Ứng dụng hữu ích của Gas hydrates trong ngành công nghiệp dầu khí. Cung cấp các thông tin cần thiết cho các kỹ sư dầu khí nhằm đáp ứng cho nhu cầu năng lượng không chỉ của riêng nước ta mà còn trên thế giới.
Trang 1Geological Society, London, Special Publications
new articles cite this article
to receive free e-mail alerts when here
click
request
Permission
part of this article
to seek permission to re-use all or here
click
Subscribe
Collection London, Special Publications or the Lyell
to subscribe to Geological Society, here
click
Notes
© The Geological Society of London 2014
Trang 2Physical/chemical properties of gas hydrates and application to world
margin stability and climatic change
E D S L O A N , JR
Center for Hydrate Research, Colorado School o f Mines, Golden, CO 80401, USA
Abstract: The major points in this paper concern: (a) physical and chemical properties and
(b) applications of those properties Three questions are addressed: What are hydrates?
What is our knowledge about their thermodynamic and kinetic properties? What are the
applications to the environment and climate stability?
The physical and chemical characteristics of hydrates are approximated by three heuristics:
(1) physical properties approximate those of ice, (2) phase equilibrium characteristics are set
by the size ratio of guest within host cages, and (3) thermal properties are set by hydrogen-
bonded crystals with cavity size ratios Knowledge of hydrate kinetics is substantially lacking,
but it appears that formation kinetics derive from aggregation of water clusters at interfaces
A significant future challenge is to characterize hydrates directly (through NMR, Raman, dif-
fraction, etc.) for both thermodynamics and kinetics
Hydrocarbons in natural hydrates represent twice the amount of all combined fossil fuels
Most recovered samples have been small, dispersed (even dissociated) particles with isolated
examples of massive hydrates Hydrates probably will not contribute significant methane to
the atmosphere in the near future Ocean hydrates and air hydrates from Antarctic ice are
indicators of ancient climatic changes
Gas clathrates (commonly called hydrates) are
crystalline compounds which occur when water
forms a cage-like structure around smaller
guest molecules The proper name 'clathrate'
was given to the class by Powell (1948) from
the Latin 'clathratus' meaning to encage While
they are more commonly called hydrates, a care-
ful distinction should be made between these
non-stoichiometric clathrate hydrates and other
stoichiometric hydrate compounds which occur
when water combines with various salts via cou-
lombic forces, but without cages
Gas hydrates of current interest are composed
of water and the following eight molecules:
methane, ethane, propane, isobutane, normal
butane, nitrogen, carbon dioxide and hydrogen
sulphide Yet, other apolar components between
the sizes of argon (0.35 nm) and ethylcyclohexane
(0.9 nm) can form hydrates Hydrate formation is
a possibility anywhere water exists in the vicinity
of such molecules, both naturally and artificially,
at temperatures above and below 273 K when the
pressure is elevated
Since the time of their discovery in 1810 by Sir
Humphrey Davy, hydrates have been a labora-
tory curiosity, displaying many unusual proper-
ties However, it is primarily due to their
crystalline, non-flowing nature that hydrates
became of interest to the hydrocarbon industry
at the time of their first observance in pipelines
(Hammerschmidt 1934) For the last 60 years
hydrates have been considered a nuisance because they block hydrocarbon flow channels, jeopardize the foundations of deep-water plat- forms and pipelines, collapse drilling tubing, and foul process heat exchangers and expanders Another application of hydrates is as a poten- tial future energy resource Hydrates act to con- centrate hydrocarbons; 1 m 3 of hydrates may contain as much as 180 SCM of gas Three dec- ades ago (Makogon 1965) it was recognized that large natural reserves of hydrocarbons exist in hydrated form, both in deep oceans and
in the permafrost Evaluation of these reserves
