Crustal fingering facilitates free-gas methane migration through the hydrate stability zone

Significance

Widespread seafloor methane venting has been reported in many regions of the world oceans, challenging our current estimate of global carbon budget. Yet, we still do not fully understand the fundamental mechanisms by which methane gas migrates through the deep marine sediments, feeding these vents. A key challenge is the formation of methane hydrate, an ice-like solid that forms from a methane–water mixture under pressure and temperature conditions typical of deep marine settings. Here, we study the mechanics of gas percolation under hydrate-forming conditions using experiments and computational modeling. We uncover a phenomenon, which we call crustal fingering, that helps explain how, counterintuitively, hydrate formation may facilitate instead of prevent methane gas migration through deep ocean sediments.

Abstract

Widespread seafloor methane venting has been reported in many regions of the world oceans in the past decade. Identifying and quantifying where and how much methane is being released into the ocean remains a major challenge and a critical gap in assessing the global carbon budget and predicting future climate [C. Ruppel, J. D. Kessler. Rev. Geophys. 55, 126–168 (2017)]. Methane hydrate (${\text{CH}}_4\cdot 5.75{\text{H}}_2\text{O}$) is an ice-like solid that forms from methane–water mixture under elevated-pressure and low-temperature conditions typical of the deep marine settings ($>$600-m depth), often referred to as the hydrate stability zone (HSZ). Wide-ranging field evidence indicates that methane seepage often coexists with hydrate-bearing sediments within the HSZ, suggesting that hydrate formation may play an important role during the gas-migration process. At a depth that is too shallow for hydrate formation, existing theories suggest that gas migration occurs via capillary invasion and/or initiation and propagation of fractures (Fig. 1). Within the HSZ, however, a theoretical mechanism that addresses the way in which hydrate formation participates in the gas-percolation process is missing. Here, we study, experimentally and computationally, the mechanics of gas percolation under hydrate-forming conditions. We uncover a phenomenon—crustal fingering—and demonstrate how it may control methane-gas migration in ocean sediments within the HSZ.

A plethora of field observations, including Hydrate Ridge in the Cascadia margin (1–6), the Blake Ridge offshore northeast US continental margin (7), Hikurangi margin offshore New Zealand (8, 9), Vestnesa Ridge offshore west Svalbard (10–14), and a few other locations (15–19), suggests that free-gas methane venting can coexist with and persist within hydrate-bearing formations. Such coexistence is found in nature over a wide range of pressure, temperature, and compositional conditions. Yet, hydrate equilibrium thermodynamics predicts three-phase equilibrium only along the triple-point line (20, 21), which prescribes a precise set of pressure, temperature, and compositional conditions that are likely rare occurrences in marine settings. To explain the field observations, some argue that the coexistence of free gas, saline water, and hydrates is a true three-phase equilibrium facilitated by pore-scale effects, such as capillarity (22), salinity (23), or thermal anomalies (24). These effects modify the pressure ($P$) and temperature ($T$) at the triple point, allowing for more common occurrence of the three-phase coexistence. Others argue that the three-phase coexistence is, in fact, a thermodynamic nonequilibrium sustained by high rates of gas flux and slow kinetics of hydrate formation, as supported by field-scale observations (5, 25–27) and, more recently, by laboratory experiments at the core scale (28–30) and pore scale (31–33), as well as multiphase flow modeling (34–36). Despite much effort in understanding the problem from a thermodynamic perspective, few have addressed the fluid-mechanics puzzle of how the formation of solid hydrate, instead of clogging gas-migration pathways, can facilitate free gas flow in porous media.

Here, we address these questions by investigating the flow of hydrate-forming gas at the pore scale. We simplify the flow geometry within a porous medium or a self-propagating fracture to that of a Hele–Shaw cell, composed of two parallel plates separated by a thin gap (SI Appendix, Fig. S1A)—a classic and commonly used experimental analog for Darcy flow (37–40). Under hydrate-forming $P$, $T$ conditions, we consider gas flow that is driven by an imposed fluid-pressure gradient generated by depressurization and gas compressibility, rather than buoyancy (Materials and Methods). The above simplifications allow us to focus on the two critical aspects of this problem: gas flow and hydrate formation.

