In an effort to avoid the use of natural gas $($a fossil fuel$)$ and with the purpose of utilizing

more sustainable alternatives, engineers are investigating the effect of utilizing biogas as

fuel to generate the hot water used in the air handling units. Biogas is obtained from the

anaerobic decomposition of organic matter and it usually has a mixture of methane and

carbon dioxide. Depending on the process and feedstock utilized, the mixtures can be as

shown in Table $1.$

Table $1$: Composition of biogas and natural gas $($percentages by volume$)$

Consider the following reactions for each type of fuel:

Natural gas:

$C{H}_4+2(O_2+3\mathrm{.}76N_2)--C{O}_2+2H_{2}O+7\mathrm{.}52N_2$

Biogas $1$:

$(0\mathrm{.}3C{H}_4+0\mathrm{.}7CO2)+0\mathrm{.}6(O_2+3\mathrm{.}76N_2)--C{O}_2+0\mathrm{.}6H_{2}O+2\mathrm{.}256N_2$

Biogas $2$:

$((\frac{3}{5})C{H}_4+(\frac{2}{5})CO2)+(\frac{6}{5})(O_2+3\mathrm{.}76N_2)--C{O}_2+(\frac{6}{5})H_{2}O+4\mathrm{.}512N_2$

Biogas $3$:

$(0\mathrm{.}95C{H}_4+0\mathrm{.}05CO2)+1\mathrm{.}9(O_2+3\mathrm{.}76N_2)-C{O}_2+1\mathrm{.}9H_{2}O+7\mathrm{.}144N_2$

Determine the following:

Calculate the HHV and LHV for each of the fuels

Determine the reactions for complete combustion of each of the fuels with $x$

$100\%$ of the theoretical amount of air $($similar to example seen in class$).$

Applying an energy rate balance at steady state and varying $x$ from $1$ to $4,$ plot the

adiabatic flame temperature for each fuel from $100\%$ theoretical air to $400\%$ of

theoretical air. Include the $4$ fuels in the same plot.