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The effective thermal conductivity of methane hydrate-bearing seasand
J. Chem. Thermodynamics 132 (2019) 423–431
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The effective thermal conductivity of methane hydrate-bearing seasand Shicai Sun a,b,⇑, Jianrui Zhao a, Jie Zhao a, Yuchao Hao a, Jing Yang c a Shandong Key Laboratory of Civil Engineering Disaster Prevention and Mitigation, College of Civil Engineering and Architecture, Shandong University of Science and Technology, Qingdao 266590, China b State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation (Southwest Petroleum University), Chengdu 610500, China c College of Chemical and Environmental Engineering, Shandong University of Science and Technology, Qingdao 266590, China
a r t i c l e
i n f o
Article history: Received 18 September 2018 Received in revised form 14 January 2019 Accepted 26 January 2019 Available online 28 January 2019 Keywords: Methane hydrate Seasand Sample preparation Saturation Thermal conductivity Model
a b s t r a c t The thermal properties of hydrate-bearing sediments can help to evaluate the stability of hydrate reservoir and improve the safety of natural gas hydrate exploitation. In this work, the thermal conductivities of methane hydrate and methane hydrate-bearing seasand were investigated by the transient plane source (TPS) technique. The high-quality samples of hydrate were prepared by synergistic uses of a variety of methods, i.e., the ‘‘seeding” ice, simultaneous slowly heating and slowly supplying gas, temperature oscillation and aging method. The measured thermal conductivity of methane hydrate is 0.4877– 0.5467 Wm1K1 with the temperature 263.2–283.1 K and the pressure 4.0–9.5 MPa. The effective thermal conductivities of the saturated seasand sample, supersaturated seasand sample and unsaturated seasand sample (Here, the ‘‘saturated”, ‘‘unsaturated” and ‘‘supersaturated” refers to the three relationships between the pore volume of seasand and the volume of ice powder, respectively) are 1.1310– 1.2703 Wm1K1, 1.0070–1.1490 Wm1K1, 0.9221–1.1980 Wm1K1 with the pressure 8.0 MPa and the temperature 253.8–281.2 K, respectively. The effective thermal conductivities of the saturated sample, supersaturated sample and unsaturated sample are 1.1280–1.1402 Wm1K1 (1.1331– 1.5974 Wm1K1), 1.0172–1.0252 Wm1K1 (1.0181–1.2032 Wm1K1), 0.9154–0.9388 Wm1K1 (0.9401–1.1543 Wm1K1) with the pressure 4.0–10.0 MPa and the temperature 263.2 K (275.2 K), respectively. The relationship between the effective thermal conductivity and methane hydrate saturation in the sample are ke,saturated > ke,supersaturated > ke,unsaturated. The results suggest that the thermal conductivities of methane hydrate and methane hydrate-bearing seasand are positively correlated with the temperature and the influence of the gas phase pressure is negligible. Besides, the effective thermal conductivity shows a sudden increase near to the phase equilibrium temperature. Due to the complex of actual samples, the same classic theory model cannot accurately predict three samples simultaneously. Ó 2019 Elsevier Ltd.
1. Introduction The abundant natural gas hydrate resources in the seabed sediments and permafrost region are considered to be one of the most promising new energy [1]. However, natural gas hydrates are a ‘‘double-edged sword” that, while bringing abundant resources to humans, may also cause environmental and geological disasters such as global warming, submarine geological collapse and landslides [2,3]. The stability zone of natural gas hydrates is determined by the thermodynamic phase equilibrium, geothermal gradient and pressure gradient. The changes of temperature and pressure have a great influence on it, especially temperature fluctuations. Therefore, the thermal properties of hydrate-bearing sed-
⇑ Corresponding author. E-mail address: [email protected] (S. Sun). https://doi.org/10.1016/j.jct.2019.01.023 0021-9614/Ó 2019 Elsevier Ltd.
iments can help to evaluate the stability of hydrate reservoirs and the formation of submarine landslides so as to improve the safety of natural gas hydrate mining. At present, the research on the thermal properties of natural gas hydrates is relatively less and the existing experimental data have a large difference [4–9]. Besides, the views on the effects of temperature and pressure on the thermal properties are also different. Cook and Leaist [9] used the hot plane method to measure the thermal conductivity of methane hydrate to be 0.45 Wm1K1 at about 213.2 K. Huang and Fan [4] measured the thermal conductivities of the compacted/uncompacted methane hydrate sample. The thermal conductivity value of the uncompacted sample was 0.334–0.381 Wm1K1, and the thermal conductivity of the compacted sample was 0.568– 0.587 Wm1K1. Besides, the thermal conductivity increased with the increase of temperature. In contrast, Waite et al. [6,10] showed that the thermal conductivity of methane hydrate was negatively
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of the thermal conductivity of pure hydrate or hydrate-bearing sediments are different so that it is necessary to conduct an indepth research. The measurement method of thermal conductivity can be roughly divided into two categories: steady state method and non-steady state method [17]. The steady state method requires a steady state temperature field within the test sample, so the application is subject to many restrictions. The nonsteady-state method has the advantages of short measurement time, high precision, and easy environmental conditions, which is widely used. The non-steady state method mainly includes hot wire method, tropical method, probe method, and TPS technique. Each method has its own characteristics and application scope. Even if the same method is employed, the samples obtained by different preparation method have a great influence on the results. In this work, the TPS technique was used to study hydrate thermal properties. The main component of naturally occurring gas hydrates is methane gas, so the thermal properties of methane hydrate and methane hydrate-bearing seasand were investigated. This work will provide important basis for natural gas hydrate production.
correlated with the temperature, suggesting that it may be that the hydrate sample contained pore gas and unconverted ice; when the pressure was increased, the thermal conductivity of the hydrate sample increased rapidly. Rosenbaum et al. [5] reported that the thermal conductivity of the compacted methane hydrate sample decreased slightly with the increase of temperature, and the average thermal conductivity was about 0.68 ± 0.01 Wm1K1. Therefore, it can be seen that the thermal conductivity of methane hydrate is 0.33–0.68 Wm1K1 and the dependences on the temperature are inconsistent. Similarly, the literature conclusions on the effective thermal conductivity of hydrate-bearing sediments differ more greatly. Li et al. [7,11] used a single-sided transient plane source (TPS) technique to measure the effective thermal conductivity of methane hydratebearing porous media. The results showed that the effective thermal conductivity decreased with the increase of the sample porosity and was weakly negatively correlated to the temperature. Huang [12] found that the effective thermal conductivity of silica sand with saturated methane hydrate was about 1.1 Wm1K1 in the temperature range of 263.2–277.2 K. Waite et al. [13] measured the effective thermal conductivity of methane hydrate in silica sand in a certain range of temperature and pressure using the probe method. They found that the effective thermal conductivity was inversely proportional to the temperature and proportional to gas phase pressure. Wang et al. [8] found that the effective thermal conductivity was proportional to the hydrate saturation, water content and quartz sand thermal conductivity in the sample. But Yang et al. [14] showed that the effective thermal conductivity was inversely related to the hydrate saturation while it was positively correlated with the initial water content and the sediment thermal conductivity. The effective thermal conductivity of unconsolidated sediments in gas hydrate reservoirs at the Mallik Gas Hydrate Production Research Base was approximately 2.5–3.0 Wm1K1 [15]. Using the petrophysical model and the geothermal gradient, Henninges et al. [16] estimated the effective thermal conductivity of Mallik gas hydrates to be about 2.35–2.77 Wm1K1. It can be seen from the above literatures that due to the differences in equipment, methods and samples, the experimental data
2.1. Experimental equipment An experimental setup was built for the measurement of hydrate thermal conductivity, which consisted of hydrate formation system and thermal conductivity measurement system, as shown in Fig. 1. The hydrate formation system included a hydrate reactor, a buffer tank, an air-cooling bath, a gas supply unit, a vacuuming device and data acquisition unit. The hydrate reactor was made of cylindrical stainless steel, the inner diameter and the length of which was 52 mm and was 30 mm, respectively. So the effective volume of the reactor was about 64 ml. During the experiments, the reactor was submerged in the air bath. The temperature range of the air bath was 253.2–373.2 K with a heating rate of 2.0–3.0 K/min and a cooling rate of 0.7–1.0 K/min. The buffer tank with a capacity of 1 L was placed in the air bath, which can
Pressure Transducer
Pressure Guage P
2. Experimental
Vacuum Guage
P
P
P Buffer Tank Gas Flux Monitor
Supercharging Equipment
Temperature Transducer
Pressure Transducer P
Vacuum Container
Vacuum Pump
T Air Bath
CH4
Reactor
Hotdisk Probe Pt100
Fig. 1. Hydrate formation and thermal conductivity measurement system.
Hotdisk Thermal Constants Analyser
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S. Sun et al. / J. Chem. Thermodynamics 132 (2019) 423–431 Table 1 Experimental materials. Material a
CH4 Natural seasand Deionized water a
Component
Purity
Analytical method
Supplier
CH4
0.999
Gas chromatography
Nanjing Special Gas Factory of China Taken from the offshore area of Qingdao, China Laboratory-made
CH4 was delivered by the supplier and used without any further treatment. The standard uncertainty of CH4 purity on the basis of molar fraction is 0.001.
