An anaerobic digester needs to be designed to digest primary sludge and recover bioenergy from the

waste. The wastewater flow rate is $35$ ML$/$d$.$ The quantity of dry solids and ultimate BOD influent loading

$($Si$)$ are $0\mathrm{.}16$ kg$/$m$3$ and $0\mathrm{.}14$ kg$/$m$3$ of wastewater respectively. Using the other design assumptions given

in the table, determine the following:

a$.$ Calculate the volume of the anaerobic digester.

b$.$ Find the volumetric loading of the digester.

c$.$ What is the mass of solids synthesized per day?

d$.$ Compute the volume of methane production per day.

e$.$ What is the volume of total gas produced per day?

Design assumptions

Temperature $300$C

Sludge moisture content $92\mathrm{.}5\%$

Sludge specific gravity $1\mathrm{.}02($g$/$cm$3)$

Yield coefficient $0\mathrm{.}05$ kg of cells$/$kg

ultimate BOD utilised

Endogenous coefficient $0\mathrm{.}03$ per day

Efficiency of waste utilization $0\mathrm{.}65$

Biogas composition $65\%$ methane