Energy Fuels 2009, 23, 4995–5002 Published on Web 08/31/2009
: DOI:10.1021/ef900179y
Dependence of Depressurization-Induced Dissociation of Methane Hydrate Bearing Laboratory Cores on Heat Transfer Hiroyuki Oyama,*,† Yoshihiro Konno,†,‡ Yoshihiro Masuda,§ and Hideo Narita† † Methane Hydrate Research Center, National Institute of Advanced Industrial Science and Technology (AIST), 17-2-1, Tsukisamu Higashi 2jyou, Toyohira-ku, Sapporo, Hokkaido, Japan, 062-8517, ‡Department of Geosystem Engineering, School of Engineering, University of Tokyo, and §Frontier Research Center for Energy and Resources (FRCER), School of Engineering, University of Tokyo
Received March 2, 2009. Revised Manuscript Received August 11, 2009
Depressurization is considered a promising technique of producing gas from methane hydrate reservoirs. This report presents a dissociation model and an experimental study of core on gas production to clarify the dissociation characteristics during depressurization. The dissociation model can be expressed as a function of heat transfer and mass transfer. In our experiments, we used an artificial sedimentary core and performed several depressurization experiments under various production pressure conditions. The temperature, pressure, and production volumes of gas and water were measured in response to time. By comparing the developed dissociation model with our core experimental results, it is clearly demonstrated that the model can describe the experimental results well and that the heat transfer from the surroundings is predominant in our experimental case. In addition, we conclude that our developed model can predict the quantitative characteristics during the gas production process from core.
processes can be identified through sensitivity analyses.3-8 However, the potential of producing gas from hydrate reservoirs has not been fully investigated. Therefore, a method of acquiring data from numerous dissociation experiments performed in a laboratory is necessary to assess the efficiency of the process and establish the decomposition model.9-11 Kim et al. and Clarke and Bishnoi12,13 carried out many experiments to determine the apparent dissociation rate. Bishnoi and co-workers carried out their experiment in batch-type reactors and eliminated the heat transfer and mass transfer by increasing the stirring rate. In contrast, when methane hydrate dissociation occurs in the core, it is impossible to eliminate the heat transfer and mass transfer from the apparent dissociation rate. In our previous work,14 we reported an experimental formula for calculating the overall dissociation coefficient for depressurization; however, the previous formula was derived empirically and not theoretically. In this study, we constructed a theoretical model of methane hydrate dissociation in sediments. We also performed an
Introduction Methane hydrates are crystalline, ice-like compounds of methane gas and water molecules that are formed under specific thermodynamic conditions. Methane hydrates in the earth’s subsurface, within/beneath permafrost and subsea environments, are believed to hold a vast amount of potentially extractable natural gas. Several processes for recovering natural gas from the gas hydrate in a sedimentary reservoir have been proposed. Sloan presented an extensive review of the suggested methods, including depressurization, thermal simulation, and inhibitor injection.1 The depressurization method seems to be a cost-effective solution to liberate natural gas from methane hydrate-bearing layers.2 Depressurization decreases the system pressure below the pressure of hydrate formation at a specific temperature. Hydrate dissociation is a complex process that occurs during heat and mass transfer with dissociation kinetics of hydrate. Because the economic feasibility and continuous production of a substance depend on chemical reactions and flow process, estimating them requires a numerical analysis simulator. The developed simulator is helpful in achieving fundamental understanding of the process and the controlling regimes (flow, heat transfer, or kinetic) of hydrate production, so that
(6) Nazridoust, K.; Ahmadi, G. Chem. Eng. Sci. 2007, 62, 6155–6177. (7) Moridis, G. J.; Sloan, E. D. Energy Convers. Manage. 2007, 48, 1834–1849. (8) Liu, Y.; Strumendo, M.; Arastoopour, H. Ind. Eng. Chem. Res. 2008, in press. (9) Yousif, M. H.; Li, P. M.; Selim, M. S.; Sloan, E. D. J. Inclusion Phenom. Mol. Recognit. Chem. 1990, 8, 71–88. (10) Kamata, Y.; Ebinuma, T.; Omura, R.; Minagawa, H.; Narita, H. decomposition behavior of artificial methane hydrate sediment by depressurization method. Proc. of ICGH 5, 2005; p paper ref. 3016. (11) Kneafsey, T. J.; Tomutsa, L.; Moridis, G. J.; Seol, Y.; Freifeld, B. M.; Taylor, C. E.; Gupta, A. J. Pet. Sci. Eng. 2007, 56, 108–126. (12) Kim, H. C.; Bishnoi, P. R.; Heidemann, R. A.; Rizvi, S. S. H. Chem. Eng. Sci. 1987, 42, 1645–1653. (13) Clarke, M.; Bishnoi, P. R. Can. J. Chem. Eng. 2001, 79, 143–147. (14) Oyama, H.; Ebinuma, T.; Nagao, J.; Suzuki, K.; Narita, H.; Konno, Y.; Masuda, Y. Dissociation Rate Analysis from Methane Hydrate-bearing Core Samples by Using Depressurization or Depressurization withWell-wall Heating Method. 2008, Offshore Technology Conference, 2008; pp OTC-19376.
