Mechanical properties of clathrate hydrates: status and perspectives

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Mechanical properties of clathrate hydrates: status and perspectives

Fulong Ning,*a Yibing Yu,b Signe Kjelstrup,cd Thijs J. H. Vlugtd and Kirill Glavatskiye

Received 11th December 2011, Accepted 8th February 2012

DOI: 10.1039/c2ee03435b

Knowledge of the mechanical properties of clathrate hydrates is central for studying the mechanical

properties of hydrate-bearing sediments, their associated applications in wellbore stability, exploitation

in stratum deformation, geological disaster prevention, and risk assessment of CO2 buried in oceans.

However, because of the limited understanding of hydrate formation conditions and limited methods to

investigate these, the understanding of the mechanical properties of hydrates is still poor and even

controversial to some extent. This paper reviews current experimental and theoretical results on

mechanical properties of hydrates, and discusses the typical difficulties faced in this area. On the

experimental side, the most important problem is obtaining pure hydrate samples. Theoretically, the

essential origin of the mechanical properties has not been explained in terms of molecular interactions.

The hope is to resolve these issues by combining novel macroscopic experiments and microscopic

methods. In order to avoid difficulties caused by impurities, it is proposed to use molecular dynamics

simulations. This technique can be used to reveal the nature of the mechanical characteristics of

hydrates at the molecular and nanometre scale. The goals of this paper are to establish a bridge between

the micromechanical nature and the macromechanical properties of hydrates, and to lay a solid

theoretical basis for the study of the mechanical properties of hydrate-bearing sediments. These goals

are important for the future safe and efficient exploitation of natural hydrates, hydrate-induced seabed

geological disaster prevention, the safety of CO2 geological burial, and the deployment of a reliable

long-term seabed-borehole coupled hydrate observation system in the integrated Ocean Drilling

Program.

aFaculty of Engineering, China University of Geosciences, 430074Wuhan,China. E-mail: [email protected]; Fax: +86 2767883507; Tel: +8618963963512bFaculty of Engineering, China University of Geosciences, 430074Wuhan,China. E-mail: [email protected]; Fax: +86 2767883504; Tel:+8613554406012cDepartment of Chemistry, Norwegian University of Science andTechnology, 95362 Trondheim, Norway. E-mail: [email protected]; Fax: +47 73550788; Tel: +47 73594179

dProcess & Energy Laboratory, Delft University of Technology, 2628CADelft, the Netherlands. E-mail: [email protected]; Tel: +31 15(0)2787551eDepartment of Chemistry, Norwegian University of Science andTechnology, 95362 Trondheim, Norway. E-mail: [email protected]; Tel: +47 47244779

Broader context

This paper reviews current experimental and theoretical results on the mechanical behaviour of ‘‘pure’’ clathrate hydrates and sums

up the difficulties faced in this area. Few mechanical properties are reported, and their measurements are difficult, partly because it is

almost impossible to obtain pure hydrate samples. Experimental conditions, types of hydrate formers, residual liquid water, gas or

ice, and micropores in the samples hamper accurate measurements. In order to make further progress in this area, novel experiments

at the macroscopic level and advanced simulation techniques at the molecular scale are urgently required. Molecular interactions are

speculated to affect the hydrates’ mechanical behaviours, in a way different from those of ice. Molecular dynamics (MD) simulations

can be expected to contribute to a better understanding of the mechanical properties of hydrates, especially those of CH4 and CO2

hydrates, as well as the molecular mechanisms for deformation or interaction with sediment grains. We therefore propose to useMD

simulations to bridge the knowledge of macro-mechanical behaviour and of the microscopic properties of clathrate hydrates. The

work provides a solid foundation for future studies of mechanical properties of hydrate-bearing sediments and associated appli-

cations for natural gas hydrate exploitation, and environmental and climate impact studies.

This journal is ª The Royal Society of Chemistry 2012 Energy Environ. Sci., 2012, 5, 6779–6795 | 6779

http://dx.doi.org/10.1039/c2ee03435b






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1. Introduction

Clathrate hydrates (hereinafter referred to as ‘‘hydrates’’) are

non-stoichiometric crystalline inclusion compounds that can be

formed under conditions of low temperatures or high pressures,

both above and below the freezing point of water.1,2 More than

130 guest compounds are known to form hydrates with water

molecules. Typical hydrate-forming molecules are hydrophobic

natural gases such as CH4 and CO2.3 Hydrates are also known as

natural gas hydrates, or simply as hydrates. Their formation

requires relatively low temperature (normally #300 K) and high

pressure ($38 bar at 277 K) conditions.4 There are three

common types of gas hydrate structures: sI hydrate, sII hydrate,

and sH hydrate. Although other structural types such as sT type

and half-clathrate hydrates were reported,5–8 so far they exist

only in the laboratory. In a natural environment gas hydrates are

mainly sI and sII type hydrates. sH type hydrates are also

confirmed to exist in nature, as in the Gulf of Mexico and Cas-

cadia Margin.9,10 In the mid 1960s and early 1980s large reser-

voirs of gas hydrates were found in permafrost and marine areas

respectively,11,12 by an increasing number of governments, as well

as oil and gas companies. This has sparked numerous research

activities from a variety of private and academic research insti-

tutions. The findings are significant as an energy resource, and

their stability needs to be addressed as an environmental and

global change. Methane is an important green-house gas. As

a result, the research on gas hydrates has led to an explosive

growth in publications,4 and the entire research field has

expanded from the initial flow assurance for preventing blocking

of oil and gas pipelines13,14 to resource potential,15–18 safe dril-

ling,19,20 geological hazards,21,22 the carbon cycle,23 climatic

change;24–26 and even outer space hydrates.27,28 Recently, the

National Energy Technology Laboratory (NETL) of the

Department of Energy of the United States has made remarkable

progress in work on rapid formation of gas hydrates.29 This puts

forward an attractive application prospect for hydrate tech-

nology, to be used in natural gas and hydrogen storage and

transportation,30–32 CO2 capture and geological burial,33,34 gas

separation,35 cold-storage,36 and desalination of sea water.37

Probably, people could even make hydrate-based medicine

plasters or pills for treating skin disease or internal illness, for

example gastropathy. To some extent, the activity in gas hydrate

research can be seen as a country’s scientific and technological

ambition to contribute to sustainable development.

In the 21st century, the development of unconventional energy

sources such as natural gas hydrates was given official priority

because of a reduction in the amount of recoverable gas

resources and an increase in power consumption. Countries like

the United States, the United Kingdom, Japan, Canada, Ger-

many, Russia, Norway, South Korea, India and China have

performed extensive hydrate research. In particular, the United

States have implemented a program to begin hydrate exploita-

tion in the Alaska North Slope permafrost region by 2015 and to

start hydrate exploitation in marine areas by 2025.38 Japan has

also developed a plan to realize commercial exploitation of

hydrates by 2018. Brazil, Spain, Nigeria, Chile, Colombia, New

Zealand, and Peru have also expressed strong interest in

hydrates.39 Despite great achievements and progress, three

challenges in the field of hydrate development remain: a poor

6780 | Energy Environ. Sci., 2012, 5, 6779–6795

quantitative reservoir characterization, an immature exploration

and production technology, and a high risk of disrupting

geological formations and harming the environment during

exploitation. This high risk refers to drilling safety during the

process of exploration (such as wellbore instability), geological

disasters, and climate effects. Limited by the formation condi-

tions, hydrates in nature are mainly found in resource-poor,

severe environments without available infrastructure, particu-

larly in deep-water subsea sediments, freezing permafrost, and

some inland lakes.40 In particular, the degree of consolidation of

marine hydrate-bearing sediments is relatively poor.41,42 When

drilling encounters this type of sediment, factors including the

heat generated from the drilling tool friction, the salt in the drilling

fluid, and the pressure changes in the wells, can very soon lead to

decomposition of the hydrates in the sediment. If solid hydrates

act as cement or have a framework support function, the

decomposition will lead to borehole collapse and enlarge the hole.

Besides, the water and gas from hydrate dissociation will increase

the pore pressure,43 resulting in an effective stress reduction

around the borehole. Moreover, the water increases the sediment

water content, weakens the link between the particles, and is

detrimental to the wall stability of the well. Therefore, when

drilling through hydrate-bearing sediments, the borehole insta-

bility problem is relatively prominent and is one of themajor risks

faced during natural gas hydrate exploration via well drilling.44–46

In the production process of gas from hydrates, hydrate dissoci-

ation may induce a variety of geological disasters. Typical

examples of these disasters include sediment deformation, casing

deformation, and production platform collapse.47 In addition,

existing studies have shown that submarine hydrate decomposi-

tion is a key factor that induces submarine slope failure in some of

the continental margins.21,48 Landslides can arise from hydrate

decomposition, which results in submarine rock strength reduc-

tion. Water generated from possible decomposition of hydrate

increases the fluid pressure and reduces the friction among sedi-

ment grains. Therefore, when earthquakewaves, stormwaves, sea

level fluctuations or man-made disturbances occur, the hydrate

zone in the seabed can very well induce subsea landslides or

mudslides. Thus, the understanding of mechanical properties of

hydrate-bearing sediments is important (see Fig. 1).