is highly uncertain, yet even the most conserva- tive estimates concur that there is twice as much energy in hydrated form as in all other hydrocarbon sources combined While one com- mercial example exists of gas recovery from hydrates (Sloan 1998, p 525 if), the economics
of in situ hydrate dissemination in deep-water- permafrost environments will prevent their recovery until the next millennium There is a national project to drill hydrates in 1999 in off- shore Japan
Questions relating hydrate stability to atmos- pheric methane were first raised by Kvenvolden
& McMenamin (1980), but degrees of ocean methane hydrate release scenarios have been considered by Nisbet (1989, 1992), M a c D o n a l d (1990), Legett (1990) and others (Fei 1991; Englezos 1992; Hatzikiriakos & Englezos 1993;
SLOAN, E D JR 1998 Physical/chemical properties of gas hydrates and application to world margin stability and climatic change In: HENRIET, J.-P & MIENERT, J (eds) Gas Hydrates: Relevance to World Margin Stability and Climate Change Geological Society, London, Special Publications, 137, 31-50
Trang 332 E.D SLOAN JR
Fig 1 Three unit crystals and their component cavities
Kvenvolden 1993; Cranston 1994; Yakushev
1994; Harvey & Huang 1995) The purpose of
this paper is to review physico-chemical proper-
ties of gas hydrates as applied to world margin
stability and climatic changes
Following this introduction, the second sec-
tion addresses the question 'What are hydrates
and how do they form?' In parallel with this
foundation, the second section also considers
the question, 'What are the physico-chemical
properties of hydrates?' The third section deals with applications of physico-chemical properties
to questions of margin stability and climatic change The third section also provides a brief lit- erature review of methane dissociation from hydrates The fourth and final section deals with some basic research needs The reader may wish to investigate these details further via refer- ences contained in several monographs (Mako- gon 1997; Sloan 1998)
Trang 4PHYSICAL/CHEMICAL PROPERTIES OF GAS HYDRATES 33
What are hydrates and how do they form?
Hydrates normally form in one of three repeating
crystal structures shown in Fig 1 Structure I
(sI), a body-centred cubic structure forms with
small natural gas molecules found in situ in
deep oceans Structure II (sII), a diamond lattice
within a cubic framework, forms when natural
gases or oils contain molecules larger than
ethane but smaller than pentane; sII represents
hydrates which commonly occur in production
and processing conditions, as well as in many
cases of gas seeps from faults in ocean environ-
ments
Physical properties of the newest hydrate
structure H (Ripmeester et al 1987; Mehta &
Sloan 1993, 1994a,b, 1996) are in the initial
stages of description The hexagonal structure
H (sH) has been shown by Ripmeester (1991)
to have cavities large enough to contain
molecules the size of common components of
n a p h t h a and gasoline In addition, Sassen &
M a c D o n a l d (1994) have found one instance of
H y d r a t e crystal structures
Table 1 provides a hydrate structure summary
for the three hydrate unit crystals (sI, sII and
sH) shown in Fig 1 The crystals structures are
given with reference to the water molecule skele-
ton, composed of a basic 'building block' cavity
which has 12 faces with five sides per face (abbre-
viated as 5 ) By linking the vertices of 5 cav-
ities one obtains sI Linking the faces of 512
cavities results in sII In sH a layer of linked 512
cavities connects layers of other cavities
Interstices between the 512 cavities are larger
cavities which contain 12 pentagonal faces and
either two, four or eight hexagonal faces
(denoted as 51262 in sI, 51264 in sII or 51268 in
sH) In addition sH has a cavity with square, pen-
tagonal and hexagonal faces (435663) Figure 1 depicts the four cavities of sI, slI and sH In Fig 1 an oxygen atom is located at the vertex
of each cavity angle; the lines represent hydrogen bonds by which one chemically bonded hydrogen connects to lone pair electrons on a neighbouring oxygen atom