In a quiescent multiphase environment consisting of a single gas bubble in a liquid water bath, we observed that the solidification of hydrate occurs along the gas–liquid interface to form a thin hydrate crust (Fig. 2A and Movie S1). This is analogous to the formation of hydrate crust on free-rising gas bubbles in the ocean (41) and offshore pipelines (42). Once the crust forms, the extremely slow diffusion of water and methane within hydrate hinders its continued growth (43–45). As a result, the interfacial hydrate grows to a finite thickness within the time scale of the experiment (Fig. 2A) and serves as a transport barrier for further exchange across the interface (34, 46).

Fig. 2.

Experimental observations of hydrate crust formation and crustal fingering. (A) During a quiescent experiment, an initially smooth Xe bubble surface becomes rougher as hydrate crust forms on the gas–liquid interface. (B) Three primary mechanisms that control crustal fingering dynamics. (C) Snapshots during a depressurization experiment at 0.5 MPa/min (that induces expansion and gas flow). The magenta circles mark locations of crust rupturing, which do not always coincide with the front of the gas finger because the entire length of the crust is susceptible to break.

As we induce gas flow through depressurization at a constant rate (SI Appendix), the interfacial hydrate crust serves not only as a transport barrier, but also as a flow resistor. Inspection of the experiment (Fig. 2C and Movie S2) suggests that three primary mechanisms control the observed gas-migration pattern (Fig. 2B): crust rupturing, gas flow, and crust formation. Because the hydrate crust is rigid, it takes a threshold pressure across the hydrate layer before it ruptures at a point and releases the entrapped gas. Crust rupturing occurs repeatedly and intermittently during the experiments (Fig. 2C, magenta circles; see also refs. 29 and 30) and is likely controlled by the local pressure difference and crust tensile strength (47–50). The location of the thinnest crust corresponds to weaker tensile strength and, thus, is more prone to rupture. Due to the subcooling effect on hydrate growth rate (33), crust that forms later in the experiment grows more slowly and, thus, appears thinner (SI Appendix, Fig. S3). Once the gas breaks through, its continued flow creates additional gas–liquid interface, promoting the formation of hydrate at the interface. The gas finger continues its movement until a combination of reduced driving pressure and thickened crust fully arrests its flow, at which point the crust ruptures at a different location to give birth to a new fingering branch. Under these coupled processes, the displacement of gas into liquid does not follow that of typical two-phase flow through fractures and porous media [e.g., viscous fingering or stable displacement (38)]. A new pattern of gas percolation emerges, where continuous gas flow modulated by the spontaneous interfacial hydrate formation leads to the evolution of crustal gas fingers, or crustal fingering (Fig. 2C).

We describe the key observations of the experiments using a phase-field model (Materials and Methods and SI Appendix), which incorporates the primary mechanisms of gas flow and crust formation and captures the crustal fingering pattern qualitatively (Fig. 3A and Movie S3). The rate of depressurization or gas flow, $Q_{\text{outlet}}$, enters through the mass conservation equation as a boundary condition. The rate of hydrate formation $R_s$, which is determined by local thermodynamic forcing such as subcooling, is imposed in our model. A larger $R_s$ corresponds to a stronger subcooling and a faster rate of hydrate crust formation (33) (SI Appendix, Fig. S3). Our model does not describe the mechanics of crust rupturing, and we do not include thermal or salinity effects in the thermodynamic component of the model.

Fig. 3.

