ESTIMATING THE IN SITU MECHANICAL PROPERTIES OF SEDIMENTS CONTAINING GAS HYDRATES

Richard Birchwood∗∗∗∗, Rishi Singh, and Ali Mese Schlumberger

1325 South Dairy Ashford Road Houston, Texas 77077

U.S.A.

ABSTRACT Estimating the in situ mechanical properties of sediments containing gas hydrates from seismic or log data is essential for evaluating the risks posed by mechanical failure during drilling, completions, and producing operations. In this paper, a method is presented for constructing correlations between the mechanical properties of gas hydrate bearing sediments and geophysical data. A theory based on micromechanics models was used to guide the selection of parameters that govern the physical behavior of sediments. A set of nondimensionalized relations between elastoplastic properties and those that could be inferred from log or seismic data was derived. Using these relations, a correlation for the Young’s modulus was constructed for sands with methane and THF hydrate using data from a wide variety of sources. It was observed that the correlation did not fit data obtained from samples with high THF hydrate saturations, due possibly to the existence of cohesive mechanisms that operate in such regimes.

Keywords: gas hydrates, mechanical properties, geomechanical properties, Young’s Modulus, elastoplastic, micromechanics, correlation, wellbore stability

∗ Corresponding author: Phone: +1 281 285 1822 Fax +1 281 285 1537 E-mail: rbirchwood@slb.com

INTRODUCTION This paper provides a set of generalized relations that could be used for constructing correlations between the mechanical and geophysical properties of rocks containing clathrate hydrates. The paper focuses on drained elastoplastic properties, typically obtained via triaxial load testing or other similar mechanical tests, and geophysical properties measured using surface acquisition methods or borehole logging tools. It is desirable to be able to construct correlations that would allow rock deformation and failure to be forecast from geophysical data or attributes that could be derived from such data. There is increasing interest in gas hydrates due to their enormous potential as energy sources. However, drilling and producing in gas hydrates zones poses several challenges [1,2]. During drilling, the unconsolidated sediments in which

gas hydrates are found are prone to washouts and various modes of chemical and stress-induced failure. Temperature and pressure disturbances caused by the drilling process can lead to dissociation of gas hydrates. Dissociation results in the reduction of load bearing capacity, and the expansion of gas accompanying dissociation can lead to an abrupt increase in the pore pressure [3] thereby weakening the sediment further. Even if the consequences are not catastrophic, poor hole conditions can diminish the quality of logs in hydrate zones. Other problems can occur during completion and production of wells drilled in gas hydrate zones. Poor hole conditions can result in ineffective cement bonding, leading to gas leakage outside the casing. Loss of formation competence due to gas hydrate removal can cause sand production, formation subsidence, and casing failure.

Proceedings of the 6th International Conference on Gas Hydrates (ICGH 2008), Vancouver, British Columbia, CANADA, July 6-10, 2008.

If effective drilling, completion, and production strategies are to be realized, methods for predicting the mechanical properties of sediments containing gas hydrates are required. Mechanical failure models that fail to account for the strengthening effects of gas hydrates run the risk of being unnecessarily conservative and are therefore likely to lead to inefficient operational practices. Similar consequences may result if elastic-brittle models are applied to the soft plastic sediments that typically host gas hydrates. For this reason, models of mechanical failure in such settings should account for plasticity. However, elastoplastic models require several input properties. Conventionally, core tests are used to determine the plasticity properties of rocks. This paper provides a physically based formalism for constructing correlations that could be used to predict the static drained elastoplastic properties of two-component granular materials based on material- or stress-related attributes that could be measured or inferred from non-invasive surface or borehole acquisition methods. Correlations are widely used in practice to predict the brittle-elastic properties of rocks. Methods for estimating the static Young’s modulus have been contrived by several authors [4, 5, 6, 7]. Correlations for estimating the static Poisson’s ratio from the dynamic Poisson’s ratio have been similarly devised [5, 7, 8]. An empirical correlation for evaluating the Biot’s constant was developed by Krief et al. [9]. Correlations for estimating the unconfined compressive strength (UCS) of rocks have been constructed by several authors and are reviewed in Chang [10]. Additional correlations for this purpose have been formulated by Plumb et al. [11] and Qui et al. [12]. Plumb [13] provided graphical illustration of correlations between rock strength parameters (UCS, friction angle) and rock properties that could be derived from seismic or borehole data. Although various physical arguments were invoked by several of the preceding authors, none of these works utilized mathematical analysis of micromechanical models as a basis for formulating correlations. Moreover, there are no published correlations for estimating the static drained mechanical properties of sediments containing gas hydrates from non-invasive surface or borehole acquisition data.

