Kinetic Behaviors of Methane Hydrate Formation in Porous Media in

Mar 13, 2014 - Guangzhou Center for Gas Hydrate Research, Chinese Academy of Sciences, ... formation experiments in porous media in the presence of...
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Kinetic Behaviors of Methane Hydrate Formation in Porous Media in Different Hydrate Deposits Bo Li,†,‡,§ Xiao-Sen Li,*,†,‡ Gang Li,†,‡ Yi Wang,†,‡ and Jing-Chun Feng†,‡,§ †

Key Laboratory of Renewable Energy and Gas Hydrate, Guangzhou Institute of Energy Conversion, Chinese Academy of Sciences, Guangzhou 510640, Guangdong, PR China ‡ Guangzhou Center for Gas Hydrate Research, Chinese Academy of Sciences, Guangzhou 510640, Guangdong, PR China § University of Chinese Academy of Sciences, Beijing 100083, PR China ABSTRACT: The kinetic characteristics of methane hydrate formation in porous media are investigated in three experimental apparatus with different scales. A total of 18 experimental formation runs are implemented in these apparatus (6 runs in each device). The kinetic model proposed by Li et al. [Chem. Eng. Sci., 2014, 105, 220−230] is employed to simulate these hydrate formation processes, and the applicability of this model in different hydrate deposits is confirmed by comparing the experimental data with the numerical prediction. It is found that the reaction rate constant k decreases sharply with the increase of the size of the apparatus, which indicates that the hydrate formation rate is inversely proportional to the scale of the hydrate deposit. In addition, both the initial phase saturations and the properties of the porous media show extraordinary effects on the formation kinetics of methane hydrate. microscopic techniques, Jin et al.10 found that the hydrate growth in porous media occurred in two steps: film-like hydrate formation at the gas−water interface in the first step and water molecules entering the hydrate phase from the cracks in the film in the second step. Through direct morphology observation, Babu et al.11 observed the nucleation of hydrate crystals on the surface of the activated carbon grain. It was found that the pore space, particle size, and water saturation might affect the methane hydrate formation in porous media. Jung et al.12,13 found that the nucleation occurred at the interface between the gas and water phases in capillary tubes in the pores and that the hydrate formation could be promoted by the increased interfacial area between gas and water. In general, the mechanism of methane hydrate formation in porous media is still unclear. On the basis of the reported enhanced effect of some chemicals on the hydrate formation rate in pure water systems,14−16 some other researchers have performed hydrate formation experiments in porous media in the presence of chemical additives to further enhance the formation rate. Kumar et al.17 investigated the CO2 hydrate formation kinetics in silica gels and found that sodium dodecyl sulfate (SDS) could promote the hydrate formation rate and reduce the induction time. Dicharry et al.18 also reported that the CO2 hydrate formation rate and the total amount of hydrate formed could both be promoted by use of SDS in porous silica gels. It was suggested that when SDS was present, CO2 hydrate was formed not only at the gas−water interface but also in the bulk water phase. Zhong et al.19 found that the addition of the additive tetrahydrofuran (THF) to the silica sand particles

1. INTRODUCTION Gas hydrates are crystalline solid compounds usually formed by water and small gas molecules when they are located at suitable thermodynamic pressure−temperature conditions.2 The most common hydrate-forming gas is methane, and they have been proven to exist in tremendous amounts within gas hydrates in permafrost and below the sea floor. These naturally occurred methane hydrates may provide a new and potentially huge energy resource to meet the world’s increasing energy demands.3 The reaction of methane hydrate formation is generally described by the following equation: CH4 + NH H 2O ⇔ CH4 ·NH H 2O + ΔH

(1)

where NH is the hydration number, which is in the range of 5.77 to 7.40,3 and ΔH is the formation enthalpy. In recent years, this crystallization process has been proven to be an effective method of methane separation from gas mixtures (e.g., CH4 + N2).4−7 To commercially extract the natural gas from geologic hydrate reservoirs in the future, it is important to have a full understanding of the mechanisms of hydrate formation and dissociation in porous media. Recently, researchers have made some progress in investigating the formation behaviors of methane hydrate in porous media. Linga et al.8 performed methane hydrate formation experiments in a water-saturated silica sand bed, and found that the water-to-hydrate conversion was much higher than that in a pure water system in a stirred vessel. Then, Linga et al.9 further carried out the hydrate formation experiments in two different crystallizers with six kinds of gas systems. The results showed that the hydrate formation rate for all the systems was significantly higher in a fixed bed column compared to that in a stirred tank reactor. However, they did not explain the mechanism responsible for this enhanced rate in the silica sand bed. Using the attenuated total reflection infrared (ATR-IR) spectroscopic and optical © 2014 American Chemical Society

Received: Revised: Accepted: Published: 5464

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Figure 1. Schematic design of the three apparatus.

