McCabe-Thiele Diagrams: Screencasts
Demonstrates conceptually how to step off stages on a McCabe-Thiele diagram.
We suggest that after watching this screencast, you list the important points as a way to increase retention.
Uses an interactive simulation to describe the impact of the state of the feed to a distillation column on the liquid and vapor flow rates in the column.
We suggest that after watching this screencast, you list the important points as a way to increase retention.
Uses mass balances to derive the equation for the q-line used in the McCabe-Thiele method, which is used to analyze a distillation column for a binary mixture.
We suggest that after watching this screencast, you list the important points as a way to increase retention.
Important Equations:
Operating line (rectifying line):
\[y = \frac{L}{V} x + \frac{D}{V} x_D\]
where \(L\) is the total liquid flow rate, \(V\) i the total vapor flow rate, \(D\) is the total distillate flow rate, \(x\) is the liquid mole fraction of the more volatile component at a specified point, \(x_D\) is the mole fraction of the more volatile component in the distillate, and \(y\) is the vapor mole fraction of the more volatile component at a specified point.
\[R = \frac{L}{D}\]
where \(R\) is the reflux ratio.
Operating line in terms of reflux ratio:
\[y= \left( \frac{R}{R + 1} \right) x +\left( \frac{1}{R + 1} \right) x_D\]
Boil-up ratio definition:
\[V_B = \frac{\overline V}{B}\]
where \(V_B\) is the boil-up ratio, \(\overline V\) is the molar flow rate of vapor in stripping section, and \(B\) is the total bottoms flow rate.
Definition of \(\overline L\) over \(\overline V\) in terms of \(V_B\):
\[\frac{V_B + 1}{V_B} = \frac{\overline L}{\overline V}\]
\(\overline L\) is the total molar flow rate of liquid in stripping section (not the same as \(L\))
Operating line of stripping section:
\[y = \frac{\overline L}{\overline V} x – \frac{B}{\overline V} x_B\]
where \(x_B\) is the mole fraction of the more volatile component in the bottoms.
Definition of \(q\) (from mole balance around feed stage):
\[q = \frac{\overline L – L}{F}\]
\[1 – q = \frac{V – \overline V}{F}\]
where \(q\) is the feed quality, and \(F\) is the total molar flow rate of the feed stream.
\(q\)-line equation:
\[y = \frac{q}{q – 1} x – \frac{z_F}{q -1}\]
where \(z_F\) is the mole fraction of the more volatile component in the feed.