In this paper, a method is presented for constructing correlations based on nondimensionalized relationships. The relevant parameters used in such relationships are derived from an examination of micromechanical models. Although the ensuing description emphasizes gas hydrate bearing sediments as an application, the method should apply to any binary system of granular materials. Extension of the underlying theory to aggregates containing three or more components should also be apparent. THEORY Physical Assumptions In order to provide a physical basis for the construction of correlations, micromechanical models governing the deformation of granular materials were examined. It was assumed that clathrate hydrates initially form in the pore space of a sediment. A dry isotropic sediment/hydrate aggregate was assumed in which the clathrate hydrate deposits were taken to be particulate in nature. Experiments performed on glass beads containing THF hydrates suggest that this assumption may be reasonable for low to moderate hydrate saturations [14]. At high hydrate saturations, the THF hydrate may cement the grains or form a continuous matrix and therefore the proceeding theoretical analysis is not strictly applicable to such cases. However, this does not mean that correlations devised on the basis of the proceeding theory will be invalid at high saturations. While physical arguments may serve as a guide to the construction of correlations, the validity of correlations ultimately depends on how well they match data. In the following discussion, the term “grain” will refer to a mineral grain whereas the term “particle” will be used to refer to all constituents of the aggregate (hydrate and mineral grain) unless otherwise specified. To simplify the analysis, a binary system of spherical particles will be assumed in which each substance (mineral and hydrate) has a uniform diameter and identical physical properties. To construct physically-based correlations, it is necessary to identify which parameters control the deformation of the aggregate when it is loaded at a fixed confining pressure in a drained triaxial

loading test. From a survey of literature on micromechanical models [15, 16, 17, 18, 19] and some physical reasoning, it is evident that the dynamic and static deformations of such an aggregate should be controlled by the following physical attributes. 1) The particle diameters of the grain (dg) and the hydrate (dh).

2) The densities of the grain (ρg), the hydrate (ρh), and the dry aggregate (ρb). The dry aggregate includes the clathrate hydrate.

3) Inter-granular sliding friction coefficients that govern friction at grain-to-grain contacts (µgg), hydrate-to-hydrate contacts (µhh), and grain-to-hydrate contacts (µgh).

4) Cohesion at hydrate-to-hydrate contacts (chh) and at grain-to-hydrate contacts (cgh). These are each assumed to be constant for a given sediment-hydrate combination. Further, as is generally assumed for unconsolidated sediments, cohesion at grain-to-grain contacts may be treated as negligible or non-existent.

5) Contact density distribution functions that describe the expectation of finding contacts in a given direction. In this case, four such distributions are used, governing grain-to-grain, grain-to-hydrate, hydrate-to-grain, and hydrate-to-hydrate contacts. In a triaxial test, and for an isotropic material, the contact density distribution functions are independent of orientation in the initial isotropic stress state, prior to axial compression. As axial compression occurs, the contact density distribution functions generally evolve and become dependent on angular orientation [15]. However, the evolution described above is wholly determined by the initial state of the system and the applied stresses. Thus, it is only necessary to specify the contact density distribution functions in the initial isotropic stress state.

