Ind. E n g . Chem. R e s . 1987,26, 1127-1132
IF (U.GT.HILIM) THEN COMP=U-HILIM U=U-COMP C C SET T H E COMPENSATION IF CONTROL C ACTION AT LOWER LIMIT ELSEIF (U.LT.LOLIM) THEN COMP=U-LOLIM U=U-COMP C C SET THE COMPENSATION IF CONTROL C ACTION NOT SATURATED ELSE COMP=O.O ENDIF Literature Cited Astrom, K. J.; Wittenmark, B. Computer Control Systems: Theory and Design; Information and System Science Series; PrenticeHall: Englewood Cliffs, NJ, 1984. Clark, D.; Hastings-James, R. Proc. Inst. Electr. Eng. 1971, 118, 1503-1506. Dahlin, E. B. Znstrum. Control Syst. 1968, 41, 77-83. Garcia, C. E.; Morari, M. Ind. Eng. Chem. Process Des. Dev. 1982, 21, 308-323. Garcia, C. E.; Morshedi, A. M. “Solution of the Dynamic Matrix Control Problem Via Quadratic Programming (QDMC)”, Proceedings of the Canadian Industrial Computing Society, Ottawa, Ontario, Canada, 1984.
1127
Gill, P. E.; Murray, W.; Saunders, M. A.; Wright, M. H., Report SOL 84-6,1984; Systems Optimization Laboratory, Stanford University, Stanford, CA. Harris, T. J.; MacGregor, J. F.; Wright, J. D. Can. J. Chem. Eng. 1982, 60,425-432. Kestenbaum, A.; Shinnar, R.; Thau, F. E. Ind. Eng. Chem. Process Des. Deu. 1976, 15, 1-13. Khandria, J.; Luyben, W. L. Ind. Eng. Chem. Process Des. Deu. 1976, 15, 278-284. Kuest, J. L. Optimization Techniques with Fortran; McGraw-Hill: New York, 1973. Marshall, J. IEE Control Eng. Ser. 1979, 1. Martin, G. D. AZChE J. 1981,27, 748-805. Mosler, H.; Koppel, L.; Coughanowr, D. AIChE J . 1967,13,768-778. Palmor, Z.; Shinner, R. Znd. Eng. Chem. Process Des. Deu. 1979,18, 8-30. Richalet, J.; Rault, A.; Testud, J. L.; Papon, J. Automatica 1978,14, 413-428. Rosenbrock, H. H. Comput. J . 1960,3, 175-184. Segall, N. L., M. Eng. Thesis, McMaster University, 1983. Segall, N. L.; MacGregor, J. F.; Wright, J. D. Report 1008, 1986; Process Control Laboratory, McMaster University, Hamilton, Canada. Segall, N. L.; Taylor, P. A. Znd. Eng. Chem. Process Des. Dev. 1986, 25, 495-498. Smith, C. L. Digital Computer Process Control; Intext Educational: Scranton, PA, 1972. Wong, P. M., M. Eng. Thesis, McMaster University, 1983. Wong, P. M.; Taylor, P. A.; Wright, J. D. Report 1007,1986; Process Control Laboratory, McMaster University, Hamilton, Canada.
Received for reuiew April 24, 1986 Accepted February 17, 1987
A Modified Oldershaw Column for Distillation Efficiency Measurements Mohammad A. Kalbassi and Michael W. Biddulph* Department of Chemical Engineering, University of Nottingham, University Park, Nottingham, U . K .
