Graphical Solution on the Y-X Diagram

The material balance equations, or operating lines (Equations 5.13 and 5.14) together with the feed stage heat balances (Equations 5.16 and 5.17), and the equilibrium relation, (Equation 5.12) form the basis for the McCabe-Thiele (McCabe and Thiele, 1925) graphical solution ofbinary distillation on a Y-X diagram. 

The phase equilibrium data, or Equation 5.12, are first plotted on a YX diagram 

It is also known that D=V, and when this expression for D is substituted in the above equation, the result is Y=X= Kj. That is, the rectifying section operating line intersects the diagonal at the distillate composition. Similarly, it may be shown that the stripping section operating line intersects the diagonal at Y = X = Xf the bottoms composition. 

FIGURE 5.5 Plots of (/-lines for different feed thermal conditions. 

Equation 5.19 is known as the -line equation. The (/-line represents the feed thermal conditions and is the locus of intersection points of the operating lines above and below the feed tray. It is a straight line with a slope of qHq - 1) and an intersection point with the diagonal at Y = X = Xp. This may be shown by setting Y = X in Equation 5.19 and solving forX. 

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