Transient hydraulic fracturing and gas release in ... - Wiley Online Library

Article Volume 12, Number 12 29 December 2011 Q12022, doi:10.1029/2011GC003841 ISSN: 1525‐2027

Transient hydraulic fracturing and gas release in methane hydrate settings: A case study from southern Hydrate Ridge Hugh Daigle Department of Earth Science, Rice University, Houston, Texas 77005, USA Now at Chevron Energy Technology Company, 1500 Louisiana Street, Houston, Texas 77002, USA ([email protected])

Nathan L. Bangs Institute for Geophysics, University of Texas at Austin, Austin, Texas 78758, USA

Brandon Dugan Department of Earth Science, Rice University, Houston, Texas 77005, USA [1] Episodic seafloor methane venting is associated with focused fluid flow through fracture systems

at many sites worldwide. We investigate the relationship between hydraulic fracturing and transient gas pressures at southern Hydrate Ridge, offshore Oregon, USA. Two colocated seismic surveys, acquired 8 years apart, at Hydrate Ridge show seismic amplitude variations interpreted as migration of free gas in a permeable conduit, Horizon A, feeding an active methane hydrate province. The geophysical surveys also reveal transients in gas venting to the water column. We propose that episodic gas migration and pressure fluctuations in the reservoir underlying the regional hydrate stability zone (RHSZ) at southern Hydrate Ridge influence methane supply to the RHSZ and are linked with periodic fracturing and seafloor methane venting. We model the effect of pore pressure variations within the deep methane source on fracturing behavior with a 1D model that couples multiphase flow, hydrate accumulation, and pore pressure buildup. As the reservoir pressure increases, fractures open when the pore pressure exceeds the hydrostatic vertical effective stress. Gas then flows through the fractures and vents at the seafloor while hydrate precipitates in the fracture system. We show that active seafloor gas venting occurs for approximately 30 years, and that the available methane reservoir is exhausted 30 to 55 years after the onset of pressure buildup. This provides important constraints on the time scale of transient fluid flow at southern Hydrate Ridge, and illustrates how pore pressure pulses affect fluid flow and fracturing behavior in active methane hydrate provinces. Components: 9700 words, 8 figures. Keywords: Hydrate Ridge; Ocean Drilling Program; gas hydrates; hydraulic fracturing. Index Terms: 3004 Marine Geology and Geophysics: Gas and hydrate systems; 5104 Physical Properties of Rocks: Fracture and flow. Received 22 August 2011; Revised 7 November 2011; Accepted 17 November 2011; Published 29 December 2011. Daigle, H., N. L. Bangs, and B. Dugan (2011), Transient hydraulic fracturing and gas release in methane hydrate settings: A case study from southern Hydrate Ridge, Geochem. Geophys. Geosyst., 12, Q12022, doi:10.1029/2011GC003841.

Copyright 2011 by the American Geophysical Union

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DAIGLE ET AL.: HYDRAULIC FRACTURING AT HYDRATE RIDGE

1. Introduction [2] Seafloor venting of methane gas is a widespread phenomenon, occurring worldwide in a variety of geological settings [Judd, 2003]. Introduction of methane into the water column has important implications for ocean chemistry, marine biology, global carbon cycling, and global climate. Of particular interest are sites with significant plumes of methane bubbles emanating from the seafloor. These sites may represent site‐specific methane fluxes of 104–106 mol day−1 [e.g., Martens and Klump, 1980; Hovland and Judd, 1992; Hornafius et al., 1999]. Methane venting at these locations is often heterogeneous in space and time, with discrete venting episodes lasting days to weeks [e.g., Tryon et al., 2002], and switching of active venting among multiple locations [e.g., Shipboard Scientific Party, 2003]. [3] The subsurface near active or fossil seafloor methane vents that have been sampled by scientific ocean drilling often has shallow gas hydrate accumulations, frequently in the form of hydrate‐ filled fractures [e.g., Shipboard Scientific Party, 2003; Expedition 311 Scientists, 2006; Mazumdar et al., 2009; Riedel et al., 2010; Torres et al., 2011]. This suggests some relationship between fracturing processes and transport of methane gas into and through the hydrate stability zone. Liu and Flemings [2006, 2007] and Daigle and Dugan [2010a] have examined the coexistence of methane gas and hydrate within the hydrate stability zone as a result of high pore water salinity caused by salt exclusion from the hydrate crystal structure. These models predict a high‐salinity anomaly associated with gas transport through the hydrate stability zone. High‐salinity anomalies are observed beneath some venting locations (e.g., the summit of southern Hydrate Ridge [Liu and Flemings, 2006]). At other locations that are inferred to be inactive (i.e., previous vents that are no longer actively expulsing fluid) there are no observed salinity anomalies (e.g., the flanks of Hydrate Ridge [Liu and Flemings, 2006] and the Ulleung Basin offshore Korea [Torres et al., 2011]). Other studies have suggested rapid transport of gas through fracture systems in which hydrate formation is inhibited either by water availability or hydrate nucleation kinetics [e.g., Tréhu et al., 2004; Scandella and Juanes, 2011]. Any model that successfully describes methane gas transport through the hydrate stability zone and seafloor venting must therefore combine focused flow and inhibition of hydrate formation. We present a model that links episodic hydrofracturing and venting at Hydrate

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Ridge, offshore Oregon, caused by changes in the pressure of the gas reservoir supplying methane beneath the summit of southern Hydrate Ridge. This model allows us to constrain primary controls on system dynamics and time scales associated with transient behavior.