This paper describes experimental studies using a conventional and a modified 3.8-cm-tray diameter Oldershaw column with external downcomers. The point efficiencies evaluated using the modified column are much lower due to the tendency of the new column not t o support the froth by its wall and to reduce the wetted wall effects. The point efficiencies measured in the modified column are in close agreement with predictions from large-scale tray efficiency measurements and would lead to conservative designs of large distillation columns. T h e surface tension behavior of the systems studied suggests that highly surface tension positive systems exhibit higher point efficiencies than neutral and negative systems. For many years workers in the field of distillation have tried to simulate the behavior of large distillation columns by using laboratory-scale studies. Recent mathematical simulation of the tray models by high-speed digital computer (Biddulph 1975), and also the deficiencies of the prediction methods (Lockett and Ahmed, 1983) together with unavailability of field data, necessitates an easy method to obtain point efficiency data for the design of a distillation column. One of the difficulties associated with the use of small columns is that of “wall supported“ froth which has been referred to by Ashley and Haselden (1972), Thomas and Hag (19761, Lockett and Ahmed (1983), Young and Weber (19721, Standart (19741, Zuiderweg (1969))Sargent et al. (1964), Bubble Tray D e s i g n Manual (1958))Dribika (1986), Pruden et al. (1974), and Finch and Van Winkle (1964).
* Corresponding author. 0888-5885/87/2626-1127$01.50/0
Early studies of surface tension positive and negative systems using laboratory-scale “Oldershaw” columns (Zuiderweg and Harmens 1958) revealed higher efficiencies for positive systems due to the Marangoni effect on froth formation, the lower efficiencies evaluated for the negative system being explained in terms of contraction effects on the froth. However, the reverse was observed in the “spray” regime (Bainbridge and Sawistowski, 1964), which was interpreted in terms of “Marangoni” effects on droplet formation. Other effects such as liquid holdup (Haselden and Thorogood, 1964; Fane and Sawistowki, 1969; Brown and England, 1961; Finch and Van Winkle, 1964; Umholtz and Van Winkle, 1957; Hellums et al., 1958; Jeromin et al., 1969; Sargent et al., 1964) have also been considered. There is evidence that the deep froths formed in conventional Oldershaw columns are due to the wall effects supporting the froth which result in high point efficiencies, often exceeding 100%. Under these conditions, the effi0 1987 American Chemical Society
1128 Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987
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as compared with 12-15.5 cm with the unmodified column; see Figure 2.
e I
1
Figure 2. Operation of the standard and modified column. System: methanol/water. Run 112a (left): froth height, 2 cm; point efficiency, 0.7722,0.8356; vapor velocity, 0.405 m/s. Run 112b (right): froth height, 15 cm; point efficiency, 1.01,0.8268; vapor velocity, 0.45 m/s.
MODIFIED
STANDARD
Figure 1. Standard and modified Oldershaw column. Table I. Column Characteristics ~~
~~
tray diam., cm column diam. above the tray, cm no. of holes hole diameter, mm weir height, mm 9 ' 0 free area hole pitch, mm
Oldershaw -modified 3.8 3.8 3.8 6.4 46 46 1.1 1.1 2.5 2.0 8 8 3.8 3.8
ciency is affected by the F-Factor (Ellis and Legg, 1962; Ellis and Bennett, 1960). I t is also shown that negative systems exhibit unreliable efficiencies. In this work a new column design is described to simulate the conditions encountered on large trays, which avoids wall-supported froth. Some observations are also reported concerning froth formation on large trays in terms of the liquid holdup.
