Multicomponent Distillation Underwoods Methods

We present here the Underwood equations for mult1-component d1st1llat1on w1th constant relat1ve volat1l-1ty and constant molar flows. The analys1s 1s based on cons1der1ng a two-product column w1th a s1ngle feed, but the usage can be extended to all kinds of column sect1on 1nterconnect1ons.

It 1s 1mportant to note that add1ng more components does not g1ve any add1t1onal degrees of freedom 1n operation. Th1s 1mpl1es that for an ord1nary two-product d1st1llat1on column we st1ll have only two degrees of freedom, and thus we w1ll only be able to spec1fy two var1ables, e.g. one property for each product. Typ1cally, we spec1fy the pur1ty (or recovery) of the l1ght key 1n the top and of the heavy key 1n the bottom (the key components are defined as the components between wh1ch we are perform1ng the spl1t). The recover1es for all other components and the 1nter-nal flows (L and V) w1ll then be completely deter-m1ned.

por a b1nary m1xture w1th g1ven products, as we 1ncrease the number of stages, there develops a p1nch zone on both s1des of the feed stage. For a multicom-ponent m1xture, a feed reg1on p1nch zone only develops when all components d1str1bute to both products, and the m1n1mum energy operat1on 1s found for a par-t1cular set of product recover1es, somet1mes denoted as the preferred spl1t. If all components do not d1str1b-ute, the p1nch zones w1ll develop away from the feed stage. Underwood's methods can be used 1n all these cases, and are espec1ally useful for the case of 1nfin1te number of stages.

The Basic Underwood Equations

The net material transport (w) of component i upwards through a stage n 1s:

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