Inside each cavity resides a maximum of one guest molecule, typified by the eight guests asso- ciated with 46 water molecules in sI (21512] 6151262] 46H20), indicating two 512 cavities and six 51262 cavities in sI Similar formulae for slI and sH are (161512] 8151264] 136H20) and (31512] 2[435663] 1 [51268] 34H20), respectively Structure I, a body-centred cubic structure, forms with natural gases containing molecules smaller than propane; consequently sI hydrates
are found in situ in deep oceans with biogenic
gases containing mostly methane, carbon dioxide and hydrogen sulphide Structure II, a diamond lattice within a cubic framework, forms when natural gases or oils contain molecules larger than ethane but smaller than pentane; slI repre- sents hydrates from thermogenic gases Forma- tion of Structure H hydrate requires a small occupant (like methane, nitrogen or carbon diox- ide) for the 512 and 435663 cages, but the molecules in the 51268 cage should be larger than 0.7 nm but smaller than 0.9 nm (e.g methyl- cyclohexane)
F r o m this point onward the review will emphasize sI hydrates which form with biogenic gases As will be shown later, most oceanic hydrates are believed to be of biogenic gas origin, with only anecdotal evidence for thermo- genic gas hydrates
However, slI will also be briefly discussed in case thermogenic hydrates are found in substan-
tial quantities in the future Booth et al (1996) suggests that most in situ hydrates have been
found near faults, so that gas migration path- ways might be available for both biogenic and thermogenic gases
Number of cavities/unit cell 2 6
Average cavity radius (A) 3.95 4.33
20 20 36
34
* Variation in distance of oxygen atoms from the centre of the cage
3- Number of oxygen atoms at the periphery of each cavity
Trang 534 E D SLOAN JR
Time-independent properties resulting f r o m
hydrate crystal structures
In this section three types of properties related to
the foregoing crystal structures are discussed:
mechanical properties; the guest/host size ratio
concept; and how to use the size ratio to qualita-
tively explain phase equilibrium conditions In
this section phase equilibria and the size ratio
are qualitatively shown to explain several ther-
mal properties, and a property summary is pro-
vided for methane hydrates for those who wish
to assume that methane alone is the gas present
in ocean hydrates
Mechanical properties of hydrates As m a y be
calculated via Table 1, if all the cages of each
structure are filled, all three hydrates have the
amazing property of being approximately 85%
(mol) water and 15% gas The fact that the
water content is so high suggests that the
mechanical properties of the three hydrate struc-
tures should be similar to that of ice A compar-
ison of ice with s! and sII hydrate mechanical
properties is shown in Table 2 M a n y mechanical
properties of sH have not been measured to date
Guest~cavity size ratio." a basis for property under-
standing The occupied hydrate cavity is a func-
tion of the size ratio of the guest molecule within
the host cavity To a first approximation, the concept of 'a ball fitting within a ball' is a key
to understanding m a n y hydrate properties After an introduction, the concept is related to phase equilibrium conditions before relating the same concept to thermal properties later in this section
Figure 2 (corrected from von Stackelberg 1949) may be used to illustrate five points regard- ing the guest/cavity size ratio for hydrates formed of a single guest component in either sI
or sII
9 The sizes of stabilizing guest molecules range between 0.35 and 0.75nm Below 0.35rim molecules will not stabilize sI, and above 0.75 nm molecules are too large for slI cav- ities
9 Some molecules are too large to fit the smal- ler cavities of each structure (e.g C2H6 fits in the 51262 of sI; or C3H8 and i-C4H10 each fit the 51264 of slI)
9 Other molecules such as CH4 and N2 are small enough to enter both cavities (denoted
as either 512+ 51262 in sI or 512 + 51264 in slI) when hydrate forms with those single com- ponents Kuhs et al (1996) have recently shown that two N2 molecules can be accom- modated in the 51264 cavity at pressures greater than 0.5 kbar