In this state, the mean partial coordination numbers and the quantities of various types of particles may be substituted for contact density distribution functions. Thus, the deformation process may be assumed to depend on the number of grains per unit volume (ng), the number of hydrate particles per unit volume (nh), and the mean partial coordination numbers (Ngg, Ngh, Nhg, and Nhh), where as above, the subscripts represent

the nature of the contact. Because ngNgh = nhNhg, Nhg will be eliminated from the list of independent variables.

6) Distribution functions for the coordination numbers of each type of particle contact (grain-grain, grain-hydrate, hydrate-grain, hydrate-hydrate). No theory has been developed for the distributed coordination numbers of multicomponent particulate systems, and few experiments have been performed to measure these distributions [20]. Thus, only the mean values of these distributions (Ngg, Ngh, and Nhh) will be specified. In other words, the role of higher order moments will be neglected.

7) The normal and shear elastic stiffnesses of particulate contacts. It will be assumed that in the initial state, these are known functions of the material properties of the sediment. For Hertz-Mindlin contacts, the contact stiffnesses will also depend on the loading path required to reach the initial state of confinement [21]. The complication introduced by this history dependence will be ignored. Thus the contact stiffnesses are functions of the Young’s moduli and Poisson’s ratios of the grain and hydrate (Eg, Eh, vg, vh).

8) The confining pressure, pc. This quantity controls the initial state of stress of the specimen. Additionally, since the confining pressure applied to the circumference of the specimen is held constant during triaxial loading, the variable pc

also controls subsequent deformation of the sample by serving as a boundary condition that must be honored at all times.

9) The axial strain rate. The role of this quantity will be neglected since creep effects are not being considered in this paper.

10) The temperature. The role of this quantity will be ignored in the proceeding analysis.

It should be observed that clathrate hydrate content has been omitted from the above list. Clathrate hydrate content affects deformation insofar as it exerts control over physical attributes that are already included in the above list. It is assumed that the medium deforms plastically via sliding at grain contacts, i.e., the contribution of particle rotation to deformation is ignored. Rolling contact, rather than sliding contact, is expected to dominate the final stages of shear banding [22, 23].

Derivation of Nondimensionalized Relations Based on the foregoing, it is possible to state that any macroscopic property, η, that governs elastoplastic deformation should depend on the following parameters:

,,,,,,,,,,,( ghgghghgbhghg EEdd µµννρρρηη =

),,,,,,,, chghhghgghhghhh pnnNNNccµ , (1)

where pc is the confining pressure. This equation may be modified by introducing the relations:

ggnd3

61

)1( πϕ =− (2)

hhhyd nds 3

61πϕ = (3)

hhydgb s ϕρρϕρ +−= )1( , (4)

where ϕ is porosity and shyd is the clathrate hydrate saturation. Using Equations 2, 3, and 4 to eliminate ng, dh and ρh in Equation 1 yields

,,,,,,,,,( gghghgbghydg EEsd µννρρηη =

),,,,,,,,, chhhghgghhghhhgh pnNNNcc ϕµµ . (5)

Equation 5 defines the variables that control any elastic or plasticity property of the aggregate, including acoustic velocities, which can be expressed thus:

,,,,,,,,( hghgbghydgpp EEsdVV ννρρ=),,,,, chhhghgg pnNNN ϕ (6)

,,,,,,,,,( gghghgbghydgss NEEsdVV ννρρ=

),,,, chhhgh pnNN ϕ , (7)

where Vp is the compressional wave velocity and Vs is the shear wave velocity. Equations 6 and 7 were derived with the assumption that acoustic waves induce strains that are too small to produce slip at contacts. Therefore Vp and Vs should be

independent of the cohesive and frictional properties at contacts. Note that both acoustic velocities are frame velocities. Where necessary, acoustic velocities measured in fluid-saturated sediments should be corrected using Gassman’s relations or some other fluid substitution method [21]. It is now assumed that Equation 6 can be inverted for Ngg, i.e., that if all the other variables in Equation 6 are fixed, there exists a one-to-one relation between Vp and Ngg. This is physically reasonable — Vp should increase monotonically with Ngg. Consequently, Ngg may be replaced in Equation 5 by Vp so that

