Energy Fuels 2010, 24, 5493–5507 Published on Web 09/30/2010
: DOI:10.1021/ef100596x
Destabilization of Marine Gas Hydrate-Bearing Sediments Induced by a Hot Wellbore: A Numerical Approach Tae-Hyuk Kwon,† Ki-Il Song,‡,§ and Gye-Chun Cho*,‡ †
Earth Sciences Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road Berkeley, California 94720, United States, and ‡Department of Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology (KAIST ), Daejeon 305-701, Korea. §Present address: Faculty of Civil Engineering, University Technology MARA Malaysia, 40450 Shah Alam, Selangor, Malaysia. Received May 11, 2010. Revised Manuscript Received September 8, 2010
This study addresses a numerical approach for exploring how thermal change destabilizes marine gas hydrate-bearing sediments. The underlying physical processes of hydrate-bearing sediments, such as hydrate dissociation, self-preservation, pore pressure evolution, gas dissolution, and sediment volume expansion, are incorporated with the thermal conduction, pore fluid flow, and mechanical response of sediments. Two-dimensional numerical modeling is conducted using a verified finite difference method, in which a steady-state hot wellbore transfers heat to the surrounding hydrate-bearing sediments, resulting in dissociation of methane hydrate. During gas hydrate dissociation, excess pore fluid pressure is generated such that the sediments undergo plastic deformation in the dissociation region and uplift at the seafloor. Sediment stability in the early stage of heat transfer is governed by the intensity of the heat source and the thermal conductivity of the sediments with gas hydrates in place. Later on, excess pore fluid pressure diffusing from the dissociation region destabilizes the shallower overlying sediments. Case studies show that the stability of sediments experiencing thermal change is worsened by an increase in the intensity of the heat source and the initial hydrate saturation. In addition, a decrease in the permeability, initial free gas saturation, and sediment strength also decreases the stability of sediments. A considerable uplifting deformation of the overlying sediments and a sediment failure in a cylindrical or conical shape around a wellbore are observed when the factor-of-safety becomes less than one.
technology is stretching to the deeper ocean in an effort to resolve energy-related problems.2 Gas hydrate dissociation in sediments is presumed to destabilize the hydrate-sediment system by generating an excess pore fluid pressure,3-9 releasing the cementation of soil particles caused by solid hydrates,10 and freshening the pore water, which leads to structural change in fine-grained sediments.11
1. Introduction Gas hydrates are solid compounds in which gas molecules are caged within solid lattices of water molecules. Natural gas hydrate-bearing sediments are found in continental margins or permafrost environments where the pressure and temperature satisfy the stability conditions. Since their discovery in the 1970s, natural gas hydrates have aroused interest in terms of marine science, new energy resources, global climate concerns, and safety issues related to gas hydrate dissociation. There are a number of ways in which hydrate-bearing sediments are destabilized: spontaneously, as part of geologic processes, unavoidably, as part of petroleum drilling and production operations, or intentionally, as part of gas extraction from the hydrate itself. Because dissociation of gas hydrate tends to generate an excess pore fluid pressure which results in decreasing the effective stress of sediments, it is likely to cause a breakdown of offshore structures or slope failure. This behavior has the potential to lead to a major mass-transport event accompanied by a catastrophic tsunami or releasing methane into the water column.1 Thus, any activities in hydrate-bearing sediments require careful attention, particularly as current
(3) Kayen, R. E.; Lee, H. J. Pleistocene slope instability of gas hydrate-laden sediment on the Beaufort sea margin. Mar. Geotechnol. 1991, 10, 125–141. (4) Kleinberg, R. L.; Flaum, C.; Griffin, D. D.; Brewer, P. G.; Malby, G. E.; Peltzer, E. T.; Yesinowski, J. P. Deep sea NMR: Methane hydrate growth habit in porous media and its relationship to hydraulic permeability, deposit accumulation, and submarine slope stability. J. Geophys. Res.: Solid Earth 2003, 108, (B10), 2058, DOI: 10.1029/2003JB002389. (5) Sultan, N.; Cochonat, P.; Foucher, J. P.; Mienert, J. Effect of gas hydrates melting on seafloor slope instability. Mar. Geol. 2004, 213 (1-4), 379–401. (6) Xu, W. Y.; Germanovich, L. N. Excess pore pressure resulting from methane hydrate dissociation in marine sediments: A theoretical approach. J. Geophys. Res.: Solid Earth 2006, 111, B01104, DOI: 10.1029/2004JB003600. (7) Moridis, G. J.; Kowalsky, M. B. Response of oceanic hydratebearing sediments to thermal stresses. SPE J. 2007, 12 (2), 253–268. (8) Nixon, M. F.; Grozic, J. L. H. Submarine slope failure due to gas hydrate dissociation: a preliminary quantification. Can. Geotech. J. 2007, 44 (3), 314–325. (9) Kwon, T. H.; Cho, G. C.; Santamarina, J. C. Gas hydrate dissociation in sediments: Pressure-temperature evolution. Geochem. Geophys. Geosyst. 2008, 9, Q03019, DOI: 10.10292007GC001920. (10) Freij-Ayoub, R.; Tan, C.; Clennell, B.; Tohidi, B.; Yang, J. H. A wellbore stability model for hydrate bearing sediments. J. Pet. Sci. Eng. 2007, 57 (1-2), 209–220. (11) Francisca, F.; Yun, T. S.; Ruppel, C.; Santamarina, J. C. Geophysical and geotechnical properties of near-seafloor sediments in the northern Gulf of Mexico gas hydrate province. Earth Planet. Sci. Lett. 2005, 237 (3-4), 924–939.