9 The largest molecules of a gas mixture
Table 2 Comparison of properties of ice and sI and slI hydrates
Linear thermal expansion 200K (K -1) 56 • 10 -6 77 • 10 -6 52 • 10 -6
Adiabatic bulk compression: 273 K (10-11 Pa) 12 14 est 14 est
Speed long sound: 273 K (km -1) 3.8 3.3 3.6
220 58.1
0.4• 0.51•
Modified after Davidson (1983) and Ripmeester et al (1994)
Trang 6PHYSICAL/CHEMICAL PROPERTIES OF GAS HYDRATES 35
512 + 51262 ) S-I
Fig 2 Sizes of hydrate cavities and guest molecules
usually determines the structure formed For
example, because propane and i-butane are
present in m a n y thermogenic natural gases,
they will cause sII, to form In such cases,
methane will distribute in both cavities of
sII and ethane will enter only the 51264
cavity of sII
Molecules which are very close to the
hatched lines separating the cavity sizes
appear to exhibit the most non-stoichiome-
try due to their inability to fit securely within the cavity
Table 3 shows the size ratio o f several c o m m o n gas molecules within each of the four cavities of
sI and sII Note that a size ratio (guest molecule/cavity) of approximately 0.9 is neces- sary for stability of a simple hydrate, indicated
by :~ When the size ratio exceeds unity, the molecule will not fit within the cavity and the
Trang 736 E D SLOAN JR
Table 3 Ratios of molecular diameters* to cavity diameterst for some molecules including natural gas hydrate formers
Molecule Cavity type = >
Guest diameter (,&)
(Molecular diameter) / (cavity diameter) Structure I Structure II
* Molecular diameters obtained from von Stackelberg & Miiller
t Cavity radii from Table I minus 1.4 A water radii
:~ Indicates the cavity occupied by the single hydrate guest
(1954)
structure will not form When the ratio is signifi-
cantly less than 0.9 the molecule cannot lend sig-
nificant stability to the cavity
Consider the single guest ethane, which forms
in the 51262 cavity in sI because ethane is too
large for the small 512 cavities in either structure
and too small to give much stability to the large
51264 cavity in sII Similarly, propane is too
12,4 large to fit any cavity except the 5 6 cavity in
slI, so that gases of pure propane form slI
hydrates from free water On the other hand,
methane's size is sufficient to lend stability to
the 512 cavity in either sI or slI, with a preference
for sI because CH4 lends slightly higher
stability to the 51262 cavity in sI than the 51264
cavity in slI
is plotted against temperature, with gas composi-
tion as a parameter, for methane + propane mix-
tures Consider a gas of any given composition
(marked 0 - 1 0 0 % propane) on a line in Fig 3
At conditions to the right of the line, a gas of
that composition will exist in equilibrium with
liquid water The mutual solubility of the
aqueous and hydrocarbon phases is only a few
parts per thousand The interface is the only
point where the two ingredients are in sufficient
concentrations (85% water, 15% hydrocarbon)
to form hydrates
As the temperature is reduced (or as the pres-
sure is increased) hydrates form from gas and
liquid water at the Fig 3 line for the given gas
composition At that condition three phases
(liquid water + hydrates + gas (Lw + H + V))
will be in equilibrium With further reduction
of temperature (or increase in pressure) the fluid phase which is not in excess (gas in ocean environments) will be exhausted To the left of the line hydrate will exist in two-phase equili- brium with excess water
All of the conditions given in Fig 3 are for temperatures above 273 K and pressures along the lines vary exponentially with temperature Put explicitly, hydrate stability at the three- phase ( L w - H - V ) condition is always much more sensitive to temperature than to pressure Figure 3 also illustrates the dramatic effect of gas composition on hydrate stability; as any amount of propane is added to methane the structure changes (sI ~ sII) to a hydrate with much wider stability conditions Note that at
275 K a 50% decrease in pressure is needed to form sII hydrates, when only 1% propane is in the gas phase, sII forms at higher temperatures than sI
