Figure 1.26 Distillation column.
n ynj and xn+1,j and flowrates are Vn and Ln+1. The distillate flowrate and composition are D and xDj. The steady-state component balance is
Under total reflux conditions, D is equal to zero and Ln+1 is equal to Vn. Therefore ynj is equal to Xn+ij.
Let us define a continuous variable h as the distance from the top of the column down to any tray. The discrete changes in liquid composition from tray to tray can be approximated by the differential equation dxj
— « xnj - xn+i,j At total reflux this equation becomes dxj dh = xnj- ynj
Note that this is the same equation as developed for residue curves.
The significance of this similarity is that the residue curves approximate the column profiles. Therefore a feasible separation in a column must satisfy two conditions:
1. The distillate compositions xDj and the bottoms compositions xBj must lie near a residue curve.
2. They must lie on a straight line through the feed composition point Zj.
We will use these principles in Chapters 2 and 5 for analyzing both simple and complex distillation systems.
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