Table 2 Specification of natural seasand.
a b
Particle size/lm
<4
4–63
63–250
250–500
500–2000
>2000
Volume percentage/%a Porosity/%b
0.000 39.93
0.000
22.173
77.827
0.000
0.000
The percentage of particle size is on a basis of volume fraction. The standard uncertainty is 0.001. The porosity was calculated by the weight difference between dry seasand and saturated seasand with water. The standard uncertainty is 0.01.
be used to pre-cool the gas and maintain the system stability of the temperature and pressure. The gas supply unit included gas cylinder and supercharging equipment. The vacuuming device mainly comprised a vacuum pump and a vacuum container. The gas flux was monitored by a gas flux monitor supplied by China Beijing Qixing Huachuang Company. The temperature inside the reactor was monitored by the platinum resistance thermometer sensor Pt100 (with an uncertainty of ±0.1 K), which was located below the center of the reactor. There were two pressure gauges for displaying the pressure of gas supply unit and pressure regulator, respectively. The pressures of the reactor and the buffer tank during the experiments were detected by pressure transducers with an uncertainty of ±0.1 MPa. All signals during the experiments were recorded in real time by the Agilent data acquisition instrument 34970A. The thermal conductivity of hydrate was measured by Hot Disk thermal constants analyzer, which was made by Sweden Hot Disk AB Company. It was based on TPS technique. Hot Disk probe was a double spiral shape, which acted both as a heat source to increase the sample temperature and as a resistance thermometer to record the temperature. According to the hydrate sample, the type 8563 of Hot Disk probe was employed in this work. The probe was located in the middle of the reactor, which was inserted and fixed from the top of the reactor. 2.2. Experimental materials The materials used in experiments included methane gas, natural seasand and deionized water, as shown in Table 1. The purity of methane gas was 99.9% (molar fraction), which was provided by Nanjing Special Gas Factory of China, and no further treatment was carried out before the experiments. The deionized water was prepared by our laboratory. The natural seasand was taken from the offshore of Qingdao, China. The particle size of the seasand was measured and analyzed by Malvern laser particle size analyzer (MS2000) before the experiments, as shown in Table 2. In experiments, the hydrate samples were prepared using ice powder. In order to minimize the interference of pore gas between ice powder particles, the standard sieve with a pore size of 75 lm was used to screen ice powder, that is, the ice powder with the particle size less than 75 lm was employed in the experiments. The natural seasand and ice powder were uniformly mixed in a liquid nitrogen cup, and then charged into the reactor to synthesize the hydrate samples. According to the proportion of the seasand pore volume occupied by ice powder, three kinds of ice powder-seasand mixture were used to synthesize hydrate samples, i.e., seasand saturated by ice powder, seasand supersaturated by ice powder and seasand unsaturated by ice powder.
2.3. Preparation of hydrate samples The quality of hydrate sample has a great influence on the measurement accuracy of the thermal property, so it is very important to prepare a high-quality hydrate sample. The solubility of methane gas in water is low, which causes the formation rate of hydrate to be very slow so that the conversion rate of water is extremely low [1]. In addition, the gas-liquid interface is obvious in the static reaction system, and hydrate nucleation generally first occurs at the gas-liquid interface. Therefore, the solid hydrate slowly covers the entire interface, thereby reducing or isolating the contact between gas and water, so-called armor effect [18]. So it is difficult to completely convert water into hydrate during a limited experimental period, thereby affecting the quality of hydrate sample and the measurement accuracy of the thermal property. In order to increase the conversion rate of water, some promotion technologies, for examples, surfactant, ‘‘seeding” ice method and mechanical stirring and so on, are generally used [18–24]. Mechanical agitation can shorten the induction time of hydrate formation and increase the conversion rate, but the Hot Disk probe is installed in the reactor so that this method is not suitable in this work. Surfactants have a significant effect on hydrate formation [14–17], but they may affect the purity of the hydrate samples so as to affect hydrate thermal property. Huang and Fan [4] found that sodium dodecyl sulfate (SDS) had little effect on hydrate thermal conductivity, while Rosenbaum et al. [5] considered that the residual water-surfactant affected the measurement results. Ice powder has a large specific surface area and polyhedral units produced by melting ice, which are favorable for hydrate formation, so it is often used to synthesize hydrates. Hwang et al. [21] considered that the melting ice provided a template for hydrate nucleation and could absorb the heat generated by the hydrate formation. Sloan and Fleyfel [22] proposed a melting reaction model of hydrates to explain the kinetic characteristics and induced phenomena. Stern et al. [18,23,24] used ice powder with a particle size of 180–250 lm to synthesize methane hydrate under static conditions with 25–35 MPa above freezing point, and obtained highquality methane hydrate, which was called ‘‘seeding” ice method. Hydrate formation by ice powder has the advantages of short induction time, high conversion rate and no residual impurities, but the pores of ice powder are easy to retain gas. Some literatures reported that the residual gas can be removed by mechanical compaction after the preparation of the hydrate sample was completed [6,7,10,11,25]. Although mechanical compaction can effectively reduce the pores, it is easy to cause the damage or defects of the hydrate crystal, thereby affecting the thermal conductivity. In this work, a modified ‘‘seeding” ice-compacted ice powder method was proposed and a variety of other methods, i.e., simultaneous slowly
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Fig. 2. Ice production apparatus, ice powder and loading ice powder into the reactor in the freezer.
heating and slowly supplying gas, temperature oscillation and aging method, were used in combination to prepare hydrate samples. In the process of hydrate formation, the temperature oscillation method was employed to promote the complete conversion of water (ice) and improve the purity (quality) of hydrate samples. Before preparing the ice powder, the following work has to be done firstly. Hydrate formation requires a high pressure and low temperature condition, so the experimental equipment must be rigorous air tightness. The reactor was rinsed three times with deionized water and then dried by a blower. The air bath was maintained at 263.2 K, and then the buffer tank was pressurized with methane gas to the required pressure. Methane gas was pre-cooled to prevent the ice powder from being melted by the high temperature gas directly entering the reactor. Besides, the dried reactor and the sampler were also pre-cooled in a freezer to prevent the ice powder from being melted during loading and compacting the ice powder with the sampler. The ice powder production apparatus, designed by Qingdao Institute of Marine Geology, was used to prepare the ice powder. The ice powder production apparatus, granular ice powder and ice powder loading into the reactor in the freezer were shown in Fig. 2. First of all, the deionized water was atomized by an atomizer to obtain the droplets with a particle size of microns. In the liquid nitrogen environment, these droplets froze rapidly to become ultra-fine ice powder. The standard sieve was cooled in advance with liquid nitrogen and then was used to screen the ice powder to obtain the desired granules of ice powder. The mesh size of standard sieve was 75 lm, thus the maximum particle size of the granular ice used in this work was 75 lm. Simultaneously, the quantitative natural seasand was pre-cooled in a liquid nitrogen cup. After the preparation of ice powder, the quantitative ice powder was also poured into the liquid nitrogen cup. Then the ice powder and natural seasand were mixed evenly in the liquid nitrogen environment. After the above steps were completed, the hydrate sample synthesis was carried out as follows. The ice powder-seasand mixture was transferred to the freezer as soon as possible, and then the mixture was filled into the reactor in the freezer. Since the residual free gas and unconverted ice (water) in the hydrate sample have great influence on the thermal property, the quantitative ice powder-seasand mixture was charged into the reactor, and then the mixture was compacted by the sample. Certainly, for the pure methane hydrate, only quantitative ice powder was charged into the reactor. The entire reactor was filled with either the ice powder or the mixture. After the reactor was installed in the freezer, it was quickly transferred to a low temperature air bath (pre-cooled to 263.2 K). Afterwards, the remaining installation was completed in the air bath in the shortest time. The reactor was vacuumed for 20 min and maintained for more than 2 h to check for leaks again. Once the temperature inside the reactor was stabilized, the precooled methane gas in the buffer tank was slowly charged into the reactor. While charging the reactor with gas, the air bath temperature was adjusted immediately so that the reactor was pressurized and heated at the same time. Finally, the temperature in
the reactor was stabilized at about 273.4 K and the pressure was about 10.0 MPa. Methane gas reacted quickly with ice powder with almost no induction time. At the beginning of hydrate formation within 24 h the pressure dropped significantly, therefore, secondary pressurization was carried out. After the pressure was stabilized in the end, the temperature of the air bath was adjusted so that the temperature was oscillated more than three cycles between 263.2 and 278.2 K to increase the granular ice (water) conversion degree. The hydrate samples were aged for three days under the conditions of stable temperature and pressure to eliminate possible residual water. Simply, the volume of ice powder was approximately considered to be the volume of methane hydrate in this work so that the samples prepared by three kinds of ice powder-seasand mixture were approximately considered to the seasand saturated/supersaturated/unsaturated by methane hydrate. And then the temperature and pressure in the reactor were stepwise changed to measure the thermal conductivity under different temperature and pressure conditions. Generally, the sample temperature, probe type and cable type are easily determined while determining the test time and output power of Hot Disk thermal constants analyzer require a large number of repeated experiments. In this work, the probe type 8563 was used and the parameters of test time and output power are determined through many experiments as shown in Table 3. Each test was conducted three times at a time interval of 15–20 min, taking the average of the three measurements as the measured value for that point. In summary, hydrate formation was finished through slowly heating and slowly pressuring the system simultaneously. Mathane gas reacted rapidly with ice powder, and then the temperature oscillating method was used to further increase the ice powder (water) conversion degree. The advantages of the above process were as follows. Using ‘‘seeding” ice method to prepare methane hydrate can effectively avoid the interfacial tension because granular ice has a large specific surface area. Methane gas molecules were adsorbed directly into the skeleton structure of compacted granular ice to form stable hydrate. When the temperature was about 273.2 K, the ice particle surface has a water film with a suitable thickness for gas molecules to enter [12]. In order to avoid the armor effect [18] during hydrate formation, slowly charging gas method was utilized so that the surroundings of the granular ice achieved the desired gas concentration synchronously as much as possible. Simultaneous heating during gas
Table 3 The parameters of test time and output power.a Sample
Output power/W
Test time/s
Ice powder Methane hydrate Methane hydrate-bearing seasand
0.2–0.45 0.1–0.2 0.20–0.45
20 160 80
a The standard uncertainties of output power and test time are 0.01 W and 1 s, respectively.