*To whom correspondence should be addressed. E-mail: h.oyama@ aist.go.jp. (1) Sloan, E. D. Clathrate Hydrates of Natural Gases, 2nd ed.; Marcel Dekker, 1998. (2) Kurihara, M.; Sato, A.; Ouchi, H.; Narita, H.; Masuda, Y.; Saeki, T.; Fujii, T. Prediction of Gas Productivity from Eastern Nankai Trough Methane-Hydrate Reservoirs. .Offshore Technology Conference, 2008; pp OTC-19382. (3) Sung, W.-M.; Huh, D.-G.; Ryu, B.-J.; Lee, H.-S. Korean J. Chem. Eng. 2000, 17, 344–350. (4) Tang, L.-G.; Li, X.-S.; Feng, Z.-P.; Li, G.; Fan, S.-S. Energy Fuels 2007, 21, 227–233. (5) Gerami, S.; Pooladi-Darvish, M. J. Pet. Sci. Eng. 2007, 56, 146– 164. r 2009 American Chemical Society
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: DOI:10.1021/ef900179y
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gas (i.e., methane), an aqueous solution of the gas, and a crystalline gas hydrate in pore spaces. Water vapor is negligible in the pore spaces. Though it is explained later in the Dissociation Characteristics section, water in the pore was almost pushed out by dissociation gas during B f C trajectory in Figure 1. We thought about the water that remains on the sand surface. The remained pores were mainly filled by methane gas. Ice generation by methane hydrate dissociation latent heat was observed at the condition of low production pressure. However, generated ice had a small influence on our experimental results. This indicated that the ice formation region was small, and the phenomenon of ice occurred within a very short time. Therefore, we also made the following assumptions: (i) A gas flow path is generated during the initial depressurization process toward production pressure. (ii) With continuous gas production at the production pressure C, the core temperature equals the threephase equilibrium temperature of the corresponding pressure. (iii) Ice forms when the production pressure is low. However, we ignored ice formation in this model.
Figure 1. Schematic diagram of the depressurization process. When depressurization occurs, the core temperature and pressure change along the A f D trajectory.
experimental study to compare with the model when applying the depressurization process to the synthetic hydrate-bearing core sample under various production conditions. The aims of the study were to: (i) elucidate the theoretical dissociation model taking the heat transfer and deviation from chemical equilibrium into account; (ii) observe the pressure, temperature, and gas and water production changes in the dissociation process during depressurization; and (iii) evaluate the overall methane hydrate dissociation rate constant in comparison with our dissociation model.
Hydrate dissociation is described as kf
srs CH4 þhw H2 O MH f
ð1Þ
kb
where hw, kf, and kb are the hydration number and the forward and backward reaction rate constants, respectively. If the system is closed, methane hydrate would reach a chemical equilibrium with balanced forward and backward reactions. The decomposed methane gas escapes through the pore space after depressurization in the experimental system. In addition, heat is supplied from the ambient environment. The system can not keep chemical equilibrium, and methane hydrate dissociation progresses. As the dissociation model, Bishnoi and co-workers derived an apparent dissociation rate.12,13 Their experiments were carried out in batch-type reactors. They eliminated the heat transfer and mass transfer by increasing the stirring rate. In the methane hydrate bearing core, it is impossible to eliminate the heat transfer and mass transfer. Therefore, a dissociation model should consider these transfers. The mass transfer effect is described as the ratio between the methane concentrations before (point B in Figure 1) and after (point C) depressurization, R (e1). At point C, the reaction rates can be described as follows
Dissociation Model Tracing Pressure and Temperature during Depressurization. Here, we consider the gas hydrate at a stable condition before depressurization, and the pressure is then reduced to the unstable condition. To represent the thermal conditions and dissociation behavior, we plotted the pressure and temperature (P-T ) trajectory of this dissociation process onto the phase diagram shown in Figure 1. The (P-T ) trajectory of this figure is summarized by the experimental result of our previous experimental work.14 In this figure, P is pressure (MPa), T is temperature (K), and the subscript refers to the condition point under consideration. From this figure, the depressurization process is divided into four stages as follows: (a) A f B trajectory: The sample is depressurized, but the methane hydrates are maintained in a stable condition. In this stage, the hydrate does not dissociate. (b) B f C trajectory: The methane hydrate becomes unstable with continuing depressurization. The core temperature decreases as a result of endothermic hydrate dissociation along the equilibrium curve. (c) Point C: Production pressure point. Dissociation progresses because of the heat supplied from the area surrounding the core. (d) C f D trajectory: The pressure does not change because the methane hydrate is completely dissociated. Heat transfer from the area surrounding the core raises the core temperature.
