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Journal of Contaminant Hydrology
journal homepage: www.elsevier.com/locate/jconhyd
Impact of groundwater flow on methane gas migration and retention in
unconsolidated aquifers
Gilian Schout
a,b,c,⁎
, Niels Hartog
a,c
, S. Majid Hassanizadeh
a
, Rainer Helmig
d
, Jasper Griffioen
b,e
a
Earth Sciences Department, Utrecht University, 3584 CB Utrecht, the Netherlands
b
Copernicus Institute of Sustainable Development, Utrecht University, 3584 CB Utrecht, the Netherlands
c
KWR Water Cycle Research Institute, 3433 PE Nieuwegein, the Netherlands
d
Institute for Modelling Hydraulic and Environmental Systems, Universität Stuttgart, Pfaffenwaldring 61, 70569 Stuttgart, Germany
e
TNO Geological Survey of the Netherlands, 3584 CB Utrecht, the Netherlands
ABSTRACT
Methane leaking at depth from hydrocarbon wells poses an environmental and safety hazard. However, determining the occurrence and magnitude of gas migration
at ground surface is challenging, as part of the leaking gas is retained during upward migration. We investigated migration through unconsolidated sedimentary
aquifers using a two-phase, two-component (water and methane) flow and transport model constructed in DuMu
x
. A sensitivity analysis for migration through a 60 m
thick sandy aquifer showed that retention by dissolution can be significant even with low groundwater Darcy velocities of 1 m.yr
−1
. Retention was negligible in the
absence of groundwater flow. Besides groundwater velocity, both hydrogeological (permeability, entry pressure, pore-size distribution, and residual gas saturation)
and leakage conditions (depth, magnitude and spatial dimensions) determined model outcomes. Additional simulations with interbedded finer grained sediments
resulted in substantial lateral spreading of migrating gas. This delayed upward migration and enhanced retention in overlying sandy units where groundwater
velocities are highest. Overall, the results of this study show that for unconsolidated aquifer systems and the most commonly observed leakage rates (0.1–10 m
3
.d
−1
),
significant amounts of migrating methane can be retained due to dissolution into laterally flowing groundwater. Consequently, resulting atmospheric methane
emissions above such leaks may be delayed with decades after the onset of leakage, significantly reduced, or prevented entirely.
1. Introduction
The reliance on fossil fuel resources for the majority of the world's
energy supply has resulted in a large number of onshore hydrocarbon
wells, conservatively estimated at over 4 million (Davies et al., 2014).
In spite of efforts to maintain the vertically isolating function of geo-
logical formations that are penetrated when installing and operating
such wells, failure of the wellbore system is a commonly observed
problem (Davies et al., 2014) and can lead to leakage of hazardous
liquids and gases. Furthermore, research has shown that this risk con-
tinues or may develop even after the active life-time of wells and their
abandonment (Kang et al., 2014;Townsend-Small et al., 2016). Parti-
cularly, upward leakage of methane through anthropogenically opened,
unintended connections between hydrocarbon reservoirs and the
shallow subsurface has become a growing concern worldwide as it may
contribute to greenhouse gas emissions (Kang et al., 2014), deteriorate
water quality (Vengosh et al., 2014), and form an explosion hazard
(Chilingar and Endres, 2005). On top of that, leaky wells could serve as
pathways for the migration of other fluids when the downhole condi-
tions are actively changed, for example when hydraulic fracturing is
carried out (Brownlow et al., 2016)orCO
2
is stored (Gasda et al., 2004)
in nearby wells. Thus, their presence may also hamper the safe im-
plementation of future uses of the subsurface.
To be able to quantify and mitigate these risks, the accurate de-
tection of gas leakage is vital. This is typically achieved by measure-
ments of either sustained casing pressure (SCP) or surface casing vent
flow (SCVF) at the wellhead (King and King, 2013). However, these
measurements may only reflect a part of the total leakage flux, as a
significant fraction of leaking gas can escape the wellbore system en-
tirely and enter the surrounding geology (Forde et al., 2019), which is
also referred to as gas migration. Lackey and Rajaram (2018) identified
three main mechanisms that may lead to gas migration: (1) gas cir-
cumvention, when gas migrates through a cemented outer annulus and
a section of low quality cement is overlain by a section of higher quality
cement, causing the gas to migrate outwards, (2) groundwater cross-
flow, when gas leaks through an uncemented outer annulus and is
transported into the surrounding formation by lateral groundwater
flow, and (3) SCP-induced gas migration, when the gas pressure at the
bottom of the surface casing exceeds the hydrostatic pressure leading to
gas ‘overflow’.
