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Gas invasion into water-saturated, unconsolidated porous media: Implications for gas hydrate reservoirs
Earth and Planetary Science Letters 312 (2011) 188–193
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Earth and Planetary Science Letters journal homepage: www.elsevier.com/locate/epsl
Gas invasion into water-saturated, unconsolidated porous media: Implications for gas hydrate reservoirs Kristen E. Fauria a, b, Alan W. Rempel a,⁎ a b
Department of Geological Sciences, University of Oregon, United States Department of Civil and Environmental Engineering, University of California, Davis California 95616, United States
a r t i c l e
i n f o
Article history: Received 2 May 2011 Received in revised form 22 August 2011 Accepted 25 September 2011 Available online 1 November 2011 Editor: G. Henderson Keywords: gas hydrates multiphase flow gas transport bubbles fracture capillary forces
a b s t r a c t Gas transport through unconsolidated porous media has been a recent focus in studies of hydrate reservoir dynamics and is important in numerous other geophysical contexts. We conduct experiments to examine the controls on gas invasion through sieved sands that are suspended within the water column as air is injected slowly from below. We monitor the thickness of the free-gas column that accumulates beneath the sand to gauge the difference between the gas and liquid pressure, or overpressure, just prior to gas invading and passing through the sand layer. Comparing the threshold overpressures for initial gas invasion using different particle sizes, our experiments demonstrate the control of capillary forces when the effective stress supported by particle contacts is sufficiently large. At lower effective stresses (smaller sediment overburdens) we observe gas invasion before the capillary-controlled threshold overpressure is reached. These results demonstrate a transition from capillary invasion at high effective stresses to fracture-dominated invasion at low effective stresses. Moreover, video documentation reveals evidence for transitions from capillary to fracture-dominated behavior within single invasion episodes as the rising gas nears the sediment surface. After the initial invasion episode in each experiment, we infer that observed reductions in the overpressure needed for subsequent invasions are caused by bubble break-up and retention within the sediment column. These experiments highlight the importance of effective stress and pore size in determining the mode of gas passage through unconsolidated sediments. We discuss the implications of our findings for the dynamics of gas hydrate reservoirs and other geophysical systems. © 2011 Elsevier B.V. All rights reserved.
1. Introduction The buoyant rise of gas bubbles and other low-density fluids through liquid-infiltrated, unconsolidated porous media is of critical importance to the dynamics of gas hydrate (e.g., Buffett, 2000; Daigle and Dugan, 2010; Haeckel et al., 2004; Liu and Flemings, 2006, 2007; Torres et al., 2004) and conventional hydrocarbon reservoirs (e.g., Schowalter, 1979; Smith, 1966), the viability of some CO2 sequestration strategies (e.g., Ide et al., 2007; Juanes et al., 2006; Woods and Farcas, 2009), the venting of biogenic gasses from swamps, estuaries, and lakes (e.g., Algar and Boudreau, 2009, 2010; Barry et al., 2010; Boudreau et al., 2005), the efficacy of air sparging (e.g., Ahlfeld et al., 1994; Corapcioglu et al., 2004; Roosevelt and Corapcioglu, 1998), and the degassing of magmatic systems (e.g., Bachmann and Bergantz, 2006; Belien et al., 2010). Transport can only be initiated when conditions enable the buoyant phase to displace the more dense pore liquid and/or the solid particles. For example, in cases where the solid particles behave as a rigid matrix that is wetted by the liquid phase, the onset of
⁎ Corresponding author. E-mail address: [email protected] (A.W. Rempel). 0012-821X/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.epsl.2011.09.042
gas infiltration requires that the gas pressure overcome the capillary barrier to passing through constrictions, referred to below as “pore throats”. If pore throats are sufficiently small, however, the gas pressures that develop can become large enough to overcome the forces that hold solid particles together so that a fracture is initiated and accommodates comparatively rapid gas transport. Here, we describe a sequence of experiments in non-cohesive sands that probe the conditions under which gas invasion occurs by either overcoming capillary resistance or displacing particles and propagating a fracture. It has long been recognized that the migration and entrapment of hydrocarbons in commercially relevant concentrations is strongly influenced by the effects of capillarity (e.g., Schowalter, 1979; Smith, 1966). Non-wetting, buoyant fluids (i.e. gas or oil) are found in sediments beneath caprocks with pore throats that are too small to enable further displacement of the denser, wetting phase (i.e. water). Where the stratigraphy is favorable, a connected layer of the buoyant fluid can collect until its thickness becomes large enough that the pressure difference between the two fluids is sufficient to cause their interface to deform into the pore throats and push the wetting phase aside. Though common, such “capillary invasion” is not the only mode by which the buoyant fluid can be transported through more fine-grained porous media. Field data obtained from drilling
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operations where active natural oil and gas seeps occur (e.g., Reilly and Flemings, 2010) and from immediately beneath marine hydrate layers (e.g., Flemings et al., 2003; Tréhu et al., 2004) demonstrate that the pore pressure can increase to near lithostatic levels. The least compressive stress in marine sediments is typically expected to be oriented in the horizontal plane so these high pressures are expected to cause the dilation of fractures and promote rapid fluid escape (Mourgues et al., 2011). Geochemical evidence has tied the destabilization of gas hydrates in marine sediments to past episodes of climate change that involved the release of large volumes of greenhouse gasses (e.g., Dickens, 2003; Kennet et al., 2000). The amount of methane that can reach the atmosphere as a result of hydrate dissociation depends on whether the gas transport is sufficiently rapid to limit the oxidation of methane to form carbon dioxide, which is much more soluble in water and a less potent greenhouse gas. At the other end of the gas-mobility spectrum, the extreme pressures that develop when gas is trapped in sediments can pose a significant hazard. For example, the extraction of offshore oil commonly requires drilling through hydrate reservoirs and underlying free-gas reserves, potentially destabilizing the hydrate and releasing large quantities of methane into the pore space. The fate of the bubbles that result depends on whether gas is able to rise by displacing the pore liquid and/or the sediment particles. Several lines of evidence suggest that methane bubbles can coexist with gas hydrate and aqueous solutions within the gas hydrate stability zone (GHSZ). For example, episodic gas escape from the seafloor likely requires that a free gas source is feeding vents near the crest of Hydrate Ridge, on the Cascadia margin (Heeschen et al., 2003). Increases in bulk density that accompany the retrieval of sediment cores from the GHSZ have been interpreted to indicate the presence of in situ free gas that escaped between the time of core logging and the ship-board measurements (Tréhu et al., 2004). Seismic surveys show “wipe-out zones” within the GHSZ that are interpreted as areas where free gas is present in the sediment column (Liu and Flemings, 2006). Salinity profiles of near-seafloor sediment show that the chloride concentration in the pore water is elevated to greater than 1500 mM, consistent with the formation of hydrate from gas bubbles near the seafloor (Liu and Flemings, 2006). X-ray computer tomography (CT) images of near-seafloor sediment samples also suggest the presence of gas within hydrate layers (Abegg et al., 2003). The inferred free gas in the GHSZ at Hydrate Ridge and other hydrate reservoirs requires further explanation because the local pressure and temperature conditions imply that free gas is not in equilibrium with hydrate and aqueous solutions that have salinities typical of seawater (∼ 550 mM Cl −). Several mechanisms have been proposed to allow free gas to enter the GHSZ in high-flux regions. One hypothesis asserts that gas transport through the GHSZ takes place because the exclusion of salt during hydrate formation increases the pore–water salinity and modifies the equilibrium conditions to allow free gas and hydrate to coexist with liquid water at colder temperatures (shallower depths) than would otherwise be expected (Liu and Flemings, 2006, 2007; Milkov et al., 2004). These models predict the formation of hydrate from gas bubbles in the largest pore spaces that are available, thereby forcing gas transport through sequentially smaller pore throats until capillary effects seal the sediment from further gas invasion. Gas pressure subsequently builds until fractures form and facilitate rapid gas transport through the GHSZ. An alternative model that does not appeal to salinity changes argues that free gas is normally prevented from entering the GHSZ by capillary transport barriers, but that the pressure beneath the GHSZ eventually builds enough that gas is able to fracture the sediment column (Haeckel et al., 2004; Hornbach et al., 2004; Torres et al., 2004). Gas transport through the GHSZ is then presumed to be rapid enough that kinetic effects prevent the system from reaching thermodynamic equilibrium. These models of gas transport depend on a transition from capillary invasion, in which gas displaces liquid to move through the pore
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throats of a rigid network of sediment particles (see Fig. 1a.), to fracturedominated invasion, in which gas moves sediment particles out of the way (see Fig. 1b). Discrete element modeling predicts that gas will fracture cohesive sediments within the GHSZ when the particle radius is sufficiently small (i.e. 0.1 μm, see Fig. 15 of ref. (Jain and Juanes, 2009)), and that gas will move through the pore throats (capillary invasion) when the particle radius is larger (i.e. 50 μm, see Fig. 14 of ref. (Jain and Juanes, 2009)). Experiments by Boudreau et al. (2005) demonstrate that clays act initially like an elastic solid in response to stresses imparted by gas bubbles, but that higher pressures illicit a plastic response that results in the development of fractures so that gas bubbles form non-equant shapes that resemble corn flakes; by comparison gas bubbles exhibit more equant, rounded shapes in sands. The transition from capillary-controlled to fracture-dominated gas invasion has not previously been demonstrated in non-cohesive sediments. We describe experiments in sieved sands that enable us to delineate conditions under which gas displaces solid particles to propagate a fracture, as opposed to those in which the sediment matrix remains rigid and gas simply overcomes capillary forces to invade through pore throats, displacing the liquid. Our results show how this transition in behavior is controlled by changes in effective stress and the size of pore throats. After describing our experiments
water fixed particles
gas
a. Capillary invasion
water moving particles
gas
b. Fracture-dominated invasion Fig. 1. Schematic diagrams showing different modes of gas transport. a. Capillary invasion, in which the sediment matrix is rigid and gas transport occurs by displacing the liquid phase. b. Fracture-dominated invasion, in which sediment particles are forced aside by high gas pressures.
