Volume 110, Issue B4
Geomagnetism and Paleomagnetism/Marine Geology and Geophysics
Free Access

A laboratory investigation into the seismic velocities of methane gas hydrate-bearing sand

Jeffrey A. Priest

Jeffrey A. Priest

Challenger Division for Seafloor Processes, Southampton Oceanography Centre, University of Southampton Waterfront Campus, Southampton, UK

Also at School of Civil Engineering and the Environment, University of Southampton, Highfield, UK.

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Angus I. Best

Angus I. Best

Challenger Division for Seafloor Processes, Southampton Oceanography Centre, University of Southampton Waterfront Campus, Southampton, UK

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Christopher R. I. Clayton

Christopher R. I. Clayton

School of Civil Engineering and the Environment, University of Southampton, Highfield, UK

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First published: 14 April 2005
Citations: 174

Abstract

[1] Remote seismic methods, which measure the compressional wave (P wave) velocity (Vp) and shear wave (S wave) velocity (Vs), can be used to assess the distribution and concentration of marine gas hydrates in situ. However, interpreting seismic data requires an understanding of the seismic properties of hydrate-bearing sediments, which has proved problematic because of difficulties in recovering intact hydrate-bearing sediment samples and in performing valid laboratory tests. Therefore a dedicated gas hydrate resonant column (GHRC) was developed to allow pressure and temperature conditions suitable for hydrate formation to be applied to a specimen with subsequent measurement of both Vp and Vs made at frequencies and strains relevant to marine seismic investigations. Thirteen sand specimens containing differing amounts of evenly dispersed hydrate were tested. The results show a bipartite relationship between velocities and hydrate pore saturation, with a marked transition between 3 and 5% hydrate pore saturation for both Vp and Vs. This suggests that methane hydrate initially cements sand grain contacts then infills the pore space. These results show in detail for the first time, using a resonant column, how hydrate cementation affects elastic wave properties in quartz sand. This information is valuable for validating theoretical models relating seismic wave propagation in marine sediments to hydrate pore saturation.

1. Introduction

1.1. Nature and Distribution of Marine Gas Hydrates

[2] Methane gas hydrates are solid, ice-like, clathrate compounds formed from hydrogen-bonded cages of water molecules enclosing methane molecules [Sloan, 1998]. These compounds are metastable and exist only under certain pressure and temperature conditions which exist naturally in deep marine sediments and in polar regions where permafrost is present. The estimated global volume of methane stored in hydrate ranges from 2 to 4 × 1016 m3 at STP (temperature of 273.15 K and pressure of 101.325 kPa) [Kvenvolden, 1988] which, combined with its metastability, has led to hydrates becoming of international importance with regard to: their potential as a future energy resource [Collett and Ladd, 2000; Kvenvolden, 1998]; their role in global warming [Haq, 1998]; and their potential as a geotechnical hazard [Ashi, 1999; Berndt et al., 2002; Kayen and Lee, 1991; Mienert et al., 1998; Popenoe et al., 1993].

[3] To assess the impact of methane hydrates within these areas of interest, an understanding of the areal extent of gas hydrates, their distribution within the seabed and their relationship with the host sediment is required. Quantifying the extent and distribution of gas hydrates within the sediment column has normally been undertaken using seismic reflection profiling, with P waves being the main propagating waveform. Historically, the identification of gas hydrates has been inferred indirectly by the presence of a bottom simulating reflector (BSR), which is assumed to occur at the hydrate stability boundary where hydrate-bearing strata overly strata containing free gas [Shipley et al., 1979; White, 1979]. Initial hypotheses suggested the BSR and the strength of the BSR were related to the volume of gas hydrate in the sediment [Hyndman and Spence, 1992]. It was also assumed that low-amplitude reflections observed above some BSRs [Shipley et al., 1979] could be used to assess the concentration of gas hydrate within the stability zone [Lee et al., 1992]. However, the use of differing seismoacoustic acquisition techniques, such as multichannel seismics, ocean bottom seismometers [Katzman et al., 1994; Vanneste et al., 2002], deep tow seismics [Gettrust et al., 1999], vertical seismic profiling [Bangs et al., 1993; Holbrook et al., 1996], and down hole logging [Guerin et al., 1999; Lee and Collett, 2001], has led to a greater understanding of the nature of the BSR. The BSR is now considered to result from free gas in sedimentary layers beneath the hydrate stability zone (HSZ) [Holbrook et al., 1996; Korenaga et al., 1997; MacKay et al., 1994; Minshull et al., 1994; Singh et al., 1993]. The low-amplitude reflections above the BSR may result from homogeneous sediment overlying sharp reflections caused by sedimentary layers containing free gas [Holbrook et al., 1996], or equally be due to attenuation of seismic energy as a result of scattering and destructive interference. To further complicate the use of the BSR as a proxy measurement of gas hydrate occurrence, gas hydrates have also been found where no BSR is present [Paull et al., 1996].