As gas migrating outside the wellbore may become trapped, dis-
solved or degraded (Cahill et al., 2018), surficial or shallow
https://doi.org/10.1016/j.jconhyd.2020.103619
Received 6 September 2019; Received in revised form 17 January 2020; Accepted 23 January 2020
⁎
Corresponding author at: Earth Sciences Department, Utrecht University, 3584 CB Utrecht, the Netherlands.
E-mail address: g.schout@uu.nl (G. Schout).
Journal of Contaminant Hydrology 230 (2020) 103619
Available online 24 January 2020
0169-7722/ © 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/BY/4.0/).
T
groundwater wells may only detect leakage after long periods of time,
or possibly never. Measurements of soil gas migration are typically
carried out using surface flux chambers (Erno and Schmitz, 1996). In
the vadose zone, oxidation and dispersion of methane has indeed been
shown to be capable of masking leaking wells from being detected at
the surface entirely (McMahon et al., 2018;Schout et al., 2019). Fur-
thermore, a recent field experiment where methane was released in a
shallow aquifer showed that the combined effects of trapping and dis-
solution of leaking gas in the saturated zone significantly reduced the
amount of gas that reached the surface (Cahill et al., 2018). Lastly,
several field-based studies have shown that anaerobic methane oxida-
tion coupled to either sulphate reduction (Van Stempvoort et al., 2005;
Wolfe and Wilkin, 2017) and/or reduction of iron and manganese
oxides (Schout et al., 2018;Woda et al., 2018) can lead to attenuation
of a migrating methane plume. With increasing depth and longer mi-
grating pathways leaking gas can become more severely affected by
these attenuation and retention processes, and in turn surficial or
shallow subsurface measurements become increasingly less reliable
tools for detecting gas migration. Indeed, the fate of methane from leaks
occurring at depths greater than 10 m was identified as a key knowl-
edge gap in studying gas migration (Cahill et al., 2019).
Given the complexity and related costs of measuring gas leakage in
field or experimental settings, methane migration has also been as-
sessed by means of multiphase numerical flow and transport simula-
tions. Several studies have aimed to determine ranges of possible gas
migration flow rates from the reservoir depth to shallow aquifers
through high permeability pathways, such as faults or improperly ce-
mented annuli (Kissinger et al., 2013;Nowamooz et al., 2015;Reagan
et al., 2015;Schwartz, 2015). Tatomir et al. (2018) simulated migration
of methane at great depth (~1500 m) into an inclined, regional aquifer.
Breakthrough times of gaseous methane at various offset distances from
the leak origin were calculated, that could for example correspond to
conductive faults connecting the deep aquifer with an overlying
freshwater aquifer. Rice et al. (2018) investigated SCP-induced gas
migration through a shale formation present at the bottom end of the
surface casing into an overlying shallow aquifer. They showed that for
given source zone pressures, the permeability distribution and the
parametrization of the capillary pressure saturation and relative per-
meability functions of the shale formation controlled the flow rate of
methane into the overlying aquifer. Depending on these properties,
flow rates at the base of the aquifer can be slow, which may allow
methane contamination to go undetected.
Other studies assumed leakage to a shallow aquifer system occurred,
and focused on the migration and attenuation of methane therein. Roy
et al. (2016) coupled their multiphase model to a reactive transport
simulator and showed that in confined aquifers, anaerobic methane
oxidation coupled to sulphate reduction could attenuate a migrating
dissolved methane plume significantly. This attenuating effect was even
larger in unconfined aquifers, where aerobic methane oxidation was
also possible. Moortgat et al. (2018) simulated gas phase methane mi-
gration through an aquifer system characterized by the presence of
highly permeable pathways such as fractures and fluvial channels. They
showed that rapid lateral gas migration over distances of several kilo-
meters is possible through these features, but that migration is much
less rapid in unfractured media. D'Aniello et al. (2019) simulated
leakage of methane from a geothermal well into a 2 m thick surficial
unconsolidated aquifer. Given the limited thickness and because mass
transfer of methane to the aqueous phase was ignored, retention of
methane in this aquifer was limited. Klazinga et al. (2019) carried out
2D simulations imitating the field experiments by Cahill et al. (2017)
where methane gas was injected up to 10 m depth in a sandy aquifer.
Lateral migration of the gas phase was shown to be significant even
over such a relatively shallow interval, as a result of anisotropic sedi-
ments, and the presence of low permeability layers. Furthermore, wider
plumes and larger groundwater flow velocities resulted in larger
amounts of methane that were retained in the aquifer.