forward reaction; vf ¼ kf ½MH backward reaction; vb ¼ -kb R½CH4 3 fR½H2 Oghw
ð2Þ ð3Þ
where vf and vb are the reaction rates for forward and backward chemical reactions, respectively. The concentration of chemical species is shown within square brackets. From the sum of forward and backward reactions, the overall dissociation rate Vdiss can be described as Vdiss ¼ νf þνb ¼ kf ½MH -kb 3 R½CH4 fR½H2 Ohw g
ð4Þ
The methane hydrate dissociation rate Vdiss is experimentally estimated using the overall dissociation rate constant as
Model Construction. To clarify the gas production process at point C, which is the main stage of dissociation at core experiments, we constructed a dissociation model. We considered a three-phase system of a one-component
Vdiss 4996
d½MH ¼ koverall ½MH dt
ð5Þ
Energy Fuels 2009, 23, 4995–5002
: DOI:10.1021/ef900179y
Oyama et al.
where t is the time after depressurization, and koverall is the overall dissociation rate constant. Here, we compare eqs 4 and 5, and koverall is rewritten as koverall ¼ kf -kb
R½CH4 fR½H2 Oghw ½MH
ð6Þ
At point B, the forward and backward reactions are balanced (koverall = 0) and parameter R becomes unity (R = 1). Now, the backward rate constant is rewritten as kb ¼
½MH ½CH4 ½H2 Ohw
kf
ð7Þ
On substituting the kb of eq 7 into eq 6, we obtain the overall dissociation coefficient as ( koverall ¼kf
R½CH4 fR½H2 Oghw 1½MH ½CH4 ½H2 Ohw ½MH
\koverall ¼ kf ð1 -Rhw þ1 Þ
)
ð8Þ Figure 2. Schematic diagram of the experimental apparatus used in measurements.
In the above equations, the methane concentration R[CH4] is approximately equal to the methane concentration in the pore spaces at the production pressure. At point C, we obtain parameter R as PC zC RTC PC 1 ¼ zC RTC ½CH4
R½CH4
¼
\R
Here, as Qaround is the total heat input and is associated with eq 2, the hydrate dissociation rate per unit time can be expressed as Qaround ΔHðTC Þ Qaround \ j ΔHðTC Þ j
ð9Þ
koverall ¼ kf
hw þ1 ) PC 1 1zC RTC ½CH4
PB zB RTB
ð10Þ
ð11Þ
Finally, from eqs 10 and 11, koverall is introduced as ( koverall ¼ kf
) zB TB PC hw þ1 1zC TC PB
¼
-
d½MH ¼ kf ½MH dt
¼ kf ½MH
where j is the percentage of contribution to the dissociation of Qaround; ΔH(TC) and [MH]C0 are the latent heat of hydrate dissociation per mole and the initial methane hydrate concentration at point C, respectively. Each parameter of eq 13 is a time-dependent variable. However, the time dependencies of parameters are weak, and we determine the kf under the approximation that the other parameters are constants. In our analysis, the methane concentration used is the initial value at point C because it is a predictable value in experiment. Thus, to apply the assumption [MH] ∼ [MH]C0, we obtain the linear approximation coefficient kf as Qaround 1 ð14Þ kf ∼ j ΔHðTC Þ ½MHC0
To eliminate methane concentration [CH4], we consider the system to be in chemical equilibrium. Substituting R = 1, B point values (PB, TB), and zB into eq 9, we express [CH4] as ½CH4 ¼
dð½MHC0 -½MHÞ dt
ð13Þ
where zC is the gas compressibility factor under the (PC, TC) condition and R is the gas constant. From eqs 8 and 9, we rewrite the overall dissociation coefficient as (
¼
From eqs 12 and 14, we describe the overall dissociation rate constant as ) ( Qaround zB TB PC hw þ1 ð15Þ 1koverall ∼ j ΔHðTC Þ½MHC0 3 zC TC PB
ð12Þ
This equation shows the apparent dissociation rate including mass transfer effect in pore spaces. The forward rate constant kf should be determined by another consideration. Additionally, it is necessary to contain the influence of heat transfer effect. In the depressurization process, the gas production rate is limited by heat transfer.5,15 We now consider an additional assumption: (iv) Heat transfer from ambient environments caused methane hydrate dissociation in pore spaces.