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and presenting our findings below, we discuss their implications for hydrate-reservoir dynamics. 2. Experimental design We designed a simple apparatus to monitor the difference in gas and water pressure, or overpressure, when a gas column first invades a water-saturated sand layer from below. Fig. 2 shows a portion of our plexiglass tank during a typical experiment. A wedge-shaped wire mesh was sealed against the tank sides with a thin rubber strip and loaded with a layer of sieved sand across the 15 × 5 cm tank crosssection to a specified thickness that we varied to control the effective stress at the mesh apex. The tank was filled initially with water and a hydraulic connection across the sand layer was maintained throughout the course of each experiment by an external hose that connected the top and bottom of the tank. We introduced gas (air) at a rate of approximately 80 ± 5 ml/min through a needle at the tank base. In each experiment, the gas migrated to the base of the sediment and accumulated in a wedge-shaped column beneath. We monitored the gas-column evolution and recorded its maximum thickness h immediately prior to the first instant that gas was seen to emerge from the other side of the sand layer. The pressure difference between a gas bubble Pg and the surrounding liquid Pl is equal to the product of the surface energy γgl and the curvature K of the gas–liquid interface so that Pg −Pl ¼ γg l K : At the base of the gas column, the gas–liquid interface is macroscopically flat (i.e. K ¼ 0) so we infer that Pg|base = Pl|base at this depth. Assuming that the gas may be treated as inviscid and neglecting its small density, this implies that the gas pressure at the column apex Pg|apex ≈ Pg|base = Pl|base. Since the water in the sediment column is essentially stagnant prior to gas invasion, it is expected to maintain a hydrostatic pressure gradient and the liquid pressure at the apex is Pl|apex ≈ Pl|base−ρlgh, where ρl ≈ 10 3 kg/m 3 is the liquid density, g ≈ 10 m/s 2 is the acceleration of gravity, and h is the gas-column
height. Near the apex we assume that the gas–liquid interface approaches a constant curvature Kapex as it begins to invade the pore throats above so that the gas–liquid pressure difference, or overpressure, can be written as ΔP≡Pg apex −Pl apex ≈ρl gh≈γgl Kapex :
ð1Þ
The maximum curvature Kc that can be attained before gas infiltrates the sediment pores is controlled by the size of pore throats near the apex so that for the idealized case where the gas–liquid interface takes the form of a sequence of hemispherical caps of radius Rc, we have that Kc ¼ 2=Rc . Eq. (1) predicts that when the sediment matrix behaves in a rigid fashion so that gas invasion through pore throats of a fixed radius Rc is inhibited by capillary forces, the critical gas-column height needed to initiate infiltration approaches a constant value of hc ¼ γgl Kc =ðρl g Þ≈2γgl =ðρl gRc Þ. In the field of petroleum engineering the overpressure ρlghc is referred to as the “displacement pressure” (e.g., Smith, 1966). Control over the typical size of pore throats Rc is achieved in our apparatus by varying the particle size in the sediment layer (to ensure that the mesh had a negligible influence on gas transport, the screens were also changed so that in all experiments opening dimensions were comparable to the average particle size and larger than pore constrictions). We also have control over the sediment thickness H that overlies the mesh apex. When transport is dominated by capillary-invasion we expect that the gas-column height h at the onset of gas invasion should be independent of H. However, this only holds when the sediment particles are prevented from moving, as is reasonable when the effective stress supported by particle contacts is sufficiently high. By adjusting the value of H we control the vertical component of the effective stress immediately above the gas column as ′
σ v ≈ðρs −ρl Þgð1−ϕÞH;
ð2Þ
where ρs ≈ 2.65 × 10 3 kg/m 3 is the density of the sediment particles, and ϕ ≈ 0.25 ± 0.05 is the porosity. We conducted experiments using three different size classes of sand that were sieved to limit the range of particle diameters between a) 1.83–2.63 mm, b) 0.84–1.00 mm, and c) 0.45–0.71 mm. The particles were introduced gradually at the top of the water-filled tank and settled under gravity to form a random-close-packed network on top of the mesh. In all of our experiments we used a quartz-rich sand that is preferentially wetted by the liquid rather than the gas phase. The results described below support our expectation that the characteristic sizes of the pore throats that inhibit capillary infiltration scale with particle size. For each particle size, we controlled the thickness H of sediment and recorded the gas-column thickness h at which gas invasion was observed. Between experiments we used a rod to mix the sand to reduce any preferential alignment of the sand particles and to remove small bubbles that were trapped during previous invasion episodes. 3. Results
Fig. 2. Experimental set-up. Gas rises into a water-filled plexiglass tank and accumulates in a gas column beneath a sand layer that is suspended on a coarse wire mesh. The sand layer thickness H and gas column height h are used to calculate the effective stress σ′v and gas overpressure ΔP, as defined in the text.
For each experiment, we used Eq. (1) to calculate the overpressure ΔP using the observed gas-column height at which gas first infiltrated the sediments — termed “primary invasion” below. Fig. 3 shows our results for ΔP during primary invasion as a function of the effective stress σ′v calculated from Eq. (2) for each imposed sediment thickness. As expected for cases where gas invades the pore space by overcoming capillary forces, at high effective stress we observe that the overpressure approaches a constant level that depends inversely on the typical particle size. The labeled dashed lines give the average of the overpressure values displayed with the plain symbols; for convenience, we refer to these as the capillary overpressures ΔPc below.
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1400
500
0.84−1.00 mm, σv’≈270 Pa
1170 Pa
1200
1.83−2.63 mm, σ ’≈390 Pa
400
Overpressure, Δ P (Pa)
Overpressure, Δ P (Pa)
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1000 ′ ΔP (σ )→
800
f
v
520 Pa particle diameters:
600 400
0.45−0.71 mm
200 Pa
200
v
primary invasion
300
200
160 Pa
100
0.84−1.00 mm
110 Pa
1.83−2.63 mm 0 0
200
400
600
800
1000
1200
0
1400
0
Effective Stress, σv′ (Pa) Fig. 3. Overpressure ΔP required to initiate primary gas invasion as a function of the imposed effective stress σ′v for the three different ranges of particle diameters noted in the legend. Labeled horizontal dashed lines show threshold capillary overpressures ΔPc obtained as averages of the nearby plain symbols. Dotted line shows the best fit linear relation ΔPf = 1.9σ′v−97 Pa to the data highlighted with circled symbols (R2 ≈ 0.93). See text for further discussion.
