How to solve

$1\mathrm{.}3.$ In a test on a furnace fired with natural gas$($ composition $95\%$ methane, $5\%$ nitrogen$),$ the following flue gas analysis was obtained:$9\mathrm{.}1\%$ carbon monoxide $0\mathrm{.}2\%,$oxygen $4\mathrm{.}6\%,$nitrogen $86\mathrm{.}1\%,$ all percentages by volume. Calculate the percentage excess air flow $($percentage above stoichiometric$).$

Solution

Reaction: $C{H}_4+2O_{2}C{O}_2+2H_{2}O$

Note: the flue gas analysis is reported on the dry basis, any water formed having been condensed out.

Nitrogen is the tie component.

Basis: $100$ mol, dry flue gas; as the analysis of the flue gas is known, the mols of each element in the flue gas $($flow out$)$ can be easily calculated and related to the flow into the system.

Let the quantity of fuel $($natural gas$)$ per $100$mol dry flue gas be $x.$

Balance on carbon, mols in fuel $=$ mols in flue gas

$0\mathrm{.}95x=9\mathrm{.}1+0\mathrm{.}2,$ hence $x={9\mathrm{.}79}_{\text{m}\text{o}\text{l}}{?}_{?}$

Balance on nitrogen $($composition of air $O_{2}21$ per cent, $N_{2}79$ per cent$).$

Let $Y$ be the flow of air per $100$mol dry flue gas.

$N_2$ in air $+N_2$ in fuel $=N_2$ in flue gas

$0\mathrm{.}79Y+0\mathrm{.}059\mathrm{.}79=86\mathrm{.}1,$ hence $Y=108\mathrm{.}4(mol{)}_{{?}_{?}}$

$30$