A remote dwelling meets its energy needs by means of a diesel-engine generator s
ID: 2267800 • Letter: A
Question
A remote dwelling meets its energy needs by means of a diesel-engine generator set shown. At full load the diesel generator produces 100 kW of electric power Fuel-air mixture Tap water 0 kw Hot watet system, 150 kW Mode Me1i Diesel Waste Electricity 100 kW Organic-fluid and generator Electricity 15 kW Figure P3.21 About 10% of the fuel energy is wasted in the exhaust gas stream. The fuel-air mixture supplies 40 MJ of energy per kilogram of fuel. The hot water produced by the diesel cooling system is used in either of two modes of operation. In mode I it is circulated in radiators that provide heating to the buildings. In mode 2 it is used to run an organic fluid recuperator and generator that generates an additional 15 kW of electric power (a) At what rate (in kg/s) is fuel consumed at full load by the diesel generator in either operating mode? At what rate is energy discharged in the exhaust gas stream? (b) How would you allocate the fuel cost between the power delivered to the heating system and the electric power generated by the diesel in mode 1? (c) If the energy input from the fuel is 400 KW in either mode, and diesel fuel costs $3 per US gallon, what is the cost of fuel to operate continuously in mode 2 for 24 hours? What is the fuel cost per Kw.hr of electricity in mode 2? What is the cost of fuel per KW.hr of electricity, and per KW.hr of heating, in mode 1?Explanation / Answer
10% of fuel loss is 10/100 = 0.1; so 90% of fuel is 40MJ*0.9= 36MJ
Energy input (MJ) = power * time = 36MJ.
OPerating time is not provided, neither is efficiency of diesel generator dg.
Energy output = 100KW. for producing 100 KW the input power should be 100KW + losses.
input energy assuming dg runs for 1 hour 100kw * 1hour = 100Joules, 1 hour = 3600seconds
so for 36000000/3600 = 10000KW, for 10000 kw 36000000Joules in 1 hour so it takes 10 litres of oil to produce 10000kw for 1 litres/second for 100kw. energy discharged in gas = 4MJ in hour = 1111J/s
b) Fuel cost is based on 100KW electrical power + 150KW heating total 250 KW consumes around 2.5litres of fuel with loss ten percnt it is suggested to take 3 litres of fuel
c) total load in mode two for 24 hours = 24*150Kw =3600KWH. but 15KW is generated by recuperator 15*24= 360
3600-360 = 3240KWH. 1 gallon = 3.78 litres. for 3240KW we need 3 litres = 3 dollarsfor every hour s0o 24/3.78 =7gallons = 21$ for
in mode one 100KW cost of fuel 1/3 =0.333litres = 0.087*3$= 0.261$
3$ for 150KWh it is 0.261+.13= -391 = approximately 4$
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