Problem 10.6 - Cooling Tower for the Cogeneration System for Ohio University

Recall Problem 8.3, in which Athenai Power Consulting proposed a cogeneration system for Ohio University to provide both 1 MW electric power and hot water at around 60°C. After evaluating the system they decided that the closed feedwater heater was an unnecessary complexity, and that the hot water heater design required an unusually large insulated water storage tank, since it was the only means of condensing the steam. Athenai decided to propose a unique new design including a much smaller hot water storage tank in the hotwell of the condenser (no insulation required) and an induced draft cooling tower, as shown in the following schematic diagram:

Athenai decided to retain the unique aspect of the power plant being that the turbine output at state (2) is at 100°C and atmospheric pressure, which eliminates the need for an open feedwater-heater/deaerator and enables the condenser to directly heat the water to the required temperature. The problem was that the hot water is not used continually and since it was the only means of condensing the steam an extremely large hot water storage tank was needed to absorb this heat during low usage times. The new proposal enables a much smaller hot water storage tank conveniently located within the hotwell of the condenser since the condenser cooling load is now shared between the hot water heating system and an induced draft cooling tower, as shown in the diagram. The cooling tower circulating pump can be controlled as needed based on the hot water heating requirement.

• 1) Neatly sketch the complete power plant cycle on the P-h diagram provided, indicating clearly all the stations (1) through (4) on the diagram. Using the Steam Tables determine the enthalpy values at each of the stations and indicate the values obtained on the P-h diagram.
• 2) With the required turbine power output of 1 MW determine the mass flow rate of the steam [kg/s].
• 3) Determine the power required to drive the feedwater pump [kW].
• 4) 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.)
• 5) 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 90°C at station (3) [kW]. (Note that this is the maximum power that can be used by the hot water heater)
• 6) Given the typical conditions at stations (7) and (8) determine the maximum hot water flow rate that this system can produce, when the cooling tower circulating pump is switched off [kg/s].
• 7) Given the conditions at stations (5) and (6) determine the maximum condenser cooling water flow rate required in order to condense and subcool the steam as shown when the hot water circulating pump is switched off [kg/s].
• 8) In the lull period when no water heating is required, then the induced draft cooling tower will need to cool the coolant by evaporation from a maximum of 60°C at station (6) to 25°C in the water reservoir (station (5)). With the aid of a Psychrometric Chart provided below determine the mass flow rate of the dry air through stations (9) - (10), as well as the mass flow rate of the makeup water from the Hocking river. Determine also the volumetric flow rate of the humid air at station (10), Clearly mark and label the relevant values on the Psychrometric Chart, including the values of enthalpy (h), relative humdity () and specific humidity () of stations (9) and (10) respectively.
• 9) Discuss the proposed system with respect to its environmental impact and feasibility, and compare this approach to the previous proposed system shown in Problem 8.3.

Justify all values used and derive all equations used starting from the basic energy equation for a flow system, mass flow rate equations similar to those developed in Chapter 10c, and the basic definition of thermal efficiency (th).