Distillate/Feed Material Balance Split ◾  25
For example, with 1,000 kg/h of feed, F, to an ethanol/
water distillation column with 100 kg/h of distillate, D, that
is rich in ethanol and 900 kg/h of bottoms, B, that is mostly
water, the ratio of distillate to feed, D/F, is 100/1,000 = 0.10.
If the feed stream concentration is 0.08 kg ethanol per kg of
feed, that is, X F , and the ethanol concentration in the bottoms,
X B , is 1,000 ppm, that is, 0.001 kg ethanol per kg of bottoms,
and the distillate concentration, X D , is 0.95 kg ethanol per kg
of distillate, the ratio of distillate/feed, D/F, is equal to (0.08 −
0.001)/(0.95 − 0.001) = 0.0832 and D = 0.083 × 1,000 = 83 kg/h.
The bottoms flow rate is 1,000 − 83 = 917 kg/h.
In graphical calculations, Equation 4.3 is known as the
inverse lever–arm rule. A graph of the weight fraction of
component 1 versus component 2 gives a straight line that
connects the bottoms, feed, and distillate compositions. The
feed flow rate is proportional to the length of the entire line
called a lever (X D − X B ). The distillate flow rate is proportional to the length of the inverse lever arm (X F − X B ), and the
bottoms flow rate is proportional to the length of the other
inverse lever arm (X D − X F ). The D/F ratio will be somewhere
between 0.0 (no distillate and all bottoms) and 1.0 (all distillate and no bottoms).
One result of studying the material balance split can be to
understand that the compositions and flow rates of both the
distillate and bottoms streams interact with each other and cannot be independently controlled. If the feed flow rate and one
of the product stream flow rates are fixed, then the flow rate of
the other product stream must be the difference between them,
or accumulation would occur. Compositions of the distillate and
bottoms streams are directly linked by the material balances.
Control of the distillate and bottoms quality can be achieved
by controlling the separation power base and material balance
split to achieve the desired compositions. The flow rates of the
distillate and bottoms streams change as necessary to maintain
the material balance and achieve the target compositions.