The capillary overpressures are larger for smaller particle sizes; the ratios of ΔPc between the different particle sizes that we used are comparable to the expected ratios of pore throat sizes and corresponding gas–liquid interfacial curvatures at the onset of infiltration. The circled symbols in Fig. 3 at lower effective stresses all have notably lower ΔP than the capillary overpressures ΔPc needed for primary invasion at higher effective stresses. The dotted black line labeled ΔPf(σ′v) gives the least-squares best linear fit to these circled symbols, which are drawn from the data for all three particle-size classes. The good fit suggests that gas invasion occurs at a threshold overpressure that increases with effective stress and does not depend on the sediment particle size. This is consistent with the expectation that gas can displace sediment particles and invade the sediments by propagating a fracture when the effective stress is sufficiently low that ΔPf b ΔPc. The displacement of sediment particles is expected to begin when the overpressure exceeds the least compressive stress, which in natural sediments is typically in the horizontal plane. In our experiments the proximity of the container walls may cause enhanced resistance to lateral particle motion. Assuming that σ′v and the least compressive stress are nevertheless proportional to each other, the inferred linear dependence of ΔPf on σ′v is in agreement with the predictions of hydraulic fracture models applied to petroleum reservoirs (Mourgues et al., 2011). After the primary gas invasion episodes, all of our experiments require lower levels of overpressure to induce gas infiltration during subsequent, or secondary episodes. Fig. 4 summarizes the observations from two experimental runs, showing the peak overpressure for six secondary invasion episodes through the 0.84–1.00 mm particle diameter sediment and eight secondary invasion episodes through the 1.83–2.63 mm sediment. The minimum overpressure that is reached when gas escape terminates is also recorded for both the primary and secondary invasion episodes. Fig. 4 displays one example where the effective stress was sufficiently high that primary gas invasion occurred within the capillary-dominated regime (black stars), and one example where the effective stress was low enough that primary gas invasion was fracture-controlled. We expect capillary-invasion to take place without displacing the sediment particles and we do not discern a qualitative difference between the subsequent behavior for the two cases. This suggests that the lower overpressures that characterize secondary invasion episodes are likely caused by some mechanism other than the enlargement of pore throats near the wedge apex.
20
40
60
80
100
Elapsed Time (s) Fig. 4. Overpressure ΔP(h) time series inferred from the observed gas-layer thicknesses h after the primary gas invasion episodes for two illustrative examples with the particle size ranges and effective stress levels noted in the legend. Average overpressures required for secondary invasion are shown with the labeled dot-dashed lines. See text for further discussion.
The lower overpressures required for secondary invasion are consistent with a mechanism involving bubble break-up and retention in the sediment column (Belien et al., 2010). Prior to primary gas invasion episodes, we took measures to ensure that no bubbles were present in the sediment column. Following some experiments we observed, however, that bubbles remained in the sand after gas invasion episodes. If gas bubbles left behind in the sand were connected to the gas column below, then the effective column height would be larger than its measured thickness below the wedge apex. Assuming a trapped gas thickness above the wedge apex of δh and that the liquid pressure readjusts to a hydrostatic distribution between invasion episodes, the overpressure at the top of the trapped portion of the gas column exceeds the value inferred at the wedge apex by δP = ρlgδh, and the effective stress is lower than the level inferred near the apex by δσ′v = (ρs −ρl)g(1−ϕ)δh. For the data shown in Fig. 4, if we assume that secondary invasion episodes follow the fracture-dominated trend established for the primary invasion episodes (shown by the dotted line in Fig. 3) then we expect ΔP(h+ δh) ≈1.9σ′v(H−δh) + 97 Pa. Using the arguments above to calculate ΔP(h+ δh) ≈ΔP(h)+ δP and σ′v(H−δh) ≈σ′v(H)−δσ′v leads to an inferred trapped gas thickness of
δh≈
1:9σ ′v ðH Þ−97Pa−ΔP ðhÞ ; ρl g þ 1:9ðρs −ρl Þg ð1−ϕÞ
where ΔP(h) and σ′v(H) are calculated from Eqs. (1) and (2) using the observed values of h and H. From this calculation, the data summarized in Fig. 4 imply that the average trapped gas thickness extends 7.9 mm (the values for all 6 episodes range from 6.1 to 9.0 mm) above the wedge apex for the sediment with particle diameters ranging from 0.84 to 1.00 mm (the total sediment layer thickness was 22 mm for this case) and 16 mm (the values for all 8 episodes range from 16 to 17 mm) above the wedge apex for the sediment with particle diameters ranging from 1.83 to 2.63 mm (the total sediment layer thickness was 32 mm). The corresponding average overpressures ΔPδh at the top of the inferred trapped-gas layers are approximately 230 Pa within the 0.84–1.00 mm diameter sand and 270 Pa within the 1.83–2.63 mm diameter sand. Since ΔPδh b ΔPc ≈ 520 Pa for the 0.84–1.00 mm diameter sand, fracture-dominated invasion initiated from the top of a connected trapped-gas column is consistent with the secondary invasion data for this sediment.
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For the 1.83–2.63 mm diameter sand, the value of ΔPδh ≈ 270 Pa calculated assuming fracture-dominated invasion is greater than ΔPc ≈ 200 Pa. This suggests that we should have expected invasion to occur at a lower average ΔP(h) than the 110 Pa observed for this case. If we assume that secondary invasion follows the capillarycontrolled trend instead so that ΔP(h) + δP ≈ ΔPc, the trapped gas thickness is inferred to be
δh≈
ΔPc −ΔP ðhÞ : ρl g
This would imply that the trapped gas thickness extends approximately 9.2 mm (the values for all 8 episodes range from 7.4 to 12.5 mm) above the wedge apex for the 1.83–2.63 mm diameter sediment. For the 0.84–1.00 mm diameter sand, a similar calculation would imply a value of δh that exceeds the entire sediment layer thickness. We infer that the secondary invasion episodes shown in Fig. 4 that followed a fracture-dominated primary invasion are also most consistent with a fracture-dominated mechanism during secondary invasion. By contrast, the secondary invasion episodes that followed a capillary-controlled primary invasion are most consistent with a capillary-controlled mechanism during secondary invasion as well. During some experiments conducted at high σ′v we were able to observe a transition from capillary-controlled invasion to sediment fracturing within a single invasion episode. A photograph capturing this behavior is shown in Fig. 5. This primary invasion episode began with ΔP ≈ ΔPc. As gas neared the sediment surface, however, a fracture opened near the tank wall and we were able to observe the macroscopic displacement of sediment particles in the upper few centimeters. As gas rises in a thick sediment column, it encounters lower and lower overburden stress. A transition to fracturepropagated invasion occurs when the effective stress is low enough that the overpressure overcomes the resisting interparticle stresses. A further consequence of such behavior is the development of pockmark craters at the sediment surface, as shown in Fig. 6.
Fig. 5. Fracturing in the upper centimeters of a thick sediment column (particle diameters 0.45–0.71 mm, σ′v ≈ 103 Pa, black ticks on right side are at 5 cm intervals). Although the overpressure at the onset of gas invasion was consistent with a capillary-controlled mechanism, the reduced effective stress near the sediment surface facilitated fracture development just below the point of gas exit from the saturated sand.
Fig. 6. View from the top of a sediment layer showing a crater created during gas escape from the 0.45–0.71 mm sediment. Graph paper grid contains 2 mm squares.
The online supplementary information contains links to video clips showing representative experimental runs.