Experimental Methods Experimental Apparatus. To justify the reliability and accuracy of our dissociation model, we performed dissociation experiments with artificial methane hydrate sediment. A schematic diagram of the experimental apparatus is shown in Figure 2. A triaxial pressure vessel was used to apply confining and pore pressures independent of the artificial core, using a rubber sleeve and syringe pumps (Teledyne Isco, 500D). The maximum confining pressure was 15.0 MPa, and the pore pressure was adjusted to 1.5 MPa less than the confining
(15) Konno, Y.; Masuda, Y.; Oyama, H.; Kurihara, M.; Ouchi, H. JAPT (in Japanese) 2009, 74, 165–174.
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: DOI:10.1021/ef900179y
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Table 1. Summary of Experimental Conditions and Results run 1
run 2
run 3
run 4
run 5
sample length [mm] sample diameter [mm] sample weight [g] sample volume [cm3] porosity [%] pore volume [cm3] hydrate saturation [%] water saturation [%] gas saturation [%] effective permeability [mD] absolute permeability [mD]
149.6 50 553.7 293.8 38.2 112.3 64.4 19.1 16.5 3.9 1810
148.6 50 552.1 291.8 38.0 110.8 44.8 44.7 10.5 122.5 1825
149.8 50 537.3 294.1 39.7 116.7 28.0 46.0 26.1 285.0 3870
148.1 51 544.9 302.5 40.5 122.6 59.4 29.2 11.4 1.2 4046
148.8 51 551.9 304.0 39.5 120.2 27.2 48.2 24.6 164.7 1500
initial temperature [C] initial pressure [MPa]
12.3 10.5
12.1 10.7
12.3 10.6
12.7 10.4
12.5 10.3
6.4 6.7 10-5 0.09 13.9 0.12
4.2 3.2 10-4 0.30 9.5 0.12
6.4 5.5 10-5 0.18 9.0 0.12
6.1 1.3 10-4 0.11 13.4 0.09
4.0 3.0 10-4 0.49 8.7 0.11
production pressure [MPa] hydrate dissociation rate [s-1] sensible heat/latent heat total gas production [Nl] total water production [l]
pressure. As shown in Figure 2, the vessel was positioned vertically, and the fluids were allowed to escape from the top of the vessel. Pressure transducers were placed at the top- and bottom-end plugs. Five thermocouples (Type-T) were attached to determine the surface temperature of the core specimen. Three thermocouples measured the core side surface temperature at 2.5, 7.5, and 12.5 cm from the core bottom, and two thermocouples measured the core bottom (0 cm) and top (15 cm) surface temperatures. Temperature and pressure (pore pressure) inside the core were simultaneously measured using three fiberoptic sensors, which were injected into the core center and positioned at 2.5, 7.5, and 12.5 cm from the core bottom. During the dissociation of methane hydrate, the pore pressure was controlled using a back-pressure control valve (BPCV). The gas and water dissociated from methane hydrate were measured at atmospheric pressure using a gas meter and electric balance placed downstream of the BPCV. Temperature, pressure, and time variations of the gas and water volumes produced were also measured. Preparation of the Methane Hydrate-Bearing Core. Methane hydrates in sandy sediments were formed under pressure and temperature conditions in excess of the equilibrium three-phase (water/hydrate/vapor) line. Toyoura standard sand, with an average diameter of 220 μm, was used for an artificial methane hydrate sedimentary core. The core specimens were about 50.0 mm in diameter and 150.0 mm in length; they were placed in the triaxial pressure vessel covered with a rubber sleeve to apply a confining pressure. The initial water content of the wet sand was controlled to obtain the desired methane hydrate saturation (14%). Artificial sandy sediments containing methane hydrate were produced by injecting the methane gas into a wet sand pack with controlled water content under the confining pressure. A methane gas pressure of 10.0 MPa was injected into the sandy sediment. The purity of the methane gas was greater than 99.5%. The confining pressure also increased during gas injection because the confining pressure was maintained at 1.5 MPa higher than the pore pressure. After gas injection, the confining pressure was held constant at 11.5 MPa, and the core temperature was then decreased to 1.0 C. The initiation of methane hydrate formation began with an abrupt decrease in pressure. When the pore pressure was decreased to approximately 6.0 MPa, the hydrate formation reaction was effectively stopped, and the hydrate saturation obtained was nearly 50.0%. To obtain a water-saturated core sample by purging the remaining gas, distilled water was injected at a constant flow rate into the pore spaces using a syringe pump (Teledyne Isco, 500D). The pore pressure was maintained constant during water injection using the BPCV. After the remaining gas was purged,
