Page 172 - Geothermal Energy Renewable Energy and The Environment

158 Geothermal Energy: Renewable Energy and the Environment

For the conditions stipulated for the ideal case above, H is 2166 kJ/kg, and the work thus per-
2*
formed becomes
w = 2804 kJ/kg – 2166 kJ/kg = 638 kJ/kg.

The resulting efficiency is then

eff = (2804 kJ/kg – 2166 kJ/kg)/(2804 kJ/kg – 1980 kJ/kg) = 0.77.

For a geothermal site to be useful, it must have the capacity to produce steam at a sufficiently
high rate to make generation of electricity economically feasible. Although conditions such as con-
struction costs, exploration investment, access to electrical infrastructure, and other considerations
have a large effect on the economic viability of a site (see Chapter 13 for a detailed discussion of
the economics of geothermal energy production), it is generally considered a necessity that a site
be capable of generating more than a megawatt (MW) of power. For the realistic case considered
above in which 638 kJ/kg of fluid were available for work, the flow rate necessary to generate 1 MW
would be

1,000,000 J/s∕638,00 J/kg = 1.6 kg/s.

Such a flow rate must be sustained for years in order to be viable.
An additional parameter that must be accounted for when generating power from geothermal
resources concerns the pressure at the wellhead and its relationship to the flow rate of fluid through
the turbine. From Figure 9.2 it is clear that pressure has an effect on performance, since it will
establish the conditions for the initial enthalpy of our fluid and the enthalpy difference between ini-
tial and final states. The highest possible pressure is that of the reservoir itself. Since most geother-
mal reservoirs have sufficient pressure such that fluids will exit the well without pumping, the well
will pressurize if the wellhead is closed to flow by the wellhead valve. The pressure at the wellhead
when the wellhead valve is closed is called the closed-in pressure (P ). The actual closed-in pres-
cl
sure will depend upon the pressure and temperature properties of the reservoir and the depth of the
well. The minimum pressure possible is that at the cooling tower that cools the condensed fluid at
the end of the thermodynamic cycle.
The power output of the turbine (and hence the maximum possible output of the generator) is
a product of the mass flow rate times the enthalpy change per unit of mass. The mass flow rate is
dependent on the pressure driving the fluid flow. However, the power output will also be a function
of the enthalpy drop across the system, which is a function of the pressure drop between inlet and
exit points of the turbine. To understand how these factors interrelate, we will consider an isentropic
(that is, ideal) turbine system. The fluid at the wellhead has an entropy determined by the wellhead
closed in pressure, P , and the temperature. We will assume that the P and T are that of the maxi-
cl
mum enthalpy, that is at 235°C and a pressure of about 30 bars. The enthalpy is 2804 kJ/kg. The
mass flow rate can be expressed as a function of the pressure ratio between the closed-in pressure
and the effective pressure using (DiPippo 2008)

m = m max × √[1 – (P/P ) ]. (9.6)
2
cl
The value for m max can be established by well tests—assume it is 5 kg/s. Table 9.2 shows the
relationship between mass flow rate and the ratio of the pressures. Note that the maximum flow rate
is achieved with the greatest pressure differential, and that it drops to zero when there is no pressure
diference.