Crustal fingering facilitates free-gas methane
migration through the hydrate stability zone
Xiaojing Fu
a,b,1,2
, Joaquin Jimenez-Martinez
c,d,e,1,2
, Thanh Phong Nguyen
d
, J. William Carey
d
, Hari Viswanathan
d
,
Luis Cueto-Felgueroso
f
, and Ruben Juanes
g,h,2
a
Department of Earth and Planetary Science, University of California, Berkeley, CA 94670;
b
Department of Mechanical and Civil Engineering, California
Institute of Technology, Pasadena, CA 91125;
c
Department of Water Resources and Drinking Water, Swiss Federal Institute of Aquatic Science and
Technology, Dubendorf 8600, Switzerland;
d
Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM 87545;
e
Department of Civil, Environmental and Geomatic Engineering, Swiss Federal Institute of Technology, Zurich 8093, Switzerland;
f
Department of
Hydraulics, Energy and Environment, Technical University of Madrid, Madrid 28040, Spain;
g
Department of Civil and Environmental Engineering,
Massachusetts Institute of Technology, Cambridge, MA 02139; and
h
Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of
Technology, Cambridge, MA 02139
Edited by David A. Weitz, Harvard University, Cambridge, MA, and approved November 3, 2020 (received for review May 30, 2020)
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
(CH
4
·
5
.
75H
2
O) is an ice-like solid that forms from methane–
water mixture under elevated-pressure and low-temperature con-
ditions 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 frac-
tures (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, experimen-
tally 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.
methane hydrate
|
pattern formation
|
microfluidics
|
phase-field method
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 condi-
tions. 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 compo-
sitional 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 sus-
tained 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 mod-
eling (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 frac-
ture to that of a Hele–Shaw cell, composed of two parallel plates
separated by a thin gap (
SI Appendix
, Fig. S1
A
)—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 buoy-
ancy (
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 solidifi-
cation of hydrate occurs along the gas–liquid interface to form a
thin hydrate crust (Fig. 2
A
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
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 typi-
cal 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 facili-
tate instead of prevent methane gas migration through deep
ocean sediments.
Author contributions: X.F., J.J.-M., T.P.N., J.W.C., L.C.-F., and R.J. designed research; X.F.,
J.J.-M., T.P.N., J.W.C., and H.V. performed research; X.F. and J.J.-M. analyzed data; and
X.F., J.J.-M., J.W.C., L.C.-F., and R.J. wrote the paper.y
The authors declare no competing interest.y
This article is a PNAS Direct Submission.y
Published under the
PNAS license.y
1
X.F. and J.J.-M. contributed equally to this work.
y
2
To whom correspondence may be addressed. Email: rubyfu@caltech.edu, juanes@
mit.edu, or joaquin.jimenez@eawag.ch.y
This article contains supporting information online at
https://www.pnas.org/lookup/suppl/
doi:10.1073/pnas.2011064117/-/DCSupplemental
.y
First published November 30, 2020.
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EARTH, ATMOSPHERIC,
AND PLANETARY SCIENCES
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), form-
ing 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 inva-
sion
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
.
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. 2
A
) and serves as a
transport barrier
for further
exchange across the interface (34, 46).
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. 2
C
and
Movie S2) suggests that three pri-
mary mechanisms control the observed gas-migration pattern
(Fig. 2
B
): 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 intermit-
tently during the experiments (Fig. 2
C
, magenta circles; see also
refs. 29 and 30) and is likely controlled by the local pressure dif-
ference 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 addi-
tional 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 dif-
ferent 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 contin-
uous gas flow modulated by the spontaneous interfacial hydrate
formation leads to the evolution of crustal gas fingers, or
crustal
fingering
(Fig. 2
C
).
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 qual-
itatively (Fig. 3
A
and
Movie S3). The rate of depressurization
or gas flow,
Q
outlet
, enters through the mass conservation equa-
tion 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
corre-
sponds 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.
Additional simulations with our model suggest that, once
the crust ruptures, the competition between local gas-flow rate
(imposed by
Q
outlet
) and crust-formation rate (controlled by
R
s
)
is crucial in determining the pattern and dynamics of gas migra-
tion (Fig. 3
B
). When hydrate forms significantly faster than gas
flows, the crust can fully arrest gas flow (Fig. 3
B
, 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. 3
B
, blue outline). The rest of the phase
diagram suggests a wide range of conditions that allow for contin-
uous gas displacement in the form of a single meandering crustal
finger (Fig. 3, yellow outline) or multiple fingering branches
(Fig. 3
B
, green outline). These crustal fingers serve as prefer-
ential pathways that facilitate gas flow. Additional experiments
under different depressurization rates (Fig. 3
C
) and simulations
(Fig. 3
B
,
R
s
= 1
/
0
.