,,,,,,,,,,,( hhghgghghgbghydg EEsd µµµννρρηη =),,,,,,, chhhghphhgh pnNNVcc ϕ . (8)

At sufficiently low hydrate saturations, mechanical properties are independent of the properties of the hydrate. Consequently Equation 8 reduces to

),,,,,,,,( cpggggbgglowlow pVEd ϕµνρρηη = .

(9) However, at higher hydrate saturations, hydrate particles become load bearing and their geometrical and physical properties become important. In this regime, Vs will be sensitive to these properties. It is now assumed that Equation 7 can be inverted for Nhh, i.e., that if all the other variables in Equation 7 are fixed, there exists a one-to-one relation between Vs and Nhh. This is again physically reasonable — Vs should increase monotonically as the number of contacts between neighboring hydrate grains increases. Consequently, Nhh may be replaced in Equation 8 by Vs so that

,,,,,,,,,( gghghgbghydghighhigh EEsd µννρρηη =

),,,,,,,,, chsghphhghhhgh pnVNVcc ϕµµ . (10)

Equations 9 and 10 are general relations that can be used for the construction of correlations. However, these equations are cumbersome to apply in their current form, and various simplifications are needed. Simplification is possible by applying these equations to a specific

binary sediment-hydrate system. This constraint fixes the quantities dg, ρg, gE , hE , gν , hν , ggµ ,

ghµ , hhµ , ghc and hhc . It is desirable to eliminate

Ngh and nh from Equation 10. There is no exact theoretical expression for the mean partial coordination number, ghN . However, approximate

theoretical relations for the partial mean coordination numbers of multimodal particulate systems have been derived [24, 25, 26]. An examination of the expressions developed by Ouchiyama and Tanaka [25] reveals that ghN and

hhN can be modeled approximately as follows:

),,,,( ϕghhghhhh ddnnNN = (11)

),,,,( ϕghhgghgh ddnnNN = . (12)

However, ng and dh can be eliminated as before using Equations 2 and 3. Hence Equations 11 and 12 simplify to

),,,( ϕghydhhhhh dsnNN = (13)

),,,( ϕghydhghgh dsnNN = . (14)

The relations of Ouchiyama and Tanaka [25] can be inverted such that nh can be derived as a function of Nhh. Therefore Equation 13 can be re-expressed as

),,,( ϕghydhhhh dsNnn = . (15)

Substituting Equation 15 into Equation 14 gives the following relation for Ngh:

),,,( ϕghydhhghgh dsNNN = . (16)

Finally, substituting Equations 15 and 16 into Equation 10, and making use of the fact that Equation 7 can be inverted to give Nhh in terms of Vs gives

,,,,,,,,,( gghghgbghydghighhigh EEsd µννρρηη =),,,,,,, csphhghhhgh pVVcc ϕµµ . (17)

Dimensional analysis may now be employed to reduce the number of independent variables in

Equations 9 and 17. In general, η is either dimensionless (e.g., Poisson’s ratio, dilation angle) or has the dimensions of pressure (e.g. Young’s modulus, UCS, cohesion hardening parameters, etc.). For purposes of nondimensionalization, dg, ρg, and Vp are selected as scaling variables; however, other combinations of scaling variables are possible (e.g.: {pc, dg, ρg}, { pc, dg, Vp}). With this choice of scaling variables, the terms

ghhg cEE ,, and hhc (which have dimensions of

pressure) are scaled by the quantity 2pgVρ leading

to four dimensionless variables of the form

2pgV

c

ρ, where c is constant for a fixed sediment-

hydrate combination. However, without loss of generality, all four variables may be replaced by a

single variable, 2

*

pgV

cc

ρ= , where c is an

arbitrary scaling variable with dimensions of pressure. Non-dimensionalizing therefore leads to the following relations between dimensionless quantities:

