Transfer units graphical integration

Figure 9-72. Graphical integration number of transfer units for Example 9-11.

An alternate method to determining the number of transfer units is the graphical integration of dy/(y - y). The procedure is basically the same as for absorbers, that is ... 

Ploty, from y bottoms to y overhead versus l/(y - y). The position of y-feed can be noted on the graph, and the integration so arranged as to reveal the split betiveen rectifying and stripping transfer units. The total number by this method should check closely with the graphical step-wise method. 

Figure 9-125. Graphical integration to determine number of transfer units.

The number of transfer units is obtained by graphical or numerical integration of equations 11.101, 11.103 or 11.104. 

The use of Figure 11.40 will slightly overestimate the number of stages and a more accurate estimate would be made by graphical integration of equation 11.104 but this is not justified in view of the uncertainty in the prediction of the transfer unit height. Molecular weights SO2 = 64, H20 = 18, air = 29... 

Rackett, H. G. Chem. Eng. Albany 71 (21 Dec. 1964) 108. Modified graphical integration for determining transfer units. 

The relation between interfacial and bulk concentrations is that of Eq. (13.157), (y -y)/(x -x) = -kL/kG. At a series of values of x, corresponding values of y and y may be read off with the graphical constructions shown on Figures (b) and (c) of this example. The values for slope = — 1 are tabulated, but those for slope = oo are calculated from the equations of the equilibrium and operating lines and are not recorded. The integrands of Eq. (13.160) also are tabulated for both cases, and the numbers of transfer units are obtained by integration with the trapezoidal rule ... 

When Henry s law is valid [Eq. (lc)], Eq. (18a) can be analytically integrated alternatively, the graphical form shown in Fig. 8 can be used for evaluating Nqq. Expressions for cases in which the equilibrium curve cannot be linearly approximated are available in several texts, such as Hines and Maddox (1985). Figure 8 shows that the number of transfer units increases with the ratio ttiGm/ m When this ratio increases above unity, the number of transfer units, and therefore column height, rapidly increase ... 

Related Calculation. When the equilibrium and/or operating lines are curved, Eqs. (11.27) and (11.28) do not apply exactly. In this case, it is necessary to base the design on the individual number of transfer units for the liquid resistance and integrate graphically to determine Nt. This is illustrated in the following example. 

Figure 16-2. Analysis of number of transfer units (A) determination of equilibrium or interfacial values, (B) graphical integration of Eq. (16-71 shown for stripping section of Exanyle 16-1...

For cases where equilibrium curve and operating line are very close at the dilute end of the column, with a concentration of transfer units at the end, m2 should be the true slope of the equilibrium curve at and m2 that of the reciprocal of the slope at Xst- Other corrections for handling cases of more complicated curvature of equilibrium and operating lines are discussed in detail by Scheibel and Othmer (5). Graphical solutions of Eqs. (8,29) and (8.30) are available (5, 6), and the equations may be applied to the integrals of Eqs. (8.19) to (8.22) by the substitution of the proper units, as outlined in (1) above. 

In general, when the operating fine and equilibrium curve are not straight, the number of transfer units must be determined by numerical or graphical integration of Equation 15.3 or 15.5 or other equivalent form of these equations. 

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