Many research groups have investigated mechanical properties

of hydrate-bearing sediments. The Winters and Waite group of

the U.S. Geological Survey49–53 has used the Gas Hydrates and

Sediment Testing Laboratories Instrument (GHASTLI) to

conduct studies on mechanical properties of hydrate-bearing

sediments in the permafrost and marine areas, as well as on

synthetic sediments in the laboratory. In addition, the Santa-

marina group of the Georgia Institute of Technology54–57 has

used triaxial measurements to test various mechanical properties

of laboratory-synthesized and ocean hydrate-bearing sediments,

including the bulk modulus, the stress–strain curve, Poisson’s

ratio, the shear strength etc. The Tohidi Group at Heriot-Watt

University in the UK58 has used a triaxial instrument to test the

mechanical properties of hydrate-bearing quartz sand samples. It

was found that the elastic modulus of hydrate-bearing sediments

sharply decreased with hydrate decomposition and generated

a greater transient response. Several scholars in Japan including

Masui,59 Hyodo,60 and Miyazaki61 studied hydrate cores

collected from the Nankai Trough and synthetic methane (CH4)

This journal is ª The Royal Society of Chemistry 2012


Fig. 1 Typical processes connected with the mechanical properties of hydrate-bearing sediments in oceans.

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hydrate-bearing samples. Their results showed that upon an

increase in hydrate saturation, the shear strength and the elas-

ticity modulus of the samples tended to increase. In Canada, Wu

and Grozic62 have focused on the study of CO2 hydrate and

determined the effect of CO2 hydrate decomposition on the

mechanical properties of the sand laden sediments. The results of

these group studies collectively indicate that the mechanical

properties of hydrate-bearing sediments primarily depend on the

hydrate distribution pattern in the sediments, hydrate content,

pore pressure (i.e., effective stress), stress history, and porosity as

well as the particle size of the sediment skeleton and mineral

composition of the sediments. Therein, the hydrate content

reflects the contribution of the mechanical behaviour of pure

hydrates to that of sediments.

Because direct measurements of mechanical properties of pure

hydrates are currently insufficient, the understanding of the

effects of the mechanical properties of hydrates on sediment is

not sufficient.63 When the hydrate can be considered as part of

the solid skeleton of sediments50,56,64,65 or cementation,66 the

mechanical properties of the hydrates themselves play a decisive

role in the mechanical properties of the sediments. Gabitto and

Tsouris67 therefore proposed the following functional relation-

ship between the undrained shear strength of the hydrate-bearing

sediment and the hydrate saturation:

Su ¼ a$s00 þ bqh

�Sh

3

�2(1)

where Su is the undrained shear strength of the hydrate-braring

sediment; a reflects the friction and pore pressure in the sedi-

ments; b is an indication of the hydrate’s ability to contribute to

the strength of the hydrate-bearing sediment; qh is the strength of

pure hydrate; Sh is the hydrate saturation; and 3 is the porosity.

Therefore, knowledge of mechanical properties of hydrates is

essential for an understanding of the mechanical properties of

hydrate-bearing sediments and their mechanical response to

hydrate dissociation.


At the same time, global climate change and extreme weather

have already lead to increasingly serious environmental and

social problems. Large amounts of greenhouse gas emissions

seems to be the origin. Research shows that greenhouse gases,

specifically CO2, generated by human activity affect global

rainfall, leading to extreme weather and induction of floods.68,69

Global warming can eventually lead to submarine CH4 hydrate

decomposition, escape of the dissociated CH4 gas into the

atmosphere, accompanied by geological disasters in the seabed,

while escalating global warming, thereby forming an environ-

mentally detrimental circle.70 Thus, reducing CO2 emissions to

ease the greenhouse effect is important, and CO2 capture and

storage (CCS) is suggested. The necessary storage technology

requires confirmation of the elasticity and mechanical strength of

the generated CO2 hydrate film.71 Similarly, the use of a CO2

replacement method to extract CH4 from marine hydrates72 is

likely to lead to sediment deformation during production20

because of the difference in mechanical properties between CH4

hydrates and CO2 hydrates. In addition, development of hydrate

technology for transport and storage of gas, like the shape and

size of the transportation and storage system, requires informa-

tion on the strength of the solid hydrate.73

In summary, in natural gas hydrate exploitation, industrial

hydrate applications, and environmental and climate impact

studies, the mechanical behaviour of hydrates, especially those of

CH4 and CO2 hydrates, as well as the internal mechanisms of

their deformation and interaction characteristics with the sedi-

ment grains should be fully understood. However, because of the

harsh conditions of hydrate formation and stability, which lead

to difficulties in the determination of mechanical properties of

pure hydrates and to limited data collection and low accuracy,

many aspects of the mechanical properties and deformation

mechanisms of hydrates are still unclear. The purpose of this

perspective is to summarize the current research results on the

mechanical properties of clathrate hydrates, to analyze the state-

of-the-art on this issue, and to point out future research focus

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and directions which can enhance understanding hydrate-

bearing sediments and hydrate technology applications in the

future.

Fig. 2 Apparatus used to study the dilatational wave velocity of

propane hydrate by Stoll and Bryan.74

2. Experimental data

Mechanical properties of hydrates can be obtained directly from

experiments. However, such observations are difficult, because of

stringent thermodynamic conditions for hydrate formation and

stability. The common experimental techniques for character-

ization of mechanical properties must be modified to meet this

challenge. Stable hydrate samples need be synthesized in situ. So

almost all mechanical measurement equipment for hydrates

contains two parts: a hydrate formation unit and a mechanical

measurement unit. The former one builds on principles devel-

oped by Deaton and Frost in 1946. Usually, it includes a pressure

cell or a pressure chamber containing liquid, water or ice,

a pressure and temperature control module (some of them with

a flow control module) and a data acquisition module. The

pressured hydrate formers such as CH4, C2H6, CO2 and so on are

admitted into the chamber through the pressure control module.

The temperature control module makes sure that the hydrate

formers and the liquid water or ice in the pressure chamber can

be synthesized into hydrates under the wanted pressure condi-

tions. Some hydrate formation apparatuses have stirring-com-

pacting devices which can be used to increase the speed of

hydrate formation and compact the synthesized samples. When

the hydrate samples are made, they quickly undergo a conven-

tional measurement to determine their mechanical properties.

2.1 Elastic property test—an indirect method

Some mechanical properties of pure hydrates, or parameters

related to elasticity mechanics such as Young’s modulus, shear

modulus, Poisson’s ratio and so on, were initially obtained for

hydrates from indirect methods like acoustic measurements

following additional calculations. An ultrasonic pulse-trans-

mission method was first used to study the dilatational wave

velocity of propane hydrate by Stoll and Bryan.74 This is illus-

trated in Fig. 2. A pair of acoustic transducers was mounted to

the sidewalls of the pressure chamber to measure wave velocity.

The sending unit was excited by an amplified pulse from a stan-

dard pulse generator, and the receiving unit was coupled directly

to an oscilloscope with a calibrated time base. The resonant

frequency of the transducer was set in the range of 100–500 kHz.

These authors determined that the wave velocity of propane

hydrate, several days (10 days) after compression at constant

temperature (2 �C) and gas pressure (�70 psi), increased from

1418 m s�1 to 2400 m s�1, and no volume change occurred during

this process.74 Therefore, it was believed that diffusion of residual

water and gas molecules in the sample may have led to the

formation and growth bonds among hydrate flakes, indicating

defects in the method of sample production. Helgerud75 sug-

gested that the obtained wave velocity could not be used to assess

the elastic properties of propane hydrate. Following these initial

tests and improved experiments, sonic tests were conducted on

two groups of propane hydrate samples.76 The compressional

wave velocity in the first group of samples above 0 �C was 2050

m s�1, the compressional wave velocity below 0 �C was �3225 m


s�1, and the shear wave velocity was �1675 m s�1. The

compressional wave velocity in the second group of samples

below 0 �C was 3075 m s�1, and the shear wave velocity was 1750

m s�1. Simultaneously, through the measured acoustic velocity

and density of the sample at �16.5 �C, the calculated bulk

modulus and shear modulus were 5.8 GPa and 2.3 GPa,

respectively. When the sample was at �1.1 �C, the volume and

shear modulus were 5.6 GPa and 2.4 GPa, respectively. Later, the

Brillouin spectroscopy technique was used to measure the wave

velocity of CH4 and xenon hydrates.77 The hydrate samples were

polycrystalline and artificially grown at the bottom of a 10 cm

long quartz tube (1.5 mm id, 6.5 mm od). A highly polished

quartz plug was cemented to the bottom of the sample tube to

provide laser beam entry, while the other end of the quartz tube

was flared and ground for pressure sealing to the gas handling

system which permitted a continuous flow of methane (or xenon)

gas and water vapour through the cell. After formation, the

hydrate samples were cooled to �10 �C. Then the Brillouin

spectrometer was used to observed hydrate/ice spectra. The

above measurements provided the ratio of compressional wave

velocity in the hydrate and ice at �10 �C, in which the ratio for

xenon hydrate was 0.76 and CH4 hydrate was 0.88. Then,

according to the average compressional wave velocity of the ice,

the compressional wave velocity of CH4 hydrate was calculated

as 3400 m s�1. Kiefte et al.78 also used Brillouin spectroscopy,

which measured the formation of sI-type hydrates from CH4,

H2S, and SO2 as well as the formation of sII-type hydrates from

C3H8, tetrahydrofuran (THF), Freon, and SF6 for different

temperatures and pressure conditions; the compressional wave

velocities were 3369 m s�1, 3355 m s�1, 3144 m s�1, 3698 m s�1,

3665 m s�1, 3459 m s�1, and 3390 m s�1, respectively. The C3H8

and THF hydrate measurements were inconsistent with the

previously reported measurements of propane and THF hydrate.

