McCabe-Thiele approach

The McCabe-Thiele approach has been developed to describe the Sorbex process (76). Two feed components, A and B, with a suitable adsorbent and a desorbent, C, are separated ia an isothermal continuous countercurrent operation. If A is the more strongly adsorbed component and the system is linear and noninteracting, the flows ia each section of the process must satisfy the foUowiag constraints for complete separation of A from B ... 

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. 

In a rectifying process the column has reflux, and evaluating its performance must consider the reflux ratio as well as the other factors. Example 17.2 uses the McCabe-Thiele approach to solve such a column at certain defined conditions. 

The McCabe-Thiele approach is applicable to any binary system, even if nonideal, as will be evidenced by an unusual shape of the equilibrium curve. As normally used, the procedure requires... 

The lower part of the column is covered by stepping off stages in a fashion similar to that in the upper part of the column, and the final conni of theoretical stages is then determined. The Ponchon-Savarit method may be used for many situations more complex lhan the simple one just described mixed vapor-liquid distillate product, side draw streams, multiple feeds, and so on. Standard unit operations textbooks should be consulted for more dentils on this methnd. As mentioned, it suffers from a need for enthalpy-concentration data, but even a crude approximation based on linear variation of enthalpy with concentration can be better than the McCabe-Thiele approach if there is a very large difference in the latent heats of vaporization of the iwo components being distillnd. 

In the remainder of this chapter these principles will be applied to generalize the McCabe-Thiele approach and the Kremser equation for a variety of unit operations. A listing of various applications is given in Table 14-1. 

The McCabe-Thiele approach for a binary mixture can be described as follows. First, we take the vapor-liquid equilibrium diagram y/x plot). Then we draw the operating lines based on the mass balance for the liquid and the vapor phase. There is one operating line for the stripping section and one for the top (rectification or enriching) section. The assumption of (in each case) constant molar flows of liquid and vapor ensures strictly straight operating lines. 

Gas scrubbers are operated in countercurrent flow and are typically equipped with structured packings or trays. The degree of removal of gaseous components depends on their solubility in the liquid absorption agent and thus on pressure and temperature, and on the liquid-to-gas ratio, which is defined as the ratio of the carrier fluid flow to the gas flow. For the design of an absorption column, the McCabe-Thiele approach is used, as already examined for distillation in Section 3.3.2.2. 

Example 3.3.7, the McCabe-Thiele approach - already examined for distillation (Section 3.3.2) and absorption (Section 3.3.3) - is the common technique used to design an extraction process ... 

In this chapter, attention will be directed to several of the other separation processes and their design using the equilibrium stage technique. Most of these will involve systems where the McCabe-Thiele approach can be used since temperature effects in many of the processes are minimal. 

Since liquid-liquid equilibrium is seldom available in algebraic form, the calculations tend to be iterative or graphical. A modified McCabe-Thiele approach can be used if y data versus x data are available. The coordinates for the diagram are the mass fraction of solute in the extract phase and the... 

Using the McCabe-Thiele approach for a binary separation, determine (a) the minimum reflux ratio, (b) the minimum LjV in the rectifying section of the column, (c) the condenser duty under minimum reflux conditions, (d) the LJV ratio and the external reflux ratio if the condenser duty is fixed at 250 kW, (e) the number of theoretical plates required with the condenser duty set at 250 kW, and (f) the number of theoretical plates required under total reflux conditions. 

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