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FIG 11.26. With Vfixed, the only variable capable of independent manipulation is D.
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continuous tower, V/F were maintained constant, manipulation of D/V would also be manipulation of D/F. Batch distillation is an unsteady-state process, because bottoms composition is continually changing as long as distillate is being withdrawn. If D/V is constant, y will change as z changes. Constant D/V is essentially constant separation and constant withdrawal of distillate. Distillate composition will then vary with time as the light component is removed from the tower. Start,ing with an initial charge IV*, containing ICO molt fraction of the lighter component, at any time t there remains
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TV = W, - Dt (11.22)
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The bottoms composit ion x: at time t can be found from the material balance of the light component:
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W x = W,x, - DJy dt x = (11.23)
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Woxo - DJy dt Wo - Dt
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The point to be remembered is that constant D/V will produce variable distillate composition. Distillate is collected in a receiver whose final contents must meet a certain specification. Thus the average va.lue of
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NOW y can be found from x, using the modified Fenske equation.
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Distillation
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y, designated 9, is the controlled variable:
DJydt = D t Jydt =t
(11.24)
9 Withdrawal of distillate is to be stopped when g falls to its desired value. The disadvantages of constant-distillate-rate control are these: 1. If D/V is relatively high, separation will be low, and withdrawal This means of distillate must be stopped at a relatively high value of 2. that recovery of light ends will be poor. 2. If D/V is reduced to enhance recovery, the distillation may consume an unreasonable amount of time and energy.
Constant-composition Control
A more efficient way to operate a batch still is on the basis of constant distillate composit ion. Because bottoms composition continually changes, scparat,ion must also change if constant distillate composition is to bc maintained. Consequent ly, D/V will be high at the beginning of a batch and will gradually be reduced to zero by the distillate-compositiorl controller, when all of the recoverable product has been withdrawn. A control system operating on t,his basis appears in Fig. 11.26. The temperature controller would require reset action, to maintain constant quality with changing distillate rate. Toward the end of the distillat,ion, the flow of product will not 0111~ diminish, but it s rate of change will also diminish. As a result, all of the light component cannot economically be removed, so a decision must be made as to when to stop withdrawal. This decision can be made on an economic basis by comparing the distillate flow times its value against operating costs. When the two are equal, the point of diminishing returns has been reached, as indicated in Fig. 11.27. Another factor limiting the amount of recoverable distillate is t he holdup of liquid in the trays of the column. Before the next higher boiling product can be wit,hdrawn as distillate, the mixture held on the trays must be removed as a slop cut. This mat erial is collected in its own receiver and rekrned to the reboiler with a later batch of feed
Dxvolue FIG 11.27. When the rate of remuneration equals the operating cost, distillation should be terminated.
Time
1 Applications
Constant y _
\ Constant D D-----b----
Constant D -\
Time
Time
FIG 11.28. Optimal distillate rate is intermediate between constant-rate and constantcomposition programs.
stock. The piping arrangement for withdrawal of distillate, shown in Fig. 11.26, has been designed to minimize holdup. It can be seen that multicomponent separations may be accommodated without difficulty in a batch still. A separate receiver is necessary for each product, and manual operations are required to change receivers and to readjust the set point of the temperature (or composition) controller. But with each addit,ional product cut there is also a slop cut,. Hence as t he number of products increases, the percentage of the batch recovered as product diminishes.
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