),,,,,( *****cggglowlow pc ϕµνρηη = (18)

,,,,,,,,( ****hhghgghghydhighhigh cs µµµννρηη =

),, *cpϕγ , (19)

where 2* / pgVρηη = if η has dimensions of

pressure, ηη =* if η is dimensionless, and

g

b

ρρρ =*

s

p

V

V=γ 2

*

pg

cc V

pp

ρ= . (20)

Equations 18 and 19 constitute a basis for devising correlations between mechanical properties and geophysical data in a binary sediment-hydrate system. However, since

g

hhyd

g

b sρρφφ

ρρρ +−== 1* , (21)

and in view of the fact that g

h

ρρ

is fixed for a

given binary sediment-hydrate system,

),(**hydsφρρ = . (22)

Substituting Equation 22 into the dimensionless relations 18 and 19, and making use of the fact that

ghgghg µµνν ,,, and hhµ are fixed for a given

binary sediment-hydrate system, the dimensionless relations simplify to

),,( ****clowlow pc ϕηη = (23)

),,,,( ****chydhighhigh pcs ϕγηη = . (24)

All five independent variables, ϕγ ,,, *cshyd and *cp , can be measured or inferred from geophysical

data. It is sometimes convenient to re-scale Equations 9 and 17 using the scaling variables pc, dg, and ρg. Making use of the same simplifications that lead to Equations 23 and 24 produces

),,( **** ϕαηη plowlow V= (25)

),,,,( ***** ϕαηη sphydhighhigh VVs= , (26)

where the mechanical properties on the left hand side with units of pressure are now scaled by pc and

c

pc=*α c

gpp p

VVρ

=* c

gss p

VVρ

=* .(27)

As before, c is an arbitrary scaling variable with dimensions of pressure. In subsequent analysis, c will be set to 1 MPa. In the next section, a correlation for the static drained Young’s modulus will be derived on the basis of Equations 25 and 26. EXPERIMENTAL DATA Description of Data The results of triaxial tests conducted on a wide variety of unconsolidated sand specimens were obtained from the literature [27-33] in order to extract the static drained Young’s modulus. The

average Young’s modulus was evaluated in this study, i.e., the gradient of the more or less straight part of the rising limb of the axial stress-strain curve. Table 1 lists the data that was acquired. The data includes one set of THF hydrate samples and several methane hydrate samples. The methane hydrate samples selected from Masui et al. [28] were synthetic and prepared using the ice-seeding technique. The other two methane hydrate sample sets were of natural origin. The triaxial tests conducted by Winters et al. [32] and Yun et al. [33] were undrained. In the case of Winters, the pore pressure was measured and it was possible to extract effective stress properties. Reference Description of

Sand Grain

Diameter, D50 (mm)

Hydrate

[27] Hostun dense siliceous sand

0.32 None

[28] Reconstituted Toyoura sand

0.17 Methane

[29] Nankai Trough sand

0.082-0.16 Methane

[30,31] Gulf of Mexico sand

0.096 None

[32] Mallik sand 0.311 Methane [33] Reconstituted

Ottawa sand 0.12 THF

Table 1. Triaxial test samples used for analysis.

Yun et al. [33] used three different hydrate saturations in their experiments — 0%, 50%, and 100% — however, pore pressure was only measured in the 0% case. For the 100% case, pore pressure is irrelevant. Analysis of the hydrate-free samples by both Yun et al. [33] and Birchwood [34] suggested that these samples exhibited a drained response due to inadequate saturation or even cavitation. Pore pressure was not measured in the samples with 50% hydrate saturation and it is therefore not possible to say for certain whether a similar drained response would have occurred in these samples. However, since sample preparation methods were similar in all cases right up to freezing, it is quite possible that a drained response would have occurred in these samples as well. For this reason, these samples were not included in the optimization scheme for finding mechanical property correlations (described in the next section) but were included in final plots showing the goodness of fit of these correlations.

