Methane Hydrate Formation and Thermal Based Dissociation

Article pubs.acs.org/IECR

Methane Hydrate Formation and Thermal Based Dissociation Behavior in Silica Glass Bead Porous Media Garrett C. Fitzgerald,†,⊥ Marco J. Castaldi,*,‡ and Judith M. Schicks§ †

Henry Krumb School of Mines, Earth & Environmental Engineering, Columbia University, 550W 120 Street, Room 926, New York, New York 10027, United States ‡ The City College of New York, City University of New York, 140th Street, Convent Avenue Steinman Hall, Room 307, New York, New York 10031, United States § Helmholtz Centre Potsdam German Research Centre for Geosciences GFZ, Telegrafenberg, Potsdam, Brandenburg D-14473, Germany ABSTRACT: Formation and thermal based dissociation of methane pore space hydrate has been studied at various initial hydrate saturations and heating rates utilizing a 1.3 cm3 glass bead sample pack. Initial hydrate formation occurred rapidly after pressurization and proceeded at a higher rate for systems with the lower initial water saturation. Peak initial formation rates for 21%, 41%, and 60% initial water saturation was 4.3 × 10−6, 1.44 × 10−6, and 1.7 × 10−6 mol/s, respectively. Three distinct stages of formation were observed for hydrate growth in porous media; a rapid initial formation regime determined by the enclathration reaction followed by a slow mass limited diffusion regime again followed by a second rapid and discrete formation period. Peak efficiency rates ranged from 74% to 81%. Experimental and numerical results showed slightly higher efficiency rates and maximum cumulative efficiency values for lower heating rate conditions. Lower heating rates produce a higher cumulative efficiency at the trade-off of less total hydrate being dissociated. Cumulative production efficiencies were greater for conditions of higher initial hydrate saturation, with values at 62% for 18% hydrate saturation and 72% for 50% hydrate saturation.

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INTRODUCTION The recent expansion and industrial development of hydraulic fracturing has caused a resurgence of natural gas usage and interest promoting a major industry shift to utilize this resource which will likely result in increased usage. To ensure the industry developments are sustained, natural gas supplies need to be secured for many years. One currently abundant but untapped source is gas hydrates. Natural gas hydrates are a unique nonconventional energy source with the potential to play a major role in natural gas production over the next decades. Hydrates are a solid, ice like crystalline material that forms when water is present with small gas molecules at sufficiently low temperatures and high pressures. Gas hydrates can form with a number of different guest molecules, but naturally occurring hydrates generally are composed primarily of CH4.1 The estimated resource potential for gas hydrates is high but varies between 1−5 × 1015 m3 and 1.2 × 1017 m3 of CH4 bound in natural gas hydrates,2 whereas the most widely cited3 estimate of global hydrate-bound gas is 21 × 1015 m3. Research on its extraction has developed extensively over the past several decades with the number of planned industrial scale production tests increasing each year. Gas hydrates are stable as long as they are in mechanical, thermal, or chemical equilibrium with their environment. Thus, hydrate dissociation can be driven by disturbance of these equilibrium conditions such as pressure reduction,4 thermal stimulation,5 or the introduction of a chemical inhibitor.6 Interest in these methods of hydrate dissociation is important due to immense demand for natural gas, the continued progression toward lower carbon fuels, and the comparatively large amount of CH4 available in the hydrate phase. © 2014 American Chemical Society

Hydrate formation in the bulk phase and porous media has been extensively studied. Many researchers have investigated formation characteristics and behavior as a function of porous media conditions in an effort to better understand formation morphologies and the repeatability of hydrate growth in laboratory systems.7−9 Zhao et al. have investigated hydrate formation and dissociation behavior in a 5 L reactor via the thermal dissociation method.10 Three hydrate dissociation steps were observed during thermal stimulation that were influenced by heat transfer in both the sediment and the reactor walls. They reported that greater dissociation temperatures resulted in larger temperature gradients in the radial direction of their reactor. They also observed two stages of hydrate formation: hydrate first forming at the surface of the reactor walls and then developing within the reactor. It was suggested that hydrate forms at the surface of the reactor first where heat can be conducted away rapidly via the high thermal conductivity of the steel walls. When heat is also conducted out of the sediment, the hydrate begins to form in the middle of the reactor as the exothermic release is removed from the system. Riestenberg et al. formed hydrates from water and CH4 with and without additional sediments in a large volume (72 L), temperature controlled pressure vessel.8 They observed that even low concentrations of suspended particles (200 mg/L) have a significant effect on the hydrate formation process in terms of largely decreasing the necessary over pressurization for Received: Revised: Accepted: Published: 6840

November 1, 2013 March 14, 2014 March 20, 2014 March 20, 2014 dx.doi.org/10.1021/ie4036737 | Ind. Eng. Chem. Res. 2014, 53, 6840−6854

Industrial & Engineering Chemistry Research

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bearing sediments using thermal stimulation, but the efficiency of this method remains questionable. In contrast, the results of a laboratory test using an in situ heat source for the thermal stimulation seems to be promising. Schicks et al. demonstrated that only 15% of the produced CH4 has to be burned to provide enough heat for the dissociation of the hydrate bearing sediment.22

