Tetrahydrofuran

ARTICLE pubs.acs.org/EF

Laboratory Measurements of the Effects of Methane/Tetrahydrofuran Concentration and Grain Size on the P-Wave Velocity of Hydrate-Bearing Sand Feng-Guang Li, Chang-Yu Sun,* Qin Zhang, Xiao-Xiang Liu, Xu-Qiang Guo, and Guang-Jin Chen* State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Beijing, 102249, China ABSTRACT: An experimental apparatus was developed to measure P-wave velocity (VP) of gas-hydrate-bearing sediment. Tetrahydrofuran (THF) was added to quicken the hydrate formation in the porous media and to synthesize hydrate-bearing sediments with uniform distribution. Methane acted as a free gas to participate in the hydrate formation. Five experimental runs were performed to examine the influence of sediment grain size and THF concentration on VP. The P-wave velocity and the amplitude for the first arrival wave signal were collected in real time during hydrate formation process. The experimental data showed that VP increases monotonically with the increase of hydrate saturation in the sediment pore space and finally tends to be a constant value. This final VP value increases with the increase of initial THF content, but the effect of sand grain size on VP is inconclusive. The variations of amplitude for the first arrival wave signal with elapsed time during hydrate formation illustrates that the amplitude increases with the increase of hydrate saturation until it attains a maximum value and then decreases gradually due to the effect of free methane gas penetrating into the hydrate-bearing sediment. The acoustic velocity of THF-hydrate filled sediment was also predicted based on the extended contact cement theory. The predicted results were close to the experimental data obtained in this work.

1. INTRODUCTION Natural gas hydrates have been encountered in porous sediments under marine seabed and permafrost regions.1 The study of hydrate has been carried out extensively because of potential applications in solving energy and environmental problems.2
4 The investigations of the properties of hydrate-bearing sediments, such as lithology, hydrate saturation, permeability, density, and P-wave velocity, are extremely important to evaluate the hydrate resources in situ and even to exploit it in the future.5
10 Because it is difficult to investigate properties of natural gas hydrate samples at in situ conditions, hydrate synthesized in laboratory has been used instead to examine the corresponding properties.8,9,11 To characterize the properties of hydrate-bearing sediment reliably, it is crucial to synthesize the representative samples. However, it is challenging work since the solubility of methane in water is low and a considerably long time is required to form hydrate within the sediment. Waite et al.8 tested the properties of clathrate hydrate in partially water-saturated sediment. It was found that the hydrate saturation in the sediment was relatively limited and the formation process was extremely slow. The maximum hydrate concentration in the pore space reached 70% and the experiment took about 1400 h until the measured compressional wave speed stabilized. The pore space of the sediment is extremely difficult to fully saturate with hydrate in the laboratory. It is known that tetrahydrofuran (THF) is miscible with water at all molar ratios, which enables hydrate to form rapidly, and the formed hydrate is then dispersed homogenously in the sediment. Therefore, THF has been used as a substitute for methane to form hydrate in laboratory studies.12,13 Acoustic wave velocity is an important geophysical property, which can give information about lithology, saturation, and in situ conditions of sediments.7 The acoustic wave velocity measurements in laboratory can provide important reference for r 2011 American Chemical Society

the geological explanation of seismic prospecting data. Measuring the acoustic P-wave velocities (VP) is generally considered to be the most commonly applied exploration technique to detect the hydrate-bearing sediment. However, interpreting seismic data requires the interpretation of the seismic properties of hydrate-bearing sediments, which has proved problematic because of the difficulties in recovering intact hydrate-bearing sediment samples and in performing valid laboratory tests. Priest et al.14 synthesized valid laboratory samples containing different amounts of evenly dispersed hydrate and tested the compressional wave velocity and shear wave velocity. The results illustrated that methane hydrate initially cements sand grain contacts and then infills the pore space. Pearson et al.12 performed acoustic velocity measurements on hydrate-bearing sediment formed from porous samples saturated with a mixture of THF and water. VP of hydrate formation in both Berea sandstone and Austin chalk samples increases rapidly (from 2500 to 4500 ms
1 and 1400 to 5000 ms
1 for Berea sandstone and Austin chalk samples, respectively) when hydrates begin to form in the cores but soon approaches to a limiting value; further lowering the temperature does not appreciably increase the P-wave velocity. However, THF forms structure II hydrate and only occupies the large cavities of hydrate cage. This is different from the natural hydrate-bearing sediments, where the small and large cavities of hydrate cage are chiefly occupied by methane molecular. In this work, an experimental apparatus was developed to measure P-wave velocity of gas-hydrate-bearing sediment. THF was added to quicken the hydrate formation in the porous media Received: December 8, 2010 Revised: April 21, 2011 Published: April 25, 2011 2076