Table 1. System Properties of the Three Experimental Apparatus devices

radius R (m)

height H (m)

side length L (m)

inner volume V (L)

sand porosity ϕ

surface area-to-volume ratio RSv (m2/m3)

reaction rate constant k (kg/(m2 Pa s))

SHS CHS PHS

0.025 − 0.25

0.20 − 0.60

− 0.18 −

0.393 5.832 117.8

42.13% 47.19% 43.50%

90.00 33.33 11.33

50.59 25.42 8.06

be distributed in the pores of porous media in the form of small spherical “gas bubbles”, and AS is computed to be the total surface area of these gas bubbles. The parameters of the reaction rate constant and the activation energy are obtained by fitting the experimental formation data from the PHS. Then the methane hydrate formation processes under other different conditions in the PHS are predicted using the new model and two other kinetic models of Sun et al.25 and Moridis et al.,26 and the predicted results are compared with the corresponding experimental data. The results show that the model proposed by Li et al.1 can predict methane hydrate formation more precisely than the other two models. In the present work, three experimental apparatus with different scales are employed simultaneously to conduct the methane hydrate formation experiments. Six formation runs under different conditions are implemented in each device. Then the formation data are correlated with the kinetic model of Li et al.1 to (i) obtain the reaction rate constants in different hydrate deposits and to (ii) investigate the prediction abilities of this model in different hydrate deposits. Afterward, the hydrate formation behaviors in these apparatus are compared with each other, and the effect of the initial phase saturations on the hydrate formation processes is analyzed. Furthermore, the sensitivity of hydrate formation rate to the properties of porous media is also evaluated.

could also reduce the nucleation time and significantly increase the methane recovery from the low-concentration coal mine methane gas (30 mol % CH4/N2). These studies are mainly based on the strategy of increasing the gas−water contact area available for the kinetic hydrate formation using chemical additives. To date, many studies have been reported about the kinetic investigations of hydrate formation and dissociation in pure water systems.20−23 The general formulation of the kinetic model for describing hydrate formation and dissociation can be expressed as follows:20,24 ⎛ ΔE ⎞ ∂mH = k exp⎜ − a ⎟AS(fg − feq ) ⎝ RT ⎠ ∂t

(2)

where mH is the mass of the formed hydrate (kg), k the reaction rate constant (kg/(m2 Pa s)), ΔEa the activation energy (J/ mol), R the gas constant (J/(mol K)), T the local temperature (K), and AS the reaction surface area (m2); fg and feq are the local fugacity and the equilibrium fugacity of methane gas under the local temperature, respectively (Pa). Generally, the total surface area of the formed hydrate particles is considered to be AS. However, the experimental results of Mohebbi et al.23 indicate that the gas consumption rate is not dependent on the surface area of the hydrate particles but is controlled by the mass transfer at the gas−water contact interface. In other words, AS is actually the contact area between the gaseous and aqueous phases. Recently, Li et al.1 proposed a new kinetic model for the description of methane hydrate formation in porous media based on the experimental results from a pilot-scale hydrate simulator (PHS). In this model, the methane gas is supposed to

2. EXPERIMENTAL APPARATUS AND PROCEDURE 2.1. Hydrate Simulators. Figure 1 shows the schematic design of the hydrate simulator used for the hydrate formation and dissociation research in porous media. The hydrate simulator shown in this figure actually stands for three different 5465

