2.9 (a) The body‐centered cubic arrangement of the dodecahedral cages (blue color) in the structure I unit cell. Note that the dodecahedral cage in the center of the unit cell is rotated 90° with respect to the other cages. The space between the dodecahedral cages is divided into tetrakaidecahedral cages. (b) In the structure II unit cell, the dodecahedra are placed between non‐adjacent points of a diamond lattice shown by red spheres. The dashed red line connecting the diamond lattice points passes through the opposing pentagonal faces of the dodecahedral cage. (c) The packing of the properly placed dodecahedral cages (in blue) within the diamond lattice gives rise to hexakaidecahedral cages (clear color) surrounding the diamond lattice points. See Chapters 3 and 4 for a full discussion of these structures. Source: Figure prepared Dr. S. Takeya.
Figure 2.10 Pioneers of clathrate science in the mid‐1900s. Top row, George A. Jeffrey. Bottom row from left to right, Joan H. van der Waals, Donald W. Davidson, and Yuri A. Dyadin. Source: Reproduced with permission from International Union of Crystallography, Reproduced with permission from the Royal Netherlands Academy of Arts and Sciences, Reproduced with permission from Elsevier.
With the knowledge of the structures of hydrates in hand, what remained to be explained was the quantitative nature of the guest–host association, which was neither covalent nor ionic. This came by way of a statistical thermodynamic model of clathrate structures developed by Joan H. van der Waals (Figure 2.10), later collaborating with J.C. Platteeuw and coworkers, then working at Shell Laboratories in Amsterdam [95]. In this model, the guest molecules are “dissolved” in a host lattice of water molecules, hence the name “solid solution model.” The impetus for this work came from Powell's groundbreaking solution of the crystal structure of quinol guest–host compounds, the first clathrates. van der Waals' first model dealt with the quinol clathrates with space‐filling cavities of a single kind, which he later extended to clathrate hydrates with multiple cage types and guest molecules of one or more kinds. By assuming a specific mathematical form for the guest–host interaction potential, the solid solution theory provided a formalism to calculate cage occupancies at different temperatures and pressures, guest hydration numbers, and heats of enclathration. The potential chosen to describe guest–host interaction was the Lennard‐Jones 12–6 potential, thus allowing neutral, non‐polar guest molecules to be treated. After the model successfully described xenon hydrate properties, van der Waals and Platteeuw cautiously suggested that a hydrate with a non‐polar polyatomic guest molecule like methane might also be modeled this way. The van der Waals–Platteeuw theory is discussed in detail in Chapter 7.
2.7 Clathrate Hydrate Science – A New Era
With a successful description of hydrate structures and development of a statistical thermodynamic model, a new era in clathrate hydrate research began. In summary, up until 1960, except for a few isolated contributions (especially the diffraction studies in the 1950s), hydrate scientific research was dominated by European researchers stumbling across hydrates while doing other work, and, later, by doing concentrated curiosity‐driven scientific research on hydrates.
Starting in the 1950s and 1960s, physical chemistry‐based laboratory work of note in the area of gas hydrate research was carried out in the Applied Thermodynamics Laboratory in Delft (G.A.M. Diepen), the Institute of Inorganic Chemistry, Soviet (now Russian) Academy of Sciences, Siberian Branch, Novosibirsk (Yuri A. Dyadin, Figure 2.10), and the University of Pittsburgh (George A. Jeffrey). At the National Research Council of Canada in Ottawa, Donald Davidson (Figure 2.10) started a fundamental gas hydrate research program featuring multi‐technique approaches to study hydrate properties and dynamics. Contributions of these scientists are discussed in detail in the chapters that follow.
2.8 Clathrate Hydrates in Engineering
In contrast to the largely European efforts in developing clathrate hydrate science, the early North American hydrate experiences fell much more along practical lines. E. Hammerschmidt (see Figure 2.8), an engineer at Texoma Energy, read Schröder's book1 and review article, and in 1933, this led him to the realization that it was gas hydrates (and not ice) that formed plugs in gas pipelines, thus causing flow problems [96]. This led to the phase equilibrium studies of natural gas components and water by W.M. Deaton and E.M. Frost (US Bureau of Mines) [97], Donald Katz (University of Michigan), Riki Kobayashi (Rice University), and coworkers. These important advances in the engineering and thermodynamics of gas hydrates, particularly for species in natural gas, are covered admirably in Dendy Sloan and Carolyn Koh's book on Clathrate Hydrates of Natural Gases [98]. This work resulted in general procedures for the prediction of solid hydrate formation under engineering conditions, usually based on gas gravity, and recipes for their prevention. The state of the art of this approach to hydrate prediction and prevention can be found, e.g. in the Handbook of Natural Gas Engineering (1959) [99]. This work would only develop along more knowledge‐based lines once the hydrate crystal structures and a theoretical description in the form of the “solid solution” theory became available in the late 1950s. Further development took place in describing guest–host interactions e.g. the work of McKoy and Sinanoglu on the use of the Kihara potential in the solid solution theory as an alternative to the Lennard‐Jones 12–6 potential [100]. The Kihara potential is similar to the Lennard‐Jones potential but considers molecules to have a hard, impenetrable core at the center. The modeling of phase equilibria was advanced considerably by Parrish and Prausnitz [101] who introduced the Kihara potential into the van der Waals and Platteeuw model and developed a particularly useful form for the computation of hydrate phase equilibria and cage occupancies. The first molecular simulations on clathrate hydrates were performed in 1972 by Tester, Bivens, and Herrick who used canonical Monte Carlo simulations to explicitly calculate guest–water interaction terms in the cages for use in the van der Waals–Platteeuw theory, without using the approximate Kihara potential form [102]. These simulations were followed in 1982 by the work of John S. Tse and Donald Davidson who improved the intermolecular potential representations of the water–guest interactions in the Monte Carlo simulations [103]. The first molecular dynamics simulations on hydrate phases were performed shortly afterward on structural characterizations of methane hydrate by J.S. Tse et al. [104].
With a good understanding of the nature of clathrate hydrates in hand, impressive strides were made in both experimental and predictive work on the phase equilibria of hydrates. In the 1960s and 1970s, a new generation of hydrate researchers arose in the United States and Canada: Gerald D. Holder in Pittsburgh, E. Dendy Sloan Jr. at the Colorado School of Mines (CSM), Donald B. Robinson at the University of Alberta, Raj Bishnoi at the University of Calgary. Much of the emphasis of these researchers was to deal with flow assurance problems involving hydrates: hydrate inhibition, hydrate plug prevention, and decomposition. In many of the laboratories mentioned above, hydrates became a continuing research theme which in many cases still continues – sometimes again with a new generation of hydrate researchers.
Another stream of hydrate research emerged when the US Office of Saline Water started a number of projects on the desalination of sea water. Hydrates were seen as one route to producing fresh water, with some advantages over the straightforward freezing of salt water to exclude salt. Allan Barduhn (University of Syracuse) investigated a large number of potential hydrate formers as potential desalting agents, including a number of chlorofluorocarbons (CFCs). Although hydrate desalination went as far as the pilot plant stage in the 1960s, so far a viable technology has not been developed.
2.9 Clathrate Hydrates in Nature
Hydrates of natural gas in nature were the subject of some speculation [105] before Yuri F. Makogon first reported the existence of natural gas hydrates associated with the Messoyakha gas field in Siberia in 1965 [106]. Onshore permafrost hydrates in Canada [107] and marine