206
Ind. f n g . Chem. Fundam. 1986, 25, 206-211
Brown, R. A. S.; Govier, G. W. Can. J. Chem. Eng. 1965, 43, 224. Fernandes, R. C. Ph.D. Dissertation, University of Houston, Houston, TX. 1981. Fernandes, R. C.; Sernlat, R.; Dukler, A. E. AIChE J. 1963, 29, 981. Govier. 0. W.; Aziz, K. "The Flow of Complex Mixtures in Pipes"; Van Nostrand Reinhold: New York, 1972. Govier, G. W.; Brown, R. A. S.; Sullivan, G. A. Can. J. Chem. Eng. 1960, 38,62. Govier, G. W.; Radford, B. A,; Dunn, J. S. C.Can. J . Chem. Eng. 1957, 35, 58. Govier, G. W.; Short, W. L. Can. J. Chem. Eng. 1956, 3 6 , 195. Griffith, P.; Wallis, G. B. J. Heat Transfer 1961,83,307. Harmathy, T. Z. AIChE J. 1960, 6 , 281. M a , Y.; Atsuura, H. Kagaku Kogaku Rombunshu 1976, 2 , 212. Ishigai, S.; Yamane, M.; Roko. K.; Takagi, T.; Tanada, K. Bull. JSME 1985, 8 , 383. Laird, A. D. K.; Chisholm, D. Ind. Eng. Chem. 1956, 48, 1361. Miller, A. MSc. Thesis, Technion-Israel Institute of Technology, Haifa, Israel, 1981. Miller, A.; Oreii, A. Proc. Int. Heat Transfer Conf., 7th, 1982 1982, 2 , 437. Moissis, R . J . Heat Transfer 1963, 8 5 , 366.
Nicklin, D. J.; Wiikes, J. 0.: Davidson, J. F. Trans. Inst. Chem. Eng. 1962, 40, 61. Nicoiitsas, A. J.; Murgatroyd, W. Chem. Eng. S d . 1966,23,934. Rembrand, R. M.Sc. Thesis, Technlon-Israel Institute of Technology, Haifa, Israel, 1979. Subbotin, V. I.; Pokhvaiov, Y. E.; Leonov, V. A. Therm. Eng. (Engl. Transl.) 1977, 24, 48. Subbotin, V. I.; Pokhvalov, Y. E.; Mikhailov, T. E.; Kronin, I. V.; Leonov, V. A. Therm. Eng. (Engl. Transl.) 1976,23,48. Takahama, H.; Kato, S. Int. J. Mdtiphase Flow 1980, 6 , 203. Taitel, Y.; Dukier, A. E. Progress Report; University of Houston: Houston, TX, 1976. Wallis, G. B. "One-Dimensional Two-Phase Flow"; McGraw-Hili: New York, 1969. Zuber, N.; Findlay, J. A. J. Heat Transfer 1965, 8 7 , 453. Zuber, N.; Hench, J. Report No. 62 GL 100, General Electric Co., 1962.
Received for review October 24, 1983 Revised manuscript received March 6, 1985 Accepted June 26, 1985
Critical Superheat for Flashing of Superheated Liquid Jets Yoshlro Kltamura, Hlrolchl Morlmltsu,t and Teruo Takahashl Department of Industrial Chemistty, Okayama University, Okayama 700, Japan
Experiments were carried out to study the flashing of superheated liquid jets by the ejection of water and ethanol into a vacuum chamber through long nozzles. Superheated liquids were observed to spray in two different patterns: complete flashing and a two-phase vapor-liquid effluent. Complete flashing occurs at a temperature far above the liquid's bubble point corresponding to the pressure in the chamber; the two-phase effluent, spraying due to the bubble formation in the nozzle, occurs at temperatures closer to the bubble point. The two-phase effluent is likely to occur when the nozzle is shorter. The critical superheat above which the complete flashing occurs is correlated by an empirical equation on the basis of bubble growth rate in superheated liquids, measured by a high-speed motion picture.