The authors concluded that this difference was a result of

insufficiencies in previous studies. Bathe et al.79 also investigated

the elastic behaviour of polycrystalline THF hydrate in the

temperature range 183 to 256 K. An aqueous solution of

THF$17H2O was prepared from THF and distilled water. The

hydrate specimens with flat and parallel faces, 2 cm long, were

obtained by slow freezing of the vigorously shaken mixture (277



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K) in completely filled cylindrical plastic containers with lids at

both ends. Quartz transducers were wrung down onto the spec-

imens. Ultrasonic wave velocity measurements were made by the

pulse echo overlap technique to an absolute accuracy of about �20 m s�1. Their measurements found that the shear wave velocity

of the clathrate had an anomalous increase with the temperature.

A variety of shortcomings in the above describedmeasurements

of hydrate acoustic velocities have been pointed out.75 For

example, the measured samples from Stoll and Bryan74 contained

residual water and propane. The samples that Pandit and King76

measured were actually a mixture of propane hydrates and ice.

Erroneous assumptions were also present in the calculation

methods of Bathe et al.79 Berge et al.80 were never able to produce

a non-porous sample of Freon-11 hydrate. Therefore, their data

cannot be easily used to produce estimates of the elastic moduli of

sII gas hydrate.75 The results of Whiffen et al.77 and Kiefte et al.78

seem to be themost reliable, but relatively few datawere included,

for instance nodata on shearwave velocities.Moreover, itwas not

really known that the wave velocities they measured at ultra high

frequency and short wavelengths were appropriate for macro-

scopic average properties at the well log or seismic scales.75

Afterwards, Waite and Helgerud81 adapted the experimental

method of Stern et al.82,83 to first synthesize a hydrate sample in

a custom-built cylindrical pressure vessel (Fig. 3) and then

compress it so that the porosity of the sample decreased from the

initial 28% to 2% or less. This action reduced the impact of the

porosity and residual gases. Both pressure vessel pistons house

a 1 MHz center-frequency piezo-electric transducer (either P- or

S- wave) used for pulse-transmission wave speed measurements.

Fig. 3 (A) Pressure vessel for hydrate sample preparation. Poly-

crystalline methane hydrate was grown directly in the sample chamber

with a diameter of 25.4 mm, then uniaxially compacted in situ to a length

of about 30 mm. Wave speed measurements were also completed in situ.

The sample length was monitored using a linear conductive plastic (LCP).

(B) Transducer assembly schematic. A 1 MHz center frequency S- or P-

wave transducer was used to measure shear and/or compressional wave

speed throughout the compaction process.81


The measured compressional and shear wave velocities at 277 K

were 3650 m s�1 and 1890 m s�1, respectively, which were used to

calculate Poisson’s ratio, the bulk modulus, the shear modulus

and Young’s modulus of CH4 hydrate. Later, the experimental

method was enhanced further for measuring the CH4 hydrate

and ice acoustic velocity as well as the corresponding elastic

parameters (Poisson’s ratio, bulk modulus, shear modulus and

Young’s modulus).75 These parameter values were used to

simulate the effects of hydrate on the wave velocity of the sedi-

ment. When the pressure was in the 4000–4750 psi range with

a temperature of�5 to 15 �C, the compressional wave velocity of

the fully dense hydrate was smaller than that of fully dense ice,

the shear wave velocity was larger than that of ice, the CH4

hydrate compressional wave velocity and bulk modulus were

smaller than those of ice, and the shear modulus was larger

than that of ice. Overall, it was more difficult to compress

polycrystalline hydrate samples with multiple pores than

polycrystalline ice with multiple pores.

Except the calculations for corresponding elastic mechanical

parameters of hydrates by the acoustic measurements, X-ray

diffraction,84–86 neutron diffraction28,84,87,88 and Raman spectros-

copy85,86method were also used to measure the unit cell volume as

a function of pressure and calculate the corresponding isothermal

bulk modulus BT of hydrates by the definitions as follows:

kT ¼ � 1

V

�vV

vP

�T

;BT ¼ 1=kT (2)

Where kT is the isothermal compressibility coefficient, MPa�1; V

is volume, �A3; P is pressure, MPa; T is temperature, K.

The simplest solution is to use a linear equation of state for eqn

(2). Klapproth et al.84 adopted this method to obtain the

isothermal bulk moduli of hydrogenated and deuterated sI

methane hydrates; about 9.11GPaat 271Kand8.21GPa at 273K

under 60 MPa respectively. The average value of isothermal bulk

moduli within 100 MPa was about 9.03 GPa.89 They also calcu-

lated that the corresponding adiabatic compressibilities were

about 10 GPa and 8.92 GPa. For deuterated sI N2 hydrate, the

calculated bulk modulus between 50 MPa and 250 MPa gas

pressurevariedbetween2.5GPaand4.2GPa, respectively.87These

unusually low values were attributed to the fact that the non-

equilibriumfillingwas inhomogeneous and incomplete.87Thebulk

modulus for sII N2 hydrate was almost constant in the same

pressure range investigated and amounted to about 11.5 GPa,

which was slightly higher than the corresponding bulkmodulus of

ice Ih.87So in their further neutrondiffraction studies,88 the derived

bulkmodulus for deuterated sI and sIIN2 hydratewithin 100MPa

is about 7.9 GPa and 8.6 GPa, respectively.89

A bit complicated solution is to use a fit to Birch–Murnaghan

equation of state90 which derived from eqn (2) to calculate the

isothermal bulk modulus.28,86 The standard Birch–Murnaghan

equation is expressed as follows:

PðVÞ ¼ 3BT

2

��V0

V

�7=3

��V0

V

�5=3��1þ 3

4ðB0

T � 4Þ��

V0

V

�5=3

�1

��

(3)

Where V0 is the phase volume at zero pressure, BT0 is an

additional fitting coefficient. When BT0 ¼ 4, the third-order eqn

(3) becomes the second-order form. Using this solution, the



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calculated isothermal bulk modulus for hydrogenated sI

methane hydrate and Xe hydrate under high pressure conditions

were about 7.4 GPa85 and 9 � 1 GPa,86 respectively, while for

deuterated sI methane hydrate, it was about 9.7 GPa calculated

by Ogienko et al.89 from the original data of Loveday et al.28

Obviously, the measurement methods, different experimental

conditions including temperature, pressure, hydrate sample

compaction, and particle size also affect test results; among

these, the hydrate sample compaction and particle size are the

most influential ones.91 For different temperatures, the

compressional wave velocity of CH4 hydrates samples decreases

with an increase in temperature. The velocity decreased from

3800 m s�1 to 3546 m s�1 and varied greatly in the near freezing

point.92 The compressional wave and shear wave velocities varied

less with temperature in fully dense methane hydrate than it did

in dense ice Ih.75 While the THF hydrate compressional and

shear wave speed measurements showed that when the temper-

ature was increased to 256 K from 183 K, the compressional

wave speed decreased from 3600 m s�1 to 3500 m s�1 and that the

shear wave speed decreased from 1610 m s�1 to 1660 m s�1. It can

be deduced that during the heating process, the adiabatic bulk

modulus decreased from 9.0 to 8.2 GPa, and the Poisson’s ratio

decreased to 0.355 from 0.37.79 In terms of pressure influence, the

shear wave speed of sI-type CH4 hydrates and sII-type CH4–

C2H6 hydrates decreased with an increase in the confining pres-

sure. Its variation with pressure in fully dense methane hydrate

was less than that in fully dense ice Ih. Changes in the

compressional wave speed with pressure were larger than those

reported for ice.75,91 In the pressure range of 9.6–38MPa, with an

increase in pressure, the CH4 hydrate compressional wave speed

increased from 3049 to 3337 m s�1.92 In addition, the shear

modulus of hydrates increased with an increase in axial pressure,

whereas the opposite effect was observed for ice.91 The adiabatic

bulk modulus of the CH4 hydrates had an almost linearly

increasing relationship with increasing pressure.3 In the high-

pressure conditions, the in situ elasticity tests of single crystal

CH4 hydrates showed that the shear wave speed of the CH4

hydrates was very close to that of ice and showed a slight

decrease (2000–1850 m s�1) with an increase in pressure (0.02–0.6

GPa). However, there was a large difference in the compression

wave velocity of the CH4 hydrates compared with that of ice.