*To whom correspondence should be addressed. Telephone: 82-42350-3622. Fax: 82-42-350-3610. E-mail:
[email protected]. (1) Rothwell, R. G.; Thomson, J.; Kahler, G. Low-sea-level emplacement of a very large Late Pleistocene ‘megaturbidite’ in the western Mediterranean Sea. Nature 1998, 392 (6674), 377–380. (2) Hadley, C.; Peters, D.; Vaughan, A.; Bean, D. Gumusut-Kakap project: Geohazard characterization and impact on field-development plans. In The 2008 International Petroleum Technology Conference, Kuala Lumpur, 2008. r 2010 American Chemical Society
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Cementation does not significantly affect the strength and stiffness of hydrate-bearing sediments until the gas hydrates occupy more than 40% of the pore space.12-14 Any change in the pore water concentration as a result of fresh water added from hydrate dissociation may disturb the sediment structure causing changes in volume or effective stress. Excess pore fluid pressure induced by hydrate dissociation is thought to be the most critical cause of destabilization. This is particularly due to the relatively low permeability of hydrate-bearing sediments15 and that a number of oceanic gas hydrate deposits are classified as fine-grained sediments.11 Given that hydrate dissociation generates excess pore fluid pressure, several theoretical and numerical studies have provided insight into the quantification of excess pore fluid pressure and the associated fluid flow but without consideration of geomechanical aspects.6,7 Previous studies on wellbore stability10,16 and slope stability8 indicate that mechanical destabilization of sediments, boreholes, or submarine slopes may occur when gas hydrate dissociation is induced by thermal changes. However, those models simplify the dissociation process with some assumptions and cannot take into consideration sediment compressibility, gas solubility, and the presence of free gas. Recently, the integration of a geomechanical simulator (i.e., FLAC3D) and a simulator describing fluid flow, heat transport, and thermodynamic behavior of gas hydrates (i.e., TOUGH-HYDRATE) has been presented for the geomechanical analysis of hydrate-bearing sediments.17,18 However, the code for coupling of two simulators has been found to be technically challenging for users. Drilling and operating a wellbore through hydrate deposits in order to produce from underlying hydrocarbon reservoirs has been avoided in recent years due to the insufficient knowledge on the geomechanical behavior of dissociating hydrate-bearing sediments. Thus, this study addresses a comprehensive numerical approach for examining the instability problems in gas hydrate-bearing sediments induced by thermal changes (e.g., result of hot hydrocarbon production) and explores how thermal changes destabilize gas hydrate-bearing sediments. The hydrate dissociation process is incorporated with thermal conduction, fluid flow, and mechanical response of sediments. Two-dimensional numerical modeling is conducted using a verified finite difference method (FLAC2D), in which a steady-state hot wellbore transfers heat to the surrounding hydrate-bearing sediments, resulting in dissociation
Figure 1. Pressure evolution during thermal stimulation of methane hydrate: Lw, liquid water; H, hydrate; V, CH4 in vapor phase. The phase boundary PB corresponds to methane hydrate in aqueous solution containing 3.5% NaCl in Table 1 as P[kPa] = exp(42.047 9332/T [K]).
of methane hydrate and a mechanical failure of the sediments. Case studies are performed to explore the effects of key parameters on sediment destabilization. 2. Underlying Processes during a Thermal Stimulation: Consideration in Numerical Modeling Consider a mass of gas hydrate-bearing sediments, of which the pressure (P)-temperature (T) condition is within the stability zone of hydrate formation, subjected to thermal stimulation. It is assumed that gas hydrates are disseminated with low-to-medium hydrate saturation (e.g., less than 40%) in fine-grained sediments (e.g., silty-to-clay soils). As the heat is transported and the temperature increases, significant processes develop in the hydrate-bearing sediments (Figure 1). Thus, the following section explores these processes and discusses how to consider them in numerical modeling. 2.1. Heat Transport. Heat transport occurs unavoidably during petroleum drilling and production operations when an uninsulated wellbore is in place to produce hot reservoir fluids from deeper reservoirs. In addition, heat may be transported intentionally as part of potential gas production from hydrate itself when hot water injection might be used. In all cases, heat flows into the hydrate-bearing sediments and can be transported by convection (or advection) and conduction. In marine sediments, conduction is a more common phenomenon than convection due to the low permeability of gas hydrate-bearing sediments. The thermal conductivity (or thermal diffusivity) of hydratebearing sediments is a complex feature of soil mineralogy, porosity, and pore fluid composition (i.e., water, gas hydrate, and free gas). Moreover, heat conduction invokes a phase transformation of the hydrate. Heat transfer raises the temperature of hydrate-bearing sediments, causing gradual dissolution or dissociation which therefore leads to a change in the phase composition of the pore fluids. Any physical and chemical process induced by a temperature change affects the thermal conduction behavior of marine hydrate-bearing sediments. However, the detailed examination of heat transfer in hydrate-bearing sediments is beyond the scope of this study. In our numerical modeling, it is considered that the thermal conductivity of the media is constant. The heat transport
(12) Tohidi, B.; Anderson, R.; Clennell, M. B.; Burgass, R. W.; Biderkab, 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. (13) Yun, T. S.; Francisca, F. M.; Santamarina, J. C.; Ruppel, C., Compressional and shear wave velocities in uncemented sediment containing gas hydrate. Geophys. Res. Lett. 2005, 32, (10), L10609, DOI: 10.1029/2005GL022607. (14) Yun, T. S.; Santamarina, J. C.; Ruppel, C. Mechanical properties of sand, silt, and clay containing tetrahydrofuran hydrate. J. Geophys. Res.: Solid Earth 2007, 112, (B4), B04106, DOI: 10.1029/2006JB004484. (15) Nimblett, J.; Ruppel, C. Permeability evolution during the formation of gas hydrates in marine sediments. J. Geophys. Res.: Solid Earth 2003, 108, (B9), 2420, DOI: 10.1029/2001JB001650. (16) Birchwood, R.; Noeth, S.; Hooyman, P. Wellbore stability model for marine sediments contanining gas hydrates. In AADE 2005 National Technical Conference and Exhibition, Houston, TX, 2005; pp AADE-05NTCE-13. (17) Rutqvist, J.; Moridis, G. J. Numerical Studies on the Geomechanical Stability of Hydrate-Bearing Sediments. SPE J. 2009, 14 (2), 267–282. (18) Rutqvist, J.; Moridis, G. J.; Grover, T.; Collett, T. Geomechanical response of permafrost-associated hydrate deposits to depressurization-induced gas production. J. Pet. Sci. Eng. 2009, 67 (1-2), 1–12.
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can be described by Fourier’s heat conduction law as follows: ∂T ∂ T ¼ K 2 ∂t ∂x 2
where K ¼
kt Cp Fsed
in Figure 1). In reality, the hydrate stability curve should be expressed as a broad band that reflects different boundaries for different pore sizes (e.g., works by Anderson et al.22 and Kwon et al.23) rather than a single phase boundary. Contrary to the fact that a single phase boundary causes instantaneous dissociation as temperature increases, a broad margin across the PT boundary is expected to result in gradual dissociation. This is due to hydrates in smaller pores dissociating at lower temperatures than those in larger pores.22,23 However, the presented study assumes pure methane as hydrate-forming gas, 3.5% wt of NaCl aqueous solution as pore water, and no pore size effect on hydrate stability for simplicity. During isothermal heating, dissociation produces high excess fluid pressure releasing gas-saturated water and water vaporsaturated gas. The increase in pressure along the PT boundary hinders further dissociation (i.e., self-preservation).9 Therefore, partial dissociation during thermal stimulation is characterized by a pressure-temperature evolution along the phase boundary until all the hydrate has dissociated (B to C in Figure 1). Higher gas hydrate concentration causes higher fluid pressure generation during dissociation and extends self-preservation behavior during thermal stimulation.9 This study uses an analytical model proposed by Kwon et al.9 to calculate the excess pore fluid pressure and the volume fraction of methane hydrate during the hydrate dissociation (i.e., B to C in Figure 1). Table 1 lists the parameters used for modeling of the gas hydrate dissociation. Details of the hydrate dissociation model are described in Appendix S1, which is given in the Supporting Information. Three phases, water (with dissolved gas), free gas (with water vapor), and mineral, remain in sediments when the gas hydrate is completely dissociated. Under constrained volume expansion, the thermal expansion of the phases causes an increase in the pore fluid pressure of sediments (C to D in Figure 1). This study disregards the thermal expansion of the phases as it induces only a minute increase in fluid pressure (e.g., less than 100 kPa by a temperature increase of 1 °C; refer to Figure 2a) in comparison with hydrate dissociation. 2.4. Generation of Excess Pore Fluid Pressure. Thermal stimulation of hydrate-bearing sediments under an undrained condition (i.e., no mass flux condition) can cause a large increase (several megapascals) in the fluid pressure when volume expansion is restricted by the high skeletal stiffness Bsk of the medium. The results in Figure 2, which are calculated by using the equations in Appendix S1 (refer to the Supporting Information), show that the pore fluid pressure during the partial dissociation is primarily determined by the increase in temperature. It is also shown that the pore fluid pressure after the complete dissociation is strongly dependent on the initial volume fractions of the hydrate Sh0 and the free gas Sg0. The existence of a gas phase acts as a cushion against the pressure increase, diminishing the self-preservation behavior and accelerating the gas hydrate dissociation (Figure 2b). In the absence of a fluid flux, a significantly high increase in temperature is needed for a complete dissociation. For example, a 5 °C increase in temperature is needed for a complete dissociation of a 10% volume fraction of methane hydrate. A lower temperature increase is sufficient for the dissociation of the same amount in gassy or soft sediments.
