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Computer studies have shown that there is a program of distillate withdrawal which will recover the maximum amount of product of specified average composition in a specified time interval8 Figure 11.28 shows how this program falls between that of constant distillate rate and In effect, the final bottoms composition constant distillate composit8ion. will be lowest because both y and D/T are low when distillation is terminated.
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FIG 11.29. The optimal policy varies distillate composition with rate in a programmed manner.
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FIG 11.30. The set point of the temperature (or composition) controller may be adjusted automatically with a summing device and a manual set station.
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Plotting dkillate rate vs. c:omposit8ion for each of these three programs gives an indication of how t,hc o@imal program might be implemented. A typical plot, is ronstruckd in Fig. 11.29. The optimal program calls for varying the set point of the temperature (or composition) controller based on the current value of dist illatc flow. Although the optimal program is not linear, it cm1 be approximat~ed to a satisfactory degree by a simple linear equation:
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where lr = slope ijo = intercept This linear expression may be readily implement ed with t,he arrangement of analog devices pict,ured in I ig. 11.30. SUMMARY
simple
Unfortunately it, is impossible to cover even a sampling of the variety of distillat ion columns t hat are in service in industry. They are nearly as individualistic as people. Consequently much is left to the practitioner in t,he way of interpreting the design rules contained herein in terms of his own problems. In t,his regard, a word of warning: do not att,empt, t,o make your particular scparat,ion fit the struct ure of the control system. Rather take care to mold the conkpl system to the peculiarit,ies of t hc separation. One very important, cslass of separut,ion is omitted from t,his chapter, closehowever. It includes all the most difficult problemsPextremely boiling mixtures and constant-boiling mixtures (azeotropes). The reason for the omission is that distillation alone is insufficient for t,heir separation. They will be discussed in as much det,ail as seems reasonable after a brief treatment of extraction in the next chapter.
REFERENCES
1. MacMullan, E. C., and F. G. Shinskey: Feedforward Analog Computer Control of a Supcrfractionator, Control Z&q., Rlarch, 1064.
Applications
Lupfer, D. E., and M. L. Johnson: Automatic Control of Distillation Columns to Achieve Optimum Operation, ISA Trans., April, 1964. Luyhen, W. L., and J. A. Gerster: Fcedforward Control of Distillation Columns, Id. &g. Chem., October, 1964. Fenske, M. R.: Fractionation of Straight-run Pennsylvania Gasoline, 1nnd. .%g. Chem., May, 1932. The Foxboro Company: Fractionating Column Heat Input Control by Pressure Drop Method, Application Eng. Data 282-14. Van Kampen, J. A.: Automatic Control by Chromatograph of the Product, Quality of a Distillation Column, Convention on Advances in Automatic Control, Nottingham, England, April, 1965. Stanton, B. D., and A. Bremer: Controlling Composition of Column Product, Control Eng., July, 1962. Converse, A. O., and G. 1). Gross: Optimal Distillate Rate Policy in Batch Distillation, 1nd. Eng. Chem., August, 1963.
ROBLEMS
11 .I For the column with S = 361 at V/F = 5, and r = 0.50, calculate the j/F required to raise y to 0.97 and the resultant value of 2. Estimate dy/d(D/F). 11.2 Repeat the above calculations for V/F = 2.5. 1 1 . 3 A particular column is fed a binary mixture containing 80 to 90 percent
ght component. Distillate is to be controlled to a purity of 99.9 percent. Brite the feedforward control equation assuming a constant V/F ratio. Repeat )r const,ant heat input. II .4 Feed to a tower contains 5 percent propane, 50 percent isobutane, and 0 percent normal butane, with the balance being higher-boiling components. he feed is analyzed by chromatograph for propane and isobutane. ;\ll the ropane in the feed goes out in the distillate. Under normal conditions, the ottom stream contains 2 percent isobutane, if the distillate composition is conrolled at 5 percent normal butane. Write the feedforward control equation, valuating all coefficient,s. 1 1 . 5 In the example used in the text, the value of dist,illate is $l.OO/gal and hat of the bottoms product is $0.40/gal. Steam costs $l.OO/l,OOO lbs, and 1 lb 3 sufficient to vaporize 1 gal of product. Estimate the optimum V/F ratio for ontrol of y at 0.95, with z at 0.50. 11.6 Repeat the calculation for z = 0.60. Can V/F be optimally programmed rom a measure of feed composition 11.7 Calculate XYo for a column that is split ting feed containing 12 percent )wer-boiling component into a 90 percent pure distillate and a bottoms product ontaining onIy 0.6 percent lower-boiling component.
lthough distillation may be the most common mass transfer operation, it is also the most difficult to assimilat e. Indeed, the separation between components is noticeably obscure, because they occupy the same phase. Other mass transfer operations involve separation or combination of different phases: 1. Vapor-liquid: absorption, humidification 2. Liquid-liquid (immiscible) : extraction 3. Liquid-solid : evaporation, crystallization 4. Vapor-solid : drying Because of t,his distinction, one of t,he exit &reams in each of the above is eit her pure, as the vapor from an evaporator, or in an equilibrium stat e independent of material-balance considerat ions. Although materialbalance control can bc enforced in each of these mass transfer operations, the separation between phases generally simplifies its formulation by 345
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