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Dissociation Behavior of Pellet-Shaped Methane-Ethane Mixed Gas Hydrate Samples T. Kawamura, K. Ohga, and K. Higuchi Graduate School of Engineering, Hokkaido University, Sapporo, Hokkaido, 060-8648 Japan
J. H. Yoon, Y. Yamamoto,* T. Komai, and H. Haneda National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki, 305-8569 Japan Received August 5, 2002. Revised Manuscript Received February 17, 2003
The dissociation kinetics of methane and methane-ethane hydrates was investigated under a variety of experimental conditions. Hydrates of pure methane or methane-ethane mixtures were prepared. The composition and structure of methane-ethane mixed hydrates were identified using Raman spectroscopy and gas chromatographic analysis of the hydrate phase. With these hydrate powders, pellet-shaped samples that mimic a naturally occurring hydrate in ocean sediment were prepared. The dissociation rates of gas hydrates were measured in pure water and a viscous fluid mixed to imitate drilling mud fluids under several isothermal and isobaric conditions. Gas bubbles generated by dissociation affected the dissociation rate, possibly because gas bubbles near the active surface resisted heat flux during dissociation. For methane-ethane mixed hydrates, the calculated time profile agrees well with the experimental results when the composition of the vapor phase is identical with that of the hydrate phase. It indicates that the free gas composition around the dissociation surface is determined by the kinetics of dissociation and not by thermodynamic equilibrium. The dissociation rates of gas hydrates in viscous fluids were essentially proportional to the concentration of fluid.
Introduction Natural gas hydrates that exist under the sea floor are thought to constitute a large natural gas reservoir and are expected to be an energy resource in the future.1 To make recovery of natural gas from hydrates commercially viable, hydrates must be dissociated in situ.2 The dissociation rate, which depends on T-P and other environmental conditions, is an essential parameter needed to evaluate the feasibility of successful recovery. In addition to methane hydrate (C1 hydrate), a considerable amount of methane-ethane mixed hydrate (C1C2 hydrate) is found in ocean deposits.3 Because C1-C2 hydrate can be considered to be more stable than C1 hydrate,4,5 the dissociation behavior is expected to be different. However, the dissociation kinetics and dynamic behavior of such a practical mixed gas hydrate are not well understood. In this study, dissociation rates of C1 hydrate and C1C2 hydrate were determined under a variety of experimental conditions. C1 hydrate and C1-C2 hydrate were * Corresponding author. Tel: 0298-61-8428. Fax: 0298-61-8706. E-mail:
[email protected]. (1) Okuda, Y. Petrotech 1993, 16, 300-305. (2) Ji, C.; Ahmadi, G.; Smith, D. H. Chem. Eng. Sci. 2001, 56, 58015814. (3) Brooks, J. M.; Cox, H. B.; Bryant, W. R.; Kennicutt, M. C.; Mann, R. G.; Mcdonald, T. J. Org. Geochem. 1986, 10 (1-3), 221-234. (4) Yoon, J. H.; Chum, M.-K.; Lee, H. AIChE J. 2002, 48 (6), 13171330. (5) Sloan, E. D.; Fleyfel, F. Fluid Phase Equil. 1992, 76, 123-140.
synthesized by an ice-gas interface method.6,7 Raman spectrometry and gas chromatography were used to determine the structure and composition of C1-C2 hydrate. Results were used to estimate the dissociation temperature, heat of dissociation, and the density of the hydrate, values that are needed for model calculations discussed below. Dissociation rates were measured under isothermal and isobaric conditions in pure water. Based on one-dimensional thermal conduction theory, an analytical model was used to describe the dissociation behavior.8 Because of the practical implications, the dissociation behavior of C1-C2 hydrate in viscous fluids such as drilling mud9 was also investigated. Experimental Section Determination of Hydrate Composition and the Structure. Pure methane (C1) and methane-ethane (C1-C2) mixtures were used to form gas hydrate pellets. The purity of C1 gas is more than 99.9%, and the initial composition of the C1C2 mixture used to make C1-C2 hydrate is 0.901(C1)/0.099(C2) in mole fraction. All samples were synthesized in a highpressure vessel at 271.2 K and 8.5-10 MPa using the icegas interface method.6,7 To achieve complete hydration it is (6) Handa, Y. P. J. Chem. Thermodyn. 1986, 18 (10), 915-921. (7) Kawamura, T.; Komai, T.; Yamamoto, Y.; Nagashima, K.; Ohga, K.; Higuchi, K. J. Cryst. Growth 2002, 234, 220-226. (8) Kelker, S. K.; Selim, M. S.; Sloan, E. D. Fluid Phase Equil. 1998, 150, 371-382. (9) Berthezene, N.; de Hemptinne, J. C.; Audibert, A.; Argillier, J. F. J. Petro. Sci. Eng. 1999, 23, 71-81.
