66
3 Gas Hydrates
we will defer the surface and interfacial free energies of clathrate hydrates to Sect. 4.3,
and here we only limit ourselves to a few other major thermodynamic properties in
the bulk of clathrate hydrates.
Clathrate hydrates are, by definition, multi-component systems. Thermodynamically, clathrate hydrates can be viewed as solid solutions of guest gases in the host
water, like alloys [47]. An important feature that is common to all types of clathrate
hydrates is that the concentration of the gas that can be contained inside clathrate
hydrate as a guest is much higher than the solubility of the same gas in liquid water.
For example, 1 m
3 of methane hydrate can contain as much as 170 m
3 of methane
gas at the standard temperature and pressure (STP) [1]. In contrast, the solubility
of methane in liquid water is of the order of 10
−3 in mole fractions at pressures for
which methane hydrate is stable [48]. This much greater gas contents in the clathrate
form than the solubility of the same guest gas in liquid water at the same pressure
and temperature gives rise to thermodynamic stability of clathrate hydrates.
Freezing point depression of ice in electrolytes is a common phenomenon. Since
the solubility of a salt in liquid water far exceeds the “solubility” of the same salt in
ice, if it could be regarded a “solid solution” [49], the free energy reduction due to
the entropy of mixing is far greater in liquid water than in ice. The consequence is
that a salt solution can remain thermodynamically stable below 273.16 K. In other
words, the melting point of ice can be lowered by the dissolution of salts. Likewise,
clathrate hydrates could be viewed as a kind of “melting point elevation of ice”.
The much higher guest gas contents in the clathrate form than the solubility of the
same guest gas in liquid water renders the entropy of mixing in the clathrate form
greater than that in the aqueous solution. The resulting free energy reduction aids its
thermodynamic stability at higher temperatures than 273.16 K.
3.2.1 Phase Diagrams of Clathrate Hydrates at Relatively
Low Pressures
Phase diagrams are probably one of the most studied thermodynamic aspects of
clathrate hydrates [1]. Since clathrate hydrate must consist of at least two components
of the guest and the host, its phase diagram is more complex than that of pure water.
For the simplest case of a single-component guest, the Gibbs phase rule (Eq. 1.1.1)
states that the number of the degree of freedom is four minus the number of phases
present in the system. The minimum number of the phases allowed is one where three
parameters of temperature, pressure, and composition can be independently varied.
Such phase diagrams require three-dimensional descriptions that are not convenient
to express on a two-dimensional paper. Alternatively, either (1) pressure–temperature
phase diagram at a fixed composition, (2) pressure–composition phase diagram at a
fixed temperature, or (3) temperature–composition phase diagram at a fixed pressure
can be expressed on a two-dimensional paper. Here, we only limit ourselves to
qualitative descriptions of single-component guest clathrate hydrate phase diagrams.
3 Gas Hydrates
we will defer the surface and interfacial free energies of clathrate hydrates to Sect. 4.3,
and here we only limit ourselves to a few other major thermodynamic properties in
the bulk of clathrate hydrates.
Clathrate hydrates are, by definition, multi-component systems. Thermodynamically, clathrate hydrates can be viewed as solid solutions of guest gases in the host
water, like alloys [47]. An important feature that is common to all types of clathrate
hydrates is that the concentration of the gas that can be contained inside clathrate
hydrate as a guest is much higher than the solubility of the same gas in liquid water.
For example, 1 m
3 of methane hydrate can contain as much as 170 m
3 of methane
gas at the standard temperature and pressure (STP) [1]. In contrast, the solubility
of methane in liquid water is of the order of 10
−3 in mole fractions at pressures for
which methane hydrate is stable [48]. This much greater gas contents in the clathrate
form than the solubility of the same guest gas in liquid water at the same pressure
and temperature gives rise to thermodynamic stability of clathrate hydrates.
Freezing point depression of ice in electrolytes is a common phenomenon. Since
the solubility of a salt in liquid water far exceeds the “solubility” of the same salt in
ice, if it could be regarded a “solid solution” [49], the free energy reduction due to
the entropy of mixing is far greater in liquid water than in ice. The consequence is
that a salt solution can remain thermodynamically stable below 273.16 K. In other
words, the melting point of ice can be lowered by the dissolution of salts. Likewise,
clathrate hydrates could be viewed as a kind of “melting point elevation of ice”.
The much higher guest gas contents in the clathrate form than the solubility of the
same guest gas in liquid water renders the entropy of mixing in the clathrate form
greater than that in the aqueous solution. The resulting free energy reduction aids its
thermodynamic stability at higher temperatures than 273.16 K.
3.2.1 Phase Diagrams of Clathrate Hydrates at Relatively
Low Pressures
Phase diagrams are probably one of the most studied thermodynamic aspects of
clathrate hydrates [1]. Since clathrate hydrate must consist of at least two components
of the guest and the host, its phase diagram is more complex than that of pure water.
For the simplest case of a single-component guest, the Gibbs phase rule (Eq. 1.1.1)
states that the number of the degree of freedom is four minus the number of phases
present in the system. The minimum number of the phases allowed is one where three
parameters of temperature, pressure, and composition can be independently varied.
Such phase diagrams require three-dimensional descriptions that are not convenient
to express on a two-dimensional paper. Alternatively, either (1) pressure–temperature
phase diagram at a fixed composition, (2) pressure–composition phase diagram at a
fixed temperature, or (3) temperature–composition phase diagram at a fixed pressure
can be expressed on a two-dimensional paper. Here, we only limit ourselves to
qualitative descriptions of single-component guest clathrate hydrate phase diagrams.