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pipelines connected to the steel, the deionized water was injected to the vessel from the top side after the gas injection. Then the gas could gradually penetrate into the top section because of buoyancy while the water could flow downward under the effect of gravity. Thus, the gas and water could still be fully contacted with each other in the SHS. Once the system pressure was increased to a proper level (13.00−20.00 MPa), the vessels were closed and the temperature of the water bath was set down to start the hydrate formation. The formation temperature was in the range of 280.15 to 282.05 K. During the formation stage, the pressure and temperature data were logged by the computer at 20 s intervals. When the pressure gradually decreased to a certain level, the current formation run was terminated and the next one was started. A total of six formation runs under different conditions were implemented in each device. 2.3. Experimental Determination of Hydrate Mass. The method described by Li et al.1 and Linga et al.9 is used to calculate the hydrate mass history in each experimental run. Assuming the incompressibility of the solid sand grains, the total pore volume Vp remains unchanged at each time point. That is, the gas, water, and hydrate saturations (SG, SA, and SH, respectively) should follow the following relationship:

high-pressure vessels: the small-scale hydrate simulator (SHS), the cubic hydrate simulator (CHS), and the pilot-scale hydrate simulator (PHS). This is because all the devices in the system are nearly the same except the simulator itself. The details of the system properties of these hydrate simulators are shown in Table 1 and are described in the following sections. 2.1.1. Small-Scale Hydrate Simulator (SHS). The SHS is a small cylindrical stainless steel vessel with the effective inner volume of 0.393 L (0.20 m length and 0.050 m diameter, Table 1). The maximum working pressure of the SHS is 20 MPa, and the desired low-temperature conditions are provided by a water bath (−15 to 30 °C, ± 0.1 °C). The inlet and the outlet are located at the top and the bottom of the vessel, respectively, where two pressure transducers are located to measure the pressure change during the hydrate formation. Three Pt100 thermometers are situated along the length of the vessel and inserted into the porous media to monitor the temperature change. 2.1.2. Cubic Hydrate Simulator (CHS). The CHS is a cubic three-dimensional stainless steel vessel with the maximum working pressure of 25 MPa. The length of each side in the CHS is 0.18 m, and the effective inner volume is 5.832 L, as shown in Table 1. The whole reactor is also placed in a water bath of which the temperature can be controlled in the range of −15 to 30 °C, ± 0.1 °C. It is divided into four identical regions with three horizontal layers (layers A, B, and C). Several vertical and horizontal wells are used to connect the inside of the CHS with other outside devices shown in Figure 1. These wells are inserted into different areas of the reactor, and fluids can be injected or produced through the small grooves that are uniformly distributed along the circumference of each well. Detailed information of the well design and distribution can be obtained in the literature.27,28 The temperature change in the CHS is monitored by 75 Pt100 thermometers that are evenly distributed in the vessel. 2.1.3. Pilot-Scale Hydrate Simulator (PHS). Like the SHS, the PHS is also a cylindrical stainless steel vessel that can be pressurized as high as 30 MPa. Its effective inner volume is 117.8 L, with a length of 0.60 m and a diameter of 0.50 m. Under the synergistic effect of a water jacket and a cold refrigeration room, the working temperature of the PHS can be maintained stable in a range that is the same as that used with the SHS and CHS. Two pressure transducers are located at the top and the bottom of the PHS to measure the pressure change. The evolution of the temperature in the PHS is monitored by 147 thermometers which are also placed in three horizontal layers (layers A, B, and C, which equally divide the inner volume into four regions). The well design of the PHS is similar to that of the CHS, and it has been described in detail in the literature.1,29 2.2. Procedure. Before the hydrate formation process, the raw dry quartz sand with a size range between 300 and 450 μm was tightly packed in all three vessels. After that, the residual air remaining in the pores was removed by a vacuum pump. On the basis of the water flooding method, the porosities of the SHS, CHS, and PHS were experimentally determined to be 42.13%, 47.19%, and 43.50%, respectively, as summarized in Table 1. Then the vessels were pressurized with methane gas (99.99% purity) and deionized water injection. To make the injected gas and water distribute as homogeneously as possible in the vessel, the method described by Li et al.1 was employed in the CHS and PHS systems during the gas and water injection process. For the SHS system, as there were only two

SG + SA + SH = 1

(3)

The three phase saturations are calculated as vmnm,G SG = Vp SA =

SH =

(4)

mW0 − NH(nm0 − nm,G − nm,W )MW ρW Vp

(5)

(nm0 − nm,G − nm,W )MH ρH Vp

(6)

