Ind. Eng. Chem. Res. 1990,29, 927-928
to sample as frequently as needed to give good performance. Therefore, the ratio T/T should be kept below 0.5 for proper sampling. Conclusions The first-order Dahlin control algorithm contains the parameter A, which is used for tuning. This paper presented a method to obtain a first estimate to an optimum value of A. Tuning equations that relate A to the process and sampling parameters ( T , T ) were given. The validity of these tuning equations holds only in the range of sampling time to time constant ratio ( T I T )of 0.001-0.5. The T/7values greater than 0.5 have an insufficient sampling rate for the control algorithm to provide good control. Acknowledgment Financial support for M. Medina from the National Science Foundation through Grant RCD-8854860 is gratefully acknowledged. Nomenclature E,, = present error for discrete controller E,,-l = previous error for discrete controller FOPDT = first-order-plus deadtime IAE = integral of the absolute error ISE = integral of the squared error Kp = process gain, %ACO/%ATO M,, = present output from discrete controller M,-l = previous output from discrete controller
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Laplace transform variable tol = closed-loop deadtime, min to, = process deadtime, min T = sampling time, min z = z-transform variable U = change in process input A 0 = change in process output A’= closed-loop time constant, min 7 = process time constant, min s =
L i t e r a t u r e Cited Chiu, K.; et al. Digital Control Algorithms, Part I: The Dahlin Algorithm. Instrum. Control Syst. 1973,46, 10. Condon, B. T.; Smith, C. A. A Comparison of Controller Algorithms as Applied to a Stirred Tank Reactor. Presented a t the ISA Meeting, Anaheim, CA, 1977a. Condon, B. T.; Smith, C. A. A Sensitivity Analysis on Dahlin’s Control Algorithm. ISA Trans. 1977b, 16 (4), 23-30. Dahlin, E. B. Designing and Tuning Digital Controllers. Int. Cem. Semin. 1968, 41, 6. Smith, C. L. Digital Computer Process Control;Intext Educational Publishers: New York, 1972. Smith, C. A.; Corripio, A. B. Principles and Practice of Automatic Process Control; John Wiley and Sons: New York, 1985.
Sylvia Bray, Maximino Medina, Carlos A. Smith* Chemical Engineering Department University of South Florida Tampa, Florida 33620
Received for review July 17, 1989 Revised manuscript received February 1, 1990 Accepted February 26, 1990
CORRESPONDENCE Comments on “Studies on Gas Holdup in a Bubble Column Operated at Elevated Temperatures” Sir: In a recent paper, Zou et al. (1988) propose a gas hold-up correlation for bubble columns operated a t high temperatures: -0.1544 po + p, 1.6105 0.5897 tg = 0.11285(
5)
u (+)
(7)
(1)
In our opinion, the large increase in gas holdup predicted by this gas hold-up correlation with an increase in vapor pressure (P,) is caused by a misinterpretation of their experimental gas hold-up measurements. Zou et al. only measured the gas velocity a t the feed, and they did not presaturate the air feed. Therefore, the true average superficial gas velocity for their experiments increases with an increase in temperature and height due to evaporation. It can be calculated that the superficial gas velocity used by Zou et al. increases by a factor of
the relatively low bubble column ( L = 1.05 m) used by Zou et al., the air will not be completely saturated a t the exit of the column, and therefore, the increase in the superficial gas velocity due to evaporation will be less (by an unknown quantity) than predicted by the above eq 2. The fact, however, remains that the true average superficial gas velocity for their experiments increases with an increase in temperature, and because the increase in gas velocity due to evaporation is unknown, no conclusions can be drawn as to the influence of temperature on gas holdup. The correlation of Zou et al. should therefore, in our opinion, not be used for the design of bubble columns a t elevated temperatures. Nomenclature g = gravitational constant, m/sz H = dispersion height, m Po = total pressure of the system, Pa P, = saturated vapor pressure of the liquid, Pa U , = superficial gas velocity, cm/s
Greek Letters
due to evaporation in the extreme case of a complete saturation of the air a t the exit of the bubble column. In 0888-5885/90/2629-0927$02.50/0
cG = gas holdup c12 = liquid holdup
0 1990 American Chemical Society
Ind. Eng. Chem. Res. 1990,29,928
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liquid viscosity, Paas density of liquid, kg/m3 = surface tension, N/m
pL = pL = u
Literature Cited Zou, R.; Jiang, X.; Li, B.; Zu, Y.; Zhang, L. Studies on Gas Holdup in a Bubble Column Operated a t Elevated Temperatures. Ind.
Eng. Chem. Res. 1988,27, 1910-1916. Peter M. Wilkinson, Laurent L. van Dierendonck* Department of Chemical Engineering Rijksuniversiteit Croningen Nijenborgh 16, 9747 AG Groningen, The Netherlands and DSM Research, P.O. Box 18 6160 M D Geleen, The Netherlands
Response to Comments on “Studies on Gas Holdup in a Bubble Column Operated at Elevated Temperatures” Sir: We thank Wilkinson and Dierendonck (1990) very much for their comments on our paper (Zou et al., 1988). Their comments make our field of vision wider. We discussed the effect of temperature on gas holdup from the viewpoint of application, while Wilkinson and Dierendonck do so from the viewpoint of the degree of saturation of the gas by liquid, which we considered. The conclusions reached by Wilkinson and Dierendonck and by us seem to be different. However, after serious analysis, the conclusions aren’t contradictory but are only different from the viewpoint of the discussions. The existence of the end of the column is the main cause of the resulting “end effect”. But as Qu (1981) showed, the influence of the column height, H, on this effect is negligible when H 3 1 m. Since the temperature inside the column is equal to that of the U-tube and the ratio of the column liquid to the liquid in the U-tube replaced by column liquid is very large in our experiments, the property of the liquid inside the column and the property of the liquid in the U-tube are the same, and our experiments are certainly correct. In our paper we mainly paid attention to the feed rates and the production capacity of the reactor and not to the degree of saturation of gas by liquid. We didn’t discuss the effect of the temperature on the gas holdup from the viewpoint of the degree of saturation of gas by liquid as Wilkinson and Dierendonck did. But our conclusions and the conclusions of Wilkinson and Dier-
0888-5885/90/2629-0928$02.50/0
endonck are not contradictory. The correction in our paper indeed reflects well the relationship of gas holdup, temperature, and the physical property for the air-water and air-alcohol systems. Literature Cited Qu, Yantao. The Process and the Equipment in Basic Organic Chemical Industry; Chemical Industry Press: Beijing, 1981. Wilkinson, P. M.; Dierendonck, L. L. v. Comments on “Studies on Gas Holdup in a Bubble Column Operated a t Elevated Temperatures”. lnd. Eng. Chem. Res. 1990, preceding paper in this issue. Zou, Renjun; Jiang, Xinzhen; Li, Baozhang, Zu, Yong; Zhang, Laiqi. Studies on Gas Holdup in a Bubble Column Operated at Elevated Temperatures. Ind. Eng. Chem. Res. 1988, 27 (lo), 1910-1916.
* In accordance with the authors’ wishes, their family name is listed first. Zou Renjun*
Hebei Academy of Sciences Shijiazhuang, The People’s Republic of China
Zhang Laiqi Northwestern University Xi’an, The People’s Republic of China
0 1990 American Chemical Society
