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72 MATHEMATICAL MODELS OF CHEMICAL ENGINEERING SYSTEMS
rates over the weirs from known tray holdups. We will defer any discussion of
the very real practical problems of solving this large number of equations until
Part II.
If we listed all the variables in this system and subtracted all the equations
describing it and all the parameters that are fixed (all feeds), we would find that
the degrees of freedom would be equal to the number of sidestreams plus two.
Thus if we have no sidestreams, there are only two degrees of freedom in this
multicomponent system. This is the same number that we found in the simple
binary column. Typically we would want to control the amount of heavy key
impurity in the distillate x,,, HK and the amount of light key impurity in the
bottoms xg, LK.
3.13 BATCH DISTILLATION WITH HOLDUP
Batch distillation is frequently used for small-volume products. One column can
be used to separate a multicomponent mixture instead of requiring NC - 1 continuous
columns. The energy consumption in batch distillation is usually higher
than in continuous, but with small-volume, high-value products energy costs
seldom dominate the economics.
Figure 3.14 shows a typical batch distillation column. Fresh feed is charged
into the still pot and heated until it begins to boil. The vapor works its way up
the column and is condensed in the condenser. The condensate liquid runs into
FIGURE 3.14
Batch distillation.