hydrate formation. Rees et al. studied hydrate formation in laboratory compacted sand samples and natural sediment cores.11 They reported hydrate formation from samples with initial water saturations of 0.59 and 0.75 and a water conversion rate to hydrate of 70%. Hydrate formation was observed within ten minutes of the system entering the hydrate stability zone during a pressurization process. Hydrate formation reported by Rees et al. did not form in the same morphology between multiple tests, displaying nonrepeatable behavior and indicating nonhomogeneous and partially stochastic formation behavior. They reported a correlation of hydrate forming preferentially in areas where there was lower initial water saturation. Stevens et al., Klapproth et al., and Bagherzadeh et al. have all reported hydrate formation occurring more rapidly in sandstone cores with lower initial water saturation.12−15 Bagherzadeh suggested that two step hydrate formation can depend on initial water saturation conditions. Multistage hydrate formation caused by hydrate film formation has been reported16,17 in the literature where periods of minimal or very slow formation are followed by a “punch through” event in which previously entrapped water is exposed to CH4 gas and the diffusion limited regime is eliminated. Jin et al.19 have reported visual confirmation of the two step hydrate formation and shell growth phenomena of hydrate formation in porous media. They observed hydrate formation over a 1000 min period and recorded two discrete formation events. The first occurring just minutes after pressurization and the second about 200 min into the formation process. The initial discrete formation event resulted in 25% water conversion, and the second event increased the water conversion to 42% followed by a slow rise to an end conversion of 50%. They suggest hydrate forms as a film at the interface between the gas and water phase as suggested by Linga et al. and Kneafsey et al.; however, no one has attempted to quantify the formation rates in the different regimes.16,17 Due to the micromechanistic nature of hydrate formation, it has been historically difficult or impossible to determine formation kinetics from a macroscale study. Mourdrakovski et el. have shown via H magnetic resonance microimaging that on a macroscale hydrate formation appears homogeneous; however, improved spatially resolved imaging has demonstrated that hydrate formation is heterogeneous and stochastic.18 It is important to note that formation rates observed on macroscale systems are unable to provide a mechanistic understanding of hydrate formation and thus are not attempted in this work. Hydrate dissociation has been the subject of significant research both experimentally and through numerical simulation. The need for an efficient hydrate dissociation program is motivated from competing sources of natural gas recovery that have been developed over the past decades and are seemingly a mature technology. Due to the complex nature of natural hydrate reserves, the production behavior can be difficult to accurately model. Dissociation characteristics are dependent on system permeability, initial water, gas, and hydrate saturation, temperature−pressure conditions, and reservoir type [Class I, II, III, and IV].17 Hydrate dissociation via thermal stimulation has been investigated at various scales from the small scale reactors20,21 to large laboratory systems22,5 and limited field scale tests such as the MH21 Mallik hot water circulation tests. During the gas production test in Mallik, 470 m3 (surface conditions) of CH4 was produced from dissociated hydrates within 123.7 h.23 This test was certainly successful in terms of demonstrating the possibility of producing CH4 from hydrate-

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EXPERIMENTAL METHOD An apparatus has been designed to investigate the kinetics and behavior of gas hydrate formation and dissociation via in situ Raman spectroscopy and visual microscopy. The system consists of a small scale, high pressure cell with an internal volume of 1.3 mL. A technical sketch of the pressure cell is shown in Figure 1. Along the central axis of the cylindrical

Figure 1. Sketch of the optical pressure cell (details specified in the text).

pressure cell, a small resistive heating element (100 Ohm resistor) is installed to provide electrical heating during dissociation experiments. The cell is constructed from a single stainless steel plate and is fitted with a 3.0 cm diameter quartz glass window on the upper side of the cell. The lower side of the cylindrical cell consists of a polycarbonate window bored through and sealed with the positive and negative leads to the resistive heating element. The sample cell body has an internal water-glycol flow loop that provides the necessary cooling and keeps the entire cell at the desired set point temperature. The water-glycol flow is controlled using a temperature control bath with a set point outlet temperature. The pressure cell is enclosed in an insulating shell that keeps the system at the constant set point temperature and minimizes heat transfer to the ambient room conditions during experiments. The unit can be operated between −27 and 80 °C and can withstand pressures up to 10 MPa. The cell is equipped with three Omega T type thermocouples, labeled TC1, TC2, and TC3 with an uncertainty of ±0.5 °C, located at 0, 0.3, and 0.6 cm from the heater surface, respectively, as shown in Figure 2. The pressure is monitored with a Hottinger Baldwin Messtechnik P3MB pressure transducer with a relative tolerance of ±0.01%. The pressure cell can be operated with or without a continuous gas/ fluid flow. Flow into and out of the system is measured using a F230-FA-11-Z Bronkhorst gas flow meter. Figure 3 presents a schematic drawing of the system displaying instrument location and flow paths. 6841

dx.doi.org/10.1021/ie4036737 | Ind. Eng. Chem. Res. 2014, 53, 6840−6854


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typically 1−2 °C, the cell is briefly purged and then pressurized with methane gas over a 60 s period to the pressure set point of 61 bar. When the pressure in the cell reaches 61 bar, the inlet valve is closed, creating a closed and fixed volume system. In all formation tests, the cell pressure immediately begins to decrease due to conversion of water and CH4 gas to hydrate. The formation process has been investigated for initial water saturations of 21%, 41%, and 60% of the pore space volume and is discussed in the following sections. The observed hydrate formation exhibited three distinct hydrate formation regimes with two discrete formation events occurring. Discrete and multistage hydrate formation events have been observed in porous media by several researchers13,14,16 and are generally observed as a break through event that exposes free water to gaseous hydrate formers. However, due to the microscopic and stochastic nature of hydrate formation, these rapid growth events are likely an accumulation of smaller nucleation events. These random nucleation events are observed on a macroscale as a total system pressure reduction, which essentially averages the random nucleation and growth events resulting in a pressure profile more smooth and uniform than the actual hydrate formation phenomena. It has been suggested that an initial rapid growth rate is associated with hydrate film formation at the interface between the CH4 gas phase and the liquid water; this film subsequently barricades remaining free water from methane gas thus creating a diffusion limited system. The formation regime that occurs after the initial rapid formation is mass limited and is likely controlled by the slow diffusion of methane from the gas phase through the hydrate shell.24 The second discrete event is attributed to shell breakage or cracking which exposes the trapped free water and allows a more rapid hydrate formation that is no longer diffusion limited.17 In all of the formation experiments conducted in this study, a rapid initial hydrate formation period was observed immediately following pressurization. This initial hydrate formation period, referred to as stage I formation, consistently exhibited the highest formation rates of all the formation events. The rate of methane conversion to the hydrate phase

Figure 2. Internal view of pressure cell with annotated thermocouple locations.

Hydrate Formation. Prior to each hydrate formation process, the sample volume is filled and tightly packed with 250−500 μm spherical glass beads. The glass beads are prepared to the desired water saturation by placing 15 g of beads in a clean dry glass vial and adding the necessary mass of water to reach the specified initial pore volume water saturation. The water/bead mixture is then mixed vigorously until the sediment has a visually homogeneous water distribution. Experiments with initial water saturations of 50% or greater tend to experience draining effects as the water will accumulate at the lower portions of the sediment. Once the wetted glass bead mixture has been prepared, the sample cell is filled, packed, and sealed while the sample cell is kept at the set point temperature of 1.5−2 °C. The mass of partially saturated glass beads placed in the cell is measured with a digital balance to determine the mass of water in the system. On the basis of the known water saturation and glass and water density, the mass of water available for hydrate formation in the cell is determined. After the cell has been sealed and the bead pack has reached thermal equilibrium with the sample cell walls,

Figure 3. Schematic drawing of pressure cell, gas delivery and collection system, and Raman/confocal microscope. 6842



