, K.; Nagahama, K.; Hirata, H. Generalized Interaction Parameters for the Peng-Robinson Equation of State Carbon-Dioxide-n-Paraffin Binary Systems. Fluid Phase Equilib. 1981, 7, 219-231. Kubota, H.; Ikawa, T.; Tanaka, Y.; Makita, T.; Miyoshi, K. VaporLiquid Equilibria of Non-azeotropic Halogenated Hydrocarbon Mixtures under High Pressure. J. Chem. Eng. Jpn. 1990, 23, 155-159. Kumagai, K.; Yada, N.; Sato, H.; Watanabe, K. Measurements of PVTx Properties of the Binary Refrigerant HCFC 142b + HCFC 22 System. J. Chem. Eng. Data 1991,36, 236-240. Lee, M. J.; Chao, Y. L. Correlation of Thermophysical Properties of Halogenated Refrigerants. Fluid Phase Equilib. 1991, 67, 111-125. Lee, M. J.; Chao, Y. L. ThermophysicalAnalysis on CFC-alternatives for Refrigeration System. J . Chin. Imt.Chem. Eng. 1992, in press. Loi, N. D. Liquid-Steam Balance Test Plant and Meter Readings for an R12/Rll Mixture. Luft Kaeltetech. 1983,19, 37-40. Maezawa, Y.; Sato, H.; Watanabe, K. Saturated Liquid Densities and Bubble Point Pressures of the Binary HCFC 22 + HFC 152a System. Fluid Phase Equilib. 1991,61, 263-273. Meskel-Lesavre, M.; Richon, D.; Renon, H. Bubble Pressures and Liquid Molar Volumes of the System Chlorotrifluoromethane1,1,2-Trichlorotrifluoroethane.J. Chem. Eng. Data 1982a, 27, 16C-165. Meskel-Lesavre, M.; Richon, D.; Renon, H. Bubble Pressures and Saturated Liquid Molar Volumes of TrichlorofluoromethaneChlorodifluoromethane Mixtures. Representation of Refrigerant-Mixtures Vapor-Liquid Equilibrium Data by a Modified Form of the Peng-Robinson Equation of State. Fluid Phase Equilib. 1982b,8, 37-53. Mollerup, J.; Fredenslund, A. Vapour-Liquid Equilibria in the Freon 12-Freon 13 System. J. Chem. Eng. Data 1976, 21, 299-301. Nishiumi, H.; Arai, T.; Takeuchi, K. Generalization of the Binary Interadion Parameter of the Peng-Robinson Equation of State by Component Family. Fluid Phase Equilib. 1988,42, 43-62. Oba, S.; Suzuki, S.; Tanaka, H.; Nagahama, K.; Hirata, M. Generalization of Binary Interaction Parameters of the Peng-Robinson Equation of State: Binary Systems Containing Methane and n-Paraffins. Sekiyu Gakkaishi 1985,28, 202-209. Patel, N. C.; Teja, A. S. A New Cubic Equation of State for Fluids and Fluid Mixtures. Chem. Eng. Sci. 1982,37,463-473. Peng, D.-Y.; Robinson, D. B. A New Two-Constant Equation of State. Ind. Eng. Chem. Fundam. 1976,15,59-64. Pennington, W . A.; Reed, W. H. Azeotrope of 1,l-Difluoroethaneand Dichlorodifluoromethane as a Refrigerant. Chem. Eng. B o g . 1950,46, 464-466. Piacentini, A.; Stein, F. P. An Experimental and Correlative Study of the Vapor-Liquid Equilibria of the Tetrafluoromethane System. Chem. Eng. Prog. Symp. Ser. 1967, No. 63, 28-36. Proust, P. C.; Stein, F. P. Vapor-Liquid Equilibria of the Carbon Tetrafluoride-ChlorotrifluoromethaneSystem at 199.80 K. J. Chem. Eng. Data 1979,24,341-343. Soave, G. Equilibrium Constants from a Modified Redlich-Kwong Equation of State. Chem. Eng. Sci. 1972,27, 1197-1203. Soave, G. Application of a Cubic Equation of State to Vapor-Liquid Equilibria of Systems Containing Polar Compounds. Inst. Chem. Eng. Symp. Ser. 1979, No. 56, 1.2/1-1.2/16. Spauschus, H. 0.Compatibility Requirements for CFC Alternatives. Int. J. Refrig. 1990 13, 73178. Stein. F. P.: Proust. P. C. VaDor-Liauid Eauilibria of the TrifluoromethaneLTrifluorochloromethane System. J. Chem. Eng. Data 1971,16, 389-393. Valtz, A.; Laugier, S.; Richon, D. Bubble Pressures and Saturated Molar Volumes of Difluoromonochloromethane-Fluorochloroethane Binary Mixtures: Experimental Data and Modelling. Int. J. Refrig. 1986, 9, 282-289. Valtz, A.; Laugier, S.; Richon, D. Bubble Pressures and Saturated Liquid Molar Volumes of Trifluorotrichloroethane-Fluorochlorohydrocarbon Mixtures. Experimental Data and Modelization. J . Chem. Eng. Data 1987,32, 397-400.