Meandering dynamics and pattern formation of crustal fingering. (A) Simulation snapshots showing gas (black) fingers into the ambient liquid (dark gray) while encrusted by a layer of hydrate (white). (A, Right) Experimental snapshots showing similar meandering behavior of a hydrate-crusted gas finger (depressurizing at 0.5 MPa/min). Note the experimental images are from the same experiment shown in Fig. 2 and have been rotated 90° clockwise. (B) Phase diagram of gas-migration behavior illustrated by simulated patterns at $t=24$ for a gas bubble expanding in a square domain under various $Q_{\text{outlet}}$ and $R_s$. $R_s=0$ corresponds to simulations where hydrate does not form. (C) Snapshots from three experiments with different depressurization rates. The dashed red circles mark the original gas bubbles, outside of which crustal fingers are formed during depressurization. The finger width decreases with decreasing depressurization rate.

Additional simulations with our model suggest that, once the crust ruptures, the competition between local gas-flow rate (imposed by $Q_{\text{outlet}}$) and crust-formation rate (controlled by $R_s$) is crucial in determining the pattern and dynamics of gas migration (Fig. 3B). When hydrate forms significantly faster than gas flows, the crust can fully arrest gas flow (Fig. 3B, red outline)—a scenario likely responsible for the clogging behavior observed in gas conduits in the field (51, 52) and intermittent flow dynamics observed in core-scale experiments (29, 30). When hydrate does not form, our model recovers stable gas expansion expected for regular gas bubbles (Fig. 3B, blue outline). The rest of the phase diagram suggests a wide range of conditions that allow for continuous gas displacement in the form of a single meandering crustal finger (Fig. 3, yellow outline) or multiple fingering branches (Fig. 3B, green outline). These crustal fingers serve as preferential pathways that facilitate gas flow. Additional experiments under different depressurization rates (Fig. 3C) and simulations (Fig. 3B, $R_s=1/0.8$) both suggest that crustal finger width is regulated by the imposed flow rate: A higher flow rate leads to wider finger channels.

The rich dynamics of crustal fingering provides clues to understand gas migration within the hydrate stability zone (HSZ): When the local gas-flow rate is sufficiently high, hydrate formation does not necessarily clog fluid pathways, but, instead, can form hydrate-encrusted channel that facilitates gas flow. Such insight informs our understanding of the temporal variability and spatial organization of subsurface gas migration at the field scale. To illustrate this, we simulated field-scale gas migration fueled by periodic recharge events below the Bottom Simulating Reflector (SI Appendix, Fig. S4). We considered that gas is supplied by a deep source (53) with periodic recharge episodes and parameterize its dynamics by its recharge frequency ($f$) and episode strength ($Q_{\text{in}}$) (Fig. 4A). We assumed a uniform sediment permeability and did not consider preexisting faults or fractures that could dominate flow pathways. To our surprise, we found that coupling time-varying gas flow with concurrent hydrate solidification is sufficient to recover several hydrate-derived features commonly observed in the field (Fig. 4 B and C and Movie S4). When recharge episodes are strong (Fig. 4 B and C, Upper), our model predicts the formation of vertical and hydrate-walled gas conduits (10, 52, 54, 55) that sometimes terminate before reaching the seafloor (8, 9). The spatial density of conduits appears to decrease with decreasing recharge frequency. When recharge episodes are weak and infrequent (Fig. 4 B and C, Left Lower), upward gas flow becomes completely arrested to form hydrate-crusted gas pockets (56). However, when recharge episodes are weak, but frequent (Fig. 4 B and C, Right Lower), the interactions among conduits become highly nonlinear and form complex patterns. The subsurface hydrate fabric becomes multitextured, consisting of vertical conduits, lateral conduits, gas pockets, and clogged conduits, as has been observed in the field (8, 9). During these complex interactions, it is the availability of local gas pressure that determines whether a conduit will sustain its upward growth, divert laterally, or terminate.

Fig. 4.

Subsurface hydrate fabric as shaped by crustal fingering processes. (A) Time series of imposed gas flux at the bottom boundary, representing infrequent (Left) and frequent (Right) recharging. (B) Simulation snapshot at $t=105$ for different recharge frequencies (Left and Right) and for strong (Upper) and weak (Lower) recharge episodes. BSR, Bottom Simulating Reflector. (C) Different types of hydrate-derived features evolve, depending on different styles of recharge dynamics.

