A complete$-$mix activated sludge system with recycle is used to treat municipal

wastewater after primary sedimentation. The characteristics of the primary effluent are:

flow $=1000\frac{m^3}{d},$bsCOD$=192\frac{g}{m^3},nbVSS=30\frac{g}{m^3}$ and inert inorganics $=10\frac{g}{m^3}.$

The aeration tank MLVSS $=2500\frac{g}{m^3}.$ Using these data and the kinetic coefficients

given below, design a system with a $6-$d SRT and determine the following:

i$.$ What is the effluent bsCOD concentration?

ii$.$ What value of $$ should be used so that the MLVSS concentration is $2500\frac{g}{m^3}?$

iii. What is the daily sludge production in $k\frac{g}{d}$ as VSS and TSS$?$

iv$.$ What is the fraction of biomass in the MLVSS$?$

v$.$ What are the observed solids yield in $g$ VSS $\frac{?}{g}$ bsCOD and $g$ TSS$/$g bsCOD?

vi$.$ What is the oxygen requirement in $k\frac{g}{d}?$

Kinetic coefficients:

$k=12\mathrm{.}5g$ COD $\frac{?}{g}VSS.d{K}_s=10$gCO$\frac{D}{m^3}$

$Y=0\mathrm{.}40gVSS\frac{?}{g}$ COD used $k_d=0\mathrm{.}10gVSS\frac{?}{g}VSS.d$

$f_d=0\mathrm{.}15gVS\frac{S}{g}VSS$ Biomass $VSS\frac{?}{TSS}=0\mathrm{.}85$

Biomass VSS $\frac{?}{?}$ TSS $=0\mathrm{.}85$

Formulas:

$S=\frac{K_s[1+(k_d)SRT]}{SRT(Yk-k_d)-1},x_T=(\frac{SRT}{})[\frac{Y(S_0-S)}{1+(k_d)SRT}]+(f_d)(k_d)x(SRT)+x_{o,i}(\frac{SRT}{}),$

$x=(\frac{SRT}{})[\frac{Y(S_0-S)}{1+(k_d)SRT}],P_{x,VSS}=\frac{x_{T}V}{SRT},Y_{\text{o}\text{b}\text{s}}=\frac{P_{x,VSS}}{Q(S_0-S)}$

$Y_{\text{o}\text{b}\text{s}}=\frac{P_{x,TSS}}{Q(S_0-S)},R_o=Q(S_o-S)-1\mathrm{.}42P_{x,\text{b}\text{i}\text{o}}$

$P_{x,TSS}=\frac{QY(S_0-S)}{1+(k_d)SRT}(\frac{1}{0\mathrm{.}85})+\frac{f_d(k_d)YQ(S_0-S)SRT}{1+(k_d)SRT}(\frac{1}{0\mathrm{.}85})+Q{x}_{o,i}+Q(TS{S}_0-VS{S}_0)$