Figure 3 provides a convenient illustration of two common ways to dissociate hydrates By increasing the temperature at constant pressure, the system is moved first to the three-phase line, where dissociation occurs at constant tem- perature and pressure with input of the heat of dissociation Alternatively by decreasing the pressure the system is moved to the three-phase line, so that the temperature is lower than ambi- ent and heat flows to dissociate the hydrate When the hydrate is massive and the initial temperature is close to the ice-point, removal of the heat of formation will cause the temperature
to drop below the 273 K so that any residual water may be converted to ice Yakushev & Isto-
min (1991) and Gudmundssen et al (1994) both
Trang 8PHYSICAL/CHEMICAL PROPERTIES OF GAS HYDRATES 37
ooooo Data of Oeaton + Front ( 1 9 4 6 )
Calculated from CSMHYD
1 0 I i l l i r l l l | l l l i l l l l l l l l | l l l i l l l l l l t l i l l l l
Fig 3 Hydrate formation conditions for mixtures of methane and propane from water and gas
suggest that ice cladding can inhibit further
hydrate dissociation
Any discussion of hydrate phase equilibrium
would be incomplete without remarking that
hydrates provide the most-used case of statistical
thermodynamics to predict phase equilibria by
industry The van der Waals & Platteeuw
(1959) model was formulated after the determi-
nation of sI and sII crystal structures shown in
Fig 1 With this elegant mathematical model,
one may predict the three-phase pressure or tem-
perature of hydrate formation, knowing the gas
composition For further discussion see Sloan
(1998, Chap 5)
properties (heat of dissociation, thermal conduc-
tivity and thermal expansivity) are discussed in
relation to the above size ratio of guest:host
and phase equilibrium conditions
(AHd) is defined as the enthalpy change to dis-
sociate the hydrate phase to a vapour and
aqueous liquid, with values given at temperatures
just above the ice-point The heat effect due to
this phase change is generally much larger than
the sensible heat effect (which uses heat capaci-
ties, Cp) without a phase change
Thermodynamics provide a convenient result
of being able to obtain properties like AHd,
which are difficult to measure, using the easily
measured three-phase lines like those shown in Fig 3, along with the Clausius-Clapeyron equa- tion:
A H d _ zRd(lnP)
where z and R represent the compressibility and the universal gas constant, respectively Equa- tion (1) provides the surprising facility of being able to estimate values from AHd from the slope of the in P vs (l/T) lines
Sloan & Fleyfel (1991) show that to a fair engi- neering approximation (+ 10%) AHd is: (1) a function not only of the hydrogen bonds in the crystal but also of cavity occupation; (2) indepen- dent of guest components; and mixtures of simi- larly-size components, and (3) without an occupant, cavity dissociation is more difficult, resulting in a higher AHd
As one illustration, simple hydrates of C3H8 or i-C4H10 have a similar AHd of 129 and 133 kJmo1-1 (Handa 1986) because they both occupy the 51264 cavity, although their size ratios are somewhat different (0.943 and 0.976) This similarity of AHd is remarkable, but it is due to both the stabilization of the 51264 cavity and the similar hydrogen-bonded water unit cell skeleton
Similar statements could be made about the AHd values for other simple hydrate formers which occupy similar size cavities, such as C2H6
Trang 938 E D SLOAN JR
( A H d = 7 2 k J m o 1 - 1 , Handa 1986) and CO2
( A H d = 7 3 k J m o l , Long 1994) in the 51262
cavity, or CH4 and HzS (AHd within 3% of
each other, Long 1994) which occupy both 512
and 51262 as simple hydrates
As a second illustration, mixtures of C3Hs
+ C H 4 shown in Fig 3 have a value of
AHd = 79 kJ mo1-1 over a wide range of compo-
sition In such mixtures C3H8 occupies most of
the 51264 cavities, while CH4 occupies a small
number of 51264 and many 512 cavities In fact,
most natural gases (which form sII) have similar
values of AHd
The reader should note that Skovborg & Ras-
mussens (1994) concerns about the above
approximation were addressed by Sloan & Fley-
fel (1992), and that the approximations were later