4. Discussion and conclusions Our experiments in non-cohesive, water-infiltrated sediments demonstrate a transition from capillary-controlled gas invasion at higher effective stresses to fracture-dominated invasion at lower effective stresses. The overpressure required for gas invasion can be much lower than that which would be consistent with capillary resistance to invading pore throats of a typical size in undisturbed sediments. This suggests the possibility that free gas might be much more mobile in marine sediments than would otherwise be expected. It also suggests that the potential for fluid migration in other contexts, for example during the sequestration of CO2, might be larger than expected from model treatments that ignore the potential for buoyant fluids to open fractures (e.g., Woods and Farcas, 2009). The pronounced reductions we observed in the overpressure required for secondary invasion episodes are consistent with a prominent role for bubble break-up and gas retention within the sediment during our experiments. Bubbles that are trapped within the GHSZ would be expected to promote hydrate formation in highly localized zones and may explain some of the segregated hydrate nodules and filled fractures that are sometimes observed (e.g. Borowski, 2004; Haeckel et al., 2004; Hester and Brewer, 2009; Torres et al., 2008). Importantly, we find that fractures develop in an otherwise nominally homogeneous sediment. However, in marine sediments that are pervaded by faults, we would expect that fractures would preferentially follow these preexisting zones of weakness (Hornbach et al., 2004). If the gas retained between successive secondary invasion episodes tends to occupy the same pores, this suggests a mechanism for developing preferential migration pathways that may limit the efficacy of remediation efforts by air sparging (Ahlfeld et al., 1994). Once gas invasion begins, our experiments are characterized by the escape of large enough gas volumes that the overpressure drops well below the level required to sustain ongoing gas escape (e.g. see Fig. 4). Instead, we find that gas invasion is episodic and the transport time through a sediment layer is much shorter than the time between invasion episodes. If similar behavior is typical of free-gas transport through the GHSZ this would favor more efficient delivery of methane to the seafloor than a scenario involving gradual, continuous gas release. Applying these results to the retention of commercial hydrocarbon reservoirs, this also suggests a mechanism for causing hydrocarbon reserves beneath some caprocks to fluctuate in thickness, but remain considerably
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thinner than required for the overpressure to reach the displacement pressure (Schowalter, 1979; Smith, 1966). Gas invasion can transition from capillary invasion to fracturedominated invasion as gas nears the sediment surface, where the effective stress is reduced. In our experiments, such behavior is characterized by the formation of crater-like pockmarks. The much larger pockmarks sometimes observed on the sea floor (Davy et al., 2010) may require sediment failure over a depth range comparable to the entire GHSZ thickness, or the thickness above some other, deeper seal (Reilly and Flemings, 2010). The effective stresses encountered towards the base of most gas hydrate deposits are much higher than those in our experiments. However, the grain sizes that are typical of marine sediments can be much smaller than the sediments we used so that the capillary entry pressures are also higher. Our experiments suggest that fracturedominated gas invasion is most likely to occur when free gas is present close to the seafloor. However, the non-hydrostatic pressure gradients associated with upwards fluid flow can help to unload sediment grains and facilitate fracture-dominated invasion at greater depths (Flemings et al., 2003; Reilly and Flemings, 2010; Tréhu et al., 2004). Poroelastic effects may also be important for enabling particle rearrangements when the gas overpressure is much lower than the capillary entry pressure. Experiments focused on examining these complications would be a useful extension of the current work. Acknowledgments Funding for this work was provided by grant #47851-G8 from the American Chemical Society's Petroleum Research Fund. The revised manuscript benefitted from the thoughtful comments of two anonymous reviewers, relayed to us by Editor Gideon Henderson. Appendix A. Supplementary data Supplementary data to this article can be found online at doi:10. 1016/j.epsl.2011.09.042. References Abegg, F., Bohrmann, B., Freitag, J., Kuhs, W., 2003. Fabric of gas hydrate in sediments from Hydrate Ridge—results from ODP Leg 204 samples. Geo-Mar. Lett. 27, 269–277. Ahlfeld, D.P., Dahmani, A., Ji, W., 1994. A conceptual model of field behavior of air sparging and its implications for application. Ground Water Monit. Rem. 14, 132–139. Algar, C.K., Boudreau, B.P., 2009. Transient growth of an isolated bubble in muddy finegrained sediments. Geochim. Cosmochim. Acta 73, 2581–2591. Algar, C.K., Boudreau, B.P., 2010. Stability of bubbles in a linear elastic medium: implications for bubble growth in marine sediments. J. Geophys. Res. 115, F03012. doi:10.1029/2009JF001312. Bachmann, O., Bergantz, G.W., 2006. Gas percolation in upper-crustal silicic crystal mushes as a mechanism for upward heat advection and rejuvenation of nearsolidus magma bodies. J. Volcanol. Geotherm. Res. 149, 85–102. Barry, M.A., Boudreau, B.P., Johnson, B.D., Reed, A.H., 2010. First-order description of the mechanical fracture behavior of fine-grained surficial marine sediments during gas bubble growth. J. Geophys. Res. 115, F04029. doi:10.1029/2010JF001833. Belien, B., Cashman, K.V., Rempel, A.W., 2010. Gas accumulation in particle-rich suspensions and implications for bubble populations in crystal-rich magma. Earth Planet. Sci. Lett.. doi:10.1016/j.epsl.2010.06.014. Borowski, W.S., 2004. A review of methane and gas hydrates in the dynamic, stratified system of the Blake Ridge region, offshore southeastern North America. Chem. Geol. 205, 311–346.
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Boudreau, B.P., Algar, C., Johnson, B.D., Croudace, I., Reed, A., Furukawa, Y., Dorgan, K.M., Jumars, P.A., Grader, A.S., Gardiner, B.S., 2005. Bubble growth and rise in soft sediments. Geology 33, 517–520. Buffett, B.A., 2000. Clathrate hydrates. Annu. Rev. Earth Planet. Sci. 28, 477–507. Corapcioglu, M.Y., Cihan, A., Drazenovic, M., 2004. Rise velocity of an air bubble in porous media: theoretical studies. Water Resour. Res. 40, W04214. doi:10.1029/ 2003WR002618. Daigle, H., Dugan, B., 2010. Effects of multiphase methane supply on hydrate accumulation and fracture generation. Geophys. Res. Lett. 37, L20301. doi:10.1029/ 2010GL044970. Davy, B., Pecher, I., Wood, R., Carter, L., Gohl, K., 2010. Gas escape features off New Zealand: Evidence of massive release of methane from hydrates. Geophys. Res. Lett. 37, L21309. doi:10.1029/2010GL045184. Dickens, G.R., 2003. Rethinking the global carbon cycle with a large, dynamic and microbially mediated gas hydrate capacitor. Earth Planet. Sci. Lett. 213, 169–183. Flemings, P.B., Liu, X., Winters, W.J., 2003. Critical pressure and multiphase flow in Blake Ridge gas hydrates. Geology 31, 1057–1060. Haeckel, M., Suess, E., Wallman, K., Rickert, D., 2004. Rising methane gas bubbles form massive hydrate layers at the seafloor. Geochim. Cosmochim. Acta 68, 4335–4345. Heeschen, K.U., Trehu, A.M., Collier, R.W., Suess, E., Rehder, G., 2003. Distribution and height of methane bubble plumes on the Cascadia margin characterized by acoustic imaging. Geophys. Res. Lett. 30. doi:10.1029/2003GL016974. Hester, K.C., Brewer, P.G., 2009. Clathrate hydrates in nature. Annu. Rev. Marine Sci. 1, 303–327. Hornbach, M.J., Saffer, D.M., Holbrook, W.S., 2004. Critically pressured free-gas reservoirs below gas-hydrate provinces. Nature 427, 142–144. Ide, S.T., Jessen, K., Orr Jr., F.M., 2007. Storage of CO2 in saline aquifers: effects of gravity, viscous, and capillary forces on amount and timing of trapping. Int. J. Greenhouse Gas Control 1, 481–491. Jain, A.K., Juanes, R., 2009. Preferential mode of gas invasion in sediments: grain-scale mechanistic model of coupled multiphase fluid flow and sediment mechanics. J. Geophys. Res. 114. doi:10.1029/2008JB006002. Juanes, R., Spiteri, E.J., Orr, F.M., Blunt, M.J., 2006. Impact of relative permeability hysteresis on geological CO2 storage. Water Resour. Res. 42, W12418. doi:10.1029/ 2005WR004806. Kennet, J.P., Cannariato, K.G., Hendy, I.L., Behl, R.J., 2000. Carbon isotopic evidence for methane hydrate instability during quaternary interstadials. Science 288, 128–133. Liu, X., Flemings, P.B., 2006. Passing gas through the hydrate stability zone at southern Hydrate Ridge offshore Oregon. Earth Planet. Sci. Lett. 241, 211–226. Liu, X., Flemings, P.B., 2007. Dynamic multiphase flow model of hydrate formation in marine sediments. J. Geophys. Res. 112, B03101. doi:10.1029/2005JB004227. Milkov, A.V., Dickens, G.R., Claypool, G.E., Lee, Y.