1.2. Hydrate Quantification

[4] Improved seismic methods, which now include both P wave and S waves, and the use of waveform inversion techniques [Korenaga et al., 1997; Singh et al., 1993; Tinivella and Lodollo, 2000] have improved the velocity determination between differing reflectors beneath the seafloor. However, estimating the gas hydrate volume within sediments from these acquired velocity profiles is problematic. Two differing approaches have been made to relate the hydrate fraction (or hydrate saturation) and velocity in ocean sediments. In the first, empirical methods use versions of Wyllie's time average or Wood's equation calibrated with laboratory data [Lee et al., 1996] which are not representative of those found in the hydrate stability region [Dvorkin and Nur, 1998]. The second approach has been to use theoretical effective medium models to predict the physical properties of bulk sediment from the elastic properties of individual constituents. Differing models have been developed to account for the inclusion of hydrate within sediment using modified versions of the Gassmann equation [Ecker et al., 1998; Helgerud et al., 1999], modified versions of the Biot equation [Carcione and Tinivella, 2000; Gei and Carcione, 2003] and a differential effective medium approach (DEM) [Jakobsen et al., 2000]. The model outputs depend on whether the relationship between hydrate and sediment is defined either as hydrate cement at grain contacts; uniform hydrate cementation of individual grains leading to cementation between grains; hydrate acting as a mineral grain supporting the sediment frame; or hydrate growing wholly within the pore fluid and not interacting with the sediment frame. The predicted hydrate pore saturation differs significantly according to which model is used.

[5] Analyses have been undertaken by combining a variety of independent estimates of hydrate concentrations, such as resistivity logs, chloride anomalies, and gas evolution measurements (during hydrate dissociation) with acoustic data to validate the models. Ecker et al. [2000] and Helgerud et al. [1999] analyzed seismic data obtained from the Blake Ridge during Leg 164 of the Ocean Drilling Program (ODP) concluding that the hydrate acted as a mineral grain supporting the sediment frame. However, Chand et al. [2004] undertaking a comparison of the differing effective medium models, using data obtained from the Blake Ridge and from the Mallik 2L-38 permafrost gas hydrate well, Mackenzie Delta, Canada, concluded the DEM model was the most consistent with those data sets, suggesting hydrate acted as a cement. These contradictory conclusions regarding the interaction between hydrate and sediment highlight the importance of validating seismic models with laboratory data obtained on laboratory synthesized hydrate-bearing sediment.

2. Background

2.1. Hydrate Formation

[6] To avoid interpretive complications associated with partially dissociated and physically altered recovered core material, hydrates have been synthesized in the laboratory. Unfortunately, the solubility of methane gas in water is low, and in the laboratory, methane hydrate is generally formed at the water-gas interface in a three-phase system (water/gas/hydrate) which tends to restrict further hydrate formation [Makogon, 1981]. To speed up solid hydrate formation, researchers have employed agitation of the system [Englezos et al., 1987] or grinding [Handa, 1986] to provide new initiation points for continued growth. However, the porous nature of hydrates formed using these methods does not correspond to that found in nature [Sloan, 1998]. An alternative method of forming polycrystalline gas hydrates was developed by melting fine ice particles in the presence of methane gas [Stern et al., 1996].

[7] The technique of bubbling gas through a saturated medium to form methane hydrates in porous media has been widely used and has met with limited success. In fine grained specimens (clays), the homogenous migration of gas through the specimens is restricted by the low specimen permeability leading to fractured channels of hydrate throughout the specimen [Brewer et al., 1997; Chuvilin et al., 2002]. In coarse specimens (sands), more disseminated hydrates are possible, however the accurate estimation of volume and distribution of these hydrates is lacking; also, hydrate blockage at the point of entry can prevent further injection of methane gas after initial hydrate formation [Stoll, 1974; Stoll and Bryan, 1979; Stoll et al., 1971; Winters et al., 2000, 2002].

[8] Because of the difficulty in forming methane gas hydrate, differing hydrate formers have been used such as propane [Stoll, 1974; Stoll and Bryan, 1979; Stoll et al., 1971], and analogues of natural gas including tetrahydrofuran (THF) [Bathe et al., 1984; Berge et al., 1999; Kiefte et al., 1985; Kunerth et al., 2001; Pearson et al., 1986] and Freon-11 (CCL3F) [Berge et al., 1999], all of which require less onerous stability conditions. These compounds form structure II gas hydrates which have different crystal structure to methane hydrate (structure I), which may lead to differing mechanical properties. Structure I hydrates are predominantly found in nature although structure II hydrates have been recovered in some regions (e.g., Gulf of Mexico [Brooks et al., 1994] and Caspian Sea [Ginsburg et al., 1992]).

2.2. Elastic Wave Velocities of Synthetic Gas Hydrates in Porous Media

[9] In laboratory experiments on methane gas hydrated sands the measured value of Vp, has varied from 2690 m s−1 [Stoll, 1974; Stoll and Bryan, 1979; Stoll et al., 1971] up to 4000 m s−1 [Winters et al., 2002], although in each case the distribution of hydrate within the specimen could not be controlled nor the volume of hydrate formed quantified. Pearson et al. [1986] undertook velocity measurements while using THF as a hydrate former and reported Vp of 4500 m s−1 (for a hydrated sandstone) while Kunerth et al. [2001] reported Vp of 3400 m s−1 (for a hydrated sand). Berge et al. [1999] reported both Vp and Vs as a function of hydrate pore saturation in sands using Freon-11. They found that below a critical hydrate concentration within the pore space ∼35%, Vp was not significantly affected and Vs was unable to be measured. As the hydrate concentrations exceeded 35%, Vp and Vs increased abruptly from 1710 to 3810 m s−1 and from 1500 to 2200 m s−1, respectively, for a final hydrate content of 55%.

[10] Virtually all velocity measurements on saturated hydrated sands have been obtained using ultrasonic frequencies (0.25–1 MHz) which may not be directly applicable to seismic velocity data obtained from geophysical surveys at frequencies <500 Hz. This is due to frequency-dependent velocity dispersion. The total velocity dispersion can vary between 2 and 25% depending on rock type, saturation conditions and effective stress [Winkler, 1986]. Best et al. [2001] measured Vp of 1600 and 1800 m s−1 at frequencies of 800 Hz and 342 kHz, respectively, for poorly sorted marine sediments. In homogeneous unconsolidated sands, Stoll [2002] reported Vp velocities varying from ∼1580 m s−1 at 50–200 Hz to ∼1750 m s−1 at 20–50 kHz.