Introduction When a liquid is ejected from a nozzle into a pressure zone below the saturated vapor pressure a t the liquid's temperature, the liquid flows as a superheated jet, a metastable state. The presence of a sufficient number of nuclei causes the abrupt growth of bubbles and explosively breaks the jet to attain a final two-phase equilibrium state. Such phenomena, called flashing, have wide industrial, agricultural, and household utilization. Numerous studies have been made on the thermodynamics of the process from metastable to equilibrium state, bubble nucleation, and growth in superheated liquids (Westwater, 1956; Tong, 1965; Bankoff, 1966; Forster and Zuber, 1954; Plesset and Zwick, 1954; Scriven, 1959; Dergarabedian, 1953; Hooper and Abdelmessih, 1966; Cole and Shulman, 1966; Kosky, 1968; Theofanous et al., 1969; Blander and Katz, 1975; Lackme, 1979). However, few studies have been made for the practical purpose of understanding the flashing of superheated liquids (Brown and York, 1962; Lienhard and Stephenson, 1966; Lienhard, 1966; Lienhard and Day, 1970; Sher and Elata, 1977; Suzuki and Yamamoto, 1978; Suma and Koizumi, 1977). Recently, attention has been paid to flashing as an important process in the desalination of saltwater and the recovery of energy from warm wastewater (Miyatake et al., 'Present address: Titan Kogyo Co., LM., Ube, Yamaguchi 755,
Japan. 0196-4313/86/1025-0206$01.50/0
Table I. Dimensions of Nozzle nozzle no. d. mm 1 0.36 2 0.55 3 0.54 4 0.84 5 0.84 6 0.86 7 1.60
1. mm 27.0 32.3 28.0 47.4 94.5 68.0 100.0
lld 75.0 58.7 51.8 56.4 112.5 79.1 62.5
1975, 1979; Simpson and Lynn, 1977). Most of the previous investigators injected highly pressurized hot water into a space held at 1-atm pressure. Few experiments were conducted under the reducedpressure conditions which may be needed in the practical applications mentioned above. Furthermore, little attention was paid to the condition under which flashing would occur, except for the work of Brown and York (1962),who observed the minimum superheat for flashing at 1-atm pressure. Thus, the purpose of this work is to study quantitatively the critical downstream superheat at which flashing occurs over a wide range of downstream pressures. Experimental Section Figure 1 shows the schematic diagram of the experimental apparatus. The piping system, made of copper tubes, was carefully joined without leaks and insulated with glass wool. Ball valves were used in the flow system and were always kept fully open during the operation to prevent undesirable cavitation. The test section, indicated 0 1986 American
Chemical Society
lnd. Eng. Chem. Fundam., Vol. 25, No. 2, 1986 207
P
Figure 1. Schematic diagram of experimental apparatus: 1,pressure regulator; 2, liquid reservoir; 3, orifice flowmeter;4, water bath; 5, thermocouple; 6, vacuum chamber (test section); 7, nozzle, 8, acrylic resin plate; 9, mercury vacuum gauge; 10, cold trap; 11,vacuum pump.
Figure 2. Details of nozzle: 1, nozzle (stainless steel tube); 2, brass disk; 3, O-ring; 4, thumbscrew cap; 5, nipple; 6, brass tube; 7, rubber seal; 8, wall of vacuum chamber; 9, cap.
