Need for Multiple Stages

Countercurrent flow of streams with contact in multiple stages provides more amount of separation for a given liquid-to-gas ratio. Note the increase in concentration of solute in leaving solvent, and the decrease of solute concentration in the leaving gas stream.

End concentrations can be connected to make the operating line for the countercurrent cascades. Step construction between the operating line of cascade and equilibrium curve will give the count of number of stages.

The operating line indicates the relation between the gas and liquid concentration at any level in the tower.

\[G_s(Y_0-Y_2) = L_s(X_1-X_0) \qquad \Longrightarrow \quad Y_0-Y_2 = \frac{L_s}{G_s}(X_1-X_0)\] Slope of operating line of countercurrent cascades is given by \(L_s/G_s\).