Production rate in a batch reactor

The integrated form of the design equation gives the reaction time needed to achieve the conversion Xa of an initial number of moles of reactant, Wao- At the end of the reaction, the products must be removed 

The reaction time, corresponding to the maximum rate of production of P is found by differentiating eqn. (23) with respect to t and placing the differential equal to zero. This leads to the expression 

If k and are known, this expression may be solved by trial-and-error to give tjn, the batch reaction time corresponding to the greatest production rate. 

Differentiation of this expression in order to find the time corresponding to the maximum rate of production yields a very complex expression. Instead, we find the minimum value of (l/. p) by differentiating the reciprocal of eqn. (27) and this shows that 

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Flo. 1.10. Maximum production rate in a batch reactor with a shut-down time ts... 

Expand the above development in terms of maximizing the productive rate in a batch reactor. ... 

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