-J., Borowski, W.S., Torres, M.E., Xu, W., Tomaru, H., Tréhu, A.M., Schultheiss, P., 2004. Co-existence of gas hydrate, free gas, and brine within the regional gas hydrate stability zone at the southern summit of Hydrate Ridge (Oregon margin): evidence from prolonged degassing of a pressurized core. Earth Planet. Sci. Lett. 222, 829–843. Mourgues, R., Gressier, J.B., Bodet, L., Bureau, D., Gay, A., 2011. “Basin scale” versus “localized” pore pressure/stress coupling — implications for trap integrity evaluation. Mar. Pet. Geol. 28, 1111–1121. Reilly, M.J., Flemings, P.B., 2010. Deep pore pressures and seafloor venting in the Auger Basin, Gulf of Mexico. Basin Res. 22, 380–397. Roosevelt, S.E., Corapcioglu, M.Y., 1998. Air bubble migration in a granular porous medium: experimental studies. Water Resour. Res. 34, 1131–1142. Schowalter, T.T., 1979. Mechanics of secondary hydrocarbon migration and entrapment. AAPG Bull. 63, 623–760. Smith, D.A., 1966. Theoretical considerations of sealing and non-sealing faults. AAPG Bull. 50, 363–374. Torres, M.E., Wallmann, K., Tréhu, A.M., Bohrmann, G., Borowski, W.S., Tomaru, H., 2004. Gas hydrate growth, methane transport, and chloride enrichment at the southern summit of Hydrate Ridge, Cascadia margin off Oregon. Earth Planet. Sci. Lett. 226, 225–241. Torres, M.E., Tréhu, A.M., Cespedes, N., Kastner, M., Wortmann, U.G., Kim, J.H., Long, P., Malinverno, A., Pohlman, J.W., Riedel, M., Collett, T., 2008. Methane hydrate formation in turbidite sediments of northern Cascadia IODP Expedition 311. Earth Planet. Sci. Lett. 271, 170–180. Tréhu, A.M., Flemings, P.B., Bangs, N.L., Chevalier, J., Gracia, E., Johnson, J., Liu, C.-S., Liu, X., Reidel, M., Torres, M.E., 2004. Feeding methane vents and gas hydrate deposits at south Hydrate Ridge. Geophys. Res. Lett. 31, L23310. doi:10.1029/2004GL021286. Woods, A.W., Farcas, A., 2009. Capillary entry pressure and the leakage of gravity currents through a sloping layered permeable rock. J. Fluid Mech. 618, 361–379.
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Earth and Planetary Science Letters journal homepage: www.elsevier.com/locate/epsl
Gas invasion into water-saturated, unconsolidated porous media: Implications for gas hydrate reservoirs Kristen E. Fauria a, b, Alan W. Rempel a,⁎ a b
Department of Geological Sciences, University of Oregon, United States Department of Civil and Environmental Engineering, University of California, Davis California 95616, United States
a r t i c l e
i n f o
Article history: Received 2 May 2011 Received in revised form 22 August 2011 Accepted 25 September 2011 Available online 1 November 2011 Editor: G. Henderson Keywords: gas hydrates multiphase flow gas transport bubbles fracture capillary forces
a b s t r a c t Gas transport through unconsolidated porous media has been a recent focus in studies of hydrate reservoir dynamics and is important in numerous other geophysical contexts. We conduct experiments to examine the controls on gas invasion through sieved sands that are suspended within the water column as air is injected slowly from below. We monitor the thickness of the free-gas column that accumulates beneath the sand to gauge the difference between the gas and liquid pressure, or overpressure, just prior to gas invading and passing through the sand layer. Comparing the threshold overpressures for initial gas invasion using different particle sizes, our experiments demonstrate the control of capillary forces when the effective stress supported by particle contacts is sufficiently large. At lower effective stresses (smaller sediment overburdens) we observe gas invasion before the capillary-controlled threshold overpressure is reached. These results demonstrate a transition from capillary invasion at high effective stresses to fracture-dominated invasion at low effective stresses. Moreover, video documentation reveals evidence for transitions from capillary to fracture-dominated behavior within single invasion episodes as the rising gas nears the sediment surface. After the initial invasion episode in each experiment, we infer that observed reductions in the overpressure needed for subsequent invasions are caused by bubble break-up and retention within the sediment column. These experiments highlight the importance of effective stress and pore size in determining the mode of gas passage through unconsolidated sediments. We discuss the implications of our findings for the dynamics of gas hydrate reservoirs and other geophysical systems. © 2011 Elsevier B.V. All rights reserved.
1. Introduction The buoyant rise of gas bubbles and other low-density fluids through liquid-infiltrated, unconsolidated porous media is of critical importance to the dynamics of gas hydrate (e.g., Buffett, 2000; Daigle and Dugan, 2010; Haeckel et al., 2004; Liu and Flemings, 2006, 2007; Torres et al., 2004) and conventional hydrocarbon reservoirs (e.g., Schowalter, 1979; Smith, 1966), the viability of some CO2 sequestration strategies (e.g., Ide et al., 2007; Juanes et al., 2006; Woods and Farcas, 2009), the venting of biogenic gasses from swamps, estuaries, and lakes (e.g., Algar and Boudreau, 2009, 2010; Barry et al., 2010; Boudreau et al., 2005), the efficacy of air sparging (e.g., Ahlfeld et al., 1994; Corapcioglu et al., 2004; Roosevelt and Corapcioglu, 1998), and the degassing of magmatic systems (e.g., Bachmann and Bergantz, 2006; Belien et al., 2010). Transport can only be initiated when conditions enable the buoyant phase to displace the more dense pore liquid and/or the solid particles. For example, in cases where the solid particles behave as a rigid matrix that is wetted by the liquid phase, the onset of
⁎ Corresponding author. E-mail address: [email protected] (A.W. Rempel). 0012-821X/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.epsl.2011.09.042
gas infiltration requires that the gas pressure overcome the capillary barrier to passing through constrictions, referred to below as “pore throats”. If pore throats are sufficiently small, however, the gas pressures that develop can become large enough to overcome the forces that hold solid particles together so that a fracture is initiated and accommodates comparatively rapid gas transport. Here, we describe a sequence of experiments in non-cohesive sands that probe the conditions under which gas invasion occurs by either overcoming capillary resistance or displacing particles and propagating a fracture. It has long been recognized that the migration and entrapment of hydrocarbons in commercially relevant concentrations is strongly influenced by the effects of capillarity (e.g., Schowalter, 1979; Smith, 1966). Non-wetting, buoyant fluids (i.e. gas or oil) are found in sediments beneath caprocks with pore throats that are too small to enable further displacement of the denser, wetting phase (i.e. water). Where the stratigraphy is favorable, a connected layer of the buoyant fluid can collect until its thickness becomes large enough that the pressure difference between the two fluids is sufficient to cause their interface to deform into the pore throats and push the wetting phase aside. Though common, such “capillary invasion” is not the only mode by which the buoyant fluid can be transported through more fine-grained porous media. Field data obtained from drilling
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operations where active natural oil and gas seeps occur (e.g., Reilly and Flemings, 2010) and from immediately beneath marine hydrate layers (e.g., Flemings et al., 2003; Tréhu et al., 2004) demonstrate that the pore pressure can increase to near lithostatic levels. The least compressive stress in marine sediments is typically expected to be oriented in the horizontal plane so these high pressures are expected to cause the dilation of fractures and promote rapid fluid escape (Mourgues et al., 2011). Geochemical evidence has tied the destabilization of gas hydrates in marine sediments to past episodes of climate change that involved the release of large volumes of greenhouse gasses (e.g., Dickens, 2003; Kennet et al., 2000). The amount of methane that can reach the atmosphere as a result of hydrate dissociation depends on whether the gas transport is sufficiently rapid to limit the oxidation of methane to form carbon dioxide, which is much more soluble in water and a less potent greenhouse gas. At the other end of the gas-mobility spectrum, the extreme pressures that develop when gas is trapped in sediments can pose a significant hazard. For example, the extraction of offshore oil commonly requires drilling through hydrate reservoirs and underlying free-gas reserves, potentially destabilizing the hydrate and releasing large quantities of methane into the pore space. The fate of the bubbles that result depends on whether gas is able to rise by displacing the pore liquid and/or the sediment particles. Several lines of evidence suggest that methane bubbles can coexist with gas hydrate and aqueous solutions within the gas hydrate stability zone (GHSZ). For example, episodic gas escape from the seafloor likely requires that a free gas source is feeding vents near the crest of Hydrate Ridge, on the Cascadia margin (Heeschen et al., 2003). Increases in bulk density that accompany the retrieval of sediment cores from the GHSZ have been interpreted to indicate the presence of in situ free gas that escaped between the time of core logging and the ship-board measurements (Tréhu et al., 2004). Seismic surveys show “wipe-out zones” within the GHSZ that are interpreted as areas where free gas is present in the sediment column (Liu and Flemings, 2006). Salinity profiles of near-seafloor