Extraction - Principles of Chemical Separations with Environmental Applications - page 144

5.10 Immiscible extraction: McCabe-Thiele analysis

Some extraction systems are such that the solvent and diluent phases are almost com-
pletely 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 char-
acterization 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 extrac-
tion is analogous to the analysis for absorption and stripping processes. Consider the flow
scheme shown in Figure 5.23,

where F D = mass flowrate of diluent (feed)

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

E j = mass flowrate of extract (spent solvent phase) leaving stage j

Y j =

/

weight ratio of solute in solvent leaving stage j (kg A kg S )

R j =

mass flowrate of raffinate (purified product) leaving stage j

F S = mass flowrate of solvent.

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

x y

X = and Y = [ only true for immiscible systems! ] (5.17)

1 − x 1 − y

where X is kg solute / kg diluent and Y is kg solute / kg solvent.

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

Control volume

F D ,X 0 X j − 1 X j R N ,X N

1 2

j N

E 1 , Y 1 Y j +1 F S , Y N +1

Y j

Figure 5.23 Countercurrent cascade schematic.