The meanings of the variables are explained in detail in Nomenclature. On the basis of the recorded experimental P−T data, the molar volume of methane gas vm and the amount of gas dissolved in the water nm,W are calculated using the Peng− Robinson EOS and Henry’s law, respectively. After that, the other four unknown variables (SG, SA, SH, and nm,G) could be obtained by combining eqs 3−6. Finally, the hydrate mass mH existing in the vessel is mH = ρH SHVp

(7)

3. NUMERICAL SIMULATION 3.1. Numerical Code and Kinetic Model. We employ the parallel version of the TOUGH+HYDRATE (T+H) code26 to conduct the numerical simulation in this work. This code can model nonisothermal hydration reactions, phase behavior, and flow of fluids and heat under conditions typical of natural methane hydrate deposits in complex geologic media. The model accounts for heat and four mass components (i.e., water, methane, hydrate, and chemical inhibitors such as salts and alcohols) that are partitioned among four possible phases: gas, aqueous liquid, ice, and hydrate. It includes both an equilibrium and a kinetic model for hydrate formation and dissociation. The equilibrium model has been validated by Li et al. using the experimental data from the CHS and the PHS mentioned above,30−32 and it is the common choice for the evaluation of 5466

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⎛ ΔE ⎞ ∂mH = k exp⎜ − a ⎟SA β(1 − SH)β NV(4πrp2)SG 2/3(fg − feq ) ⎝ RT ⎠ ∂t

Table 2. Simulation Parameters of the Hydrate Deposits parameter

value

radius of sand grains rp hydrate-forming gas density of hydrate ρH26 intrinsic permeability K salinity hydration activation energy ΔEa wet thermal conductivity kΘRW dry thermal conductivity kΘRD composite thermal conductivity model26 capillary pressure model36

3.75 × 10−4 m CH4 0.925 g/mL 5.0 × 10−11 m2 (= 50.0 darcies) 0 8.09 × 104 J/mol 3.1 W/(m·K) 1.0 W/(m·K) kΘC= kΘRD + (SA1/2 + SH1/2)(kΘRW − kΘRD) + φSIkΘI Pcap = −P01 [(S*)−1/λ − 1]1−λ S* = (SA − SirA)/(SmxA − SirA) 0.29 0.45 105 Pa krA = (SA*)m krG = (SG*)mG SA* = (SA − SirA)/(1 − SirA) SG* = (SG − SirG)/(1 − SirA) 3.572 3.572 0.03 0.30

SirA λ P01 relative permeability model26

m mG SirG SirA

(8)

where β is the reduction exponent, NV the number of voids in the porous media, and rp the radius of the sand grains (m). This model is based on the consideration that the gas consumption rate should be controlled by the mass transfer at the gas−water contact area, not at the interface of the hydrate particles. The detailed derivation of this model can be found in the literature.1 In this work, the kinetic model shown in eq 8 is employed and added into the T+H code to further investigate its prediction performance in different hydrate deposits. 3.2. Domain Discretization. The SHS and the PHS are both discretized into a two-dimensional and axially symmetric mesh. For the SHS, the domain is discretized into 12 × 22 = 264 (r, z) gridblocks. The elements at z = 0.10 m (the topmost) and z = −0.10 m (the bottommost) as well as r = 0.025 m (the rightmost) are the impermeable stainless steel with constant P and T conditions. For the PHS, it is discretized into 47 × 102 = 4794 (r, z) elements, of which 4600 are the inner active gridblocks. It is identical to the mesh used in our previous studies.1,30,31 The CHS is discretized into a threedimensional mesh which consists of 22 × 22 × 22 = 10 648 elements in (x, y, z). The stainless steel is represented by the six outtermost layers, and the number of active elements in the CHS mesh is 8000. 3.3. System Properties and Simulation Parameters. Tables 1 and 2 show, respectively, the system properties of the three experimental apparatus and the simulation parameters of the hydrate deposits. The reaction rate constant k listed in Table 1 is obtained by fitting the experimental formation data of each device, which will be discussed later. In Table 2, the radius of the sand grains is the average value of the quartz sand, and the intrinsic permeability K is measured by Li et al.35 to be approximately 50.0 darcies using the same sand in a permeability measurement apparatus. The activation energy ΔEa is 8.09 × 104 J/mol in this simulation.1 The salinity of the

the gas production potential from the real hydrate deposits because of its simplicity and low computational demand.26,33,34 In addition, the original kinetic model of the T+H code has also been proven to be not very suitable for the methane hydrate formation description in porous media by Li et al.1 On the basis of the six groups of experimental formation data from the PHS, they have proposed and further validated a new kinetic model, which is formulated as