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supply can increase the diffusion rate of gas molecules, which facilitates the advancement of the hydrate layer into the interior of the ice powder. The temperature oscillating method and secondary gas supply can effectively promote the hydrate formation and thus improve the quality of hydrate samples. When hydrate thermal conductivity was measured with Hot Disk thermal constants analyzer, the temperature and pressure of the system must be stable. 3. Results and discussion Before experiments, the thermal conductivity of the compacted ice powder was firstly measured to verify the feasibility of the above method. Besides, it was useful to check the compacted degree of the ice powder. In this work, the thermal conductivity of the compacted ice powder at 268.2 K in the vacuum environment is 2.2213 Wm1K1, which is very similar to that of ice at the same temperature measured by other researchers [10,26–29]. The thermal conductivity of methane gas is very small, about 0.03 Wm1K1 [8], so that the methane gas contained in hydrate sample easily interfere with the measurement results. Therefore, it can be concluded that the compacted ice powder with the sampler can effectively reduce the sample porosity in this work. The compacted ice powder provides a skeleton structure for the hydrate formation and the hydrate sample has less pore gas. Methane hydrate and methane hydrate-bearing seasand were formed using the above method and the thermal conductivities were measured under different conditions. 3.1. Methane hydrate The measured thermal conductivities of methane hydrate are shown in Table 4 and Fig. 3. It can be seen that the thermal conductivity of methane hydrate exhibits a positive trend with temperature and increases from 0.4877 Wm1K1 at 263.2 K to 0.5467 Wm1K1 at 283.1 K with the pressure 9.5 MPa. Moreover, the gas phase pressure has little effect on the thermal conductivity of methane hydrate between 4.0 MPa and 9.5 MPa. The thermal conductivities show a sudden increase near to the phase equilibrium temperature. Huang and Fan [4] used SDS to promote methane hydrate formation in silica sand and found that the thermal conductivities of both the compacted and uncompacted hydrate samples exhibited a positive trend with temperature. The results of this work are between those of the compacted and uncompacted sample. Although the addition of SDS can promote the formation of hydrate, as an impurity, it may affect hydrate thermal conductivity. The mechanical compaction can effectively reduce the porosity of the hydrate sample, but it is likely to cause hydrate crystal fragmentation [7,11]. The experimental results show that the synthesis method of hydrates with compacted granular ice can avoid the problems caused by surfactant and mechan-
Table 4 Thermal conductivities of methane hydrate with the temperature 263.2–283.1 K and the pressure 4.0–9.5 MPa.a T/K
p = 9.5 MPa k/Wm1K1
p = 6.0 MPa k/Wm1K1
p = 4.0 MPa k/Wm1K1
263.2 267.2 271.1 275.3 279.2 280.9 283.1
0.4877 0.4868 0.4904 0.4936 0.5117 0.5258 0.5467
0.4851 0.4884 0.4892 0.4925 0.4946
0.4846 0.4864 0.4953 0.4926
a The symbol T, p and k represent the temperature, pressure and thermal conductivity, respectively. The standard uncertainties u are u(T) = 0.1 K, u(p) = 0.1 MPa, u(k) = 0.0001 Wm1K1.
Fig. 3. Thermal conductivity of methane hydrate with the temperature 263.2– 283.1 K and the pressure 4.0–9.5 MPa.
ical compaction. In this work, a modified ‘‘seeding” ice-compacted ice powder method was proposed and a variety of other methods, i.e., simultaneous slowly heating and slowly supplying gas, temperature oscillation and aging method, were used in combination to remove the residual ice crystals as much as possible so as to obtain pure hydrate. Stern et al. [18] used ‘‘seeding” ice powder method to produce 15 samples that showed consistent and reproducible reaction process, methane consumption, XRD patterns and physical appearances. Furthermore, these samples occupied cylindrical volume as the initial seeding ice and the samples contained almost the same porosity. That is to say, the initial ice powder constructs the skeleton of methane hydrate sample, and the skeleton changes little after hydrate formation. Similarly, for the samples of methane hydrate-bearing seasand formed by this method, the initial contact state of the ice powder with seasand particles can also approximate the contact state between methane hydrate and seasand particles. Therefore, it is reasonable to assume that these samples of methane hydrate (methane hydrate-bearing seasand) obtained in this work are nearly identical. In addition, the same measurement method of thermal conductivity is employed in the experiments. So the measured results are more consistent and reproducible. 3.2. Methane hydrate-bearing seasand 3.2.1. The influence of temperature Naturally occurring gas hydrates exist in sediments so that it is more practical to study the effective thermal conductivity of hydrate-bearing sediments with different saturations. In experiments, the samples of methane hydrate-bearing seasand with three different saturations were prepared, i.e., saturated sample, supersaturated sample and unsaturated sample, and the effective thermal conductivities were measured with the pressure 8.0 MPa and the temperature 253.8–281.2 K, as shown in Table 5 and Fig. 4. It can be seen that for the saturated sample, supersaturated sample and unsaturated sample the effective thermal conductivities are 1.1310–1.2703 Wm1K1, 1.0070–1.1490 Wm1K1, 0.9221–1.1980 Wm1K1, respectively. The effective thermal conductivity is positively correlated with temperature, which is the same trend as that of pure methane hydrate. Huang [12] reported that the effective thermal conductivity of 125–300 lm silica sand saturated by methane hydrate increased with the increase of temperature, and the effective thermal conductivity was 1.0–1.1 Wm1K1 in the temperature range of 263.2–277.2 K. Moreover, at around 281.2 K, which is near to the phase equilib-
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Table 5 Effective thermal conductivity of methane hydrate-bearing seasand at p = 8.0 MPa.a Saturated sample
Supersaturated sample 1
T/K
ke /Wm
253.8 257.2 258.6 260.2 263.2 266.2 267.6 269.2 272.0 272.95 275.2 278.2 281.2
1.1341 1.1331 1.1342 1.1354 1.1341 1.1440 1.1460 1.1472 1.1494 1.1310 1.1331 1.1382 1.2703
K
1
Unsaturated sample 1
T/K
ke/Wm
253.8 256.5 259.1 261.1 263.1 265.5 267.8 270.6 273.4 275.2 277.1 279.2 281.1
1.0070 1.0161 1.0212 1.0221 1.0220 1.0230 1.0221 1.0202 1.0173 1.0153 1.0221 1.0331 1.1490
K
1
T/K
ke/Wm1K1
253.8 256.3 258.5 261.0 263.1 265.7 268.2 270.7 273.3 275.3 277.4 279.2 281.2
0.9221 0.9265 0.9284 0.9253 0.9293 0.9350 0.9373 0.9366 0.9342 0.9396 0.9522 0.9753 1.1980
a The symbol T, p and ke represent the temperature, pressure and effective thermal conductivity, respectively. The standard uncertainties u are u(T) = 0.1 K, u(p) = 0.1 MPa, u (ke) = 0.0001 Wm1K1.
Fig. 4. Effective thermal conductivity of methane hydrate-bearing seasand versus temperature.
rium temperature, the effective thermal conductivity shows a sudden increase. This phenomenon indicates that the heat transfer performance is enhanced near to hydrate equilibrium sate that can be used as a signal for the onset of hydrate dissociation [29]. The low thermal conductivity is one of the important reasons why natural gas hydrates can exist in shallow submarine sediment. It can also be seen from Fig. 4 that the effective thermal conductivities of methane hydrate-bearing seasand samples with different saturations differ largely. At the same temperature, the effective thermal conductivity exhibits an obvious trend, i.e., ke,saturation > ke,supersaturation > ke,unsaturation. Here, ke,saturation, ke,supersaturation and ke,unsaturation represent the effective thermal conductivity of the saturated sample, supersaturated sample and unsaturated sample, respectively. This trend is related to the macroscopic distribution patterns, the component and their inherent thermal conductivity. Natural gas hydrates mainly occur in the form of layers, blocks, dispersions and veins, which can directly indicate the abundance of hydrates in sediments and is very important for the exploration and evaluation of hydrate resource. These macroscopic distribution pattern may be expressed as the contact relationship between hydrates and sediments at the microscopic level, that is, porefilling type (i.e. hydrate floats in pore fluid), contact type (i.e. hydrate contacts with the sediment particles) and cementing type (i.e. hydrate cements the sediment particles). The hydrate distribution pattern is related to sediments, gas sources, pore fluids, and
formation conditions. If the sediments are saturated by the pore fluid and the gas source is sufficient, the hydrates will cement the sediment particles in the end, i.e. cementing type. If the hydrates are suspended in the pore fluid, i.e. pore-filling type, there are some migration channels between the hydrates and the sediments so that the pores are filled with the pore water, dissolved gas or free gas. When the pore water is excessive, it is easy to form the contact type [30–32]. It is clear that the distribution pattern of hydrates in the sediment directly affects the effective thermal conductivity. In this work, the ice powder and seasand are evenly mixed so that ice powder must be in contact with sediment particles and the mixture of seasand and ice powder can be considered as loose sediments. Methane gas is sufficient so that the ice powder is completely converted into the hydrate. As mentioned above, Stern et al. [18] considered that methane hydrate that was formed by the seeding ice directly replaced the location of the ice in the sediments. That is to say, the initial seasand and ice powder particles construct the sample skeleton of methane hydrate-bearing seasand, so the initial contact state of the ice powder with seasand particles can also approximate the contact state between methane hydrate and seasand particles. Therefore, regardless of whether the seasand is saturated with ice powder, the distribution pattern of the formed hydrate is more likely to be contact type and the components in the formed sample include seasand, methane hydrate and pore methane gas. For the saturated and supersaturated samples, the pores in the sample are relatively less so that the content of methane gas in the pores is less. However, the proportion of hydrates in the supersaturated sample is larger; correspondingly, the proportion of seasand is smaller. For the unsaturated sample, there are relatively more pores in the sample. The thermal conductivities of seasand, methane hydrate and methane gas are about 5.0 Wm1K1 [33], 0.5 Wm1K1, 0.03 Wm1K1 [7], respectively. According to the above analysis, the effective thermal conductivity of methane hydrate-bearing seasand exhibits an obvious trend, i.e., ke,saturation > ke,supersaturation > ke,unsaturation. 3.2.2. The influence of gas phase pressure The effect of gas phase pressure on the effective thermal conductivity of methane hydrates-bearing seasand with different saturations was also investigated in this work in the pressure range of 4.0–10.0 MPa and at the temperature of 263.2 K and 275.2 K, as shown in Table 6 and Fig. 5. The effective thermal conductivities of the saturated sample, supersaturated sample and unsaturated sample are 1.1280–1.1402 Wm1K1, 1.0172–1.0252 Wm1K1, 0.9154–0.9388 Wm1K1 with the pressure 4.0–10.0 MPa and the temperature 263.2 K, respectively. The effective thermal con-
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S. Sun et al. / J. Chem. Thermodynamics 132 (2019) 423–431 Table 6 Effective thermal conductivity of methane hydrate-bearing seasand at 263.2 and 275.2 K.a T/K
p/MPa
Saturated sample ke/Wm1K1
Supersaturated sample ke/Wm1K1
Unsaturated sample ke/Wm1K1
263.2
4.0 6.0 8.0 10.0
1.1280 1.1301 1.1341 1.1424
1.0172 1.0180 1.0220 1.0252
0.9154 0.9141 0.9293 0.9388
275.2
4.0 6.0 8.0 10.0
1.5974 1.1343 1.1331 1.1371
1.2032 1.0143 1.0154 1.0181
1.1543 0.9451 0.9401 0.9480
a The symbol T, p and ke represent the temperature, pressure and effective thermal conductivity, respectively. The standard uncertainties u are u(T) = 0.1 K, u(p) = 0.1 MPa, u (ke) = 0.0001 Wm1K1.
