We simulate methane hydrate formation with multiphase flow and free gas within the regional hydrate stability zone (RHSZ). We find that hydrate distribution and fracture behavior are largely determined by the phase of the methane supply. We allow free gas to enter the RHSZ when porewater salinity increases to the value required for three-phase equilibrium. Fractures nucleate when the excess pore pressure exceeds the vertical hydrostatic effective stress. At Hydrate Ridge, where methane supply is dominantly free gas, hydrate saturation increases upwards and fractures nucleate high within the RHSZ, eventually allowing gas to vent to the seafloor. At Blake Ridge, where methane supply is dominantly in the dissolved phase, hydrate saturation is greatest at the base of the RHSZ; fractures nucleate here and in some cases could propagate through the RHSZ, allowing methane-charged water to vent to the seafloor.
 Significant fracture-hosted methane hydrates have been encountered at Keathley Canyon Block 151 in the northern Gulf of Mexico [Cook et al., 2008], at Hydrate Ridge offshore Oregon [Tréhu et al., 2006], and in the Krishna-Godavari Basin offshore India [Collett et al., 2007]. Daigle and Dugan  showed that hydraulic fractures can form in marine hydrate systems with sufficiently rapid methane supply and low initial sediment permeability; if methane supply is too slow or permeability too high relative to water flux, fracture-hosted hydrates, if present, most likely formed by hydrate heave or in preexisting fractures. The model assumes a constant flux of methane-charged water. However, flux in hydrate systems is often variable [e.g., Tryon et al., 2002], and field evidence indicates that methane may exist in some cases as free gas within the regional methane hydrate stability zone (RHSZ) [e.g., Wood and Ruppel, 2000; Tréhu et al., 2004]. We adapt the model of Daigle and Dugan  to investigate how variable flux and multiphase flow affect hydrate saturation and fracture generation.
 The RHSZ is the depth interval in which structure I methane hydrate is stable at seawater salinity (3.35% NaCl by mass) and hydrostatic pressure. Free gas may occur within the RHSZ if three-phase equilibrium conditions are met. Two processes that may allow this are increased fluid pressure driven by gas buoyancy [e.g., Flemings et al., 2003] and triple point temperature depression caused by excess porewater salinity [Zatsepina and Buffett, 1998]. We consider the latter case as excess salinity appears to be associated with gas occurrence in the RHSZ at Hydrate Ridge [Liu and Flemings, 2006] and in the Mackenzie Delta [Wright et al., 2005].
 We modify the model of Daigle and Dugan  to include multiphase flow with a constant basal pressure. This boundary condition reflects a large source reservoir analogous to a water-drive hydrocarbon system and is a more reasonable assumption than constant flux for many settings. We apply this model to Hydrate Ridge, a system with no water-phase overpressure [Dugan, 2003] and Blake Ridge, a system with water-phase overpressure of several MPa [Flemings et al., 2003]. Our results illustrate how the phase of methane supplied to the RHSZ affects hydrate and fracture distribution.
2. Hydrate Formation and Fracture Generation
 We simulate 1-D, multiphase flow with fixed geothermal gradient (dT/dz), seafloor depth (dsf) and seafloor temperature (Tsf). We solve mass balances for methane, salt, and water. Hydrate forms when the methane concentration exceeds the local solubility. We compute solubility using the method of Bhatnagar et al.  and update for changes in salinity using the method of Duan et al. . Fluxes are computed from Darcy's law. Water viscosity is assumed constant, and gas viscosity is computed from the Lennard-Jones potential [Bird et al., 2007]. Relative permeabilities are calculated using Corey's model [Bear, 1972] assuming residual water and gas saturations of 10% and 2%, respectively [e.g., Liu and Flemings, 2007]. As hydrate forms, we reduce permeability by assuming that hydrate forms a uniform coating on the pore walls [e.g., Kleinberg et al., 2003].
 The pressures of the water and gas phases (Pw, Pg) are linked by the capillary pressure Pc such that Pg = Pw + Pc. Pc is computed as
where ϕ is porosity, k is permeability, Sh is hydrate saturation, σgw is the gas-water interfacial tension (0.072 J m−1 [Henry et al., 1999]) and J is a dimensionless function that describes changes in Pc as gas displaces water [Bear, 1972; Liu and Flemings, 2007]. Equation (1) assumes that hydrate forms a uniform coating on grains. Initial conditions are zero methane concentration and salt concentration equal to seawater everywhere. Dissolved methane concentration at the base of the domain (twice the thickness of the RHSZ) is set equal to the solubility at the base of the RHSZ (BRHSZ). At the base of the domain, we specify a constant water-phase overpressure (pressure in excess of hydrostatic) Pw* and compute Pg from equation (1).
