Chapter 8, Problem 2P

In chemical engineering, plug flow reactors (that is, those in which fluid flows from one end to the other with minimal mixing along the longitudinal axis) are often used to convert reactants into products. It has been determined that the efficiency of the conversion can sometimes be improved by recycling a portion of the

FIGURE P8.2

Schematic representation of a plug flow reactor with recycle.

$\text{In }\frac{1+R\left(1-X_{Af}\right)}{R\left(1-X_{Af}\right)}=\frac{R+1}{R\left[1+R\left(1-X_{Af}\right)\right]}$

Where $X_{Af}=$ the fraction of reactant A that is converted to product B. The optimal recycle rate corresponds to the minimum-sized reactor needed to attain the desired level of conversion. Use a numerical method to determine the recycle ratios needed to minimize reactor size for a fractional conversion of $X_{Af}=0.9$.