Table 2. Summary of Experimental Conditions and Results (Continued) run 6
run 7
run 8
run 9
run 10
run 11
147.2 51 529.9 300.8 42.2 126.8 45.3 28.4 26.3 60.0 8500
147.1 50 527.2 288.8 39.8 114.8 59.5 26.2 14.2 110.0 3100
148.3 50 529.9 291.2 40.2 117.1 53.3 45.1 1.6 110.0 4000
148.1 51 530.9 302.5 42.5 128.7 58.5 32.1 9.4 250.0 6000
147.5 50 549.2 289.6 37.1 107.4 46.1 48.5 5.4 180.0 6000
147.3 50 542.5 289.2 37.5 108.5 81.0 17.9 1.1 380.0 3300
12.1 10.6
12.3 10.6
12.3 10.6
12.0 10.5
12.1 10.4
12.0 10.6
3.1 4.5 10-4 0.35 13.3 0.12
8.4 1.3 10-5 0.02 13.1 0.12
8.4 7.0 10-6 0.02 10.3 0.12
3.0 5.2 10-4 0.28 13.6 0.12
2.5 6.0 10-4 0.49 8.7 0.12
1.3 1.3 10-3 0.38 14.4 0.09
we set the BPCV to the production pressure. After the outlet stop valve was closed, the pore pressure and temperature were set to about 10.0 MPa and 12.5 C, respectively. Experimental Conditions. The experiments were performed by varying the gas production pressure while maintaining all other initial conditions constant. Lower production pressures corresponded to a higher degree of depressurization. The conditions of the core specimens for all experiments are summarized in Tables 1 through 4. In these tables, the methane hydrate saturations, gas, and water were calculated from a mass balance. To determine the mass balance, the injected water weight was continuously measured, and we assumed the total gas volume containing the core was equal to the gas volume. The initial conditions and production pressure values are also listed in Tables 1 through 4. The output of dissociated water and gas was measured using a gas meter and an electric balance. From these measurements, we obtained both the production volume of gas and water during experiment and also the total volumes when the experiment was completed. To measure the total gas volume, the BPCV was set to atmospheric pressure for the remaining released gas. Changes in temperature and pressure at each elapsed time were also observed. The effective water permeability was measured before the dissociation experiment, and the absolute permeability was measured after the dissociation experiment. 4998
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: DOI:10.1021/ef900179y
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Table 3. Summary of Experimental Conditions and Results (Continued) run 12
run 13
run 14
run 15
run 16
run 17
146.7 50 540.6 288 37.8 108.8 28.7 80.3 57.0 5830
148.13 50 516.2 290.9 41.2 119.8 85.6 3.2 11.2 41.7 -
150.2 50 539.1 294.9 39.6 116.9 59.0 20.3 20.6 219.0 2326
138.8 50 502.9 272.5 39.5 107.6 35.5 32.7 31.7 270.0 9000
146.2 51 521.4 298.7 41.8 124.9 47.7 38.8 13.5 110.1 1913
150 51 538.9 306.4 41.4 126.9 53.6 37.8 8.7 87.3 2509
12.2 11.4
12.4 10.3
12.1 10.0
12.3 10.4
11.9 10.0
12.6 10.7
0.2 3.3 10-3 9.4 0.11
6.3 9.3 10-5 0.07 18.1 0.08
2.5 9.3 10-4 0.36 13.9 0.08
8.3 7.7 10-7 0.03 10.2 0.13
4.0 3.7 10-4 0.25 11.5 0.05
4.0 2.3 10-4 0.25 12.3 0.14
Table 4. Summary of Experimental Conditions and Results (Continued) run 18
run 19
run 20
run 21
run 22
run 23
149.5 51 527.3 305.4 42.7 130.4 53.5 30.0 16.5 11.9 3687
148.6 51 533.1 303.6 41.5 126.0 66.2 25.8 8.0 49.2 2553
148.2 51 549.7 302.7 39.8 120.5 73.8 18.4 7.8 21.4 2349
148.5 51 538.5 303.4 41.4 125.5 51.8 22.7 25.5 1476
143.3 51 513.4 292.7 42.0 123.0 63.2 31.8 5.0 14.0 2968
149.1 51 546.0 304.6 40.7 124.1 78.9 0.0 28.7 10652
12.1 10.0
12.2 10.1
12.3 10.0
11.9 10.2
12.2 10.0
12.3 10.0
Figure 3. Example of the depressurization process. Changes in elapsed time at a production pressure of 4 MPa. (a) Pressure change, (b) core temperature (core center) change, and (c) cumulative gas and water production.