dx.doi.org/10.1021/ef101665v | Energy Fuels 2011, 25, 2076–2082

Energy & Fuels

ARTICLE

Table 1. Physical Properties of the Sand Sedimenta property

a

Figure 1. (a) Schematic of the experiment apparatus for online measuring VP of THF-hydrate bearing sediment during the hydrate formation. 1: gas cylinder; 2, 3, 4, 11: valve; 5: reactor; 6: Piezo-electric transducer; 7: sediment; 8: hand lever; 9: bottom gas entrance; 10: thermocouple; 12: air bath; 13: temperature digital display; 14: pressure digital display; 15: ultrasonic pulser/receiver; 16: digital oscilloscope; 17: computer recording system. (b) Inner part of the high pressure reactor.

and to synthesize hydrate-bearing sediment, making hydrate form and distribute evenly. Methane was added as a free gas to participate in the hydrate formation. Compared with pure THF hydrate, for hydrate formed by methane þ THF system, THF chiefly occupies the large cavities of hydrate cage and methane enters the small cavities. This is closer to the natural hydratebearing sediments states. Meanwhile, VP was monitored throughout the whole experiment to evaluate the variation of acoustic properties with the formation of hydrate. The variation of the amplitude for the first arrival wave signal with elapsed time was also obtained. It is helpful to understand the waveform evaluation and interpret the P-wave velocity of THF hydrate formed in sediments with methane acting as a free gas.

2. EXPERIMENTAL SECTION 2.1. Apparatus. The experimental apparatus used in this work for measuring P-wave velocity of gas hydrate-bearing sediment is shown in Figure 1. It mainly consisted of a reactor, an air bath, a gas filling system, and a P-wave measuring and recording system as shown in Figure 1a.

20
40 mesh

40
60 mesh

60
80 mesh

grain diameter, mm

0.45
0.90

0.30
0.45

0.20
0.30

density, g 3 cm
3

1.58

1.51

1.49

sample porosity, %

36.28

37.77

39.10

The uncertainties of sediment density and porosity are (0.1%.

The reactor, with a diameter of 130 mm and a height of 150 mm, was made by Jiangsu Hai’an Oil Scientific Research Apparatus Co., Ltd., China, and the maximum working pressure was 32.0 MPa. A thermocouple with a precision of (0.1 K was inserted into the sediment to detect the temperature variations during hydrate formation. The system pressure was monitored by an absolute pressure transducer with an accuracy of 0.5% mounted at the top of the reactor. Figure 1b shows the inner structure of the reactor. Two detectors of piezo-electric transducer were placed at the bottom and top of the reactor, respectively. The top one was connected with a hand lever which can move upward and downward in the vertical direction to change the distance between the two acoustic detectors, and the maximum distance available is 60 mm. The ultrasonic waves through the hydrate-bearing sandy sediment were sent and received using the detectors. The frequency of the piezoelectric transducer was 500 kHz-1.0 MHz and the applied pulse voltage was 400 V. The received signal was sent back to the pulse sender machine (model 5077PR, made by Olympus NDT) where it was amplified, digitized, and displayed on a digital oscilloscope (TBS2012B, made by Tektronix, Inc.), and then analyzed and recorded with software on the computer. Based on the measurement uncertainties of travel time and sample length, we attribute a ( 0.5% uncertainty to our measured VP data. 2.2. Material. Unconsolidated quartz grains were used as the experimental sediment to form hydrate. It was first washed for several times with deionized water and then dried in an oven over 393.2 K for 12 h. After that, it was sieved into three different types for use, 20
40, 40
60, and 60
80 meshes, respectively. The properties of three different types of sediment are listed in Table 1. Methane with a purity of 99.9% was supplied by Beijing AP Beifen Gases Industry Co. Ltd. The THF aqueous solution was prepared with pure THF (99.8%) and deionized water. The stoichiometric molar ratio of THF for hydrate formation is 5.9%. 2.3. Procedure. Both hydrate concentration and distribution play an important role in investigating the acoustic properties of hydratebearing sediment.9 THF was then used to synthesize hydrate in view that it is miscible with water and hydrate formed could homogeneously disperse in the pore space. The following experimental procedure was used to prepare the representative hydrate sample: (1) Before the reactor was loaded with sediments, it was thoroughly cleaned with deionized water and then dried. A thermocouple was assembled through the side wall of the reactor to detect the temperature variations during hydrate formation in the sediment. (2) The sediment together with saturated THF solution was loaded into the reactor under the room temperature. There was still some free space above the sediment in the reactor, as show in Figure 1b. Circular stainless steel was placed between the sediment and the upper wall of the reactor. The gas-filling line was installed and an absolute pressure transducer was mounted at the top of the reactor. (3) After the sediment was loaded into the reactor, the sample was jacketed with two flexible membranes by rotating the hand lever. An effective pressure applied to the sand sample was 500 kPa. The sample after jacketed was approximately 50 mm high. 2077