An additional set of dense sand samples by Wong [35] was also analyzed but these were found to give consistently higher Young’s moduli than the other samples, due most likely to their dense interlocking fabric. These samples were eventually dropped from the analysis. Numerical Search Scheme A numerical search scheme was employed to find the optimal correlation for the static Young’s modulus. Unfortunately, compressional and shear wave acoustic velocities were not available for most samples, so it was not possible to search the entire space of independent variables. Instead, the nondimensionalization scheme of Equations 25 and 26 was chosen, and a correlation was sought between the dimensionless static drained Young’s modulus E/pc, of the test samples and the

independent variables ,, *αhyds and ϕ .

Henceforth, the asterisk will be dropped from α* for convenience. The numerical scheme initially assumes an algebraic expansion of the form

+++++= 2132143210

* nhyd

nmmhyd

m saasaaa ϕαϕη6543

65nhyd

nnhyd

n saa αϕα + (28)

and sequentially eliminates terms that are insensitive to the data. Equation 28 allows for pairwise coupling between the independent variables. The sequential elimination scheme prevents overfitting of data and leads to correlations that are relatively free of bias. A load-bearing model whereby the Young’s modulus was assumed to be independent of clathrate hydrate saturation until a critical saturation was attained was also tested. The form of the model was the same as Equation 28 except that shyd was set equal to the critical saturation,

crithyds for crit

hydhyd ss ≤ . The critical hydrate

saturation was treated as an unknown variable to be optimized by the search scheme over a reasonable range (between 15% and 50%). Results The numerical search scheme produced the following solution for the dimensionless Young’s modulus:

022.1

371.1

5831.0

4.80090.7858.90

ααhyd

c

s

p

E ++= . (29)

The load-bearing model produced inferior results. Equation 29 indicates that the dimensionless Young’s modulus decreases with the dimensionless confining pressure and increases with clathrate hydrate saturation. The last term in Equation 29 governs the coupling between the clathrate hydrate saturation and the effective confining pressure. This coupling ensures that the dimensional Young’s modulus becomes increasingly insensitive to the confining pressure as the clathrate hydrate saturation increases. No significant correlation was detected between the dimensionless Young’s modulus and the porosity. Figure 1 shows the degree of fit between the correlation and the data. The fit appears to be reasonable; however, some scatter can be seen. This scatter is to be expected, in view of the different origins of the samples and the fact that two of the governing dimensionless parameters were excluded from the search. The data of Yun et al. [33] with 50% hydrate saturation is consistent with the general trend, although it was not included in the search scheme.

Figure 1 Comparison between measured and predicted dimensionless Young’s modulus.

In order to see the outliers better, the nondimensionalization and logarithm were removed from the plot of Figure 1. Figure 2 shows the resulting plot with two distinct outliers circled, corresponding to samples tested by Yun et al. [33]. These samples were fully saturated with THF hydrate and were tested at confining pressures of 0.5 MPa and 1 MPa. The empirical correlation underpredicts their Young’s moduli by

33% and 19%, respectively. However, it is clear that there is something unusual about these samples because the one tested at a confining pressure of 0.5 MPa had a Young’s modulus of 1.37 GPa whereas the one tested at 1 MPa had a lower Young’s modulus of 1.20 GPa. However,

