In an activated sludge reactor, the growth is autocatalytic in that more cells you have the greater the

growth rate.

cells $+$ nutrients $$ more cells $+$ products

The cell growth rate $r_g,$ and the rate of nutrient consumption, $r_s$ are directly proportional to the

concentration of cells for a given set of conditions. The rate $(r_s)$ and nutrient concentration $x_s=$

data are given in the table below.

For a nutrient feed rate of $1k\frac{g}{h}$ with $C_{S0}=0\mathrm{.}25\frac{g}{d}{m}^3,$ determine:

$($a$)$ CSTR size for $80\%$ conversion of substrate.

$($b$)$ What conversion could be achieved for $80d{m}^3$ CSTR$?$ An $80d{m}^3$ PFR$?$

$($c$)$ How could you arrange the PFR and CSTR in series to achieve $80\%$ conversion and minimum total

volume? Support your answer.

Before entering an underground utility vault to do repairs, a work crew analyzed the gas in the vault and

found that it contained $20m\frac{g}{m^3}$ of hydrogen sulfide $(H_2(S)).$ Because the allowable exposure level is $12$

$m\frac{g}{m^3},$ the work crew began ventilating the vault with a blower. The volume of the vault is $200m^3$ and

the flow rate of the air containing $0\mathrm{.}1m\frac{g}{m^3}$ is $10\frac{m^3}{m}in.$ Assume the vault behaves as a CSTR and

that the $H_{2}S$ is nonreactive in the time period considered.

$($a$)$ How long will it take to lower the $H_{2}S$ to a level that will allow the work crew to enter?

$($b$)$ The odor threshold for $H_{2}S$ is $0\mathrm{.}2m\frac{g}{m^3}.$ How long will it take to make the space not smell like

$H_{2}S?(H_{2}S$ has a "rotten egg" smell$).$