dx.doi.org/10.1021/ef101665v |Energy Fuels 2011, 25, 2076–2082

Energy & Fuels

ARTICLE

Table 2. Final P-Wave Velocity of Each Experiment Run When Hydrate Formation Finisheda run

sediment size, mesh

THF, mol %

Vf, m 3 s
1

VP, m 3 s
1

1

20
40

3.0

1706 (9)

3295 (13)

2 3

20
40 40
60

5.9 3.0

1782 (7)

3984 (15) 3457 (14)

4

40
60

5.9

1718 (8)

5

60
80

5.9

3711 (16) 3859 (17)

a

Vf: P-wave velocity for the THF solution-bearing sediment. VP: P-wave velocity for THF hydrate-bearing sediment. (4) The connected pipeline was first put under vacuum at room temperature. After that, the valve between the connected pipeline and the reactor was opened and the reactor was vacummized for only about 2 min to reduce the evaporation of the THF. The temperature of the air bath was set to 278.2 K and methane gas was injected into the reactor to check the leak of the system. Meanwhile, the ultrasonic pulser/receiver and digital oscilloscope were started up to be ready for collecting wave signal. (5) After the leak test, methane gas was continuously injected into the reactor from the bottom for about 1 min until the pressure was about 12.0 MPa so as to form hydrate quickly. Then the injection valve was shut off and the free gas would accumulate at the top of the reactor. Meanwhile, the variations of temperature and pressure were recorded from the beginning of the injection of gas, and data collecting was continued until the end of the experimental run. The wave signals were also collected by a software program at the same time. The above experimental procedure was repeated for other experimental runs at different sand particle size and THF concentration to test the variation of P-wave velocity during the hydrate formation.

3. RESULTS AND DISCUSSION Five experimental runs were performed to measure the P-wave velocity during the hydrate formation and to interpret the influence of sediment size and THF concentration on the final P-wave velocity. The experimental conditions and results for the five runs are listed in Table 2. There are three groups of sediment size: 20
40, 40
60, and 60
80 mesh, and two groups of THF concentration used: 3.0 and 5.9 mol %. The pore volume for all five runs is saturated with THF solution at the beginning of the experiment. For each experimental run, hydrate grows continuously and hydrate saturation in the porous space increases gradually. Correspondingly, the P-wave velocity of hydratebearing sediment also varies with the continuous formation of hydrate and the change of hydrate saturation, which is related to the amount of THF aqueous in the pore space, methane consumption, and the experimental pressure and temperature conditions. Therefore, there exists a certain relationship between the hydrate saturation and P-wave velocity. It is known that THF
17H2O aqueous solution forms structure II hydrate at atmospheric pressure when below 277.6 K.13 It is very difficult to quantify the exact hydrate concentration during the hydrate formation because hydrate can form even without the existence of methane. Methane gas injected was in general excessive and impossible to convert into hydrate completely. Even so, there still exists a certain relationship between P-wave velocities and the final state of hydrate after a long time of hydrate formation. For all five experimental runs, the similar pattern of hydrate growth was observed. The experimental run 5 was taken as an example to

Figure 2. Variations of temperature and pressure with elapsed time for run 5.

