# Figure 191

Effect on calculation of rectifying section when:

A. Guess for R is too small, or

B. Guess for xq is too close to 1.00000

overhead). These sensitivities often give good clues to the need for feedforward compensation or for terminal composition feedback control.

3. Column gains for feedforward compensation. For example, if feed composition changes, what changes in boilup and reflux do we need to hold terminal compositions constant? Steady-state accuracy is required.

4. Ability to estimate the cost penalty of producing excessively pure product by excessive boilup and reflux. Shinskey and Douglas and Seemann1 have been particularly interested in this. Again, steady-state accuracy is required.

As it turns out, for most of these concerns, we use one of two types of programs: (1) Column terminal conditions are fixed at new, different values from those of design, and reflux is varied by trial and error until the materialbalance equation and tray-to-tray calculations converge, or (2) with fixed reflux or boilup, we change a terminal condition such as distillate flow and find the corresponding change in terminal compositions. The first of these we have labeled 'Type A" and the second we call 'Type B."

Gains for Feedback Control

### Case 1

Consider Figure 19.2 where top-product flow is set by flow control, reflux flow is set by condensate receiver level control, boilup is fixed by flow control of steam or other heating medium, and bottom-product flow is determined by column-base level control. As shown by the dotted line, we wish eventually to control column top composition by manipulating distillate flow. Let us assume that feed rate, feed composition, feed enthalpy, and boilup are fixed and that we wish to find the changes (i.e., "gains") of top and bottom compositions in response to a change in D, the top-product rate.

The starting point is a set of "prep" equations that reflect the desired change in distillate, AZ). The new distillate flow is:

B' = B - AD (since F is fixed at 1.00) /3' = VJB' L'R=LR- AD R' = L'JD'

1. With these equations in hand, assume a new value of xD - x'D and calculate a new xR:

2. Calculate:

starting at the column base and working up.

3. Calculate:

Continue calculating y and x alternately until the number of times y has been calculated equals Nt.