Immiscible extraction McCabe-Thiele analysis

Xj = weight ratio of solute in diluent leaving stage j (kg A/kg D) 

Ej = mass flowrate of extract (spent solvent phase) leaving stage j Yj = weight ratio of solute in solvent leaving stage j (kg A/kg S) 

Rj= mass flowrate of raffinate (purified product) leaving stage j Fs= mass flowrate of solvent. 

The assumption that the diluent and the solvent are totally immiscible means that their flowrates (Fd and Fs) are constant, so that the weight ratios can be found from weight fractions  

The notation here may be confusing, because there is no vapor phase involved. The difference between x and y (or X and Y) is that x s are used to describe the amount of the solute in the 

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All extraction systems are partially miscible to some extent, but when partial miscibility is very low, the system may be treated as completely immiscible and McCabe-Thiele analysis is appropriate. 

Some extraction systems are such that the solvent and diluent phases are almost completely immiscible in each other. Hence, separation yields an extract phase essentially free of diluent and a raffinate phase that is almost pure diluent. This greatly simplifies the characterization of the system. When partial miscibility for an extraction process is very low, the system may be considered immiscible and application of McCabe-Thiele analysis is appropriate. It is important to note that McCabe-Thiele analysis for immiscible extraction applies to a countercurrent cascade. The McCabe-Thiele analysis for immiscible extraction is analogous to the analysis for absorption and stripping processes. Consider the flow scheme shown in Figure 5.23,... 

The McCabe-Thiele analysis for dilute immiscible extraction is very similar to the analysis for dilute absorption and stripping discussed in Chapter 12. It was first developed by Evans (1934) and is reviewed by Robbins (1997). In order to use a McCabe-Thiele type of analysis we must be able to plot a single equilibrium curve, have the energy balances automatically satisfied, and have one operating line for each section. 

All extraction systems are partially miscible to some extent. When partial miscibility is very low, as for toluene and water, we can treat the system as if it were conpletely immiscible and use McCabe-Thiele analysis or the Kremser equation. When partial miscibility becomes appreciable, it can no longer be ignored, and a calculation procedure that allows for variable flow rates must be used. In this case a different type of stage-by-stage analysis, which is very convenient for ternary systems, can be used. For multiconponent systems, corrputer calculations are required. 

D19. Many extraction systems are partially miscible at high concentrations of solute, but close to immiscible at low solute concentrations. At relatively low solute concentrations both the McCabe-Thiele and trianglar diagram analyses are applicable. This problem explores this. We wish to use chloroform to extract acetone from water. Equilibrium data are given in Table 13-4. Find the number of equilibrium stages required for a countercurrent cascade if we have a feed of 1000.0 kg/h of a 10.0 wt % acetone, 90.0 wt % water mixture. The solvent used is chloroform saturated with water (no acetone). Flow rate of stream Eq = 1371 k. We desire an outlet raffinate concentration of 0.50 wt % acetone. Assume immiscibility and use a weight ratio units graphical analysis. Conpare results with Problem 13.D43. 

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