10.1021/ef020174x CCC: $25.00 © 2003 American Chemical Society Published on Web 03/19/2003
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Figure 1. Prepared hydrate pellet. Height: 6 mm, diameter: 12 mm, weight: 0.48 to 0.52 g. necessary to keep samples in the vessel for at least 3 days. After hydration, each sample was quickly transferred to a coldvessel at 139 K under atmospheric pressure; it is reasonable that the composition of the sample will remain essentially constant under these conditions. It has been reported that the guests ratio per water molecule is quite high when this synthesize technique is adapted.6,7,10 To measure the composition of C1-C2 hydrate samples, gases generated from hydrates were collected and analyzed by gas chromatography. A laser Raman microprobe spectrometer (Jobin Yvon Ramanor T6400) with a beam spot size of 1 µm was used for structural identification of the mixed hydrates. The wavelength of Ar+ laser was set for 514.5 nm. The refracted light was detected with a triple monochromator and CCD detector with a slit size of 250 µm. Preparation of Hydrate Pellet Sample. Hydrate powder obtained above was shaped in pellets; the apparatus used has a pair of mold and pushing rod made of stainless steel. Prepared hydrate powder was put in the mold, and pressed by 120 MPa by the rod. To prevent dissociation of sample, the mold and the rod were cooled to below 170 K with liquid nitrogen. The size and weight of each pellet were made uniform. The diameter, thickness, and weight were 12 mm, 6 mm, and 0.48-0.52 g, respectively. The porosity of the pellet was estimated (see next section) after determination of the density of each hydrate. It is advantageous to be able to define the objective sample when this method is adapted. A typical hydrate pellet is shown in Figure 1. Measurement of Dissociation Rate. The hydrate pellet was dissociated in pure water or a viscous fluid that imitated drilling mud that was used to examine the influence of viscosity. The faux drilling mud consisted of water, electrolytes, and a viscous medium such as XANVIS (Telnite Co. Ltd.), which is made from xanthan gum consisting of two glucose, two mannose, and one glucuronic acid.11,12 The polymer backbone consists of 1,4 linked β-D-glucose and is therefore identical in structure to cellulose. The concentrations of aqueous xanthan gum solutions were between 0.2 and 1.2 wt %. During dissociation, the pellet sample was soaked in pure water or xanthan gum solution. The system was pressurized with the C1 or C1-C2 gas that was used to synthesize each hydrate sample. The system pressure and the bulk gas composition were kept constant by using a buffer cylinder. A schematic of the experimental apparatus used in this work is shown in Figure 2. The optical cell, covered with a sapphire window, has an inner volume of about 2 mL and can accommodate a maximum pressure of 15 MPa. The gas inlet and outlet and a thermocouple are also equipped with the cell. Water or xanthan gum solutions were injected into the optical (10) Hirai, H.; Kondo, T.; Hasegawa, M.; Yagi, T.; Yamamoto, Y.; Komai, T.; Nagashima, K.; Sakashita, M.; Fujihisa, H.; Aoki, K. J. Phys. Chem. B 2000, 104, 1429-1433. (11) Jansson, P. E.; Kenne, L.; Lindberg, B. Carbohydr. Res. 1975, 45, 275-282. (12) Melton, L. D.; Mindt, L.: Rees, D. A.; Sanderson, G. R. Carbohydr. Res. 1976, 46 (2), 245-257.