Table 3. Experimental Conditions and the Absolute Average Deviations (AAD) between the Experimental Data and the Predicted Results of the SHS, CHS, and PHSa device

run

T0 (K)

P0 (MPa)

Pend (MPa)

SG0

SA0

nm0 (mol)

TB (K)

Δt (days)

AAD (%)

data processing

SHS

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

281.18 281.15 282.13 281.75 281.67 281.15 282.86 282.68 282.62 282.50 283.04 282.59 282.14 282.50 282.15 282.15 283.97 282.08

13.00 14.00 16.01 13.92 17.03 14.20 18.00 18.93 19.58 18.14 18.92 19.02 17.55 19.98 18.39 18.86 18.00 18.33

10.53 9.08 7.78 8.75 10.13 9.31 12.80 14.46 13.18 13.69 13.57 13.51 13.31 9.20 9.04 8.56 9.09 10.61

0.228 0.309 0.396 0.412 0.433 0.467 0.437 0.523 0.617 0.620 0.624 0.634 0.301 0.320 0.334 0.359 0.397 0.467

0.772 0.691 0.604 0.588 0.567 0.533 0.563 0.477 0.383 0.380 0.376 0.366 0.699 0.680 0.666 0.641 0.603 0.533

0.308 0.435 0.621 0.560 0.720 0.646 12.608 15.632 18.861 17.696 18.437 18.861 164.36 194.76 188.37 205.90 213.26 256.24

281.05 281.05 282.05 281.65 281.45 281.05 281.55 281.37 281.32 281.35 281.35 281.96 280.15 281.68 281.15 281.54 281.43 281.73

1.205 3.163 8.458 4.622 5.736 4.531 6.497 6.500 14.39 8.660 11.29 13.39 10.27 33.26 41.49 39.76 40.08 40.44

13.7 4.0 5.1 5.1 5.7 7.3 3.7 4.4 6.8 9.7 5.7 7.7 10.5 8.5 7.4 5.0 2.9 6.5

fitted fitted fitted fitted predicted predicted fitted fitted fitted fitted predicted predicted fitted fitted fitted fitted predicted predicted

CHS

PHS1

SG0 is the initial gas saturation. SA0 is the initial water saturation. nm0 is the initial methane amount. TB is the boundary temperature. Δt is the duration of each experimental run. AAD is the absolute average deviation of the predicted results from the experimental data. a

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Figure 2. Experimental data (Exp.) and fitted results of the system pressure and the hydrate mass in the SHS during hydrate formation in runs 1−4 in Table 3.

Figure 3. Experimental data (Exp.) and fitted results of the system pressure and the hydrate mass in the CHS during hydrate formation in runs 1−4 in Table 3.

kinetic model (eq 8) in different hydrate deposits, we have carried out six experimental runs of methane hydrate formation in the SHS, CHS, and PHS, as shown in Table 3. The experimental data including the pressure P and the calculated hydrate mass mH of runs 1−4 in each device are fitted with the kinetic model to obtain the reaction rate constant k. The fitted k is 50.59, 25.42, and 8.06 kg/(m2 Pa s) for the SHS, CHS, and PHS, respectively, as listed in Table 1. The absolute average deviations (AAD) between the experimental data and the fitted results are shown in Table 3, in which the average AAD of runs 1−4 is 7.0%, 6.1%, and 7.8% for the SHS, CHS, and PHS, respectively. A general observation is that k varies with the scale of the hydrate simulators. Figures 2, 3, and 4 show the experimental data and the fitted results of the system pressure and the hydrate mass in the SHS, CHS, and PHS, respectively, during hydrate formation in runs 1−4. We can see that the

deionized water is 0. Other related parameters are referred to the literature.1,30 3.4. Initial and Boundary Conditions. A total of six formation runs under different conditions are implemented in each hydrate simulator. The initial conditions of these experiments are shown in Table 3, which includes the initial temperature T0, initial formation pressure P0, initial gas and water saturations (SG0 and SA0, respectively), and the total amount of injected methane nm0 in each run. The Pend represents the end-point pressure of the hydrate formation. The formation time Δt is the duration of the experimental run. The temperature of the water bath is taken as the boundary temperature TB in the numerical simulation.

