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Generating Power Using Geothermal Resources 167

energy for power generation, the heat that is in the condensed liquid that separates from the vapor
during expansion is lost.
In a dual-flash plant, a high-pressure turbine specifically designed to operate within a relatively
narrow pressure and temperature interval is worked upon by the vapor, which is cooled by a rela-
tively modest amount (path A* to 2), perhaps down to 140°C–160°C. Hot water that has separated
from the vapor (A–B) is collected and flashed at lower pressure (point B). This additional vapor is
either introduced to a different turbine specifically designed to operate at high efficiency at lower
pressure and temperature conditions, or is introduced to a different part of the turbine that is simi-
larly designed to operate efficiently at a lower pressure and temperature. The primary advantage of
this dual-flash process is the recovery of a significant fraction of the heat that otherwise would have
been lost in the water that was discharged from the turbine complex. The end state for this process
would be point 3.

The end sTaTe: condensers and coolinG Towers
As noted previously in Chapter 3, the thermodynamic efficiency of a system is ultimately determined
by the magnitude of the temperature difference between the initial and final state of the fluid. For
the generating systems discussed thus far, an important element for establishing high efficiencies is
an effective cooling process that will maximize the temperature drop between the turbine inlet and
the exhaust system of the generating plant. To accomplish cooling, the steam that exits the turbine
generally flows through a condenser in which cooling water extracts a sufficient amount of heat
from the steam to cause the steam to condense to liquid water. This change in temperature also
drops the pressure of the system at the exit, which contributes importantly to the overall variation in
state variables (pressure and temperature) across the entire turbine flow field. In addition, the pres-
sure in the condenser is maintained mechanically.
Cooling is often accomplished by spraying water into the flowing steam stream from the turbine and
collecting the resulting liquid. The mass flow of cooling water needed to sufficiently cool the incoming
steam to the point it will condense must be sufficient to decrease the steam enthalpy to that of water
on the liquid saturation curve at the target temperature for the system. From our previous discussions,
we considered an end point temperature of 25°C, for which the enthalpy of liquid water is 104.9 kJ/
kg. If we assume that the temperature of the steam as it leaves the turbine is 50°C, the enthalpy of the
steam when it leaves the turbine is 2592 kJ/kg. This requires that 2487.1 kJ/kg be removed from the
steam coming in to the condenser to condense all of it to liquid water. The heat capacity of water is
approximately 4.2 kJ/kg-K for the conditions we are considering. If we assume the flow rate from the
turbine is 2.5 kg/s, the mass flow rate of cooling water can be calculated from the relationship

m = m × (ΔH/C × ΔT), (9.13)
cw
te
pw
where m is the mass flow rate of vapor from the turbine, ΔH is the required change in enthalpy to
te
achieve the desired end state, C is the heat capacity of water, and ΔT is the change in temperature
pw
required to reach the end state condition. For our case, m must be
cw
m = 2.5 kg/s × {2487.1 kJ/kg/(4.2 kJ/kg-K × 25 K)} = 59.2 kg/s.
cw
This value is the maximum needed for this scenario, since it only considers modest heating of the
cooling water (25°C) and does not consider the heat transfer associated with evaporation. In fact,
the condenser is needed simply to convert steam to liquid, in order to drop the pressure across the
turbine by reducing the fluid volume from that of steam to that of liquid. The liquid water that usu-
ally is condensed in the condenser will therefore not be at the end state temperature of 25°C, but at
some other higher design temperature. In addition, although converting 100% of the steam to liq-
uid would provide the greatest efficiency, conversions of 80–95% would still provide a sufficiently