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9.2.1 EfficiencyCalculations Example 9-11 LHV, HHV Efficiency and Heat Rate Calculations Given a 2.0 MWAC fuel cell operating on 700 lb/hr of methane, what is (a) the HHV60 thermal input of the methane gas, (b) the LHV thermal input, (c) the HHV electric efficiency, (d) the LHV electric efficiency, and (e) the HHV heat rate? Assume the higher and lower heating value of methane as 23,881 and 21,526 Btu/lb respectively. Solution: (a) The HHV thermal input of the methane gas is ⎛ 23,881 Btu, HHV ⎞⎛ 1 MMBtu ⎞ HHV Thermal Input = (700 lb/hr CH4 )⎜ 1lb CH ⎟⎜⎝ 106 Btu ⎟⎠ =16.716 MMBtu/hr or HHVThermalInput=(16.716MMBtu/hr)⎜⎝3.412MMBtu ⎟⎠=4.899MWt (b) The LHV thermal input of the methane gas is LHV Thermal Input = (700 lb/hr CH or ⎝4⎠ ⎛ 1MW ⎞ ⎛ 21,526 Btu, LHV ⎞⎛ 1 MMBtu ⎞ ⎜⎟ ) ⎜ ⎟ = 15.068 MMBtu/hr 4⎜ 1lbCH ⎟⎝106Btu ⎠ ⎝4⎠ ⎛ 1MW ⎞ LHV Thermal Input = (15.068 MMBtu/hr)⎜⎝ 3.412 MMBtu ⎟⎠ = 4.416 MWt (c) The HHV electrical efficiency is ⎛Output⎞⎛2.0MW ⎞ Electrical Efficiency (HHV) = ⎜ ⎟ = ⎜ AC ⎟ = 40.8% HHV ⎝ Input, HHV ⎠ ⎝ 4.899 MWt, HHV ⎠ (d) The LHV electrical efficiency is ⎛Output⎞⎛2.0MW ⎞ Electrical Efficiency (LHV) = ⎜ ⎟ = ⎜ AC ⎟ = 45.3% LHV ⎝ Input, LHV ⎠ ⎝ 4.416 MWt, LHV ⎠ Note: Because a fuel's LHV is less than or equal to its HHV value, the LHV efficiency will always be greater than or equal to the HHV efficiency. (e) Heat rate is the amount of heat (Btu/hr) required to produce a kW of electricity. Alternatively it can be thought of as an inverse efficiency. Because 1 kW is equivalent to 3,412 Btu/hr, a heat rate of 3,412 Btu/kWh represents an efficiency of 100 percent. Note 60 Heating values are expressed as higher or lower heating values (HHV or LHV). Both higher and lower heating values represent the amount of heat released during combustion. The difference between the HHV and LHV is simply whether the product water is in the liquid phase (HHV), or the gaseous phase (LHV). 9-17PDF Image | Fuel Cell Handbook (Seventh Edition)
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