1. Separation Columns (Distillation, Absorption and Extraction)
Dr. Kh. Nasrifar
Department of Chemical and Petrochemical Engineering

2. MULTICOMPONENT DISTILLATION: Empirical Correlations
The Erbar-Maddox correlation is given in this section, as it is now generally considered to give more reliable predictions. Their correlation is shown in Figure 11.11; which gives the ratio of number of stages required to the number at total reflux, as a function of the
reflux ratio, with the minimum reflux ratio as a parameter. To use Figure 11.11, estimates of the number of stages at total reflux and the minimum reflux ratio are needed.

4. Minimum number of stages (Fenske equation)

5. Fenske equation
In terms of light key and heavy key components, the previous equation can be written as
where LK is the average relative volatility of the light key with respect to the heavy key, and xLK and xHK are the light and heavy key concentrations. The relative volatility is taken as the geometric mean of the values at the column top and bottom temperatures. To calculate these temperatures initial estimates of the compositions must be made, so the calculation of the minimum number of stages by the Fenske equation is a trial and-error procedure.

6. Fenske equation

7. Minimum reflux ratio: Underwood equation
The underwood equation is used for estimating minimum reflux ratio:

8. Underwood Equation
Where  is the root of the following equation

9. Feed-point location
Kirkbride equation

10. Example (Erbar-Maddox method)
Estimate number of stages by changing reflux ratio.

11. Solution

12. Solution

13. Solution

14. Example:
Estimate the position of the feed point for the separation considered in the previous Example for a reflux ratio of 3.

15. Example