Modified Column The idea that a modification is desirable grew after calculating the point efficiencies of highly positive aqueous systems using a standard Oldershaw column (Figure 11) and studying the mechanism of froth formation in small columns. One of the systems of interest, methanollwater, had been studied before, and point efficiencies had been measured in larger scale columns (Lockett and Ahmed, 1983; Biddulph and Dribika, 1986). Clearly the point efficiencies measured from small-column experiments were excessive. Based on our observations, it was decided to design a column with a similar form to that of the standard 01dershaw column used during our experiments but with an expansion above the tray to try to avoid the wall supporting the froth. Figure 111shows the new column and compares it with the previous arrangement. The two columns had the characteristics given in Table I. The experiments with the modified column appeared to give a much more representative froth for the outlet weir height used. A froth height of 1.5-2.5 cm was obtained
Experimental Section A 10-L reboiler was provided with a heating mantle and covered by a jacket, together generating a heat input of 1300 W. The column was operated a t total reflux and atmospheric pressure and was contained within a heated cabinet to remove the possibility of heat losses. Each experiment was of about 4-h duration to achieve steadystate conditions, the cabinet temperature being monitored regularly and adjustments made if necessary. The froth height was measured against a scale placed behind the column. The samples were collected in precooled bottles. Prior to sampling, a small amount of liquid was withdrawn from each sample point to ensure representative sampling. The samples were analyzed by a gas-liquid-chromatographic technique. The boil-up rate was measured by direct collection of the reflux. Results Four different systems were studied: methanol/water, ethanollwater, n-propanollwater, and methanollnpropanol. The equilibrium data of Maripuri and Ratcliff (1972), Stabinkov et al. (1972), and Smirnov and Vestin (1959) were used, respectively. These data were reported to be thermodynamically consistent by Gemhling and Onken (1977). The equilibrium data of Dribika and Biddulph (1986) was used for the neutral system methanol/ n-propanol. In each system a comparison between the efficiencies of the unmodified and the modified columns was made. The column superficial F-Factor was maintained constant except for n-propanollwater when two F-Factors were studied. Figures 3-5 illustrate the comparison of the point efficiencies and froth heights for the aqueous systems using the two columns. It is apparent that the wall supported froth gives rise to high efficiencies by providing extra interfacial area. Figure 6 shows a comparison of the point efficiencies for the system methanollwater, measured in the modified column, with those of Biddulph and Dribika (1986), inferred from measurements in a 1-m-long rectangular sieve tray simulator column with a 2.5-cm-high outlet weir, and Lockett and Ahmed (1983), where point efficiencies were deduced from measurements in a 59-cmdiameter sieve tray column with a 5-cm-high outlet weir providing a much greater liquid holdup. A comparison is shown in Figure 7 for the surface tension neutral system of methanolln-propanol based,on experiments with an
Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 1129
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Figure 3. Point efficiencies and froth heights of methanol/water system by standard and modified column. F-Factor, 0.4.
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efficiency. This is in agreement with the experimental observations of Lockett and Uddin (1980), Biddulph and Dribika (1986), and Dribika and Biddulph (1986). It is also
1130 Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987
08
MOLE F R A C T I O N nHEPTANE
Figure 8. Eficiencies and froth heights of n-heptaneltoluene system (a survey): 1,Medina et al.; 2, Zeiderweg and Harmens; 3, Fane and Sawistowski. Also see Table 11. Table 11. Data for Figure 8
column diameter or dimension, cm outlet weir height, cm vapor velocity, ms-' no. of holes hole diameter. mm
1 3.81 0.5
55 1.1
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3 7.62 0.633 2.54 0.33 0.35 46 3.81
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worth noting that in the positive and negative composition ranges on either side of the azeotrope (Figure 5 ) , the efficiencies are comparable.
Discussion The measurements reported here clearly demonstrate the contribution of the wall supported froth to the high efficiencies evaluated. Furthermore, the modification encourages steady operating conditions. It seems likely that with the conventional column, the wetted wall effects due to returning small droplets colliding with the wall, some being carried over to the top sampling point, contributed to fluctuating point efficiencies. However, with the expansion above the plate reducing the vapor velocity, these effects have been markedly reduced. Other studies have indicated that the size of the pilot test column has a direct influence on wall effects and consequently on the measured point efficiency. Studies of the system n-heptaneltoluene were carried out by Medina et al. (1979), Zuiderweg and Harmens (1958), and Fane and Sawistowski (1969). Figure 8 (Table 11) illustrates the measured efficiencies which resulted from these studies. Medina et al. (1979) and Zuiderweg and Harmens (1958) used columns very similar to the unmodified column described here and reported efficiencies of the order of 80-90%, whereas Fane and Sawistowski (1969), despite a large liquid holdup on their tray, reported lower efficiencies from their larger tray. The system N2/02had been studied extensively in the past by Brown and England (1961), Ellis and Catchpole (1964), and Haselden and Thorogood (1964). A comparison of those results in terms of point efficiencies and froth heights is shown on Figure 9 (Table 111). The same trend is observd: the larger tray with the
MOLE% NITROGEN
Figure 9. Efficiencies and froth heights of nitrogen/oxygen system (a survey): 1, Haselden and Thorogood; 2, Ellis and Catchpole; 3, Brown and England. Also see Table 111.