interpret the above relationship from the variation of temperature/pressure, P-wave velocity, and the amplitude for the first arrival wave signal with elapsed time. 3.1. Variation of P-Wave Velocity with the Formation of Hydrate. Figure 2 shows the variations of temperature and pressure with elapsed time during the process of hydrate formation for experimental run 5, where the sediment size was 60
80 mesh and THF concentration in aqueous solution was 5.9 mol %. As THF can decrease the equilibria pressure of hydrate formation, hydrate growth rate increases rapidly after methane gas was injected at high pressure into the reactor. From Figure 2, it can be found that the system pressure decreases from 13.52 to 11.29 MPa dramatically in 4.2 min, showing that large amount of methane gas was consumed and converted to hydrate, which mainly occupies the small cavity of hydrate structure. Meanwhile, the temperature of the samples dramatically increased by 25.5 K (from 278.1 to 303.6 K) in about 70 s due to the exothermic effect of hydrate formation. After the stage of initial rapid formation of hydrate of about 7 h, the system pressure and temperature decrease slowly. The variations of both temperature and pressure imply the variation of the saturation of hydrate in porous sediment. The sudden decrease of temperature and pressure from 20 to 30 h is due to the temperature of the air bath being adjusted from 278.2 to 275.2 K with the aim to examine the effect of temperature on VP. The results indicated that VP was not affected by the variation of temperature examined in this work. Afterward, the system pressure and temperature tend to be a constant value. Figure 3 shows the variations of P-wave velocity with the elapsed time during the hydrate formation for run 5. It can be found that VP increases with the hydrate growth. Figure 4 shows the wave signal at typical moment of A, B, C, and D marked in Figure 3. At point A, when methane gas was not yet injected, hydrate formation experiment just started and little hydrate formed. The measured VP value for THF aqueous solution saturated sediments is 1856 ms
1 (Figure 4a). After about 0.6 h at point B, when methane gas injection already finished, VP increases to 3078 ms
1 (Figure 4b). The VP increases linearly up to point C at 1.3 h, where it has the value of 3585 ms
1 (Figure 4c). Afterward, the increase trend of VP decreases with time and from point D, at 7 h, it tends to achieve a stable value of 3827 ms
1 (Figure 4d). After point D, the P-wave velocity remains constant. 3.2. Variation of Amplitude for the First Arrival Wave Signal. Figure 5 shows the variations of amplitude for the first 2078

dx.doi.org/10.1021/ef101665v |Energy Fuels 2011, 25, 2076–2082

Energy & Fuels

ARTICLE

arrival wave signal with elapsed time for experimental run 5, which provide an explanation of our observed waveform evaluation. It can be found that the amplitude of the first arrival wave signal does not behave in the same way as that of the VP. The amplitude increases quickly over the process of hydrate growth for the first 7 h, and then goes down slowly while P-wave velocity tends to be a constant value at the same period. This phenomenon relates to the intensity of attenuation of the wave signal when it passes through hydrate-bearing sediment. According to Priest et al.,15 the attenuation of

seismic energy was mainly due to three different phenomena, including (1) geometric spreading, (2) scattering, and (3) intrinsic attenuation. For the geometric spreading attenuation, it is independent of the material adopted in the experiment. And scattering is related to the wavelengths close to the size of any heterogeneity in the porous sediment. This could not be avoided but this effect can be reduced by choosing experimental grain size. So the primary influence of the acoustic wave signal depends on the intrinsic attenuation, which attributes to the characteristics of the material (grain

Figure 3. Variation of VP with elapsed time for run 5.

Figure 5. Variation of the amplitude for the first arrival wave signal with elapsed time for run 5.

Figure 4. P-wave signal at a given moment during hydrate formation for run 5: (a) t = 0.0 h; (b) t = 0.6 h; (c) t = 1.3 h; (d) t = 7.0 h. 2079