Figure 2 Comparison between measured and

predicted Young’s modulus. Outliers are circled. uniaxial stress tests performed by Parameswaran et al. [36] and Cameron et al. [37] on Ottawa sands that were fully saturated with THF hydrate also yielded Young’s moduli that were in excess of 1 GPa. Consequently it would appear that the empirical correlation tends to underpredict the Young’s moduli at high saturations. One possible explanation is that a different physical mechanism operates at such high saturations. It is possible, for example, that in such regimes, THF hydrate cements the grains or forms a continuous matrix with a high cohesive strength. Following this logic, a transition from frictional to cohesive behavior would be expected to occur over a range of clathrate hydrate saturations. However, not enough experimental data at high clathrate hydrate saturations was available to verify the existence and nature of this transition zone. There was a gap in the saturations of our samples between 68% and 100%. Given the limited amount of data that is available, it is advisable not to apply the correlation when the clathrate hydrate saturation exceeds 50%. Furthermore, use of the correlation should be limited to effective confining pressures between 50 kPa and 1 MPa. Figure 3 shows the Young’s modulus predicted by the correlation plotted as a function of clathrate hydrate saturation at several fixed effective confining pressures. The effect of confining pressure diminishes with increasing hydrate

saturation. Additionally, the presence of clathrate hydrate appears to influence the Young’s modulus even at very low concentrations. To a certain extent, this effect would appear to be a genuine reflection of the data, particularly that of Masui [28, 29]. This fact is demonstrated in Figure 4 which plots the static Young’s modulus vs. the hydrate saturation at an effective confining pressure of 1 MPa. The data of Yun et al. [33]

Figure 3 Plots of Young’s modulus vs. clathrate hydrate saturation at fixed effective confining

pressures generated using the empirical correlation (Equation 29).

with 50% THF hydrate saturation is also included. Significant increases in hydrate saturation can be seen in the individual data sets of Masui [28, 29] well before a hydrate saturation of 35%. The value of 35% represents a typical load bearing saturation for clathrate hydrates that grow in the pore space. As indicated earlier, the load bearing model did not fit the data for the static Young’s modulus very well. Although the empirical curve shown in Figure 4 provides a plausible fit to the data, it is also evident that the data contains significant scatter and is fairly sparse, and that although a reasonably rigorous search procedure was employed, it is possible that other curves might fit the data equally well. Therefore more data is required at low hydrate saturations before drawing conclusions about the variation of Young’s modulus in this regime. The empirical correlation of Equation 29 should be regarded as the best fit that could be derived from the limited data currently available in the public domain.

Figure 5 shows the variation of the Young’s modulus with effective confining pressure. Hydrate-free sediments obey the power law

544.0cpE ∝ . (30)

However, as the clathrate hydrate saturation increases, the static Young’s modulus becomes relatively insensitive to the effective confining pressure at low confining pressures.

Figure 4 Young’s modulus vs. clathrate hydrate saturation at fixed effective confining pressure of 1 MPa. Both the data and the empirical correlation (Equation 29) are shown.

Figure 5 Plots of Young’s modulus vs. effective confining pressure at fixed clathrate hydrate

saturation. Conclusion A set of generalized dimensionless relations for constructing correlations between geophysical properties and the elastoplastic properties of sediments containing clathrate hydrates was derived using parameters extracted from micromechanics models. The relations were applied to triaxial test data for sands containing

THF and methane hydrate. A search over a limited set of independent dimensionless variables yielded a correlation between the dimensionless static drained Young’s modulus, the dimensionless effective confining pressure, and the clathrate hydrate saturation. An examination of outliers in the data indicated that the correlation tended to underpredict the Young’s modulus at high clathrate hydrate saturations, possibly because of the introduction of cohesive mechanisms not present at lower saturations. The static Young’s modulus also seemed to be affected by the presence of clathrate hydrates in small quantities below the load bearing threshold for clathrate hydrates growing in the pore space. However, more data is required to verify this observation. Due to the limited amount of data used in this study, it was recommended that the correlation should not be applied when the clathrate hydrate saturation exceeds 50%, or when the effective confining pressure falls outside the range 50 kPa

≤≤ cp 1 MPa.

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