confirmed by Long (1994) and shown to apply to
Structure H by Mehta (1996)
Thermal conductivity Stoll & Bryan (1979) first
measured thermal conductivity of propane
hydrates to be a factor of 5 less than that of ice
(2.23 W m -1 K-l) Cook & Laubitz (1981), Ross
& Andersson (1982), Cook & Leaist (1983) and
Asher (1987) confirmed the low thermal conduc-
tivity of hydrates, as well as similarities of the
values for each structure The thermal conductivity
of the solid hydrate (0.49 W m -1 K -a) more closely
resembles that of liquid water (0.605 W m -1 K 1)
Ross et al (1981) also determined that tetrahy-
drofuran hydrate thermal conductivity was pro-
portionally dependent upon temperature, but
had no pressure dependence Ross & Andersson
(1982) suggested that this behaviour, which had
never before been reported for crystalline organic
materials, was associated with the properties of
glassy solids
In the hydrate lattice structure, the water
molecules are largely restricted from translation
or rotation, but they do vibrate anharmonically
about a fixed position This anharmonicity pro-
vides a mechanism for the scattering of phonons
(which normally transmit energy) providing a
lower thermal conductivity Tse et al (1983b,
1984) and Tse & Klein (1987a) used molecular
dynamics to show that frequencies of the guest
molecule translational and rotational energies
are similar to those of the low frequency lattice
(acoustic) modes
Tse (1994) notes that weak coupling between
the guest and host lattice does not noticeably
affect most structural thermodynamic and
mechanical properties, but such coupling has a
marked effect on the transport of heat As defects
normally serve to decrease any crystal thermal
conductivity, hydrate cavities might be consid-
ered as severe defects which result in anoma-
lously low values of thermal conductivity
Thermal expansion of hydrates Linear thermal
expansion coefficients of hydrate (dl/ldT) for
structures I, II and ice have recently been deter- mined through dilatometry by Roberts et al
(1984) and through X-ray powder diffraction
by Tse et al (1987) The values for sH hydrate
at 200 K have been measured for hexamethy- lethane (HME) and 2,2-dimethylbutane (DMB)
at 150 and 200K by Tse (1990) who noted that cubic expansion values are similar to those of sI and sII, but that there is a difference in the direction of linear expansion for sH At 200K linear thermal expansions are: sI (77 • 10 -1 K-l); sII (52 • 10-6K-1); sH ( a = 6 7 x 10 -6, c = 5 9 x 10-6K -1 for DMB) and ice (a = 56 • 10 -6, c = 57 x 10 -6 K-I)
Through constant pressure molecular dynamic calculations for thermal expansion of ice and of empty structure I, Tse & Klein (1987) determined that the high hydrate thermal expansivity is due
to anharmonic behaviour in the water lattice Tse (1994) suggests that this results from colli- sions of the guest molecule with the cage wall, which exerts an internal pressure to weaken the interaction between the water hydrogen bonds
Summary of physico-chemical properties of methane hydrates In the next section, on 'Appli-
cations to margin stability and climatic changes,
it is argued that most oceanic hydrates are cur- rently assumed to be sI of biogenic methane, due to the anecdotal instances of thermogenic hydrates with significant amounts of propane and higher hydrocarbons While there seems to
be concurrence on this point in the literature, there are several exceptions cited in the Gulf of Mexico and the Caspian Sea
As a summary of the physico-chemical proper- ties, Table 4 provides a listing of the methane hydrates properties which will be of interest in quantifying any exploration, formation or disso- ciation modelling
The modeller will, of course, wish to account for the system fraction which is hydrate, relative
to free gas, water and sediment In the absence of measurements or theory, a linear combination on
a mole fraction basis is usually assumed Handa
& Stupin (1992), Zakrzewski & Handa (1993) and, recently, Bondarev et al (1996) have indi-
cated that the linear approximation is flawed
Kinetics o f formation as related to hydrate crystal structures
