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that as the efficiency goes up, the heat rate goes down. The HHV heat rate for this example can be calculated easily from either the HHV efficiency or the thermal input. Both methods are demonstrated below: ⎛ 3412 Btu/kWh ⎞ ⎛ 3412 Btu/kWh ⎞ Btu ⎜ Efficiency, HHV ⎟ = ⎜⎝ 40.8% ⎟⎠ = 8,360 kWh (HHV) Heat Rate (HHV) = or Heat Rate (HHV) = Note: The LHV to HHV ratio of 90 percent for methane (21,526/23,881 = 90 percent) is typical for natural gas, while this ratio is roughly 94 percent for fuel oils. Common coals typically have a LHV to HHV ratio of 92 to 96 percent depending upon the hydrogen and moisture content61. Typically, gas turbine based cycles are presented on an LHV basis. Conventional power plants, such as coal-, oil-, and gas-fired steam generator/steam turbine cycles are presented on an HHV basis within the U.S. and on an LHV basis throughout the rest of the world. Example 9-12 Efficiency of a Cogeneration Fuel Cell System Given the system described in Example 9-11, what is the combined heat and power efficiency assuming that cycle produces 2 tons/hr of 150 psia/400 oF steam? Assume a feedwater temperature of 60 oF. Solution: Before calculating the cogeneration efficiency, first determine the heat duty associated with steam production. This requires knowledge of the steam and feed water enthalpies, which can be found in the ASME Steam Tables (11) as indicated below: ⎝⎠ ⎛ Input, HHV ⎞ ⎛16,716,000 Btu/hr ⎞ Btu ⎜ Output ⎟ = ⎜ 2,000 kW ⎟ = 8,360 kWh (HHV) ⎝⎠⎝⎠ Temperature (oF) Steam 400 Pressure (psia) 150 180 Enthalpy (Btu/lb) 1219.1 28.6 Feedwater The steam heat duty is calculated as 60 ⎛1MMBtu ⎞ HeatDuty=(massflow)(Changeinenthalpy)=(4000lb/hr)(1219.1−28.6Btu/lb)⎜⎝106Btu ⎟⎠=4.762MMBtu/hr Alternatively, this heat duty can be expressed as 1.396 MWt, [4.762 / 3.412 = 1.396 MW]. Thus, the combined heat and power efficiency is calculated as 61 The difference between the LHV and HHV heating values can be estimated by (1055 Btu/lb)*w, where w is the lbs moisture after combustion per lb of fuel. Thus, w can be determined from the fuel's hydrogen and moisture content by w= moisture + 18/2 * hydrogen. [e.g., for a fuel with 10% moisture and 4% hydrogen, the LHV to HHV difference is 485 Btu/lb, [i.e., 1055*(0.10 + 0.04*9)=485.] 9-18PDF Image | Fuel Cell Handbook (Seventh Edition)
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