Stagewise and Differential Mass Transfer Contacting

Mass transfer separation processes, e.g., distillation, gas absorption, etc., are normally treated in terms of stagewise or differential procedures. In a stagewise procedure, concentration changes are taken to occur in distinct jumps, as, for 

In the stagewise simulation method the procedure is based on the assessment of the separation achieved by a given number of equilibrium contacting stages. The concept of the equilibrium stage is illustrated, for a particular stage n of the cascade, as shown in Fig. 1.25. 

According to this assumption the two streams are so well mixed that the compositions of each phase within the stage are uniform. Further, the mass transfer is so efficient that the compositions of the streams leaving the stage are in equilibrium. 

The actual stage can be a mixing vessel, as in a mixer-settler used for solvent extraction applications, or a plate of a distillation or gas absorption column. In order to allow for non-ideal conditions in which the compositions of the two exit streams do not achieve full equilibrium, an actual number of stages can be related to the number of theoretical stages, via the use of a stage-efficiency factor. Also it will be seen that a rate approach will account for this. 

In this type of apparatus, the two phases do not come to equilibrium, at any point in the contactor and the simulation method is based, therefore, not on a number of equilibrium stages, but rather on a consideration of the relative rates of transport of material through the contactor by flow and the rate of interfacial mass transfer between the phases. For this, a consideration of mass transfer rate theory becomes necessary. 

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