When the pressure rose from 0.02 to 0.6 GPa, the compressional

wave speed increased from 3760 to 4000 m s�1.93 Except on wave

speed, the pressure also has a great influence on the bulk

modulus, which is explicitly deduced from eqn (2) and the Birch–

Murnaghan equation. Especially, if the pressure increases more

than 1GPa, structural changes in hydrates will cause the differ-

ence in the bulk moduli.28,85 In addition, the initial density of

hydrate samples synthesized in the laboratory is usually relatively

low. After compaction, the density increases and the compres-

sional wave speed increased accordingly while the attenuation

gradually decreased. When the density increased to 890 kg m�3,

the speed was 3259 m s�1.92 This is because the compaction

process induces bonding between hydrate particles, which results

in an increase in the wave speed. This increase was larger than the

change in wave speed induced by the pure decrease in density,

and the phenomenon was faster in ice than in the hydrate. The

amount of hydrate in the samples also had an impact on the wave

speed. Experiments on Freon hydrates showed that when the


hydrate content in the sample was low, the compressional wave

speed was 1400 m s�1; however, when the hydrate content

reached 68%, the compressional wave speed was 2500 m s�1.80

Table 1 lists an overview of the measurements and calculations

for corresponding elastic mechanical parameters of ice as well as

of sI- and sII-type clathrate hydrates in the existing literature.

Measurements of the mechanical properties of sH-type clathrate

hydrate are very rare at present. Ogienko et al.89 derived the

isothermal bulk modulus of deuterated sH methane hydrate

under high pressure conditions (1.08–2.25 GPa)—about 13.8

GPa—by using the data of Loveday et al.28 Hirai et al.85 obtained

the isothermal bulk modulus of str.A methane hydrate, which

was considered as sH hydrate; it was about 9.8 GPa. These values

were close to those of sI and sII hydrates. It is suggested that the

difference in mechanical properties among different hydrate

structures is less than the difference in mechanical properties

of hydrate and ice. Thus, the mechanical properties of sI- and

sII-type hydrates have served as an approximation to that of

sH-type hydrates in some cases.

2.2 Mechanical strength test—a direct method

It was first believed that the strength of pure hydrates was similar

to that of ice, but higher than that of snow.100 For example, in

studies of the geological storage of CO2, according to the tensile

strength of ice (5 � 105–1.6 � 106 N m�2),101 the mechanical

strength of CO2 hydrate films was approximately 106 N m�2.71

However, because of possible sample impurities, such as the

presence of liquid water and ice in the sample, the formation of

a second ice layer in the compaction/deformation process or an

insufficiency of confining pressure affects the applicability of this

approximate value.3 Later, Stern et al.82,83 proposed to minimize

the impact of residual water and gas by growing aggregates of

pure methane hydrate. Test specimens were grown under static

conditions by combining cold, pressurized CH4 gas with granu-

lated H2O ice which was grown from triply distilled water and

ground to obtain a 180–250 mm grain size distribution, and then

warming the reactants to promote hydrate formation. The

strengths of several methane hydrate specimens prepared by the

above methods were measured in constant-strain-rate tests in

compression, at conditions ranging from temperatures of 140 to

200 K, confining pressures of 50 to 100 MPa, and strain rates

3.5 � 10�4 to 10�6 s�1. The testing apparatus was a 0.6 GPa gas

deformation apparatus shown in Fig. 4. The confining pressure

medium was N2 or He gas. Sample interiors were connected to

room conditions by aid of small-diameter tubing to allow initial

compaction to eliminate porosity. The moving piston compacted

the sample axially against the internal force gauge at a fixed

selected displacement rate. During the experimental process, the

differential force and piston displacement were recorded, cor-

rected for changes from initial cross-sectional area and length to

instantaneous values, and converted to corresponding mechan-

ical parameters by some relationships.83 Their test results showed

that the steady-state strength and yield strength were in the range

of 60 to 102 MPa and 71 to 100 MPa respectively, under the

aforementioned experimental conditions. The strength of CH4

hydrates was near that of ice, but there were significant differ-

ences in their strength and rheology. In the temperature interval

260 # T # 287 K, the strength of CH4 hydrate was much higher



Table 1 Elastic properties of ice, sI hydrate and sII hydrate obtained from experimentsa

Parameters Ice Ih Structure I hydrate Structure II hydrate

Compressional wavespeeds, Vp (m s�1)

3870.1 (253–268 K, 22–33 MPa)(1);3900 � 40 (260 K)(2); 3914–4018(237.5 K, 0–280 MPa)(3); 3940 (247K)(4); 3890 (248 K, 0 MPa)(5);3990(248 K, 210 MPa)(5); 3864 (253–268K, 22.4–32.8 MPa)(6)

3778 (CH4 at 258–288 K, 27.6–62.1MPa)(7); 3400 (CH4 at 263 K)(8); 3650� 50 (CH4 at 277 K, 100 MPa)(2);3766 (CH4 at 253–288 K, 30.5–97.7MPa)(6); 3369 (CH4 at 263 K)(9); 3355(H2S at 268 K)(9); 3144 (SO2 at 268K)(9); 2910 (Xe at 263 K)(9)

3821.8 (CH4 and C2H6 at 253–283 K,30.5–91.6MPa)(6,7); 3513 (THF at 256K)(10); 2400 (C3H8 at 275 K)(11); 3250–2050 (C3H8 at 256.5–275.4 K)(12);3698 (C3H8 at 273 K)

(9); 3665 (THF at273 K)(9); 3459 (Freon-11 at 273 K)(9);3390 (SF6 at 268 K)

(9); 2500 (Freon-11at 275 K)(13);

Shear wavespeeds, Vs (m s� 1)

1949.3 (253–268 K, 22–33 MPa)(1);1970 � 20 (260 K)(2); 1995–1935(237.5 K, 0–280 MPa)(3); 1990 (247K)(4); 1900 (248 K, 0 MPa)(5); 1870(248 K, 210 MPa)(5); 1942.4 (253–268K, 22.4–32.8 MPa)(6)

1963.6 (CH4 at 258–288 K, 27.6–62.1MPa)(7); 1890 � 30 (CH4 at 277 K,100MPa)(2); 1957 (CH4 at 253–288 K,30.5–97.7 MPa)(6)

2001.14 (CH4 and C2H6 at 253–283K, 30.5–91.6 MPa)(6,7); 1663 (THF at256 K)(10); 1675–NA (C3H8 at 256.5–275.4 K)(12); 1890 (THF at 273 K)(9);

Vp/Vs 1.99(14); 1.98 � 0.02 (260 K)(2) 1.92(14); 1.93 � 0.01 (CH4 at 277 K)(2) 1.91(14)

Poisson’s ratio, n 0.3301 (253–268 K, 22–33 MPa)(1);0.33 � 0.01 (260 K)(2); 0.3310(253–268 K, 22.4–32.8 MPa)(6)

0.317 � 0.006 (CH4 at 277 K)(2);0.3151 (CH4 at 253–288 K, 30.5–97.7MPa)(6)

0.31119 (CH4 and C2H6 at 253–283K, 30.5–91.6 MPa)(6,15); 0.355 (THFat 256 K)(10)

Shear modulus,G (GPa)

3.9(14);3.483 (253–268 K, 22.4–32.8MPa)(1); 3.6 � 0.1 (260 K)(2); 3.3 (248K, 0 MPa, 210 MPa)(5); 3.459(253–268 K, 22.4–32.8 MPa)(6)

2.4(14); 3.2 � 0.1(CH4 at 277 K)(2);3.541 (CH4 at 253–288 K, 30.5–97.7MPa)(6)

3.5 (THF at 273 K)(9); 3.6764 (CH4

and C2H6 at 253–283 K, 30.5–91.6MPa)(6); 2.65 (THF at 256 K)(10)

Adiabatic bulkmodulus, BS

9.24–10.59 (237.5 K, 0–280 MPa)(3);8.8(14); 9.084 (253–268 K, 22.4–32.8MPa)(1);9.5 (0 MPa)(5); 10.6 (210MPa)(5);9.07 (253–268 K, 22.4–32.8MPa)(6)

8.39 (CH4 at 253–288 K, 30.5–97.7MPa)(6); 7.7 � 0.2 (CH4 at 277 K)(2);5.6(14); 8.762 (CH4 at 258–288 K,27.6–62.1 MPa)(7); 8.92 (CH4-D2O at273 K, 60 MPa)(16); 10 (CH4 at 271 K,60 MPa)(16); 7.4(CH4)