as item 8 in Figure 1, was a vacuum chamber made of a steel pipe tee of 200-mm i.d. Both sides were covered by 18mm acrylic resin plates. The nozzle was set at the upper part of the chamber. Details of the nozzle are shown in Figure 2. The nozzles were made of stainless steel tubes fixed to brass disks with epoxy resin. The dimensions of the nozzles used in the present work are shown in Table I. All the nozzles were long enough to eliminate eddies formed at the entrance which might affect the stability of the jet (Kitamura and Takahashi, 1978). The temperature of the liquids was measured by a copper-constantan thermocouple inserkd into a brass tube upstream of the nozzle by about 15 cm. The pressure in the chamber was measured by a mercury manometer. The superheat used in this work is defined as the difference between the measured temperature of the liquid leaving the nozzle and its bubble-point temperature corresponding to the pressure in the chamber. The flow rate was not controlled by valves but by the pressure level in the reservoir. The breakup pattern was photographed with a high-speed flash. The growth rate of bubbles was observed by a high-speed motion picture a t 4000-6500 frames/s. The experimental liquids used were ethanol and four kinds of water: city water, deionized water, degassed and deionized water, and deionized water aerated for 30 min a t atmospheric pressure. Extra pure grade ethanol was used as received.
Table 11. Critical Superheat for Flashing of City Water nozzle no. T." C pn. lo3 Pa T.,OC AT. K u, m / s 1 86.4 4.13 29.5 56.9 5.88 1 82.0 53.7 3.87 28.3 6.29 6.78 1 82.6 54.3 3.87 28.3 7.99 1 82.0 52.1 4.19 29.9 4.19 29.7 8.99 1 81.0 51.3 9.04 50.3 27.8 1 78.1 3.73 10.3 48.1 4.27 30.0 1 78.1 7.10 49.0 2.20 19.0 3 68.0 8.22 3 69.7 47.2 2.73 22.5 9.53 44.6 23.4 3 68.0 2.89 9.65 44.0 3.33 25.9 3 69.9 10.1 3 66.2 42.5 2.93 23.7 11.1 3 65.4 39.5 3.33 25.9 11.6 3 64.0 38.1 3.33 25.9 8.00 4 72.3 42.7 4.13 29.6 9.40 4 71.0 39.8 4.53 31.2 10.2 4 71.2 39.7 4.60 31.5 10.5 4 67.5 36.3 4.53 31.2 10.7 4 68.8 36.1 4.93 32.7 11.0 4 68.0 36.0 4.73 32.0 11.6 4 61.3 32.3 4.00 29.0 6.86 5 72.1 45.6 3.47 26.5 8.39 5 69.1 42.6 3.47 26.5 9.35 40.1 5 66.9 3.53 26.8 5.79 31.2 7 60.2 4.00 29.0 6.71 7 60.7 33.0 3.73 27.7 7 59.5 7.71 28.8 4.40 30.7 7.81 7 59.4 30.4 4.00 29.0 8.36 7 58.5 28.5 4.27 30.0 9.55 28.7 7 58.7 4.27 30.0 9.75 32.2 7 58.0 25.8 4.80 Table 111. Critical Superheat for nozzle no. T.O C pn, lo3 Pa 1 51.8 6.00 1 57.9 7.05 1 53.2 6.67 54.1 6.91 1 1 52.7 7.20 48.8 6.40 1 47.5 6.40 1 2 45.7 6.90 44.5 6.85 2 45.9 7.41 2 46.4 7.42 2 43.6 6.97 2 2 46.6 7.91 2 43.8 7.92 44.7 7.68 2 37.5 6.80 3 43.1 8.61 3 36.8 7.04 3 33.5 6.36 3
Flashing of Ethanol T.," C AT. K u. m / s 20.3 31.5 6.69 23 34.9 9.73 22.1 10.3 31.1 22.7 10.6 31.4 10.7 23.4 29.3 21.4 11.7 27.4 21.4 12.4 26.1 7.66 22.6 23.1 8.33 22.5 22.0 22.1 9.72 23.8 22.5 10.7 23.9 20.8 10.9 22.8 21.6 12.0 25.0 18.8 12.5 25.0 20.2 12.5 24.5 15.1 12.8 22.4 13.6 16.6 26.5 14.1 14.1 23.0 12.2 15.1 21.3
Results and Discussion Critical SuDerheat for Flashing. Figure 3 shows typical photographs of the breakup pattern of superheated water jets. When the water was cold, a typical turbulent jet was observed, as shown in (A). At the higher superheat, large bubbles were formed in the jet and the jet broke into segments as shown in (B). When the superheat was much greater, jets exploded suddenly but segments were still observed, as shown in (C).As the superheat rose slightly beyond a critical value, complete flashing occurred and no segments were observed, as shown in (D). In this paper, the critical superheat for flashing is defined as the condition under which phenomena like (D) are observed. The distance between the efflux of the jet and its complete breakup corresponds to the delay time during which bubble nuclei survive and grow rapidly, causing the jet to disintegrate completely. The critical superheat values for flashing measured in this way are listed in Tables I1 and 111. The effect of
208
Ind. Eng. Chem. Fundam.. Vol. 25, No. 2, 1986
i
1' -J v
F
, ,
A
.
