### 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 η_{th}
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 η
_{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. 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 η_{th}.