 Hydraulic fractures form when the total excess pore pressure exceeds the vertical hydrostatic effective stress (σvh′). We define the normalized overpressure as λT* = PT*/σvh′, where PT* is the sum of the water- and gas-phase overpressures, and assume fractures form when λT* = 1. We stop the simulation once fractures form. We assume that the sediment has no tensile strength or cohesion, and that hydrate does not affect sediment strength or local stress conditions. Since fine-grained marine sediments typically have small cohesion and tensile strength [Behrmann, 1991] and hydrate tends to increase sediment strength [e.g., Yun et al., 2007], the true time to fracture may be somewhat longer than we predict since PT* will have to overcome additional sediment strength. For shallow hydrate systems with low Sh, we expect these effects to be negligible.
 Our model for Hydrate Ridge assumes dsf = 800 m, Tsf = 277 K, dT/dz = 0.053 K m−1 [Tréhu, 2006]. ϕ and k are based on bulk density logs and laboratory measurements of permeability [Lee and Collett, 2006; Tan et al., 2006]. We compute Pc using the J-function of Liu and Flemings , and assume Pw* = 0 [Dugan, 2003]. The salinity at the BRHSZ increases to the triple point after 250 years; after this, free gas migrates upwards into the RHSZ. After 1.9 × 103 years, enough hydrate forms at 38 mbsf (Sh = 0.85) to increase PT* to the point where fractures form (Figure 1). Since more salt is required to reach the triple point as temperature and pressure decrease, Sh increases upwards within the RHSZ. This is consistent with trends of Sh inferred from porewater chlorinity [Shipboard Scientific Party, 2003] and acoustic logs [Lee and Collett, 2006] showing Sh increasing from ∼0 near the BRHSZ (∼140 mbsf) to ∼0.15 at 60–80 mbsf at Sites 1244, 1245, and 1250. Our computed Sh are much larger than this. This may be due in part to our J-function, which defines the Pc response as gas enters the pore space; the true Pc response for these sediments is unconstrained. The hydrate growth habit exerts additional control on permeability reduction and Sh. Pore-filling hydrate reduces permeability more rapidly than pore-coating hydrate [Liu and Flemings, 2007], allowing fractures to form at shorter time and lower Sh. Assuming pore-filling hydrate at Hydrate Ridge produces fractures lower in the RHSZ after 103 years with maximum Sh = 0.6 (Figure S1 of the auxiliary material), but this does not alter trends of Sh and salinity with depth.
 Our model for Blake Ridge assumes dsf = 2781 m, Tsf = 276.4 K, dT/dz = 0.04 K m−1 [Shipboard Scientific Party, 1996]. ϕ is based on the bulk density log from ODP Leg 164 Site 997 [Lee, 2000]. k and a J-function are estimated from pore throat measurements made by mercury injection capillary pressure [Henry et al., 1999]. We assume Pw* = 4 MPa at the base of the model domain from pressure core data [Flemings et al., 2003]. After 1.6 × 104 years, Sh = 0.72 at the BRHSZ (∼455 mbsf), and PT* at this point exceeds σvh′ (Figure 1). However, because of the water flux driven by the Pw*, the salinity within the RHSZ never increases to the point required for three-phase equilibrium. Thus methane is supplied to the RHSZ as a dissolved phase in the porewater. At the time when fracturing occurs, hydrate has formed in almost the entire RHSZ and Sh = 0.02–0.08 below 30 mbsf, except at the BRHSZ where Sh = 0.72. The trend of Sh decreasing upwards from a maximum at the BRHSZ is consistent with a system where methane is supplied only as a dissolved phase in the porewater [e.g., Rempel and Buffett, 1997], and matches the Sh values and trend with depth inferred from acoustic logs at Blake Ridge [Lee, 2000].
 The differences between Hydrate Ridge and Blake Ridge illustrate how Sh and fracture behavior are determined by the phase of methane supply (Figure 2). Hydrate Ridge is a gas-dominated system. Since there is no water flux (i.e., Pw* = 0), hydrate may only form if methane is supplied by gas flux. Fractures form at the top of the gas column where hydrate formation has caused a sufficient increase in Pc. Fractures will propagate upwards to the seafloor as λT* approaches 1 shallower in the RHSZ; this eventually will allow gas to vent to the seafloor. The result is a mixture of fracture-hosted and disseminated hydrate, since disseminated hydrate forms before fractures. This hydrate distribution is consistent with observations from image logs and cores at Hydrate Ridge [Shipboard Scientific Party, 2003; Weinberger and Brown, 2006]. Blake Ridge is a water-dominated system. The water flux, driven by Pw*, removes excess salt generated by hydrate formation, so while gas can exist below the RHSZ, methane may only be transported into the RHSZ by flux of methane-charged porewater. Fractures form at the BRHSZ and may propagate upwards as λT* approaches 1. This will result in focused water flux where fractures intersect the seafloor.