dx.doi.org/10.1021/ef101665v |Energy Fuels 2011, 25, 2076–2082

Energy & Fuels size, mineralogy, pore-filling material, saturation, etc.) and the frequency of the elastic wave.16 For dry unconsolidated sandy sediment, the P-wave signal could not pass through the sand packs due to complete attenuation. As with water-saturated sand packs, lower acoustic frequency wave signals can pass through the samples, but the amplitude is weak. The formed hydrate stiffens the sand sample and allows higher frequencies to pass through the hydratebearing sediment and lower frequencies to pass through more efficiently. Therefore, the amplitude increases with the increase of hydrate concentration.8 A little decrease of amplitude, illustrated in the top right corner of Figure 5, attributes to the effect of injection of methane gas. Because methane was injected from the bottom of the reactor, large amounts of methane gas bubbles may exist in the aqueous solution, which would greatly attenuate most of the frequencies. With more hydrate forms, the role of hydrate transforms from part of pore fluid to a kind of cement and it would surround and cement the sandy sediment grains. The effect of attenuation of the sand grains becomes weak with more and more hydrate formed to cement the sand particles, and high frequencies wave signal becomes more detectable. When the VP achieves a final constant value, the amplitude does not keep stable but decreases gradually and achieves a constant value after 80 h. This phenomenon is related to the free methane gas at the top of the reactor. After the rapid formation of hydrate in the first 7 h, THF was almost all transformed to hydrate and methane gas dissolved in the THF solution was greatly consumed, the hydrate formation process is close to end and the P-wave velocity and amplitude achieves the maximum value. Because THF molecule is large, it could not enter the small cavities of structure II hydrate. In comparison, small methane molecule can be trapped into the small cavities. Methane will continue entering the small cavities of hydrate although the cement process almost ends. But further formation of hydrate depends on the diffusion of free methane gas from the top to the bottom of the reactor. This is because it is extremely difficult for free methane gas to migrate from the top to the bottom of the reactor in a short period because permeability of hydrate-bearing sediment is comparatively small, and there exists a concentration gradient of methane within the hydrate-bearing sediment. In addition, with the formation of hydrate, some little fracture would occur within the hydrate-bearing sediment due to the effect of hydrate cementing and expanding. Free methane gas could then migrate to the bottom of the reactor. This can also be deduced from the pressure
time curve in Figure 2. Although the P-wave velocity was kept constant since 7 h, the system pressure continued to drop from 11.2 to 10.8 MPa at the end of the experiment. The diffusion or migration of methane gas from the top to the bottom of the reactor within hydrate-bearing sediment will therefore make the higher frequencies attenuate and could not pass through the hydrate-bearing sediment, resulting in the decrease of the amplitude of the P-wave signal. It is known that free gas is associated with hydrate at many offshore locations. The presence of free gas below the gashydrate-bearing sediments is necessary to form a strong BSR. During the experimental process in this work, the decrease of amplitude of P-wave for the first arrival wave signal was observed with the diffusion or migration of methane gas from the top to the bottom of the reactor as shown in Figure 5. 3.3. Final Stable P-Wave Velocity Values. The VP for the THF solution-bearing sediment and the final maximum VP value of each experimental run achieved after the completion of

ARTICLE

hydrate formation are listed in Table 2. The corresponding parameters for each experimental run such as sediment size and initial THF molar concentration are also listed in Table 2. Before the formation of hydrate, VP varies from 1706 to 1782 ms
1 for THF aqueous solution saturated sediment. VP achieves a maximum value of 3295
3984 ms
1 after the completion of hydrate formation for five runs. For experimental runs 1 and 2, they were performed in the sandy sediments with same 20
40 grain mesh but with different initial THF molar concentration. The initial THF content of run 2 is the stoichiometric concentration for hydrate formation, while it is larger than the unstoichiometric concentration of run 1. From the final VP value for these two runs, it can be found that VP increases with the increase of initial THF content. This is also the same case for experimental runs 3 and 4 with same 40
60 grain mesh but with different initial THF molar concentration. Compared with that initial THF at 3.0 mol %, more hydrate formed in porous space at 5.9 mol % THF content and hydrate saturation is then higher. Experimental runs 2, 4, and 5 were performed in sandy sediments of different sand grain mesh but at same THF molar concentration. It can be found that the VP value is close and the effect of sand gain size is ambiguous. Because THF contents for these three runs are all at the stoichiometric concentration, the final hydrate saturation is similar, resulting in the similar VP value. 3.4. Modeling Prediction. There are several recent attempts to build the relationship between hydrate saturation and P-wave velocity in natural hydrate-bearing sediments. Dvorkin et al.17 proposed four possible pore scale hydrate distributions. Model 1: hydrate in fluid phase as part of pore fluid; Model 2: hydrate in the void space as part of the solid phase; Model 3: hydrate only at grain contacts as cement; Model 4: hydrate coating grains and partly playing the role of cement at grain contacts. In the natural marine environment or permafrost regions, it is a controversial topic about hydrate distribution in the sediment pore space. The well log data, as in the Machenzie Delta, NWT, Canada (Mallik 2 L-38), showed that hydrate typically is dispersed in the pore space of sandy sediment and gravels but absent in silty layers lowing comparable porosity values.18 However, laboratory results suggested that the formed hydrate in the gas-rich conditions predominantly surrounded and cemented the sediment grain particles.8,9 Priest et al.19 tested the seismic velocities of hydratebearing specimens which were formed by using “excess water” technique and “excess gas” method, respectively. The measured results suggest that the influence of gas hydrate on acoustic velocity is strongly dependent on the morphology of formed hydrate in the pore space. Even though laboratory hydrate formation studies provide a method of judging which hydrate distribution model is appropriate for a given geologic environment. For hydrate distribution Model 1, the formed hydrate is suspended in the fluid which slightly increases the bulk moduli of the pore fluid and has no contribution to the shear moduli of the sand packs. Therefore, it has little effect on the P-wave velocity. For hydrate distribution Model 2, the formed hydrate acts as part of the sediment frame. Though it is simply accounted for a second mineral, it still has little effect on the P-wave velocity due to the big difference of physical properties between hydrate and quartz sand. On the contrary, for Models 3 and 4, hydrate acts as cement at the grain contacts, which has great effect on elastic properties. Thus, it increases the P-wave velocity greatly. The extended contact theory (CCT) of Dvorkin et al.20 could describe the high cement concentrations in that even the entire pore space may be filled with cement. In this work, elastic properties of 2080

