3.2.7 Analysis of existing columns: the Smith-Brlnkley method
The Smith and Brinkley (58) method is more convenient for the analysis of existing columns than for the design of new ones. This method applies to absorption and extraction as well as distillation. For distillation, this method gives
hi is a correlating factor, defined by Eqs. (3.28a) and (3.286). If the feed is mostly liquid,
If the feed is mostly vapor
KL and K\ are determined at the effective top and bottom section temperatures. If the temperature profile is available (e.g., from a computer simulation), the effective temperature is the arithmetic average of all tray temperatures in the column section. Alternatively, an arithmetic average of the feed-stage and end-stage temperatures is often used:
Strictly speaking, Eq. (3.24) does not apply to a column with a partial condenser, since it ignores any difference between the overhead and reflux compositions. However, a partial condenser can be closely approximated by increasing N by 1 (58).
Application. Previous methods (Sees. 3.2.1 to 3.2.6) produce a design. They take product compositions and deliver the number of stages, reflux, and optimum feed stage. The Smith-Brinkley method rates a column using the reverse sequence of steps. It takes the number of stages, reflux ratio, and actual feed location, and yields the product compositions.
Once a base case is available, small changes in variables can be easily made. For instance, for a change in feed temperature, half the change is added to tn and the other half to tm. For a change in reflux rate, the extra liquid is added to Sm and Sn. If the changes are large, some trial-and-error solution is required in which tm and tn are varied. This is analogous to an operator who adjusts the control temperature by trial and error until the desired end products are obtained.
The above features make the Smith-Brinkley method valuable for on-line optimization (e.g., using microprocessor or computer control). It can be beneficial for assessing the effects of perturbations on column performance and driving the control point toward an optimum. It is also valuable for off-line optimization and for revamp studies. Rice (58a) extended the Smith-Brinkley method to yield individual stage temperatures and compositions and successfully applied it for control.
Example 3.6 A depropanizer capable of providing 20 theoretical stages, with a feed point on the 9th stage from the top, is available to separate the mixture in Example 2.4. The reflux ratio is 1.5.
(a) Would the column achieve the separation?
fi>) What effect would raising the reflux ratio by 13 percent have on the product purity?
Data: Dew point at top of column = 70°F
Bubble point at bottom of column = 308°F Temperature at feed stage (approx.) = 211°F
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