Page 61 - Geothermal Energy Renewable Energy and The Environment

44 Geothermal Energy: Renewable Energy and the Environment

is at a depth of 1500 meters and a temperature of 250°C. If a production well extracts that water
at a high rate, it is reasonable to assume that the fluid will lose an insignificant amount of heat to
the surrounding environment as it ascends the well. Since no heat is removed from or added to
the fluid, the ascent is adiabatic. Since the process is irreversible (as we have noted previously, no
process in nature will take place reversibly when rapid changes are occurring under classically
geothermal conditions), the process occurs at constant enthalpy (i.e., is isenthalpic) but not con-
stant entropy (i.e., isentropic). During the ascent, the pressure continuously drops. At the point
the pressure corresponds to the boundary between liquid and vapor, which is at approximately
40 bars pressure for fluid at 250°C, steam will begin to separate from the liquid, forming small
bubbles. The process of vapor formation and separation from liquid water is called “flashing.”
When the phase boundary is encountered, the fluid temperature will migrate along the set of con-
ditions defined by the phase boundary as the fluid ascends. This occurs because the change from the
liquid phase to the vapor phase requires energy, the so-called heat of vaporization. As a result, the
temperature of the fluids (liquid and steam) will decrease as the fluids ascend and steam continues
to evolve from the liquid. Although this process occurs rapidly, it is not instantaneous. As a result,
fluids that exit the wellhead will be a hot mixture of liquid water and steam. In the following discus-
sion we will assume the exiting temperature is 100°C.
Since neither heat nor mass are being added to or removed from our idealized system, the com-
bined fluid (liquid + vapor) enthalpy is constant and the mass (liquid + vapor) is constant. This fact
leads to the important concept of heat and mass balance that is crucial when evaluating a geother-
mal system. Since the process is considered to be isenthalpic, we can write the following equation
that describes the enthalpies of the phase components in our system at the beginning and end point
of the extraction and separation process

o + (1 – x) × H
o ,
o = x × H
H l250 C l100 C v,100 C
where the subscripts l and v stand for liquid and vapor, respectively, and x is the fraction of the mass
of the system that is liquid. Since the total mass fraction must equal 1.0, by definition, the mass frac-
tion of the vapor phase must be 1 – x.
This simple relationship is useful for understanding the characteristics of a geothermal system.
If, for example, we have put in place a well that has reached a depth of 3 km with a bottom hole
pressure of 1000 bars, and fluid is exiting the wellhead at a temperature of 100°C and 1 bar, and
the fluid consists of 70% liquid and 30% steam we can readily establish that the enthalpy in the
reservoir is

(0.7 × 419 J/gm) + (0.3 × 2676 J/gm) = 1096 J/gm,
l
v
which would indicate that the reservoir working fluid temperature was about 240°C (enthalpy val-
ues for coexisting liquid and vapor are given in Table 3.3).
The heat and mass balance equation can be generalized to account for any component of the
system that represents a concentration (mass or energy) that is conserved in the system:

C reservoir = x × C + (1 – x) × C .
l
v
Ideally, this relationship allows one to use chemical analyses and energy measurements made at
the wellhead to establish characteristics in a reservoir. In reality, a number of issues require thought-
ful consideration in order to appropriately apply this relationship. In later chapters we will discuss
in more detail the particular features that contribute to nonideal behavior and how best to account
for them.
Diagrammatically, the behavior of the system can be portrayed in a pressure–enthalpy diagram,
contoured for temperature (Figure 3.9). The arrow at 250°C and 1000 bars represents an initial