Question

1. Calculate the thermoeconomic cost of the produced electricity using the internal combustion device described in homework 7. with and without the heat exchanger. Use the results you calculated to answer this question. This question is focusing on the thermoeconomic costs. The electricity is produced for 10 hours a day, five days per week during a one year cycle.

The following cost information is given for the internal combustion device. The cost of the device is $125,000 and it has a lifetime of 15 years. The cost of the fuel is $0.121/Kg and its heating value (energy content) is 47 MJ/Kg. There is service contract that costs $2500 /year to cover the periodic maintenance and supervision of the unit. Consider that the fuel cost and the service contract will remain constant over the life of the device and neglect interest costs. The cost of the water put into the heat exchanger can be neglected because in the overall system design it is recirculated.

The installed cost of the heat exchanger is $15,000 and it has a lifetime of 10 years. Without the heat exchanger the water heated in the heat exchanger would be heated by burning the above fuel in a boiler that is 57% efficient. The heated water produced in the heat exchanger can be sold to a neighboring business at a price of $0.04/(Kg of water delivered).

1b, Would you invest in this device with or without the heat exchanger if the cost of electricity from the grid is $0.147/kWh? Use the thermoeconomic results calculated in this assignment to justify your recommendation. Do not include the performance measures and carbon dioxide production considerations or the performance consideration in this problem.

PROBLEM 7:

1. Consider an internal combustion device that powers a generator to produce 550 kW of electrical power. Air enters the device at 300K, 1bar and is heated to a temperature of 1300 K by a heat addition process caused by combustion. This high temperature air is then compressed and expanded to produce the power output and exits at a temperature of 833 K and a pressure of 1.2 bars. The efficiency of this power producing device is 0.28 and the generator efficiency is 0.87.   The fraction of the heat input to the system that is lost as heat from the power producing device is 0.30.  

Determine the mass flow rate for this device. The specific heat of the air moving through the system, c_p, is 1,070 J/(Kg K) and the density is 1.15 kg/m³ at 1 bar and 300 K.

Determine the first law efficiency for this system.

1b. It has been suggested to recover the waste from the exhaust of the internal combustion device described in question 1 above using a heat exchanger. The heat exchanger is an adiabatic device, there is no heat loss to the surroundings.   A heat exchanger is a device that transfers heat from a hot fluid flow to a cold fluid flow, usually without mixing them. In this case the air flow will be used to heat a flow of water, 0.00134 Kg/s , that enters the device at a temperature of 290 K. The specific heat of the water is 4,120 J/(Kg K).

The performance of the heat exchanger is described by its effectiveness which is defined as the ratio of the actual heat transfe r rate to the maximum possible heat transfer rate.

Effectiveness = ? = q_actual/((mc)_minimum(T_{hot, in} – T_cold,in)

Where: q_actual = actual heat transfer rate, (mc)_minimum = minimum product of the mass flow rate times the fluid’s specific heat, T_{hot, in} = the hot fluid temperature at the inlet, T_cold, = the cold fluid temperature at the inlet.

The effectiveness for the proposed heat exchanger is 0.72, a practical value. Determine the temperature of the water exiting the heat exchanger and the first law energy factor when the power output and the heat transferred to the water are considered to be the desired outputs.

Answer 1