4. RESULTS AND DISCUSSION 4.1. Hydrate Formation Data and Numerical Prediction. To investigate the prediction performance of the 5468

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Figure 4. Experimental data (Exp.) and fitted results of the system pressure and the hydrate mass in the PHS during hydrate formation in runs 1−4 in Table 3.

Figure 5. Experimental data (Exp.) and predicted results of the system pressure and the hydrate mass in the SHS during hydrate formation in runs 5 and 6 in Table 3.

fitted curves match very well with the experimental data, which indicates the reliability of the fitted k. After the k is determined, it is adopted in the numerical simulation to predict the hydrate formation processes of the other two runs (runs 5 and 6 in Table 3). The predicted results of the system pressure and the hydrate mass history in the SHS, CHS, and PHS are then compared with the corresponding experimental data, which are shown in Figures 5, 6, and 7, respectively. Good agreements are observed between the experimental data and the numerical prediction, which demonstrate that the kinetic model could be applied in hydrate deposits with different scales and that the reaction rate constant k is indeed different in these apparatus. The average deviations (AAD) between the experimental data and the numerical prediction are 6.5%, 6.7%, and 4.7% for the SHS, CHS, and PHS, respectively, as listed in Table 3. 4.2. Characteristics of the Reaction Rate Constant k. On the basis of the experimental and numerical simulation

results in the three hydrate simulators, it can be seen that the reaction rate constant k changes with the scale of the hydrate deposits, while it can maintain its constant features when the size of the hydrate deposit is determined. As shown in Table 1, k decreases with the increase of the size of hydrate deposit, which may be caused by the heat-transfer effect during hydrate formation in porous media. During the crystallization process of methane hydrate, heat is released continuously from the exothermic reaction of hydrate formation, as shown in eq 1. The released heat (ΔH) needs to be transferred from the center to the constant-T boundary effectively to keep the lowtemperature condition for hydrate formation. Otherwise the released heat will conversely inhibit the crystallization process, and the inner temperature may be raised to a very high level which is unfavorable for further hydrate formation. The heattransfer rate should be dependent on the surface area of the boundary SB and the total volume of the hydrate deposit VD. We define the surface area-to-volume ratio RSV as 5469

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Figure 6. Experimental data (Exp.) and predicted results of the system pressure and the hydrate mass in the CHS during hydrate formation in runs 5 and 6 in Table 3.

Figure 7. Experimental data (Exp.) and predicted results of the system pressure and the hydrate mass in the PHS during hydrate formation in runs 5 and 6 in Table 3.

R SV =

SB VD

different scales, we have conducted another three formation cases through numerical simulation. In these cases, the initial pressure, initial temperature, and gas and water saturations are P0 = 18.00 MPa, T0 = 281.15 K, SG0 = 0.40, and SA0 = 0.60, respectively. The boundary temperature TB = 281.15 K, and it is kept constant. The predicted histories of P and mH (per unit volume) of the three apparatus are shown in Figure 9. It can be seen from Figure 9 that under the same initial and boundary conditions, the smaller the hydrate deposit is, the faster the system pressure decreases. The formation processes are stopped when the pressure drops to 8.00 MPa, at which the durations of the formation in the SHS, CHS, and PHS are 9.47, 23.18, and 62.49 days, respectively. This indicates that the gas in the pores is consumed with higher rate in smaller apparatus, and it will take more time to synthesize hydrate samples in larger hydrate deposits. This is also in accordance with the experimental observations of Δt shown in Table 3. In addition,

(9)

The RSV provides a relative measure of the heat-transfer abilities of the hydrate deposits. A larger deposit is usually accompanied by a smaller RSV, which means the heat-transfer resistance increases with the scale of the hydrate deposit. It is calculated to be 90.00, 33.33, and 11.33 m2/m3 for the SHS, CHS, and PHS, respectively, as shown in Table 1. The k versus RSV is plotted in Figure 8. It clearly shows that k drops down sharply with the decrease of RSV, which indicates that the hydrate formation rate is inversely proportional to the scale of the hydrate deposit. 4.3. Comparison of Hydrate Formation Behaviors in Different Scales. Up to now, we have obtained appropriate k for the prediction of methane hydrate formation in porous media in the three apparatus (SHS, CHS, and PHS, Table 1). To compare the formation behaviors of methane hydrate in 5470