The answer to the questions, 'What are hydrates?' and 'Under what condition do hydrates form?' in the previous sections is much
Trang 10PHYSICAL/CHEMICAL PROPERTIES OF GAS HYDRATES 39
Table 4 Selected properties for methane hydrate
Property (unit) Value or correlation
Dissociation pressure (KPa) 1
Heat of dissociation (kJ tool- )
Heat capacity (J K -1 mo1-1) 1 1
more certain than answers to 'How do hydrates
form?' The question of 'Why do hydrates
form?' is not considered The mechanism and
rate (i.e the kinetics) of hydrate formation are
controversial topics at the forefront of current
research
The kinetics of hydrate formation are clearly
divided into three parts: (a) nucleation of a criti-
cal crystal radius, (b) growth of the solid crystal,
and (c) the transport of components to the grow-
ing solid-liquid interface All three kinetic com-
ponents are currently under study, but a
satisfactory answer has not been found to any
of them Skovborg (1993) proposed the most
recent quantitative model, based upon mass
transport as a limiting factor Skovborgs model
was based in part on a re-analysis of the data
measured by Englezos et al (1987a,b) The
latter researchers proposed the best extant crystal
growth model In the current work an hypothesis
is summarize for a nucleation mechanism of
hydrates, based upon the above overview of the
crystal structures
In a series of successively revised mechanisms
for the nucleation hypothesis (Sloan 1990;
Sloan & Fleyfel 1991; Mtiller-Bongartz et al
1992) it has been proposed that clusters at the
interface may grow to achieve a critical radius
as shown schematically in Fig 4 Christiansen
& Sloan (1994) extended the hypothesis model,
with the following elements
9 Pure water exists with many transient, labile
ring structures of pentamers and hexamers
9 Water molecules form labile clusters around
dissolved guest molecules These clusters are
quantified in units of four water molecules as
a function of dissolved guest size range The
number of water molecules in each cluster
shell (i.e the coordination number) for nat-
ural gas components are: methane (20),
ethane (24), propane (28), iso-butane (28),
nitrogen (20), hydrogen sulphide (20) and
carbon dioxide (24)
9 Clusters of dissolved species combine to
form unit cells To form sI, coordination numbers of 20 and 24 are needed for the
512 and the 51262 cavities, respectively; sII requires coordination numbers of 20 and 28 for the 512 and 51264 cavities Nucleation is facilitated if labile clusters are available with both types of coordination numbers for either sI (e.g CH4+C2H6 mixtures)or sII (e.g CH4+C3H8 or most unprocessed natural gases) If the liquid phase has clusters
of only one coordination number, nucleation
is inhibited until the clusters can transform
to the other size, by making and breaking hydrogen bonds
An activation barrier is associated with the cluster transformation If the dissolved gas is methane, the barrier for transforming the cluster coordination number from 20 (for the
512 ) t o 24 (for the 51262 ) is high, both because the guest cannot lend much stability to the larger cavity and because the 51262 cavities outnumber the 512 in sI by a factor of 3 Energy for transformation of m e t h a n e - water clusters from 20 to 28 is higher than that from 20 to 24, because methane is not large enough to stabilize the 51264 cavity
If the dissolved gas is ethane with a water coordination number of 24, the transforma- tion of empty cavities with coordination numbers is likely to be rapid, due to the
12 2 12 high ratio (3:1) of 5 6 to 5 cavities in
sI If the dissolved gas is propane with a coordination number of 28, transformation
to sII is likely to be slow because 51264 cav- ities are outnumbered by the 512 cavities by
a factor of 2
Table 5 shows limited experimental confir- mation of nucleation rate as a function of available labile cavities D a t a in the table were measured at constant pressure differ- ence ( p e x p peq) at 0.5~ and shows that methane and propane have long induction times, while short induction times were obtained for ethane, CH4 + C2H6, CH4 + C3H8, and natural gas mixtures