Staged Operations The Equilibrium Stage

Analysis of these processes by the equilibrium-stage model proceeds in two steps. In the first step, the two phases are visualized as entering a stirred tank or its equivalent where they are allowed to come to equilibrium. The two phases are then conceptually withdrawn and separated, and the concentrations in each phase are calculated by means of appropriate mass balances and equilibrium data. We practice this step extensively in this chapter using both analytical expressions and specially designed geometrical constructions termed operating diagrams. 

In the second step of the process, the two phases are contacted only for a finite time interval leading to incomplete equilibrium. This step, which has to be carried out experimentally, reflects conditions that prevail in an actual operation. The resulting concentration changes, which differ from those attained at equilibrium, are cast in the form of a fractional approach to equilibrium or stage efficiency E. The value of this efficiency is then grafted onto the results of the first step to arrive at an estimate of the actual prevailing concentrations. 

Staged operations (a) single stage (b) co-current (c) countercurrent (d) crosscurrent. 

when E = 1, the fractional approach to equilibrium is 1, and equilibration is consequently complete. When E is zero, no transfer takes place and the concentration remains frozen at the level Xp of the incoming feed. 

Mass Transfer and Separation Processes Principles and Applications 

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