(19); 9 � 1(Xe)(20)

8.505 (CH4 and C2H6 at 253–283 K,30.5–91.6 MPa)(6)

Isothermal bulkmodulus, BT

8.97–10.28 (237.5 K, 0–280MPa)(3);9.2 (248 K, 0 MPa, 210MPa)(5)

7.1 � 0.3 (CH4 at 277 K)(2); 8.21(CH4-D2O at 273 K, 60 MPa)(16); 9.11(CH4 at 271 K, 60 MPa)(16); 9.7(CH4)

(17); 7.9 (N2 at 273 K)(18);

8.27 (THF at 256 K)(10); 8.5 (THF at273 K)(9); 8.6 (N2 at 273 K)(18); 17.3(O2 at 273 K)

(18); 11.5 (N2 at 273 K)(21)

Adiabatic Young’smodulus (GPa)

9.5 � 0.2 (260 K)(2) 8.5 � 0.2 (CH4 at 277 K)(2) —

Isothermal Young’smodulus (GPa)

9.5 (268 K)(14); 9.1 � 0.3 (260 K)(2) �8.4 (268 K)(14); 7.8 � 0.3 (CH4 at277 K)(2)

7.17 (THF at 256 K)(10); �8.2(268 K)(14)

Adiabatic bulkcompression (Pa)

12 � 10�11 (273 K)(14) �14 � 10�11 (273 K)(14) �14 � 10�11 (273 K)(14)

a (1) (Helgerud et al., 2003. pulse-transmission method, v ¼ 1

2$½ððVp=VsÞ2 � 2Þ=ððVp=VsÞ2 � 1Þ�K ¼ rðVp

2 � 4

3Vs

2Þ;G ¼ rvS2);94 (2) (Waite et al., 2000.

Pulse-transmission method, porosity of H2O ice sample was below 1%, CH4 hydrate sample was below 2%);81 (3) (Gagnon et al., 1987. Brillouinspectroscopy method, the densities of the ice samples were 0.9228–0.9500 g cm�3);95 (4) (Smith and Kishoni, 1986. Pulse-echo method);96 (5) (Shaw,1986. Pulse-transmission method, the density of ice Ih is 0.921 g cm�3 at 0 MPa and 0.941 g cm�3 at 210 MPa);97 (6) (Helgerud et al. 2009. Pulse-transmission method, the density of ice Ih was 0.920–0.923 g cm�3, for the CH4 hydrate 0.924–0.933 g cm�3 and for CH4–C2H6 was 0.917–0.931 gcm�3);91 (7) (Helgerud et al., 2003. Pulse-transmission method);98 (8) (Whiffen et al., 1982. Brillouin spectroscopy method, the cage occupancy ofCH4 hydrate was 90%);77 (9) (Kiefte et al., 1985. The density of H2S hydrate was 1.058 g cm�3, SO2 hydrate was 1.303 g cm�3, Xe hydrate was 1.731g cm�3, C3H8 hydrate was 0.883 g cm�3, THF hydrate was 0.979 g cm�13, Freon-11 hydrate was 1.156 g cm�3, SF6 hydrate was 1.179 g cm�3);78 (10)(Bathe et al., 1984. Ultrasonic method);79 (11) (Stoll and Bryan, 1979. Pulse transmission method);74 (12) (Pandit and King, 1982. Pulse-transmissionmethod, the density of the C3H8 hydrate was 0.85 g cm�3);76 (13) (Berge et al., 1999. Pulse transmission method);80 (14) (Sloan and Koh, 2008);3 (15)(Bylov and Rasmussen, 1997);99 (16) (Klapproth et al., 2003);84 (17) (Loveday et al., 2001);28 (18) (Chazallon and Kuhs, 2002. The isothermal bulkmoduli were deduced from the volume–pressure data by the Birch–Murnaghan equation of state);88 (19) (Hirai et al., 2001);85 (20) (Sanloup et al.,2002);86 (21) (Kuhs et al.,1997).87

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than that of ice. At a temperature just below the freezing point of

water, and at a constant strain rate, the strength of CH4 hydrate

was at least 20 times higher than that of ice, and this difference

increased with decreasing temperature.102 In the compression


deformation process, CH4 hydrates also exhibited monotonic

work hardening (or strain hardening) that continues over more

than 15% strain, whereas H2O ice ordinarily exhibited a strength

maximum before levelling off to steady flow stress, usually within



Fig. 4 Triaxial gas deformation apparatus for methane hydrate. A

confining medium gas (N2 or He) provided pressure for the indium-

jacketed sample within the cylindrical pressure vessel. A sliding piston

moved through dynamic seals from below to impose constant axial

shortening. Hydrate samples were mounted on to a ‘‘venting’’ internal

force gauge permitting sample communication with room pressure and

allowing initial hydrostatic pressurization to eliminate residual porosity

prior to deformation. The gas collection system (shown at top) was

attached during several tests to monitor possible loss of methane gas

during deformation.83

Fig. 6 Stress–strain curves for samples of pure methane hydrate vs. ice,

each tested at 260 K with a confining pressure of 100MPa, at a strain rate

of 3.5 � 10�6 s�1.63

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the first 5–10% of strain (Fig. 5). From X-ray analysis, it was

determined that the CH4 hydrate underwent a process of solid-

state disproportionation or exsolution during deformation at

conditions well within its conventional stability field.82,83 In

addition, Hyodo et al.,103 at Yamaguchi University in Japan,

mixed water and methane under conditions of low temperature

and high pressure (10 �C, 10MPa) to form granular hydrates and

generated an almost pure hydrate sample by compaction

molding. High pressure-low temperature triaxial equipment was

used to measure the compressive strength of the hydrate. This

was carried out, setting strain rates of 0.l% per min, l.0% per min,

temperatures of 5 �C,�5 �C,�30 �C and a confining pressure of

Fig. 5 Stress–strain curves of deformed methane hydrate compared to

polycrystalline H2O ice. While the strengths of the two compounds are

comparable, methane hydrate undergoes systematic strain hardening to

an extreme degree (over 18% strain) while H2O ice typically displays an

ultimate yield strength followed by relaxation to steady-state behaviour.83


0, 4, 6, and 8 MPa. This work gave a push to further develop

measurements of mechanical strength of pure hydrates. Helgerud

et al.75,91 improved the experimental method of Stern et al.83 and

showed that the ability of hydrates to resist axial compression

was higher than that of ice. For example, in Fig. 6, surprisingly,

the strength of CH4 hydrate appears to be nearly 30 times higher

than that of ice.63,104 The mechanical strength of CO2 hydrates

has also been studied. It was found that the mechanical strength

of the CO2 hydrate film was primarily related to the thickness of

the film.71 This behaviour might indicate that the approximation

71 for the mechanical strength of CO2 hydrate film can not fully

reflect or represent the mechanical strength of bulky hydrates due

to scale effects of material mechanics. Furthermore, the strength

of a CO2 hydrate film in CO2-saturated water was higher than the

strength and hardness in CO2-nonsaturated water. A free water

molecule model was used to explain this phenomenon, which

suggested that CO2-saturated water did not have free water

molecules to dissolve CO2 gas. This effect led to the anomalous

mechanical properties of the CO2 hydrate film, i.e., the film

maintained its mechanical properties even after damage in CO2-

saturated water. In addition, when the temperature of CO2

hydrate was below the decomposition temperature, its strength

was 10 times larger than that at lower temperatures. The tensile

strength of the CO2 hydrate film was 1.73 to 2 times larger than

the shear strength.105 In addition to the strength test of poly-

crystalline hydrates, a monocrystalline THF hydrate was also

used for a flexural strength test. The results showed that the stress

increased less when the strain was lower than 0.3 � 10�3 s�1;

however, when the strain exceeded 0.6 � 10�3 s�1, the stress

appeared to have a linearly increasing relationship with the

strain. The strength of the THF hydrate was 0.89–44 MPa, and

the Young’s modulus was 0.36–32 GPa.106

Similarly, it was found that the sample temperature, confining

pressure, and strain rate have important effects on the strength of

pure hydrates. The strength and static shear characteristics of

CH4 hydrates are very sensitive to temperature. Especially when

the sample is applied to a confining pressure, the effect of



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temperature on the strength of CH4 hydrates is clear.107 Under

conditions of high pressure and low temperature, the compres-

sive strength of hydrates and ice increase with decreasing

temperature or increasing confining pressure, and the strength of

the hydrates is stronger than that of ice.103,108 When the experi-

mental conditions are close to hydrate stability boundary

conditions, the compressive strength and shear characteristics are

almost identical to those of ice, and the initial shear modulus of

ice is higher than that of the hydrates. The shear moduli of these

two materials both increase with a decrease in temperature and

an increase in the confining pressure.108 On the other hand, the

secant modulus of CH4 hydrates has a slight tendency to decrease

with increasing confining pressure and is affected greatly by the

strain rate, but not by the temperature. As the strain rate

increases from 0.15 to 1.5%, the modulus increases by 50% to

80%. The stress-strain behaviour is almost not affected by the

confining pressure and temperature in the small strain region

from initial strain up to 1.5%, while the strain rate has

a tremendous influence on the mechanical behaviour at the whole

strain region.109 In addition, the deviatoric stress and the

maximum deviatoric stress increase with a decrease in tempera-

ture and an increase in the strain rate. When the confining

pressure is less than 10 MPa, the deviatoric stress and the

maximum deviatoric stress increase with an increase in the

confining pressure. When the confining pressure reaches 15–20

MPa, the change in the deviatoric stress and the maximum

deviatoric stress with confining pressure is not obvious.107

Fig. 7 Schematic picture of CH4 and CO2 partly filled hydrate as con-

structed in MD simulations of gas hydrates. Oxygen atoms are colored

red, hydrogen atoms are colored white, carbon blue atoms are colored

green, and dashed lines denote hydrogen bonds.