2. Hydrate Ridge Background and Data Description [4] Hydrate Ridge is a bathymetric high ∼25 km long and ∼15 km wide oriented roughly NNE‐SSW about 80 km offshore Oregon, USA landward of the Cascadia deformation front (Figure 1). The northern and southern summits of Hydrate Ridge are areas of active methane seeps and gas vents [Kulm et al., 1986; Torres et al., 1999; Tréhu and Bangs, 2001]. Methane gas has been observed venting to the water column as discrete plumes and flares from several sites at northern and southern Hydrate Ridge [Torres et al., 1999; Tréhu and Bangs, 2001; Bangs et al., 2011]. The location of venting at southern Hydrate Ridge has been observed to change on time scales of months to years. Gas flow rates up to 107 m yr−1 have been observed at discrete vents at the summit of southern Hydrate Ridge (SHR), representing methane flux up to 1000 mol m−2 day−1 [Torres et al., 2002; Tryon et al., 2002]. Ocean Drilling Program (ODP) Leg 204 investigated 9 sites on SHR. The highest hydrate saturations (Sh = 50%) were inferred near the summit of SHR from logging‐ while‐drilling (LWD) resistivity and acoustic data [Lee and Collett, 2006] and pore water chemistry [Liu and Flemings, 2006], with hydrates present as veins, nodules, and fracture fill, as well as disseminated throughout the pore space [Shipboard Scientific Party, 2003]. [5] Based on seismic, LWD, and core data, methane is inferred to be supplied to SHR through a 2–4 m thick permeable zone of coarse‐grained turbidites located 15–20 m below the base of the regional hydrate stability zone (RHSZ) at the summit of SHR [Tréhu et al., 2004]. The gas pressure in Horizon A beneath the summit of SHR is inferred to be at or near the lithostatic pressure, and hydraulic fracturing has been invoked to explain the presence of hydrate‐ filled fractures and rapid gas flux that has been observed at SHR [Tréhu et al., 2004; Weinberger and Brown, 2006]. Model results have shown that formation of hydrate in sediment pore space at SHR can decrease permeability to the point that fluid pressure in excess of lithostatic pressure is required to maintain the observed flow rates by porous 2 of 15


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sents a viable mechanism to explain discrete seafloor venting of methane at many sites worldwide.

3. Model Details 3.1. Domain and Environmental Parameters

Figure 1. Location of Hydrate Ridge offshore Oregon, USA. NHR: Northern Hydrate Ridge; SHR: Southern Hydrate Ridge. Bathymetry contour interval 500 m. Rectangle at SHR shows approximate area of seismic survey shown in Figure 2.

medium flow [Daigle and Dugan, 2010a, 2010b]. At flow rates of tens to hundreds of cm yr−1, which have been inferred near vents and seeps at SHR [Torres et al., 2002], this process requires hundreds to a few thousand years to generate fractures [Daigle and Dugan, 2010a]. Fractures, however, may be generated more quickly with higher flow rates. [6] Two co‐located seismic surveys collected in

2000 and 2008 reveal the dynamic nature of the gas reservoir feeding Horizon A beneath SHR [Bangs et al., 2011] (Figure 2). Differences in seismic amplitudes in Horizon A between the two surveys are inferred to result from migration of gas within Horizon A. In particular, a high‐amplitude area northeast of the summit of SHR migrated ∼100 m updip between the two surveys, and the amplitude of Horizon A directly beneath the summit region increased significantly (Figure 2). From these features we interpret migration of gas through Horizon A toward the summit of SHR at a rate of roughly 12.5 m yr−1 (100 m over 8 years). [7] We model the mechanical and hydrologic responses of the sediments at the summit of SHR to an increase in gas pressure in Horizon A, corresponding to the gas migration inferred from the amplitude differences between the two seismic surveys. We use a one‐dimensional model that couples multiphase fluid flow, hydrate formation, and pore pressure buildup to determine how changes in the deep methane reservoir affect sediment fracturing and methane discharge to the seafloor at SHR. We show that the venting behavior and hydrate distribution at SHR are a direct result of these pressure buildup and fracturing processes, and that this repre-

[8] Our model uses the methodology of Daigle and Dugan [2010a]. We simulate fluid flow and methane hydrate formation in a 1‐dimensional domain with fixed seafloor depth of 780 m, seafloor temperature of 277 K, and geothermal gradient of 0.053 K m−1 [Tréhu, 2006], parameters which represent the conditions near the southern summit of Hydrate Ridge. The seafloor temperature and geothermal gradient define the thickness of the RHSZ. We define a porosity‐depth (8‐z) profile and permeability‐porosity (k‐8) relationship [m2] [Daigle and Dugan, 2010b]: 8 ¼ 0:53ez=1400 ;

ð1Þ

k ¼ eð13840Þ ;

ð2Þ

where z is depth below the seafloor [m]. Equation (1) is based on measured porosity data from ODP Leg 204 [Riedel et al., 2006] and equation (2) is based on measured permeability at in situ conditions from Tan et al. [2006]. Our model includes three components (water [superscript w], methane [superscript m], salt [superscript s]) that may be present in three phases (aqueous [subscript w], hydrate [subscript h], gas [subscript g]). We conserve mass by solving mass balance equations for all components: i @ h @ @ @c j 8Sj j cxj j~ q j jj cxj ¼ 8Sj j Dxj x ; @z @t @z @z

ð3Þ

where Sj is the fraction of pore volume occupied by phase j (water, hydrate, gas), rj is the bulk density of phase j [kg m−3], cxj is the mass concentration of component x in phase j, ~ q j is the flux of phase j [m s−1], and Dxj is the diffusion coefficient of component x in phase j [m2 s−1]. We assume rw = 1024 kg m−3, rh = 930 kg m−3, chm = 0.134 [Davie and Buffett, 2001], and Dwm = Dws = 10−9 m2 s−1 [Liu and Flemings, 2007]. Gas density is computed from the ideal gas law. Solubility of methane in water is computed using the method of Bhatnagar et al. [2007], and we assume that cws is initially 3.35% by mass. Equation (3) is solved explicitly for methane and implicitly for salt and water using a forward‐in‐time, centered‐in‐space finite difference scheme. We further assume: salt is only present in the aqueous phase; dissolved salt and methane do not affect the density of the pore fluid; the mass fraction 3 of 15


