$.$ The sewage plant of a city of about $110000$ inhabitants processes $17000$ m$3$

$/$day of waste

water. The sludge send to the biodigester is about $220$ ton$/$day$.$ The total solid content

of this residue is $3\%$ and $55\%$ that of Volatile Solids. The specific production potential is

$0\mathrm{.}215$ Nm$3$ CH$4/$kg VS$.$ The engine power efficiency is $30\%$ and $70\%$ that of the heat

recovered from the engine. Assume a biogas composition of $65\%$ in methane.

Calculate:

a$)$ production of biogas, in Nm$3$

$/$h

b$)$ electrical power and heating generated by the engine, in kW

c$)$ Assuming the same production of sludge per inhabitant, represent the power

capacity as a function of the number of inhabitants of a geographic area.

d$)$ Calculate the biogas plant economic benefit assuming a value for the electricity and

natural gas consumption avoided.