In the current study, we do not consider the mechanical interactions among the fluids, solid hydrates, and sediment grains and how they may affect gas migration. In particular, as fluid-driven fracturing is a prevalent mode of gas transport in soft sediments (56–59) and often concurs with hydrate growth (9, 28, 54), one would need to model both the fracturing (60–63) and the crustal fingering process to fully resolve the fluid–grain mechanics at the pore scale. Therefore, our model does not directly address the open question of what determines the dominant modes of hydrate occurrence within sediments at the core scale (64). Nevertheless, our mechanistic description of crustal fingering provides a crucial fluid-mechanics piece to decipher the puzzle of how methane gas migrates through the hydrate stability zone (Fig. 1) and offers an alternative to existing theories of gas migration (36). In addition, while it is commonly accepted that most marine hydrates on Earth have formed out of dissolved methane that has previously migrated in place or generated in situ biogenically (36, 65), our work suggests that, at the geologic field scale, some of the subsurface hydrate fabric we observe today could be a record of the dynamic history of deep-sea methane venting coupled with the formation of hydrate along the gas-migration pathways within the marine sediments over long periods of time (5). The theoretical framework we propose (Fig. 4), although lacking details of geologic features (e.g., faults or preferential pathways), can be a good starting point to connect the increasing amount of seafloor data on methane-venting dynamics (6, 17, 66) with geophysical constraints on the subsurface hydrate-derived plumbing structure (8–10, 26, 55, 67) to answer the question of where and how much methane is being released into the ocean through these naturally occurring methane seeps (68).

Fig. 1.

Methane-gas migration through shallow marine environment and the hydrate stability zone. Shown is a representation of a methane-rich gas reservoir (black) feeding the upward migration of methane gas through the seafloor sediments (gray) into the ocean-water column (blue), forming seafloor methane seeps (bubbly plume). The methane HSZ on earth is approximately 600 to 1,400 m below the ocean surface. (Upper Insets) Two primary modes of gas migration in shallow sediments are 1) capillary invasion in a rigid-like sediment, where gas pressure overcomes capillary force to move between sediment pores, and 2) fracturing, where gas pressure is sufficient to mobilize sediment grains to initiate and propagate fractures. (Lower Inset) A mode of methane-gas migration within the HSZ proposed in this work: crustal fingering.

Materials and Methods

Laboratory Experiments.

We conducted experiments using a high-pressure microfluidic device developed at Los Alamos National Laboratory (69). The microfluidic Hele–Shaw cell (SI Appendix, Fig. S1A) was made of two parallel glass plates with dimensions 14 mm $\times 14$ mm and a gap thickness of 1 mm. The entire cell was sealed off and pressurized within a high-pressure flow loop maintained at a constant temperature of 25 °C. We imaged the experiments using a charge-coupled device camera (Olympus DP72), which recorded the experiments through a microscope (Olympus MVX10) positioned in front of the viewing window of the high-pressure device. We adopted xenon (Xe) and water (${\mathrm{H}}_2$O) as the experimental analogue to the methane hydrates system. This choice was made for the following reasons: 1) Xe hydrates form at more easily accessible experimental conditions; 2) both Xe and methane form structure I hydrate up to 1.8 GPa, which is the most common structure observed in nature; and 3) Xe–water and methane–water system exhibit similar thermodynamic phase behaviors (46). We are not aware of studies that report the mechanical properties (e.g., tensile strength) of Xe hydrate. However, based on similar studies of ${\mathrm{C}\mathrm{O}}_2$ hydrate (48), we speculate that Xe hydrates and ${\mathrm{C}\mathrm{H}}_4$ hydrates are mechanically similar. Any difference in their mechanical properties will not fundamentally change the primary mechanisms that make up crustal fingering—crust rupture, gas flow, and new crust growth.