ð1Þ
where T is the temperature, κ is the thermal diffusivity of the medium (m2 s-1), which indicates how a thermal front moves through a media, kt is the thermal conductivity (W m-1 K-1), Cp is the specific heat (J kg-1 K-1), and Fsed is the density of the sediment. Water and methane hydrate have similar values of thermal conductivity (0.56 W m-1 K-1 for water at 0 °C and ∼0.6 W m-1 K-1 for methane hydrate).19 Thus, the hydrate presence does not increase the thermal conductivity of the sediments significantly (e.g., there is an increase of less than 1% for a hydrate saturation of 10%).19 In addition, with the use of an effective medium model, it has been presented that an increase from 0% to 10% in the methane hydrate saturation leads to a decrease of approximately 5% in the specific heat and an increase of approximately 5% in the thermal diffusivity.19 In contrast, hydrate dissociation releases free gas that is likely to render a decrease in the density, specific heat, and thermal conductivity of a sediment. Yet, the effect of free gas generation on the thermal diffusivity of hydrate-bearing sediments has not been well understood, though it is presumed that the changes in density and specific heat will compensate the thermal conductivity decrease (i.e., κ = kt/(CpFsed)). Therefore, it is justified assuming a constant thermal conductivity (and thermal diffusivity) and disregarding the heat of hydrate dissociation when hydrate saturation is low and thermal propagation is a fairly slow process (e.g., the thermal front propagates less than 10 m for 1 year of heating). However, such an assumption that hydrate dissociation would not significantly alter the thermal diffusion rate is a reasonable approximation only under limited conditions (e.g., hydrate saturation of 10% for the Reference case, refer to the latter sections). 2.2. Gas Hydrate Dissolution. The increase in temperature within the stability zone (A to B in Figure 1) causes hydrate dissolution due to the increased gas solubility in the surrounding pore water. Hydrate dissolution generates water and dissolved gas without free gas. The relatively small change (of up to hundreds of kilopascals) in the pore fluid pressure that accompanies this dissolution might be critical at shallow sediments in the upper few meters from the seafloor.5,20,21 However, this study puts more emphasis on the consequences of hydrate dissociation rather than hydrate dissolution as hydrate dissociation renders a much more significant amount of excess pore fluid pressure than hydrate dissolution does.9,21 2.3. Gas Hydrate Dissociation. Hydrate dissociation starts when the PT state reaches the equilibrium boundary (point B (19) Waite, W. F.; Stern, L. A.; Kirby, S. H.; Winters, W. J.; Mason, D. H. Simultaneous determination of thermal conductivity, thermal diffusivity and specific heat in sI methane hydrate. Geophys. J. Int. 2007, 169 (2), 767–774. (20) Sultan, N. Comment on “Excess pore pressure resulting from methane hydrate dissociation in marine sediments: A theoretical approach” by Wenyue Xu and Leonid N. Germanovich. J. Geophys. Res.: Solid Earth 2007, 112, B02103, DOI: 10.1029/2006JB004527. (21) Xu, W. Y.; Germanovich, L. N. Reply to comment by Nabil Sultan on “Excess pore pressure resulting from methane hydrate dissociation in marine sediments: A theoretical approach. J. Geophys. Res.: Solid Earth 2007, 112, B02104, DOI: 10.1029/2006JB004722. (22) Anderson, R.; Llamedo, M.; Tohidi, B.; Burgass, R. W. Experimental measurement of methane and carbon dioxide clathrate hydrate equilibria in mesoporous silica. J. Phys. Chem. B 2003, 107 (15), 3507– 3514.
(23) Kwon, T. H.; Kim, H. S.; Cho, G. C. Dissociation behavior of CO2 hydrate in sediments during isochoric heating. Environ. Sci. Technol. 2008, 42 (22), 8571–8577.
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Table 1. Parameters Used for Modeling of the Gas Hydrate Dissociation parameters
definitions [dimension]
values used
Bsk ΔHsolution kTH
bulk modulus of sediments [GPa] enthalpy of the solution [J mol-1] gas solubility at temperature T Henry’s law [mol m-3 Pa-1]
kH° M m mh mw nHFG nh naq ng P PTeq
Henry’s constant at 298 K [mol m-3 Pa-1] mass molecular weight [g mol-1] of methane hydrate (= mgas þ χmw) of water mole of hydrate-forming gas [mole] in hydrate phase in aqueous phase in gas phase fluid pressure: gas or water [Pa] equilibrium pressure on the hydrate stability boundary at temperature T gas constant [J mol-1 K-1] molar mass ratio of hydrate-forming gas to gas hydrate [-]
R Rm
-50 330 for CH4 in 3.5 wt % seawatera - ΔHsolution 1 1 kTH ¼ kH ° exp T T298:15K R 3.908 10-6 for CH4 in 3.5 wt % seawatera ΔMh is the mass of gas hydrate dissociated. 124 for CH4 3 6H2O 18
PTeq[kPa] = exp(R þ β/T[K]) R = 42.047, β = -9332 for CH4 for 3.5 wt % NaCl aqueous solutionb 8.315 Rm ¼
S Sh Sw Sg T V ε φ F Fh Fw χ σ0
molar mass of hydrate - forming gas molar mass of gas hydrate
for methane hydrate, Rm = 0.129 for hydration number χ = 6. Sh0 þ Sw0 þ Sg0 = 1 Sh0 = Vh0/Vp0 = 0.1 for reference case Sw0 = Vw0/Vp0 = 0.9 for reference case Sg0 = Vg0/Vp0 = 0 for reference case
volume fraction in pores [-] of gas hydrate of water of free gas absolute temperature [K] volume [m3] volumetric strain [-] porosity of the sediment [-] mass density [kg m-3] of gas hydrate of water hydration number [-] effective stress [Pa]
910 for methane hydrate 998 for pure water and 1035 for seawater 6.0 for methane hydrate
a The methane solubility in 3.5 wt % seawater is modified using the data from Sun and Duan.42 b The expression for the phase boundary from Sloan43 is modified for methane hydrate in aqueous solution containing 3.5 wt % NaCl using the data computed with HWHYD software (2001; a demo version of this software is available at http://www.pet.hw.ac.uk/research/hydrate).