Fig. 5. Effective thermal conductivity of methane hydrate-bearing seasand versus gas phase pressure.
ductivities of the saturated sample, supersaturated sample and unsaturated sample are 1.1331–1.5974 Wm1K1, 1.0181– 1.2032 Wm1K1, 0.9401–1.1543 Wm1K1 with the pressure 4.0–10.0 MPa and the temperature 275.2 K, respectively. It can be seen that the effective thermal conductivity of hydrate samples slightly increases with the increase of gas phase pressure. Relatively, the thermal conductivity of the unsaturated samples changes obviously. But the effect of gas phase pressure is relatively very small. Waite et al. [13] synthesized methane hydrate-bearing silica sand with ice powder and measured the effective conductivity of the samples containing 1/3 and 2/3 methane hydrate content in the pressure range of 3.5–27.6 MPa at 263.2 K. The results showed that the effective thermal conductivity of the two samples increased with the increase of gas phase pressure. Since the fraction of methane hydrate with relatively low thermal conductivity increases in the sample, replacing the silica sand (seasand) with high thermal conductivity, to result in the decrease of the effective thermal conductivity of the sample. Similarly, the effective thermal conductivity shows a sudden increase at the temperature 281.2 K and pressure 4.0 MPa, which indicates that the structure of hydrate sample may be changed close to the equilibrium state. In addition, Fig. 5 further confirms the relationship between the effective thermal conductivity and methane hydrate saturation in the sample, i.e., ke,saturation > ke,supersaturation > ke,unsaturatin, which also suggests good repeatability of the experiments. 3.3. Classical theoretical model verification In this work, the classical models [12,27] including parallel distribution (PD) model, continuous distribution (CD) model, random
distribution model, two-phase Maxwell model or three-phase QP model are used to simulate the effective thermal conductivity of three hydrate samples, i.e., saturated, supersaturated and unsaturated sample. The CD model considers that when the multiphase medium is continuously distributed along the direction of heat flow, the effective thermal conductivity is expressed as the weighted harmonic mean of the multiphase thermal conductivity. The effective thermal conductivity calculated by CD model is thought as the minimum value. The PD model considers that when the multiphase medium is distributed in parallel along the direction of heat flow, the effective thermal conductivity is expressed as the weighted arithmetic mean of the multiphase thermal conductivity. The effective thermal conductivity calculated by PD model is thought as the maximum value. The RD model is based on the random distribution hypothesis of multiphase medium. The effective thermal conductivity is expressed as a weighted geometric mean of the multiphase thermal conductivity. The two-phase Maxwell model is suitable for non-contact random distribution of uniform solid particles in a homogeneous continuous medium. The quadratic parallel model-QP model is suitable for determining the effective thermal conductivity of three-phase media [34]. The expressions of PD model, CD model, RD model, two-phase Maxwell model and three-phase QP model are
ke ¼
X
ke ¼ ð ke ¼
ki u
X
Y
ke ¼ kl
ui =ki Þ
ð1Þ - 1
ki ui
2/kh þ ð3 2/Þks ð3 /Þkh þ /ks
X 1=2 2 ke ¼ ð ki ui Þ
ð2Þ ð3Þ ð4Þ ð5Þ
where ke , ks and kh is the effective thermal conductivity of methane hydrate-bearing seasand, seasand and methane hydrate, respectively, Wm1K1; / is the porosity of seasand, %; ki is the thermal conductivity of component i, Wm1K1; ui is the volume percentage of component i in the sample, %. The application of these models is based on the following assumptions. For the saturated sample, the seasand pores are completely occupied by methane hydrate. For the supersaturated sample, the seasand pores are also ideally occupied by excess methane hydrate. For the unsaturated sample, the seasand pores occupied by methane hydrate and methane gas. The particle pore of ice powder is neglected and the volume of ice powder is approximately considered as the volume of methane hydrate. According to the above assumptions, the saturated and supersaturated samples
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Table 7 The components and corresponding percentage of samples.a
a
Component
Saturated
Supersaturated
Unsaturated
Volume/ml
Percent/%
Volume/ml
Percent/%
Volume/ml
Percent/%
Seasand Methane hydrate Methane gas Total
38.44 25.56 0.00 64
60.06 39.94 0.00 100
26.43 37.57 0.00 64
41.30 58.70 0.00 100
38.44 6.10 19.46 64
60.06 9.53 30.41 100
The standard uncertainty of volume is 0.01 ml. The percentage is on a basis of volume fraction and the standard uncertainty is 0.01.
Fig. 6. The predicted values and measured values of the three samples.
ideally contain only two components, i.e., methane hydrate and natural seasand. However, the unsaturated sample contains methane hydrate, seasand and methane gas. As mentioned above, the effective volume of the reactor was about 64 ml and the entire reactor was filled with the ice powder-seasand mixture. As shown in Table 2, the porosity of seasand is 39.93%. So for the saturated sample, the volume of seasand is 38.44 ml, and the volume of methane hydrate is 25.56 ml. For the supersaturated sample, 44.00 ml seasand was used to prepare the ice powder-seasand mixture so that the volume of seasand is 26.43 ml and the volume of methane hydrate is 37.57 ml. For the unsaturated sample, the volume of seasand is 38.44 ml, and the volume of methane hydrate is 6.10 ml. Based on the above analysis, the component of the samples and the percentage of each component are shown in Table 7. Using the measured data in this work, the relationship between methane hydrate thermal conductivity and temperature is expressed as
kh ¼ 1:6178 10
- 5
T 3 1:2983 10
T 309:1684
-2
T 2 þ 3:4729 ð6Þ
The relationship between seasand thermal conductivity and temperature is expressed as [15]
ks ¼ 5:004 0:0075 ðT 273:15Þ
ð7Þ
For the saturated samples and supersaturated samples, the calculated effective thermal conductivities by four models, i.e., PD model, CD model, RD model and Maxwell model, are compared with experimental measurements, as shown in Fig. 6(a) and (b). It can be seen from Fig. 6(a) that the calculated values of the Maxwell model and the RD model are basically the same; however, the calculated value of the CD model are basically consistent with the experimental results of the saturated samples. For the supersaturated samples, the calculated values are quite different, and none of them can match the experimental results very well, which are between the calculated values of the CD model and RD model as shown in Fig. 6(b). For the unsaturated sample, the sample contains three components of seasand, methane hydrate and methane gas. The calculated effective thermal conductivities by PD model,
CD model, random distribution model and three-phase QP model, are compared with experimental results, as shown in Fig. 6(c). It can be seen that the calculated value by the RD model is basically consistent with the experimental results of the unsaturated sample. Due to the difference in the component, component fraction and distribution of the three samples, the same model cannot be simultaneously used to simulate three samples. Moreover, the above assumptions also affect the calculated values. Therefore, the further improvement for the models is needed. 4. Conclusions The high-quality samples of hydrate were synergistically prepared by multiple methods including the ‘‘seeding” ice, simultaneous slowly heating and slowly supplying gas, temperature oscillation and aging method. The ‘‘seeding” ice method can effectively provide a large contact area; The slowly supplying gas method can ensure the ice powder to obtain the desired gas concentration synchronously; The simultaneous heating during gas supply can increase the diffusion rate of gas molecules to facilitate the hydrate forward growth; The temperature oscillation and aging method can further eliminate residual ice powder (water) as much as possible. The measured results show that the thermal conductivities of methane hydrate and methane hydrate-bearing seasand are positively correlated with the temperature and the effect of the gas phase pressure is negligible. The effective thermal conductivity shows a sudden increase near to the phase equilibrium temperature. The relationship between the effective thermal conductivity and methane hydrate saturation in the sample are ke,saturation > ke,supersaturation > ke,unsaturation. The experimental results are compared with the classical theoretical models and found that the same model cannot be simultaneously used to simulate three samples. Acknowledgements This work was funded by the Open Fund (PLN201604) of State Key Laboratory of Oil and Gas Reservoir Geology Exploitation (Southwest Petroleum University), China Geological Survey Project
S. Sun et al. / J. Chem. Thermodynamics 132 (2019) 423–431
‘Natural Gas Hydrate Test Technology and Simulation Experiment’ (DD20160216) and SDUST Research Fund (Grant No. 2015KYTD104). We thanks for the valuable suggestions of anonymous reviewers. The experiments were finished in Qingdao Institute of Marine Geology. References [1] E.D. Sloan, C.A. Koh, Clathrate Hydrates of Natural Gases, CRC Press, 2007. [2] S.G. Hatzikiriakos, P. Englezos, The relationship between global warming and methane gas hydrates in the earth, Chem. Eng. Sci. 48 (23) (1993) 3963–3969. [3] A. Revil, Thermal conductivity of unconsolidated sediments with geophysical applications, J. Geophys. Res. Solid Earth 105 (B7) (2000) 16749–16768. [4] D.Z. Huang, S.S. Fan, Thermal conductivity of methane hydrate formed from sodium dodecyl sulfate solution, J. Chem. Eng. Data 49 (5) (2004) 1479–1482. [5] E.J. Rosenbaum, N.J. English, J.K. Johnson, D.W. Shaw, R.P. Warzinskil, Thermal conductivity of methane hydrate from experiment and molecular simulation, J. Phys. Chem. B 111 (46) (2004) 13194–13205. [6] W.F. Waite, L.A. Stern, S.H. Kirby, W.J. Winters, D.H. Mason, Simultaneous determination of thermal conductivity, thermal diffusivity and specific heat in sI methane hydrate, Geophys. J. R. Astron. Soc. 169 (2) (2007) 767–774. [7] D.L. Li, J.W. Du, H. Song, D.Q. Liang, X.Y. Zhao, X.Y. Yang, Measurement and modeling of the effective thermal conductivity for porous methane hydrate samples, Sci. China Chem. 55 (3) (2012) 373–379. [8] B. Wang, Z. Fan, P. Lv, J. Zhao, Y. Song, Measurement of effective thermal conductivity of hydrate-bearing sediments and evaluation of existing prediction models, Int. J. Heat Mass Transf. 110 (2017) 142–150. [9] J.G. Cook, D.G. Leaist, An exploratory study of the thermal conductivity of methane hydrate, Geophys. Res. Lett. 10 (5) (1983) 397–399. [10] W.F. Waite, J. Pinkston, S.H. Kirby, Preliminary laboratory thermal conductivity measurements in pure methane hydrate and methane hydrate-sediment mixtures: a progress report, in: Proceedings of the Fourth International Conference on Gas Hydrate, 2002, pp. 728–733. [11] D.L. Li, D.Q. Liang, Experimental study on the effective thermal conductivity of methane hydrate-bearing sand, Int. J. Heat Mass Transf. 92 (2016) 8–14. [12] D.Z. Huang, Thermal Conductivity of Gas Hydrate and Hydrate Bearing Porous Media Dissertation, University of Science and Technology of China, Hefei, 2005. [13] W.F. Waite, B.J. Demartin, S.H. Kirby, J. Pinkston, C.D. Ruppel, Thermal Conductivity Measurements in Porous Mixtures of Methane Hydrate and Quartz Sand, Geophys. Res. Lett. 29 (24) (2002) 821–824. [14] L. Yang, J. Zhao, B. Wang, W. Liu, M. Yang, Y. Song, Effective thermal conductivity of methane hydrate-bearing sediments: experiments and correlations, Fuel 179 (2016) 87–96. [15] J.F. Wright, F.M. Nixon, S.R. Dallimore, J. Henninges, M.M. Cote, Thermal conductivity of sediments within the gas hydrate bearing interval at the Mallik 5L–38 gas hydrate production well, J. Geophys. Res. Solid Earth 585 (2005) 10. [16] J. Henninges, E. Huenges, H. Burkhardt, In situ thermal conductivity of gashydrate-bearing sediments of the Mallik 5L–38 well, J. Geophys. Res. Solid Earth 110 (B11) (2005) 206.