3. Theoretical and molecular data

In general, mechanical experiments of hydrates are time

consuming and costly. Furthermore, experiments on mechanical

properties of hydrates are easily affected by sample purity and

external factors, so the experimental results reported do not

necessarily reflect properties of pure compounds. Therefore,

using theoretical and molecular models to calculate mechanical

properties becomes another option and method for the study of

mechanical behaviour of clathrate hydrates. For example, by

molecular simulation methods, one can easily study pure

compounds. In the simulations, particle trajectories are calcu-

lated by classical mechanics, and analyzed by statistical

mechanics. Thermodynamic properties are obtained from this.

Up to now, theoretical analysis and molecular simulation have

only been used to study the elastic properties of hydrates. Studies

on hydrate strength behaviour are very rarely reported.

Under the assumption that the nature of pure hydrate and ice

Ih were similar, Whalley110 used a theoretical method which

applied the relationship between compressional wave speed,

isothermal compressibility and Poisson’s ratio, combined with

Helmholtz energy to calculate the compressional wave speed of

CH4 hydrate (Vph ¼ 3660 m s�1) and the compressional wave

speed ratio of hydrates and ice (Vph/Vpi), setting some of the

thermophysical properties of gas hydrates to be equal to those of

ice, and others slightly different. The Vph/Vpi value of sI-type

hydrates was 0.939 and that of sII-type hydrates was 0.945.

Later, under the condition of quasiharmonic approximation,

lattice dynamics were used to estimate the moduli of sI methane

hydrate based on a rigorous mechanics-based approach and to

calculate the compressional wave speed of CH4 hydrate at 260 K


as 2490m s�1.111 Whalley’s results were similar to the actual

results, but errors occurred in the calculation.75 Therefore, this

calculation method was amended and extended by Helgerud.75

At 273 K, the corrected ratios of the compressional wave

velocities of the hydrate and ice, Vph/Vpi, for the sI-type and for

the sII-type were 0.976 and 0.961, respectively. This calculation

was then applied to the calculation of the shear wave speed of

pure hydrate.75 Upon further research and the advancement of

molecular modeling technology, the calculation of mechanical

properties of pure hydrates from the initial sound speed calcu-

lation was extended to direct calculation of mechanical param-

eters-like moduli. For example, using a first-principles method,

CH4 hydrate elastic parameters were calculated, the results being

consistent with previous experimental data.112

Another method is molecular dynamics (MD) simulation. It is

a well established computer simulation method for studying

material properties at a molecular level, and a powerful tool

studying relationships of molecular and macroscopic properties.

Molecular force fields are needed as inputs. The method uses

classical Newtonian mechanics to generate typical trajectories of

molecular systems and extract samples to calculate time-average

properties. A direct link is therefore obtained between the

molecular and macroscopic properties. This advantage has

resulted in broad usage of MD simulation in physics, chemistry,

biology, materials science, medicine and other fields. MD simu-

lation has also been applied to study clathrate hydrates since the

1980s113,114 and has been used widely in the field of hydrate

research. There are currently more than 500 articles about this

subject. The rapid progress of modern computer technology has

allowed MD simulations on hydrate systems from the level of

a single cell (contains 46 water molecules)113 to a 90-unit cell

(contains 4140 water molecules),115 and the maximum simulation

time has increased from 30 ps to 5 �ıs.116 So far, MD has been

used to study hydrate formation and decomposition



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mechanisms,117,118 inhibition mechanisms of kinetic inhibitors,119

hydrate crystal dynamics,120 equilibrium and stability,121 thermal

conductivity and thermal expansion,122,123 and hydrogen

storage.124 A breakthrough in the research of mechanism of

hydrate nucleation and growth was made especially by MD

simulations.116,118,125–129 However, studies of the mechanical

properties of hydrates are still rare.

A recent study has been done to investigate mechanical

behaviour of pure hydrates.130 Isotropic NPT and NVT MD

were performed on a supercell of CH4 and CO2 hydrate systems

which consists of 3 � 3 � 3 unit cells (36.09 � 36.09 � 36.09 �A

initial lattice parameters) and has periodic boundary conditions.

A picture of a hydrate partly filled with CH4 and CO2 is illus-

trated in Fig. 7. The compression and thermal expansion of the

CH4 hydrate, the CO2 hydrate, and mixtures with different ratios

of the two hydrates were studied. The calculated bulk modulus of

CH4 hydrate was about 9.5 GPa for 271.15 K and 10MPa, which

is close to the experimental value under these conditions,

approximately 9.03 Gpa.84 The inverse of the bulk modulus, the

isothermal compressibility of CO2 hydrates, is given in Fig. 8 for

the same temperature and a pressure range of 0 to 100 MPa. The

Fig. 8 The isothermal compressibility coefficient (kT) of methane and

CO2 hydrate as a function of pressure range of 10–100 MPa at 271.15 K

and 153 K.130 The values of lines were plotted by numerical differentia-

tion according to the eqn (2). The values of the isothermal compressibility

were obtained by computing volume fluctuations in NPT ensemble

according to the definition kT ¼ (kT<V>)�1$(<V2>�<V>2),157 where k is

the Boltzmann constant; T is temperature; V is volume. The bulk

modulus of the hydrate was calculated from BT ¼ 1/kT.

Table 2 Elastic properties of pure hydrate by theoretical calculationa,b

Structuretype

Poisson’sratio, n

Compressionalwave speedsVp(m s�1)

Shear wavespeedsVs(m s�1)

Rwhy

I 0.2776(1) 3756(2); 2490(3); 3981(1) 2209(1) 0.II 0.32(4) — — 0.

a (1) (Miranda andMatsuoka, 2008. Cage occupancy was 100%, T¼ 0 K)112; (and Vpi ¼ 4000 m s�1 110; (3) (Shpakov et al., 1998. Cage occupancy was 100%K)75; (5) (Ning et al., 2011. Cage occupancy was 100%,T¼ 271.15 K)130. b Themeasured and calculated can be found in the corresponding references.


modulus varied between 8.5 and 9.1 GPa. With an increase in the

amount of CO2, the bulk modulus of the mixed hydrate

decreased significantly (see Fig. 8). These variations should be

taken into account during methane recovery from methane

hydrates in deep oceans by replacing methane with CO2.

Table 2 shows current theoretical and molecular calculation

results of the mechanical parameters of pure clathrate hydrate.

4. Discussions and perspectives

On the basis of the above analysis of experimental and compu-

tational results, we shall point at directions for future research,

which can add presently missing knowledge.

4.1 The essential causes of the differences in mechanical

properties between hydrate and ice

The hydrogen bonding properties of hydrates and ice are similar,

i.e., the hydrogen bond lengths (1% larger for hydrates than for

ice) and the oxygen bond angles (3.5� larger for hydrates than for

ice) are similar.63 When the cages formed by water molecules in

a hydrate are fully filled with gas molecules, the hydrate will

contain 85 mol % water and 15 mol % gas.3 This makes it is easy

to compare mechanical properties of hydrates to those of ice. For

example, the Poisson ratios of hydrate and ice are almost iden-

tical,131,132 and the compressional and shear wave velocities of the

hydrate and ice are also similar.91 However, as shown in Table 1

and in the aforementioned experimental studies, the elastic

mechanical parameters of pure hydrate and ice show larger

differences in shear, volume and Young’s moduli. Results for

pure hydrates are then significantly smaller than those of ice.