2.5. Fluid Flow and Pressure Diffusion. The excess pore fluid pressure produced by hydrate dissociation subsequently generates a pressure gradient within the sediment. Overpressurized pore fluids (water and free gas) are then dissipated to lower pressurized zones. The assumption of no mass flux that was previously made for calculating excess pore pressure and hydrate quantity is relaxed at this stage. The fluids flow outside the dissociation zone while the gas hydrate dissociates as the temperature increases. The pore fluid flow in sediments can be expressed in terms of Darcy’s fluid transport law as follows: k q ¼ - ðrP - Fw gÞ μ
dissociation (e.g., transient flow characteristics). In general, gas will flow when the volume fraction of free gas Sg exceeds the gas percolation threshold (i.e., defined as the critical gas saturation where the gas phase forms long-range connectivity along the flow direction in a porous medium; typically Sg > 0.2-0.3); thereafter, limited water flow is expected, leaving a residual water saturation that may exceed Sw = 0.4.24-26 It is presumed that water is the dominant phase to flow over gas because the scope of the presented study is confined to low hydrate saturation and fine-grained sediments. When hydrate saturation is greater than 40% and consequently the free gas released by hydrate dissociation percolates through pore throats, multiphase flow analyses are required. 2.6. Effective Stress Reduction and Sediment Weakening. As a consequence of the overall processes, the generation of excess pore fluid pressure leads to a reduction of effective stress and a volume expansion of sediments. In general, the
ð2Þ
where q is the seepage velocity vector (m s-1), k is the intrinsic permeability (m2), μ is the viscosity of the fluid (Pa s), Fw is the mass density of water (kg cm-3), and P is the fluid pressure (Pa). The parameter g is a vector of gravity (i.e., downward). The elevated pore fluid pressure, calculated by using the hydrate dissociation model, is applied as an initial condition for the flow analysis. It is assumed in the flow analysis that sediments are water-saturated and have the single-phase flow of water, although there is a change in the volume fractions of phases in the pore space during hydrate
(24) Larson, R. G.; Scriven, L. E.; Davis, H. T. Percolation theory of 2 phase flow in porous-media. Chem. Eng. Sci. 1981, 36 (1), 57–73. (25) Bryant, S.; Blunt, M. Prediction of relative permeability in simple porous-media. Phys. Rev. A 1992, 46 (4), 2004–2011. (26) McDougall, S. R.; Sorbie, K. S. Estimation of critical gas saturation during pressure depletion in virgin and water flooded reservoirs. Pet. Geosci. 1999, 5 (3), 229–233.
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Failure indicates a state where sediments are deformed (or displaced) by more than several meters so that the mechanical response is not numerically converged in the simulation. In this study, the mechanical stability of the deposit is evaluated by calculating the factor-of-safety (FOS) which is defined as the ratio of the shear strength of the sediment deposit to the subjected shear stress. The factor-of-safety accounts for the weakest shear resistance of soils along a potential failure zone. The strength-reduction technique was used to evaluate the factor-of-safety. The strength-reduction technique is typically applied in factor-of-safety calculations by progressively reducing the shear strength of a material to bring the sediment deposit to a state of limiting equilibrium.27 In the strength-reduction technique, a series of simulations are made using trial values of strength parameters (e.g., cohesion c and friction angle φ), which is divided (or multiplied) by the factor of F (e.g., ctrial = c/F and tan φtrial = {tan φ/F }) until it reaches the limiting equilibrium state. While automatically performing a series of simulations by changing the strength properties, the factor-of-safety F is found to correspond with the point of stability and the critical failure (slip) surface is determined.28 3. Numerical Simulation: Effect of a Hot Wellbore 3.1. Scope of Simulation. This study explores the destabilization of marine gas hydrate-bearing sediments subjected to a thermal loading through a two-dimensional numerical modeling. As oil and natural gas in deep ocean reservoirs have a high geothermal temperature (of approximately 30-65 °C km-1), the production of hot hydrocarbons transfers heat to the surrounding soils and consequently causes a thermal disruption of hydrate stability.7,10,29 A hot wellbore is considered as a long line-type of thermal loading with a constant temperature of 30 °C. A verified finite difference method, FLAC2D, is used as a means of considering the physical processes and capturing the geomechanical responses induced by the thermal change of marine gas hydrate-bearing sediments.28 3.2. Algorithm for Thermal-Hydraulic-Mechanical Coupled Analyses. Thermal conduction, hydrate dissociation, fluid flow, and mechanical response are sequentially solved by updating the inputs for the next step in the numerical simulation. The overall algorithm for sequentially coupled thermal-hydraulicmechanical (THM) analysis is as follows (Figure 3): (1) Consider a finite time step (Δt). (2) Thermal conduction analyses: the thermal conduction is analyzed using eq 1, and the temperature distribution is obtained. (3) Hydrate dissociation analyses: the excess pore fluid pressure induced by the thermal change, and hydrate dissociation is calculated using the suggested analytical model (refer to Appendix S1 in the Supporting Information). If any hydrate exists (Sh >0) and the temperature exceeds the hydrate stability boundary (T > Teq) at a certain grid point, the pore pressure P of the grid point increases to re-establish a new equilibrium pressure Peq. The remaining hydrate fraction Sh is calculated with consideration of the volumetric strains and pressure increase. If the conditions for hydrate dissociation (i.e., hydrate presence and thermodynamical stability) are not satisfied, the pore pressure and hydrate
Figure 2. Thermal stimulation of methane hydrate-bearing sediments at initial conditions of T = 9 °C and P = 11.2 MPa, and the sediment stiffness of Bsk = 200 MPa. Dissociation begins at a temperature of 12 °C: (a) pressure evolution and (b) change in hydrate volume fraction.
mechanical strength and stiffness of particulate materials are governed by the effective stress (i.e., skeletal force); hence, a reduction of effective stress weakens the sediment in terms of strength and stiffness. Numerical analyses of an elastoplastic isotropic model with a Mohr-Coulomb yield criterion show that sediments tend to yield and behave plastically when the stress state exceeds the tension limit (i.e., tension failure) or touches the Mohr-Coulomb yield surface (i.e., shear failure). As pore-filling, load-carrying, or cementing hydrates disappear during dissociation, the strength and stiffness of hydratebearing sediments will be degraded. It is expected that mechanical responses (i.e., deformation) will be worse if the degradation of mechanical properties is considered and updated at every time step in the numerical simulations. Meanwhile, it has been reported that cementation does not significantly affect the strength and stiffness of hydratebearing sediments until the gas hydrates occupy more than 40% of the pore space.12-14 It is justifiable to assume that the mechanical properties of sediments (i.e., elastic modulus, cohesion, and friction angle) are kept constant in numerical simulations under a limited situation when the hydrate saturation is lower than 40%.