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JCT 2018-777
Contents lists available at ScienceDirect
J. Chem. Thermodynamics journal homepage: www.elsevier.com/locate/jct
The effective thermal conductivity of methane hydrate-bearing seasand Shicai Sun a,b,⇑, Jianrui Zhao a, Jie Zhao a, Yuchao Hao a, Jing Yang c a Shandong Key Laboratory of Civil Engineering Disaster Prevention and Mitigation, College of Civil Engineering and Architecture, Shandong University of Science and Technology, Qingdao 266590, China b State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation (Southwest Petroleum University), Chengdu 610500, China c College of Chemical and Environmental Engineering, Shandong University of Science and Technology, Qingdao 266590, China
a r t i c l e
i n f o
Article history: Received 18 September 2018 Received in revised form 14 January 2019 Accepted 26 January 2019 Available online 28 January 2019 Keywords: Methane hydrate Seasand Sample preparation Saturation Thermal conductivity Model
a b s t r a c t The thermal properties of hydrate-bearing sediments can help to evaluate the stability of hydrate reservoir and improve the safety of natural gas hydrate exploitation. In this work, the thermal conductivities of methane hydrate and methane hydrate-bearing seasand were investigated by the transient plane source (TPS) technique. The high-quality samples of hydrate were prepared by synergistic uses of a variety of methods, i.e., the ‘‘seeding” ice, simultaneous slowly heating and slowly supplying gas, temperature oscillation and aging method. The measured thermal conductivity of methane hydrate is 0.4877– 0.5467 Wm1K1 with the temperature 263.2–283.1 K and the pressure 4.0–9.5 MPa. The effective thermal conductivities of the saturated seasand sample, supersaturated seasand sample and unsaturated seasand sample (Here, the ‘‘saturated”, ‘‘unsaturated” and ‘‘supersaturated” refers to the three relationships between the pore volume of seasand and the volume of ice powder, respectively) are 1.1310– 1.2703 Wm1K1, 1.0070–1.1490 Wm1K1, 0.9221–1.1980 Wm1K1 with the pressure 8.0 MPa and the temperature 253.8–281.2 K, respectively. The effective thermal conductivities of the saturated sample, supersaturated sample and unsaturated sample are 1.1280–1.1402 Wm1K1 (1.1331– 1.5974 Wm1K1), 1.0172–1.0252 Wm1K1 (1.0181–1.2032 Wm1K1), 0.9154–0.9388 Wm1K1 (0.9401–1.1543 Wm1K1) with the pressure 4.0–10.0 MPa and the temperature 263.2 K (275.2 K), respectively. The relationship between the effective thermal conductivity and methane hydrate saturation in the sample are ke,saturated > ke,supersaturated > ke,unsaturated. The results suggest that the thermal conductivities of methane hydrate and methane hydrate-bearing seasand are positively correlated with the temperature and the influence of the gas phase pressure is negligible. Besides, the effective thermal conductivity shows a sudden increase near to the phase equilibrium temperature. Due to the complex of actual samples, the same classic theory model cannot accurately predict three samples simultaneously. Ó 2019 Elsevier Ltd.
1. Introduction The abundant natural gas hydrate resources in the seabed sediments and permafrost region are considered to be one of the most promising new energy [1]. However, natural gas hydrates are a ‘‘double-edged sword” that, while bringing abundant resources to humans, may also cause environmental and geological disasters such as global warming, submarine geological collapse and landslides [2,3]. The stability zone of natural gas hydrates is determined by the thermodynamic phase equilibrium, geothermal gradient and pressure gradient. The changes of temperature and pressure have a great influence on it, especially temperature fluctuations. Therefore, the thermal properties of hydrate-bearing sed-
⇑ Corresponding author. E-mail address: [email protected] (S. Sun). https://doi.org/10.1016/j.jct.2019.01.023 0021-9614/Ó 2019 Elsevier Ltd.
iments can help to evaluate the stability of hydrate reservoirs and the formation of submarine landslides so as to improve the safety of natural gas hydrate mining. At present, the research on the thermal properties of natural gas hydrates is relatively less and the existing experimental data have a large difference [4–9]. Besides, the views on the effects of temperature and pressure on the thermal properties are also different. Cook and Leaist [9] used the hot plane method to measure the thermal conductivity of methane hydrate to be 0.45 Wm1K1 at about 213.2 K. Huang and Fan [4] measured the thermal conductivities of the compacted/uncompacted methane hydrate sample. The thermal conductivity value of the uncompacted sample was 0.334–0.381 Wm1K1, and the thermal conductivity of the compacted sample was 0.568– 0.587 Wm1K1. Besides, the thermal conductivity increased with the increase of temperature. In contrast, Waite et al. [6,10] showed that the thermal conductivity of methane hydrate was negatively
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of the thermal conductivity of pure hydrate or hydrate-bearing sediments are different so that it is necessary to conduct an indepth research. The measurement method of thermal conductivity can be roughly divided into two categories: steady state method and non-steady state method [17]. The steady state method requires a steady state temperature field within the test sample, so the application is subject to many restrictions. The nonsteady-state method has the advantages of short measurement time, high precision, and easy environmental conditions, which is widely used. The non-steady state method mainly includes hot wire method, tropical method, probe method, and TPS technique. Each method has its own characteristics and application scope. Even if the same method is employed, the samples obtained by different preparation method have a great influence on the results. In this work, the TPS technique was used to study hydrate thermal properties. The main component of naturally occurring gas hydrates is methane gas, so the thermal properties of methane hydrate and methane hydrate-bearing seasand were investigated. This work will provide important basis for natural gas hydrate production.
correlated with the temperature, suggesting that it may be that the hydrate sample contained pore gas and unconverted ice; when the pressure was increased, the thermal conductivity of the hydrate sample increased rapidly. Rosenbaum et al. [5] reported that the thermal conductivity of the compacted methane hydrate sample decreased slightly with the increase of temperature, and the average thermal conductivity was about 0.68 ± 0.01 Wm1K1. Therefore, it can be seen that the thermal conductivity of methane hydrate is 0.33–0.68 Wm1K1 and the dependences on the temperature are inconsistent. Similarly, the literature conclusions on the effective thermal conductivity of hydrate-bearing sediments differ more greatly. Li et al. [7,11] used a single-sided transient plane source (TPS) technique to measure the effective thermal conductivity of methane hydratebearing porous media. The results showed that the effective thermal conductivity decreased with the increase of the sample porosity and was weakly negatively correlated to the temperature. Huang [12] found that the effective thermal conductivity of silica sand with saturated methane hydrate was about 1.1 Wm1K1 in the temperature range of 263.2–277.2 K. Waite et al. [13] measured the effective thermal conductivity of methane hydrate in silica sand in a certain range of temperature and pressure using the probe method. They found that the effective thermal conductivity was inversely proportional to the temperature and proportional to gas phase pressure. Wang et al. [8] found that the effective thermal conductivity was proportional to the hydrate saturation, water content and quartz sand thermal conductivity in the sample. But Yang et al. [14] showed that the effective thermal conductivity was inversely related to the hydrate saturation while it was positively correlated with the initial water content and the sediment thermal conductivity. The effective thermal conductivity of unconsolidated sediments in gas hydrate reservoirs at the Mallik Gas Hydrate Production Research Base was approximately 2.5–3.0 Wm1K1 [15]. Using the petrophysical model and the geothermal gradient, Henninges et al. [16] estimated the effective thermal conductivity of Mallik gas hydrates to be about 2.35–2.77 Wm1K1. It can be seen from the above literatures that due to the differences in equipment, methods and samples, the experimental data
2.1. Experimental equipment An experimental setup was built for the measurement of hydrate thermal conductivity, which consisted of hydrate formation system and thermal conductivity measurement system, as shown in Fig. 1. The hydrate formation system included a hydrate reactor, a buffer tank, an air-cooling bath, a gas supply unit, a vacuuming device and data acquisition unit. The hydrate reactor was made of cylindrical stainless steel, the inner diameter and the length of which was 52 mm and was 30 mm, respectively. So the effective volume of the reactor was about 64 ml. During the experiments, the reactor was submerged in the air bath. The temperature range of the air bath was 253.2–373.2 K with a heating rate of 2.0–3.0 K/min and a cooling rate of 0.7–1.0 K/min. The buffer tank with a capacity of 1 L was placed in the air bath, which can
Pressure Transducer
Pressure Guage P
2. Experimental
Vacuum Guage
P
P
P Buffer Tank Gas Flux Monitor
Supercharging Equipment
Temperature Transducer
Pressure Transducer P
Vacuum Container
Vacuum Pump
T Air Bath
CH4
Reactor
Hotdisk Probe Pt100
Fig. 1. Hydrate formation and thermal conductivity measurement system.
