Mechanical Properties of Methane & Propane Hydrate

The problem is to estimate the elastic and plastic properties of a hydrocarbon-water hydrate deposit forming in a condensate pump at approx 1100psi, 55oF (13oC). The particular mixture of methane and propane is stable at 635psi, 63.5oF (44bar, 17.5oC).

Estimation of mechanical properties is attempted using Prof.Ashby's "Isomechanical Classes of Materials" technique whereby:

  1. Materials are grouped by bond-type (and length) and crystal structure into classes (e.g. fluorite-structured transition metal oxides)

  2. The parameters that control the mechanisms of plasticity for each material are normalised in a physically-sensible manner (e.g. stress/shear-modulus, or activation-energy/R.melting-temperature)

  3. Within each class the normalised parameters have very similar values, and the mean values can be used as a good estimate of the properties of other materials of the same class for which detailed measurements are not available, e.g.(Tm/GoK).dG/dT below.

This is described in Ch.18 of Frost & Ashby's "Deformation Mechanism Maps", Pergamon Press, 1982.

Thermophysical Properties

For the structure II hydrates, with approx. 18 moles of water per propane molecule, the bond-type and length is almost identical to that of water-ice, i.e. it is hydrogen-bonded. The strength of hydrogen bonds are weakly dependent on bond-orientation, so several different crystal structures are possible for water-ice. However, ice I, II and III have broadly similar mechanical properties so it appears that the detailed crystal structure does not have a great effect on the strength of the material.

Thus it appears very likely that the hydrates fall into the same isomechanical class as water-ice because the bonding is very similar, although the crystal structure is different. The density of hydrate at 0.78 x 10-3 kg/cm3 is low compared to that of water ice so it is to be expected that the elastic properties will be similarly reduced, simply on a basis of the number of H- bonds per unit volume. Therefore it seems sensible to estimate the fundamental elastic moduli of hydrate to be 78% of that of ice.

(A few of the carbon atoms of the hydrocarbon might participate in H-bonding, so some of this reduction in density may be due to the different atomic masses of carbon and oxygen, at most (17.9+3)*16 to (17.9*16 + 3*12), i.e. propane-hydrate is 96% the mass it would be if the carbons were replaced by oxygens, so this effect is insignificant.)

The normalised parameter which is most useful in correlating the mechanical properties of materials in the same class is the melting temperature. There is no melting data available for hydrate, only decomposition data. An alternative normalision can be obtained from the energy of formation divided by the gas constant R, the result of which has dimensions of temperature:

Heat of Formation

water 188.0 kJ/mol

hydrate 195.3 kJ/mol (188 + 7.54)

Hf/R

water 22.62 K

hydrate 23.50 K

This also leads to a first-guess estimate of a melting point for the hydrate of 10.6oC, we know this is too low since it must be above the measured decomposition temperature of 17.5oC, but it is reassuringly close, evidence that ice and hydrate are in fact iso-mechanically similar.

The shear modulus of water ice at OoK is 4.04 GPa. The modulus drops approximately linearly with temperature at a rate of 3.75 x10-3 GPa.K-1, so the shear modulus at the melting point (273 K) is 3.01 GPa (extrapolating to 300K would make it 2.91 GPa). The important normalised parameter is the dimensionless rate of modulus decrease: (Tm/GoK).dG/dT which for ice is -0.254.

If we take the 0oK shear modulus for hydrate to be 78% of 4.04 GPa we get 3.15 GPa at 0 K. Using the same rate of modulus decrease: (Tm/GoK).dG/dT) of -0.254, and using a melting point of 18oC (291K), we get a shear modulus at 13oC of 2.36 GPa. However an ounce of experiment is worth a ton of theory and this value should be treated as the gross estimate that it is.

(On the phone I just quoted the extrapolated 300K value for water-ice of 2.91 GPa.)

Plasticity Properties

The important thing about ice, and by extrapolation hydrates, is that it is immensely strong, much stronger at temperatures close its melting point than any other class of material (strength being considered normalised with respect to the moduli). Ice also has a plasticity mechanism not found in any other material: dislocation glide controlled by proton-hopping. However this high strength should not blind us to the fact that we are dealing with a material at over 90% of its melting point and that therefore its strength is strongly affected by thermal activation and hence extremely time-dependent.

It is difficult to measure the elastic moduli except by ultrasonic methods, any slowly applied stress just causes the material to creep. Conventional mechanical testing machines are usually used to impose strain rates of about 0.001 per second, "quasistatic" strengths (at 10-6/s) will be perhaps only 20% of the testing-machine measured strength. Wang's data gives approx. 4.7 MPa dropping to around 1 MPa for quasistatic loading. Conversely, a very rapid explosive shock (about 100/s) will "see" a much higher strength, perhaps a factor of 10 higher (see Goodman, Frost & Ashby's paper). Thus the slow buildup of a deposit will be dominated by the "slow" strength, but a pre-existing plug could withstand a much higher pressure for a very short period of time.

These strengths for ice could be crudely scaled by the ratio of the shear moduli for ice and hydrate, i.e. hydrate would be only about 80% as strong. Clearly the scatter and the rate-dependence of the data for ice mean that estimates of strength could be at best within a factor of 3 of the real values.

Philip Sargent
February 3rd 1989

To: Dr. John E. Arregger
J.E.Arregger & Co. Ltd.
16A King Street
Twickenham TW1 3SN

(01)-891-1242

enc.

Ch18 of Frost & Ashby,
Acta Met. 43 665-695, Goodman, Frost & Ashby
short paper by Sinha
1 page from Wang 1982.