(27) Dawson, E. M.; Roth, W. H.; Drescher, A. Slope stability analysis by strength reduction. Geotechnique 1999, 49 (6), 835–840. (28) FLAC-Fast Lagrangian Analysis of Continua, version 5.0; Itasca: Minneapolis, Minesota, 2005. (29) Briaud, J. L.; Chaouch, A. Hydrate melting in soil around hot conductor. J. Geotech. Geoenviron. Eng. 1997, 123 (7), 645–653.
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Figure 3. Algorithm for the sequentially coupled analyses in the numerical code.
Trehu et al.,30 Mesri,31,32 Henninges et al.,33 Santamarina and Ruppel,34 Cortes et al., and 35 Waite et al.36). The presence of thin sandy (or silty) layers within claylike host sediments have occasionally been found in many natural hydrate deposit settings (e.g., Keathley Canyon in the northern Gulf of Mexico).37 Nevertheless, this study considers a uniform fine-grained soil (i.e., clay) as a host medium for simplification. The sediment is assumed to have a thermal conductivity of 2 W m-1 K-1 and a corresponding thermal diffusivity of 5.3 10-7 m2 s-1, both of which are within the ranges of the published data.33-35 Because of a lack of directly measured data on the permeability of the hydrate-bearing sediments, an arbitrary value of low-permeable clay sediments (the permeability of water phase, k=1 mD) is selected for this study. The undrained shear strength of fine-grained sediments, particularly for normally consolidated clays, is primarily dependent on sediment porosity and overburden effective stress. The undrained shear strength is expressed as a function of the overburden effective stress σv0 (or the confining mean effective stress σo0 ): Su = 0.22σv0 for normally consolidated clays,31,32 Su = sin φ/(1 þ sin φ)σo0 for kaolinite (where φ is the friction angle),14 or Su = aσo0 þ bqh(Sh/n)2 (where a and b are empirical parameters, n is the porosity, qh is a nominal value for the hydrate strength, and Sh is the
fraction at a certain grid point remain unchanged. (4) Pressure diffusion analyses: a flow analysis is performed using eq 2 in order to obtain the distribution of pore fluid pressure induced by the pressure diffusion in the medium. The excess pore fluid pressure (i.e., calculated at step 3 using the hydrate dissociation model) is used as an initial condition for flow analysis. It is assumed in the flow analysis that sediments are water-saturated and have the single-phase flow of water. (5) Geomechanical analyses: the effective stress is calculated from the total stress and pore fluid pressure. With the use of the elasto-plastic Mohr-Coulomb model, the geomechanical response is assessed in terms of shear strains and deformation. (6) Instability analyses: the factor-of-safety (FOS), which reflects the degree of instability, is evaluated by the strength reduction technique. (7) Finite time increment and iteration: after updating changes in properties including porosity, hydrate saturation, water saturation, gas saturation at step 5 (i.e., after geomechanical analyses), and the time, this procedure is repeated for a time period of interest. 3.3. Geologic Conditions and Input Properties. The 1245 site of Hydrate Ridge on the Cascadia continental margin (ODP Leg 204) is selected as a model site for hydrate stability and hydrate occurrence.30 The geologic conditions and sediment properties for the thermal, hydraulic, and mechanical analyses are tabulated in Table 2. The hydrate stability zone is determined on the basis of the water column depth (i.e., 870 m) and the geothermal condition of formation (i.e., seafloor temperature of 4 °C and geothermal gradient of 55 °C/km; see Table 2). It is considered that the methane hydrate occurs from 50 to 130 mbsf with a pore saturation of 10% as shown in Figure 4a. It is assumed that the hydrate-forming gas is pure methane and that an aqueous solution containing 3.5% wt of NaCl acts as the pore water. The mechanical and thermal properties of hydrate-bearing sediments used here are obtained from the published data of natural hydrate-bearing sediments (e.g., Yun et al.,14
(33) Henninges, J.; Huenges, E.; Burkhardt, H. In situ thermal conductivity of gas-hydrate-bearing sediments of the Mallik 5L-38 well. J. Geophys. Res.: Solid Earth 2005, 110, B11206, DOI: 10.1029/ 2005JB003734. (34) Santamarina, J. C.; Ruppel, C. The impact of hydrate saturation on the mechanical, electrical, and thermal properties of hydrate-bearing sand, silts, and clay. In The 6th International Conference on Gas Hydrates, Vancouver, Canada, 2008. (35) Cortes, D. D.; Martin, A. I.; Yun, T. S.; Francisca, F. M.; Santamarina, J. C.; Ruppel, C. Thermal conductivity of hydrate-bearing sediments. J. Geophys. Res.: Solid Earth 2009, 114, B11103, DOI: 10.1029/2008JB006235. (36) Waite, W. F.; Santamarina, J. C.; Cortes, D. D.; Dugan, B.; Espinoza, D. N.; Germaine, J.; Jang, J.; Jung, J. W.; Kneafsey, T. J.; Shin, H.; Soga, K.; Winters, W. J.; Yun, T. S. Physical properties of hydrate-bearing sediments. Rev. Geophys. 2009, 47, RG4003, DOI: 10.1029/2008RG000279. (37) Cook, A. E.; Goldberg, D.; Kleinberg, R. L. Fracture-controlled gas hydrate systems in the northern Gulf of Mexico. Mar. Pet. Geol. 2008, 25 (9), 932–941.
(30) Trehu, A. M.; Bohrmann, G.; Rack, F. R.; Torres, M. E. Proceedings of the Ocean Drilling Program, Initial Reports, 2003. (31) Mesri, G. Discussion on “New design procedure for stability of soft clays. J. Geotech. Eng., ASCE 1975, 101 (4), 409–412. (32) Mesri, G. A Re-evaluation of Su(Mob) =0.22σ0 p using laboratory shear tests. Can. Geotech. J. 1989, 26 (1), 162–164.
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Therefore, the assumption South China Sea; GMGS1). of homogeneous methane hydrate is valid here. In natural geologic settings, stress anisotropy is unavoidable. This study excludes the effect of the stress anisotropy on mechanical behavior of hydrate-bearing sediments, so that the sediment behavior due solely to hydrate dissociation is highlighted. The horizontal stresses are assumed to be the same as the vertical stresses; thus, the isotropic stress condition is satisfied. The time period covered in each simulation is 20 years with a finite time increment of 0.01 year. This corresponds to a typical production life span of a hydrocarbon reservoir. During the numerical simulation period, the geothermal temperature, excessive pore fluid pressure, hydrate volume fraction, deformation, and FOS are monitored in terms of space and time (at t = 0, 1, 2, 5, 10, 20 years). All the simulation results presented in the following sections are based on the algorithm described in section 3.2.