Under different experimental conditions, especially under

different temperature conditions, the mechanical strength and

shear properties of pure hydrate and ice are significantly

different.82,83 While under extremely high-pressure conditions

(over 1 Gpa), gas hydrates will have structural transitions from

hydrate phases to the relatively dense ice phases.28,133,134 This

behaviour also probably suggests that in essence the hydrates

and ice are different under the most industrial operations and

natural conditions. In addition, the hydrate appears to be

isotropically elastic, unlike ice.3 Therefore, the traditional use of

ice as a reference for mechanical properties of pure clathrate

hydrate is actually incorrect.102 Sloan3 provided two key reasons

for the obvious differences between the mechanical properties of

CH4 hydrate and ice. The first reason was that under the same

stress conditions, the diffusion of water molecules is lower in the

atio of compressionalave speeds in gasdrate and ice, Vph/Vpi

Bulk modulus,B (GPa)

Shearmodulus,G (GPa)

Young’smodulus(GPa)

939(2); 0.976(4) 8.3(1); 8.5–9.5(5) 4.3(1) 11.07(1)

945(2); 0.961(4) — — —

2) (Whalley, 1980). The value was calculated according toVph/Vpi¼ 0.939, T ¼ 260 K)111; (4) (Helgerud, 2001. Cage occupancy was 100%, T ¼ 273detailed temperature and pressure conditions under which these data were



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hydrate than in ice by nearly two orders of magnitude. The

second reason was that the sI-type hydrate cell unit is almost

twice the magnitude of that of ice. These explanations have not

yet been confirmed by experiments or simulations, however. So

far, the essential mechanism for the difference in the mechanical

properties of hydrate and ice is still not so clear.

As shown in Table 1, according to studies by Pandit and

King76 and Kiefte,78 the elastic properties of hydrates with

different structures are different (sI-type and sII-type). For

example, the compressional wave speed value was found to

significantly depend on the composition of hydrates and the cage

occupancy.3 Moreover, lattice dynamics calculations also

showed that the adiabatic elastic modulus of the CH4 hydrate

was higher than that of the hypothetical empty hydrate cavity.111

In addition, the guest molecules also have a significant effect on

the mechanical properties of the clathrate hydrate.63 For

example, the film strength of CO2 hydrates does not increase with

decreasing temperature, which is in contrast with the perfor-

mance of the CH4 hydrate. When Kiefte et al.78 found that the

experimentally measured compressional wave speed was lower

than the value theoretically predicted by Whalley,110 they

attributed the difference to the absence of interaction between

the host cages and the guest molecules. Inspired by these results,

we can speculate that the special hydrate lattice structure, the

interactions among the host molecules in the lattice, the guest

molecules, and the host–guest molecules are the underlying

reasons for the differences in the mechanical properties of the

hydrates and the ice. In particular, the host–guest molecule

interaction is likely to affect the elasticity and the mechanical

strength of the hydrates. This speculation compares well with

explanations for the differences in thermal conductivity and

thermal expansion between hydrate and ice135–137 as revealed by

molecular simulation138,139 and various experiments.140–142 In

addition, studies of the relationship among the compressive

strength, temperature, confining pressure and density of CH4

hydrates have revealed that the compressive strength increases

with decrease in temperature, increase in confining pressure and

increase in density. However, for ice, even if the compressive

strength increases with decreases in temperature and increases in

the confining pressure at low density, its dependence on

temperature and confining pressure is less pronounced at high

density.143 This behaviour may support another viewpoint, that

the lattice structure of the hydrate and the host–guest molecular

interactions are the major reasons for the differences in

mechanical characteristics of hydrate and ice at high density.

Under high density conditions, the crystal characteristics of the

hydrate play a decisive role. However, no current research

directly confirms this speculation on the essential cause for the

differences in the mechanical properties of the hydrate and ice.

There are also few studies on the effects of cage occupancy,

particularly the effects of empty cages or different guest mole-

cules, on the mechanical properties of pure clathrate hydrate. We

therefore conclude that the study of the mechanical properties of

hydrates will benefit from investigations on the molecular scale.

4.2 Effects of the samples

We have discussed above that the measured mechanical prop-

erties of pure hydrate are affected by external factors such as the


confining pressure, strain rate, temperature of sample as well as

internal factors such as sample density, residual water, gas, or ice

and micropores inside the sample. To obtain uniform samples of

pure hydrate is very difficult. In most cases, synthetic samples of

hydrates are polycrystalline and impure. For example, the

sample used in propane hydrate experiments was a mixture of

propane hydrate and ice.76 It was not possible to obtain a 100%

non-porous hydrate sample in the study of the mechanical

properties of Freon (Freon-11) hydrate.80 During the hydrate

formation process, the presence of residual gas144 led to multiple

micropores in the samples. The diameter of these pores was 100–

500 nm, sometimes even 1 mm.145 The pore sizes of the CH4, Ar,

and N2 hydrates were between 100–400 nmwith a pore volume of

25–40%, and the pore size of the CO2 hydrates was 20–100 nm

with a pore volume of 10–20%.145 Other researchers synthesized

CH4 hydrate samples with 20–70 mm average grain diameters and

�20% intergranular porosity.146 Obviously, the presence of

micropores may have a great influence on certain macroscopic

physical properties.127,145 Although the experimental method of

Stern et al.82,83,104 can possibly minimize the effects of ice, residual

water or gas, the size of the ice powder particles in the experiment

will still have an impact on the formation of hydrates. In addi-

tion, during the measurements of mechanical properties, hydrate

decomposition may occur, and ice may be regenerated. An X-ray

analysis of the deformed samples revealed that ice encompassed

about 25% of the sample volume,83 which also has a great impact

on the experimental results. Although Helgerud made a signifi-

cant improvement on the experimental method of Stern et al.,75

the effects of micropores were not eliminated.

Another question regarding samples is the use of THF hydrate

as an analogue for gas hydrates in studies of mechanical prop-

erties. THF hydrate can form clathrate hydrate rapidly and

uniformly, without gas in the formation.147 In addition, because

the THF hydrate under normal temperature and pressure is more

stable than the CH4 hydrate, conventional equipment can be

used for experimental studies.56,65,148,149 Thus, THF hydrate is

often used as an alternative to study the mechanical properties of

pure hydrates including CH4 and CO2. Although the structures

of CH4 hydrate (sI-type) and THF hydrate (sII-type) are

different, some researchers still think that the two have similar-

ities in mechanical properties.147 However, the use of THF

hydrate as a substitute for CH4 hydrate research has been

debated.150

Another factor is the grain size. A field-obtained hydrate grain

diameter is typically 300–600 mm, while the average indoor

synthetic hydrate particle diameter is approximately 40 mm.151,152

Therefore, the feasibility of using a synthetic hydrate to extrap-

olate mechanical properties of hydrates in nature is also an issue

worth studying.

4.3 Perspectives

Although much progress has been made by combining experi-

mental and theoretical methods in the study of mechanical

properties of pure hydrates, we are still far from a precise

determination of mechanical parameters and a corresponding

extension and application to hydrate-bearing sediments. A major

issue is whether the experimental and theoretical results truly

reflect intrinsic mechanical properties of the pure hydrates, given



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the difficulty in obtaining a well defined sample. On the other

hand, evidence keeps accumulating, pointing at a difference in

mechanical properties of hydrate and ice. If valid, the essential

question on their underlying cause remains open. Clearly better

techniques are needed for further studies on the macroscopic

level. It will also be helpful to investigate mechanical properties

of hydrates and ice at a microscopic or molecular level.

Hydrate formation and growth is a stochastic process from

a non-equilibrium to an equilibrium state, a process controlled

by heat and mass transfer. The growth is largely affected by

ambient conditions and has high randomness, high likelihood of

residual water or gas presence. This fact also suggests obtaining

uniform pure hydrates is almost impossible under present tech-

nology conditions. Reducing the effect of residual water, gas and

micropores as much as possible is always one of many hard

efforts in mechanical measurement of hydrates. A promising

emerging macroscale technique, which may improve the

production of samples, and give larger size and defect-free

hydrate samples, are hydrate film or membrane studies. This

innovative technique is used for instance to measure the hydrate

film or membrane strength71,105 or the friction force of hydrate

film or membrane. Perhaps rapid and continuous hydrate

formation techniques developed by National Energy Technology

Laboratory (NETL)29 can also be used to form a hydrate shell or

ball via a water droplet and measure mechanical properties

without having samples of conventional cylindrical shapes and

sizes. The idea is simply illustrated in Fig. 9.

Although at present nanoindentation and atomic force

microscopy (AFM) can be used to measure the micro-mechanical

properties of many materials, the observations and measure-

ments of hydrate micro-mechanical behaviour are still great

challenges because of rigorous hydrate stability conditions.

Therefore, it is necessary to find new ways to compensate for the

limitations and supplement experimental studies.

According to Section 3 above, we expect that MD can eluci-

date mechanical properties of hydrates in many ways. As

Fig. 9 Simple schematic diagram of proposal for mechanical test of

approximate pure hydrate shell or small hydrate ball. The small hydrate

shell or ball can be formed by the rapid and continuous hydrate forma-

tion techniques developed by NETL.29 For the hydrate shell, its

mechanical parameters are functional dependence on shell thickness d.

