Gas Turbine RatedPower 4.75 MW electricity each Number of GasTurbines 2 Steam Tu

Question

Gas Turbine RatedPower                                            4.75 MW electricity each

Number of GasTurbines                                              2

Steam Turbine RatedPower                                        3.25 MW electricity each

Number of SteamTurbines                                          1

Fuel                                                                             Natural Gas

HeatRate                                                                    14468 Btu/kWhr

Fuel FlowRate                                                2050 Therm/hr

Combined Cycle Efficiency

including cogenerationheat                                           0.7634

CapacityFactor                                                           0.735

Capacity factor is a fraction of the number of hours in ayear that a power plant is operating. For example, if a capacityfactor is 0.5, the power plant will operate 50% of all hours (8760hours in a year) in a year, i.e. the plant runs 4380 hours/year.Determine

(a)               the rated electricity output of the plant

(b)              the thermal efficiency of the gas turbine based on heat rate

(c)               the thermal efficiency of the gas turbine based on electricityoutput

(d)              the thermal efficiency of the combined cycle based on electricityoutput

(e)               the useful thermal energy used for cogeneration

(f)                the power produced by the plant in a year in MWhr

(g)              the fuel cost of the plant per year for the natural gas price of$8.50 per million Btu

Note: 1 Therm = 100,000 Btu

Explanation / Answer

For a gas turbine-based cogeneration system, the waste heat inthe turbines' exhaust can be recovered to produce steam either forprocess use only (simple cogeneration) or for both bottoming-cyclepower production and process use (combined-cyclecogeneration). (a)   the ratedelectricity output of the plant: (4.75 MW(2))+(3.25 MW (1)) = 12.75MW    ? (b)   the thermal efficiencyof the gas turbine based on heat rate: 3412/14468Btu/kWhr = .2358 = 24% (c)   the thermal efficiencyof the gas turbine based on electricity output: efficiency = Pe/ input = 9.5MW/ 2163KJ/h= .0043 = ? (d)   the thermal efficiencyof the combined cycle based on electricity output: efficiency = Pe/combined input = 12.5MW/2163KJ/h = .0059 = ? (e)    the useful thermalenergy used for cogeneration: 0.75634 * (2050Btu(therm)/h) = 1550.4units ? (f)    the powerproduced by the plant in a year in MWhr: 12.5Mw ( 8060hr in 1 yr) = 100,750MWhr (g)   the fuel cost of theplant per year for the natural gas price of $8.50 per millionBtu: 8.5 * 43(100,750) = 3.6 X10^7   ? (b)   the thermal efficiencyof the gas turbine based on heat rate: 3412/14468Btu/kWhr = .2358 = 24% (c)   the thermal efficiencyof the gas turbine based on electricity output: efficiency = Pe/ input = 9.5MW/ 2163KJ/h= .0043 = ? (d)   the thermal efficiencyof the combined cycle based on electricity output: efficiency = Pe/combined input = 12.5MW/2163KJ/h = .0059 = ? (e)    the useful thermalenergy used for cogeneration: 0.75634 * (2050Btu(therm)/h) = 1550.4units ? (f)    the powerproduced by the plant in a year in MWhr: 12.5Mw ( 8060hr in 1 yr) = 100,750MWhr (g)   the fuel cost of theplant per year for the natural gas price of $8.50 per millionBtu: 8.5 * 43(100,750) = 3.6 X10^7   ?

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