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during the first discrete formation period averaged between 5− 8 × 10−7 mol/s for all ten formation tests, with peak initial formation rates reaching as high as 4 × 10−6. Table 1 shows the

outlined in Figure 4 with stage I being the initial and rapid decline in pressure; stage II is the much slower decline in pressure that is followed by another rapid pressure decline indicating stage III formation. No stage III formation regime was observed for test series one (Swi 21%). Stage IV is the final stage of formation that occurs after the second discrete formation period and is the slowest formation regime and likely diffusion limited. The second hydrate formation regime observed, hereafter referred to as stage II, was 2 orders of magnitude lower than both stage I and stage III formation rates, as summarized in Table 1. For test series 2, shown with single dashed lines in Figure 4, the stage II begins 1 h after pressurization and lasts for roughly 2 h before hydrate formation rates increase again into stage III. The stage II formation regime for test series 3 (60% Swi) occurs later in the formation process and lasts significantly longer than that observed in test series 2 (41% Swi). Stage II was observed to last for 11 h in experiment (3-c) and 35 h in experiment (3-d), as can be seen in Figure 5. The rate of formation during stage II ranged from 2.95 × 10−9 mol/s for test series 1 (21% Swi) to 2.22 × 10−9 mol/s for test series 2 (41% Swi); test series 3 (60% Swi) had a formation rate of 2.76 × 10−9 mol/s. The third formation period, stage III, is the second rapid and discrete formation event which occurs at 11 and 35 h for test series 3 and happens much earlier at about 3− 4 h for test series 2 and is not observed in test series 1. Figures 6−8 show both the pressure and formation rate during three representative hydrate formation experiments for systems with 21%, 41%, and 60% initial water saturation (Swi), respectively. Plotted on the left ordinate is the formation rate in log scale in units of moles of CH4 gas consumed per second; the right ordinate shows the system pressure and the horizontal axis is time in units of hours. The initial water saturation affects the proportion of total water converted to hydrate via the stage I formation period. The initial hydrate formation (stage I) accounted for between 5% and 11.5% hydrate pore volume saturation for all test conditions. The first region of hydrate formation accounted for 11.5%, 9%, and 5% of pore volume saturation for tests with initial water saturations of 21%, 41%, and 60%, respectively. Thus, the lower the initial water saturation, the greater are the amounts of hydrates that form during the initial stage I period. Literature has shown via magnetic resonance imaging (MRI) data that hydrate formation occurs more rapidly in sediments with lower initial water saturations.14 For the lower initial water saturation experiments, stage I formation accounted for 60− 75% of the total hydrate formed whereas for test series 2 (41% Swi) and series 3 (60% Swi) the stage I accounted for 21% and 8% of total hydrate formed, respectively. The rate of hydrate formation during stage I formation produced higher initial peak formation rates for samples with 21% Swi compared to the two experiments with higher water saturation, as can be seen from the formation rates shown via hollow squares in Figures 6−8. The amount of hydrate formation in the stage I regime was correlated to initial water saturations and proceeded for a longer duration and thus reached greater hydrate saturations for tests with lower initial water saturations. The trends in hydrate formation observed for the three initial water saturation conditions behaved in a repeatable manner in terms of trends and formation rates; however, the onset and duration of stage II and stage III formation were somewhat stochastic. Formation proceeded more rapidly at the initial stages for the lower water saturation than it did for higher water

Table 1. Hydrate Formation Rates for Various Initial Water Saturation Conditions, Corresponds to Figures 4−7 mean hydrate formation rate [mol/second] initial water saturation, %

stage I

stage II

stage III

stage IV

21 41 60

3 × 10−7 4 × 10−7 3 × 10−7

3 × 10−9 3 × 10−8 7 × 10−9

2 × 10−7 7 × 10−8

2 × 10−9 3 × 10−9

formation rates for the different stages of formation for three different initial water saturations. The values shown in Table 1 represent the best linear fit for the slope of the discrete formation periods. Although the pressure decrease approaches a linear decline, the formation rate is significantly higher at initial nucleation events and as such the peak formation rates can be an order of magnitude larger than the average formation rates for that regime, i.e., the initial formation rate displays exponential trends. Although the formation results observed are quantified as a formation rate, it is necessary to note that these are macroscopic measurements and should not be confused with kinetic or mechanistic rates; no attempt was made to extract kinetic behavior from the macroscopic formation behavior. Figure 4 shows the pressure reduction during hydrate formation for 6 of the 10 experiments listed in Table 2. On

Figure 4. System pressure during the first 12 h of hydrate formation for 21% (solid lines), 41% (dashed lines), and 60% (dash-dot lines) initial water saturation with annotated formation regimes (stages I− IV).

the right ordinate of Figure 4, the pressure, in bars, is plotted against time from the initial pressurization on the horizontal axis. As hydrate formation progresses forward in time, the system pressure is reduced as gas is converted to hydrate. The rate of the change in pressure is used to determine the rate of CH4 gas consumption from the gas phase to the hydrate phase. Two separate formation tests are shown for each of the initial water saturations tested (21%, 41%, and 60%). The solid lines represent formation of hydrate from an initial water saturation (Swi) of 21%; single dashed lines show Swi of 41%, and dashdot lines show Swi of 61%. Figure 5 shows the complete formation period, for up to 80 h as required for the 60 Swi experiments, and is simply a broader scale view the data presented in Figure 4. The three stages of hydrate formation are 6843



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Table 2. Summary of Initial Conditions, Testing Parameters, and Production Efficiencies for the Full Array of Thermal Stimulation Experimentsa test

Sh [%]

Sw [%]

Sg [%]

Q (watts)

peak efficiency rate

max cumulative efficiency

recovery efficiency at max cumulative efficiency

end of test recovery efficiency

1-a 1-b 1-c 2-a 2-b 2-c 2-d 3-b 3-c 3-d

15 20 18 36 35 32 37 50.5 47 51

7.6 4.6 6.5 11 12 14 10 18 21 18

77.4 75.4 75.5 53 53 53 53 31.5 32 31

0.25 0.5 1 0.25 0.5 1 1.6 0.5 1 1.6

74.4 73.8 73.7 83 81.6 79.8 78.5 81.1 78.7 80.2

63 62 57 74 73 70 70 73 70 72

13 20 33 10 18 30 35 13 20 35

26 41 54 22 40 75 81 36 56 79

a

Results from tests 1-d and 3-a are not presented in this table due to data collection errors.

Figure 5. System pressure during full hydrate formation for 21% (solid lines), 41% (dashed lines), and 60% (dash-dot lines) initial water saturation with annotated formation regimes (stages I−IV).

Figure 7. Hydrate formation rate [mol/s] (left ordinate) and system pressure [bar] (right ordinate) for test series 41% initial water saturation.

