Optimal Performance for Maximum Production Rate

The performance of a batch reactor may be optimized in various ways. Here, we consider the case of choosing the cycle time, tc, equation 12.3-5, to maximize the rate of production of a product. For simplicity, we assume constant density and temperature. 

The greater the reaction time f (equation 12.3-21), the greater the production per batch, but the smaller the number of batches per unit time. Since the rate of production, Pr, is the product of these two, a compromise must be made between large and small values oft to maximize Pr. 

This may also be seen from limiting values obtained from equation 12.3-22  

To obtain the value of t for maximum Pr, consider equation 12.3-22 with fAl = 0, /a2 = /a(0- Then the equation may be written as 

Equation 12.3-33 is solved for t, and the result is used in equation 12.3-32 or its equivalent to obtain the maximum value of Pr. 

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