sediment show that the chloride concentration in the pore water is elevated to greater than 1500 mM, consistent with the formation of hydrate from gas bubbles near the seafloor (Liu and Flemings, 2006). X-ray computer tomography (CT) images of near-seafloor sediment samples also suggest the presence of gas within hydrate layers (Abegg et al., 2003). The inferred free gas in the GHSZ at Hydrate Ridge and other hydrate reservoirs requires further explanation because the local pressure and temperature conditions imply that free gas is not in equilibrium with hydrate and aqueous solutions that have salinities typical of seawater (∼ 550 mM Cl −). Several mechanisms have been proposed to allow free gas to enter the GHSZ in high-flux regions. One hypothesis asserts that gas transport through the GHSZ takes place because the exclusion of salt during hydrate formation increases the pore–water salinity and modifies the equilibrium conditions to allow free gas and hydrate to coexist with liquid water at colder temperatures (shallower depths) than would otherwise be expected (Liu and Flemings, 2006, 2007; Milkov et al., 2004). These models predict the formation of hydrate from gas bubbles in the largest pore spaces that are available, thereby forcing gas transport through sequentially smaller pore throats until capillary effects seal the sediment from further gas invasion. Gas pressure subsequently builds until fractures form and facilitate rapid gas transport through the GHSZ. An alternative model that does not appeal to salinity changes argues that free gas is normally prevented from entering the GHSZ by capillary transport barriers, but that the pressure beneath the GHSZ eventually builds enough that gas is able to fracture the sediment column (Haeckel et al., 2004; Hornbach et al., 2004; Torres et al., 2004). Gas transport through the GHSZ is then presumed to be rapid enough that kinetic effects prevent the system from reaching thermodynamic equilibrium. These models of gas transport depend on a transition from capillary invasion, in which gas displaces liquid to move through the pore
189
throats of a rigid network of sediment particles (see Fig. 1a.), to fracturedominated invasion, in which gas moves sediment particles out of the way (see Fig. 1b). Discrete element modeling predicts that gas will fracture cohesive sediments within the GHSZ when the particle radius is sufficiently small (i.e. 0.1 μm, see Fig. 15 of ref. (Jain and Juanes, 2009)), and that gas will move through the pore throats (capillary invasion) when the particle radius is larger (i.e. 50 μm, see Fig. 14 of ref. (Jain and Juanes, 2009)). Experiments by Boudreau et al. (2005) demonstrate that clays act initially like an elastic solid in response to stresses imparted by gas bubbles, but that higher pressures illicit a plastic response that results in the development of fractures so that gas bubbles form non-equant shapes that resemble corn flakes; by comparison gas bubbles exhibit more equant, rounded shapes in sands. The transition from capillary-controlled to fracture-dominated gas invasion has not previously been demonstrated in non-cohesive sediments. We describe experiments in sieved sands that enable us to delineate conditions under which gas displaces solid particles to propagate a fracture, as opposed to those in which the sediment matrix remains rigid and gas simply overcomes capillary forces to invade through pore throats, displacing the liquid. Our results show how this transition in behavior is controlled by changes in effective stress and the size of pore throats. After describing our experiments
water fixed particles
gas
a. Capillary invasion
water moving particles
gas
b. Fracture-dominated invasion Fig. 1. Schematic diagrams showing different modes of gas transport. a. Capillary invasion, in which the sediment matrix is rigid and gas transport occurs by displacing the liquid phase. b. Fracture-dominated invasion, in which sediment particles are forced aside by high gas pressures.
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and presenting our findings below, we discuss their implications for hydrate-reservoir dynamics. 2. Experimental design We designed a simple apparatus to monitor the difference in gas and water pressure, or overpressure, when a gas column first invades a water-saturated sand layer from below. Fig. 2 shows a portion of our plexiglass tank during a typical experiment. A wedge-shaped wire mesh was sealed against the tank sides with a thin rubber strip and loaded with a layer of sieved sand across the 15 × 5 cm tank crosssection to a specified thickness that we varied to control the effective stress at the mesh apex. The tank was filled initially with water and a hydraulic connection across the sand layer was maintained throughout the course of each experiment by an external hose that connected the top and bottom of the tank. We introduced gas (air) at a rate of approximately 80 ± 5 ml/min through a needle at the tank base. In each experiment, the gas migrated to the base of the sediment and accumulated in a wedge-shaped column beneath. We monitored the gas-column evolution and recorded its maximum thickness h immediately prior to the first instant that gas was seen to emerge from the other side of the sand layer. The pressure difference between a gas bubble Pg and the surrounding liquid Pl is equal to the product of the surface energy γgl and the curvature K of the gas–liquid interface so that Pg −Pl ¼ γg l K : At the base of the gas column, the gas–liquid interface is macroscopically flat (i.e. K ¼ 0) so we infer that Pg|base = Pl|base at this depth. Assuming that the gas may be treated as inviscid and neglecting its small density, this implies that the gas pressure at the column apex Pg|apex ≈ Pg|base = Pl|base. Since the water in the sediment column is essentially stagnant prior to gas invasion, it is expected to maintain a hydrostatic pressure gradient and the liquid pressure at the apex is Pl|apex ≈ Pl|base−ρlgh, where ρl ≈ 10 3 kg/m 3 is the liquid density, g ≈ 10 m/s 2 is the acceleration of gravity, and h is the gas-column
height. Near the apex we assume that the gas–liquid interface approaches a constant curvature Kapex as it begins to invade the pore throats above so that the gas–liquid pressure difference, or overpressure, can be written as ΔP≡Pg apex −Pl apex ≈ρl gh≈γgl Kapex :
ð1Þ
The maximum curvature Kc that can be attained before gas infiltrates the sediment pores is controlled by the size of pore throats near the apex so that for the idealized case where the gas–liquid interface takes the form of a sequence of hemispherical caps of radius Rc, we have that Kc ¼ 2=Rc . Eq. (1) predicts that when the sediment matrix behaves in a rigid fashion so that gas invasion through pore throats of a fixed radius Rc is inhibited by capillary forces, the critical gas-column height needed to initiate infiltration approaches a constant value of hc ¼ γgl Kc =ðρl g Þ≈2γgl =ðρl gRc Þ. In the field of petroleum engineering the overpressure ρlghc is referred to as the “displacement pressure” (e.g., Smith, 1966). Control over the typical size of pore throats Rc is achieved in our apparatus by varying the particle size in the sediment layer (to ensure that the mesh had a negligible influence on gas transport, the screens were also changed so that in all experiments opening dimensions were comparable to the average particle size and larger than pore constrictions). We also have control over the sediment thickness H that overlies the mesh apex. When transport is dominated by capillary-invasion we expect that the gas-column height h at the onset of gas invasion should be independent of H. However, this only holds when the sediment particles are prevented from moving, as is reasonable when the effective stress supported by particle contacts is sufficiently high. By adjusting the value of H we control the vertical component of the effective stress immediately above the gas column as ′
σ v ≈ðρs −ρl Þgð1−ϕÞH;
ð2Þ
where ρs ≈ 2.65 × 10 3 kg/m 3 is the density of the sediment particles, and ϕ ≈ 0.25 ± 0.05 is the porosity. We conducted experiments using three different size classes of sand that were sieved to limit the range of particle diameters between a) 1.83–2.63 mm, b) 0.84–1.00 mm, and c) 0.45–0.71 mm. The particles were introduced gradually at the top of the water-filled tank and settled under gravity to form a random-close-packed network on top of the mesh. In all of our experiments we used a quartz-rich sand that is preferentially wetted by the liquid rather than the gas phase. The results described below support our expectation that the characteristic sizes of the pore throats that inhibit capillary infiltration scale with particle size. For each particle size, we controlled the thickness H of sediment and recorded the gas-column thickness h at which gas invasion was observed. Between experiments we used a rod to mix the sand to reduce any preferential alignment of the sand particles and to remove small bubbles that were trapped during previous invasion episodes. 3. Results
Fig. 2. Experimental set-up. Gas rises into a water-filled plexiglass tank and accumulates in a gas column beneath a sand layer that is suspended on a coarse wire mesh. The sand layer thickness H and gas column height h are used to calculate the effective stress σ′v and gas overpressure ΔP, as defined in the text.