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example, mH rises sharply from about 9.54 to 13.94 kg when SG0 is raised from 0.20 to 0.40. This is because the surface area of the gas bubbles increases with the gas saturation, and it further results in faster mass-transfer rate between the gaseous and aqueous phases for hydrate crystallization. However, when the SG0 rises to a certain level (e.g., SG0 = 0.60 in this study), the acceleration effect of gas saturation on hydrate formation is not obvious anymore. This indicates that the aqueous phase is also an important factor that determines the hydrate formation kinetics, which is in accordance with the conclusions of Babu et al.11 4.5. Sensitivity to the Properties of the Porous Media. On the basis of the consideration that the hydrate is formed in the pores of the porous media, the properties of the hydrate deposit (such as the radius of sand grain rp and the sand porosity ϕ) may affect the formation kinetics. Thus, we further perform another two simulation runs with different rp and ϕ to investigate the hydrate formation behaviors in different porous media in the PHS. The formation conditions in the reference case include P0 = 18.00 MPa, T0 = TB = 281.15 K, SG0 = 0.40, SA0 = 0.60, rp = 375 μm, and ϕ = 43.5%. The formation time is set to Δt = 30 days. Figure 11 shows the effects of the properties of the porous media on P and mH during hydrate formation in the PHS. If the hydrate is formed in the pores with smaller sand grains of rp = 175 μm, the system pressure drops much faster to about 7.91 MPa, while it reduces to only 10.71 MPa in the reference case (Figure 11). In addition, the total amount of the formed hydrate increases by about 32.2% under the condition of rp = 175 μm. This is because the number of sand grains with this smaller radius is larger than that of the reference case in the PHS. It can provide more effective pores for the gas occupancy, and the gas−water contact area is raised accordingly to result in a faster heat- and mass-transfer rate for the growth of methane hydrate. Generally, hydrate formation is favored by a smaller radius of sand grains in porous media. When the porosity of the porous media in the PHS is decreased from 43.5% to 33.5%, the pressure also drops faster than that of the reference case, as shown in Figure 11. This is because a decrease of ϕ will lead to a smaller amount of

Figure 8. Relationship between the reaction rate constant k and the surface area-to-volume ratio RSV.

it is shown in Figure 9 that the hydrate mass (per unit volume) in the SHS increases with the highest rate, while the hydrate formation rate in the PHS is always lower than that in the other two devices. Generally, it is more preferred to form hydrates with faster rates in smaller-scale hydrate deposits. 4.4. Effects of Gas and Water Saturations on Formation Kinetics. Figure 10 shows the evolution of the system pressure P and the hydrate mass mH under different initial gas and water saturations in the PHS. The SG0 and SA0 are the initial phase saturations, and they are assigned with different values in three cases (SG0 = 0.20, 0.40, and 0.60, respectively). The initial formation pressure is 18.00 MPa, and the initial formation temperature and the boundary temperature are both 281.15 K. The duration of each formation run is set to Δt = 30 days. It is shown in Figure 10 that the total pressure reduction ΔP decreases with the increase of SG0. This is because higher SG0 means a larger amount of methane gas in the pores, and it will take more time for the additional gas to be converted to the solid hydrate phase. On the other hand, Figure 10 shows that the hydrate formation rate increases with the rise of SG0. For

Figure 9. Evolution of the P and mH (per unit volume) during the hydrate formation in different apparatus. 5471

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Figure 10. Evolution of the P and mH under different initial gas and water saturations in the PHS.

Figure 11. Effects of the properties of the porous media on P and mH during hydrate formation in the PHS.

