The separation of two liquids from each other by fractional distillation may be accomplished in two general ways: (1) the batch, or intermittent, method and (2) the continuous method. In the former, the composition and temperature at any point in the system are changing continually; in the latter, conditions at any point are constant.
It will be recalled that a fractionating column consists of a system up through which vapors are passing and down through which a liquid is running, countercurrent to the vapor, the liquid and vapor being in more or less intimate contact with each other. Furthermore, the vapor and liquid tend to be in equilibrium with each other at any point in the column, the liquid and vapor at the bottom of the column being richer in the less volatile component than at the top. It is evident, therefore, that the action of such a column is similar to that of a scrubbing or washing column, where a vapor is removed from a gas that is passing up through the column, by bringing into contact with it, countercurrent, a liquid in which the vapor is soluble, and that will remove it from the gas.
Sorel's Method. Sorel (Ref. 17) developed and applied the mathematical theory of the rectifying column for binary mixtures. He calculated the enrichment, the change in composition from plate to plate, by makiii^energy and material balances around each plate and assumecf that equilibrium was attained between the vapor and liquid leaving the plate. He proceeded stepwise through the column T>y applying this method successively from one plate to the next.
Owing to the steady-state condition involved in continuous distillation, its analysis is simpler than batch operation and so will be considered first.
The equations for SoreFs method will be derived for the case illustrated in Fig. 7-1. The column is assumed to be operating continuously on a binary mixture with the feed entering on a plate between the top and bottom. The column is provided with heat for reboiling by conduction such as steam coils in the kettle; the case of the use of live or open steam will be considered later. A simple total condenser
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