dx.doi.org/10.1021/ef101665v |Energy Fuels 2011, 25, 2076–2082

Energy & Fuels

ARTICLE

THF hydrate-bearing sediment were then estimated by the extended CCT theory. The pore space of the sediment was assumed to be filled with THF hydrate because water could almost completely convert into hydrate when the molar fraction of THF solution is 5.9%. The elastic moduli K and G of a dense, random pack of identical elastic spheres with THF hydrate were calculated by eq 117
 nð1
φc Þ 4 3 3nð1
φc Þ Kh þ Gh Sn , G ¼ K þ Gh Sτ K ¼ 6 3 5 20

Table 3. Parameters Used for Model Predictions constituent quartz hydrate a

bulk modulus, GPa

shear modulus, GPa

36.6a

45.0a

7.7

a

Taken from Dvorkin et al.

density, g 3 cm
3

3.2 a

0.90 a

17

Table 4. Modeling Prediction Results of VPa

ð1Þ

run 2

run 4

run 5

measured

3984

3711

3859

contact cement (Model 3)

3812

3868

3877

surround and cement grains (Model 4)

3663

3718

3725

where Kh and Gh are the bulk and shear moduli of the hydrate, respectively; φ c is the critical porosity of the uncemented grain sand pack (φ c = 0.4); and n is the average number of contacts per grain, 8.5. Parameters Sn and Sτ are determined according to Dvorkin and Nur.21 The calculated method is as follows:

where F is bulk density of hydrate and sediment matrix frame, and it is calculated by

Sn ¼ An ðΛn ÞR2 þ Bn ðΛn ÞR þ Cn ðΛn Þ

ð2Þ

F ¼ ð1
φÞFsolid þ φFhydrate

An ðΛn Þ ¼
0:024153 3 Λn
1:3646

ð3Þ

Bn ðΛn Þ ¼ 0:20405 3 Λn
0:89008

ð4Þ

Cn ðΛn Þ ¼ 0:00024649 3 Λn
1:9846

ð5Þ

Sτ ¼ Aτ ðΛτ , vq ÞR2 þ Bτ ðΛτ , vq ÞR þ Cτ ðΛτ , vq Þ

ð6Þ

Aτ ðΛτ , vq Þ ¼
10
2 3 ð2:26v2q þ 2:07vq þ 2:3Þ 3 Λτ 0:079vq þ 0:1754vq
1:342 2

ð7Þ Bτ ðΛτ , vq Þ ¼ ð0:0573v2q þ 0:0937vq þ 0:202Þ 3 Λτ 0:0274vq þ 0:0529vq
0:8765 2

ð8Þ Cτ ðΛτ , vq Þ ¼ 10
4 3 ð9:654v2q þ 4:945vq þ 3:1Þ 3 Λτ 0:01867vq þ 0:4011vq
1:8186 2