,
.. ..
.
-.
,
C
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Figure 5. Bubble-growing process photographed by B high-speed cinecamera (d = 0.84 mm;u = 10.02 mjs; pa = 19 mmHg; AT = 1G.7 K 5500 frames/&
D
Figure 3. Breakup pattern of superheated water jets 88 single-phase effluent (d = 0.54 mm). (A) u = 8.50 m/s; p o = 760 mmHg; AT negative. (B) u = 8.65 m/s; p o = 22 mmHg; A T = 28.5 K. (C) u = 8.22 m/s; p o = 23 mmHg; AT = 45.4 K. (D) u = 8.22 m/s; p o = 20 mmHg; AT = 48.0 K.
l-
0
V
a
vv 40
O G
wv
-
000
-
WV
30 -
0
v
0 B O
.
0
0
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4
6
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12 tmls I
14
Figure 4. Critical superheat for flashing of water jet ejected from various nozzles.
suspended solids and noncondensing gas on the critical superheat was examined by use of city water, deionized water, degassed water, and aerated water. Figure 4 shows that the effects are negligible, small in comparison with effecta of changes in both the liquid velocity and the nozzle diameter. The critical superheat decreased with increases of both the liquid velocities and the nozzle diameters, as shown in Figure 4. Although similar effects of these factors were observed during the ethanol ejection, the critical superheat values for ethanol were lower than those for water, as shown in Table 111. Growth Rate of Vapor Bubbles. Bubble growth in uniformly superheated liquids is given by
R = CJa[a(t - tn)]1/2
c
x [mml Figure 6. Bubble growth data. Each key show growth of individual bubble generated in the jet (d = 0.84 mm; u = 10.02 m/s; AT = 16.7 K).
I
A
2
(1)
where the constant C is 2(3/r)'I2 according to Plesset and
Zwick (1954) and Scriven (1959) and r'/* in Forster and Zuber's (1954) analysis. The growth rate of vapor bubbles in superheated liquids was measured hy Dergarabedian (1953), Hooper and Abdelmessih (1966), Cole and Shulman (1966), and Kosky (1968). Although their experimental growth rates at low superheats are in good agreement with eq 1, those a t higher superheats, at high Jakob numbers, are much smaller than the prediction from eq 1(Cole and Shulman, 1966). The disagreement between the experimental and theoretical growth rates is caused by the lack of equilibration between the temperature of bubble walls and the external pressure (Kosky, 1968; Theofanous et al., 1969). The conditions of the present experiment correspond to high Jakob numbers. Thus, the bubble growth can be written as
R = 4Ja[ra(t - tn)]1/2
(2)
where 4 is the correction factor, correspondingto the ratio of experimental to theoretical growth rates. Figure 5 shows an example of a high-speed motion picture from which bubble growth rates could be measured. In the measurements of bubble growth rates, the superheats were maintained less than the critical value for flashing because the patterns, as shown in Figure 5, were certainly expected. From eq 2 the following relation between R and x is obtained.
R2 = (&Ja)%a(x
- xn)/u
(3)
The bubble growth data are shown according to eq 3 in Figure 6 from which the growth rate can be obtained. Figure 7 shows the empirical correlation of 6 with the ratio of vapor to liquid density, where the equilibrium values corresponding to the pressure in the vacuum
Ind. Eng. Chem. Fundam.. Vol. 25, No. 2. 1986 209
-
10
1
a
10
I
.
