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notes: (1) Data from Gallant, Ref. 9; (2) data from Robinson and Gilliland, Ref. 6; (3) data from Van Winkle, Ref. 4.

notes: (1) Data from Gallant, Ref. 9; (2) data from Robinson and Gilliland, Ref. 6; (3) data from Van Winkle, Ref. 4.

The inaccuracy due to this assumption is usually minor. It is substantial (11) only where the feed split significantly affects the separation; typically with very few stages (about five or fe'ver) and very high relative volatility (>3).

2.2.3 McCabe-Thlele diagrams: line equations

Equilibrium curve (Figs. 1.1a, 2.9b). This curve is the locus of all equilibrium points. For a given liquid composition it gives the equilibrium vapor composition, yn, and vice versa. An equilibrium stage n is represented as a point (xn,yn) on the equilibrium curve where x„ and yn are the liquid and vapor compositions leaving the stage.

45° diagonal line (Fig. 2.96). This line is the locus of all the points where

Component balance (operating) lines (Fig. 2.96). The component balance equations, Eqs. (2.9) and (2.10), can be represented as straight lines on an x-y diagram. The rectifying section component balance line is the locus of points that obey the rectifying section component balance, Eq.

(2.9). Similarly, the stripping section component balance line is the locus of points that obey the stripping section component balance, Eq.

Unfortunately, component balance lines are referred to as "operating lines." The author believes that operating lines is a poor choice of words, since it states little about the physical nature of these lines. The term component balance lines is far more descriptive and appropriate, and will be used in this book.

Slopes of component balance (operating) lines. Equations (2.9) and (2.10) indicate that the slopes of the component balance lines are L/V and L'fV for the rectifying and stripping sections, respectively. As L < V [Eq. (2.11)] andL' > V" [Eq. (2.12)], the slope of the rectifying section component balance line is smaller than unity, while that of the stripping section component balance line is greater than unity.

When latent heat varies from stage to stage, so do the LiV and L'fV ratios. For this reason, when the constant molar overflow assumption (Sec. 2.2.2) does not apply, the component balance relationship becomes a curve instead of a straight line.

Intersection of component balance (operating) lines with diagonal. The point where the rectifying section component balance line intersects the 45° diagonal line satisfies both Eqs. (2.9) and (2.18). Solving these simultaneously and then using Eq. (2.11) gives

Dxp v-l

Both Eqs. (2.9) and (2.19) are for a column equipped with a total condenser (Fig. 2.1a). Since a total condenser is not an equilibrium stage (Sec. 2.1.1), the first equilibrium stage is inside the column. If the condenser is partial (Fig. 2.76), then it is the first equilibrium stage. In this case, yD replaces xD in Eq. (2.9), D is identical to Vv and L0 is zero. Substituting in Eq. (2.9) gives

"Stage" 0

0 0

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