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Figure 2. Seismic amplitude of Horizon A from seismic surveys acquired in (left) 2008 and (middle) 2000, and (right) the amplitude difference between the two surveys. ODP Leg 204 Sites are shown for reference. Three features are identifiable in both surveys, and are marked to show movement between the two surveys. The northernmost extent of the high amplitude region (red line) appears to have moved ∼100 m to the southwest (updip). Another high‐amplitude region in the 2000 survey located southeast of Site 1247 (black line) migrated ∼100 m south between surveys. The southernmost limit of the highest amplitudes in the 2000 survey (brown line) migrated ∼350 m south, passing Sites 1249 and 1250. The map of amplitude difference (Figure 2, right) shows areas where seismic amplitudes increased between 2000 and 2008 (hot colors), which is interpreted to indicate an increase in gas saturation in Horizon A. The most notable increase occurred at the SHR summit region, and between Sites 1247 and 1249. This is interpreted as evidence of flux of gas into Horizon A beneath the summit region.

of water in the aqueous phase is close to unity; consumption of water by hydrate formation is negligible compared to the available water supply; diffusion only occurs in the aqueous phase; and the flux of the hydrate phase is zero. Our assumption that the density of the pore fluid is invariant may be an oversimplification at high salinities, but the increase in pore water density that results from salinity increase will be a localized effect within the fractures. We also assume an equilibrium model in which hydrate formation is assumed to be much faster than fluid and mechanical responses. We do not consider heat of hydrate formation in our model since we assume that the total volume of hydrate that forms in fractures is small compared to the bulk sediment volume, and that any heat produced by this mechanism will dissipate rapidly by lateral thermal conduction as shown by Liu and Flemings [2006]. The thermal diffusivity of the sediments is on the order of 10−6 m2 s−1 [e.g., Cathles and Chen, 2004], so diffusion of heat out of the domain is expected to be 3 orders of magnitude more rapid than diffusion of solutes.

3.2. Pressures and Fluxes [9] Water‐ and gas‐phase fluxes are computed

from Darcy’s law: ~ qj ¼

kkrj @P *j ; j @z

ð4Þ

where krj is the relative permeability of phase j, mj is the dynamic viscosity of phase j [Pa s], and P*j is the pressure in excess of hydro‐ or gas‐static of phase j [Pa]. Relative permeability is calculated using Corey’s model assuming residual water and gas saturations of 10% [Liu and Flemings, 2007; Bear, 1972]. Water viscosity is 0.001 Pa s, and gas viscosity is computed from the Lennard‐Jones potential [Bird et al., 2007]. We impose boundary conditions of P* w = 0 [Dugan, 2003] and P* g increasing with time at the base of the domain. The condition of P* w = 0 implies that methane gas is the only fluid flux from Horizon A into the RHSZ. We do not model flow within Horizon A itself. Our model domain extends from the seafloor to the 4 of 15


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intersection of Horizon A with the overlying sediments, so the pressure conditions in Horizon A are treated as boundary conditions based on inferred fluid flow. As hydrate forms and the pore space decreases, the permeability is reduced by a factor of (1‐Sh)2 [Kleinberg et al., 2003]. We assume that any pore system dilation that results from increased pore fluid pressures [e.g., Garg et al., 2008] is negligible, and do not consider local increases in fluid pressure due to hydrate formation. Any pore pressure increases associated with fluid flow or hydrate formation will result in a very small elastic strain on the system [e.g., Lambe and Whitman, 1969], but we neglect this effect to understand the basic behavior of the system. This may result in an underestimation of the time required for gas front propagation through the system since increased pore fluid pressures will increase the three‐phase equilibrium temperature and thus require larger salinities to achieve equilibrium. For example, the ∼0.2 MPa increase in pore fluid pressure predicted by Garg et al. [2008] for a gas flux of 26 mm yr−1 at southern Hydrate Ridge will cause the time for the gas front to propagate to the seafloor to be underestimated by ∼6%. We do not consider heat transport since advective heat transport by gas flow alone is not sufficient to perturb the temperature gradient [Liu and Flemings, 2006; Daigle and Dugan, 2010a]. [10] Below the RHSZ, gas accumulates at a rate

determined by the reservoir pressure boundary condition we impose at the base of the domain. We assume that gas saturation must reach a threshold value of 10% before the gas may form an interconnected phase and flow [e.g., Tréhu et al., 2004; Liu and Flemings, 2007]. If gas is present, we assume that cwm is equal to the local solubility value, and any methane in excess of solubility exists in the gas phase. Within the RHSZ, hydrate forms from any methane in excess of the solubility value. As hydrate forms, the salinity of the surrounding pore fluid is increased since the hydrate crystal structure excludes salt ions [Egeberg and Dickens, 1999]. The increased salinity depresses water activity, which causes a decrease in the three‐phase equilibrium temperature for hydrate, aqueous methane, and methane gas [Sloan, 1990]. We compute the change in three‐phase equilibrium temperature due to salinity changes using the method of De Roo et al. [1983]. If salinity at a given point within the RHSZ increases to the value required for three‐phase equilibrium for the in situ temperature and pressure, formation of hydrate ceases and free gas may be present. Previous studies of Hydrate Ridge have shown that this requires hydrate fill 40–80% of the pore space [Daigle and Dugan,

2010a; Liu and Flemings, 2006]. Methane gas may thus invade the RHSZ if sufficient salt is produced by hydrate formation and is not removed by flux of pore water [Daigle and Dugan, 2010a; Liu and Flemings, 2007, 2006]. [11] The gas‐phase pressure changes in the RHSZ

as a result of the reservoir pressure boundary condition as well as formation of hydrate. Due to the curvature of the gas‐water interface, the pressure of the gas phase is greater than the pressure of the water phase by an amount equal to the capillary pressure Pc [Pa]. Capillary pressure is computed as Pc ¼ J gw