Hotdisk Thermal Constants Analyser
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S. Sun et al. / J. Chem. Thermodynamics 132 (2019) 423–431 Table 1 Experimental materials. Material a
CH4 Natural seasand Deionized water a
Component
Purity
Analytical method
Supplier
CH4
0.999
Gas chromatography
Nanjing Special Gas Factory of China Taken from the offshore area of Qingdao, China Laboratory-made
CH4 was delivered by the supplier and used without any further treatment. The standard uncertainty of CH4 purity on the basis of molar fraction is 0.001.
Table 2 Specification of natural seasand.
a b
Particle size/lm
<4
4–63
63–250
250–500
500–2000
>2000
Volume percentage/%a Porosity/%b
0.000 39.93
0.000
22.173
77.827
0.000
0.000
The percentage of particle size is on a basis of volume fraction. The standard uncertainty is 0.001. The porosity was calculated by the weight difference between dry seasand and saturated seasand with water. The standard uncertainty is 0.01.
be used to pre-cool the gas and maintain the system stability of the temperature and pressure. The gas supply unit included gas cylinder and supercharging equipment. The vacuuming device mainly comprised a vacuum pump and a vacuum container. The gas flux was monitored by a gas flux monitor supplied by China Beijing Qixing Huachuang Company. The temperature inside the reactor was monitored by the platinum resistance thermometer sensor Pt100 (with an uncertainty of ±0.1 K), which was located below the center of the reactor. There were two pressure gauges for displaying the pressure of gas supply unit and pressure regulator, respectively. The pressures of the reactor and the buffer tank during the experiments were detected by pressure transducers with an uncertainty of ±0.1 MPa. All signals during the experiments were recorded in real time by the Agilent data acquisition instrument 34970A. The thermal conductivity of hydrate was measured by Hot Disk thermal constants analyzer, which was made by Sweden Hot Disk AB Company. It was based on TPS technique. Hot Disk probe was a double spiral shape, which acted both as a heat source to increase the sample temperature and as a resistance thermometer to record the temperature. According to the hydrate sample, the type 8563 of Hot Disk probe was employed in this work. The probe was located in the middle of the reactor, which was inserted and fixed from the top of the reactor. 2.2. Experimental materials The materials used in experiments included methane gas, natural seasand and deionized water, as shown in Table 1. The purity of methane gas was 99.9% (molar fraction), which was provided by Nanjing Special Gas Factory of China, and no further treatment was carried out before the experiments. The deionized water was prepared by our laboratory. The natural seasand was taken from the offshore of Qingdao, China. The particle size of the seasand was measured and analyzed by Malvern laser particle size analyzer (MS2000) before the experiments, as shown in Table 2. In experiments, the hydrate samples were prepared using ice powder. In order to minimize the interference of pore gas between ice powder particles, the standard sieve with a pore size of 75 lm was used to screen ice powder, that is, the ice powder with the particle size less than 75 lm was employed in the experiments. The natural seasand and ice powder were uniformly mixed in a liquid nitrogen cup, and then charged into the reactor to synthesize the hydrate samples. According to the proportion of the seasand pore volume occupied by ice powder, three kinds of ice powder-seasand mixture were used to synthesize hydrate samples, i.e., seasand saturated by ice powder, seasand supersaturated by ice powder and seasand unsaturated by ice powder.
2.3. Preparation of hydrate samples The quality of hydrate sample has a great influence on the measurement accuracy of the thermal property, so it is very important to prepare a high-quality hydrate sample. The solubility of methane gas in water is low, which causes the formation rate of hydrate to be very slow so that the conversion rate of water is extremely low [1]. In addition, the gas-liquid interface is obvious in the static reaction system, and hydrate nucleation generally first occurs at the gas-liquid interface. Therefore, the solid hydrate slowly covers the entire interface, thereby reducing or isolating the contact between gas and water, so-called armor effect [18]. So it is difficult to completely convert water into hydrate during a limited experimental period, thereby affecting the quality of hydrate sample and the measurement accuracy of the thermal property. In order to increase the conversion rate of water, some promotion technologies, for examples, surfactant, ‘‘seeding” ice method and mechanical stirring and so on, are generally used [18–24]. Mechanical agitation can shorten the induction time of hydrate formation and increase the conversion rate, but the Hot Disk probe is installed in the reactor so that this method is not suitable in this work. Surfactants have a significant effect on hydrate formation [14–17], but they may affect the purity of the hydrate samples so as to affect hydrate thermal property. Huang and Fan [4] found that sodium dodecyl sulfate (SDS) had little effect on hydrate thermal conductivity, while Rosenbaum et al. [5] considered that the residual water-surfactant affected the measurement results. Ice powder has a large specific surface area and polyhedral units produced by melting ice, which are favorable for hydrate formation, so it is often used to synthesize hydrates. Hwang et al. [21] considered that the melting ice provided a template for hydrate nucleation and could absorb the heat generated by the hydrate formation. Sloan and Fleyfel [22] proposed a melting reaction model of hydrates to explain the kinetic characteristics and induced phenomena. Stern et al. [18,23,24] used ice powder with a particle size of 180–250 lm to synthesize methane hydrate under static conditions with 25–35 MPa above freezing point, and obtained highquality methane hydrate, which was called ‘‘seeding” ice method. Hydrate formation by ice powder has the advantages of short induction time, high conversion rate and no residual impurities, but the pores of ice powder are easy to retain gas. Some literatures reported that the residual gas can be removed by mechanical compaction after the preparation of the hydrate sample was completed [6,7,10,11,25]. Although mechanical compaction can effectively reduce the pores, it is easy to cause the damage or defects of the hydrate crystal, thereby affecting the thermal conductivity. In this work, a modified ‘‘seeding” ice-compacted ice powder method was proposed and a variety of other methods, i.e., simultaneous slowly
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Fig. 2. Ice production apparatus, ice powder and loading ice powder into the reactor in the freezer.
heating and slowly supplying gas, temperature oscillation and aging method, were used in combination to prepare hydrate samples. In the process of hydrate formation, the temperature oscillation method was employed to promote the complete conversion of water (ice) and improve the purity (quality) of hydrate samples. Before preparing the ice powder, the following work has to be done firstly. Hydrate formation requires a high pressure and low temperature condition, so the experimental equipment must be rigorous air tightness. The reactor was rinsed three times with deionized water and then dried by a blower. The air bath was maintained at 263.2 K, and then the buffer tank was pressurized with methane gas to the required pressure. Methane gas was pre-cooled to prevent the ice powder from being melted by the high temperature gas directly entering the reactor. Besides, the dried reactor and the sampler were also pre-cooled in a freezer to prevent the ice powder from being melted during loading and compacting the ice powder with the sampler. The ice powder production apparatus, designed by Qingdao Institute of Marine Geology, was used to prepare the ice powder. The ice powder production apparatus, granular ice powder and ice powder loading into the reactor in the freezer were shown in Fig. 2. First of all, the deionized water was atomized by an atomizer to obtain the droplets with a particle size of microns. In the liquid nitrogen environment, these droplets froze rapidly to become ultra-fine ice powder. The standard sieve was cooled in advance with liquid nitrogen and then was used to screen the ice powder to obtain the desired granules of ice powder. The mesh size of standard sieve was 75 lm, thus the maximum particle size of the granular ice used in this work was 75 lm. Simultaneously, the quantitative natural seasand was pre-cooled in a liquid nitrogen cup. After the preparation of ice powder, the quantitative ice powder was also poured into the liquid nitrogen cup. Then the ice powder and natural seasand were mixed evenly in the liquid nitrogen environment. After the above steps were completed, the hydrate sample synthesis was carried out as follows. The ice powder-seasand mixture was transferred to the freezer as soon as possible, and then the mixture was filled into the reactor in the freezer. Since the residual free gas and unconverted ice (water) in the hydrate sample have great influence on the thermal property, the quantitative ice powder-seasand mixture was charged into the reactor, and then the mixture was compacted by the sample. Certainly, for the pure methane hydrate, only quantitative ice powder was charged into the reactor. The entire reactor was filled with either the ice powder or the mixture. After the reactor was installed in the freezer, it was quickly transferred to a low temperature air bath (pre-cooled to 263.2 K). Afterwards, the remaining installation was completed in the air bath in the shortest time. The reactor was vacuumed for 20 min and maintained for more than 2 h to check for leaks again. Once the temperature inside the reactor was stabilized, the precooled methane gas in the buffer tank was slowly charged into the reactor. While charging the reactor with gas, the air bath temperature was adjusted immediately so that the reactor was pressurized and heated at the same time. Finally, the temperature in
the reactor was stabilized at about 273.4 K and the pressure was about 10.0 MPa. Methane gas reacted quickly with ice powder with almost no induction time. At the beginning of hydrate formation within 24 h the pressure dropped significantly, therefore, secondary pressurization was carried out. After the pressure was stabilized in the end, the temperature of the air bath was adjusted so that the temperature was oscillated more than three cycles between 263.2 and 278.2 K to increase the granular ice (water) conversion degree. The hydrate samples were aged for three days under the conditions of stable temperature and pressure to eliminate possible residual water. Simply, the volume of ice powder was approximately considered to be the volume of methane hydrate in this work so that the samples prepared by three kinds of ice powder-seasand mixture were approximately considered to the seasand saturated/supersaturated/unsaturated by methane hydrate. And then the temperature and pressure in the reactor were stepwise changed to measure the thermal conductivity under different temperature and pressure conditions. Generally, the sample temperature, probe type and cable type are easily determined while determining the test time and output power of Hot Disk thermal constants analyzer require a large number of repeated experiments. In this work, the probe type 8563 was used and the parameters of test time and output power are determined through many experiments as shown in Table 3. Each test was conducted three times at a time interval of 15–20 min, taking the average of the three measurements as the measured value for that point. In summary, hydrate formation was finished through slowly heating and slowly pressuring the system simultaneously. Mathane gas reacted rapidly with ice powder, and then the temperature oscillating method was used to further increase the ice powder (water) conversion degree. The advantages of the above process were as follows. Using ‘‘seeding” ice method to prepare methane hydrate can effectively avoid the interfacial tension because granular ice has a large specific surface area. Methane gas molecules were adsorbed directly into the skeleton structure of compacted granular ice to form stable hydrate. When the temperature was about 273.2 K, the ice particle surface has a water film with a suitable thickness for gas molecules to enter [12]. In order to avoid the armor effect [18] during hydrate formation, slowly charging gas method was utilized so that the surroundings of the granular ice achieved the desired gas concentration synchronously as much as possible. Simultaneous heating during gas
Table 3 The parameters of test time and output power.a Sample
Output power/W
Test time/s
Ice powder Methane hydrate Methane hydrate-bearing seasand
0.2–0.45 0.1–0.2 0.20–0.45
20 160 80
a The standard uncertainties of output power and test time are 0.01 W and 1 s, respectively.
