Flow rate, (lbmol)/min

*From Luyben, Process Modeling, Simulation, and Control for Chemical Engineers, McGraw-Hill, New York, 1973. note: To convert pound-moles per minute to kilogram-moles per minute, multiply by 0.454.

(13-179) and (13-180) to obtain the equilibrium compositions (x,)0 and (x,)„ leaving the decanter. The UNIQUAC equation was used with data from Gmehling and Onken (Vapor-Liquid Equilibrium Data Collection, DECHEMA Chemistry Data Ser., Vol. 1 (parts 1-10). Frankfurt, 1977) to obtain the activity coefficients needed in Eq. (13-179). Reboiler and decanter volumetric holdups were assumed constant at 1.0 m3 (35.3 ft3), and volumetric tray holdups were computed from

where (p^)n is the liquid density; An, the cross-sectional area of the active portion of the tray = 0.23 m2 (2.48 ft2); hw, the weir height = 0.0254 m (0.0833 ft); and hc, the weir crest, assumed to be constant at 0.00508 m (0.0167 ft). Accordingly, volumetric tray holdup was constant at 0.007 m3 (0.247 ft3).

Assume that at t = 0+ the feed rate to tray 23 is disturbed by increasing it by 30 percent to 130 mol/min without a change in composition. The resulting ethanol liquid mole fraction on several trays is tracked in Fig. 13-109. Above tray 16, ethanol concentration remains very small. Below tray 9, ethanol concentration initially decreases fairly rapidly but

then increases slowly and steadies out at significantly higher values than at the initial steady state. Tray 10 is one of the last trays to reach the new steady-state condition, which takes somewhat more than 200 min. This may be compared with initial residence times in the decanter and reboiler of approximately 50 and 250 min respectively. The movement through the column of concentration fronts for all three components is shown in Fig. 13-109. For the first 5 to 10 min, below tray 16, benzene and ethanol fronts shift downward. Then a reversal occurs, and the fronts shift upward until the new steady state is attained. The upward shift is expected because the increased feed rate increases the water-benzene entrainer ratio. The duration of the initial, temporary downward shift is highly dependent on tray holdup and is due to "wash-out" with the feed liquid. This phenomenon is also observed in the dynamic studies of Peiser and Grover [Chem. Eng. Prog., 58(9), 65 (1962)].

FIG. 13-109a Responses after a 30 percent increase in the feed flow rate for the multicomponent-dynamic-distillation example of Fig. 13-100. Profiles of liquid mole fractions at several times.

FIG. 13-109a Responses after a 30 percent increase in the feed flow rate for the multicomponent-dynamic-distillation example of Fig. 13-100. Profiles of liquid mole fractions at several times.

Timt, min

FIG. 13-109b Responses after a 30 percent increase in the feed flow rate for the multicomponent-dynamic-distillation example of Fig. 13-100. Alcohol mole fractions on several trays. (Prokopakis and Seider, Am. Inst, Chem. Eng. J., 29,1017 (1983).]

If the feed rate is decreased, the trends of curves in Fig. 13-109 are reversed. The disturbance of other variables such as feed composition, boil-up ratio, and recycle of water-rich effluent from the decanter produces similar shifts in the steep concentration fronts, indicating that azeotropic towers are among the most sensitive separation operations, for which dynamic studies are essential if reli able process control is to be developed. Such studies indicate the importance of adjusting aqueous-phase recycle and reboiler duty to diminish the movement of steep concentration fronts and the possibility of multiple regimes of operation including unstable regimes, as shown by Magnussen et al. [Inst. Chem. Eng. Symp. Ser. 56 (1979)].

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