There were two ports that controlled fluid input to and output from the cell. To prepare the experiments, we first injected deionized water through the water port to fill the entire gap at ambient pressure. Then, a bubble of Xe gas was introduced into the water bath through the Xe port. Next, in order to pressurize the system to hydrate-forming conditions (P = 7.5 MPa and T = 25 °C), we closed off the water port while keeping the Xe gas bubble connected to a pressure-valve-controlled Xe gas supply. This ensured that the gas phase could be readily replenished and stay pressurized instead of dissolving into water at a higher pressure. We kept the system pressurize at P = 7.5 MPa and obtained visual confirmation that a hydrate shell had formed along the gas–liquid interface (Movie S1). Once the hydrate-crusted gas bubble was established, we induced gas flow in the domain by depressurizing the entire cell via fluid withdrawal from the water port. Prior to depressurization, we closed off the Xe port to ensure that no additional gas would be introduced into the system. We imposed a constant rate of depressurization (0.02, 0.5, and 2 MPa/min) at the water port.

In SI Appendix, we provide additional details on the validation of solid hydrate formation in the experiments, as well as a discussion on the effects of subcooling on the crustal fingering process.

Phase-Field Modeling.

We develop a continuum-scale phase-field model to study gas–liquid–hydrate systems far from thermodynamic equilibrium (34). In this model, we tracked the volumetric fractions of fluid/solid phases (${\varphi }_{\alpha }$), as well as the pointwise mole fraction of Xe ($\chi$). We started by designing a simplified Gibbs free energy ($F$) for the three phases (gas, liquid, and hydrate) as a function of $\chi$ and temperature ($T$) (SI Appendix). The proposed free energy $F$ was incorporated into a phase-field model to study the nonequilibrium thermodynamics of the three-phase system. The evolution of the system variables ($\chi$ and ${\varphi }_{\alpha }$) was driven by potentials $\mathrm{\Psi }$, which are variational derivatives of $F$. To describe the evolution dynamics, we start by imposing mass conservation of the total mixture (Xe plus water):

$$\frac{\partial \rho }{\partial t}+\nabla \cdot \left(\rho \mathbf{u}\right)=0.$$ [1]

Additionally, we prescribe the conservation of mass of Xe using a Cahn–Hilliard-type equation for $\chi$:

$$\frac{\partial \rho \chi }{\partial t}+\nabla \cdot \left(\rho \chi \mathbf{u}\right)-R_{\chi }\nabla \cdot \left(D\left(\left\{{\varphi }_{\alpha }\right\}\right)\rho \nabla {\mathrm{\Psi }}_c\right)=0.$$ [2]

We complete the system with a nonconserved Allen–Cahn evolution equation for ${\varphi }_{\alpha }$ in an advective form:

$$\frac{\partial {\varphi }_{\alpha }}{\partial t}+\mathbf{u}\cdot \nabla {\varphi }_{\alpha }+R_{\varphi }{\mathrm{\Psi }}_{\alpha }=0.$$ [3]

The evolution equations are then coupled with a simplified description for three-phase Hele–Shaw flow (70):

$$\mathbf{u}\left(x,y\right)=\frac{-k}{\mu \left({\varphi }_g,{\varphi }_l,{\varphi }_s\right)}\nabla p.$$ [4]

The full details of the model are provided in SI Appendix.

Numerical Simulations.

We discretized all of the equations using finite elements and adopted a two-step segregated solution strategy to solve the system of equations. In step one, the system of four constrained partial differential equations in Eqs. 2 and 3 were solved by using a monolithically coupled implicit time integration scheme. In step 2, the pressure problem, as prescribed by Eq. 4 and Eq. 1, was solved implicitly by using updated phase solutions from step 1. Time steps were determined dynamically to ensure stability and convergence. Additional details on the laboratory-scale and field-scale simulations are provided in SI Appendix.

Data Availability.

All study data are included in the article and SI Appendix.