Stepwise graphical calculations

The graphical construction of an extraction isotherm, an operating line, and the stepwise evaluation of the number of stages in this manner is known as a McCabe-Thiele diagram. Flistorically, it found great application in a variety of mass transfer operations, from gas adsorption through distillation to solvent extraction. Flowever, the advent of modern computational techniques has made it largely redundant, as it is often easier and certainly more accurate to calculate the cascade directly. 

To calculate the amount of catalyst for a particular case, mass and heat balance have to be considered they can be described by two differential equations one gives the differential CO conversion for a differential mass of catalyst, and the other the associated differential temperature increase. As analytical integration is not possible, numerical methods have to be used for which today a number of computer programs are available with which the calculations can be performed on a powerful PC in the case of shift conversion. Thus the elaborate stepwise and graphical evaluation by hand [592], [609] is history. For the reaction rate r in these equations one of the kinetic expressions discussed above (for example, Eq. 83) together with the function of the temperature dependence of the rate constant has to be used. 

For case B, the pseudo inlet concentration Xf can be used in the KSB equation with the actual value of X r and E-m S lF to calculate rapidly the number of theoretical stages required. The graphical stepwise method illustrated in Fig. 15-23 also can be used. The operating... 

Experiment supplies the I value corresponding to each value of s or We can therefore compute as a function of s (compare Fig. 60) and integrate the right-hand side of (39) stepwise, either graphically or numerically. After performing this calculation, the right-hand side represents a function F p) of p (or of r) from which the desired distribution function W may be calculated using equation (39). We obtain... 

A brief iteration of the stepwise process may be made, say, as per Figure 4.6, where the graphical representations are kept sparse to avoid unnecessary clutter. The calculation may be perceived as starting at D, the initial point on the 45° line, where y, = x = Xiy... 

Jenny (Ref. 10) published a graphical method for multicomponent design calculation. A few plate-to-plate calculations are made at the top and bottom of the column and above and below the feed plate. For the section below the feed plate, a y,x diagram is made for the light key component using the calculated values to place the effective equilibrium curve for this component on the diagram. The operating line is drawn in the usual manner and the plates determined by the stepwise... 

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