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Watanabe, K. A Role of Thermodynamical Properties Research on Refrigerant Mixtures. In Heat and Mass Transfer in Refrigeration and Cryogenics; Bougard, J., Afgan, N., Eds.; Hemisphere: New York, 1987; pp 343-368. Watanabe, K. Current Thermophysical Properties Research on Refrigerant Mixtures in Japan. Znt. J. Thermophys. 1990, 1 1 , 433-453. Whipple, G. H. Vapor-Liquid Equilibria of Some Fluorinated Hydrocarbon Systems. Znd. Eng. Chem. 1952,44, 1664-1667.
Yada, N.; Uematsu, M.; Watanabe, K.Study of the PVTx Properties for Binary R152a + R114 System. Trans. JAR 1988,5, 107-115. Zheng, X.-Y.; Kubota, H.; Zheng, Q.; Makita, T. High-pressure Vapor-Liquid Equilibrium Data of the HFC 134a + HCFC 141b System. J. Chem. Eng. Data 1990,35,441-444.
Receiued for review September 29, 1991 Revised manuscript receiued December 3, 1991 Accepted December 17,1991
Micromixing in Static Mixers: An Experimental Study John
R.Bourne,* Joachim Lenzner, and Sergio Petrozzi
Technisch- Chemisches Laboratorium, ETH, CH-8092 Zurich, Switzerland
Static mixers develop high rates of energy dissipation relative to an empty pipe and have short residence times, which are useful characteristics for those rapid reactions needing fast mixing to obtain high yield. Hardly any information on this application however exists. The competitive coupling of 1-and 2-naphthols with diazotized sulfanilic acid was applied in aqueous solution to two commercially available designs of static mixer. The rate of turbulent energy dissipation was deduced from the measured product distribution over a range of flow rates. Chemical reaction did not take place throughout a whole element, but was localized over a distance of around 0.01 m. The reaction zone shifted somewhat depending on the operating conditions, e.g., concentrations, which introduced some inaccuracy into the determination of energy dissipation due to ita inhomogeneity. Product distributions could nevertheless be adequately predicted using the engulfment model of micromixing as some operating conditions were changed. The mixer element having an open structure without excessive constriction of the flow gave faster micromixing and better energy utilization. This could be a clue to further improvements in design. 1. Introduction
Most experimental studies of micromixing refer to stirred tank reactors. Micromixing is however rapid, requiring only fractions of a second in most turbulent flows. It is only relevant in determining the final process result, e.g., the yield of a complex reaction, when the process itself is rapid, e.g., for reactions whose time constants are comparable with or shorter than that of micromixing. Static mixers seem to satisfy the two principal requirements when rapid processes are engineered, namely, (a) a short residence time on the order of fractions of a second and (b) a high rate of turbulent energy dissipation, probably of the order of 10L103 W-kg-', ensuring fast micromixing and, in the case of two-phase systems, also fine dispersion. Micromixing in static mixers, which is often relevant in controlling the product distributions of fast, complex reactions, appears to have received almost no attention (Godfrey, 1985). The first objective of this work was therefore general, namely, to explore the ability of two designs of static mixer to achieve rapid micromixing in the turbulent flow regime. A recent investigation into micromixing in three closely related types of static mixer using a superficial linear velocity (u) of 2 m d employed as a fast test reaction the diazo coupling of 1-naphthol and diazotized sulfanilic acid (Bourne and Maire, 1991a). Rates of turbulent energy dissipation (4 were found to be of the order of l@W-kg-', which was outside the normal operating range of this test reaction (Bourne and Maire, 1991b). Because of the limited reaction rate, it proved essential to slow down the mixing by adding carboxymethyl cellulose (CMC), so
raising the kinematic viscosity ( u ) of the reaction medium from 0.89 X lo4 to 7.9 X lo4 m 2 d in order to use the coupling of 1-naphthol. Direct application of aqueous solutions in static mixers demands faster test reactions, such as the competitive diazo couplings between 1naphthol and 2-naphthol (Bourne et al., 1992). The more specific objectives in this work were to illustrate the suitability of this new test system for characterizing micromixing in highly turbulent flows and to compare two designs of static mixer in achieving such fast micromixing. 2. Principles of Method
The simultaneous coupling of 1-naphthol (Al) and 2naphthol (A2) with diazotized sulfanilic acid (B) produces four dyes in proportions which depend upon the mixing intensity, here characterized by t, the energy dissipation rate. Full details of these reactions, chemical analysis, and kinetics are available (Bourne et al., 1992), so that here a summary will suffice. 1-Naphthol yields two monoazo isomers which can couple further to a single bisazo dye (S). 2-Naphthol couples to give a single monoazo dye (Q). A1 + B
(1)
p-R
(2)
S
(3)
S
(4)
0-R p-R
+ B -!%
B
kzP
ka
*Towhom correspondence should be addressed. Present address: Department of Chemical Engineering, Swiss Federal Institute of Technology Zurich, Universitiitsstrasse 6, CH-8092 Zurich, Switzerland.
o-R
+ -
A1 + B
k,,
A2+B-Q (5) The competitive, consecutive part of this set is characterized by the yield of S relative to the limiting reagent B, namely, XS'
0888-5885/92/2631-1216$03.00/00 1992 American Chemical Society