Figure 6. Hydrate formation rate [mol/s] (left ordinate) and system pressure [bar] (right ordinate) for test series 21% initial water saturation. Figure 8. Hydrate formation rate [mol/s] (left ordinate) and system pressure [bar] (right ordinate) for test series 61% initial water saturation.

saturations. In all tests, the range of water conversion to hydrate over the duration of the test was between 70% and 80%; the extent of formation in each stage differed for differing initial water saturations. Hydrate Dissociation. Each of the hydrate formation experiments discussed in the previous section is used as an initial condition for the thermal based dissociation experiments. The purpose of these heating experiments is to gain a better understanding of how the initial hydrate saturation and the heating rate affect the gas production rate. When considering

only the energy balance of the system, it is expected that increased hydrate saturation will lead to higher production efficiencies resulting from more energy being absorbed in hydrate dissociation rather than into the unproductive glass bead matrix. A recent publication of Jang and Santamarina reports that gas recovery is proportional to initial hydrate saturation but also to gas expansion and the sediment pore size distribution.25 However, in some porous media applications, 6844



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very high hydrate saturations may suffer from lower efficiencies due to the inability for gas to escape and move away from the hydrate dissociation front due to permeability limitations. This may induce an over pressurization within the pores resulting in a self-preservation mechanism since an increasing pore pressure reduces the driving force for dissociation.26 In regards to this experimental system, this issue is not likely to be present due to the small scale and the relatively low saturations studied, with a maximum hydrate saturation of 50% and a high permeability of the sediment type (spherical glass beads). The heating experiments were conducted at 4 different heating rates for each of the three initial hydrate saturation conditions. Table 2 outlines the initial conditions and production efficiencies for the array of heating tests conducted in this study. The resistive heating element was set at 0.25, 0.5, 1.0, and 1.6 W for each of the three initial hydrate saturation conditions, 17% Sh, 35% Sh, and 50% Sh for a total of 12 independent tests. Test names are found in the left column; the initial hydrate and water and gas saturations are presented, and the rate of thermal stimulation is shown in watts in the fifth column of Table 2. The right four columns display peak efficiency rates, maximum cumulative efficiencies, recovery efficiency, and end of test recovery efficiency. Efficiency rates and cumulative efficiencies are defined in eqs 1−4 and discussed below. Recovery efficiency is the percentage of total available hydrate that has been converted to the gas phase as defined in eq 4; the end of test recovery efficiency corresponds to the amount of hydrate that has dissociated at the end of the heating test period. The heating tests are initiated with the system near the thermodynamic equilibrium pressure−temperature condition. After hydrate formation has slowed substantially and approaches negligible formation rates, the system pressure is then rapidly lowered to 34 bar while remaining within the hydrate stability zone at the system temperature of 2 °C. The three phase equilibrium temperature for CH4 hydrate at 34 bar is 2.75 °C (CSMHyd). The system is allowed to stabilize for 1 h at the experimental starting conditions before the heating period is initiated. The heating element is set at the desired heat output using a DC power supply and held constant for the duration of each heating experiment. As soon as the heating period is initiated, the pressure transducer detects an increase in pressure as hydrate dissociates into the gas phase. The rate of pressure increase is used to calculate the rate of hydrate dissociation and thus the production efficiency as discussed below. The rate of gas production from the hydrate phase dngas/dt is calculated using the gas compressibility factor as determined by pressure and temperature conditions using the Peng−Robinson EOS and the ideal gas law. Equation 1 is used to determine gas production or hydrate formation rate from the measured rate of pressure rise or decline, respectively. dngas dt

=

dP V dt RTZ

In order to develop a metric to quantify the effectiveness of the thermal stimulation, production efficiency has been defined both in terms of an efficiency rate and a net cumulative efficiency. Equation 2 shows the production efficiency rate [ηrate] which is an indicator of how efficiently the hydrate is being dissociated at any given point in time. dngas

ηrate =

dt

Hhhv − Q̇ heat dngas dt

Hhhv

(2)

Equation 3 shows how the cumulative efficiency is calculated during the dissociation process. The cumulative efficiency is the net efficiency of the production test from the initiation of heat input to any given point in time of the experiment. When cumulative production efficiency begins to decline significantly, the production test has reached its limit in terms of the optimal efficiency in gas production and any additional heat added to the system lowers the overall production efficiency. i=t

ηcumulative =

∑i = 1

(

dngas dt

)

Hhhv Δt − Q̇ heat × (time) i=t

∑i = 1

(

dngas dt

Hhhv Δt

)

(3)

For eqs 2 and 3, Hhhv is the higher heating value of methane gas, Δt is the time interval between data point collection, time is the amount of time since heating was initiated, Q̇ heat is the thermal stimulation heating rate, and dngas/dt is the molar rate of methane production from the hydrate dissociation. The recovery efficiency is defined in eq 4 as the ratio of moles of CH4 gas produced from the hydrate phase to the total moles of CH4 stored in the hydrate phase at the beginning of the production test. ngas produced ηrecovery = nhydrate initial (4) where ngas produced is the total moles of hydrate dissociated and nhydrate initial is the total moles of hydrate in the pore space at the start of thermal stimulation tests. Figures 9−11 show the development of cumulative production efficiency as a function of the recovery efficiency. Shown on the left ordinate of the three figures is the cumulative production efficiency defined in eq 3 and plotted against the recovery efficiency (percentage hydrate dissociated) as defined in eq 4, on the horizontal axis. During each heating test, the

(1)

where dP/dt is the time rate of change of the cell pressure as measured by the pressure transducer, V is the total free volume of the system, R is the universal gas constant, T is the average gas phase system temperature measured by the three thermocouples, and Z is the compressibility factor at pressure and temperature conditions during the test as calculated from the Peng−Robinson equation of state for CH4 gas.27

Figure 9. Cumulative gas production efficiency vs the total amount of initial hydrate dissociated for various heating rates of ∼18% initial hydrate saturation. 6845