For each experiment, we used Eq. (1) to calculate the overpressure ΔP using the observed gas-column height at which gas first infiltrated the sediments — termed “primary invasion” below. Fig. 3 shows our results for ΔP during primary invasion as a function of the effective stress σ′v calculated from Eq. (2) for each imposed sediment thickness. As expected for cases where gas invades the pore space by overcoming capillary forces, at high effective stress we observe that the overpressure approaches a constant level that depends inversely on the typical particle size. The labeled dashed lines give the average of the overpressure values displayed with the plain symbols; for convenience, we refer to these as the capillary overpressures ΔPc below.
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1400
500
0.84−1.00 mm, σv’≈270 Pa
1170 Pa
1200
1.83−2.63 mm, σ ’≈390 Pa
400
Overpressure, Δ P (Pa)
Overpressure, Δ P (Pa)
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1000 ′ ΔP (σ )→
800
f
v
520 Pa particle diameters:
600 400
0.45−0.71 mm
200 Pa
200
v
primary invasion
300
200
160 Pa
100
0.84−1.00 mm
110 Pa
1.83−2.63 mm 0 0
200
400
600
800
1000
1200
0
1400
0
Effective Stress, σv′ (Pa) Fig. 3. Overpressure ΔP required to initiate primary gas invasion as a function of the imposed effective stress σ′v for the three different ranges of particle diameters noted in the legend. Labeled horizontal dashed lines show threshold capillary overpressures ΔPc obtained as averages of the nearby plain symbols. Dotted line shows the best fit linear relation ΔPf = 1.9σ′v−97 Pa to the data highlighted with circled symbols (R2 ≈ 0.93). See text for further discussion.
The capillary overpressures are larger for smaller particle sizes; the ratios of ΔPc between the different particle sizes that we used are comparable to the expected ratios of pore throat sizes and corresponding gas–liquid interfacial curvatures at the onset of infiltration. The circled symbols in Fig. 3 at lower effective stresses all have notably lower ΔP than the capillary overpressures ΔPc needed for primary invasion at higher effective stresses. The dotted black line labeled ΔPf(σ′v) gives the least-squares best linear fit to these circled symbols, which are drawn from the data for all three particle-size classes. The good fit suggests that gas invasion occurs at a threshold overpressure that increases with effective stress and does not depend on the sediment particle size. This is consistent with the expectation that gas can displace sediment particles and invade the sediments by propagating a fracture when the effective stress is sufficiently low that ΔPf b ΔPc. The displacement of sediment particles is expected to begin when the overpressure exceeds the least compressive stress, which in natural sediments is typically in the horizontal plane. In our experiments the proximity of the container walls may cause enhanced resistance to lateral particle motion. Assuming that σ′v and the least compressive stress are nevertheless proportional to each other, the inferred linear dependence of ΔPf on σ′v is in agreement with the predictions of hydraulic fracture models applied to petroleum reservoirs (Mourgues et al., 2011). After the primary gas invasion episodes, all of our experiments require lower levels of overpressure to induce gas infiltration during subsequent, or secondary episodes. Fig. 4 summarizes the observations from two experimental runs, showing the peak overpressure for six secondary invasion episodes through the 0.84–1.00 mm particle diameter sediment and eight secondary invasion episodes through the 1.83–2.63 mm sediment. The minimum overpressure that is reached when gas escape terminates is also recorded for both the primary and secondary invasion episodes. Fig. 4 displays one example where the effective stress was sufficiently high that primary gas invasion occurred within the capillary-dominated regime (black stars), and one example where the effective stress was low enough that primary gas invasion was fracture-controlled. We expect capillary-invasion to take place without displacing the sediment particles and we do not discern a qualitative difference between the subsequent behavior for the two cases. This suggests that the lower overpressures that characterize secondary invasion episodes are likely caused by some mechanism other than the enlargement of pore throats near the wedge apex.
20
40
60
80
100
Elapsed Time (s) Fig. 4. Overpressure ΔP(h) time series inferred from the observed gas-layer thicknesses h after the primary gas invasion episodes for two illustrative examples with the particle size ranges and effective stress levels noted in the legend. Average overpressures required for secondary invasion are shown with the labeled dot-dashed lines. See text for further discussion.
The lower overpressures required for secondary invasion are consistent with a mechanism involving bubble break-up and retention in the sediment column (Belien et al., 2010). Prior to primary gas invasion episodes, we took measures to ensure that no bubbles were present in the sediment column. Following some experiments we observed, however, that bubbles remained in the sand after gas invasion episodes. If gas bubbles left behind in the sand were connected to the gas column below, then the effective column height would be larger than its measured thickness below the wedge apex. Assuming a trapped gas thickness above the wedge apex of δh and that the liquid pressure readjusts to a hydrostatic distribution between invasion episodes, the overpressure at the top of the trapped portion of the gas column exceeds the value inferred at the wedge apex by δP = ρlgδh, and the effective stress is lower than the level inferred near the apex by δσ′v = (ρs −ρl)g(1−ϕ)δh. For the data shown in Fig. 4, if we assume that secondary invasion episodes follow the fracture-dominated trend established for the primary invasion episodes (shown by the dotted line in Fig. 3) then we expect ΔP(h+ δh) ≈1.9σ′v(H−δh) + 97 Pa. Using the arguments above to calculate ΔP(h+ δh) ≈ΔP(h)+ δP and σ′v(H−δh) ≈σ′v(H)−δσ′v leads to an inferred trapped gas thickness of
δh≈
1:9σ ′v ðH Þ−97Pa−ΔP ðhÞ ; ρl g þ 1:9ðρs −ρl Þg ð1−ϕÞ
where ΔP(h) and σ′v(H) are calculated from Eqs. (1) and (2) using the observed values of h and H. From this calculation, the data summarized in Fig. 4 imply that the average trapped gas thickness extends 7.9 mm (the values for all 6 episodes range from 6.1 to 9.0 mm) above the wedge apex for the sediment with particle diameters ranging from 0.84 to 1.00 mm (the total sediment layer thickness was 22 mm for this case) and 16 mm (the values for all 8 episodes range from 16 to 17 mm) above the wedge apex for the sediment with particle diameters ranging from 1.83 to 2.63 mm (the total sediment layer thickness was 32 mm). The corresponding average overpressures ΔPδh at the top of the inferred trapped-gas layers are approximately 230 Pa within the 0.84–1.00 mm diameter sand and 270 Pa within the 1.83–2.63 mm diameter sand. Since ΔPδh b ΔPc ≈ 520 Pa for the 0.84–1.00 mm diameter sand, fracture-dominated invasion initiated from the top of a connected trapped-gas column is consistent with the secondary invasion data for this sediment.
