A glass melting furnace is burning ethane (C2H4) in pure oxygen (not air). The furnace operates at an equivalence ratio of 0.9 and consumes 30 kmol/hr of ethane. (A) Determine the energy input rate based on the LHV of the fuel. Express your result in both kW and Btu/hr. (B) Determine the O2 consumption rate in kmol/hr and kg/s.
To determine the energy input rate based on the Lower Heating Value (LHV) of ethane, we need to follow these steps:
(A) Determine the energy input rate:
1. Calculate the moles of ethane burned per hour:
Ethane consumed = 30 kmol/hr
2. Calculate the lower heating value (LHV) of ethane:
The LHV of ethane is approximately 47.2 MJ/kg.
3. Calculate the mass of ethane:
Mass of ethane consumed = number of moles * molar mass
= 30 kmol/hr * 28.97 kg/kmol (molar mass of ethane)
= 869.1 kg/hr
4. Calculate the energy input rate:
Energy input rate = mass of ethane consumed * LHV
= 869.1 kg/hr * 47.2 MJ/kg
To convert MJ to kW:
1 MJ/hr = 0.27778 kW
Energy input rate (kW) = Energy input rate (MJ/hr) * 0.27778
To convert kW to Btu/hr:
1 kW = 3412.14 Btu/hr
Energy input rate (Btu/hr) = Energy input rate (kW) * 3412.14
Now let's calculate the values:
Energy input rate (kW) = 869.1 kg/hr * 47.2 MJ/kg * 0.27778
≈ 11,713 kW
Energy input rate (Btu/hr) = 11,713 kW * 3412.14
≈ 39,987,571 Btu/hr
(B) Determine the O2 consumption rate:
1. Calculate the stoichiometric ratio of oxygen to ethane:
Ethane has a molecular formula of C2H4, which requires 3 moles of oxygen for complete combustion:
C2H4 + 3O2 → 2CO2 + 2H2O
Equivalence ratio = Actual fuel-air ratio / Stoichiometric fuel-air ratio
Given equivalence ratio = 0.9
Let x be the oxygen consumed in kmol/hr.
0.9 = (30 kmol/hr * 1) / (x kmol/hr * 3)
Solving for x:
x kmol/hr = (30 kmol/hr * 1) / (0.9 * 3)
Oxygen consumption rate = x kmol/hr
2. Convert oxygen consumption rate to kg/s:
Oxygen molar mass = 32 g/mol
1 kmol = 1000 mol
1 kg = 1000 g
Oxygen consumption rate (kg/s) = (x kmol/hr * 1000 mol/kmol * 32 g/mol) / (3600 s/hr * 1000 g/kg)
Calculate the values:
x kmol/hr = (30 kmol/hr * 1) / (0.9 * 3)
≈ 11.11 kmol/hr
Oxygen consumption rate (kg/s) = (11.11 kmol/hr * 1000 mol/kmol * 32 g/mol) / (3600 s/hr * 1000 g/kg)
≈ 0.098 kg/s
Therefore, the O2 consumption rate is approximately 11.11 kmol/hr and 0.098 kg/s.