[11] To that end, a laboratory apparatus (the gas hydrate resonant column) was designed and constructed to simulate conditions that are found in naturally occurring methane hydrates. Most importantly, the resonant column also allows velocity measurements to be undertaken at frequencies that are directly applicable to in situ seismic surveys.

[12] The purpose of this paper is to report the results of a well constrained experimental study into the variations in the seismic velocities of both compressional and shear waves in methane gas hydrate-bearing sand specimens as a function of hydrate pore saturation. To achieve this, we developed a methodology for controlling the formation of gas hydrates within sand specimens where the volume and subsequent distribution of hydrate within the pore space is well constrained.

3. Experimental Method

3.1. Background

[13] The resonant column is commonly employed in geotechnical testing to determine the shear wave velocity of soils and rocks using torsional vibration. The resonant column utilizes the theory of vibration of a linearly viscoelastic cylindrical rod to quantify the velocity of propagation of a shear wave. The velocity is determined from the frequency of vibration, at resonance, of the soil column and the attached drive mechanism [Drnevich et al., 1978; Richart et al., 1970]. The torsional frequency can vary from 17 to 25 Hz for soft clay soils [Hardin and Drnevich, 1972] up to 400 Hz for stiff cemented sands [Avramidis and Saxena, 1990] falling within the frequency range and strains employed in marine seismic surveys. The standard “Stokoe” resonant column (Figure 1) applies torsional excitation only, but can be easily adapted to allow flexural excitation. Compressional wave velocity can be computed from the flexural and torsional resonance frequencies [Cascante et al., 1998]. Therefore a dedicated gas hydrate resonant column (GHRC) was designed and constructed to enable both torsional and flexural vibration modes and the provision for enhanced pressure and temperature control to generate the necessary hydrate stability conditions.

Details are in the caption following the image
Cross section through the resonant column (without pressure cell). For clarity, the pressure cell, which surrounds the specimen and drive mechanism, is omitted. Modified from Stokoe et al. [1999].

3.2. Experimental Methodology

[14] The essential features of the resonant column are shown in Figure 1. Torsional or flexural vibration is induced in the specimen by applying a sinusoidal voltage to the drive coils. This produces an oscillatory motion in the drive mechanism attached to the top of the specimen due to interaction of the electromagnetic field in the coils and the fixed magnets attached to the drive plate. The resonant frequency of the specimen and attached drive mechanism can be found by controlling the frequency and amplitude of the applied voltage. This is achieved by monitoring the electrical output of an accelerometer attached to the drive plate (Figure 1), as the drive frequency is increased incrementally through a predefined frequency range (frequency sweep). By plotting the output of the accelerometer against the frequency of the applied voltage, the resonant frequency can be easily identified as shown in Figure 2.

Details are in the caption following the image
Frequency response curve for pluviated Leighton Buzzard sand.

3.3. Theory

[15] The reduction of data from the different modes of excitation is undertaken by utilizing the theory of elasticity and assuming that the specimen obeys Hooke's law: the observed strains are linearly proportional to the applied stresses (for soils subject to low shear strains (γ) this assumption introduces negligible errors). If the specimen is fixed at the base and excited in torsion by the drive mechanism, then the particular solution can be written as
urn:x-wiley:01480227:media:jgrb14240:jgrb14240-math-0001
where I and I0 are the mass polar moments of inertia of the specimen and the drive mechanism, respectively; ωn is the first mode (natural or fundamental) resonant frequency of the vibrating system (specimen and drive mechanism); and L is the length of the specimen. Because of the complex geometry of the drive mechanism, the value of I0 is derived from calibration tests using aluminum rods of known material properties in place of the specimen. Thereafter, Vs can be determined from the resonant frequency and the geometric properties of the specimen.
[16] For flexural vibration the system is idealized as a cantilever beam with N distributed rigid masses mi at its free end. Using Rayleigh's method the particular solution can be written, assuming there is no bending moment, as [Cascante et al., 1998]
urn:x-wiley:01480227:media:jgrb14240:jgrb14240-math-0002
where ωf, E, Ib, and mT are the resonant frequency from flexure, Young's modulus, area moment of inertia, and mass of the specimen, respectively; and yci and Iyi are the center of gravity and area moment of inertia of each added mass. As the value of Iy for the drive mechanism is related to its geometry, calibration is undertaken to derive its value. From the solution for a cantilevered beam the resonant frequency can be used to determine the Young's modulus derived from flexure, denoted Eflex. This value, along with the density of the specimen ρ can be used to calculate the longitudinal velocity in the specimen Vlf from
urn:x-wiley:01480227:media:jgrb14240:jgrb14240-math-0003

