Design of Batch Process Units

When designing a process unit to operate in batch mode, it is usually desired to detennim the batch time, t, and the size factor, S, which is usually expressed as the volume per uni mass of product, that maximize an objective like the amount of product. To accomplish this a dynamic model of the process unit is formulated and the degrees of freedom adjusted, as il lustrated in the examples that follow. As will be seen, there are many ways to formulate thn optimal control problem. To simplify the discussion, models are presented and studied f various input profiles, to see how they affect the objectives. Emphasis is not placed on tht formal methods of optimization. 

Consider a batch reactor to carry out the exothermic reversible reaction  

The minimum batch time, is achieved by integrating the mass balances  

The temperature at the maximum reaction rate is obtained by differentiation of Eq. (12.1) with respect to T  

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