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supply can increase the diffusion rate of gas molecules, which facilitates the advancement of the hydrate layer into the interior of the ice powder. The temperature oscillating method and secondary gas supply can effectively promote the hydrate formation and thus improve the quality of hydrate samples. When hydrate thermal conductivity was measured with Hot Disk thermal constants analyzer, the temperature and pressure of the system must be stable. 3. Results and discussion Before experiments, the thermal conductivity of the compacted ice powder was firstly measured to verify the feasibility of the above method. Besides, it was useful to check the compacted degree of the ice powder. In this work, the thermal conductivity of the compacted ice powder at 268.2 K in the vacuum environment is 2.2213 Wm1K1, which is very similar to that of ice at the same temperature measured by other researchers [10,26–29]. The thermal conductivity of methane gas is very small, about 0.03 Wm1K1 [8], so that the methane gas contained in hydrate sample easily interfere with the measurement results. Therefore, it can be concluded that the compacted ice powder with the sampler can effectively reduce the sample porosity in this work. The compacted ice powder provides a skeleton structure for the hydrate formation and the hydrate sample has less pore gas. Methane hydrate and methane hydrate-bearing seasand were formed using the above method and the thermal conductivities were measured under different conditions. 3.1. Methane hydrate The measured thermal conductivities of methane hydrate are shown in Table 4 and Fig. 3. It can be seen that the thermal conductivity of methane hydrate exhibits a positive trend with temperature and increases from 0.4877 Wm1K1 at 263.2 K to 0.5467 Wm1K1 at 283.1 K with the pressure 9.5 MPa. Moreover, the gas phase pressure has little effect on the thermal conductivity of methane hydrate between 4.0 MPa and 9.5 MPa. The thermal conductivities show a sudden increase near to the phase equilibrium temperature. Huang and Fan [4] used SDS to promote methane hydrate formation in silica sand and found that the thermal conductivities of both the compacted and uncompacted hydrate samples exhibited a positive trend with temperature. The results of this work are between those of the compacted and uncompacted sample. Although the addition of SDS can promote the formation of hydrate, as an impurity, it may affect hydrate thermal conductivity. The mechanical compaction can effectively reduce the porosity of the hydrate sample, but it is likely to cause hydrate crystal fragmentation [7,11]. The experimental results show that the synthesis method of hydrates with compacted granular ice can avoid the problems caused by surfactant and mechan-
Table 4 Thermal conductivities of methane hydrate with the temperature 263.2–283.1 K and the pressure 4.0–9.5 MPa.a T/K
p = 9.5 MPa k/Wm1K1
p = 6.0 MPa k/Wm1K1
p = 4.0 MPa k/Wm1K1
263.2 267.2 271.1 275.3 279.2 280.9 283.1
0.4877 0.4868 0.4904 0.4936 0.5117 0.5258 0.5467
0.4851 0.4884 0.4892 0.4925 0.4946
0.4846 0.4864 0.4953 0.4926
a The symbol T, p and k represent the temperature, pressure and thermal conductivity, respectively. The standard uncertainties u are u(T) = 0.1 K, u(p) = 0.1 MPa, u(k) = 0.0001 Wm1K1.
Fig. 3. Thermal conductivity of methane hydrate with the temperature 263.2– 283.1 K and the pressure 4.0–9.5 MPa.
ical compaction. In this work, a modified ‘‘seeding” ice-compacted ice powder method was proposed and a variety of other methods, i.e., simultaneous slowly heating and slowly supplying gas, temperature oscillation and aging method, were used in combination to remove the residual ice crystals as much as possible so as to obtain pure hydrate. Stern et al. [18] used ‘‘seeding” ice powder method to produce 15 samples that showed consistent and reproducible reaction process, methane consumption, XRD patterns and physical appearances. Furthermore, these samples occupied cylindrical volume as the initial seeding ice and the samples contained almost the same porosity. That is to say, the initial ice powder constructs the skeleton of methane hydrate sample, and the skeleton changes little after hydrate formation. Similarly, for the samples of methane hydrate-bearing seasand formed by this method, the initial contact state of the ice powder with seasand particles can also approximate the contact state between methane hydrate and seasand particles. Therefore, it is reasonable to assume that these samples of methane hydrate (methane hydrate-bearing seasand) obtained in this work are nearly identical. In addition, the same measurement method of thermal conductivity is employed in the experiments. So the measured results are more consistent and reproducible. 3.2. Methane hydrate-bearing seasand 3.2.1. The influence of temperature Naturally occurring gas hydrates exist in sediments so that it is more practical to study the effective thermal conductivity of hydrate-bearing sediments with different saturations. In experiments, the samples of methane hydrate-bearing seasand with three different saturations were prepared, i.e., saturated sample, supersaturated sample and unsaturated sample, and the effective thermal conductivities were measured with the pressure 8.0 MPa and the temperature 253.8–281.2 K, as shown in Table 5 and Fig. 4. It can be seen that for the saturated sample, supersaturated sample and unsaturated sample the effective thermal conductivities are 1.1310–1.2703 Wm1K1, 1.0070–1.1490 Wm1K1, 0.9221–1.1980 Wm1K1, respectively. The effective thermal conductivity is positively correlated with temperature, which is the same trend as that of pure methane hydrate. Huang [12] reported that the effective thermal conductivity of 125–300 lm silica sand saturated by methane hydrate increased with the increase of temperature, and the effective thermal conductivity was 1.0–1.1 Wm1K1 in the temperature range of 263.2–277.2 K. Moreover, at around 281.2 K, which is near to the phase equilib-
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Table 5 Effective thermal conductivity of methane hydrate-bearing seasand at p = 8.0 MPa.a Saturated sample
Supersaturated sample 1
T/K
ke /Wm
253.8 257.2 258.6 260.2 263.2 266.2 267.6 269.2 272.0 272.95 275.2 278.2 281.2
1.1341 1.1331 1.1342 1.1354 1.1341 1.1440 1.1460 1.1472 1.1494 1.1310 1.1331 1.1382 1.2703
K
1
Unsaturated sample 1
T/K
ke/Wm
253.8 256.5 259.1 261.1 263.1 265.5 267.8 270.6 273.4 275.2 277.1 279.2 281.1
1.0070 1.0161 1.0212 1.0221 1.0220 1.0230 1.0221 1.0202 1.0173 1.0153 1.0221 1.0331 1.1490
K
1
T/K
ke/Wm1K1
253.8 256.3 258.5 261.0 263.1 265.7 268.2 270.7 273.3 275.3 277.4 279.2 281.2
0.9221 0.9265 0.9284 0.9253 0.9293 0.9350 0.9373 0.9366 0.9342 0.9396 0.9522 0.9753 1.1980
a The symbol T, p and ke represent the temperature, pressure and effective thermal conductivity, respectively. The standard uncertainties u are u(T) = 0.1 K, u(p) = 0.1 MPa, u (ke) = 0.0001 Wm1K1.
Fig. 4. Effective thermal conductivity of methane hydrate-bearing seasand versus temperature.
rium temperature, the effective thermal conductivity shows a sudden increase. This phenomenon indicates that the heat transfer performance is enhanced near to hydrate equilibrium sate that can be used as a signal for the onset of hydrate dissociation [29]. The low thermal conductivity is one of the important reasons why natural gas hydrates can exist in shallow submarine sediment. It can also be seen from Fig. 4 that the effective thermal conductivities of methane hydrate-bearing seasand samples with different saturations differ largely. At the same temperature, the effective thermal conductivity exhibits an obvious trend, i.e., ke,saturation > ke,supersaturation > ke,unsaturation. Here, ke,saturation, ke,supersaturation and ke,unsaturation represent the effective thermal conductivity of the saturated sample, supersaturated sample and unsaturated sample, respectively. This trend is related to the macroscopic distribution patterns, the component and their inherent thermal conductivity. Natural gas hydrates mainly occur in the form of layers, blocks, dispersions and veins, which can directly indicate the abundance of hydrates in sediments and is very important for the exploration and evaluation of hydrate resource. These macroscopic distribution pattern may be expressed as the contact relationship between hydrates and sediments at the microscopic level, that is, porefilling type (i.e. hydrate floats in pore fluid), contact type (i.e. hydrate contacts with the sediment particles) and cementing type (i.e. hydrate cements the sediment particles). The hydrate distribution pattern is related to sediments, gas sources, pore fluids, and
formation conditions. If the sediments are saturated by the pore fluid and the gas source is sufficient, the hydrates will cement the sediment particles in the end, i.e. cementing type. If the hydrates are suspended in the pore fluid, i.e. pore-filling type, there are some migration channels between the hydrates and the sediments so that the pores are filled with the pore water, dissolved gas or free gas. When the pore water is excessive, it is easy to form the contact type [30–32]. It is clear that the distribution pattern of hydrates in the sediment directly affects the effective thermal conductivity. In this work, the ice powder and seasand are evenly mixed so that ice powder must be in contact with sediment particles and the mixture of seasand and ice powder can be considered as loose sediments. Methane gas is sufficient so that the ice powder is completely converted into the hydrate. As mentioned above, Stern et al. [18] considered that methane hydrate that was formed by the seeding ice directly replaced the location of the ice in the sediments. That is to say, the initial seasand and ice powder particles construct the sample skeleton of methane hydrate-bearing seasand, so the initial contact state of the ice powder with seasand particles can also approximate the contact state between methane hydrate and seasand particles. Therefore, regardless of whether the seasand is saturated with ice powder, the distribution pattern of the formed hydrate is more likely to be contact type and the components in the formed sample include seasand, methane hydrate and pore methane gas. For the saturated and supersaturated samples, the pores in the sample are relatively less so that the content of methane gas in the pores is less. However, the proportion of hydrates in the supersaturated sample is larger; correspondingly, the proportion of seasand is smaller. For the unsaturated sample, there are relatively more pores in the sample. The thermal conductivities of seasand, methane hydrate and methane gas are about 5.0 Wm1K1 [33], 0.5 Wm1K1, 0.03 Wm1K1 [7], respectively. According to the above analysis, the effective thermal conductivity of methane hydrate-bearing seasand exhibits an obvious trend, i.e., ke,saturation > ke,supersaturation > ke,unsaturation. 3.2.2. The influence of gas phase pressure The effect of gas phase pressure on the effective thermal conductivity of methane hydrates-bearing seasand with different saturations was also investigated in this work in the pressure range of 4.0–10.0 MPa and at the temperature of 263.2 K and 275.2 K, as shown in Table 6 and Fig. 5. The effective thermal conductivities of the saturated sample, supersaturated sample and unsaturated sample are 1.1280–1.1402 Wm1K1, 1.0172–1.0252 Wm1K1, 0.9154–0.9388 Wm1K1 with the pressure 4.0–10.0 MPa and the temperature 263.2 K, respectively. The effective thermal con-
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S. Sun et al. / J. Chem. Thermodynamics 132 (2019) 423–431 Table 6 Effective thermal conductivity of methane hydrate-bearing seasand at 263.2 and 275.2 K.a T/K
p/MPa
Saturated sample ke/Wm1K1
Supersaturated sample ke/Wm1K1
Unsaturated sample ke/Wm1K1
263.2
4.0 6.0 8.0 10.0
1.1280 1.1301 1.1341 1.1424
1.0172 1.0180 1.0220 1.0252
0.9154 0.9141 0.9293 0.9388
275.2
4.0 6.0 8.0 10.0
1.5974 1.1343 1.1331 1.1371
1.2032 1.0143 1.0154 1.0181
1.1543 0.9451 0.9401 0.9480
a The symbol T, p and ke represent the temperature, pressure and effective thermal conductivity, respectively. The standard uncertainties u are u(T) = 0.1 K, u(p) = 0.1 MPa, u (ke) = 0.0001 Wm1K1.
