### Problem 4.6 - An Open Feedwater Heater added to the Cogeneration Steam Power Plant

This problem is an extension of Problem 4.5 in which the Athenai Power Consulting Group proposed a unique Cogeneration system for O'Bleness Hospital to provide both 500kW electric power and hot water at 60°C. On analysis we determined that the thermal efficiency ηth of the proposed power plant was 23%, which is extremely low. In an attempt to improve the plant thermal efficiency Athenai proposed a new design as shown in the following schematic diagram:

The condenser hot water heating system is retained as in the previous design with the hot water storage tank immersed in the hotwell of the condenser. The turbine outlet pressure has been reduced from the original 100 kPa to 20 kPa, and the steam condenses to a subcooled hotwell temperature of 60°C, A condensate pump increases the pressure to 200 kPa, allowing the air to separate and escape in the Open Feedwater Heater/De-aerator. A mass fraction y of saturated vapor steam at 200 kPa is tapped from the turbine and mixed with the condensate as shown, and the resulting saturated liquid mixture is then pumped to 4 MPa by the feedwater pump before being supplied to the boiler. As a young engineer at Athenai your purpose is to evaluate this new design and compare its performance to the previously proposed system.

• 1) Neatly Plot the complete cycle on the P-h (pressure-enthalpy) diagram provided, indicating clearly stations (1), (2), (3), (4), (5), (6), and (7) on the diagram. Once this is done then use the Steam Tables to determine the following:
• 2) Determine the mass fraction y of the bled steam at station (7) in order to provide a saturated liquid condition at station (5). [y = 0.103]
• 3) Determine the mass flow rate of the steam through the cycle required in order to provide the required turbine output power of 500kW. [0.554 kg/s]
• 4) Determine the overall thermal efficiency ηth of this power plant. (Recall that thermal efficiency is defined as the net work done divided by the total heat supplied externally to the boiler. You may ignore the feedwater and condensate pump power in this evaluation. [32%]
• 5) Compare the performance of the above system with that of the previously proposed system (Problem 4.5), and discuss its advantages and disadvantages.

Justify all values used and derive all equations used starting from the basic energy equation for a flow system, and the basic definition of thermal efficiency ηth.