When d is equal to the diameter of sphere, the shell becomes the hydrate

ball. By applying tensile or stress, we can measure breaking strength of

the shell and ball, and compare the differences in mechanical behaviour

between the shell and ball. Then probably we can find the effect of

residual water on mechanical properties of hydrates, even study the

friction force between hydrate grains and sediment matrix by this way.


illustrated in Fig. 7, the hydrate can be studied under conditions

of compression and tension (F) to identify the effects of host–

host and host–guest molecular interactions, as well as changes in

the ratio of guest molecules to water cavities. The mechanical

properties of the hydrate itself can be studied and compared to

the properties of ice under the same conditions. From our first

experience130 we therefore suggest that:

1) Stress–strain curves of simple hydrate structures (sI, sII

and sH) are used under full and partial occupancy conditions to

find mechanical parameters such as elastic modulus, tensile

strength, shear strength, and Poisson’s ratio can be obtained in

a controlled manner. The observations can be linked to the

effects of temperature, pressure. Important is to understand the

hydrate deformation and destructive mechanism. Examples of

relevant questions are: how many stages can one divide the

process of hydrate deformation and destruction? Are the stages

of an elastic, plastic or mixed type? Which are the accompanying

changes in structure and shape in the large and small cages? How

flexible are the hydrogen bonds during the tension and

compression process? What are the effects of guest molecules on

cage deformation under the conditions of compression and

tension?

MD simulations are well suited to answer these questions,

which all are important in understanding the mechanical nature

of hydrate crystals, their similarities or differences with the

properties of ice. In addition, stable CH4 hydrates naturally

contain about 5% to 10% empty cages,3 one may also ask: What

is the importance of these empty cages in the mechanical defor-

mation process? Current and future focus on the stress–strain

characteristics of hydrates in the presence and absence of empty

cages, will give information on the shape and structural changes

of empty cages under the conditions of tension and compression.

The role of empty cages in natural gas hydrates for the stability

can then be revealed.

2) Present studies on mechanical properties of pure hydrate

mainly focus on simple hydrates, while studies on multiple mixed

hydrates are rare. It is known from studies of exploitation of

marine hydrates, that CO2 molecules cannot completely replace

the CH4 molecules.153 Therefore, during the replacement process,

the ratio of CH4 and CO2 varies in the hydrate crystal cages.

After replacement, the reservoir contains a mixture hydrates with

the two types of guest molecules, i.e., binary hydrates. In addi-

tion, theoretically, CO2 molecules can only occupy the large cage

of sI-type hydrates, which was also observed experimentally.154

However, some experiments155,156 show that CO2 molecules can

occupy the small cage. It may be speculated that this phenom-

enon is due to the elastic behaviour of C–O bond of CO2 being

larger than that of the hydrogen bond of hydrate cages under low

temperature and high pressure compression condition, which

cause the CO2 molecules staying in the small cages.130 Therefore,

further studies should be conducted to find i.e. the critical

temperatures and pressures for small cage CO2 occupancy. The

stress and strain characteristics of the mixtures of different CH4

and CO2 hydrate ratios could also be determined at different

temperatures, pressure, and load rates under the conditions of

small cage occupancy and no small cage occupancy.

3) In Section 4.2 above, we have seen that the residual

gas144 and water has an important impact via micropores on

the physical properties of the pure hydrates,127 especially the



Fig. 10 Schematic illustration of studies of the effect of micropores, residual water and gas on mechanical properties of hydrates usingMD simulations.

One end of the simulation box will be fixed, and the other end will be applied tensile or stress F.

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elastic–plastic mechanic properties. But the exact mechanism of

how the micropores affect these properties is not very clear. MD

can probably be used to elucidate questions like the following

(Fig. 10): Under tensile and compressive conditions, how is the

distortion of the crystal lattice and stress distribution around

Fig. 11 Schematic diagram of MD simulation on the interaction between

between hydrate grain and sand grain will be filled by a dissociated water fi

destroyed by the external dynamic process for example global warming. We c

system during hydrate dissociation process. Similarly, one end of simulation bo

up of SiO2 molecules. The fixed end is heated to stimulate the hydrate dissoc


the micropores? What are the differences of the deformation

and destructive mechanisms in the presence and absence of

micropores? What is the role of excess water and gas in

micropores? In addition, the residual water or gas also affects

the mechanical properties of the hydrate.3 Because hydrates are

hydrates and sediment matrix (for example, sand grains). The interface

lm containing dissociated gas when the condition of hydrate stability is

an use the MD simulation to investigate the mechanical response of this

x is fixed and another end is applied stress. The sand grain can be is made

iation.



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hydrophilic, water molecules in the micropores will adsorb on

the internal surface of micropores. The residual gas can also

adsorb on the internal surface. The adsorption effect is like the

behaviour of shale gas or coalbed methane in the reservoirs,

which influences the mechanical properties of the hydrate.

Using MD simulation, the effects of residual water, gas,

micropore size on mechanical properties of hydrate can be

analyzed through stress–strain curves at certain temperature

and pressure conditions. The intrinsic mechanism of the effects

may be revealed, especially the hydrate crystal deformation

around the micropores and the water or gas adsorption in the

micropores.

4) The mechanical properties of the contact interface between

hydrates and sediment matrix under static and dynamic loading

conditions are key properties related to drilling and production

safety issues. The hydrates in the sediment are compressed or

separated from the matrix and even decomposed because of

overlying static loading (sediments or seawater) or seismic waves,

storms, sea level fluctuations or man-made wave disturbances

(dynamic loading), which changes the contact property between

the hydrate and sediment grains. This phenomenon in turn

changes the mechanical properties of the hydrate-bearing sedi-

ment and affects the stability of the sediment. With the use of

MD simulations one can probably also obtain mechanical

characteristics of the contact interface between hydrates and

sediment grains (e.g., sand grains) during the compression,

separation or dissociation process. The effects of hydrate disso-

ciation on the mechanical properties of sediment near the contact

interface may be elucidated from stress–strain and energy load

curves under the static and dynamic loading conditions are for

instance interesting (Fig. 11).

MD simulation is known as a powerful tool to probe the

molecular/atomic scale, but it has not yet been feasible to simu-

late micrometer performance. Systems on this scale will sharply

increase the computing time beyond present possibilities. An

issue is thus whether it is at all feasible to capture the essence of

a system with micropores with present day techniques. The

mechanical properties of the hydrate may vary with the crystal

planes, {100}, {111} and {111}. The predictive power of MDs

depends of course on the intermolecular potential models used.

For quantitative predictions, MD results need be validated with

experimental results. A variety of tools: CT, AFM, Raman

spectroscopy, nanoindentation etc. could be used for continued

progress in this field.

5. Summary

In recent times, energy shortage, global warming and natural

disasters have caused worldwide concern. Because of their

energy potential and environmental impact, gas hydrates,

especially CH4 and CO2 hydrates, have become a popular area

of research. The mechanical properties are basic physical

properties of hydrates. It sets the foundation for studying

mechanical properties of hydrate-bearing sediments, it has

a clear connection to studies of wellbore stability, exploitation

of stratum deformation, geological disaster prevention, and risk

assessment of submarine-buried CO2. The studies presented of

mechanical properties of hydrates, have focused on the

macroscopic elasticity and strength measurements, comparing


these properties to those of ice. It has not yet been possible to

involve much macroscopic plasticity and micro-mechanical

behaviour in the data interpretation. In order to make further

progress, the accuracy of current macroscopic experimental

techniques need to be improved and novel experiments at the

macroscopic level are urgently required. Experiments on the

macroscale are, however, restricted by experimental conditions

(such as low temperature and high pressure) and impurity of

samples (such as liquid water, gas, ice or micropores). Also,

although many comparative studies on the mechanics of

hydrates and ice have been conducted, the essential causes of

the differences in the mechanical of hydrate and ice are still

partly unclear. For example, the stability mechanisms of empty

cages in hydrate, the conformational changes of empty cages

and non-empty cages under the tensile and compressive

conditions and the effect of molecular interaction of host

molecules and guest molecules on the mechanical properties of

hydrates need to be evaluated. The mechanical properties of

mixed hydrates, especially those of CH4 and CO2 hydrate

mixtures, the residual water or gas, the micropores and the

interface between hydrates and sediment grains, are also seldom

discussed.

In this context, molecular dynamics simulation techniques

may prove invaluable for obtaining molecular understanding or

the origin of such properties, and for establishing a bridge

between the microscopic nature and macro-mechanical behav-

iour. In this work we have argued that such efforts should be

undertaken to aid in establishing a solid theoretical basis for

the research on mechanical properties of hydrate bearing

sediment.

Acknowledgements

The authors would like to sincerely thank Dr E. D. Sloan, Dr

Carolyn A. Koh and Dr Amadeu K. Sum for kind and valuable

discussions at the 241st ACS meeting and 7th ICGH. We are

grateful for financial support from the Norwegian Programme

for Research Cooperation with China (CHINOR) (No.208502)

and the Statoil VISTA and Anders Jahres Fonds. This work was

partly supported by the National Natural Science Foundation of

China (No.50704028, 40974071), the Natural Science Founda-

tion of Hubei Province (No. 2010CDA056) and the Funda-

mental Research Funds for the Central Universities (No.

CUGL100410).

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Mechanical properties of clathrate hydrates: status and perspectives

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