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 8 ; k ð1 Sh Þ

ð5Þ

where sgw is the interfacial tension of the gas‐water interface [J m−1] and J is a dimensionless function that describes changes in capillary pressure during drainage as gas displaces water in the pore space [Liu and Flemings, 2007; Bear, 1972]. We assume sgw = 0.072 J m−1 [Henry et al., 1999] and use a J‐function determined from mercury injection capillary pressure measurements on sediment from Ocean Drilling Program Site 1248 at Hydrate Ridge [Liu and Flemings, 2011]. [12] We assume that the shallow sediment near the

summit of southern Hydrate Ridge is under isotropic stress conditions, which is supported by chaotic fracture orientations observed in image logs [Weinberger and Brown, 2006]. Hydraulic fracturing therefore requires that the pore pressure overcome the overburden stress. When the gas pressure in Horizon A exceeds the vertical effective stress under hydrostatic conditions, hydraulic fractures form. Integration of the bulk density log from Site 1250 yields a vertical effective stress under hydrostatic conditions in Horizon A of 0.86 MPa. We assume that fractures propagate from Horizon A to the seafloor very rapidly [Valkó and Economides, 1995], in less than one model time step (∼1 h). These fractures provide a conduit linking Horizon A with the seafloor. The permeability of the fracture system is given by [Snow, 1968] k¼

a3 ; 12l

ð6Þ

where a is the fracture aperture [m] and l is the inter‐ fracture spacing [m]. We assume that the fractures have aperture of 1 mm and are spaced 1 m apart [e.g., Weinberger and Brown, 2006]. For simplicity, we assume that the fractures remain subvertical and may take any orientation in plan view. As hydrate forms in the fractures, the permeability of 5 of 15


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the fracture system is reduced by a factor of (1‐Sh)3 [e.g., Nimblett and Ruppel, 2003]. We assume that the fracture aperture is large enough that the capillary pressure of the gas phase in fractures is negligible (e.g., for a fracture with aperture 1 mm, the capillary entry pressure is 144 Pa [Pruess and Tsang, 1990], which is negligible compared with hydrostatic pressure of ∼8 MPa at the summit of SHR).

3.3. Model Implementation [13] System behavior can be divided into three distinct

stages defined by the fluid flow regime (Figure 3). In stage 1 (Figure 3a), gas accumulates in Horizon A and the pressure of the gas phase increases. Fluid flow above Horizon A occurs through the sediment pore space. We specify the rate of gas pressure increase in Horizon A, and the rate of change in methane mass m [kg] in Horizon A is given by kkrg @ dm ¼ g ASg 8 Pg g gz ; dt g @z

ð7Þ

where A [m2] is the cross‐sectional area through which fluid flow occurs above Horizon A. See Appendix A for additional details. [14] Stage 2 begins when the gas‐phase pressure in

Horizon A exceeds the vertical effective stress (Figure 3b). During this stage, fractures open, gas migrates upward, hydrate precipitates in the fractures and the local salinity increases within the fractures to the point required for three‐phase equilibrium. We do not consider lateral diffusion of salt, because salt that is lost by diffusion will be replenished rapidly by formation of additional hydrate [e.g., Liu and Flemings, 2006]. During stage 2, gas pressure in Horizon A continues to increase at the specified rate since the gas cannot yet vent through the fracture system. Flow through the sediment pore space is not considered in this stage of the simulation since flux in the fractures will be many orders of magnitude larger due to the large permeability contrast between fractures (equation (6)) and pore system (equation (2)). The change in methane reservoir mass is given by replacing the matrix porosity and permeability in equation (7) with those of the fracture system (8f, kf): kf krg @ dm ¼ g A8f Sg Pg g gz : dt g @z

ð8Þ

When the gas front reaches the seafloor, stage 3 begins, during which gas vents through the fracture system, depleting the gas pressure in Horizon A (Figure 3c). If the gas front reaches the seafloor before the gas pressure in Horizon A has reached its

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maximum value, we assume that the gas pressure in Horizon A cannot increase any more due to the high methane flux through the high‐permeability fracture system (k = 8.3 × 10−11 m2), so gas vents to the seafloor at a constant pressure gradient. As in stage 2, flow during stage 3 only considers flow through fractures and flow through the sediment pore space is neglected. Once the gas pressure in Horizon A has stopped increasing, stage 3 continues until the gas pressure in Horizon A drops below the hydrostatic vertical effective stress or the methane supply in the reservoir is exhausted. Pressure depletion during stage 3 is described by RT kkrg @ @P ¼ g A8f Pg g gz P0 ; @t mMCH4 g @z

ð9Þ

where MCH4 is the molar mass of methane and P0 is the initial pressure in Horizon A at the start of pressure depletion. See Appendix A for additional details on the derivation of equation (9). Change in methane reservoir mass is described by equation (8). We end the simulation when the reservoir pressure drops below the fracture criterion or the methane supply is exhausted.