Figure 2. Schematic illustration of experimental apparatus. Table 1. Experimental Result of Gas Analysis and Calculateda,b,c experimental calculation
gas-phase
hydrate-phase
0.901/0.099 0.901/0.099
0.714/0.286 0.761/0.239
a Ref 4. b Initial gas was C -C mixture and the mole fractions 1 2 in each phase are shown. c T-P conditions are 271.2 K and 8.5 MPa.
cell. At the same time the system pressure was decreased to the experimental pressure to initiate dissociation. During dissociation, the system was kept under isothermal and isobaric conditions. The time of dissociation is determined directly through the optical window as the time required for complete dissociation of the hydrate pellets.
Results and Discussion Hydrate Composition and Structure. It is known that both pure methane (C1) and ethane (C2) form a structure I hydrate crystal. A recent study has shown, however, that a C1-C2 gas mixture can form a structure II crystal at certain gas compositions.13-15 Knowledge of these structures is important because the heat of dissociation5 or other physical parameters required to estimate the dissociation rate depend greatly on the hydrate structure and the guest. Therefore, both the guest composition and the structure of hydrate samples were examined. The experimental results obtained by gas chromatography were compared with the results of thermodynamic calculations developed by Yoon et al.4 and are summarized in Table 1. The initial gas ratio used to make C1-C2 hydrate is 0.901(C1)/0.099(C2), and the (13) Subramanian, S.; Kini, R. A.; Dec, S. F.; Sloan, E. D. Chem. Eng. Sci. 2000, 55, 1981-1999. (14) Subramanian, S.; Ballard, A. L.; Kini, R. A.; Dec, S. F.; Sloan, E. D. Chem. Eng. Sci. 2000, 55, 5763-5771. (15) Ballard, A. L.; Sloan, E. D. Chem. Eng. Sci. 2000, 55, 57735782.
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Figure 3. Raman spectra of C1-C2 hydrate at C-H starch reason.
hydration numbers of C1 hydrate and C1-C2 hydrate were estimated to be 5.86 and 6.39, respectively, by measuring after dissociation the weight of the initial hydrate and of water. Therefore, considering the structures as crystals the cage occupancies of C1 hydrate and C1-C2 hydrate were estimated to be 0.981 and 0.887, respectively. Using eq 1, we can estimate that the densities of C1 hydrate and C1-C2 hydrate were 0.916 g/cm3 and 0.922 g/cm3, respectively. From this information, the porosity of the pellet was estimated to be 0.16 to 0.23. Dissociation Rate of Gas Hydrate (or Ice) in Water. The analytical model used in this work is based on simple one-dimensional thermal conduction.8 It is assumed that dissociation can occur only at the hydratewater interface and that the interface temperature is identical with the equilibrium dissociation temperature at the system pressure. The equation that describes gas hydrate dissociation in this system can be derived from Fourier’s law of heat conduction as follows:
∂TW ∂2 TW ) RW 2 ∂t ∂x
0 < x < X,t > 0
(2)
The boundary conditions for the system are
Figure 4. Raman spectra of C1-C2 hydrate at C-C starch reason.
composition of the hydrate phase is 0.714(C1)/0.286(C2). It shows reasonable agreement with the model calculation, with a deviation of 0.047 in mole fraction. The results of the model calculation also indicate that only a structure II hydrate can exist stably with the vapor phase under these conditions. Raman spectra are shown in Figures 3 and 4; each dotted line shows the spectral intensities obtained from C1-C2 gas mixture. The peak intensity of C1 in the large cavity (IL) is 5-fold larger than the value for the small cavity (IS) (Figure 3).13,16 Moreover, the peak at 993.3 cm-1 can be assigned to C2 in the hydrate structure II13,15 (Figure 4). From these data it is reasonable to conclude that the C1-C2 gas mixture forms a structure II hydrate. The equation used to estimate the density of the hydrate, F, in this work is a modified equation of Sloan’s:17 c
NW[WH2O + yνtotal F) NAVcell
xjWj] ∑ j)1
(1)
where NW stands for number of water molecules per unit cell, NA is Avogadro’s number, Wj is the molecular weight of component j, y is the total cage occupancy, νtotal is the total number of all cavities per water molecules in a unit cell, xj is the mole fraction of component j, Vcell is the volume of unit cell, and c is the number of components in the hydrate phase. The (16) Sum, A. K.; Burrus, R. C.; Sloan, E. D. J. Phys. Chem. B 1997, 101, 7371-7377. (17) Sloan, E. D. Clathrate Hydrates of Natural Gas, 2nd ed.; Marcel Dekker: New York, 1998; pp 241.
