Batch Reactors without Electrolyte Recycle

We will begin by deriving an integral relationship for S, the electrode area. Let us assume that a single cathodic reaction with 100% current efficiency occurs according to the equation  

The kinetic expression implying Tafel-type behavior is Eq. 3.147 (see Section 3.2.1)  

Equations (3.147) and (4.5) constitute a reactor model, the former being the reaction model and the latter an expression for the required electrode area in terms of process parameters. 

The evaluation of the integral depends on the mode of operation of the cell. Most often the mode is one of constant current supplied to a bipolar arrangement. This results in a current density which is nominally constant and for which the electrode potential, will be a complex function of c. Direct integration is therefore not possible a numerical technique must be employed using the expression for i to evaluate appropriate values of . This is why the reaction model is an essential element of the reactor model. 

The reactor model can also be expressed in terms of conversion. Remembering that the conversion X is defined as the amount of A reacted divided by the amount initially in the feed  

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