4. Results 4.1. Determination of System Parameters [15] Migration of methane gas within Horizon A is

assumed to be mediated by episodic dewatering of the subducting wedge associated with seismicity as suggested by Brown et al. [2005] at the Costa Rican margin and Westbrook et al. [1994] and Tryon et al. [2002] at the Cascadian margin. We assume that the methane gas reservoir feeding SHR is defined by the area of high amplitude in Horizon A. Based on the 2000 seismic survey, this area is roughly a rectangle with dimensions 1300 × 300 m (Figure 2). We assume that Horizon A has an average thickness of 5 m, 50% porosity, and 50% Sg where gas is present [Tréhu et al., 2004]. These parameters yield 4.88 × 105 m3 of methane in the reservoir. Within the reservoir, Horizon A has an average depth of 170 m below seafloor (mbsf), which results in an average reservoir temperature of 286 K assuming seafloor temperature of 277 K and geothermal gradient of 0.053 K m−1 [Tréhu, 2006]. From the methane equation of state of Duan et al. [1992], the bulk density of the free gas in the reservoir is 63 kg m−3. Thus the reservoir initially contains 3.07 × 107 kg of methane. The reservoir pressure is 9.36 MPa from the ideal gas law. Reservoir pressure at any point in time or space 6 of 15


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reservoir pressure and prescribe a pressure buildup curve to describe the gas‐phase pressure response in Horizon A at the summit of SHR. [16] The cross‐sectional area through which flow

occurs above Horizon A at SHR is an important parameter to constrain for reservoir depletion in equations (7) and (8). We assume that the area through which flow occurs at the summit of SHR corresponds with the area of dense microbial mats, mounded topography, and periodic gas release observed by Tryon et al. [2002]. This area is a roughly 100 m × 100 m square. Our estimates of reservoir volume and cross‐sectional area of flow are the most significant sources of error in our simulations in terms of the time scale and pressure involved in venting methane to the seafloor. Since the cross‐sectional area of seafloor venting is constrained by visual observations [Tryon et al., 2002], we assume that the error in this value is ±20%. The reservoir volume estimate likely has a larger error since we assume that gas is distributed uniformly within the reservoir and that Horizon A has a uniform thickness. The true reservoir volume may be smaller than our calculation, and we estimate that the value we use has error of ±50%. [17] We estimate the magnitude of pressure increase

and the time over which the increase occurs from seismic data (Figure 2). However, the shape of the pressure buildup over time is unconstrained. Therefore, we investigate system behavior in three different pressure increase scenarios (Figure 4). We assume that the southern edge of the gas reservoir is initially just north of the SHR summit. At the estimated gas migration rate along Horizon A of 12.5 m yr−1, the center of the reservoir would move

Figure 3. Model stages. (a) Stage 1: accumulation of gas and porous medium flow above Horizon A. (b) Stage 2: fractures form, gas front propagates through fractures as hydrate forms and increases local salinity. (c) Stage 3: gas vents to the seafloor until gas reservoir is exhausted.

may be computed by considering the vertical height above the gas‐water contact [e.g., Tréhu et al., 2004], but migration of the gas reservoir implies migration of the gas‐water contact, which will alter the results in a transient system. We use the ideal gas law to determine the maximum gas‐phase

Figure 4. Pressure buildup scenarios. Linear increase (Scenario 1; solid), exponential increase (Scenario 2; dashed), and logarithmic increase (Scenario 3; dash‐dot). 7 of 15


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Figure 5. Gas pressure in Horizon A versus time for linear pressure increase (scenario 1). The three different stages of the simulation (Figure 3) are labeled. The dotted horizontal line represents the vertical effective stress under hydrostatic conditions in Horizon A (0.86 MPa).

to the SHR summit after ∼50 years. Thus we model the gas‐phase pressure increase at the SHR summit from 0 to the maximum pressure of 9.36 MPa over 50 years. In the first scenario, we model a linear pressure increase. In the second scenario, we model an initially slow pressure increase that increases exponentially with time. In the third scenario, we model an initially rapid pressure increase with a rate of increase that decreases logarithmically with time.

4.2. Scenario 1: Linear Pressure Increase [18] With a linear increase in pressure, Pg reaches

the hydrostatic vertical effective stress in Horizon A after 4.5 years (Figure 5). Gas moves into the fracture system in the RHSZ as hydrate forms in the fractures and increases the local salinity to the conditions required for three‐phase equilibrium. After an additional 78 days, the gas front reaches the seafloor and gas vents through the fracture system. Venting at the seafloor continues for 34 years until the methane reservoir is exhausted. The total time required from the start of the simulation to depletion of the methane reservoir is 39 years. No pressure depletion occurs in stage 3 of the simulation because the methane supply is exhausted before the entire time of pressure buildup (50 years) has elapsed, and the pressure in the system returns to hydrostatic.

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Figure 6. Gas pressure in Horizon A versus time for slow, exponentially increasing pressure increase (scenario 2).

continues for 30 years. After 26 years of venting, the gas pressure in Horizon A stops increasing and the pressure is depleted through the fracture system. This pressure depletion takes 4.6 years. The gas pressure drops below the fracture criterion after a total time of 55 years from the start of the simulation.

4.4. Scenario 3: Rapid, Logarithmically Decreasing Rate of Pressure Increase [20] In this scenario, Pg reaches the vertical effec-

tive stress in Horizon A after 100 days, and the gas front reaches the seafloor through the fracture system after another 69 days (Figure 7). Venting then occurs through the fracture system for 29 years, and the methane supply is exhausted after a total time of 30 years from the start of the simulation. As in scenario 1, in this case there is no pressure

4.3. Scenario 2: Slow, Exponentially Increasing Rate of Pressure Increase [19] In this scenario, Pg reaches the vertical effec-

tive stress in Horizon A after 25 years (Figure 6). Gas moves through the fracture system and vents to the seafloor after an additional 78 days. Venting

Figure 7. Gas pressure in Horizon A versus time for fast, logarithmically decreasing pressure increase (scenario 3). The three simulation stages (Figure 3) are not plotted since stages 1 and 2 are very brief. 8 of 15


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depletion since the methane supply is exhausted before the time for pressure buildup has elapsed.

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5. Discussion

gate the sensitivity of our results to these parameters, we ran several simulations with different values of these parameters. For this sensitivity analysis we assumed a linear pressure buildup (scenario 1).

