For a binary distillation, if the pressure is fixed, a single temperature measurement will provide a reliable guide to composition. But pressure is often not very constant. Today it is sometimes deliberately allowed to float to minimize energy consumption (see Chapter 8). Even if one fixes pressure at one end of a column, it will vary at the other end as a function of boilup rate. An early approach to compensating for pressure variations was to use two temperature measurements, one usually near one end of the column and the other at an intermediate tray. One was then subtracted from the other. For binary or almost-binary distillations, this works fairly well as long as boilup does not change much. If, however, boilup does change significantly, and if the two temperature measurements are separated by a substantial number of trays, one may encounter a nonmonotonic relationship between boilup and AT. As pointed out by Boyd,3 an increase in boilup tends to decrease AT due to increased purity but to increase AT due to increased pressure drop. The composite effect is that AT has a minimum at a particular boilup. This can be very confusing to the operator and may cause instability in the AT control loop, and may either flood the column or shut it down.
This nonmonotonic relationship between AT and product composition occurs even when boilup changes do not affect AP. This is easily visualized if one considers two extreme situations. If the profile is so high in the column that the section between the two temperature points is filled with high boiler, the AT signal will be small. The AT signal will also be small if the profile is so low in the column that it is filled with low boilers. These two conditions will give similar AT signals but vastly different product compositions.
Efforts inevitably were made to stretch the AT technique to fit multicomponent distillations. Some of the difficulties encountered and some guidelines for successful application are presented by Webber.4
In another vintage paper, Vermilion5 presents a somewhat different application of differential temperature control. Here the intent apparently was not to compensate for pressure variations, but to control the temperature profile in the middle trays of the column, and thereby control terminal composition. For a 56-tray deisobutanizer, temperature was measured on trays 22 and 42 (measuring from top down). Use of the AT permitted successful control of isobutane in the bottom product.
Successful application to a C3/C4 splitter column was reported by Bonilla.6
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