A commercial food cooking process requires a flow of 0.3 Kg/s of pressurized water at 150 ºC. The process operates continuously (12 hours day – 360 days per year) and the design analysis can be taken as steady state conditions. The water is at a pressure of 6.5 bars to prevent it from flashing to steam vapor. All pressure changes in this process can be neglected for this problem and the water can be treated as an incompressible liquid with a specific heat, c, of 4050 J/(Kg K) and a density of 1090 Kg/m3. The device of interest is the boiler used to heat the water from an inlet temperature of Tin = 35 ºC. The device is heavily insulated and the total thermal resistance between it and the surroundings is RT = 0.32 K/W. The surroundings are at T∞ =25 ºC, Po = 1bar. For heat transfer process involving a variable temperature process to a uniform temperature surrounding the best average temperature to use is given by the Log-Mean temperature:
TLOG-MN = [(Tin - T∞ ) – (Tout - T∞)]/[ln[(Tin -T∞)/ (Tout - T∞)]
The surroundings can be considered to be the dead state.
The current boiler device will be retired and its replacement is under consideration. You have been tasked with investigating the recommended option. Your analysis should be based on:
a. Energy input requirements (make it work)
b. Performance on the second law basis, second law efficiency
c. Identify the Exergy Destruction in the process
d. Carbon dioxide produced in the process
e. Thermoeconomic cost
The proposal is to install a new boiler which uses a co-generation device based on an open Brayton cycle with a regenerator. The regenerator heat exchanger has an effectiveness of 0.7 and is used to preheat the air leaving the compressor before it enters the combustor using the exhaust from the turbine. Air enters the compressor at 1 bar of pressure and at the temperature of the surroundings. The isentropic efficiency of the compressor is 0.9 and it compresses the gas to a pressure of 7.5 bars. The combustor burns natural gas and heats the air flow to 1300 K. Neglect any pressure loss in the combustor. The heating value of the natural gas (CH4) is 55.5 MJ/kg, its molecular weight is 16 and its exergy is 824,350.0 kJ/kmol. The turbine expands the hot gases to a pressure of 1 bar and has an isentropic efficiency of 0.95. The generator connected to the turbine has an efficiency of 0.9. The strategy is to use the exhaust products from this cycle to heat the pressurized water from its inlet temperature to an intermediate temperature and then use the electricity produced by the Brayton cycle to electrically heat the remaining water. In the given locale it is not possible to sell any excess electricity back to the grid so the cogeneration system must be sized to meet the boiler heating load. The co-generation heat exchanger has an effectiveness of 0.8.
The Brayton cycle cost is $100,000 and has a life expectancy of 15 years.The co-generation heat exchanger cost $23,000 and has a similar life expectancy. The boiler operating cost is the same as described above. To operate the co-generation system will require an additional plant operator with an annual cost of $87,000 and the yearly cost to operate and maintain the co-generation unit is $0.004 /kWh (note this cost is per yearly energy production). The company would pay for this alternative without borrowing money. For this alternative determine:
1 Determine the total rate of energy input required to perform this process.
2 Determine the mass flow rate of air and fuel to the co-generation system to perform this operation.
3 Determine the first law efficiency of the co-generation system.
4 Determine the rate of exergy destruction of each device in this system.
5 Determine the second law efficiency of this system.
6 Determine the carbon dioxide produced daily by using this process. In your solution include the chemical reaction equation used to determine the ratio of the CO2 produced to the fuel input.
7 Determine the thermoeconomic cost for this device which corresponds to the cost of producing the hot water. NOTE: Thermoeconomic costs are based on a one year time period.
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