The effect of methane retention by dissolution into laterally flowing
groundwater has not been considered in detail in previous studies of gas
migration. In spite of the relatively low solubility of methane, dis-
solutive retention could be important in the shallow part of un-
consolidated groundwater systems, where groundwater velocities are
generally higher. Methane migration through unconsolidated aquifers
is also less likely to be dominated by quick gas phase flow through
preferential flow paths, which reduces the potential for dissolutive re-
tention. Other factors also possibly play a role, such as the increase in
methane aqueous solubility with increasing hydrostatic pressure (i.e.
depth) and the lateral spreading of the methane plume as a result of
anisotropy and low permeable layers. The interaction of these transport
processes and their influences on gas migration were studied in a
parameter sensitivity analysis based on 3D, two-phase, two-component
numerical simulations across a range of realistic conditions. The im-
pacts of horizontally layered unconsolidated aquifer systems on me-
thane migration and retention were illustrated by simulation of a
number of additional scenarios, based on the geology encountered at
two recently identified leaking wellbore sites in the Netherlands. The
overall aim of this study was to determine whether, and if so, to what
extent subsurface methane migration through laterally flowing
groundwater is impacted by methane dissolution.
2. Material and methods
2.1. Governing equations and constitutive relations
Numerical modelling was carried out using the open source multi-
physics simulation package DuMu
x
(Ackermann et al., 2017;Flemisch
et al., 2011). DuMu
x
is capable of calculating multiphase multi-
component flow and transport at the continuum scale (also referred to
as miscible two-phase flow or compositional flow). For this study, two
phases α(liquid and gas) and two components k(H
2
O and CH
4
) were
considered. The model accounts for mass transfer between the two
phases as well as the compressibility of both phases. Phase velocities are
calculated using Darcy's law. Furthermore, binary diffusion is assumed,
and the diffusive fluxes in each phase are calculated according to Fick's
law. The fully coupled mass balance equation is then formulated as
follows:
∑∑
∑
∂∂=∇∙ ⎧
⎨
⎩∇− ⎫
⎬
⎭+
∇
∙∇+
κg
ϕρXS
tρX k
μPρ
ρD X q
() ()
{}
α
αα
kα
α
αα
krα
α
αα
α
αeff α α
kk
,(1)
where Φis the porosity, ρis the density, Xis the mass fraction, Sis the
saturation, κis the intrinsic permeability tensor, k
r
is the relative per-
meability, μis the dynamic viscosity, Pis the pressure, gis the gravity
vector, D
eff
is the effective diffusion coefficient and qis a source or sink
term. A number of constitutive relationships are needed to close this
system of equations. Firstly, the sum of the saturations and that of the
mass fractions of the two components in each phase must equal 1:
∑∑
+= = =SS X X1, 1,
1
gl kg
k
klk(2)
where the subscripts g and w represent the gaseous and liquid phase,
respectively. The phase pressures are related by the capillary pressure
P
c
as given by:
−=
P
PPS()
.
glcg (3)
The formulations by Brooks and Corey (1964) were used for the
capillary pressure - saturation relationship and relative permeabilities:
=−
P
SPS()
cg e
eλ
1
(4)
⎜⎟
==−
⎛
⎝−⎞
⎠
++
kS k S S,(1)1
rl eλrg e eλ
2/ 3 2
21
(5)
G. Schout, et al. Journal of Contaminant Hydrology 230 (2020) 103619
2
where P
e
is the capillary entry pressure, S
e
is the effective saturation and
λis the pore size distribution index. S
e
is defined as:
=−
−−
SSS
SS1
ellr
gr lr (6)
where S
lr
and S
gr
are the residual (or ‘irreducible’) liquid and gaseous
saturation, respectively. According to these formulations, the relative
permeability of the gas phase is 0 as long as S
g
<S
gr
. Hence, the re-
sidual saturations in each cell have to reach at least up to the
(threshold) residual gas saturation before a neighboring cell can be
invaded by the gas phase (Fig. S1). A regularization of the Brooks-Corey
P
c
(S
g
)relationship was used for S
e
> 1 and S
e
< 0.01. To avoid nu-
merical issues with having an infinite gradient of the P
c
(S
g
)curve, the
slope of the curve when approaching these limits was extended up to
S
l
= 1 and S
l
= 0, respectively (Fig. S1).
Both water and methane components can be present in either phase.