'
10-2
'
' * , I
1U'
'
' ,,I 1
Wev
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, , I
IO
'
0 '
'
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Figure 9. A correlation of critical Jakob number with density ratio and Weber number. The solid line shows eq 5. Keys are given in Figure 8.
Figure 7. A correlation of correction factor 4 with density ratio. The solid curve s h o w eq 4. 10'
. I 03
m
7
E
BrwnBVork's data Freon-ll
G
Figure 10. Breakup pattern of superheated water jets as two-phase effluent. (E) d = 0.84 mm; u = 9.78 m1s;po = 62 mmHg; AT = 2.9 K. (F)d = 1.60 mm; u = 9.80 m/s; po = 50 mmHg; AT = 10.5 K. (G) d = 1.60 mm; u = 8.20 mfs; po = 45 mmHg; AT = 19.5 K.
0.
Figure 8. Critical Jakob number for flashing vs. Weber number based on vapor density.
chamber are used as the vapor density and the values corresponding to inlet liquid conditions as the liquid density. The data shown in the figure were obviously obtained by different experimental techniques: Hooper and Abdelmesaih (1966) reduced the pressure of a quantity of pressurized hot water suddenly down to 1atm; Cole and Shulman (1966) formed bubbles from a heat-transfer surface in a pool of liquid under subatmospheric pressure; Suzuki and Yamamoto (1978) ejected superheated liquid jets. However, all data can be correlated, apparently, by a single function, the solid curve in the figure, although they scatter considerably. The solid curve demonstrates the following relationship.
6 = 1 - exp(-2300pV/pd
F
(4)
Correlation of Critical Superheat for Flashing. Flashing phenomena are controlled by bubble growth rates in superheated liquids (Brown and York, 1962; Lienhard and Stephenson, 1966; Lienhard and Day, 1970). Thus, it is reasonable that the critical superheat for flashing should be normalized by using the Jakob number and the density ratio. In Figure 8, experimental critical superheats are shown by plotting of Jakob numbers vs. Weber numbers. The data seem not to be expressed as a single relation. Extrapolating a curve through the present data at a high Jakob number does not give a line through the data of Brown and York's at low Jakob numbers. This demonstrates the fact that bubble growth rates at high Jakob numbers are almost 1order of magnitude smaller than the theoretical predictions.
The critical Jakob number, modified by the density ratio, is shown in Figure 9. All the data, except those a t high Weber numbers (>25), are correlated by
Ja4 = lOOWe-'/'
(5)
In the present work, critical superheats for the nozzle of large diameter (1.6 mm for water) have a tendency to be lower than others, as shown in Figure 9. Furthermore, complete flashing was not observed in the ejection of ethanol from the nozzles of 0.84 and 1.6 mm because of the generation of two-phase flow in the nozzle, as mentioned later. So, the previous data at high Weber numbers may be presumed to have been obtained at a condition where complete flashing did not occur because of their using nozzles of relatively large diameters. Figure 9 and eq 5 indicate that the critical Jakob number slightly decreases with increasing Weber numbers because the aerodynamic interaction of surrounding vapor with the jet surface enhances the generation of nuclei. The effect of aerodynamic resistance on jet stability is assessed as a function of the Weber number based on the ambient fluid's density (Weber, 1931; Fenn and Middleman, 1969; Sterling and Sleicher, 1975). The rise of the local level of pressure fluctuations caused by the aerodynamic effect on jet surfaces increases the number of nuclei which can trigger the bubble growth into flashing. So, the critical superheat for flashing decreases with the increase of the Weber number. Spraying as a Two-Phase Effluent. A different behavior of the superheated liquid was observed a t temperatures closer to the bubble-point temperature corresponding to the ambient pressure. Figure 10 shows photographs of such breakup, which is different from complete
210
Ind. Eng. Chem. Fundam., Vol. 25, No. 2, 1986
than 50 flashes like the single-phase effluents. For the ejection of superheated ethanol from the long nozzles of 0.84 and 1.6 mm, however, such complete flashing was not attained under any conditions within the present experiments. Such a remark means that the minimum critical velocity for the single-phase effluent depends not only on the nozzle length but on the nozzle diameter and the surface tension of liquids.