greater liquid holdup but lower froth heights exhibits the lowest point efficiencies. Haselden and Thorogood (1964) used a foam-supporting baffle in an attempt to represent the behavior of an industrial air separation distillation column and obtained efficiencies of about 90%. Hart and Haselden (1969) used the same arrangement for their efficiency studies. One of the surface tension positive systems used in their study, benzenelh-hexane, showed efficiencies above 100% at midcomposition range. These efficiencies were discarded from their studies due to the probability of inaccurate phase data. However, Zuiderweg (1969) discussed Hart and Haseldon's work (1969) and concluded that the foam conditions produced on their plate did not resemble those of large industrial sieve plates since the drainage patterns and foam heights were different. It seems very likely that the foam supporting gauze baffle compensated for the lack of liquid holdup in simulating point efficiencies measured on the larger trays (Biddulph, 1975). It seems likely that the column wall can help to support bubbles due to surface tension forces and reduced vapor velocities near the wall. These supported bubbles assist the bubbles nearer the center of the plate to stabilize. However, in the case of larger diameter plates the supporting effect is quickly lost and the froth height is determined by the rate of buildup and breakdown of froth on the main part of the plate. The modified column described here appears to provide more reliable point efficiency values, within its definition (Standart, 1974), representative of the conditions found in the center of a large plate. Several studies have reported increased tray efficiencies as a result of increased froth heights due to increased outlet weir heights or increased vapor velocities. The amount of froth is also expected to be a function of the liquid holdup on the tray and the vapor velocity (Haselden and Thorogood, 1964; Fane and Sawistowski, 1969; Brown and England, 1961; Finch and Van Winkle, 1964; Umholtz and Van Winkle, 1957; Jeromin et al., 1969; Sargent et al., 1964). To explain the above phenomena, we refer to the results of Lockett and Ahmed (1983) and Biddulph and Dribika (1986). By use of the system methanol/water, a comparison is made between their results and our measured point efficiencies, in Figure 6, using the modified Oldershaw column. It is likely that the lower point efficiencies measured here are due to the much shorter gas and liquid contact on the tray due to lower froth height and smaller liquid holdup present. Kalbassi et al. (1987), using the system methanol/water, demonstrated that under large-scale distillation conditions, the hole size and the outlet weir height had little influence on
Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 1131
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Figure 11. Marangoni stabilizing index.
tray or point efficiencies. The large tray with an outlet weir height of 2 mm held a biphase of an average 4.5 cm in height, almost twice that measured on the modified column tray. Subsequently higher point efficiencies were deduced. These results were very encouraging for future research into using such a column to measure point efficiencies. Firstly, as the hole size has little influence on point efficiency, this can be discarded from the further work. Secondly, it is evident from the large-scale study that lower gas and liquid contact time is achieved in the modified column due to the lower liquid holdup, and an improvement of such contact is required to achieve higher point efficiencies. Further work is now in progress to increase the liquid holdup on the modified column by incorporating higher outlet weir heights without encouraging wall effeds to occur. The point efficiencies measured in the modified column can be used for a conservative design of a distillation column or be scaledup by the recent method of Dribika and Biddulph (1986) for more accurate design. It is evident that such a column can actually measure point efficiencies very close to the ones operating on an industrial tray for any system including those of extractive distillation. Figures 10 and 11illustrate the change in surface tension and the Marangoni stabilizing index, M , at boiling point for the systems studied. The surface tension measurements were carried out in a tensiometer and reported
