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82 Geothermal Energy: Renewable Energy and the Environment

will stay in solution unless the pressure is decreased, which is exactly what happens as geother-
mal fluids are brought to the surface and used to turn turbines. Consider again the pressure-
enthalpy figure we previously discussed (Figure 3.8). In this case, however, assume that the
solution is one of the fluids listed in Table 5.2, in which there are dissolved gases. When the fluid
reaches point A, steam begins to separate. Since dissolved gases have different thermodynamic
properties (which is documented by the differing log K values above), some will have begun to
exsolve from the solution prior to that point, while others will still be in solution. Once steam
forms, however, a new process begins to influence the behavior of the dissolved gases; namely,
the necessity to partition the total mass of each dissolved species between liquid and gas (steam).
Thermodynamically, this partitioning process reflects the driving force for all substances to
achieve a thermodynamic equilibrium condition, which can be expressed as (using H S as an
2
example species):

μ H S (aq) < = > μ H S (g)
2
2
where μH S (aq) and μH S (g) represent the chemical potential of the hydrogen sulfide dissolved in
2
2
the aqueous solution and in the gas phase, respectively. As previously noted, chemical potential is
the sum of all the attributes of the system that determine the thermodynamic energy of a substance
(e.g., enthalpy, entropy, PV work, etc.) and is the ultimate driving force for any chemical reaction.
At equilibrium, all the chemical potentials of the participating substances in all phases must be
equal, by definition. All compounds must obey this principle. For our considerations, the question
we must address is how to determine how much of the compound must enter the gas phase in order
for equilibrium to be achieved.
Currently, reliance is placed on experimental data to establish the partitioning relationship for any
species, since the theoretical, quantum mechanical calculations are quite daunting. The approach
used here is that of Alvarez et al. (1994), who developed the following function for describing par-
titioning behavior:

ln K = (–0.023767 × F) + {E/T × [(ρ /ρ ) – 1]}
l
D
cp
2/3
+ (F + {G × [1 – (T/T ) ]} (5.9)
cp
+ {H × [1 – (T/T )]} exp {[273.15 – T]/100}),
cp
where K is the mass ratio between the gas and liquid phases of the species of interest, T is in
D
degrees Kelvin, T is the temperature at the critical point of water (647.096 K), ρ is the density of
l
cp
water at the temperature of interest, ρ is the density at the critical point of water, and E, F, G, and
cp
H are correlation parameters that are derived from fits to the experimental data (Table 5.4).
Figure 5.6 shows the variation of the log K with temperature for H , O , CO , and H S. The
2
2
2
2
D
figure demonstrates the strong partitioning into the gas phase of these species and the strong tem-
perature dependence of the partitioning. Notice that, at high temperatures, the partitioning for these
gases is within an order of magnitude of each other. As the gases cool, the differences in thermody-
namic properties result in widely different partitioning behavior such that, at 100°C, the difference
in partitioning is more than two and a half orders of magnitude. Among other things, this means
that gas analyses carried out at a low temperature must be corrected for this contrast in partitioning
behavior if reconstruction of the water composition within a geothermal aquifer is to be obtained.
The implications for gas compositional changes for generating equipment will be discussed in more
detail in Chapter 9.