McCabe-Thiele method construction

The number of theoretical stages required can be determined from Figure 11-8 by means of a stepwise procedure similar to the McCabe-Thiele method used in distillation calculations (see Chapter 7). An operating line, QT, first must be constructed below the equilibrium curve, NO, developed from equilibrium data. Line QT can be drawn by... 

Figure 8.1.20. Vapor-liquid equilibrium curve, operating lines for enriching section and stripping section and construction of ideal stages and q Une for a feed consisting of vapor and liquid in a multistage distillation column having ideal equilibrium stages the McCabe-Thiele method.

Solution Constructed McCabe-Thiele diagram. Pinch found. (See Section 3 Fractionators Graphical Methods.)... 

Calculation Methods. An often satisfactory approximation is to take the mixture in the presence of the solvent to be a pseudobinary of the keys on a solvent-free basis, and to employ the McCabe-Thiele or other binary distillation method to find tray and reflux demands. Since the relative volatility varies with concentration of the solvent, different equilibrium curves are used for above and below the feed based on average loads in those zones. Figure 13.25 is of such a construction. 

The tray vapor and liquid compositions and enthalpies, generally available from the computer output, are first used to construct the saturated vapor and liquid enthalpy-composition curves on a light pseudocomponent basis. The H-X method is especially suited for nonideal systems where the McCabe-Thiele assumptions may be in gross error. The H-X method takes into account the variation of enthalpy with composition (Section 5.3), which is reflected in the shape of the enthalpy curves. Ideal mixtures are characterized by straight, horizontal lines while nonideal mixture lines exhibit varying slopes and curvature. 

The McCabe-Thiele constructions described in Chapter 8 embody rather restrictive tenets. The assumptions of constant molal overflow in distillation and of interphase transfer of solute only in extraction seriously curtail the general utility of the method. Continued use of McCabe-Thiele procedures can be ascribed to the fact that (a) they often represent a fairly good engineering approximation and (b) sufficient thermodynamic data to justify a more accurate approach is often lacking. In the case of distillation, enthalpy-concentration data needed for making stage-to-stage enthalpy balances are often unavailable, while, in the Case of absorption or extraction, complete phase equilibrium data may not be at hand. 

Figure 10.5 demonstrates the basic concept behind the Ponchon-Savarit method. In the McCabe-Thiele construction, material balance equations are plotted on an x-y phase equilibrium diagram, the stages being calculated by alternate use of the material balance and equilibrium relationships. The Ponchon diagram embodies both enthalpy and material balance relationships as well as... 

A rapid graphical method, related to the McCabe-Thiele procedure, has been described by Chilton and Colburn [163]. It is applicable to all mixtures for which the equilibrium curve is known. The operating line should, however, not lie too close to the equilibrium curve in the range considered. The operating line is constructed in the usual way in the equilibrium diagram, and through the point Xb a vertical line is... 

Marek (8) derived a design procedure for plate columns based on material and enthalpy balances which included the presence of a chemical reaction. For a ternary mixture a combined numerical and graphical method was suggested using a modified McCabe-Thiele construction. The problem was simplified by assuming negligible heat of reaction and 100% stage efficiency. The hypothetical reactions employed were A + B 20 and A + B Q. 

The concept will be introduced in the context of the McCabe-Thiele construction for the graphical analysis of binary distillation problems. This method uses y-x diagrams of the form shown in figure 6.2. Such diagrams are a graphical representation of equilibrium data, and so if the composition of the resultant vapour from an equilibrium stage is known, then the composition of the resultant liquid (in equilibrium with that vapour) can be obtained from the curve on the appropriate y-x diagram. 

Equations 11.21 and 11.22 and the equilibrium relationship are conveniently solved by the graphical method developed by McCabe and Thiele (1925). The method is discussed fully in Volume 2. A simple procedure for the construction of the diagram is given below and illustrated in Example 11.2. 

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