Page 191 - Separation process engineering

relationship and for y values from the operating equation. If we step off stages from the bottom up, then
we calculate x values from the operating equation and y values from equilibrium. Check this statement out
on a McCabe-Thiele diagram. When going from the bottom up, we want to solve all the operating
equations for x. As noted previously, the optimum feed stage can be determined from the test in Eq. (4-
37), and the point of intersection (Eq. 4-38) is more convenient to use than the feed line. For more
complex situations, the point of intersection of a feed line and an operating equation can be found by
simultaneously solving the equations. The biggest problem in using the Lewis method on the computer is
obtaining a good fit for the equilibrium data. The data can be fit to curves, or an interpolation routine can
be used to interpolate between data points. Burns and Sung (1996) report that linear interpolation
between data points is accurate if enough data points are entered for the equilibrium data.

One of the most convenient ways to discuss computer and calculator methods is by reference to a
flowchart. The flowchart is fairly general while computer code is very specific to the language used.
Consider the specific design problem we solved in Example 4-3. Assume that we decide to step off
stages from the top down. Now the computer or calculator program can proceed as shown in Figure 4-30.
Other flowcharts are possible. If we step off stages from the bottom up, we will calculate y from
i
equilibrium and x from the operating equation. Note that a McCabe-Thiele diagram is very useful for
i
following the logic of flowcharts. Try this with Figure 4-30.

Figure 4-30. Computer flowchart for simple distillation column