5.1. Effect of the Shape of the Buildup Curve

[24] The cross‐sectional area of flow at the SHR

[21] In scenarios 1 and 3, the methane supply was

exhausted before the entire time for pressure buildup elapsed, while in scenario 2 the simulation progressed beyond the time for pressure buildup and included pressure depletion at the end of the simulation. This difference in behavior is driven by the difference in the rate of pressure increase, which affects the net flux of methane during the simulation. During stage 1, methane gas may flow out of Horizon A through the pore system, driven by the increasing gas pressure in Horizon A. Once fractures form, the pressure continues to increase in Horizon A during stage 2 until the gas front reaches the seafloor, at which point the gas pressure in Horizon A stops increasing and gas vents through the fracture system at a constant pressure gradient. Thus, the total time required to exhaust the methane reservoir is determined by the amount of methane that leaves Horizon A during stage 1, and the amount of pressure increase during stage 2, which determines the pressure gradient during venting in stage 3. [22] In scenario 1, enough methane is driven out of

Horizon A during stage 1 that only 34 years of venting through the fracture system are required to exhaust the methane supply. In scenario 2, more time elapses during stage 1, but the gas pressure in Horizon A is generally lower than in scenario 1, so less methane leaves the system during stage 1, and more time is required to exhaust the methane supply. In scenario 3, stage 1 is much shorter than in the other two scenarios. However, the rate of pressure increase is much faster during stage 2 than in the other two scenarios, so the gas pressure in Horizon A is much higher at the start of stage 3 (∼1.4 MPa compared with 0.9 MPa for scenario 1 and 0.84 MPa for scenario 2). This drives correspondingly higher flux during stage 3, which exhausts the methane supply quickly.

5.2. Sensitivity to Reservoir Volume and Venting Area [23] Significant sources of error in our simulations

are the estimates we made of the volume of methane in the reservoir, and the cross‐sectional area through which flow occurs at the SHR summit. To investi-

summit has an inverse relationship with the time venting occurs through the fracture system (simulation phase 3) (Figure 8a). Our estimate of 104 m2 results in slightly less than 35 years of venting. Doubling this area decreases the venting time by a factor of 2; similarly, increasing the area by a factor of 4 decreases the venting time by a factor of 4. Based on the observations of Tryon et al. [2002], it is unlikely that the cross‐sectional area of flow is larger than 9 × 104 m2, which would result in only ∼3 years of venting. Our assumptions therefore make our results represent a maximum time for flow evolution and reservoir depletion. [25] The reservoir volume has a roughly linear

relationship with total time required for reservoir exhaustion (Figure 8b). Increasing the volume by an order of magnitude from our initial estimate of 4.88 × 105 m3 causes the total time to increase by a factor of ∼6.5, while decreasing the volume by an order of magnitude decreases the total time by a factor of ∼4.8. The effect of reservoir volume is thus less significant than the effect of venting area. However, our estimate of reservoir volume is affected not only by the map dimensions, but also gas saturation and porosity. In reality, the true reservoir volume is probably less than the volume we estimated, since gas saturation is likely lower toward the edges of the reservoir, and the reservoir is somewhat smaller and more irregularly shaped than the rectangle we used for the estimate. Considering this, our results again represent upper limits on the time required for reservoir depletion.

5.3. Implications for Evolution of Fluid Flow at Southern Hydrate Ridge [26] Our results have important implications for

understanding the current state of flow at SHR and predicting how the flow system will evolve. At the gas migration rate estimated from differences between the 2000 and 2008 seismic surveys, the gas reservoir we interpret from seismic data will be exhausted on a time scale of years to a few decades after seafloor methane venting begins. Our sensitivity analysis shows that variations in reservoir volume or cross‐sectional area of fluid flow at the SHR summit region yield variations in the time required to exhaust the methane supply on the 9 of 15


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Figure 8. Sensitivity analysis assuming linear pressure increase (scenario 1). Our estimated parameters are represented by stars. (a) Effect of venting area on duration of venting at the seafloor (phase 3). (b) Effect of reservoir volume on total time for methane reservoir exhaustion.

order of decades to a few centuries. However, given our best estimates of these parameters, venting should occur for 30–50 years. Thus, the intermittent venting that has been observed at the summit of SHR [Tréhu and Bangs, 2001; Torres et al., 2002; Tryon et al., 2002; Bangs et al., 2011] should continue for a few more decades. The large volumes of methane gas that drive this venting behavior presumably are driven toward the summit of southern Hydrate Ridge with some periodicity since the main driving mechanism is assumed to be dewatering of the subducting wedge [e.g., Westbrook et al., 1994; Tryon et al., 2002], which itself is a transient process. U/Th ages of authigenic carbonates from the Hydrate Ridge area suggest that rapid expulsion of methane from the seafloor and associated authigenic carbonate formation recur on time scales of thousands to tens of thousands of years [Teichert et al., 2003]. Thus, once the current venting episode wanes, the next venting episode may not occur for several thousand years. [27] During the active venting phase of our simula-

tions (phase 3), we compute methane fluxes through

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the fracture system in the range 1.6–3.8 × 104 m yr−1 (5.5–13.3 × 106 mol yr−1 at seafloor conditions of 8 MPa and 277 K) depending on the pressure buildup curve. This is extremely rapid flux compared to the background fluid flux on the order of centimeters to decimeters per year measured away from active venting sites [Torres et al., 2002; Tryon et al., 2002]. However, flow rates up to 107 m yr−1 have been measured at some active sites at northern Hydrate Ridge [Torres et al., 2002], and it is reasonable to assume that similar flow rates may occur at discrete discharge points at SHR. However, flow rates at active vents are highly variable on time scales from hours to days [Tryon et al., 2002]. During the phase of active venting through the fracture system, it is probably more realistic to assume that high flux occurs episodically, mediated by tidal fluctuations or changes in bottom water temperature [e.g., Torres et al., 2002; Tryon et al., 2002; Teichert et al., 2003], rather than continuously as we model. Fauria and Rempel [2011] suggest that pulses of large methane flux through the fracture system may temporary lower the gas‐ phase pressure in the reservoir below the fracture criterion, providing an additional mechanism for episodic high methane flux and migration of methane gas in Horizon A toward the fractures. Such a pulsed discharge scenario would require more time to exhaust the methane supply. In general, the time required to develop fracture‐hosted hydrate deposits by this mechanism is much shorter than the time required to form massive hydrates such as the thousands of years suggested from pore water geochemistry and modeling results [Torres et al., 2002; Daigle and Dugan, 2010a]. This is due to the large fluid fluxes through the fracture system, which supply large volumes of methane to the RHSZ. [28] Our results show that the gas front propagates