-
0 5
10
15 Cmls 1 Figure 11. Apparent superheat at which ethanol jets begin to flash or spray (two-phase effluent).
u
flashing shown in Figure 3. The jet began to swell, even a t low superheats, as shown in (E). At moderate superheats, spraying was observed, as shown in (F) and (G). The spray shown in Figure 10 differs, apparently, from complete flashing in the following significant way: a wideangled spraying occurs at lower superheats; jets seem to spray immediately down the nozzle exit while flashing occurs at a some distance from the nozzle exit (see Figure 3). In other words, the photographs shown in Figure 10 show no delay time for growing of bubble nuclei. Such phenomena are caused by the fact that vapor bubbles grow to a sufficiently large size in the nozzle and the jet flows out as a two-phase mixture. Such two-phase effluents were likely to occur at lower liquid velocities when the shorter nozzles were used. Superheated ethanol was found more likely to spray as a two-phase effluent than water. Furthermore, the conditions under which the two-phase effluent occurred were found to be independent of the presence of suspended solids and noncondensing gas by the use of four kinds of water described above. Figure 11 shows the apparent superheat at which ethanol jets begin to flash or spray. The apparent superheat for the effluent from the shorter nozzle a t velocities less than 12 m/s is much lower than those for the longer nozzle. As the effluent velocities increase, the apparent superheats grow to be comparable with those for the longer nozzle. The stepwise increase in the apparent superheat is coincident with the photographic observation that the two-phase effluent changes to flashing corresponding to a single-phase efflux. Furthermore, the breakup pattern of cold jets ejected from both nozzles cannot be distinguished from each other. Figure 11 indicates that a superheated liquid flows as the single-phase efflux a t velocities sufficiently above a minimum critical velocity; this velocity was observed for superheated water in a tube by Gutierrez and Lynn (1969). The data shown in Figure 11also suggest the dependence of the minimum critical velocity upon the nozzle length. An attempt was made to examine the effect of the nozzle dimensions on this minimum velocity, using the nozzles whose aspect ratio (lid) was 34.2:112.5. As the range of liquid velocities was limited by the nozzle dimensions and the pressure in the vacuum chamber, however, the quantitative relationship could not be obtained. It is qualitatively remarkable from visual observation that superheated water flowing from nozzles whose aspect ratio is greater
Conclusions In order to know the conditions under which flashing of superheated liquid should occur, experiments were carried out by ejecting superheated water or ethanol into a subatmospheric-pressure zone. The following results were obtained. (1)When superheated liquids were ejected into a vacuum chamber, complete flashing was observed at temperatures far above the bubble-point temperatures corresponding to the pressures in the chamber. The critical superheat above which stable flashing occurred was found to decrease with increases of either the liquid velocity or the nozzle diameter. (2) Growth rates of vapor bubbles were measured by a high-speed motion picture. On the basis of the experimental growth rates, the critical superheat required for flashing was