3.4. Calibration

[17] Calibration was achieved using a series of cylindrical aluminum rods with plates fixed at each end. Three differing rod configurations were used allowing the calibration rods to be connected to the drive mechanism directly or connected via a top cap (see section 3.5). These configurations were denoted rod types A, B, and C. Four calibration rods with differing rod diameters were made for each rod type. Figure 3 shows the values of I0 and Iy computed from their respective modes of vibration as a function of each rod's resonant frequency (only the two stiffest bars of rod type A are shown for flexural excitation). By rearranging equation (1) and substituting the measured resonant frequency for each rod (from torsional vibration), and from their geometric properties, the value of I0 was computed. A similar technique was employed to find Iy using equation (2) and the flexural resonance frequency. The value of I0 was dependent on the stiffness of the central aluminum column of the aluminum rods; therefore a least squares regression curve was fitted to the data (Figure 3a) to derive a value of I0 as a function of frequency, which gave a maximum error of ±0.9% (±28 m s−1) for the computed velocity of the aluminum rods compared to the value given in standard tables (=3097 m s−1). For flexural excitation values of Iy as well as depending on the stiffness of the central column depended on the geometry of the rod used and therefore did not fall onto one curve (Figure 3b) (in the derivation of equation (2) no shear force is included at the join between the central bar and the top plate). Therefore the least squares regression curve was fitted to the data obtained for rod type B (which closely matched the set up for the sand specimens), as shown in Figure 3b, and errors were computed for the minimum and maximum possible values of Iy recorded. The analysis showed that at the lowest frequency (50 Hz) the error was ±4.5% (±25 m s−1) and at the maximum recorded frequency (350 Hz) the error was ±6.3% (±158 m s−1).

Details are in the caption following the image
Calibration curves to determine (a) I0 from torsional excitation and (b) Iy from flexural excitation for the resonant column using aluminum bars of differing diameters and geometry, types A, B, and C. A least squares regression curve is fitted to all data presented in Figure 3a and only to data relating to rod type B in Figure 3b.
[18] Additional errors can occur with regard to velocity measurements due to the rigidity of the membrane enclosing the specimen and the lack of fixity between the top cap and the specimen. Drnevich [1985] suggested rubber membrane thickness <1% of specimen diameter would have negligible effect at low strain (γ < 10−4). In our experiments butyl membranes with a thickness of 0.2 mm were used, which was ∼0.3% of the specimen diameter. Fixity of the top cap is dependent on the stiffness of the specimen, imposed shearing strain, normal effective stress and friction between top cap and specimen. Given that most soils and rocks have a coefficient of friction of 0.2, to ensure fixity [Drnevich, 1978],
urn:x-wiley:01480227:media:jgrb14240:jgrb14240-math-0004
where G is shear stiffness of the specimen and σ′ is the effective confining pressure. In all our tests this condition was satisfied.

3.5. Hydrate Formation Procedure

[19] Table 1 shows the properties of 13 sand specimens measured in the resonant column containing differing volumes of hydrate in the pore space. The specimens were prepared using fine uniform Leighton Buzzard sand with an average grain size of 100 μm. The procedure for hydrate formation was based on the technique developed by Stern et al. [1996] using seed ice as nucleation points for hydrate growth. Hydrate volume was controlled by adding a known mass of triply distilled, sieved, ground ice, with a grain size between 180 and 250 μm, to a predetermined mass of air dry frozen sand. Thorough mixing of the sand and ice using a riffle box ensured a homogeneous distribution of the ice throughout the specimen. The ice was subsequently allowed to melt within the sand in an airtight bag; the resulting moist sand was then tamped within a sample mold to form a dense, 70 mm diameter by 140 mm long, solid cylindrical specimen. Before the sample mold was released an aluminum top cap was placed on top of the sand specimen to allow the drive mechanism to be attached (Figure 1). A butyl membrane fixed with O-rings to the base pedestal and top cap allowed segregation of the cell confining pressure and the pore fluid pressure (back pressure).

Table 1. Properties of Specimens Before and After Hydrate Formationa
Specimen Hydrate Saturation at 500 kPa, % Initial Porosity Porosity at 500 kPa With Hydrate
H0L 0 0.465 0.463
H0D 0 0.416 0.413
H1 1.07 0.400 0.397
H2 2.15 0.419 0.412
H3-1 3.00 0.419 0.409
H3-2 2.70 0.443 0.431
H4-1 3.75 0.423 0.407
H4-2 3.82 0.430 0.429
H5-1 4.91 0.419 0.400
H5-2 4.90 0.423 0.424
H10 9.59 0.432 0.392
H20 17.95 0.428 0.353
H40 35.27 0.428 0.279
  • a Porosity after hydrate formation is calculated assuming hydrate is part of the solid phase.

[20] A small vacuum was applied to the specimen, through the base pedestal, to allow the removal of the specimen mold and connection of the resonant column drive system. Further instrumentation included a linear variable displacement transducer (LVDT) fixed to the resonant column drive mechanism to measure axial deformation of the specimen, which was used to recalculate sample properties (volume, density, etc.) during testing, and two thermistors attached to the outside of the butyl membrane to measure the temperature within the cell. A commercial software package, GDSLab, designed by GDS Instruments Ltd., was modified to suit the requirements of the GHRC, which allowed real-time acquisition and storage of all sensor data throughout an experiment as well as pressure and temperature control.

[21] After the cell top was fitted cell pressure was applied, while simultaneously releasing the vacuum, until an effective confining pressure (σ′) of 250 kPa was achieved under atmospheric back pressure. The temperature of the cell was reduced to −15°C to refreeze the pore water. This refreezing causes a small increase in volume of the specimen measured by the axial LVDT (equivalent to 0.35% axial strain, which was partially regained during the change from ice to hydrate). Once frozen, a methane back pressure was applied to the specimen and slowly raised up to 15 MPa over a period of about 1.5 hours, while at the same time increasing the cell pressure to maintain σ′ = 250 ± 50 kPa. Both cell and back pressure are measured by in-line pressure transducers outside the cell. Once the methane pore pressure has reached its target value it was locked off and any change in methane pore pressure measured is then due to the thermal expansion of the methane gas or the taking up of the methane into the hydrate (cell pressure is controlled to maintain σ′ = 250 ± 50 kPa). These high pressures were applied to ensure a quick conversion of ice to hydrate [Hwang et al., 1990] during hydrate formation. Formation was achieved by raising the sample temperature to 8°C at a rate of approximately 15 min °C−1 and then maintaining the temperature at 8°C for a further 15 hours (this allowed sufficient time for full hydrate conversion, which was checked by monitoring the change in methane back pressure at constant temperature). The specimen temperature was then reduced to 3°C, then a reduction in methane pore pressure to 5 MPa (this was arbitrarily chosen to assist in effective stress control during testing), along with a corresponding reduction in cell pressure to maintain σ′ = 250 ± 50 kPa on the specimen, at which point resonant column measurements were undertaken.