Table 2. Geologic Conditions and Properties of the Hydrate-Bearing Sediments Used in This Study properties Geologic Conditions hydrostatic pressure at seafloor [MPa] pore fluid pressure at the sediment depth z, P [Pa] vertical effective stress at the sediment depth z, σ0 [Pa] temperature at seafloor [°C] geothermal gradient [°C km-1] hydrate occurrence zone [mbsf] volume fraction of hydrate in hydrate zone, Sh0 [%] volume fraction of free gas, Sg0 [%]
Thermal Properties thermal conductivity of sediments, kt [W m-1 K-1] thermal diffusivity of sediments, κ [m2 s-1] specific heat of sediments, Cp [J kg-1 K-1]
values
8.83a P = Fwgz þ 8.83 MPab σ0 = (Fsed - Fw)gzb 4a 55a 50-130a 10a 0a
2c 5.3 10-7 2083
Hydraulic Properties permeability of sediments, k [millidarcies, mD]
1
Mechanical Properties sediment density, Fsed [kg m-3] seawater density, Fw [kg m-3] methane hydrate density, Fh [kg m-3] mineral density, Fm [kg m-3] porosity, φ [-] bulk modulus of sediments, Bsk [MPa] shear modulus of sediments, Gsk [MPa] bulk modulus of water, Bw [GPa] apparent cohesion of sediments [kPa] friction angle of sediments [deg]
1800a 1035 910 2600 0.5 200 50 2 50 20
4. Simulation Results 4.1. Spatial Distribution of Thermal Conduction. Figure 6 shows the temperature change with time, caused by the thermal conduction from a hot wellbore. The temperature change takes place within a narrow cylindrical zone of about 10 m within 1 year and spreads to about 40 m in a radial direction after 10 years. Because of the constant temperature of the hot well (i.e., 30 °C), sediments near the well become hotter. The sediments beyond 60 m from the heat source experience no temperature change within the 20 year time frame of this study. 4.2. Spatial Distribution of Hydrate Saturation. Figure 7 shows the spatial distribution of gas hydrate in the sediment. Because of the local increase of temperature around the hot wellbore after 1-2 years, the gas hydrates near the heat source dissociate (Figures 7a,b). Furthermore, hydrates in deeper sediments experience dissociation earlier than the shallower hydrates due to the higher geothermal temperature lower down the sediment column. This is regardless of the significant increase in temperature in shallower sediments due to larger temperature difference between the wellbore and surrounding sediments (see hydrate distribution after 5-20 years; Figure 7c-e). As a result, the dissociation front at 130 mbsf propagates about 60 m from the heat source, whereas the dissociation front at 50 mbsf is limited to 12 m over a period of 20 years. The spatial distribution of the free gas saturation (see Figure S1 in the Supporting Information) is observed to reflect where hydrate dissociation occurs, mirroring the hydrate saturation in Figure 7. The gas saturation in the completely dissociated region is calculated to range approximately 10-12%, varying with the change in sediment porosity. The same phenomenon has been observed in the work by Moridis and Kowalsky.7 4.3. Spatial Distribution of Excess Pore Fluid Pressure. Figure 8 shows the spatial distribution of excess pore fluid pressure in the sediment. The gas hydrate dissociation renders
a The values are from Trehu et al.30 b g is the gravitational acceleration (g = 9.8 m/s2) and z is the sediment depth in meters. c The value is from Cortes et al.35
hydrate saturation).34 The undrained shear strength of sediment samples at site 1245 of the Cascadia margin varies irregularly from 50 to 150 kPa within a range of 0 to 180 mbsf.30 A representative value for the apparent cohesion of 50 kPa with a friction angle of 20° is taken for this study. 3.4. Modeling Condition and Mesh Configuration. A sediment deposit of 400 m deep and 200 m wide is modeled as an axisymmetric mesh with the left boundary of the mesh serving as an axis (Figure 4b). The modeled sediment deposit has a flat surface without a slope in one direction. The hot wellbore, which is a long line-type of heat source with a constant temperature of 30 °C, is placed at the left boundary. The initial temperature and fluid pressure at each node are obtained by considering the geologic conditions (Figure 5a, b). Temperature and pore pressure on the grid points along the top boundary, which represents the seafloor, are fixed during the simulation. Homogeneous pore-filling methane hydrate is given to occur from 50 to 130 mbsf with a pore saturation of 10% (Figure 5c). The 2 m wide by 2 m high element used in the model is too large to consider heterogeneities such as veins and nodules in hydrate deposits, as the scale of hydrate veins is thought to range from millimeter-to-centimeter thick based on the X-ray images of pressure cores (e.g., cores from
(38) Holland, M.; Schultheiss, P.; Roberts, J.; Druce, M. Observed gas hydrate morphologies in marine sediments. In The 6th International Conference on Gas Hydrates, Vancouver, Canada, 2008. (39) Yang, S.; Zhang, H.; Wu, N.; Su, X.; Schultheiss, P.; Holland, M.; Zhang, G.; Liang, J.; Lu, J.; Rose, K. High concentraion hydrate in disseminated forms obtained in Shenhu area, north slope of South China Sea. In The 6th International Conference on Gas Hydrates, Vancouver, Canada, 2008.
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Figure 4. Geological and environmental conditions: (a) hydrate stability zone and hydrate occurrence zone and (b) mesh configuration.
Figure 5. Initial conditions before installing a hot wellbore (t = 0 year): (a) geothermal condition, (b) hydrostatic pressure, and (c) gas hydrate saturation.
a large excess pore fluid pressure in the magnitude of several megapascals. The pore pressure increases near the hot wellbore and diffuses toward the outside of a dissociation zone for the first few years (Figure 8a-c). The deeper sediments in the hydrate occurrence zone experience a higher increase in excess pore fluid pressure (Figure 8b) when the temperature rises by the same amount (Figure 6b). This behavior is attributed to the nonlinearity of the hydrate phase boundary (as indicated by the phase boundary in Figure 1) and to the higher geothermal temperature of deeper sediments. The nonlinearity of the hydrate phase boundary implies that
the same amount of temperature increase at a higher temperature (i.e., deeper sediments) requires more hydrate dissociation to reach an equilibrium condition and leads to a higher pressure build-up. Moreover, it is confirmed that the highly overpressurized region in the vicinity of the wellbore where the hydrate dissociates, coincides with the zone of nearly zero effective stress (see Figure S2 in the Supporting Information), which is consistent with the results presented by Rutqvist and Moridis.17 In the early stage before all the gas hydrates are dissociated, the generation of excess pore fluid pressure is heavily 5500
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Figure 6. Spatial distribution of the temperature: (a) at the initial, (b) after 1 year, (c) after 2 years, (d) after 5 years, (e) after 10 years, and (f) after 20 years.
