Problem 8.3 - A Cogeneration Steam Power Plant with a Closed Feedwater Heater

What is Cogeneration? - We like the definition presented by the Midwest Cogeneration Association as follows: Cogneration is the utilization of 2 forms of energy from 1 source i.e.: hot water/heat and electricity from one gen-set.

According to Cogeneration Technologies, the world's first commercial power plant - Thomas Edison's Pearl Street Station built in 1882 - was a cogeneration plant as it made and distributed both electricity and thermal energy, thus the concept has been around for many years, With the recent interest in greener energy technologies it is currently becoming more popular.

This brings us to the current problem statement:- In an effort to decentralise the power grid and utilize the waste heat which accompanies power generation, Athenai Power Consulting have proposed a cogeneration system for Ohio University to provide both 1MW electric power and hot water at around 70°C. They realise that the average power consumption of OU is 10MW, however they believe that a significant portion of this power is required for hot water heating.

The basic approach to Athenai's unique design is shown in the following schematic diagram:

A unique aspect of the power plant is that the turbine output at state (2) is at 100°C and atmospheric pressure. This high pressure output both eliminates the need for an open feedwater-heater/deaerator and the condenser will be able to directly heat the water to the required temperature. The continuous supply of hot water is pumped directly through the hot water distribution system in the various buildings and is ultimately directed to an insulated storage tank. Thus unlike the situation in a large power plant (such as the Gavin plant) no cooling tower is required, and fresh water is added to the storage tank as needed. Notice that Athenai have also proposed a Closed Feedwater Heater in an attempt to improve the efficiency of the basic design. As a young engineer at Athenai your purpose is to complete the design and evaluate and discuss its effectiveness.

• 1) Neatly sketch the complete cycle on the P-h diagram provided, indicating clearly all the stations (1) through (8) on the diagram. Assume that the feedwater at station (5) can be heated to the saturation temperature of the steam at station (6).
• 2) Using the Steam Tables determine the enthalpy values at each of the (8) stations. Indicate the values obtained on the P-h diagram and check them for feasibility.
• 3) Neatly sketch the turbine process (1)-(6)-(2) on the h-s diagram provided. Plot also the isentropic turbine process on the diagram and estimate from the diagram the turbine adiabatic efficiency (T).
• 4) Determine the mass fraction y of the steam bled of from the turbine tap at station (6)
• 5) Determine the total power output of the turbine [kW].
• 6) Determine the power required to drive the feedwater pump [kW].
• 7) Determine the overall thermal efficiency (th) 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.)
• 8) Determine the cooling power in the condenser required to condense the steam exiting the turbine at station (2), and to subcool the condensed steam to 95°C at station (3) [kW].
• 9) Assuming that the condenser coolant water is heated by 40°C as it passes through the condenser, determine the required mass flow rate of the condenser coolant water [kg/s].
• 10) Compare this proposal to an equivalent system without the Closed Feedwater Heater, and discuss and determine to what extent the added complexity is beneficial.
• 11) Discuss the proposed system with respect to its environmental impact and feasibility.

Justify all values used and derive all equations used starting from the basic energy equation for a flow system, the basic definition of thermal efficiency (th), and the definition of adiabatic efficiency (T) of a Turbine.