correlated in terms of a Jakob number, modified by the density ratio, and a Weber number based on the vapor density. (3) A different behavior of superheated liquids was observed a t temperatures closer to the bubble-point temperatures corresponding to the pressures in the chamber. Such spraying is due to the fact that vapor bubbles are formed in the nozzle and the jet flows out as a two-phase vapor-liquid effluent. Nomenclature C = constant in eq 1 = specific heat of liquid, J/(kg K) = nozzle diameter, m Ja = Jakob number = pLc,AT/pvL k = thermal conductivity, J/(m s K) L = latent heat, J/kg 1 = nozzle length, m p o = pressure in the vacuum chamber, Pa R = bubble radius, m T = temperature of liquid, K T , = bubble-point temperature corresponding to po, K AT = superheat = T - T,, K t = time, s t o = delay time, s u = liquid velocity, m/s We = Weber number = d p v u 2 / n x = distance from nozzle exit, m xo = distance corresponding to delay time, m Greek Letters a = thermal diffusivity, m2/s p = density, kg/m3 u = surface tension of liquid, N/m 4 = correction factor Subscripts L = liquid phase V = vapor phase Literature Cited
2
Bankoff. S.G. "Advances In Chemical Engineering": Drew, T. B.. Hoopes, J. W.,Eds.; Academic Press: New York, 1966; Vol. 6, p 7. Blander, M.; Katz, J. L. AIChE J . 1975, 21, 833-848. Brown, R.; York, J. L. AIChE J . 1962, 8 . 149-153. Cole, R.; Shulman, H. L. I n t . J . Heat Mass Transfer 1966, 9 , 1377- 1390. Dergarabedlan, P. J . Appl. Mech. 1953, 20, 537-545. Fenn, R.; Middleman, S. AIChE J . 1969, 15, 379-383. Forster, H. K.;Zuber, N. J . Appl. Phys. 1954, 25, 474-470.
Ind. Eng. Chem. Fundam. 1986, 25, 211-216 Gutierrez, A.; Lynn, S. Ind. Eng. Chem. Process Des. D e v . 1868, 6, 486-49 1. Hooper, F. C.; Abdelmessih, A. H. I n “Proceedings of the 3rd Internatlomil Heat Transfer Conference, Chicago, 1966”; AIChE: New Ycfk, 1968: pp 44-50. Kitamura, Y.; Takahashi, T. I n “Proceedings of the 1st International Conference on Liquid Atomization and Spray Systems, Tokyo, 1978”; Fuel SocC ety of Japan: Tokyo, 1979; pp 1-7. Kosky, P. G. Chem. Eng. Sei. 1968, 23,695-706. Lackme, C. Int. J. Multiphase Flow 1879, 5, 131-141. Lienhard, J. H. Trans. ASME, Ser. D 1966, 88, 685-687. Lienhard, J. H.; Day, J. B. Trans. ASME, Ser. D 1970, 92, 515-522. Lienhard, J. H.; Stephenson, J. M. Trans. ASME, Ser. D 1968, 88, 525-532. Fujii, T.; Tanaka, T.; Nakaoka, T. Kagaku Kogaku Ronbunshu Miyatake, 0.; 1975, 1 , 393-398. Miyatake, 0.; Tomimura, S.; Ide, Y.; Fujii, T. Trans. SOC.Mech. Eng., Tokyo 1879, 45, 1863-1891. Plesset, M. S.; Zwick, S. A. J. Appl. Phys. 1954, 25, 493-500. Scriven, L. E. Chem. Eng. Sei. 1959, 10, 1-13.
21 1
fWr, E.; Elata, C. Id.Eng. Chem. Recess Des. Dev. 1877. 16, 237-242. Slmpson, S. G.; Lynn, S. AIChE J. 1877, 23. 888-679. S m , A. M.; Slelcher, C. A. J. FlUMh4ech. 1875, 68, 477-495. S u m , S.; Koizumi, M. Trans. SOC. Mech. Eng., Tokyo 1977, 43, 4608-4621. Suzuki, M.; Yamamoto, T. I n “Proceedings of the 1st International Confere n m on Liquid Atomization and Spray Systems, Tokyo, 1978”; Fuel Society of Japan: Tokyo, 1979; pp 37-43. Theofanous, T.; Biasi, L.; Isbin, H. S. Chem. Eng. Sei. 1969, 24,885-897. Tong, L. S. “Boiling Heat Transfer and Two-Phase Flow”; Wiley: New York, 1985; p 14. Weber, C. 2 . Angew. Math. Mech. 1931, 11, 136-154. Westwater, J. W. “Advances In Chemical Engineering”; Drew, T. B., Hoopes, J. W., Eds.; Academic Press: New York, 1956; p 2.