as shown in Figure 8d-f. The pressure diffusivity (e.g., permeability) subsequently governs the size of the overpressurized zone rather than thermal diffusivity. The thermally disturbed region and hydrate dissociation region are therefore found to be narrower than the overpressurized zone in the vicinity of the wellbore, which is consistent with the observations of Moridis and Kowalsky.7 4.4. FOS and Deformation. The FOS is evaluated by the strength-reduction method, as shown in Figure 9a. It is observed that the FOS gradually drops to less than 2 within 5 years of heat transportation to the surroundings. It must be
dependent on the heat conduction rate rather than the pressure diffusion rate. After 2 years, when gas hydrates around the hot well (within a radius of approximately 5 m) are almost consumed, no more excess pore fluid pressure is generated around the well and the pressure begins to diffuse. Furthermore, the excess pore fluid pressure front propagates much faster than the thermal front (or hydrate dissociation front) because in this case, the pressure diffusivity (approximately, c = (kBsk)/(μwφ) = 4 10-5 m2 s-1, where μw is the viscosity of water) is apparently larger than the thermal diffusivity (approximately, κ = kt/(CpFsed) = 5 10-7 m2 s-1), 5501
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Figure 7. Spatial distribution of the hydrate saturation: (a) at the initial, (b) after 1 year, (c) after 2 years, (d) after 5 years, (e) after 10 years, and (f) after 20 years.
noted that the self-weight of the overlying sediment and the shear resistance decrease as the excess pore pressure diffuses upward and the overlying sediments become shallower. Thereafter, the FOS converges, showing only a small fluctuation. This small fluctuation in FOS is attributable to the variation of the failure depth (uplifting depth) that is determined by the relative magnitude of the overburden stress plus the shear resistance of sediments versus the excess pore pressure. In FLAC code, the deformation of a mesh can be graphically presented by calculating the displacements between the
grid points. It is noted that sediments between 50 and 130 mbsf (i.e., the hydrate occurrence region) undergo a certain amount of volume expansion as shown in Figure 9b,c (also see Figure S3 in the Supporting Information). As the excess pore fluid pressure builds up as a result of the hydrate dissociation, the volume expansion of sediments pushes the surrounding medium out of the dissociation zone, rendering localized shear deformations (strains). Accordingly, it is observed that the deformed region mainly coincides with the hydrate dissociation region. It indicates that most of the primary deformation is induced by the hydrate dissociation, and the subsequent 5502
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Figure 8. Spatial distribution of the excess pore pressure: (a) at the initial, (b) after 1 year, (c) after 2 years, (d) after 5 years, (e) after 10 years, and (f) after 20 years.
pressure diffusion generates the secondary deformation around the dissociation area. The expected shear deformation at a failure condition (Figure 9d) indicates the possible failure surface, in which uplifting deformation of the overlying sediments around a wellbore may occur. The numerical simulation shows the maximum displacement of 3.16 m at the grid points for a period of 20 years. This result reveals that the hydrate occurrence region around the wellbore is the most critical area for instability perspectives (particularly with respect to the buckling of the well structure and the collapse of the borehole wall).
5. Discussion 5.1. Parametric Study. Using the simulation results in section 4 as a reference case (REF), 12 cases varying parameters such as the thermal conductivity, heat source, permeability, hydrate quantity, and sediment strength (Table 3) are explored. The results are presented in FOS terms. 5.1.1. Thermal Conductivity. The rate of thermal front propagation (i.e., thermal diffusion rate) is proportional to the thermal conductivity of a medium. Figure 10a presents the instabilities in relation to various levels of the thermal 5503
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Figure 9. Stability analysis results for the reference case: (a) factor-of-safety with time, (b) deformed shape after 20 years. Note that the displacements between the grid points in the image are amplified by a magnitude of 5. (c) Typical result of shear deformation after 20 years. (d) The expected shear deformation feature at a failure condition. Note that this result is derived by the FOS calculation using the strength-reduction technique, implying a possible failure surface.
conductivity in sediments. Those levels are expressed in order of thermal conductivity as follows: 1 W m-1 K-1 for TH1; 2 W m-1 K-1 for REF; 3 W m-1 K-1 for TH2; and 4 W m-1 K-1 for TH3. It is found that the thermal conductivity of a sediment mainly affects the initial stability. Sediments with a high thermal conductivity appear to have a lower stability in the early stages of thermal dissociation. As thermal conductivity increases (e.g., TH2 and TH3), the early FOS becomes lower than that of REF. However, their FOS values of the cases REF, TH1, TH2, and TH3 show a convergence to approximately 1.5-1.7 after 8 years. In contrast, the FOS for TH4, in which the initial condition of the heat source was higher at a temperature of 40 °C,
drops below 1. It can be seen that a larger temperature increment renders higher excess pore fluid pressure, as hydratebearing sediments preserve the equilibrium by generating a pore pressure during the thermal change. This behavior confirms that the intensity of the heat source is more important than the thermal conductivity (or thermal diffusivity) of sediments with respect to sediment stability.7 Note also that thermal conductivity (or thermal diffusivity) affects the early stability but not the long-term stability. 5.1.2. Permeability. Figure 10b presents the instabilities in relation to various levels of the permeability of water in sediments. Those levels are expressed in order of permeability as follows: HP1 for shale of 0.01 mD; REF for stiff clay of 5504
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Table 3. Summary of Simulated Cases case
wellbore temperature [°C]
thermal conductivity [W m-1 K-1]
permeability [mD]
hydrate saturation [%]
gas saturation [%]
apparent cohesion [kPa]
friction angle [deg]
REF TH1 TH2 TH3 TH4 HP1 HP2 HP3 SH1 SH2 SH3 ME1
30 30 30 30 40 30 30 30 30 30 30 30
2 1 3 4 2 2 2 2 2 2 2 2
1 1 1 1 1 0.01 100 104 1 1 1 1
10 10 10 10 10 10 10 10 20 40 10 10
0 0 0 0 0 0 0 0 0 0 10 0
50 50 50 50 50 50 50 50 50 50 50 0
20 20 20 20 20 20 20 20 20 20 20 15
Figure 10. Factor-of-safety for the cases studied: (a) TH1, TH2, TH3, and TH4; (b) HP1, HP2, and HP3; (c) SH1, SH2, and SH3; and (d) ME1.
1 mD; HP2 for soft clay of 100 mD; and HP3 for silt of 104 mD.40,41 The FOS becomes insensitive to flow characteristics when sediments are less permeable than 100 mD (e.g., less permeable than clay-like sediments, cases REF, HP1, and HP2). Therefore, the lowest boundary for FOS occurs when the sediments are less permeable than 100 mD. However, the case HP3 has a relatively high FOS. The dissociation of methane hydrate generates minimal excess
pore fluid pressure because of the fast dissipation when the permeability is larger than 104 mD (e.g., more permeable than silty sediments). Thus, sediments are less likely to fail if the grain size is coarser than silt. The ratios of the pressure diffusion rate to the thermal diffusion rate range from approximately 1 to 104 for the cases of HP1, REF, and HP2. The value of HP3 is about 106. (42) Sun, R.; Duan, Z. An accurate model to predict the thermodynamic stability of methane hydrate and methane solubility in marine environments. Chem. Geol. 2007, 244 (1-2), 248–262. (43) Sloan, E. D. Clathrate Hydrates of Natural Gas, 2nd ed.; Dekker: New York, 1998.