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rates of 0.25, 0.5, 1.0, and 1.6 W, respectively, regardless of the initial hydrate saturation. However, for 35% saturation condition with 1.0 W heating, the end of the test recovery efficiency was larger than the 18% and 50% 1.0 W heating experiments. The recovery efficiency is affected by the morphology of hydrate formation in the sample sediment: if more hydrate grows in the center of the cell near the heater, the recovery efficiency will be greater and this could be an explanation as to why test 2-c did not follow a similar trend of the other test series. These values for recovery efficiency are strongly apparatus dependent and primarily related to the size of the sediment sample in relation to the heating output. Comparing the value of peak cumulative efficiencies for the three test series, it is evident that efficiencies are lowest for test series 1, with the lowest hydrate saturation, but are similar for test series 2 and 3, with test series 2 producing slightly higher efficiencies than test series 3. The peak efficiency rates for test series 1 were around 74% and for series 2 and 3 were between 79% and 81%. In addition to the trends found regarding hydrate saturation, all test series showed slightly higher efficiency rates and maximum cumulative efficiency values at lower heating rates. The maximum value for cumulative efficiencies showed a similar trend to the efficiency rates, with the lowest hydrate saturation tests having lower cumulative rates at 62% for series 1 and 72% for both series 2 and 3 with higher initial hydrate saturations. However, although lower heating rates showed slightly better cumulative efficiency performance, the amount of hydrate dissociated, and thus gas recovered, is much lower for the lower heating rates. As shown in the two far right columns of Table 2, the amount of hydrate that is dissociated in the system at the point when cumulative efficiency reaches a maximum increases with increasing heating rate. In general, the maximum cumulative production efficiency occurred when only 10% of the hydrate was dissociated for heating rates of 0.25 W, and for higher heating rates of 0.5, 1.0, and 1.6 W, this point occurred at roughly 20%, 30%, and 35% of total hydrate dissociated, respectively. This means that although lower heating rates can produce a higher cumulative efficiency the total recoverable amount of gas is lower for lower heating rates. Similar thermal stimulation tests have been conducted on a much larger scale reactor with an internal sediment volume of 59 L, elaborated in a previous study (Fitzgerald et al.5), in order to compare small and large scale heating tests to better understand scale up issues. The general range of efficiencies that were observed for both large and small scale tests exhibited a fair amount of similarities with peak production rates ranging from 70% to 91% for the large scale tests and 74−83% for the small scale system, and the cumulative efficiencies have peak values ranging from 57% to 74% for the small scale test and 41−86% for the large scale tests. Figures 12 and 13 show previously published data for the cumulative production efficiency vs the recovery efficiency of two different initial hydrate saturations at both a high heating rate (100 W) and a low heating rate (20 W) condition. The diamond markers in Figures 12 and 13 represent 100 W heating tests and the circles show the 20 W heating test. The trends found in the recovery efficiency and heating rate are similar for both the large scale and small scale tests. Comparing Figures 9−11 with Figures 12 and 13, it is clear that on both a large scale and small scale apparatus the increased heating rate allows for greater recovery efficiency before a noticeable decline in gas production.

heat front moves outward from the heating element causing pore space hydrate to dissociate as temperatures exceed the hydrate stability conditions. As the hydrate dissociates to produce gaseous CH4 and water, the system pressure increases. The amount of hydrate that is dissociated is calculated on the basis of the pressure increase in the system as shown in eq 1. Figure 9 shows cumulative production efficiencies for three heating rates applied to samples with initial hydrate saturations of 15−20%. Figures 10 and 11 show the same range of heating

Figure 10. Cumulative gas production efficiency vs the total amount of initial hydrate dissociated for various heating rates of ∼35% initial hydrate saturation.

Figure 11. Cumulative gas production efficiency vs the total amount of initial hydrate dissociated for various heating rates of ∼50% initial hydrate saturation.

rates for samples with initial hydrate saturations of ∼35% and ∼50%, respectively. For test series 1, 2, and 3 (18%, 35%, and 50% Sh, respectively), the subscripts a, b, c, and d correspond to 0.25, 0.5, 1.0, and 1.6 W heating rates, respectively. The dashed lines indicate a heating rate of 0.25 W, the solid lines 0.5 W, and the dash-dot lines 1.0 W, and the dotted lines correspond to 1.6 W heating rates. The production efficiency profiles presented in Figures 9−11 display three prominent trends relating to the heating rate and initial hydrate saturations. The higher heating rates resulted in a greater proportion of the hydrate being dissociated, as would be expected because higher temperatures and heat flux allow a hydrate dissociation front to progress further from the heat source resulting in a greater portion of the hydrate dissociating. This trend was present for all hydrate saturations and is quantified in the far right column of Table 2. The recovery efficiency at the end of the test for all initial hydrate saturations followed a consistent trend, with final values of recovery efficiencies falling near 20%, 40%, 60%, and 80% for heating 6846



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solver due to the increased stability over the generalized alpha method. The constituent equations governing these systems are derived from the basic heat equation for energy conservation and Darcy’s law for mass and momentum conservation. These equations are modified for use in porous and multiphase systems using equivalent thermal properties based on weighted values as a function of pore space saturation (ϕx), where x represents the variable signifying gas, liquid, or hydrate phase. The model geometry is shown in Figure 14 as a cross section of the sample cell; here, the green rectangle represents the glass bead pack, and the blue line shows the boundary of the coolant flow path. Figure 15 shows the glass bead pack model geometry; in this figure, the red rectangle indicates the resistive heating element, the pink region shows the location of the porous media/bead pack, and the surrounding gray sections are the pressure vessel walls and glass windows. The porous media region is subdivided into three zones to allow for a variable hydrate distribution in the simulation. Zone 1, zone 2, and zone 3 are defined as concentric rings around the heating element with zone 1 in the innermost region and zone 3 in the outermost. The system has been modeled in a two-dimensional axisymmetric form with three primary thermal boundary conditions for heat transfer in porous media, i.e., free convection for all surfaces open to the atmosphere, a defined temperature for the surface exposed to the coolant flow, and a constant surface heat flux at the heater surface. The coolant flow boundary condition is defined as a Dirichlet condition with a fixed temperature where Tcoolant is the coolant temperature. The outward heat flux from the heater is defined as a Neumann condition with a set heat flux Qheater, and finally, the open boundary with the atmosphere is implemented with a defined temperature Tambient. The open boundary condition defined in COMSOL is used in boundaries in which heat can flow into, or out of, a domain with a specified exterior temperature. All walls, glass, and heater surfaces are constrained with a no slip boundary condition. Figure 16 shows the cross section of the system being modeled with annotations on boundary conditions. The glass bead domain has three sections, zone 1, zone 2, and zone 3. The hydrate saturation in each zone can be adjusted while keeping the total hydrate in the pore space constant. This allows for history matching of the gas production rates between experimental and simulation results. Adjustments in the hydrate saturation morphology include creating a nonhomogenous hydrate distribution within the simulated sand pack to provide an adjustable parameter that can be used to match experimental and simulation results. This data matching allows for a better understanding of experimental hydrate distribution within the bead pack. During hydrate dissociation in porous media, heat transfer coefficients such as thermal conductivity, permeability, density, mobility, and specific heat change as the hydrate dissociates to the water and gas phases. In addition to the material properties changing during the phase change, an apparent mass source is implemented to account for the gas production from hydrate dissociation. The hydrate phase is modeled as an immobile solid in the porous matrix with a thermal conductivity kh ([W/ m·K]), density ρh of 910 kg/m3, and a specific heat Cp,h (J/kg). Hydrate dissociation is an endothermic reaction and such can be modeled as a phase change from solid to liquid in a similar manner to that of ice melting. To account for the additional

Figure 12. Cumulative production efficiency vs the percent of hydrate dissociated for a large scale production test of 10% hydrate saturated sediment (adapted from Fitzgerald et al.5).