3.6. Resonant Column Measurement Procedure

[22] The measurement program was designed to characterize the dynamic response of sand specimens containing differing volumes of methane gas hydrate within the pore space under isotropic loading and unloading. Isotropic loading was applied in steps of 250 kPa up to σ′ = 2000 kPa, with the unloading steps following the same sequence in reverse. Torsional and flexural resonance frequencies were measured at each loading and unloading step. Each load step was maintained for 30 min to allow for any initial consolidation of the specimen to occur (as noted by the axial LVDT) before resonant testing was undertaken.

[23] To ensure that the measured seismic properties were comparable to those that are determined during geophysical surveys, the specimen strain amplitude was kept below the elastic threshold strain, γte, ensuring that the recorded velocity is independent of strain. Tests on unbonded Leighton Buzzard sand showed that γte occurred at strains of 10−5 at a confining pressure of 250 kPa (results by Saxena et al. [1988] suggest that γte is largely unaffected by cement bonding). The peak amplitude measured by the accelerometer at resonance is a function of the applied strain. Therefore the applied strain could be quantified from the accelerometer output and kept below γte for all tests.

4. Results and Discussion

4.1. Hydrate Formation

[24] It was initially thought that hydrate growth could be inferred from the change in methane gas pore pressure as the specimen temperature rose above 0°C similar to the method employed by Stern et al. [1996]. However, the examples of P-T histories in Figure 4 for specimens H3-2, H5-2, and H40 clearly show that a change in the gradient of the methane pore pressure versus temperature curve only occurs for specimen H40 as it approaches 0°C (pressure reduces the melting point of ice by ∼1°C). It can also be noted that the gradients of the pore pressure curves of specimens H3-2 and H5-2 are markedly different to that of specimen H40 (from when the methane gas pressure is locked off). Barrer and Edge [1967] showed that the rate of hydrate nucleation depends on the surface area of the ice-hydrate interface while recent studies have shown that ice grains with a typical diameter of 40–80 μm formed hydrate at temperatures as low as −43°C [Salamatin and Kuhs, 2002; Staykova et al., 2002, 2003] with the growth rate-dependent on the gas pressure and temperature. In our tests, it has been assumed that ice forms at grain contacts (due to capillarity and surface tension) and then infills the pore space as the water content increases. Therefore the ice will form double curvature three-dimensional volumes around contact points with a large surface area to volume ratio compared to a spherical grain (see Figure 11 in section 4.6). Hydrate formation thus commences as soon as the methane back pressure was within the hydrate stability field during the application of the methane gas into the pore space. As the hydrate saturation increases the ratio of surface area to volume reduces, slowing hydrate growth, which manifests itself as a lower gradient for gas expansion as the cell temperature is raised (specimen H40 in Figure 4, which had a hydrate saturation of 35.27%).

Details are in the caption following the image
Example of P-T histories for sand specimens with ice volumes of 2.72% (H3-2), 4.91% (H5-2) and 35.27% (H40) within the pore space. See also Table 1.

[25] As we were unable to use the change in methane pore pressure when the specimen temperature rose above 0°C to quantify hydrate saturation, the amount of hydrate in each specimen was calculated from the mass of ice added to the sand. To check the validity of this, velocity measurements were conducted on a specimen containing an assumed hydrate saturation of 36%, as the temperature was lowered from 5°C to −7.2°C. A maximum increase of 0.6% in shear velocity was observed as the temperature was lowered to −7.2°C, confirming that there was very little free water left in the specimen. All the water had previously been converted to hydrate.

[26] Although our hydrate could have been formed from water and free gas, as was achieved by Winters et al. [2002], the technique of forming hydrate from ice was preferred as it has been suggested that hydrate growth is more rapid when coming from the ice phase [Hwang et al., 1990]. Our success in forming hydrate, as discussed above, may have been partly a result of the use of ice.

4.2. Seismic Velocity Measurements: Hydrate-Bearing Specimens

[27] The experimental results for all specimens are shown in Table 2. Figure 5 shows the influence of hydrate pore saturation on the seismic velocities (Vs and Vlf) of 10 sand specimens subjected to isotropic loading and unloading. Two important conclusions can be drawn from these results: the effective stress dependence of both Vs and Vlf is reduced once the hydrate pore saturation is 3% or above; and both Vs and Vlf increase as the degree of hydrate within the pore space increases. Specimens H3-1, H4-1, and H5-1 are omitted from Figure 5 for clarity.