(40) Terzaghi, K.; Peck, R. B.; Mesri, G. Soil Mechanics in Engineering Practice, 3rd ed.; Wiley: New York, 1996; p 549. (41) Sch€ on, J. H. Physical Properties of Rocks: Fundamentals and Principles of Petrophysics; Elsevier: Oxford, U.K., 2004; Vol. 18, p 583.
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Figure 11. Deformation features of the case SH1: (a) no deformation at the initial, (b) deformed shape after 10 years, (c-e) deformed shapes from 11 to 12 years, and (f) deformed shape after 12 years to seafloor uplift.
The excess pore fluid pressure front generally propagates much faster than a thermal front (or hydrate dissociation front) because the pressure diffusivity is larger than the thermal diffusivity in most oceanic sediments. 5.1.3. Hydrate and Free Gas Saturation. Hydrate saturation is a critical aspect of the instability problem. As hydrate saturation increases, the excess pore fluid pressure is maintained longer at the equilibrium pressure during the dissociation, despite the pressure diffusion process.9 Thus, higher hydrate saturations yield higher pressure and a larger overpressurized zone. Consequently, this phenomenon increases a risk to failure as shown in Figure 10c. The sediment around the wellbore deforms considerably in the cases SH1 (Sh = 20%) and SH2 (Sh =40%) when the FOS values become less than 1. As the excess pore fluid pressure builds up, the sediments that experience hydrate dissociation expand significantly. After several years, this expansion uplifts the overlying sediments and causes failure in the form of considerable
displacement of more than several meters at the seafloor, as shown in Figure 11. The dimensions of the failure area for the case SH1 are predicted to be around 80 m deep and 20 m wide, while those of the failure area for the case SH2 are predicted to be around 130 m deep and 30 m wide. This suggests that as the sediment contains more hydrate, uplifting deformation occurs by overcoming a larger overburden effective stress. In contrast, the presence of free gas in the pores increases stability by acting as a cushion against the pressure increase (see SH3 in Figure 10c; Sg = 10%). 5.1.4. Sediment Strength. The sediment strength for the case ME1 is assumed to be smaller than the reference case (see Table 3) and decreases the apparent cohesion from 50 to 0 kPa and the friction angle from 20° to 15°. These parameters are in reasonable agreement with the previous studies (e.g., Su =0.22σv0 ).31,32 The sediment strength, mostly under the undrained condition, significantly affects the instability as shown in Figure 10d. 5506
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5.2. Implications. Any thermal change without a drainage path in a sediment formation during hot hydrocarbon production or thermal stimulation appears to generate large excess pore fluid pressure around a heat source. This observation raises two engineering concerns: (1) The sediment around a heat source experiences plastic deformation in the dissociation region and uplifting deformation at the seafloor (Figure 11). (2) The damaged sediment around the wellbore will eventually be consolidated downward by the weight of overlying sediments, as overpressurized fluids diffuse out. This post-dissociation subsidence may apply downward force to the well structures.2 Furthermore, lateral skeletal stress in a yielded zone is significantly reduced due to plastic deformation. As a result of the post-dissociation subsidence and the lack of lateral stress, a slender well structure can be damaged particularly at a region where a large volume expansion occurs and a yield zone is developed (e.g., a hydrate dissociation region). From the point of view of thermal stimulation (e.g., hot water injection), the instability in and productivity from hydrate-bearing sediments are contrary problems. A stronger heat source is beneficial for fast thermal diffusion, but it increases the likelihood of sediment failure. Considering that coarse-grained formations with high hydrate saturations are the primary targets for producing methane from natural hydrate deposits, the depressurization method is presumed to be more effective than the thermal stimulation method. The area of excess pore fluid pressure can be extended quickly and extensively, depending on the permeability of sediments. For example, a clay-like sediment (e.g., REF case) has the pressure diffusivity of ∼10-5 m2 s-1, which is approximately 2 orders of magnitude larger than the thermal diffusivity of ∼10-7 m2 s-1. As grain size increases, the disparity between these two values becomes larger. In contrast, the low thermal conductivity of oceanic sediments means that thermal conduction is slow and limited to a local area (tens of meters over a period of 10 years). This would suggest that thermal stimulation might only be used in support of the depressurization method, to aid in the efficiency of methane production.
fluid flow, and the mechanical response of sediments. The modeling methods and results presented advance the understanding of hydrate-related instability problems. The main findings are as follows: (1) Deeper sediments in the hydrate occurrence zone experience earlier gas hydrate dissociation and higher excess pore fluid pressure generation than the shallower sediments due to the positive geothermal gradient and the nonlinearity of the hydrate phase boundary. (2) Thermal change is limited to a narrow area around the heat source due to the low thermal conductivity of water-saturated sediments. Excess pore fluid pressure fronts generally propagate much faster than thermal fronts (or hydrate dissociation fronts) as pressure diffusivity is larger than thermal diffusivity in most oceanic sediments. (3) Sediments in the hydrate occurrence zone around a heat source undergo volume expansion during gas hydrate dissociation and eventually become plastic. The uplifting of sediments around a wellbore is expected to occur in cylindrical shape when the FOS becomes less than 1. (4) Sediment stability in the early stage of heat transfer is governed by the intensity of the heat source and the thermal conductivity of the sediments with gas hydrates in place. However, after most of the gas hydrates are dissociated around the heat source, the stability depends on the dissipation rate of the excess pore fluid pressure and the confining effective stress by overlying sediments. (5) The lowest boundary for the FOS of a hydrate-bearing formation is when the sediments are less permeable than clay-like sediments (e.g., 100 mD). When sediments are coarse-grained (the permeability is larger than 104 mD), the dissociation of methane hydrate generates a minimal excess pore pressure due to the fast pressure dissipation. (6) Overall, the stability of sediments experiencing thermal change is worsened by an increase in the intensity of the heat source and the initial hydrate saturation. In addition, a decrease in the permeability, initial free gas saturation, and sediment strength also decreases the stability in such sediments. Acknowledgment. We are grateful to anonymous reviewers and Emily V. L. Rees for valuable comments and suggestions. Support for this research was provided by the Basic Research Project of the Korea Insitute of Geoscience and Mineral Resources (KIGAM) funded by Korean Ministry of Knowledge Economy (Grant No. GP2010-016-2010(1)) and by the office of KAIST Energy, Environment, Water and Sustainability (EEWS) Initiative (Grant No. EEWS-2010-N01100038).
6. Conclusions In this study, a comprehensive numerical approach was addressed to explore how thermal change destabilizes gas hydrate-bearing sediments. Through numerical simulations, the effect of heat transfer was examined from a steady-state hot wellbore to surroundings over a period of 20 years. The underlying physical processes of hydrate-bearing sediments, which include hydrate dissociation, self-preservation, pore pressure evolution, gas dissolution, and sediment volume expansion, were incorporated into thermal conduction, the pore
Supporting Information Available: Analytical formulations for hydrate dissociation in sediments (Appendix S1), spatial distribution of the free gas saturation for the case REF (Figure S1), spatial distribution of the effective stress for the case REF (Figure S2), and deformation features of the formation for the case REF (Figure S3). This material is available free of charge via the Internet at http://pubs.acs.org.
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