Fig. 5. Effective thermal conductivity of methane hydrate-bearing seasand versus gas phase pressure.
ductivities of the saturated sample, supersaturated sample and unsaturated sample are 1.1331–1.5974 Wm1K1, 1.0181– 1.2032 Wm1K1, 0.9401–1.1543 Wm1K1 with the pressure 4.0–10.0 MPa and the temperature 275.2 K, respectively. It can be seen that the effective thermal conductivity of hydrate samples slightly increases with the increase of gas phase pressure. Relatively, the thermal conductivity of the unsaturated samples changes obviously. But the effect of gas phase pressure is relatively very small. Waite et al. [13] synthesized methane hydrate-bearing silica sand with ice powder and measured the effective conductivity of the samples containing 1/3 and 2/3 methane hydrate content in the pressure range of 3.5–27.6 MPa at 263.2 K. The results showed that the effective thermal conductivity of the two samples increased with the increase of gas phase pressure. Since the fraction of methane hydrate with relatively low thermal conductivity increases in the sample, replacing the silica sand (seasand) with high thermal conductivity, to result in the decrease of the effective thermal conductivity of the sample. Similarly, the effective thermal conductivity shows a sudden increase at the temperature 281.2 K and pressure 4.0 MPa, which indicates that the structure of hydrate sample may be changed close to the equilibrium state. In addition, Fig. 5 further confirms the relationship between the effective thermal conductivity and methane hydrate saturation in the sample, i.e., ke,saturation > ke,supersaturation > ke,unsaturatin, which also suggests good repeatability of the experiments. 3.3. Classical theoretical model verification In this work, the classical models [12,27] including parallel distribution (PD) model, continuous distribution (CD) model, random
distribution model, two-phase Maxwell model or three-phase QP model are used to simulate the effective thermal conductivity of three hydrate samples, i.e., saturated, supersaturated and unsaturated sample. The CD model considers that when the multiphase medium is continuously distributed along the direction of heat flow, the effective thermal conductivity is expressed as the weighted harmonic mean of the multiphase thermal conductivity. The effective thermal conductivity calculated by CD model is thought as the minimum value. The PD model considers that when the multiphase medium is distributed in parallel along the direction of heat flow, the effective thermal conductivity is expressed as the weighted arithmetic mean of the multiphase thermal conductivity. The effective thermal conductivity calculated by PD model is thought as the maximum value. The RD model is based on the random distribution hypothesis of multiphase medium. The effective thermal conductivity is expressed as a weighted geometric mean of the multiphase thermal conductivity. The two-phase Maxwell model is suitable for non-contact random distribution of uniform solid particles in a homogeneous continuous medium. The quadratic parallel model-QP model is suitable for determining the effective thermal conductivity of three-phase media [34]. The expressions of PD model, CD model, RD model, two-phase Maxwell model and three-phase QP model are
ke ¼
X
ke ¼ ð ke ¼
ki u
X
Y
ke ¼ kl
ui =ki Þ
ð1Þ - 1
ki ui
2/kh þ ð3 2/Þks ð3 /Þkh þ /ks
X 1=2 2 ke ¼ ð ki ui Þ
ð2Þ ð3Þ ð4Þ ð5Þ
where ke , ks and kh is the effective thermal conductivity of methane hydrate-bearing seasand, seasand and methane hydrate, respectively, Wm1K1; / is the porosity of seasand, %; ki is the thermal conductivity of component i, Wm1K1; ui is the volume percentage of component i in the sample, %. The application of these models is based on the following assumptions. For the saturated sample, the seasand pores are completely occupied by methane hydrate. For the supersaturated sample, the seasand pores are also ideally occupied by excess methane hydrate. For the unsaturated sample, the seasand pores occupied by methane hydrate and methane gas. The particle pore of ice powder is neglected and the volume of ice powder is approximately considered as the volume of methane hydrate. According to the above assumptions, the saturated and supersaturated samples
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Table 7 The components and corresponding percentage of samples.a
a
Component
Saturated
Supersaturated
Unsaturated
Volume/ml
Percent/%
Volume/ml
Percent/%
Volume/ml
Percent/%
Seasand Methane hydrate Methane gas Total
38.44 25.56 0.00 64
60.06 39.94 0.00 100
26.43 37.57 0.00 64
41.30 58.70 0.00 100
38.44 6.10 19.46 64
60.06 9.53 30.41 100
The standard uncertainty of volume is 0.01 ml. The percentage is on a basis of volume fraction and the standard uncertainty is 0.01.
Fig. 6. The predicted values and measured values of the three samples.
ideally contain only two components, i.e., methane hydrate and natural seasand. However, the unsaturated sample contains methane hydrate, seasand and methane gas. As mentioned above, the effective volume of the reactor was about 64 ml and the entire reactor was filled with the ice powder-seasand mixture. As shown in Table 2, the porosity of seasand is 39.93%. So for the saturated sample, the volume of seasand is 38.44 ml, and the volume of methane hydrate is 25.56 ml. For the supersaturated sample, 44.00 ml seasand was used to prepare the ice powder-seasand mixture so that the volume of seasand is 26.43 ml and the volume of methane hydrate is 37.57 ml. For the unsaturated sample, the volume of seasand is 38.44 ml, and the volume of methane hydrate is 6.10 ml. Based on the above analysis, the component of the samples and the percentage of each component are shown in Table 7. Using the measured data in this work, the relationship between methane hydrate thermal conductivity and temperature is expressed as
kh ¼ 1:6178 10
- 5
T 3 1:2983 10
T 309:1684
-2
T 2 þ 3:4729 ð6Þ
The relationship between seasand thermal conductivity and temperature is expressed as [15]
ks ¼ 5:004 0:0075 ðT 273:15Þ
ð7Þ
For the saturated samples and supersaturated samples, the calculated effective thermal conductivities by four models, i.e., PD model, CD model, RD model and Maxwell model, are compared with experimental measurements, as shown in Fig. 6(a) and (b). It can be seen from Fig. 6(a) that the calculated values of the Maxwell model and the RD model are basically the same; however, the calculated value of the CD model are basically consistent with the experimental results of the saturated samples. For the supersaturated samples, the calculated values are quite different, and none of them can match the experimental results very well, which are between the calculated values of the CD model and RD model as shown in Fig. 6(b). For the unsaturated sample, the sample contains three components of seasand, methane hydrate and methane gas. The calculated effective thermal conductivities by PD model,
CD model, random distribution model and three-phase QP model, are compared with experimental results, as shown in Fig. 6(c). It can be seen that the calculated value by the RD model is basically consistent with the experimental results of the unsaturated sample. Due to the difference in the component, component fraction and distribution of the three samples, the same model cannot be simultaneously used to simulate three samples. Moreover, the above assumptions also affect the calculated values. Therefore, the further improvement for the models is needed. 4. Conclusions The high-quality samples of hydrate were synergistically prepared by multiple methods including the ‘‘seeding” ice, simultaneous slowly heating and slowly supplying gas, temperature oscillation and aging method. The ‘‘seeding” ice method can effectively provide a large contact area; The slowly supplying gas method can ensure the ice powder to obtain the desired gas concentration synchronously; The simultaneous heating during gas supply can increase the diffusion rate of gas molecules to facilitate the hydrate forward growth; The temperature oscillation and aging method can further eliminate residual ice powder (water) as much as possible. The measured results show that the thermal conductivities of methane hydrate and methane hydrate-bearing seasand are positively correlated with the temperature and the effect of the gas phase pressure is negligible. The effective thermal conductivity shows a sudden increase near to the phase equilibrium temperature. The relationship between the effective thermal conductivity and methane hydrate saturation in the sample are ke,saturation > ke,supersaturation > ke,unsaturation. The experimental results are compared with the classical theoretical models and found that the same model cannot be simultaneously used to simulate three samples. Acknowledgements This work was funded by the Open Fund (PLN201604) of State Key Laboratory of Oil and Gas Reservoir Geology Exploitation (Southwest Petroleum University), China Geological Survey Project
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JCT 2018-777