4.0 6.0 8.0 2.0 2.0 2.0 2.2 10-4 7.8 10-5 1.8 10-5 4.3 10-4 6.5 10-4 1.1 10-3 0.22 0.09 0.02 0.41 0.35 0.30 13.7 14.6 15.5 14.2 13.3 19.8 0.10 0.10 0.09 0.10 0.09 0.06
Results and Discussion Experimental Results. The dissociation results are summarized in Tables 1 through 4. One example of the experimental results is shown in Figure 3. The figure shows the results of run no. 5, when the production pressure was at 4.0 MPa. Different production pressure results are shown in Figure 4 and Figure 5 for 6.0 MPa (run no. 19) and 8.0 MPa (run no. 20), respectively. Similar tendencies in the variation of pressure and temperature trajectories appear in all experiments. In these figures, three parameters are plotted against the elapsed time: (a) top and bottom pressure; (b) core center temperature; and (c) cumulative gas and water production. In all experiments, pressures at both core ends as well as pore pressures were simultaneously decreased by adjusting the BPCV setting during the depressurization process, as shown in Figures 3(a), 4(a), and 5(a). When the methane hydrate was in a stable condition, the reductions in pore pressure affected the core temperature only slightly. As depressurization progressed, the core temperatures were quickly decreased to near equilibrium temperatures at production pressures, as shown in Figures 3(b), 4(b), and 5(b). After the pressure reached the phase equilibrium, the core
Figure 4. Same as Figure 3 but at a production pressure of 6 MPa.
temperature and pore pressure followed the equilibrium curve. The latent heat of dissociation caused the temperature to decrease because hydrate dissociation is an endothermic reaction. At the production pressure, the entire core sample maintained the equilibrium temperature (e.g., the temperature at 7.5 cm). These pressure and temperature behaviors show that the sensible heat of the sediment was immediately consumed during the depressurization process. However, as the heat is continuously supplied from the surroundings, 4999
Energy Fuels 2009, 23, 4995–5002
: DOI:10.1021/ef900179y
Oyama et al.
Figure 6. Enlarged plot of the dissociation region and temperature profile at a production pressure of 4.0 MPa. Temperature of (a) core center and (b) core wall.
Figure 5. Same as Figure 3 but at a production pressure of 8 MPa.
methane gas was constantly produced, as shown in Figures 3(c), 4(c), and 5(c). Under these conditions, the redundant sensible heat did not remain in the core sample. During methane hydrate dissociation, the top (15 cm) temperature increased first followed at slower rate by the core center temperature (e.g., 7.5 cm from bottom). This indicates that the dissociation progressed from the ends to the center of the core. To compare the core center temperature with those at the wall surface, in Figure 6 we show an enlarged plot of the dissociation region temperature profiles obtained at a production pressure of 4.0 MPa. Figure 6(a) shows the core center temperature profiles vs time, and Figure 6(b) shows the core wall temperature vs time. These temperature profiles also indicate that the dissociation progresses from around the core toward the center. Hence, the dissociation phenomenon was driven by heat transfer processes surrounding the core. The gas and water production rates and time of the completion of production varied depending on the production pressure. As shown in Figures 3(c), 4(c), and 5(c), the rate of gas and water production increased at a lower production pressure, but the total gas and water production volumes are irrelevant to production pressure. We assumed that all methane gas was supplied from dissociate methane hydrate, and we could estimate methane hydrate concentration change from measuring the production gas volume. Therefore, from eq 5, the overall dissociation rate constant koverall was estimated by ½MH ½MH0 ½CH4 0 -½CH4 ½CH4 0 ½CH4 0 -½CH4 \ln ½CH4 0
¼
expð -koverall tÞ
¼
expð -koverall tÞ
¼
-koverall t
Figure 7. Normalized moles of methane hydrates during decomposition (enraged plot, semilogarithmic graph).