Figure 13. Cumulative production efficiency vs the percent of hydrate dissociated for a large scale production test of 31% hydrate saturated sediment (adapted from Fitzgerald et al.5).

The relationship between initial hydrate saturation and the peak and cumulative production efficiencies is also apparent in both large and small-scale production tests. As shown in Figures 12 and 13, the heating of the 30% initial hydrate saturated sediment (Figure 13) produced consistently higher production efficiencies than that of the same heating rate on a 10% initial hydrate saturated sediment (Figure 12). The trend that is not observed in both small and large-scale systems is the relationship between heating rate and gas production efficiencies. Large scale tests exhibited higher peak and cumulative efficiencies for tests with higher heating rates; for both hydrate saturation conditions, the 100 W heating test produced greater production efficiency rates and cumulative efficiencies as is evident when comparing diamonds to circle markers in both Figures 12 and 13. Numerical Simulation. The multipyhsics package COMSOL, version 4.0a, has been used as a tool to match experimental results with numerical models as a method to determine the spatial variability of hydrate formation within the apparatus used. COMSOL allows for the coupling of multiple physics modules governed by user defined PDEs that are solved via the Finite Element Method (FEM). The simulation environment used for modeling these experiments is a time dependent solver using the heat transfer in porous media module coupled with Darcy’s law. Backward differentiation formulas (BDF) time stepping was used for the time dependent 6847



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Figure 14. COMSOL geometry of full system.

satisfies eq 9; D can then be used to account for the mass source of methane from the simulated hydrate phase.

energy required during hydrate dissociation, an apparent specific heat has been defined on the basis of the enthalpy of dissociation of methane hydrate at the equilibrium temperature and pressure for methane hydrate. Using a Heaviside step function and its normalized derivative, a phase transition variable can be created. In COMSOL, this can be implemented with the internal function H = fls2chs(T − Tdis, dT), and we define eq 5 normalized such that eq 6 is satisfied. DT =

dH dT

∫−∞ Ddt = 1

(9)

During the hydrate dissociation process, gas evolution causes an increase in pore pressure and in some cases the overall system pressure. As pressure increases in the system, the dissociation temperature of gas hydrates increases according to the P−T thermodynamic equilibrium. This increase in dissociation temperature effectively delays further hydrate dissociation and must be accounted for in the model. Tdissociation is the temperature at which the hydrate is in a three phase thermodynamic equilibrium with water, gas, and hydrate at the system pressure. Tdissociation is a function of pressure, and when system temperatures rise over Tdis, the hydrate will dissociate into gas and water as governed by the switching variable H. As hydrate dissociates, the pressure in the system increases and, thus, Tdis increases, as defined from the following relation.

(5)

(6)

This describes the latent heat using only the heat of fusion for the normalized pulse DT such that an apparent specific heat is created that combines actual specific heat and the apparent specific heat seen as the latent heat of dissociation as shown in eq 7. Here, lambda is the enthalpy of dissociation of methane hydrate and Cp is the specific heat of the porous matrix including the solid hydrate phase. Cpapparent = Cp + DTλ

(8)

∞

∞

∫−∞ DTρλdT = ρλ

dH dt

D=

Tdissociation [K] = 3.406361−6 × pressure [Pa] + 264.05 [K]

(7)

(10)

The mass source is implemented in the Earth Sciences module as a function of the variable D defined below, where the rate of methane gas is modeled as an apparent mass source and is proportional to the initial pore space hydrate saturation. Equation 8 is defined as the derivative of the phase transition variable H with respect to time and is normalized such that it

The relationship between equilibrium temperature and pressure is nonlinear; however, it is modeled via a linear relationship defined in eq 10 and in order to save computational cost during numerical simulations due to the good linear approximation and the fact that pressure variations in the system are minimal. 6848



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Figure 15. COMSOL geometry of sample cell volume.

Numerical Results. Figure 17 shows simulation temperature superimposed on experimental temperature, with temperature on the left ordinate and time on the horizontal axis shown for four representative tests. Simulation results for thermocouples T1, T2, and T3 are shown in solid black lines, dashed red lines, and dash-dot blue lines, respectively. Experimental data is plotted as diamonds, open squares, and open triangles for thermocouple locations T1, T2, and T3, respectively. Figure 17a shows data for test 1-c (0.5 W, 20% Sh). Figure 17b shows test 2-b (0.5 W, 35% Sh). Figure 17c shows test 3-b (0.5 W, 50% Sh), and Figure 17d shows test 3-c (1.0 W, 50% Sh) to demonstrate results over a range of heating rates and initial hydrate saturations. Experimental and numerical temperature results are in close agreement validating the models ability to capture the transient heat transport and the development of the heat front throughout the experiment. The rate of gas production, both experimental and simulated, is calculated from the measured increase in pressure of the system during dissociation and is used to calculate a thermal production efficiency as well as a recovery efficiency as explained in the Experimental Method section. Figure 18 shows experimental and simulated pressure increases for test 1b (0.5 W, 20% Sh); in this figure, the open circles represent experimental data; the dotted line shows the simulation results for a uniform hydrate distribution, and the red line shows the simulation results for the heterogeneous hydrate distribution. The heterogeneous simulation produces both pressure and temperature results that match experimental values. The

simulation was run at various hydrate distribution conditions, and it was found that the numerical and experimental data converge when the hydrate saturation in the outer ring (zone 3) is 35% greater than the total volume averaged hydrate saturation. Figures 19−21 show the experimental and simulated production efficiency on the left ordinate in percent as calculated via eq 3 and the recovery efficiency calculated via eq 4 also on the left ordinate in percent. Experimental cumulative efficiency and recovery efficiency are plotted in solid red triangles and open squares respectively; simulated production efficiencies are shown in solid and dotted lines for the uniform and heterogeneous hydrate saturations, respectively. The homogeneous simulation have been run with the assumption of uniform hydrate distribution in the pore space. However, as is evidenced in the figures, the production and recovery efficiency tend to be greater in the uniform simulation than the experimental data. The pressure plots emphasize this behavior showing a greater increase in pressure in the simulation results than in experimental data. This can be attributed to the nonuniform hydrate distribution in the experiment compared to the uniform hydrate distribution assumed for the simulation. It has been reported in literature and observed in this reactor that the hydrate can preferentially form near the reactor walls, which means that the experimental gas evolution will be delayed compared to the simulation as the dissociation front must progress further out to reach an equivalent amount of hydrate. 6849



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Figure 16. Annotated boundary conditions.

