Question

The fuel mixer in a natural gas burner mixes methane (CH4) with air to form a combustible mixture at the outlet.

Determine the mass flow rates at the two inlets needed to produce 0.5 kg/s of an ideal combustion mixture at the outlet. Use data from the tables.

Answer 1

The mass flow rate of CH₄ is 0.0275 kg/s and the mass flow rate of air is 0.4725 kg/s

Step-by-step explanation:

The molar masses are equal to:

MCH₄ = 16.043 kg/kmol

MN₂ = 28.01 kg/kmol

MO₂ = 32 kg/kmol

MH₂O = 18.01 kg/kmol

MCO₂ = 44.01 kg/kmol

The combustion reaction is:

CH₄ + a(O₂ + 3.76N₂) = CO₂ + 2H₂O + 3.76aN₂

The O₂ balance is:

a = 1 + 1 = 2

CH₄ + 2(O₂ + 3.76N₂) = CO₂ + 2H₂O + 7.52N₂

The masses of the reactants are equal to:

mCH₄ = nCH₄ * MCH₄ = 1 * 16.043 = 16.043 kg

mO₂ = nO₂ * MO₂ = 2 * 32 = 64 kg

mN₂ = nN₂ * MN₂ = 2 * 3.76 * 28.01 = 210.64 kg

mtotal = 16.043 + 64 + 210.64 = 290.683 kg

The masses fractions are equal to:

mfCH₄ = 16.043/290.683 = 0.055

mfO₂ = 64/290.683 = 0.22

mfN₂ = 210.64/290.683 = 0.724

The mass flow rates of the reactants are equal to:

mfrCH₄ = 0.055 * 0.5 = 0.0275 kg/s

mfrair = 0.5 - 0.0275 = 0.4725 kg/s