8
) both suggest that crustal finger width is reg-
ulated by the imposed flow rate: A higher flow rate leads to wider
finger channels.
The rich dynamics of crustal fingering provides clues to under-
stand gas migration within the hydrate stability zone (HSZ):
When the local gas-flow rate is sufficiently high, hydrate forma-
tion does not necessarily clog fluid pathways, but, instead, can
A
B
C
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 inter-
face. (
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.
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ABC
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
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.
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 sup-
plied by a deep source (53) with periodic recharge episodes
and parameterize its dynamics by its recharge frequency (
f
) and
episode strength (
Q
in
) (Fig. 4
A
). We assumed a uniform sed-
iment 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 ter-
minate before reaching the seafloor (8, 9). The spatial density
of conduits appears to decrease with decreasing recharge fre-
quency. 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, lat-
eral 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.
In the current study, we do not consider the mechanical inter-
actions 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 dom-
inant 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 the-
ories 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
A
B
C
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 snap-
shot at
t
=
105 for different recharge frequencies (
Left
and
Right
) and
for strong (
Upper
) and weak (
Lower
) recharge episodes. BSR, Bottom Sim-
ulating Reflector. (
C
) Different types of hydrate-derived features evolve,
depending on different styles of recharge dynamics.
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EARTH,
ATMOSPHERIC,
AND PLANETARY SCIENCES
generated in situ biogenically (36, 65), our work suggests that,
at the geologic field scale, some of the subsurface hydrate fab-
ric 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 pro-
pose (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).
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. S1
A
) was made of two par-
allel glass plates with dimensions 14 mm
×
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 (H
2
O) as the experimental ana-
logue to the methane hydrates system. This choice was made for the
following reasons: 1) Xe hydrates form at more easily accessible exper-
imental 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 thermody-
namic phase behaviors (46). We are not aware of studies that report
the mechanical properties (e.g., tensile strength) of Xe hydrate. How-
ever, based on similar studies of CO
2
hydrate (48), we speculate that Xe
hydrates and CH
4
hydrates are mechanically similar. Any difference in their
mechanical properties will not fundamentally change the primary mech-
anisms 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 bub-
ble 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 pressur-
ized 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
(
φ
α
), as well as the pointwise mole fraction of Xe (
χ
). We started by
designing a simplified Gibbs free energy (
F
) for the three phases (gas, liq-
uid, and hydrate) as a function of
χ
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 (
χ
and
φ
α
) was driven by poten-
tials
Ψ
, which are variational derivatives of
F
. To describe the evolution
dynamics, we start by imposing mass conservation of the total mixture (Xe
plus water):
∂ρ
∂
t
+
∇·
(
ρ
u
)
=
0
.
[1]
Additionally, we prescribe the conservation of mass of Xe using a Cahn–
Hilliard-type equation for
χ
:
∂ρχ
∂
t
+
∇·
(
ρχ
u
)
−
R
χ
∇·
(
D
(
{
φ
α
}
)
ρ
∇
Ψ
c
)=
0
.
[2]
We complete the system with a nonconserved Allen–Cahn evolution
equation for
φ
α
in an advective form:
∂φ
α
∂
t
+
u
·∇
φ
α
+
R
φ
Ψ
α
=
0
.
[3]
The evolution equations are then coupled with a simplified description for
three-phase Hele–Shaw flow (70):
u
(
x
,
y
)
=
−
k
μ
(
φ
g
,
φ
l
,
φ
s
)
∇
p
.
[4]
The full details of the model are provided in
SI Appendix
.
Numerical Simulations.
We discretized all of the equations using finite ele-
ments and adopted a two-step segregated solution strategy to solve the
system of equations. In step one, the system of four constrained partial dif-
ferential 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
.
ACKNOWLEDGMENTS.
We thank Carolyn Ruppel and William Waite from
the US Geological Survey; Peter Flemings, Kehua You, and Dylan Meyer from
the University of Texas at Austin; Gareth Crutchley from GEOMAR Helmholtz
Centre for Ocean Research Kiel for insightful discussions; and David San-
till
́
an (Technical University of Madrid) and Ehsan Haghigat (MIT) for help
with the code development. This work was supported in part by the US
Department of Energy Grants DE-SC0018357 and DE-FE0013999. X.F. was
supported by the Miller Fellowship. J.J.-M. was supported by Swiss Federal
Institute of Aquatic Science and Technology and Guest Scientist status from
Los Alamos National Laboratory. J.J.-M., J.W.C., T.P.N., and H.V. were sup-
ported by US Department of Energy Basic Energy Science Program Grant
LANLE3W1. L.C.-F. was supported by Spanish Ministry of Economy and Com-
petitiveness Grants RYC-2012-11704 and CTM2014-54312-P. L.C.-F. and R.J.
were supported by MIT International Science and Technology Initiatives,
through a Seed Fund grant.
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