Details are in the caption following the image
(a) Shear wave and (b) longitudinal wave velocity versus effective confining pressure for specimens listed in Table 1. In Figure 5b, approximate gas hydrate pore saturations are given for each curve. Tests are conducted at 3°C and methane pore pressure of 5 MPa.
Table 2. Seismic Wave Velocities of Specimens Once Hydrated and at a Confining Pressure of 500 kPa
Specimen Vs, m s−1 Vlf, m s−1 Vp, m s−1
H0L 345 480 1639
H0D 383 538 1654
H1 470 653 1703
H2 656 987 1802
H3-1 1005 1461 2029
H3-2 1012 1440 1985
H4-1 852 1297 1955
H4-2 1046 1546 2055
H5-1 913 1429 2040
H5-2 1021 1480 2028
H10 1210 1737 2189
H20 1435 2213 2547
H40 1661 2630 2833

[28] Figure 6 shows the increase in both Vs and Vlf as a function of hydrate pore saturation for all test specimens at σ′ = 500 kPa during isotropic loading. Two distinct regions can be identified: from 0 to 3% hydrate pore saturation Vs and Vlf increase at a high rate; above 3–5% hydrate pore saturation, Vs and Vlf increase at a lower rate. Figure 6 also shows the uncertainty in the computed velocities due to systematic errors and calibration issues previously described in section 3.4. The results suggest a bipartite relationship between seismic velocities and hydrate pore saturation with a transition zone situated between 3% and 5% hydrate saturation of the pore space. Figure 6 also highlights the relatively large variations in velocities measured for different specimens with hydrate pore saturations in the transition zone.

Details are in the caption following the image
Variation in Vs and Vlf for all test specimens with effective confining pressure of 500 kPa. Error bars show the uncertainty in values due to systematic and calibration errors.
[29] In unconsolidated sediments subjected to isotropic loading a simple exponential relationship can be shown to exist between Vs, Vlf, and σ′:
urn:x-wiley:01480227:media:jgrb14240:jgrb14240-math-0005
where A and b are constants [Hardin and Black, 1968]. The power exponent b represents both the nature of the contact stiffness and fabric change as a function of isotropic stress [Cascante et al., 1998]. By curve fitting equation (5) to Figures 5a and 5b, the power exponents bs and bl can be obtained for shear wave velocity and longitudinal velocity, respectively. Figure 7 shows the variation in bs and bl during isotropic loading as a function of hydrate pore saturation. The nonhydrated specimens have a bs = 0.27 and bl = 0.27 for the loose sand specimen (H0L), while the dense sand specimen (H0D) has bs = 0.23 and bl = 0.22. These values are consistent with published data on remolded clean sand specimens [Cascante et al., 1998; Hardin and Drnevich, 1972]. The reduction in bs and bl from specimen H0L to H0D can be attributed to more stable contacts and smaller changes in specimen fabric during isotropic consolidation. As the volume of hydrate increases in the pore space the values for bs and bl reduce from 0.23 to about 0.01–0.05 for both exponents. The reduction in exponents bs and bl and the associated increase in seismic wave velocity occurs with very little change in fabric, which suggests that hydrate acts to increase contact stiffness by cementing the sand grain contacts. Similar results have been observed for small amounts of differing forms of cement, such as frozen capillary water or epoxy resin [Dvorkin and Nur, 1993] or Portland cement [Saxena et al., 1988].
Details are in the caption following the image
Variation in power exponent b as a function of hydrate pore saturation during isotropic loading. Sharp reduction in b shows the effect of hydrate cementation on specimen behavior.

[30] The observation of hydrate cementing the sands in our tests is not unexpected given the formation procedure adopted, which causes the water to reside at grain contacts leading to hydrate formation at the grain contacts. This is in contrast to observation during other laboratory tests [Kleinberg et al., 2003; Tohidi et al., 2001] where hydrate formed in the pore space. Again this is expected because of the formation procedure adopted by these researchers. In their method hydrate was formed from methane gas bubbles in a water saturated medium. This caused the gas bubbles to reside in the center of the pore space because of the strong relative wettability of water and hydrate formation to be initiated at the bubble surface with inward growth.

[31] This suggests that hydrate formation is dependent on the method adopted, and therefore laboratory results must be viewed in context with natural formation procedures. Our formation procedure, where hydrates grew in gas-rich environments, may be applicable to marine environments where high gas fluxes are found, such as in active venting margins (e.g., Cascadia margin, Gulf of Mexico). Hydrates which are pore-filling may therefore occur in marine environments which are water saturated and form from the dissolved phase. This assumption is further complicated by experimental results which suggest that hydrates from the dissolved phase may require initiation points to form hydrate [Tohidi et al., 2002].

4.3. Water-Saturated Velocities

[32] In seismic surveys the derived velocities are for saturated sediments, whereas the velocities calculated in the resonant column are for specimens without liquid water. Therefore, to compare GHRC data with in situ seismic data the velocities must be modified. As the shear modulus of the specimen G = ρVs2 is unaffected by fluid saturation (according to Gassmann [1951]) the saturated velocity Vs(sat) can be derived by substituting the saturated density ρsat for ρ using
urn:x-wiley:01480227:media:jgrb14240:jgrb14240-math-0006
where the saturated density ρsat is given by
urn:x-wiley:01480227:media:jgrb14240:jgrb14240-math-0007
where ρm is the density of the solid mineral phase (hydrate and sand), ρf is the density of the pore fluid, and ϕ is the porosity of the specimen.

[33] In saturated particulate materials the interaction between the fluid and the solid phase is different for flexural and longitudinal vibrations. During flexural excitation the strain field within the specimen has a triangular Navier distribution in cross section between tension and compression [Cascante et al., 1998], and the resulting velocity measurements are the same for dry and saturated specimens (apart from the difference in density between the dry and saturated case). In longitudinal vibration (seismic P waves) the strain is constant in cross section and so the stiffness of both the frame and the water is considered.