Concentrations in each phase are assumed to be at thermodynamic
equilibrium, meaning that mass transfer between the two phases occurs
instantaneously at every time step in each control volume. Methane
solubility is determined according to Henry's law and is temperature
and pressure dependent, with the Henry's coefficient based on the
IAPWS formulations (Fernández-Prini et al., 2003). A freshwater
aquifer is assumed and therefore the effects of variable salinities on
methane solubility are not considered. The solubility of methane also
determines the phase state of the model, with a gas phase appearing
once the mole fraction of methane (x
lCH4
)exceeds that of the equili-
brium (solubility) mole fraction, and vice versa. Phase appearance and
disappearance are accompanied by a primary variable switch: from P
l
and S
g
when both phases are present to P
l
and x
lCH4
when only the
liquid phase is present. Energy transport is not simulated, and the
model is considered to be in thermal equilibrium. For the spatial dis-
cretization a vertex centered finite volume method (‘box method’)is
used and a fully implicit, backward Euler method for the temporal
discretization (Helmig, 1997).
The density of the gaseous phase follows the ideal gas law. Viscosity
is calculated as described in Reid et al. (1987). In the range of tem-
perature and pressure relevant for this study, the density and viscosity
of methane gas calculated in this manner were shown to be nearly equal
to more complex equations of state (Kissinger et al., 2013). The density
and viscosity of the liquid phase are both pressure and temperature
dependent, according to the IAPWS definitions (Wagner and Pruss,
2002). The influence of the phase composition on the liquid phase
properties is not taken into account, since even at the greatest depth
considered in this study (480 m of water column) the maximum CH
4
mass concentration is negligible compared to the aqueous phase density
(~0.1%). The diffusion coefficient of water in the gaseous phase is
determined according to the method in Fuller et al. (1966) and the
diffusion coefficient of methane in the aqueous phase according to Reid
et al. (1987). Mechanical dispersion was not implemented in the model.
In multiphase systems, the dispersion coefficient is saturation depen-
dent, which would result in a much more complex system of equations
(Helmig, 1997) and excessive runtimes. Computations were performed
on a workstation and parallelized over 16 processors, resulting in
runtimes of up to 2 days for the sensitivity analysis and 4 days for the
layered scenarios.
2.2. Geological context and conceptual model
The range of hydrogeological conditions for which gas migration
was studied are representative for unconsolidated sedimentary
groundwater systems globally, but were inspired by the conditions that
prevail in the subsurface of the Netherlands. The Netherlands is one of
the major oil and gas producing nations in Europe with around 2500
onshore oil and gas wells (Schout et al., 2019). A survey of 986 gas
wells by the State Supervision of Mines (SodM) revealed some form of
well barrier failure at 227 (23%) of these wells (SodM, 2019). Ob-
servations of gas bubbles in flooded well cellars showed that leakage of
thermogenic gas occurred at at least 13 wells (1.3%). Hydro-
geologically, the country is characterized by the presence of shallow
sandy aquifer units of Plio-Pleistocene age. These aquifers can be either
phreatic or, in the northern and western part of the country, can be
confined by overlying Holocene deposits (Fig. S2). A succession of
thick, marine clays of Neogene and Paleogene age form the bedrock
below the aquifer units in nearly the entire country (de Vries, 2007).
Typically, the surface casing of oil and gas wells would at least extend
down into these clays, the depths of which can be up to around 500 m
below surface in the oil and gas producing areas (Kombrink et al.,
2012). The modelled domain is a hypothetical rectangular block of a
sandy aquifer within such a unconsolidated sedimentary sequence
(Fig. 1a). Gas migration into the base of the model is assumed. Con-
ceptually, it could be caused by a number of possible failure scenarios
occurring below the simulated part of the aquifer, including SCP-in-
duced gas migration or gas circumvention.
2.3. Domain discretization, boundary and initial conditions
The dimensions of the simulated aquifer were set to 100 × 60 × 60
m (XYZ), sufficiently large so that no boundary effects on gas migration
occurred. Owing to symmetry in the y-axis, only half of this domain is
simulated. Initial numerical testing showed that model outcomes sta-
bilized when using a grid size smaller than 1x1x1 m. Hence, a grid size
of 0.5 × 0.5 × 0.5 m was used, resulting in a total of 1,440,000 cells.
Fig. 1. Conceptual model example (a) and numerical implementation of the modelled section (b).