ð9Þ Λn ¼

2Gh ð1
vq Þð1
vh Þ Gh , Λτ ¼ πGq πGq ð1
2vh Þ

ð10Þ

where vq and vh are the Poisson’s ratios of quartz grains and hydrate, respectively. They are calculated by vq = 0.5(Kq
2/ 3Gq)/(Kq þ 1/3Gq) (Kq and Gq are the bulk and shear modulus of the quartz grains) and v h = 0.5(Kh
2/3Gh)/(Kh þ 1/3Gh), respectively. π is a constant value, 3.14. Parameter R is related to the hydrate distribution. For Model 3, R is calculated by R = 2[(φc
φ)/(3n(1
φc))]0.25 (φ is free space. It equals zero if assuming that the pore space of the sediment was filled with THF hydrate). For Model 4, R is calculated by R = [(2(φ c
φ))/(3(1
φc))]0.5 . Once the elastic moduli of THF hydrate bearing sediment are calculated, the acoustic P-wave velocity could be predicted from eq 11: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u uK þ 4 G t 3 ð11Þ VP ¼ F

a

Units for all values are m 3 s
1.

ð12Þ

The parameters used for model predictions are listed in Table 3. Due to the absence of properties for (methane þ THF) hydrate, the moduli and density of methane hydrate were used instead. The results of VP for runs 2, 4, and 5 at THF concentration of 5.9 mol % were predicted and are listed in Table 4. It is known that when THF hydrate formed at the ratio of 5.9 mol %, there was little or no water left in the sediment after enough reaction time. However, when the initial THF concentration is lower than 5.9 mol %, it is difficult to determine the conversion ratio of water and the hydrate volume in the pore space in this case. Therefore, the VP values for hydrate formed at 3.0 mol % THF were not predicted. According to Table 4, it was clear that the extended CCT theory could provide better prediction precision. For experiment runs 2 and 5, the measured P-wave velocity of 3981 and 3859 ms
1 were in close agreement with those predicted by Model 3. In comparison, the VP value of experiment run 4 was closer to that predicted by Model 4. Because the CCT theory was used to describe the cement of hydrate bearing samples, it implied that the formed hydrate in this work acted as cement at intergranular grain contacts.

4. CONCLUSIONS Five groups of hydrate samples containing different sand grain size and THF concentration were synthesized to measure the P-wave velocity during hydrate formation process using an experimental apparatus developed in this work, where methane acted as a help gas. It was found that VP is greatly dependent on different pore filling materials. Before the formation of hydrate, VP varies from 1706 to 1782 ms
1 for THF aqueous solution saturated sediment. After that, VP increases with the hydrate growth, and it achieved a maximum value of 3295
3984 ms
1 after the completion of hydrate formation. The great increase of VP mainly attributes to the change of the hydrate concentration in the pore space. In comparison, the amplitude of first arrive wave signal would increase to a maximum value with the increase of hydrate saturation, but it decreases gradually due to the effect of free methane gas penetrating into the hydrate-bearing sediment. The predicted results of THF-hydrate-bearing sediment based on the extended contact cement theory are very close to the measured data in this work. 2081

dx.doi.org/10.1021/ef101665v |Energy Fuels 2011, 25, 2076–2082

Energy & Fuels

’ AUTHOR INFORMATION Corresponding Author

*Fax: þ86 10 89732126. E-mail: [email protected] (C.Y.S.); [email protected] (G.J.C.).