Figure 17. Experimental and simulation temperature profiles of select tests.

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Figure 18. Experimental and simulation pressure evolution during dissociation test 1-b.

Figure 19. Experimental and numerical production and recovery efficiency for test 1-a.

Setting the hydrate saturation in the outer ring to be 35% greater than the total average saturation resulted in agreement between experimental and numerical results. This behavior is demonstrated in Figures 19, 20, and 21 for tests 1-b, 1-c, and 3b, respectively. Table 3 summarizes the variable hydrate distribution for a selection of experiments that demonstrated discrepancy between the experimental results and the uniform hydrate distribution simulation results. This behavior was observed for the majority of conditions tested; however, it was more dominant for lower initial saturation experiments, meaning that the systems with lower initial water saturation formed hydrate more preferably in the outer ring of the sediment. Figure 22 shows the cumulative production efficiency plotted on the left ordinate versus the percent of total hydrate dissociated on the horizontal axis for the simulation run at all experimental test conditions with initial uniform hydrate saturations of 20%, 35%, and 50% for panels a, b, and c, respectively. Efficiencies peaked at 85% for the 35% and 50%

Simulation and experimental data share the same trend in terms of the end of test recovery efficiency, showing that higher heating rates result in larger recovery efficiency. The experimental data and simulation do not match in terms of the recovery efficiency when initial hydrate saturations are uniformly distributed in the model. In the numerical simulation, the pore space has been subdivided into three zones as shown in Figure 15 that represent concentric rings of porous media. This division allows for simulation of discretely nonuniform hydrate distribution. The hydrate saturation is varied among the three pore space zones while keeping the total hydrate in the system constant. Increasing the relative hydrate distribution in favor of the outer rings produces pressure and efficiency results more consistent with experimental results. Using this data-matching tool allows for the extraction of information regarding the distribution of hydrate within the sample sand pack via adjusting the distribution of hydrate in the simulation until experimental and simulation hydrate dissociation rates converge. 6851



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Figure 20. Experimental and numerical production and recovery efficiency for test 1-c.

Figure 21. Experimental and numerical production and recovery efficiency for test 3-b.

removed, (2) increased volume averaged hydrate saturation results in greater peak and sustained production efficiencies, and (3) production efficiencies remained the highest for the midrange heating rates of 0.5 and 1.0 W; higher heating rates of 1.6 produced lower peak efficiencies in all cases, and the low heating rate of 0.25 was initially equivalent to the midrange test but quickly declined.

Table 3. Summary of Heterogeneous Hydrate Saturation Conditions hydrate saturation test name

zone 1, %

zone 2, %

zone 3, %

% increase in zone 3

1-b 1-c 3-b

11.5 4.6 43.0

20.0 18.0 50.0

24.0 24.3 55.0

20.0 35.0 10.0

■

CONCLUSION Hydrate formation in the porous media displayed multistage formation behavior. Initial hydrate formation occurred rapidly after pressurization was initiated and preceded at a higher rate for systems with the lowest initial water saturation. Peak initial formation rates for 21%, 41%, and 60% initial water saturation

Sh tests while efficiencies of 80% were found for the 20% Sh test series. Figure 22d presents a comparison of the 1.0 W heating tests for the range of hydrate saturations tested. Results from these simulations produce three major findings: (1) hydrate saturation forms in a nonuniform morphology in the pore space with a bias toward the surface where heat is 6852



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Figure 22. Simulated dissociation efficiencies for all test conditions with uniform hydrate distribution.

was 4.3 × 10−6, 1.44 × 10−6, and 1.7 × 10−6 mol/s, respectively. Three distinct stages of formation were observed for hydrate growth in porous media: a rapid initial formation regime (stage I) where the formation of the hydrate is determined by the enclathration reaction followed by a slower mass limited diffusion regime labeled stage II. Hydrate saturations of 20%, 35%, and 50% were achieved from initial water saturations of 21%, 41%, and 60% via a gas invasion of water wet glass beads. Higher heating rates achieve maximum cumulative production efficiency at greater recovery efficiency values; i.e., the point when the production efficiency begins to decline occurs after a greater amount of hydrate has been recovered for the higher heating rate conditions. The lower heating rates resulted in higher peak efficiency. The maximum cumulative efficiency was lowest for the 18% initial hydrate saturation tests with a value of around 62%; these values were around 74% for both the 35% and 50% initial hydrate saturation tests. The peak efficiency rate and max net cumulative efficiency decreases with increasing heating rate for test series 1 and 2 but did not display this behavior in test series 3 with 50% initial hydrate saturation. Peak efficiency rates were nominally higher than the max net cumulative efficiency by roughly 10% for all test conditions. Simulation and experimental data share the same trend in terms of the end of test recovery efficiency, where higher heating rates result in larger recovery efficiency. The experimental data and simulation did not align in terms of the recovery efficiency for uniform hydrate saturation simulations. This can be attributed to the assumption of uniform hydrate distribution in the model, where the comparison between simulation and experimental data suggest nonuniform hydrate distribution with a larger portion of hydrate forming on the outer portions of the reactor further

from the heating element. In the numerical simulation, the pore space has been subdivided into three zones which represent concentric rings of pore space. This division allows for simulation of nonuniform hydrate distribution. The hydrate saturation is varied among the three pore space zones while keeping the total hydrate in the system constant. Increasing the relative hydrate distribution in favor of the outer rings produces pressure and efficiency results more consistent with experimental results. Simulation results produce three major findings: (1) hydrate saturation forms in a nonuniform morphology in the pore space with a bias toward the surface where heat is removed, (2) increased volume averaged hydrate saturation results in greater peak and sustained production efficiencies, and (3) production efficiencies remained the highest for the midrange heating rates of 0.5 and 1.0 W; higher heating rates of 1.6 W produced lower peak efficiencies in all cases, and the low heating rate of 0.25 was initially equivalent to the midrange test but quickly declined. The results suggest an optimum heating rate would fall in the midrange that allows for reasonable dissociation rates while still providing enough heat flux to dissociate a substantial amount of the surrounding hydrate.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address ⊥

Rocky Mountain Institute, Snowmass Creek Road, Snowmass, Colorado 81654, United States

