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There are three streams, feed, overheads and bottoms, and three independent compo-
nents in each stream. CHEMICAL ENGINEERING
Number of variables (component ﬂow rates) D 9
Number of independent material balance
equations D 3
Number of variables to be speciﬁed for
a unique solution D 9 3 D 6
Three variables are speciﬁed; the feed ﬂow and composition ﬁxes the ﬂow of each
component in the feed.
Number of variables to be speciﬁed by designer D 6 3 D 3. Any three component
ﬂows can be chosen.
Normally the top composition and ﬂow or the bottom composition and ﬂow would be
chosen.
If the primary function of the column is to separate the benzene from the other compo-
nents, the maximum toluene and xylene in the overheads would be speciﬁed; say, at
5 kg/h and 3 kg/h, and the loss of benzene in the bottoms also speciﬁed; say, at not
greater than 5 kg/h. Three ﬂows are speciﬁed, so the other ﬂows can be calculated.
Benzene in overheads D benzene in feed benzene in bottoms.
0.6 ð 10,000 5 D 5995 kg/h

Toluene in bottoms D toluene in feed toluene in overheads
0.3 ð 10,000 5 D 2995 kg/h

Xylene in bottoms D xylene in feed xylene in overheads
0.1 ð 10,000 3 D 997 kg/h

2.11. TIE COMPONENTS
In Section 2.9 it was shown that the ﬂow of any component was in the same ratio to the
ﬂow of any other component, as the ratio of the concentrations of the two components.
If one component passes unchanged through a process unit it can be used to tie the inlet
and outlet compositions.
This technique is particularly useful in handling combustion calculations where the
nitrogen in the combustion air passes through unreacted and is used as the tie component.
This is illustrated in Example 2.8.
This principle can also be used to measure the ﬂow of a process stream by introducing
a measured ﬂow of some easily analysed (compatible) material.

Example 2.7
Carbon dioxide is added at a rate of 10 kg/h to an air stream and the air is sampled at a
sufﬁcient distance downstream to ensure complete mixing. If the analysis shows 0.45 per
cent v/v CO 2 , calculate the air-ﬂow rate.

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