 Our results have additional implications for the hydrate systems at Hydrate Ridge and Blake Ridge. Hydrate Ridge is interpreted as a hydrate system in which methane is supplied from below the RHSZ [Claypool et al., 2006] at flow rates up to 300–1000 mm yr−1 at active seeps [Torres et al., 2002]; the shallowest sediments are Pleistocene in age [Chevallier et al., 2006], and the present configuration of the RHSZ is believed to have evolved following the last glacial maximum [Bangs et al., 2005]. We predict that fractures begin forming ∼1600 years after free gas enters the RHSZ, and that gas flux into the BRHSZ is ∼350 mm yr−1 at the time of fracture initiation. While we do not constrain the time required for fractures and free gas to reach the seafloor, fracturing and fracture propagation should be relatively rapid [Valkó and Economides, 1995]. Thus our results are consistent with age constraints, flow rates, and methane supply pathways observed at Hydrate Ridge, and support interpretations of Hydrate Ridge as a young, active hydrate province dominated by flux of methane gas from a deep reservoir.
 We are able to match the observed hydrate distribution at Blake Ridge after 1.6 × 104 years, but our predicted water flux and lack of gas in the RHSZ do not match observations. We predict a water flux of 67 mm yr−1 at the time of fracturing based on k, Sh, and Pw*, in contrast with 0.2 mm yr −1 inferred from porewater chlorinity [Egeberg and Dickens, 1999]; and free gas has been interpreted in the RHSZ from seismic data [Gorman et al., 2002]. There is evidence that water and gas at Blake Ridge may flow in focused zones along unconformity surfaces, resulting in fluctuating temperatures and pressures at the BRHSZ [Hornbach et al., 2008]. The gas column we predict below the RHSZ is consistent with observations from log and seismic data [Guerin et al., 1999; Lee, 2000], and pressure core data indicate that the gas is at or near the pressure required for fracturing [Flemings et al., 2003]. Hornbach et al.  report that critically-pressured gas columns are common beneath hydrate deposits, and we propose that they are characteristic features of water-dominated systems. The discrepancy between observations and our results suggests that hydrate accumulation at Blake Ridge is driven by episodic, focused flow, and that migration of gas through the RHSZ is controlled mainly by pressure fluctuations.
 Significant flux through hydrate systems may influence the temperature due to advective heat transport. To evaluate the validity of our assumption of constant geothermal gradient, we compute the Nusselt number Nu for each site. Nu is the ratio of total heat flow to heat flow due to conduction alone [Ingebritsen et al., 2006]:
where cf is the fluid heat capacity, ρf is fluid density and qf is Darcy velocity, T is average temperature in the RHSZ, and Km is the bulk sediment thermal conductivity (∼1.0 W m−1 K−1 [e.g., Tréhu, 2006]). At Hydrate Ridge, using our computed gas flux we obtain Nu = 1.0. At Blake Ridge, using our computed water flux we obtain Nu = 3.7. There will thus be a small component of advective heat transport at Blake Ridge, but very little at Hydrate Ridge. Additional perturbations to the temperature field could be caused by latent heat of hydrate formation [e.g., Garg et al., 2008]; hydrate formation releases heat, which increases the local temperature. Increased temperature requires lower salinity and thus lower Sh to reach three-phase equilibrium, so at Hydrate Ridge gas could propagate higher into the RHSZ, forming fractures closer to the seafloor. In reality the excess heat generated by hydrate formation could be removed efficiently by lateral conductive/advective heat transfer, which we do not include in our 1-D model.
 We simulate multi-phase fluid flow at Hydrate Ridge, a gas-dominated system, and Blake Ridge, a water-dominated system. At Hydrate Ridge, free gas enters the RHSZ as hydrate forms; the gas migrates upwards by fracturing the sediment, and eventually vents to the seafloor. This results in increasing Sh upwards in the RHSZ, hydrate distributed in the pore space and in fractures, and free gas throughout the RHSZ. At Blake Ridge, free gas is unable to enter the RHSZ because water flux removes excess salt before it reaches three-phase equilibrium. Hydrate forms throughout the RHSZ, with the highest Sh at the BRHSZ. Free gas may initiate fractures only at the BRHSZ. The critically-pressured column of gas that develops beneath the RHSZ is characteristic of water-dominated systems and affects sediment column stability. Our results here provide an important delineation of the differences between water-dominated and gas-dominated systems in terms of observable characteristics and shallow geohazard assessment.
 This work was supported by the Department of Energy/National Energy Technology Laboratory Methane Hydrate Fellowship (to H. Daigle) and DOE/NETL project DE-FC26-06NT42960. Additional support was provided by Rice University and Chevron. The authors thank Xiaoli Liu for helpful reviewer comments.