-
Y*)
where Y = mole fraction of the more volatile component in the vapor phase, Y* = mole fraction of the more volatile component in the vapor phase in equilibrium with the liquid, 6, = surface tension at the boiling point (mN/m), x = mole fraction of the more volatile component in the liquid phase, and M = Marangoni stabilizing index (mN/m). Systems were defined by Zuiderweg and Harmens (1958) as positive if the surface tension of the reflux increases in the column, negative for the reverse, and neutral either if the constituent of the mixture is of the same order of surface tension or if the driving force tends to zero. The azeotropic system n-propanollwater exhibits all the behavior described here; being positive at low and negative at high n-propanol concentrations, it is neutral at the azeotropic point. The system ethanollwater also exhibits the same behavior, but only measurements on the positive side were feasible. The systems methanollwater and methanolln-propanol are “highly positive” and “neutral”, respectively. Note that with the conventional column high froths were formed for the positive and neutral aqueous system, whereas the “surface tension neutral” system of methanolln-propanol was reported (Dribika and Biddulph, 1986) to form no froths. This confirms that the froth supported by the column wall is merely a surface tension phenomena and its extent a function of pure component surface tension difference between the constituents of the mixture studied. The comparison of the point efficiencies of the neutral system methanolln-propanol with the highly positive systems of methanollwater and ethanollwater (Figure 12) suggests that the positive systems exhibit
Ind. Eng. Chem. Res. 1987,26, 1132-1140
1132
Fane, A. G.; Sawistowski, H. Inst. Chem. Eng., Symp. Ser. 1969,32,
higher point efficiencies due to the Marangoni surface renewal effects (Ellis and Biddulph, 1967). The comparison of the positive and the negative composition range point efficiencies of the n-propanollwater system indicates that since the system properties are unchanged and the variation in the mixture surface tension, and consequently the stabilizing index, is low in the composition range studied, similar point efficiencies result.
1%
Finch, R.; Van Winkle, M. Ind. Eng. Chem. Process Des. Dev. 1964, 3(2),106. Gemhling, S.; Onken, U. Vapour-liquid Equilibrium Data; Dechema Chemistry Series; Dechema: Frankfurt, 1977; Vol. 1, p 2a. Hart, D. J.;Haselden, G. G. Inst. Chem. Eng., Symp. Ser. 1969,32, 1-19. Haselden, G. G.; Thorogood, R. M. Trans. Inst. Chem. Eng. 1964, 42, T8l. Hellusm, J. D.; Braulich, C. J.; Lyda, C. D.; Van Winkle, M. AIChE J . 1958, 4(4), 465. Hofhuis, P. A. M.; Zuiderweg, F. J. Inst. Chem. Ena., - Symp. . . Ser. 1979, 56, 2.2.1. Jeromin, L.; Holik, H.; Knapp, H. Inst. Chem. Eng., Symp. Ser. 1969, 23, 5.49.5. Kalbassi, M. A. Ph.D. Thesis, University of Nottingham, England, 1987. Kalbassi, M. A.; Dribika, M. M.; Biddulph, M. W.; Kler, S.; Lavin, J. T. Proceedings of the Institute of Chemical Engineers (London) International Symposium on Distillation, Brighton, 1987. Lockett, M. J.; Ahmed, I. S.Chem. Eng. Res. Des. 1983, 61, 110. Lockett, M. J.; Uddin, M. S.Trans. Inst. Chem. Eng. 1980,58, 166. Maripuri, V. 0.; Ratcliff, G. A. J . Chem. Eng. Data 1972, 17, 366. Medina, A. G.; McDermott, C.; Ashton, T. Chem. Eng. Sci. 1979,33, 1489. Pruden, B. B.; Hayduk. W.; Laudic, H. Can. J . Chem. Eng. 1974,52 (Feb), 64. Sargent, R. W. H.; Bernard, J. 0. T.; McMillan, W. P.; Schroter, R. C. Symp. Distill., London 1964. Smirnov, N. A.; Vestin, J. Lenningrad Uniu. USSR, Fiz. Khim, 1959, 81. Stabinkov, V. N.; Matyushev, B. Z.; Protsyak, T. B.; Yushanko, M. Pushch. Prom. Kiev 1972, 15. Standart, G. L. Chem. Eng. 1974, Nou, 716. Thomas, W. J.; Hag, M. A. Ind. Eng. Chem. Process Des. Deu. 1976, 15(4), 509. Umholtz, G. L.; Van Winkle, M. Ind. Eng. Chem. 1957, 4 9 ( 2 ) , 226. Young, G. C.; Weber, J. H. Ind. Eng. Chem. Process Des. Deu. 1972, 11(3), 440. Zuiderweg, F. J.; Harmens, A. Chem. Eng. Sci. 1958, 9, 89. Zuiderweg, F. J. Inst. Chem. Eng., Symp. Ser. 1969, 32, 1:55.
