24 ◾  Distillation Control, Optimization, and Tuning
4.1 Material Balances
A total material balance for a distillation column in Chapter 2,
Figure 2.1, is shown in Equation 4.1. The individual component material balance is shown in Equation 4.2.
F = D + B
(4.1)
FX F = DX D + BX B
(4.2)
where:
F = feed stream (kg/h)
D = distillate stream (kg/h)
B = bottoms stream (kg/h)
X F = mass fraction of component in feed stream
X D = mass fraction of component in distillate stream
X B = mass fraction of component in bottoms stream
By combining Equations 4.1 and 4.2, the material balance split
is shown to be directly related to the compositions:
Material balance split = D/F = (X F − X B )/(X D − X B ) (4.3)
The distillate/feed material balance split is determined by the
concentration of light component in the feed, distillate, and
bottoms. The weight fraction of feed flow that becomes distillate product is D/F, while the remaining fraction of the feed
becomes bottoms product 1−D/F. When the value of X F represents the weight fraction concentration of light components,
the ratio of D/F is nearly equal to X F . This occurs because the
weight fraction of “lights” in the bottoms, X B , is near zero, and
the weight fraction of lights in the distillate, X D , is near one.
When D/F is greater than X F , there will be “heavies” going
over in the distillate. When D/F is less than X F , there will be
lights going down in the bottoms.