Mass transfer - Application of kinetic models of compartmentalized operations

The ideal (or theoretical) stage model assumes that the phases leaving the stage are in thermodynamic equilibrium. The flow rates and flow compositions at the stage inlet are therefore sufficient to determine the flow rates and flow compositions at the outlet.

For a real stage, thermodynamic equilibrium is not reached. Stage sizing requires data on the kinetics of material transfer between the two phases. But this is not enough. Indeed, there is a fundamental difference between the characteristic quantities of thermodynamic equilibrium and kinetic data, which lends essential complexity to any model where thermodynamic equilibrium is not reached:

• in the first case, the partition equilibrium between two phases is the same regardless of how it is reached; it can be easily determined by experimentation or accessed from databases;

• in the second case, the total quantity of material transferred from one phase to the other during an operation depends on the speed at which material transfer takes place at any given point. This local speed in turn depends on the deviation from equilibrium, the concentrations of the two phases and therefore on the implementation of contact and fluid circulation in the stage.

To be able to use kinetic data effectively, it is therefore necessary to know the flows in the device under consideration or, failing this, to make assumptions about their nature. In this respect, we will use the same flow models as those adopted for chemical reactor calculations ("perfectly agitated" flow, "piston" flow, "piston-dispersion" model...) (see [ J 1 070 , § 3]).

The calculation of non-ideal operations therefore relies on the use of the same material balances as those used for the calculation of ideal operations (overall balance, operating balance between one end of the device and a current point, etc.), but a special balance must always be added, which enables us to make joint use of the knowledge we have (or the assumptions we are led to make) about kinetic phenomena and flows in the device (see [ J 1 075 ]).

This balance is established for one of the phases....