McCabe-Thiele analysis absorption

Using the assumptions that the liquid is non-volatile and the carrier gas is insoluble, the mass balances (total and solute) are  

Xq = solute in inlet liquid stream (mole ratio) 

Subscripts correspond to stage number of exit stream 

We cannot, however, say that overall flowrates of gas and liquids are constant (except for very dilute solutions) because a significant amount of solute may be absorbed. This would increase the total flowrate of liquid, while reducing that of the gas. The compositions of the solute must therefore be expressed in mole ratios so that the basis (denominator) is constant. Mole ratios are related to mole fractions by the equations  

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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 can be used to model physical absorption and stripping processes that use equilibrium stages. 

If absorption or stripping can be assumed 1) to be isothermal and 2) to have negligible heat of absorption, then the energy balances will be satisfied. In this case the McCabe-Thiele analysis procedure can be adapted to more concentrated systems where the total flow rates L and V are not constant. We will have the desired straight operating line if we define... 

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. 

The McCabe-Thiele procedure has been applied to flash distillation, continuous countercurrent distillation, batch distillation, absorption, stripping, and extraction. What are the common factors for the McCabe-Thiele analysis in all these cases ... 

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