at t ) 0, TW ) T0
(3)
at x ) 0, TW ) T0
(4)
at x ) X, TW ) TD
(5)
at x ) X, -kW
∂TW dX ) (1 - )FHλH ∂x dt
(6)
Thus, the movement of the water-hydrate (or ice) interface X can be expressed as a function of time t as follows:
X ) ξx4RWt
(7)
2 FH λH e-ξ ξ ) (1 - )xπ erfξ FW CP,W(T0 - TD)
(8)
where ξ is given by
where RW is thermal diffusivity of water, kW is thermal conductivity of water, is porosity of the pellet, FH is density of hydrate (or ice), FW is density of water, λH is heat of dissociation of the hydrate (or ice),5 CP,W is heat capacity of water, T0 is the experimental temperature, and TD is the hydrate (or ice) dissociation temperature. TD is the equilibrium temperature under experimental pressure and its gas composition can be estimated with the “ice fugacity model”.4 Therefore TD depends highly on the experimental pressure and gas composition. This equation explains the single moving boundary model (water-hydrate boundary) without considering the effects of the ice layer that covers the hydrate surface. Moreover, each experimental pressure was chosen so that TD was never below 273.15 K. The physical parameters for the calculation are listed in Table 2. To confirm the feasibility of the experimental method used in this work, the fusion behavior of a pure ice pellet was examined. The time required for complete fusion
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Table 2. Table of Physical Parameters for Analytical Calculation physical property
value
thermal conductivity of water kW heat capacity of water CPW thermal diffusivity of water RW density of water FW density of Ice FI density of C1 hydrate FHC1 density of C1-C2 hydrate FHC12 heat of dissociation of ice λI heat of dissociation of C1 hydrate λHC1 heat of dissociation of C1-C2 hydrateλHC12 porosity of ice pellet I porosity of C1hydrate pellet HC1 porosity of C1-C2 hydrate pellet HC12
0.001314 cal/cm s °C 1.00495 cal/g °C 0.00131 cm2/s 1.00 g/cm3 0.917 g/cm3 0.916 g/cm3 0.922 g/cm3 79.7 cal/g 111.9 cal/ga 130.8 cal/ga 0.196 0.196 0.201
a Ref 5. Considering the hydration numbers of C and C -C 1 1 2 hydrate were 5.86 and 6.39, respectively.
Figure 5. Time required for complete dissociation the ice pellet at each temperature under atmospheric conditions.
Figure 6. Time required for complete dissociation of the C1 hydrate pellet in water, and the calculated value.
of the ice pellet decreases with increasing dissociation temperature (Figure 5). In addition the experimental data are in good agreement with the model calculation within a maximum deviation of 1.3 min. The C1 hydrate and C1-C2 hydrate pellets were also dissociated in pure water under isothermal and isobaric conditions. The temperature was 279.15 K and the pressures ranged from 0.8 to 4.24 MPa. The time required for complete dissociation of C1 hydrate pellets as a function of pressure is shown in Figure 6. Experimental data and calculated values obtained using the physical values listed in Table 2 show the same exponential trend. The highest pressure used is very close to the equilibrium pressure of 4.67 MPa at 279.15 K. With one exception, the experimental data are larger than calculated values over almost the entire pressure range. This may be caused by gas bubbles generated from the surface of the pellet as the hydrates dissociate. As can be seen in Figure 7, a substantial number of
Figure 7. Snapshots of dissociating pellet surfaces. Ice pellet was at 275.15 K, C1 hydrate were at 279.15 K, 3.8 MPa, respectively. Almost no bubbles are seen on the ice surface while the whole surface of the hydrate was covered with methane bubbles.
