McCabe method

The standard McCabe method that consists of the following steps (Fig. 16.1) ... 

The graphics capabiUties of the CAD/CAM environment offer a number of opportunities for data manipulation, pattern recognition, and image creation. The direct appHcation of computer graphics to the automation of graphic solution techniques, such as a McCabe-Thiele binary distillation method, or to the preparation of data plots are obvious examples. Graphic simulation has been appHed to the optimisation of chemical process systems as a technique for energy analysis (84). 

The McCabe-Thiele method employs the simplifying assumption that the molal overflows in the stripping and the rectification sections are constant. This assumption reduces the rectifying and stripping operating line equations to ... 

Operating Lines The McCabe-Thiele method is based upon representation of the material-balance equations as operating lines on the y-x diagram. The lines are made straight (and the need for the energy balance obviated) by the assumption of constant molar overflow. The liqmd-phase flow rate is assumed to be constant from tray to tray in each sec tiou of the column between addition (feed) and withdrawal (produc t) points. If the liquid rate is constant, the vapor rate must also be constant. 

A useful method for a binary mixture employs an analysis based on the McCabe-Thiele graphical method. In addition to the usual assumptions of adiabatic column and equimolal overflow on the trays, the following procedure assumes neghgible holdup of hquid on the trays, in the column, and in the condenser. 

These differential equations are readily solved, as shown by Luyben (op. cit.), by simple Euler numerical integration, starling from an initial steady state, as determined, e.g., by the McCabe-Thiele method, followed by some prescribed disturbance such as a step change in feed composition. Typical results for the initial steady-state conditions, fixed conditions, controller and hydraulic parameters, and disturbance given in Table 13-32 are listed in Table 13-33. 

For the McCabe-Thiele type of graphical calculations and shortcut methods, the Bancroft (weight-ratio) concentrations can be used on... 

For the first time through a liqmd-liquid extrac tion problem, the right-triangular graphical method may be preferred because it is completely rigorous for a ternary system and reasonably easy to understand. However, the shortcut methods with the Bancroft coordinates and the Kremser equations become valuable time-savers for repetitive calculations and for data reduction from experimental runs. The calculation of pseudo inlet compositions and the use of the McCabe-Thiele type of stage calculations lend themselves readily to programmable calculator or computer routines with a simple correlation of equilibrium data. 

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

The design of a distillation column is based on information derived from the VLE diagram describing the mixtures to be separated. The vapor-liquid equilibrium characteristics are indicated by the characteristic shapes of the equilibrium curves. This is what determines the number of stages, and hence the number of trays needed for a separation. Although column designs are often proprietary, the classical method of McCabe-Thiele for binary columns is instructive on the principles of design. 

Graphical methods at best are simply illustrative for the student today, but they are occasionally referenced by the process engineer. Extraction, like distillation can be viewed as a stage-wise operation, and hence metliods based on the McCabe Thiele approach briefly described in Chapter 4 have been applied to preliminary design cases. Indeed, both absorption and adsorption are stage-wise operations. 

One way of calculating the number of equilibrium stages (or number of theoretical plates, NTP) for a mass exchanger is the graphical McCabe-Thiele method. To illustrate this procedure, let us assume that over the operating range of compositions, the equilibrium relation governing the transfer of the pollutant from the... 

Hengstebeck [137] presents a simplified procedure for reducing a multicomponent system to an equivalent binary using the key components. From this the number of stages or theoretical plates and reflux can be determined using conventional binary procedures and involving the McCabe-Thiele method. 

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. 

The McCabe-Thiele method can be used for the design of columns with side streams and multiple feeds. The liquid and vapour flows in the sections between the feed and take-off points are calculated and operating lines drawn for each section. 

If the presence of the other components does not significantly affect the volatility of the key components, the keys can be treated as a pseudo-binary pair. The number of stages can then be calculated using a McCabe-Thiele diagram, or the other methods developed for binary systems. This simplification can often be made when the amount of the non-key components is small, or where the components form near-ideal mixtures. 

The number of stages required for a given separation can be determined from the triangular diagram using a method analogous to the McCabe-Thiele diagram used to determine the... 

The McCabe-Thiele Method is restricted in its application because it only applies to binary systems and involves the simplifying assumption of constant molar overflow. However, it is an important method to understand as it gives important conceptual insights into distillation that cannot be obtained in any other way. 

In this particular example, all these lines are closely spaced and the relevant section is enlarged in the inset of Figure 11a. By stepping off the theoretical plates as in the McCabe-Thiele method, it is seen that 18 theoretical plates are represented by the column. 

The equilibrium data are shown in Figure 11c and the problem may be solved using the method of McCabe and Thiele. All compositions are in terms of mole fractions so that ... 

The equilibrium data are plotted in Figure 1 lh. As the compositions are given as mass per cent, these must first be converted to mole fractions before the McCabe-Thiele method may be used. 

A fractionating column is required to distill a liquid containing 25 per cent benzene and 75 per cent toluene by mass, to give a product of 90 per cent benzene. A reflux ratio of 3.5 is to be used, and the feed will enter at its boiling point. If the plates used are 100 per cent efficient, calculate by the Lewis-Sorel method the composition of liquid on the third plate, and estimate the number of plates required using the McCabe-Thiele method. 

This example is solved by a simple application of the McCabe-Thiele method and is illustrated in Figure lln, where it is seen that 10 theoretical plates are required. The... 

---