’ ACKNOWLEDGMENT The financial support received from the National Natural Science Foundation of China (20925623, 21076225), NCET07-0842, Targeted Advanced Item of China University of Petroleum (QZDX-2010-02), and National 973 Project of China (2009CB219504) is gratefully acknowledged. ’ REFERENCES (1) Clennell, M. B.; Hovland, M.; Booth, J. S.; Henry, P.; Winters, W. J. Formation of natural gas hydrates in marine sediments 1. Conceptual model of gas hydrate growth conditioned by host sediment properties. J. Geophys. Res. 1999, 104 (B10), 22985–23003. (2) Sloan, E. D. Fundamental principles and applications of natural gas hydrates. Nature 2003, 426 (20), 353–359. (3) Klauda, J. B.; Sandler, S. I. Global distribution of methane hydrate in ocean sediment. Energy Fuels 2005, 19 (2), 459–470. (4) Reagan, M. T.; Moridis, G. J. Large-scale simulation of methane hydrate dissociation along the West Spitsbergen Margin. Geophys. Res. Lett. 2009, 36 doi: 10.1029/2009GL041332. (5) Pearson, C. F.; Halleck, P. M.; McGulre, P. L.; Hermes, R.; Mathews, M. Natural gas hydrate deposits: A review of in situ properties. J. Phys. Chem. 1983, 87, 4180–4185. (6) Buffet, B. A.; Zatsepina, O. Y. Formation of gas hydrate from dissolved gas in natural porous media. Mar. Geol. 2000, 164, 69–77. (7) Carcione, J. M.; Gei, D. Gas-hydrate concentration estimated from P- and S-wave velocities at the Mallik 2L-38 research well, Mackenzie Delta, Canada. J. Appl. Geophys. 2004, 56, 73–78. (8) Waite, W. F.; Winters, W. J.; Mason, D. H. Methane hydrate formation in partially water-saturated Ottawa sand. Am. Mineral. 2004, 89, 1202–1207. (9) Winters, W. J.; Waite, W. F.; Mason, D. H.; Gilbert, L. Y.; Pecher, I. A. Methane gas hydrate effect on sediment acoustic and strength properties. J. Petrol. Sci. Eng. 2007, 57, 127–135. (10) Westbrook, G. K.; Chand, S.; Rossi, G.; Long, C.; B€unz, S.; Camerlenghi, A.; Carcione, J. M.; Dean, S.; Foucher, J. P.; Flueh, E.; Gei, D.; Haache, R. R.; Madrussani, G.; Mienert, J.; Minshull, T. A.; Nouze, H.; Peacock, S.; Reston, T. J.; Vanneste, M.; Zillmer, M. Estimation of gas hydrate concentration from multi-component seismic data at sites on the continental margins of NW Svalbard and the Storegga region of Norway. Mar. Pet. Geol. 2008, 25, 744–758. (11) Winters, W. J.; Pecher, I. A.; Waite, W. F.; Mason, D. H. Physical properties and rock physics models of sediment containing natural and laboratory-formed methane gas hydrate. Am. Mineral. 2004, 89, 1221–1227. (12) Pearson., C.; Murphy, J.; Hermes, R. Acoustic and resistivity measurements on rock samples containing tetrahydrofuran hydrates: Laboratory analogues to natural gas hydrate deposits. J. Geophys. Res. 1986, 91 (B14), 14132–14138. (13) Sabase, Y.; Nagashima, K. Growth mode transition of tetrahydrofuran clathrate hydrates in the guest/host concentration boundary layer. J. Phys. Chem. B 2009, 113, 15304–15311. (14) Priest, J. A.; Best, A. I.; Clayton, C. R. I. A laboratory investigation into the seismic velocities of methane gas hydrate-bearing sand. J. Geophys. Res. 2005, 110, B04102; doi 10.1029/2004JB003259. (15) Priest, J. A.; Best, A. I.; Clayton, C. R. I. Attenuation of seismic waves in methane gas hydrate-bearing sand. Geophys. J. Int. 2006, 164, 149–159; doi 10.1111/j.1365-246X.2005.02831.x.

ARTICLE

(16) Pride, S. R.; Berryman, J. G.; Harris, J. M. Seismic attenuation due to wave-induced flow. J. Geophys. Res. 2004, 109, B01201; doi 10.1029/2003JB002639. (17) Dvorkin, J.; Helgerud, M. B.; Waite, W. F.; Kirby, S. H.; Nur, A. Introduction to physical properties and elasticity models. In Mas, M. D., Ed., Natural Gas Hydrate in Oceanic and Permafrost Environments; Kluwer: Dordrecht, Netherlands, 2000; pp 245
260. (18) Winters, W. J.; Dallimore, S. R.; Collett, T. S.; Katsube, T. J.; Jenner, K. A.; Cranston, R. E.; Wright, J. F.; Nixon, F. M.; Uchida, T. Physical properties of sediments from the JAPEX/JNOC/GSC Mallik 2L-38 gas hydrate research well. Bull. Geol. Surv. Can., Rep. 1999, 544, 95–100. (19) Priest, J. A.; Rees, E. V. L.; Clayton, C. R. I. Influence of gas hydrate morphology on the seismic velocities of sands. J. Geophys. Res., 2009, 114, B11205; doi:10.1029/2009JB006284. (20) Dvorkin, J.; Berryman, J.; Nur, A. Elastic moduli of cemented sphere packs. Mech. Mater. 1999, 31, 461–469. (21) Dvorkin, J.; Nur, A. Elasticity of high-porosity sandstones: Theory for two North Sea data sets. Geophysic 1996, 61, 1363–1370.

2082

dx.doi.org/10.1021/ef101665v |Energy Fuels 2011, 25, 2076–2082