Figure 8. Time required for complete dissociation the C1C2 hydrate pellet in water, and the calculated values.
methane gas bubbles cover the surface of the hydrates and the optical window. Because bubbles in water may insulate against heat transfer, their influence may be large enough to reduce the dissociation rate and prolong the time for complete dissociation. For a more accurate calculation, it will be necessary to modify and develop the analytical model to include bubble dynamics. The time required for complete dissociation of the C1C2 hydrate pellets as a function of pressure is shown in Figure 8. For the C1-C2 hydrate, the model calculation was carried out assuming two different environmental gas composition, (a) 0.9(C1)/0.1(C2) and (b) 0.7(C1)/ 0.3(C2). In the case of (a) 0.9(C1)/0.1(C2), a composition that is identical with the bulk gas composition, TD was estimated to be the usual equilibrium temperature in this system. But as can be seen in Figure 8, the calculated value of curve (a) does not agree with the experimental data. In contrast, the composition of 0.7(C1)/0.3(C2) is identical to the composition of gas bubbles generated by dissociation that has the same composition as the hydrate guest. Therefore, TD was estimated to be the equilibrium temperature in the gas. Using these parameters, the calculated value can reproduce the experimental data (see Figure 8, curve (b)). It becomes clear that the calculated time profile will agree well with experimentally observed results only when the gas composition is essentially identical with hydrate phase composition. This result indicates that the free gas composition around the dissociation surface is determined by the kinetics and not the equilibrium thermodynamics of dissociation. Dissociation Rate of Gas Hydrate in Aqueous Xanthan Gum Solutions. The viscosity of aqueous xanthan gum solutions was measured using a rotary
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dissociation in 0.4 wt % xanthan gum solution is 1.3fold larger than 0 wt %. In the case of 1.2 wt % xanthan gum solution, the maximum concentration used in this work, it becomes more than 2-fold larger than 0 wt %. Thus, the influence of viscosity cannot be clearly quantified. The results do suggest, however, that in the case of riser drilling the dissociation rate will be considerably slower compared with conditions in which no drilling mud is used. Conclusion Figure 9. Viscous property of xanthan gum solution.
Figure 10. Time required for complete dissociation the C1C2 hydrate pellet in xanthan gum solution (at 279.15 K, 0.1 MPa).
type viscometer at 279.15 K (Figure 9). As the concentration of xanthan gum increases from 0.2 to 1.2 wt %, the viscosity of aqueous xanthan gum solutions also increases. It is also clear that the xanthan gum solutions have non-Newtonian flow behavior (Figure 9). The C1-C2 hydrate pellets were dissociated in aqueous xanthan gum solutions at 279.15 K and 0.1 MPa, respectively. As shown in Figure 10, the dissociation rate decreases with increasing concentrations of xanthan gum. Therefore, the dissociation rate of gas hydrates in drilling mud fluids is almost inversely proportional to the concentration of mud fluid. In real drilling situations, it is recommended that the XANVIS concentration be over 0.4 wt %. In this work, time of
The dissociation rates of C1-C2 hydrate pellets were measured at several isothermal and isobaric conditions in pure water and aqueous xanthan gum solutions. In the case of pure water, the calculated time profile, which is based on one-dimensional thermal conduction, can reproduce experimentally observed results. However, it is necessary to use the hydrate guest composition for gas-phase composition instead of bulk gas composition. This result indicates that the free gas composition around the dissociation surface is determined by kinetics and not the equilibrium thermodynamics of dissociation. In other words, the gas composition of the hydrate guest, (0.7(C1)/0.3(C2)), is similar to the hydrate guest composition because gas bubbles were generated uniformly during dissociation. As the distance from the surface increases, the gas composition varies gradually to the bulk gas composition of 0.9(C1)/0.1(C2). This phenomenon can be regarded as a specific feature about dissociation behavior of a mixed gas hydrate. From a practical standpoint, this result indicates that knowledge of the composition of the hydrate phase will be an essential factor needed to estimate the dissociation rate of a gas hydrate under the sea floor. In xanthan gum solution, the time of dissociation in 0.4 wt % xanthan gum solution is 1.3-fold larger than that of 0 wt %. In the case of 1.2 wt % xanthan gum solution, which is the maximum concentration in this work, it becomes more than 2-fold larger than that of 0 wt %. It suggests that in the case of riser drilling, the dissociation rate will be considerably slower compared with that under conditions in which no drilling mud is used. EF020174X
