ENVE $314-$ Unit Operations and Processes in Environmental Engineering

Exercise Question

An activated sludge plant receives $40,000\frac{m^3}{?}$ day wastewater. The aeration tanks in the plant have a total volume of $9,000m^3.$ The estimated oxygen demand in the secondary treatment is about $363kg\frac{O_2}{?}$ day. The average dissolved oxygen concentration in the influent is $0\mathrm{.}3m\frac{g}{L}.$ The plant is located close to sea level and the annual average incoming wastewater temperature is about $20C.$

Assuming that the volumetric oxygen transfer coefficient is $3{10}^{-3}mi{n}^{-1},$ calculate the steady state dissolved oxygen concentration in the effluent wastewater. at sea level and at $20C$ is about $9\mathrm{.}1m\frac{g}{L}$

$Q_{in}=40,000\frac{m^3}{d}ay=27,778\frac{L}{m}in$

$V=9,000m^3=9{10}^{6}L$

$O_r=363kg\frac{O_2}{d}ay=252,083m\frac{g}{m}in$

$C_{in}=0\mathrm{.}3m\frac{g}{L}$

$K_{L}a=3{10}^{-3}mi{n}^{-1}$

Mass balance of dissolved oxygen in a completely$-$mixed continuous aeration tank:

$V\frac{dC}{dt}=Q{C}_{in}-QC+V{K}_{L}a(C_S-C)-O_r=0(at$ steady state $)$

$C=\frac{Q_{in}+V{K}_{L}a{C}_S-O_r}{Q-V{K}_{L}a}$

$C=\frac{27,778\frac{L}{m}in+9{10}^6(L)0\mathrm{.}3{10}^{-3}mi{n}^{-1}9\mathrm{.}1m\frac{g}{L}-252,083m\frac{g}{m}in}{27,778\frac{L}{m}in-9{10}^6(L)0\mathrm{.}3{10}^{-3}mi{n}^{-1}}$

$C=2\mathrm{.}51\frac{mg}{L}$

Bonus homework questions$*$:

Please recalculate the effluent dissolved oxygen concentration assuming that $=0\mathrm{.}78,=0\mathrm{.}96$ and influent wastewater temperature as $30C.$

If the aeration system suddenly shuts down, how long does it take for the dissolved oxygen level to drop down below $2m\frac{g}{L}?$

Please try to solve the questions on a paper and bring to my office $(Z-07,$ next to Amfi $1)$ until $01\mathrm{.}03\mathrm{.}2024.$