through the fracture system in 70–80 days as hydrate forms in the fractures and increases the local salinity. Assuming the formation of the fractures themselves is a relatively rapid process (scale of hours to days [Valkó and Economides, 1995]), gas venting may not necessarily occur through the same fractures over the entire duration of gas venting. In the case of transient venting, fractures will be held open by gas pressure during active venting, and then will close when venting stops. Once venting resumes, the gas may exploit an entirely new set of fractures [e.g., Bangs et al., 2011]. This scenario may explain the abundant hydrate‐filled fractures encountered in image logs from SHR [Weinberger and Brown, 2006] that coexist with active gas venting. The hydrate‐filled 10 of 15


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fractures may be remnants of previous venting episodes. The time we calculate for the gas front to reach the seafloor is also affected by our modeling assumptions, such as capillary pressure response, relative permeability, and rate of hydrate formation. Since our model is an equilibrium hydrate formation model, we assume that hydrate forms instantly when methane is present within the RHSZ. This may result in underprediction of the time required for gas front propagation. The capillary pressure response is constrained by laboratory measurements, but the relative permeability is not. Therefore it is difficult to say exactly how these parameters may affect the results. [29] Widespread salinity anomalies are generally

not observed in the region around southern Hydrate Ridge, and we predict that they should be a transient phenomenon. The increase in pore fluid salinity that results from the gas front propagating through the fracture system is expected to be a local phenomenon confined to the fractures themselves that dissipates by lateral diffusion once the fracturing episode ends. Since our model is one‐dimensional, we do not compute the effects of lateral diffusion on salinity. During active gas venting, any salt lost to diffusion will be replenished within the fracture system by further formation of hydrate. Liu and Flemings [2006] show that for gas flux values typical of the active venting region at southern Hydrate Ridge (∼100 mol CH4 m−2 yr−1), the rate of salinity loss due to diffusion is negligible compared to the rate of salt production by further hydrate formation. Our assumption of no lateral diffusion of salt is therefore valid since we only model the system while the gas supply is active. Once the gas supply shuts down, the excess salt within the fracture will diffuse into the surrounding pore fluid. During this process, the salinity within the fracture csf is given by ! a ffi ; csf ¼ csw þ ðc0 csw Þerf pffiffiffiffiffiffiffi 4 Dws t

ð10Þ

where csw is the salinity of the surrounding pore fluid (equal to that of seawater), c0 is the initial salinity in the fracture, and a is the width of the fracture [Carslaw and Jaeger, 1986]. Assuming c0 = 13.75%, the maximum salinity we predict in our model, d = 1 mm, and Dws = 10−9 m2 s−1, the time from equation (10) required for the salinity within the fracture to decrease to within 1% of seawater salinity is 46 days. The presence of hydrate coating the fracture walls will increase the tortuosity of the diffusion paths out of the fracture, thereby

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reducing the effective diffusivity of salt in the pore fluid. Assuming a reduced diffusivity in this case of 10−11 m2 s−1, as suggested by Liu and Flemings [2007], the time required for equilibration increases to 13 years. Therefore, once the methane supply ceases, the salinity anomaly within the fractures will diffuse away rapidly. Assuming that large‐scale gas venting episodes occur on time scales of thousands of years based on the authigenic carbonate ages reported by Teichert et al. [2003], the salinity effects of a venting and fracturing episode will be completely erased by the time the next episode occurs. [30] Our results predict that fractures may nucleate

above Horizon A and propagate to the seafloor, allowing venting of methane gas directly from Horizon A. This result is somewhat at odds with the results of Daigle and Dugan [2010a], who predict that fractures at Hydrate Ridge will nucleate within a few tens of meters of the seafloor, as a result of gas moving through the RHSZ by porous medium flow as hydrate forms within the pore space and increases the local pore fluid salinity. However, their model does not consider gas pressure fluctuations, leaving capillary pressure of the gas phase as the only available fracturing mechanism. The model presented here is probably a more accurate representation of the system, since the gas pressure in Horizon A is currently estimated to be at or near the vertical effective stress [Tréhu et al., 2004]. This suggests that the system is currently in the active venting phase (simulation phase 3) and that fractures may easily nucleate above Horizon A. [31] Overall, our results show that gas migration,

fracture formation, and methane venting at the seafloor are transient events that can change over time scales of days to years at SHR, and that any observed features are likely to persist for only a few months to years, while any active venting of gas is likely to continue only for a few more decades. These results have broader implications for methane hydrate deposits worldwide since they demonstrate rapid formation of features (e.g., fractures, hydrate distribution, etc.) and variations in methane supply over short time scales.