[34] Gassmann [1951] derived an equation to compute the bulk modulus of a fluid saturated porous medium K using the bulk moduli of the constituent parts:
urn:x-wiley:01480227:media:jgrb14240:jgrb14240-math-0008
where Kd is the bulk modulus of the solid framework of grains and Km and Kf are the bulk moduli of the grain minerals and the water, respectively. Kd can be calculated from the elastic properties obtained from the resonant column using
urn:x-wiley:01480227:media:jgrb14240:jgrb14240-math-0009
where E and G are the measured Young's modulus and shear modulus of the specimen (equivalent to the frame moduli), respectively. The solid mineral bulk modulus Km is the effective modulus for an aggregate of crystals when taken as a single crystal, on the basis of the mineralogy of the sediment. The seismic results from the resonant column suggest that hydrate becomes part of the solid phase. Therefore, in the case of mixed mineralogy (hydrate and quartz), the effective Km for the solid phase can be calculated from the individual components of the matrix using Hill's average formula [Hill, 1952]:
urn:x-wiley:01480227:media:jgrb14240:jgrb14240-math-0010
where N is the number of mineral constituents, ψi is the volumetric fraction of the ith constituent in the solid phase, and Ki is the bulk modulus of the ith constituent. Waite et al. [2000] calculated the bulk modulus of solid methane gas hydrate to be 7.7 ± 0.2 GPa. The bulk modulus of quartz sand and water are 36.6 and 2.25 GPa, respectively. Once K is calculated from equation (8), the saturated compressional wave velocity (Vp) can be calculated from
urn:x-wiley:01480227:media:jgrb14240:jgrb14240-math-0011

[35] Figure 8 presents the water-saturated Vp and Vs values computed using -(11) for all specimens as a function of hydrate pore saturation. Error bars are included to show the effect of systematic errors and uncertainty in Iy (see section 3.4). Comparing the results for Vp for hydrate pore saturation below 3–5%, with Vlf (from Figure 6 at the same saturation values) shows that Vp is less sensitive to the effects of hydrate pore saturation. This is due to the P wave modulus being dominated by the bulk modulus of the fluid, Kf. Therefore higher initial velocities and a reduction in slope for Vp (up to 3–5% hydrate saturation) are observed compared to those for Vlf. As the hydrate pore saturation reaches and passes the 3–5% value, the bulk modulus of the saturated specimen becomes less dominated by the bulk modulus of the pore fluid and more by the increasing cementation of the sand grains. Aided by the reduction in porosity (reducing pore fluid volume) this leads to a reduction in the velocity difference between Vp and Vs as hydrate pore saturation approaches its maximum value.

Details are in the caption following the image
Variation in water-saturated Vp and Vs with hydrate pore saturation of specimens listed in Table 1 at σ′ of 500 kPa. Error bars show the uncertainty in values due to systematic and calibration errors.

4.4. Vp/Vs Ratio

[36] The reduction in the influence of Kf on the saturated Vp velocity leads to significant changes in Vp/Vs ratios which are not evident in Vlf/Vs ratios. From the resonant column tests the Vlf/Vs ratios vary from ∼1.4 to 1.6, whereas the computed Vp/Vs ratios vary from ∼5.5 to 1.9. Figure 9 shows the computed Vp/Vs ratios for all specimens. The Vp/Vs ratio for nonhydrate-bearing sand was 5.53 (loose) and 3.91 (dense). These values are comparable to those measured in near surface marine sediments, including sands [Hamilton, 1979]. The addition of hydrate cement causes a large reduction in the Vp/Vs ratio from 5.53 for specimen H0L to 2.25 for specimen H3-2 (σ′ = 500 kPa), with a slight reduction to 1.9 at the maximum hydrate pore saturation (specimen H40). The value for Vp/Vs ratio at high hydrate pore saturations is comparable to values given in the literature for rocks, such as mudstones, limestones and sandstones [Castagna et al., 1984; Hamilton, 1979; Wilkens et al., 1984]. This suggests that both Vp and Vs measurements are required during geophysical surveys to detect and quantify hydrate pore saturation in marine sediments.

Details are in the caption following the image
Variation in water saturated Vp/Vs ratio as a function of hydrate pore saturation for specimens listed in Table 1 at different values of σ′.

4.5. Dissociated Sand Specimens

[37] Figure 10 shows the relationship between Vs and Vlf with σ′ during isotropic loading and unloading for a dense sand (H0D), for hydrate-bonded dense sand (H40 − 35.27% hydrate pore saturation) and for the same specimen after dissociation. The response of previously hydrated specimen H40 approximately follows the same path as specimen H0D for both Vs and Vlf which was typical for all hydrated specimens. It can be seen that hydrate formation and dissociation had little or no appreciable lasting effect on the velocity curves. The small discrepancies can be attributed to the initial variation in density and porosity, as shown in Table 1. The values of bs and bl were constant at 0.23 for all specimens which fall within the range for unbonded granular material.

Details are in the caption following the image
Relationship between (a) shear wave and (b) longitudinal wave velocity and effective confining pressure for dense sand (H0D) for hydrate-bonded dense sand (H40 − 35% hydrate pore saturation) and for the same specimen after hydrate dissociation.

4.6. Cementation Model

[38] Figure 11 presents a conceptual model of how our adopted methodology for hydrate formation and its distribution affect seismic velocities in sand. Initially, no hydrate is present in the pore space (Figure 11a) and velocity measurements show a stress dependency similar to that of an unconsolidated particulate material, given by the power exponent b ∼ 0.23 (for the dense specimen). As hydrate is introduced into the pore space cementation of the sand grains occurs. This leads to a sharp rise in both Vs and Vlf up to a critical hydrate pore saturation of 3–5%. At hydrate pore saturations less than 3%, there is insufficient hydrate present to saturate all grain contacts (Figure 11b). This leads to partial cementation of the specimen leading to a gradual reduction in b. At the critical hydrate pore saturation of around 3–5%, it is proposed that all grain contacts become cemented (Figure 11c) evidenced by the resultant velocity measurements showing no (or very low) stress dependency with b ∼ 0.05. At this point specimen velocities become sensitive to the distribution of hydrate within the specimen as evidenced by the small fluctuation in velocity (Figure 6) and b (Figure 8) for specimens H3-1 to H5-2. It is suggested that this fluctuation is possibly caused by heterogeneity in the cementation of grain contacts. Although the hydrate is homogeneously distributed on the global scale within the sand, minor variations in saturation of the contact points at the pore scale may occur in the specimen. These are assumed to be minor due to the very small value of b which highlights a low stress dependency. Increasing hydrate above the critical region causes only an enlargement in the volume of the hydrate cement at grain contacts, and a subsequent infilling of the pore space as shown in Figure 11d. This leads to a more gradual increase in velocity with increasing hydrate pore saturation.