Conclusion The modified column suggested here seems to be suitable for point efficiency measurements of highly surface tension positive and negative as well as any other systems. I t eliminates the surface tension induced wall supported froth and minimizes the wetted wall effects. The column in general encourages steady operating conditions. This development is a useful step to simulate conditions, i.e., mixed froth regime of liquid, froth, and sprays on a large tray and further work is now in progress to improve the gas and the liquid contact time on the modified column tray by incorporating higher outlet weir heights without encouraging the wall effects to occur. As such, a column can be installed without inflicting great costs; it is a useful tool to measure reliable point efficiencies. Literature Cited Ashley, M. T.; Haselden, G. C. Trans. Inst. Chem. Eng. 1972, 50. Bainbridge, G. S.; Sawistowski, H. Chem. Eng. Sci. 1964, 19, 992. Biddulph, M. W. AIChE J . 1975; 21(2), 327. Biddulph, M. W.; Dribika, M. M. AIChE J . 1986, 32(8), 1383. Brown, B. R.; England, B. L. Int. Inst. Ref. Commun., London 1961, Sept, 19. Bubble-Tray Design Manual; AIChE: New York, 1955. Dribika, M. M. PhD Thesis, University of Nottingham, England, 1986. Dribika, M. M.; Biddulph, M. W. AIChE J . 1986, 32(11), 1864. Ellis, S.R. M.; Bennett, R. J. J . Inst. Petr. 1960, 43(433), 19. Ellis, S.R. M.; Catchpole, J. P. Dechem Monogr. 1964, 55, 43. Ellis, S. R. M.; Biddulph, M. W. Trans. Inst. Chem. Eng. 1967,45, T223. Ellis, S.R. M.; Legg, R. J. Can. J . Chem. Eng. 1962, Feb, 6.
Received for review May 7 , 1986 Revised manuscript received February 8 , 1987 Accepted February 24, 1987
Heterogenizing Homogeneous Catalyst. 2. Effect of Particle Size and Two-Phase Mixed Kinetic Model Bing Joe Hwang and Tse-Chuan Chou* Department of Chemical Engineering, National Cheng Kung University, Tainan, Taiwan, Republic of China 70101
The effects of particle size and the degree of cross-linking of the resin-carrier catalyst on the oxidation of acetaldehyde were investigated. A two-phase mixed kinetic model was developed, which includes mass transfer, heterogeneous reactions, and homogeneous chain reactions. Both the experimental results and the theoretical calculations of the model show that the reaction rate for the production of peroxides is significantly affected by the particle size and the degree of cross-linking of the resin catalyst. The results also show that only a fraction of the whole catalyst particle is effectual to initiate free radicals, which then diffuse through the pores to the bulk solution where the homogeneous free-radical chain reactions occur. The free radicals in the bulk solution are heterogeneously and homogeneously terminated. The manufacture of peracetic acid (PAA) from acetaldehyde and oxygen, using homogeneous Co3+ions and heterogeneous Co-type resin as catalyst, has been discussed in previous papers (Chou and Lin, 1980,1982,1983; Chou and Lee, 1982,1985). The mechanism of the generation of peracetic acid from the partial oxidation of acetaldehyde, using a Co-type resin as catalyst, has also been proposed (Chou and Lee, 1982,1985). In the present work, 0888-5885/87/2626-1132$01.50/0
a two-phase kinetic model was developed, which should be helpful in understanding the general system in which both heterogeneous and homogeneous chain reactions occur. Various models have been proposed to explain the interaction of diffusion and reactions in the macro- and micropores of a heterogeneous catalyst (Aris, 1975; Ors and Dogu, 1979; Mingle and Smith, 1961; Frisch, 1962; Car0 1987 American Chemical Society