5.4. General Implications for Hydrate‐Bearing Sites Worldwide [32] We show that a gas reservoir of finite volume

may produce transient episodes of hydraulic fracturing, rapid gas flux, and seafloor methane venting. While active venting is observed at many sites worldwide, many sites that currently have very low methane flux exhibit evidence of active venting and 11 of 15


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fracturing at some point in the past. For example, in the Krishna‐Godavari (K‐G) Basin offshore India, evidence of a paleo‐cold seep chemosynthetic community was recovered in cores at the top of a relict gas chimney structure identified in seismic images in an area containing abundant fracture‐ filling hydrate [Collett et al., 2007; Mazumdar et al., 2009; Riedel et al., 2010]. Similarly, at several sites in the Ulleung Basin offshore Korea that were drilled to investigate chimney structures identified in seismic images, abundant fracture‐filling hydrate was observed in cores and borehole images, but evidence of significant gas venting to the seafloor was not observed [Torres et al., 2011]. In both these cases, hydraulic fracturing and gas transport through the RHSZ are interpreted to have occurred at some point in the past, driven either by shale diapirism in the case of the K‐G Basin [Riedel et al., 2010] or fluctuating rates of methane supply in the case of the Ulleung Basin [Torres et al., 2011]. Our results suggest that these features form rapidly, over a period of a few decades, and that there may be a significant number of inactive sites worldwide where this process has occurred sometime in the past. While 1‐D, steady state models of hydrate accumulation [e.g., Rempel and Buffett, 1997; Xu and Ruppel, 1999; Davie and Buffett, 2001; Bhatnagar et al., 2007; Garg et al., 2008] are useful for providing insights into background conditions and the character of regional distribution of hydrate, understanding heterogeneous hydrate accumulations requires consideration of transient processes. In general, heterogeneous accumulations of methane hydrate likely develop over short time scales associated with pulses of high methane flux into the RHSZ. As the odds of observing these processes at a given site are low, the number of active methane vents worldwide suggests just how ubiquitous these processes are.

6. Conclusions

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and venting area at the seafloor, fractures will form within a few years of the onset of pressure buildup. Once fractures form, gas is able to move upwards through the RHSZ by formation of some hydrate in the fractures (40–80% of the fracture volume), which increases the local salinity to the conditions required for the presence of gas within the RHSZ. Gas reaches the seafloor by this process after 70– 80 days. The methane reservoir is then depleted by venting through the fracture system to the seafloor after an additional 30–50 years. Reasonable variations in reservoir volume or venting area from our estimates may increase or decrease this time roughly by a factor of 4 to 6. Our results show that the observed activity at southern Hydrate Ridge is part of a highly transient process involving methane gas migration, fracture genesis, and seafloor venting with variations on time scales of years to decades. In a broader sense, we illustrate the dynamic nature of hydrate deposits and the potential transience of many observed features.

Appendix A: Derivation of Expressions for Change in Methane Mass and Pressure Depletion [34] The gas flux qg out of Horizon A is given by Darcy’s law: qg ¼

kkrg @ Pg g gz ; g @z

ðA1Þ

where the quantity Pg‐rggz is the gas‐phase overpressure. The mass flux of methane out of Horizon A dm/dt can be determined by multiplying qg by gas density, area through which flow occurs, and volume of gas, which is equal to the product of gas saturation and porosity: kkrg @ dm ¼ g ASg 8qg ¼ g ASg 8 Pg g gz : dt g @z

ðA2Þ

[33] We model methane migration and fracture

generation at southern Hydrate Ridge with a one‐ dimensional model that incorporates fluid flow, methane hydrate formation, and fracturing behavior. The modeled reservoir size and migration of gas in the reservoir is based on geophysical observations from two seismic surveys acquired 8 years apart that show amplitude changes interpreted to be methane gas migrating through the reservoir that feeds active methane venting near the summit of southern Hydrate Ridge. We show that, for our estimates of reservoir size, migration rate,

This is equivalent to equation (7). [35] In stage 3 of the simulation, when pressure

drawdown begins, the change in pressure in Horizon A is related to the mass of methane lost from Horizon A. The ratio of pressure change to initial pressure DP/P0 is related to the ratio of methane mass lost from Horizon A to initial methane mass in Horizon A Dm/m by the ideal gas law: DP Dm ¼ RT : P0 mMCH 4

ðA3Þ

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Over an infinitesimal time step Dt, Dm is given from equation (A2) with the assumption that within the fracture system Sg = 1 and 8 = 8f : kkrg @ Dm ¼ g A8f Pg g gz Dt; g @z

ðA4Þ

which can be substituted for Dm in equation (A3) to yield RT kkrg @ DP Pg g gz ¼ g A8f Dt: P0 mMCH 4 g @z

ðA5Þ

In the limit as Dt → 0, this can be written as a differential equation: RT kkrg @ @P ¼ g A8f Pg g gz P0 : @t mMCH4 g @z

ðA6Þ

This is equivalent to equation (9).

Notation A Cross‐sectional area of gas venting [m2]. a Fracture aperture [m]. cxj Mass fraction of component x in phase j [kg kg−1]. j Dx Coefficient of molecular diffusion for component x in phase j [m2 s−1]. g Acceleration due to gravity [m s−2]. J Dimensionless capillary drainage function. k Intrinsic permeability [m2]. kf Fracture system permeability [m2]. krj Relative permeability of phase j. l Inter‐fracture spacing [m]. MCH4 Molar mass of methane [kg mol−1]. m Mass of methane in reservoir [kg]. Pc Gas capillary pressure [Pa]. Pj Pressure of phase j [Pa]. Pj* Overpressure of phase j [Pa]. ~ q j Flux of phase j [m s−1]. R Universal gas constant [J mol−1 K−1]. Sj Saturation of phase j [m3 m−3]. T Temperature [K]. t Time [s]. z Depth below seafloor [m]. mj Dynamic viscosity of phase j [Pa s]. rj Bulk density of phase j [kg m−3]. sgw Gas‐water interfacial tension [J m−1]. 8 Porosity [m3 m−3]. 8f Fracture porosity [m3 m−3].

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Acknowledgments [ 36 ] This material is based upon work supported by the Department of Energy, National Energy Technology Laboratory while holding a National Research Council Research Associateship Award, under award DE‐FC26‐05NT42248 (Daigle) and DOE/NETL Project DE‐FC26‐06NT42960 (Detection and Production of Methane Hydrate) (Dugan). The authors thank X. Liu for sharing the capillary pressure data for Hydrate Ridge sediments. Reviews from S. Garg and two anonymous reviewers helped strengthen this paper.

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