where [MH]0 and [CH4]0 are initial concentration of methane hydrate and methane gas, respectively. The experimental values of [MH]/[MH]0 for production pressure at 4, 6, and 8 MPa are plotted in Figure 7. This graph is a semilogarithmic graph. From this figure, at a constant production pressure, the koverall seemed to be constant against time. The overall dissociation rate constant koverall estimated from the experiments is also summarized in Tables 1 through 4. These results indicate that as the production pressure decreases the overall dissociation rate constant increases. Dissociation Characteristics. The trajectories of pressure and temperature in the phase diagram during dissociation are similar, as shown in Figure 1. Thus, the experimental results of the depressurization process are also divided into the four stages described above. In the experiments, the (P-T) condition reaches the C point abruptly by depressurization. This termination may be due to two reasons: high core permeability and low sensible heat in the core. When the
ð16Þ
5000
Energy Fuels 2009, 23, 4995–5002
: DOI:10.1021/ef900179y
Oyama et al. Table 5. Summary of Fitting Calculation Parameters core and rubber sleeve length L 15 cm 2.5 cm core diameter radius and rubber sleeve inner radius rin 3 cm rubber sleeve outer radius rout core sample porosity 40% hydrate saturation under initial conditions 0.5 water saturation under initial conditions 0.5 gas saturation at initial conditions 0 thermal conductivity of rubber sleeve λ 0.2 W m-1 K-1 hydration number hw 6 12 C equilibrium temperature TA
diagram. This demonstrates that the sensible heat of the core was consumed in a very short period during methane hydrate dissociation. In this process, surrounding closely contacted materials supplied heat to methane hydrate. The sensible heat transfer rate was very rapped because of geometrical arrangement. For this reason, during the depressurization process toward production pressure, the dissociation mechanism is different from our model equation. After consuming the sensible heat, the dissociation process progresses at a constant production pressure. In this situation, the pressure and temperature are held at point C in Figure 1, at which another driving force for methane hydrate dissociation contributes. As described before, this driving force of dissociation is the heat transfer from the area surrounding, which contributes to the temperature increase along the C f D trajectory. Water was mainly produced in the A f C trajectory stage. In this stage, the gas volume expanded as the depressurization progressed. This expansion pushed out the surrounding pore water. Water flowed from the pore space to the outside of the core and formed a water path. Hence, some water escaped outside of the apparatus as the gas expanded. When continuous gas production began at the production pressure (point C in Figure 1), most pore spaces filled with the expanded gas. In this case, as water had entered many pore spaces, the gas followed the path that it generated in the pore spaces. Therefore, the dissociated water remained in the pore space because the gas fled more easily from it. Experimental Results Matching the Dissociation Model. We now apply the koverall of eq 15 to the experimental results. As previously noted, the concentration of methane hydrate decreased after dissociation caused by the sensible heat of the core. At point C in Figure 1, the remaining methane hydrate [MH]C0 is estimated as MMH Qcore ½MHC0 ¼ ð20Þ 16þhw 16 ΔHðTC Þ
Figure 8. Ratio of sensible heat to dissociation latent heat.
permeability is high, a pressure variation is instantaneously transmitted through the pore space, and pore pressure decreases rapidly. If the sensible heat of core is small, latent heat of hydrate dissociation easily consumes all sensible heat because hydrate dissociation is an endothermic reaction. The sensible heat of a methane hydrate-bearing core Qcore is estimated by ð17Þ Qcore ¼ ðCs Ms þCw Mw þCMH MMH ÞðTA -TC Þ where Cx is specific heat, Mx is sample mass, and the subscript x refers to the components s, w, and MH representing sand, water, and methane hydrate, respectively. Here, the gas phase was ignored because of its small specific heat. The values of Cs and Cw are from a previous study,16 and CMH is from Handa.17 The latent heat of hydrate dissociation per mol ΔH(T) is described by Holder18 as ΔHðTÞ ¼ 4:184 ð13521:0 -4:0 TÞ
ð18Þ
Therefore, the dissociation latent heat of the methane hydrate in the core was calculated by QL ¼
VtotalCH4 ΔHðTÞ 22:4
ð19Þ
where VtotalCH4 refers to the total methane volume including the core sample. The experimental values of Ms, Mw, and MMH were calculated from the sample weight and saturation for each sample, as shown in Tables 1 through 4. The VtotalCH4 values are also summarized in the tables. The ratio of sensible heat to dissociation latent heat (Qcore/ QL) was calculated from eqs 17 and 19. The results are shown in Tables 1 through 4 and Figure 8. Figure 8 shows that the sensible heat contribution to dissociation increases exponentially with decreasing production pressure. This effect reflects an advantage of the depressurization method. However, as the (Qcore/QL) ratio was less than unity, the sensible heat was not supplied in quantities sufficient to dissociate all methane hydrate. In addition, the pressure and temperature on the B f C trajectory changed very rapidly in the P-T phase
In eq 15, Qaround is assumed by applying the heat from the circulating brine through the rubber sleeve and end plugs to the core sample. Thus, Qaround is calculated using the following equation πλLðTA -TC Þ ~ ð21Þ þQtop þQbottom Qaround ¼ ðrout -rin Þ=ðrout þrin Þ where Qtop and Qbottom are the heat input from the top- and bottom-end plugs, respectively; λ is the thermal conductivity of the rubber sleeve; and L, rout, and rin are the length and the outer and inner radii of the rubber sleeve, respectively. Here we assume that Qtop and Qbottom are equal heat through the rubber sleeve. The parameters used to calculate the fitted curve are summarized in Table 5. The experimental overall dissociation coefficients and fitting results are shown in Figure 9. In this figure, the horizontal axis represents the production pressure, and the
(16) Rika-Nenpyo, Rika-Nenpyo (Chronological Scientific Tables) (in Japanese); Maruzen Co., Ltd., 2007. (17) Handa, Y. J. Chem. Thermodyn. 1986, 18, 915–921. (18) Holder, G.; Zetts, S.; Pradhan, N. Rev. Chem. Eng. 1988.
