Page 88 - Geothermal Energy Renewable Energy and The Environment

Chemistry of Geothermal Fluids 73

units of J/mole. Chemical potentials are analogous to gravitational potentials or electrical potentials.
They are a measure of the tendency of a chemical component to change from one energy state to
another. Hence, in our example, we are considering the tendency of the component SiO to exist
2
in either the quartz, cristobalite, or chalcedony configuration. As noted in Chapter 3, the stable
configuration of a system is that which provides the lowest energy state. Hence, in our example,
the criterion for identifying the stable phase is to determine for which mineral phase the chemical
potential of SiO is the lowest. Of course, this will depend on the pressure and temperature condi-
2
tions to which the system is subject.
The transition from one phase to another, such as

quartz < = > tridymite,

is a chemical reaction that will occur at some set of physical conditions. If all such physical condi-
tions are taken into account, the reaction will define a boundary, on one side of which quartz, the
reactant, will be stable and on the other side tridymite, the product, will be stable (by convention,
reactants are those phases that occur on the left side of the reaction and products occur on the right
side of the reaction). Along that boundary the chemical potential of SiO in both phases is equal
2
μ quartz = μ tridymite .

The various reactions that are possible in the example system are easily represented as expres-
sions between components since there is only one component in the system, and that component is
the only one present in the phases we are considering. However, in more complex systems, such as
those usually encountered in geothermal systems, keeping track of how all of the components are
individually changing as the physical conditions evolve is simply too cumbersome. Instead, the fol-
lowing relationship is used to account for these changes:

Δ G = ∑μ , (5.1)
i
j
j
where ∆G is the Gibbs energy of phase j and μ is the chemical potential of component i in phase j.
i
j
j
In the summation, it is convention that the products are taken as positive and the reactants are taken
as negative.
Recalling the definition of the Gibbs function in Chapter 3, it is evident that the sum of the
chemical potentials of the components of a phase express the changes in enthalpy, entropy, and PV
work that occur when a phase is affected by evolving physical conditions.
Equation 5.1 is an important general expression for all phases. It indicates that all phases that
makeup a physical system will respond to changes in their environment through the effects those
changes have on the chemical potentials of the components composing the phase. Those changes
will be expressed in a variety of ways, as will be discussed in more detail in this chapter and in
Chapter 6. But, the most dramatic change is that implied by the chemical reactions we are con-
sidering. Sufficient change in the chemical potentials of the components composing a phase will
ultimately be sufficient to make that phase unstable, relative to some other arrangements of the
components, and a reaction will occur, forming a new assemblage of phases. This then implies that
Equation 5.1 can be generalized to represent the behavior of a collection of phases,

∆G = ∑∆G , (5.2)
rx
j
where ∆G is the Gibbs energy of the reaction we are considering, at some specified pressure and
rx
temperature. Again, the same convention regarding the sign of the reactants and products is used in
the summation as in Equation 5.1.