Notes

The authors declare no competing financial interest. 6853



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(21) Pang, W.; Xu, W.; Sun, C.; Zhang, C.; Chen, G. Methane Hydrate Dissociation Experiment in a Middle-Sized Quiescent Reactor Using Thermal Method. Fuel 2009, 88, 497−503. (22) Spangenberg, E.; Giese, R.; Schicks, J. M. Experimental Simulation of Hydrate Formation and Production with the Large Laboratory Reservoir Simulator (LARS). Proceedings of the 7th International Conference on Gas Hydrates - ICGH7 , Edinburgh, Scotland, 2011. (23) Yasuda, M.; Dallimore, S. Summary of the Methane Hydrate Second Mallik Production Test. J. Jpn. Assoc. Pet. Technol. 2007, 72, 603−607. (24) Turner, D. J.; Miller, K. T.; Dendy Sloan, E. Methane Hydrate Formation and an Inward Growing Shell Model in Water-in-Oil Dispersions. Chem. Eng. Sci. 2009, 64 (18), 3996−4004. (25) Jang, J.; Santamarina, J. C. Recoverable Gas from HydrateBearing Sediments: Pore Network Model Simulation and Macroscale Analyses. J. Geophys. Res. 2011, 116, DOI: 10.1029/2010JB007841. (26) Holtzman, R.; Juanes, R. Thermodynamic and Hydrodynamic Constraints on Overpressure Caused by Hydrate Dissociation: A PoreScale Model. Geophys. Res. Lett. 2011, 38, DOI: 10.1029/ 2011GL047937. (27) Peng, D. Y.; Robinson, D. B. A New Two-Constant Equation of State. Ind. Eng. Chem. Fundam. 1976, 15 (1), 59−64.

REFERENCES rd

(1) Sloan, E. D.; Koh, C. A. Clathrate Hydrates of Natural Gases, 3 ed.; CRC Press, Taylor & Francis Group: Boca Raton, 2008. (2) Klauda, J. B.; Sandler, S. I. Global Distribution of Methane Hydrate in Ocean Sediment. Energy Fuels 2005, 19, 459−470. (3) Milkov, A. V. Global Estimates of Hydrate-Bound Gas in Marine Sediments: How Much Is Really out There? Earth-Sci. Rev. 2004, 66, 183−197. (4) Lee, J.; Park, S.; Sung, W. An Experimental Study on the Productivity of Dissociated Gas from Gas Hydrate by Depressurization Scheme. Energy Convers. Manage. 2010, 51, 2510−2515. (5) Fitzgerald, G. C.; Castaldi, M. J. Thermal Stimulation Based Methane Production from Hydrate Bearing Quartz Sediment. Ind. Eng. Chem. Res. 2013, 52 (19), 6571−6581. (6) Ostergaard, K.; Masoudi, R.; Tohidi, B.; Danesh, A.; Todd, A. A General Correlation for Predicting the Suppression of Hydrate Dissociation Temperature in the Presence of Thermodynamic Inhibitors. J. Pet. Sci. Eng. 2005, 48, 70−80. (7) Tohidi, B.; Anderson, R.; Clennell, M. B.; Burgass, R. W.; Biderkap, A. B. Visual Observation of Gas-Hydrate Formation and Dissociation in Synthetic Porous Media by Means of Glass Micromodels. Geology 2001, 29 (9), 867−870. (8) Riestenberg, D.; West, O.; Lee, S.; McCallum, S.; Phelps, T. J. Sediment Surface Effects on Methane Hydrate Formation and Dissociation. Mar. Geol. 2003, 198, 181−190. (9) Prasad, P. S. R.; Charia, V. D.; Sharmaa, D.V.S.G.K.; Murthy, S. R. Effect of Silica Particles on the Stability of Methane Hydrates. Fluid Phase Equilib. 2012, 318, 110−114. (10) Zhao, J.; Cheng, C.; Song, Y.; Liu, W.; Liu, Y.; Xue, K.; Zhu, Z.; et al. Heat Transfer Analysis of Methane Hydrate Sediment Dissociation in a Closed Reactor by a Thermal Method. Energies 2012, 5 (5), 1292−1308. (11) Rees, E. V. L.; Kneafsey, T. J.; Seol, Y.; Core, M. E. Methane Hydrate Distribution from Prolonged and Repeated Formation in Natural and Compacted Sand Samples: X-Ray CT Observations Experimental Methods. J. Geol. Res. 2011, http://dx.doi.org/10.1155/ 2011/791815. (12) Stevens, J. C.; Baldwin, B. A.; Graue, A.; Ersland, G.; Husebo, J.; Howard, J. J. Measurements of Hydrate Formation in Sandstone. Petrophysics 2008, 49, 67−73. (13) Klapproth, A.; Techmer, K.; Klapp, S.; Murshed, M.; Kuhs, W. Microstructure of Gas Hydrates in Porous Media. Phys. Chem. Ice 2007, 321−328. (14) Bagherzadeh, S. A.; Moudrakovski, I. L.; Ripmeester, J. a.; Englezos, P. Magnetic Resonance Imaging of Gas Hydrate Formation in a Bed of Silica Sand Particles. Energy Fuels 2011, 25 (7), 3083− 3092. (15) Haligva, C.; Linga, P.; Ripmeester, J. a.; Englezos, P. Recovery of Methane from a Variable-Volume Bed of Silica Sand/Hydrate by Depressurization. Energy Fuels 2010, 24 (5), 2947−2955. (16) Linga, P.; Haligva, C.; Nam, S. C.; Ripmeester, J. a.; Englezos, P. Gas Hydrate Formation in a Variable Volume Bed of Silica Sand Particles. Energy Fuels 2009, 23 (11), 5496−5507. (17) Kneafsey, T.; Tomutsa, L.; Moridis, G.; Seol, Y.; Freifeld, B.; Taylor, C.; Gupta, A. Methane Hydrate Formation and Dissociation in a Partially Saturated Core-Scale Sand Sample. J. Pet. Sci. Eng. 2007, 56 (1−3), 108−126. (18) Moudrakovski, I. L.; McLaurin, G. E.; Ratcliffe, C. I.; Ripmeester, J. a. Methane and Carbon Dioxide Hydrate Formation in Water Droplets: Spatially Resolved Measurements from Magnetic Resonance Microimaging. J. Phys. Chem. B 2004, 108 (45), 17591− 17595. (19) Jin, Y.; Konno, Y.; Nagao, J. Growth of Methane Clathrate Hydrates in Porous Media. Energy Fuels 2012, 26 (4), 2242−2247. (20) Moridis, G. J.; Reagan, M. T. Estimating the Upper Limit of Gas Production from Class 2 Hydrate Accumulations in the Permafrost: 1. Concepts, System Description, And the Production Base Case. J. Pet. Sci. Eng. 2011, 76 (3−4), 194−204. 6854


Methane Hydrate Formation and Thermal Based Dissociation

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