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Energy Fuels 2009, 23, 4995–5002
: DOI:10.1021/ef900179y
Oyama et al.
Figure 10. Distribution of the deviation parameter from equilibrium by mass transfer.
the contribution of backward reaction grows; i.e., the second term of eq 22 becomes large. Thus, it is considered that our model gives the upper limit of the overall dissociation rate constant. Our dissociation model provides a good understanding of the core experimental results with dissociation by depressurization. They suggest that heat transfer from the surrounding environment is dominant in the core dissociation process.
Figure 9. Overall dissociation coefficients (experimental results and fittings).
vertical axis represents the overall dissociation rate constant. We selected three j values: the total heat input contributing to dissociation (dashed line) and two others that are parts of the heat input contributing to dissociation (solid and dasheddotted lines). Hence, the dashed, solid, and dashed-dotted lines show the result for j = 1, j = 0.35, and j = 0.1, respectively. This figure shows that our model adequately expresses the overall dissociation rate constant characteristics. The solid line is in good agreement with the experimental results; 35% of the heat input from the surrounding area is consumed to dissociate the core sediments. Now, we evaluate the deviation from the equilibrium condition by mass transfer. The parameter zB TB PC hw þ1 ð22Þ 1zC T C P B
Conclusions We built a dissociation model for applying the depressurization method that takes into account heat transfer and mass transfer. This model was evaluated using experimental results and provided the following understanding of the dissociation characteristics after depressurization: 1. We developed a dissociation model equation for gas hydrate in a sediment core during depressurization. This equation is a function of heat input and the deviation from chemical equilibrium. 2. From the dissociation model equation, it is clear that the heat transfer from the surroundings is the dominant factor. 3. The temperature and pressure in the core sample rapidly approach the hydrate stability point during depressurization. 4. Sensible heat is not supplied in sufficient quantities to dissociate all bearing methane hydrate. This heat is rapidly consumed by hydrate dissociation during the depressurization process. 5. After reaching the production pressure, dissociation progresses with heat input from the area surrounding the core. 6. The gas production rate and the methane hydrate dissociation rate are sensitive to production pressure. 7. Water is mainly produced during the depressurization process by the expanding of the gas volume. 8. If the pressure could be lowered deeply within the hydrate zone, the sensible heat of the surrounding sediments would allow marked decomposition of the hydrate.
is the deviation part of eq 15, and Figure 10 shows the distribution of this deviation in the fitting condition. From this figure, if the production pressure is higher than 5 MPa, the value deviates from unity, and the contribution of the backward reaction in eq 1 increases. However, as the production pressure approached the equilibrium condition (PB, TB), i.e., a high production pressure condition, the fitting result in Figure 9 deviated significantly from the experimental values. This is not expressed by eq 22. This discrepancy can be attributed to two factors. One is the low relative permeability of gas, and the other is the heat input loss by water flow. Under this high-production-pressure condition, the dissociated gas does not expand much, and a considerable amount of water remains in the pore space. In this situation, the remaining water obstructs gas flow, leading to a decrease in the relative permeability of the gas. There are deviations from our assumption. The overall dissociation rate constant may become small in many cases. For example, we consider the situation that the system has pressure gradient, and a lot of ice forms in the pore space by methane hydrate dissociation latent heat. The ice formation makes the permeability low, and the system has pressure gradient inside the pore. Therefore, the overall dissociation rate is restricted in the area where pressure is high in both cases. The high pressure area makes kf small because the temperature difference becomes small in eq 21. In addition,
In an actual reservoir, this heat transfer would be caused by the sensible heat of the surrounding sand sediment. Acknowledgment. This work was financially supported by the Research Consortium for Methane Hydrate Resources in Japan (MH 21 Research Consortium) of the National Methane Hydrate Exploitation Program planned by Ministry of Economy Trade and Industry (METI). 5002
