5.2 Nucleation Rate of Gas Hydrates
121
clathrate hydrates in the emulsion [36–40]. However, an emulsion is not thermodynamically stable and its total water–oil interface area per unit mass of the emulsion
is expected to diminish with time by many orders of magnitude.
In parallel with the effort to determine the nucleation rate of clathrate hydrates,
attempts have been made to directly detect the nucleation of clathrate hydrates in
micro- and sub-micro scales using X-ray diffraction [41, 42], neutron diffraction [41,
43], Raman spectroscopy [41–44], and nuclear magnetic resonance (NMR) [45–
47]. These efforts also probed potential pathways of clathrate hydrate nucleation:
clathrate hydrates consist of several different building units (cages) per unit cell and
it is highly beneficial to know which cage forms first and how its presence may impact
the nucleation of the other cages. These efforts are ongoing, but these techniques are
not suited for measurements of the critical nucleus size, the corresponding nucleation
work, or the nucleation rate of clathrate hydrates for both the fundamental and the
practical reasons we detailed in Chaps. 1 and 2, respectively.
5.2.3 Empirical Approach
Given the unique characteristics of clathrate hydrates and the uncertainties around the
applicability of classical nucleation theory to clathrate hydrates, a prudent approach
would be a purely empirical one that does not rely on the theoretical framework of
the classical nucleation theory [22, 24, 36–40, 48–50]—one can derive empirical
equations first and worry about the physical reasoning later. In our view, establishing
a reliable method of determining nucleation rates will allow systematic comparisons
between systems of various scales and complexity, and such systematic comparisons
may provide new insights or at least some clues.
It is still early days and nucleation curves of only a handful of guest gases have been
determined using the theoretical and experimental framework outlined in Chaps. 1
and 2. These nucleation rates are summarized in the Appendix. This scarcity of nucleation rate data should not come as a surprise given that the experimental techniques
detailed in Chap. 2 are still only several years old and refinements of these techniques
are still ongoing. Some of the data summarized in Appendix were obtained before the
later refinements of the techniques took place and should be regarded as first-order
approximations.
5.2.4 Scaling Laws for the Nucleation Rates of Gas Hydrates
One of the fundamental questions in the nucleation of clathrate hydrate we saw above
is what the appropriate measure of the system size should be that can be used as the
normalization constant for its heterogeneous nucleation. The conventional wisdom
has been that a suitable measure of the system size for homogeneous nucleation is
the system volume because the number of potential nucleation sites is expected to be
121
clathrate hydrates in the emulsion [36–40]. However, an emulsion is not thermodynamically stable and its total water–oil interface area per unit mass of the emulsion
is expected to diminish with time by many orders of magnitude.
In parallel with the effort to determine the nucleation rate of clathrate hydrates,
attempts have been made to directly detect the nucleation of clathrate hydrates in
micro- and sub-micro scales using X-ray diffraction [41, 42], neutron diffraction [41,
43], Raman spectroscopy [41–44], and nuclear magnetic resonance (NMR) [45–
47]. These efforts also probed potential pathways of clathrate hydrate nucleation:
clathrate hydrates consist of several different building units (cages) per unit cell and
it is highly beneficial to know which cage forms first and how its presence may impact
the nucleation of the other cages. These efforts are ongoing, but these techniques are
not suited for measurements of the critical nucleus size, the corresponding nucleation
work, or the nucleation rate of clathrate hydrates for both the fundamental and the
practical reasons we detailed in Chaps. 1 and 2, respectively.
5.2.3 Empirical Approach
Given the unique characteristics of clathrate hydrates and the uncertainties around the
applicability of classical nucleation theory to clathrate hydrates, a prudent approach
would be a purely empirical one that does not rely on the theoretical framework of
the classical nucleation theory [22, 24, 36–40, 48–50]—one can derive empirical
equations first and worry about the physical reasoning later. In our view, establishing
a reliable method of determining nucleation rates will allow systematic comparisons
between systems of various scales and complexity, and such systematic comparisons
may provide new insights or at least some clues.
It is still early days and nucleation curves of only a handful of guest gases have been
determined using the theoretical and experimental framework outlined in Chaps. 1
and 2. These nucleation rates are summarized in the Appendix. This scarcity of nucleation rate data should not come as a surprise given that the experimental techniques
detailed in Chap. 2 are still only several years old and refinements of these techniques
are still ongoing. Some of the data summarized in Appendix were obtained before the
later refinements of the techniques took place and should be regarded as first-order
approximations.
5.2.4 Scaling Laws for the Nucleation Rates of Gas Hydrates
One of the fundamental questions in the nucleation of clathrate hydrate we saw above
is what the appropriate measure of the system size should be that can be used as the
normalization constant for its heterogeneous nucleation. The conventional wisdom
has been that a suitable measure of the system size for homogeneous nucleation is
the system volume because the number of potential nucleation sites is expected to be