Details are in the caption following the image
Conceptual model showing cementation and pore filling with increasing hydrate. (a) Assemblage of sand grains with no hydrate; (b) partial cementation at grain contacts by hydrate (<3%); (c) cementation at all grain contacts (3–5% hydrate pore saturation); and (d) increasing hydrate pore saturation (>5%) causing reduction in porosity.

5. Conclusions

[39] The results presented in this paper show that the formation of methane gas hydrate in gas-rich sediment pore space causes cementation of grain contacts, leading to a dramatic increase in seismic wave velocity (Vs and Vlf). The measurement of these geophysical properties was achieved using a specifically designed and constructed resonant column. This allowed the formation of methane gas hydrate within sand specimens and the subsequent measurement of wave velocities at frequencies and strains that are representative of in situ seismic surveys.

[40] The methodology developed for specimen preparation and subsequent hydrate formation allowed disseminated gas hydrate to form at grain contacts throughout the whole sand specimen. The volume of gas hydrate formed within the specimen could be controlled from as little as 1% saturation of the pore space to a maximum of 35% by the addition of a known mass of ground ice which was subsequently converted to gas hydrate. The assumption that the vast majority of ice was converted to hydrate was inferred from pore pressure responses during the formation procedure and by monitoring velocities during specimen cooling from 5°C to −7.5°C. This allowed us to study the effect of small changes in hydrate pore saturation on the seismic properties of fine sand specimens.

[41] Small amounts of hydrate had a large impact on both Vs and Vlf as a result of hydrate cementation at grain contacts. Cementation was assumed on the basis of the sharp reduction in the velocity-stress exponents, bs and bl. It was shown that Vp in a saturated medium, which was indirectly calculated in this study, was less sensitive to hydrate formation compared to Vlf for hydrate pore saturations less than 3–5%. This was due to the bulk modulus of the saturated hydrate-bearing sand being dominated by the bulk modulus of the fluid. At the critical hydrate pore saturation (3–5%) the bulk modulus of the specimen is dominated by the cemented grain contacts, which leads to a sharp reduction in the Vp/Vs ratio.

[42] The effect of hydrate formation on the seismic velocity of sand specimens is completely reversible upon dissociation of the gas hydrate. Measured velocities after dissociation closely resemble those for the dense sand specimen H0D which had not previously contained hydrate. The velocity-stress exponents bs and bl for the dissociated specimens show consistent trends with specimen H0D. This reduction in grain contact stiffness upon dissociation could have major implications for the stiffness of hydrate-bearing sediments in the seafloor, in marine environments where the hydrate is cementing, if subjected to changes in P-T conditions, as would the pore pressure increase from the liberation of gas trapped in the hydrate cages.

Notation

  • σ′
  • effective confining pressure.
  • γet
  • elastic strain threshold.
  • ρ
  • density of dry specimen, kg m−3.
  • ρsat
  • density of saturated specimen, kg m−3.
  • ρm
  • density of solid mineral phase, kg m−3.
  • ρf
  • density of water, kg m−3.
  • ρw
  • density of seawater, kg m−3.
  • ωn
  • angular resonance frequency, rad s−1.
  • ωf
  • flexural resonant angular frequency, rad s−1.
  • ψi
  • volumetric fraction of mineral phase.
  • ϕ
  • fractional porosity of specimen.
  • A
  • constant.
  • bs, bl
  • velocity-stress power exponent for shear and flexural waves, respectively.
  • Eflex
  • Young's modulus from flexural excitation, kPa.
  • G
  • shear modulus, kPa.
  • I, I0
  • mass polar moment of inertia of specimen and drive mechanism, respectively, kg m2.
  • Iy
  • area moment of inertia, m4.
  • Iyi
  • area moment of inertia of added mass mi, m4.
  • Ib
  • area moment of inertia of specimen, m4.
  • K,
  • saturated bulk modulus, kPa.
  • Kd
  • bulk modulus of dry specimen, kPa.
  • Kf
  • bulk modulus of water, kPa.
  • Km
  • bulk modulus of mineral matrix, kPa.
  • l
  • length of specimen, m.
  • mT
  • mass of specimen, kg.
  • mi
  • added masses at top of specimen, kg.
  • Vlf
  • longitudinal wave velocity, m s−1.
  • Vp
  • compressional wave velocity, m s−1.
  • Vs
  • shear wave velocity, m s−1.
  • Acknowledgments

    [43] This work was funded under contract EVK3-CT-2000-00043 (HYDRATECH) of the European Commission and by the UK Natural Environment Research Council. J. A. Priest also received support from UK EPSRC PhD studentship 00310758. The resonant column was designed and built in collaboration with GDS Limited, UK, with advice from Clive McCann and Jeremy Sothcott. The authors also thank JGR Associate Editor William Waite and the reviewers William Winters and Manyka Prasad for their constructive comments and suggestions during the review process.