Received for review November 14, 1983 Revised manuscript received August 21, 1984 Accepted May 30, 1985
Equilibrium Disproportionation and Isomerization of Alkylbenzenes Robert A. Alberty Chemlshy Department, Massachusetts Institute of Technology, Cambridge, Massachusetts 02 139
Equilibrium calculations on complex organic systems may be simplified by use of isomer groups, rather than individual species, and restricted Isomer groups may be used when the catalyst is selectlve. These methods are illustrated by calculations on the equilibrium disproportionation and isomerization of the alkylbenzenes at a series of H/C ratios. Comparison with data on the distribution of alkylbenzenes obtained in the conversion of methanol to gasoline using ZSM-5 illustrates the selectivity of the catalyst and the restricted equilibrium that does occur. The concept of isomer groups may be extended to whole homologous series by fixing the ethylene partial pressure. When this is done, the equilibrium distribution of isomer groups in a homologous series like the alkylbenzenes can be calculated with the same equation as used for the calculation of equilibrium mole fractions within an isomer group. The equilibrium partial pressure of ethylene is a function of the ratio of hydrogen to carbon for the homologous series. The use of this method, illustrated for the alkylbenzenes, has the additional advantage that it provides an indicator for the degree of alkylation of different homologous series in the same reaction system. Homologous series that are in equilibrium with the same partial pressure of ethylene are in equilibrium with each other.
Introduction In making equilibrium calculations on organic systems with many species, it is advantageous to use isomer group thermodynamic properties (Smith, 1959; Smith and Missen, 1982; Alberty, 1983a) because this reduces the number of “species” that have to be included in the calculation. In a second step the equilibrium mole fractions of individual species may be calculated if their Gibbs energies of formation are known. The use of isomer group thermodynamic properties has the additional advantage that thermodynamic properties of isomer groups with higher carbon numbers, where data on individual species are lacking, may be estimated by linear extrapolation (Alberty, 1983b; Alberty and Gehrig, 1984). If the catalyst is selective, the species that are not produced may be omitted from the calculation of isomer group properties. The concept of isomer groups may be extended to whole homologous series by incorporating the partial pressure of ethylene into the definition of the standard state for an isomer group in the homologous series (Alberty, 1985a). If the partial pressure of ethylene is fixed, the distribution of isomer groups within a homologous series becomes a function of temperature only; under these circumstances a homologous series behaves like an isomer group, and so we can call it a pseudoisomer group. This means that the same sort of equations which make it simple to calculate the distribution of species in an isomer group can be used 0 196-4313/86/1025-0211$0 1.50/0
to calculate the distribution of isomer groups in a homologous series group. Equilibria within a homologous series are independent of pressure because the various isomer groups can be equilibrated through disproportionation reactions; for example, for the alkylbenzenes 2CnHzn+ = Cn-lHzn-8 + Cn+lHZn-d
(1)
The equilibria within the alkene homologous series are an exception to this statement because of the volume change in the reaction (n/2)CzH4= C,Hzn a t constant pressure. It is advantageous to calculate equilibrium compositions at fixed ethylene partial pressures because a general equilibrium computer program does not have to be used and because the partial pressure of ethylene provides a useful indicator of the extent of alkylation in the homologous series. In this paper these methods are used in calculating equilibrium distributions for the alkylbenzenes at various H/C ratios (or corresponding ethylene partial pressures). Equilibrium distributions of benzene and methylbenzenes have been calculated by Egan (1960) and by Hastings and Nicholson (1961), but in actual equilibria other alkylbenzenes are also present. Voltz and Wise (1976) have pointed out that the experimental distribution of some alkylbenzenes in the gasoline produced from methanol with zeolite ZSM-5 is in reasonable agreement with equilibrium calculated from disproportionation and isomerization. 0
1986 American Chemical Society