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For the 1.83–2.63 mm diameter sand, the value of ΔPδh ≈ 270 Pa calculated assuming fracture-dominated invasion is greater than ΔPc ≈ 200 Pa. This suggests that we should have expected invasion to occur at a lower average ΔP(h) than the 110 Pa observed for this case. If we assume that secondary invasion follows the capillarycontrolled trend instead so that ΔP(h) + δP ≈ ΔPc, the trapped gas thickness is inferred to be
δh≈
ΔPc −ΔP ðhÞ : ρl g
This would imply that the trapped gas thickness extends approximately 9.2 mm (the values for all 8 episodes range from 7.4 to 12.5 mm) above the wedge apex for the 1.83–2.63 mm diameter sediment. For the 0.84–1.00 mm diameter sand, a similar calculation would imply a value of δh that exceeds the entire sediment layer thickness. We infer that the secondary invasion episodes shown in Fig. 4 that followed a fracture-dominated primary invasion are also most consistent with a fracture-dominated mechanism during secondary invasion. By contrast, the secondary invasion episodes that followed a capillary-controlled primary invasion are most consistent with a capillary-controlled mechanism during secondary invasion as well. During some experiments conducted at high σ′v we were able to observe a transition from capillary-controlled invasion to sediment fracturing within a single invasion episode. A photograph capturing this behavior is shown in Fig. 5. This primary invasion episode began with ΔP ≈ ΔPc. As gas neared the sediment surface, however, a fracture opened near the tank wall and we were able to observe the macroscopic displacement of sediment particles in the upper few centimeters. As gas rises in a thick sediment column, it encounters lower and lower overburden stress. A transition to fracturepropagated invasion occurs when the effective stress is low enough that the overpressure overcomes the resisting interparticle stresses. A further consequence of such behavior is the development of pockmark craters at the sediment surface, as shown in Fig. 6.
Fig. 5. Fracturing in the upper centimeters of a thick sediment column (particle diameters 0.45–0.71 mm, σ′v ≈ 103 Pa, black ticks on right side are at 5 cm intervals). Although the overpressure at the onset of gas invasion was consistent with a capillary-controlled mechanism, the reduced effective stress near the sediment surface facilitated fracture development just below the point of gas exit from the saturated sand.
Fig. 6. View from the top of a sediment layer showing a crater created during gas escape from the 0.45–0.71 mm sediment. Graph paper grid contains 2 mm squares.
The online supplementary information contains links to video clips showing representative experimental runs.
4. Discussion and conclusions Our experiments in non-cohesive, water-infiltrated sediments demonstrate a transition from capillary-controlled gas invasion at higher effective stresses to fracture-dominated invasion at lower effective stresses. The overpressure required for gas invasion can be much lower than that which would be consistent with capillary resistance to invading pore throats of a typical size in undisturbed sediments. This suggests the possibility that free gas might be much more mobile in marine sediments than would otherwise be expected. It also suggests that the potential for fluid migration in other contexts, for example during the sequestration of CO2, might be larger than expected from model treatments that ignore the potential for buoyant fluids to open fractures (e.g., Woods and Farcas, 2009). The pronounced reductions we observed in the overpressure required for secondary invasion episodes are consistent with a prominent role for bubble break-up and gas retention within the sediment during our experiments. Bubbles that are trapped within the GHSZ would be expected to promote hydrate formation in highly localized zones and may explain some of the segregated hydrate nodules and filled fractures that are sometimes observed (e.g. Borowski, 2004; Haeckel et al., 2004; Hester and Brewer, 2009; Torres et al., 2008). Importantly, we find that fractures develop in an otherwise nominally homogeneous sediment. However, in marine sediments that are pervaded by faults, we would expect that fractures would preferentially follow these preexisting zones of weakness (Hornbach et al., 2004). If the gas retained between successive secondary invasion episodes tends to occupy the same pores, this suggests a mechanism for developing preferential migration pathways that may limit the efficacy of remediation efforts by air sparging (Ahlfeld et al., 1994). Once gas invasion begins, our experiments are characterized by the escape of large enough gas volumes that the overpressure drops well below the level required to sustain ongoing gas escape (e.g. see Fig. 4). Instead, we find that gas invasion is episodic and the transport time through a sediment layer is much shorter than the time between invasion episodes. If similar behavior is typical of free-gas transport through the GHSZ this would favor more efficient delivery of methane to the seafloor than a scenario involving gradual, continuous gas release. Applying these results to the retention of commercial hydrocarbon reservoirs, this also suggests a mechanism for causing hydrocarbon reserves beneath some caprocks to fluctuate in thickness, but remain considerably
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thinner than required for the overpressure to reach the displacement pressure (Schowalter, 1979; Smith, 1966). Gas invasion can transition from capillary invasion to fracturedominated invasion as gas nears the sediment surface, where the effective stress is reduced. In our experiments, such behavior is characterized by the formation of crater-like pockmarks. The much larger pockmarks sometimes observed on the sea floor (Davy et al., 2010) may require sediment failure over a depth range comparable to the entire GHSZ thickness, or the thickness above some other, deeper seal (Reilly and Flemings, 2010). The effective stresses encountered towards the base of most gas hydrate deposits are much higher than those in our experiments. However, the grain sizes that are typical of marine sediments can be much smaller than the sediments we used so that the capillary entry pressures are also higher. Our experiments suggest that fracturedominated gas invasion is most likely to occur when free gas is present close to the seafloor. However, the non-hydrostatic pressure gradients associated with upwards fluid flow can help to unload sediment grains and facilitate fracture-dominated invasion at greater depths (Flemings et al., 2003; Reilly and Flemings, 2010; Tréhu et al., 2004). Poroelastic effects may also be important for enabling particle rearrangements when the gas overpressure is much lower than the capillary entry pressure. Experiments focused on examining these complications would be a useful extension of the current work. Acknowledgments Funding for this work was provided by grant #47851-G8 from the American Chemical Society's Petroleum Research Fund. The revised manuscript benefitted from the thoughtful comments of two anonymous reviewers, relayed to us by Editor Gideon Henderson. Appendix A. Supplementary data Supplementary data to this article can be found online at doi:10. 1016/j.epsl.2011.09.042. References Abegg, F., Bohrmann, B., Freitag, J., Kuhs, W., 2003. Fabric of gas hydrate in sediments from Hydrate Ridge—results from ODP Leg 204 samples. Geo-Mar. Lett. 27, 269–277. Ahlfeld, D.P., Dahmani, A., Ji, W., 1994. A conceptual model of field behavior of air sparging and its implications for application. Ground Water Monit. Rem. 14, 132–139. Algar, C.K., Boudreau, B.P., 2009. Transient growth of an isolated bubble in muddy finegrained sediments. Geochim. Cosmochim. Acta 73, 2581–2591. Algar, C.K., Boudreau, B.P., 2010. Stability of bubbles in a linear elastic medium: implications for bubble growth in marine sediments. J. Geophys. Res. 115, F03012. doi:10.1029/2009JF001312. Bachmann, O., Bergantz, G.W., 2006. Gas percolation in upper-crustal silicic crystal mushes as a mechanism for upward heat advection and rejuvenation of nearsolidus magma bodies. J. Volcanol. Geotherm. Res. 149, 85–102. Barry, M.A., Boudreau, B.P., Johnson, B.D., Reed, A.H., 2010. First-order description of the mechanical fracture behavior of fine-grained surficial marine sediments during gas bubble growth. J. Geophys. Res. 115, F04029. doi:10.1029/2010JF001833. Belien, B., Cashman, K.V., Rempel, A.W., 2010. Gas accumulation in particle-rich suspensions and implications for bubble populations in crystal-rich magma. Earth Planet. Sci. Lett.. doi:10.1016/j.epsl.2010.06.014. Borowski, W.S., 2004. A review of methane and gas hydrates in the dynamic, stratified system of the Blake Ridge region, offshore southeastern North America. Chem. Geol. 205, 311–346.
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