L, cubic), and the pilot-scale hydrate simulator (PHS, 117.8 L, cylindrical). Six formation runs under different conditions are implemented in each device, and the kinetic model of Li et al.1 is employed for the numerical simulation. The reaction rate constant k is fitted to be 50.59, 25.42, and 8.06 kg/(m2 Pa s) for the SHS, CHS, and PHS, respectively, by correlating the experimental data of runs 1−4 with the kinetic model in each device. When the obtained k is applied for the numerical prediction of methane hydrate formation in porous media under other conditions, the predicted results (including the system pressure and the formed hydrate mass) are in good agreement with the experimental data, which confirms the applicability of the kinetic model in different hydrate deposits. The results show that k decreases with the increase of the scale of the hydrate deposits, while it can maintain its constant features when the physical properties of the hydrate deposit are determined. As a relative measure of the heat-transfer abilities, the surface area-to-volume ratio RSV also drops down sharply when the scale of the hydrate deposit is enlarged. This indicates

methane gas available for hydrate formation. Certain amount of gas consumption will result in a sharper pressure drop in the case of smaller ϕ. On the other hand, although the amount of methane gas is reduced, mH still remains larger than that of the reference case in the early formation stage (about t < 15 days, Figure 11). This is because the number of voids NV shown in eq 8 will be increased under the condition of smaller porosity, and it further results in an increased gas−water contact area for hydrate formation.1 After this period, the hydrate formation rate gradually becomes lower than that of the reference case because of the much smaller pressure driving force (Figure 11). Thus, the porosities of the porous media also play a significant role in the hydrate formation process.

5. CONCLUSIONS The kinetic characteristics of methane hydrate formation in porous media are investigated in three experimental apparatus with different scales: the small-scale hydrate simulator (SHS, 0.393 L, cylindrical), the cubic hydrate simulator (CHS, 5.832 5472

dx.doi.org/10.1021/ie500580y | Ind. Eng. Chem. Res. 2014, 53, 5464−5474

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Subcripts and Superscripts

that the hydrate formation kinetics is affected by the heattransfer process in porous media. Generally, the hydrate formation rate is inversely proportional to the scale of the hydrate deposit, and it is more preferred to form hydrates with faster rates in smaller-scale hydrate deposits. In addition, the initial gas and water saturations are proven to be important factors that determine the overall hydrate formation kinetics. Sensitivity analyses indicate that the hydrate formation rate is strongly dependent on the initial phase saturations and the properties of the porous media.

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AUTHOR INFORMATION

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Corresponding Author

*Tel.: +86 20 87057037. Fax: +86 20 87034664. E-mail: lixs@ ms.giec.ac.cn.

REFERENCES

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Notes

The authors declare no competing financial interest.

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0 = denotes initial state A = aqueous phase B = boundary cap = capillary end = end point G = gas phase H = solid hydrate phase irA = irreducible aqueous phase irG = irreducible gas m = permeability reduction exponent (Table 2) mG = gas permeability reduction exponent (Table 2)

ACKNOWLEDGMENTS

The authors gratefully appreciate the National Science Fund for Distinguished Young Scholars of China (51225603), the National Natural Science Foundation of China (51004089 and 51076155), and the Science & Technology Program of Guangzhou (2012J5100012) for providing financial aid for this work.

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NOMENCLATURE AS = gas−water contact area, m2 feq = equilibrium fugacity, Pa fg = gas fugacity, Pa k = reaction rate constant, kg/(m2 Pa s) K = intrinsic permeability, m2 mH = hydrate mass, kg mW0 = initial water mass, g MH = molar mass of hydrate, 124.0 g/mol MW = molar mass of water, 18.0 g/mol nm0 = initial methane amount, mol nm,G = methane amount in gas phase, mol nm,W = methane amount in aqueous phase, mol NH = hydration number, 6.0 NV = void number P = pressure, Pa r, z = cylindrical coordinates, m rp = radius of sand grain, m R = gas constant, 8.314 J/(mol K) RSV = surface area-to-volume ratio, m2/m3 S = phase saturation SB = boundary surface area, m2 t = time, s T = temperature, K vm = molar volume of gas, ml/mol VD = total volume of hydrate deposit, m3 Vp = total pore volume, ml x, y, z = Cartesian coordinates, m ΔEa = activation energy, J/mol Δt = hydrate formation time, days ρH = hydrate density, 0.925 g/mL ρW = water density, 1.0 g/mL β = reduction exponent, 2/3 ϕ = porosity λ = van Genuchten exponent (Table 2) 5473

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