$[20$ points$]$ E$-$B Problem $4\mathrm{.}26$

You have been asked to design a reactor to treat a waste stream of ${10}^4\frac{m^3}{d}$ containing $150m\frac{g}{l}$ of phenol.

The following coefficients apply:

$Y=0\mathrm{.}6gV\frac{S_a}{g}$ phenol

hat$(q)=9g$ phenol $\frac{?}{gV{S}_a}-d$

$b=0\mathrm{.}15d^{-1}$

$K=0\mathrm{.}8m\frac{g}{l}$

You have decided to evaluate use of a fixed$-$film reactor in which you apply sufficient recycle that you can

assume the system will act like a completely mixed reactor. Assume that deep biofilm kinetics apply

$0),$ that the specific surface area of the reactor is ${10}^{7}c\frac{m^2}{c}{m}^3,$ the boundary layer thickness for the deep

biofilm is $0\mathrm{.}005cm,x_f$ is $20mgV\frac{S_a}{c}{m}^3,D=0\mathrm{.}8c\frac{m^2}{d},$ and $D_f=0\mathrm{.}8D.$ Determine the volume $V$ for this

reactor in $m^3.$