G. Schout, et al. Journal of Contaminant Hydrology 230 (2020) 103619
3
The simulation time is 20 years, during which injection of CH
4
is
continuous. For the CH
4
flux at the inlet (mol.m
−2
.s
−1
) a Neumann
type boundary was used over 8 cells from x = 40 to 42 m (2 × 1 m
2
), or
what would be 2 × 2 m
2
area when accounting for the half of the
domain that is not modelled (Fig. 1b). The remainder of the bottom face
of the model and the two lateral faces parallel to the direction of
groundwater flow are treated as no-flow boundaries for both compo-
nents. The two lateral faces perpendicular to groundwater flow are
assigned Dirichlet conditions with a pressure equal to the hydrostatic
pressure, albeit with a minor increase in pressure on one side to induce
groundwater flow. Lastly, the top face of the model is assigned a no-
flow condition for H
2
O and an outflow condition for CH
4
. This allows
methane to escape the model freely through the top boundary but keeps
water flowing strictly horizontally. Conceptually, this corresponds to
cases where the gas either escapes to the atmosphere or continues to
migrate upwards to overlying layers, depending on the depth of the top
of the domain. The model is initially fully water saturated (S
g
= 0) and
no dissolved methane is present anywhere. A thermal gradient of
31.3 °C.km
−1
is imposed in all simulations, equivalent to the average
thermal gradient found in the Netherlands (Verweij et al., 2018), on top
of the yearly average ambient air temperature of 10 °C. The density and
viscosity of water inside the model and at its lateral boundaries are
determined during an initialization phase that precedes the actual
model run.
2.4. Parameter space sensitivity analysis
A total of 17 simulations were run, together encompassing a para-
meter space representative of the expected conditions for gas migration
through unconsolidated sandy aquifers (Table 1). Groundwater flow
velocities up to 100 m.yr
−1
were considered, as observed for regional
groundwater flow in the Netherlands (Bloemendal and Hartog, 2018).
The thickness of the model is 60 m. For the base case a depth of 60 m
was chosen for the bottom of the model domain, with depths of 240 and
480 m also considered. Preliminary simulations showed that model
outcomes are insensitive to the temperature gradient however, as si-
mulations ran with a constant temperature of 10 °C yielded virtually
equal outcomes. Hence, variations in the geothermal gradient were not
considered.
Methane flow rates at the inlet were varied between 0.1 and 10 m
3
CH
4atm
.d
−1
(i.e. the volumetric CH
4
flow rate at atmospheric pressure
and 10 °C) as the majority of reported SCVF rates fall within this range.
For example, 68% of wells with SCVF in British Columbia, Canada, had
flow rates below 1 m
3
.d
−1
and 25% between 1 and 10 m
3
.d (Wisen
et al., 2019). Similarly, the vast majority of reported SCVF rates in
Alberta, Canada, are also below 10 m
3
.d
−1
(Dusseault et al., 2014). It
should be noted that very large SCVF rates exceeding 1000 m
3
.d
−1
have also been reported (e.g. Nowamooz et al., 2015), but were not
considered in this study. Imposed leakage rates were sustained for the
full 20 year simulation period. The assumption of a constant leakage
rate over long time periods was also made by Rice et al., 2018. Field
measurements of leakage from abandoned wells in Pennsylvania that
remained virtually constant over a 3 year time period support this as-
sumption (Kang et al., 2016), as do measured SCPs that sustained over
measurements periods up to nearly 10 years (Lackey and Rajaram,
2018).
While properties of sandy aquifers are well known for single-phase
problems, experimental studies where multiphase properties are de-
termined are sparse. To reduce the number of possible scenarios, three
sets of experimentally determined values for an air-water system were
used for the porosity, permeability, entry pressure, and pore size dis-
tribution (Clayton, 1999). As a base case assumption, the properties of a
coarse grained fluvial sand (D50 of 0.61 mm) were taken (Table 1). The
effect of migration through finer grained sands was considered by im-
plementing the values determined for a ‘hydraulic fill’(D50 of
0.16 mm) and a ‘clayey alluvium’(D50 of 0.09 mm). Hereafter, we refer
to these as a fine sand and very fine sand, respectively, according to the
Wentworth scale of grain size classifications (Wentworth, 1922). Given
that the transverse permeability is not known, an anisotropy factor (k
h
/
k
v
) of 5 was assumed in all simulations. Variations in anisotropy with a
k
h
/k
v
of 1 and 10 were simulated in scenarios 14 and 15, respectively
(Table 1). A residual gas saturation of 1% was assumed. The sensitivity
of model outcomes to the residual gas saturation was investigated in
scenarios 12 and 13, with values of 0% and 15%, respectively. The
residual wetting phase saturation was set to 10% for all simulations. In
scenarios 16 and 17 the inlet boundary size was changed (to 1 × 1 m
2
and4×4m
2
), while maintaining the total gas flow rate over the
boundary.
2.5. Setup of two layered case studies based on real sites
For the sensitivity analysis, a simplified, homogeneous, sandy
aquifer was considered. However, in unconsolidated sedimentary ba-
sins these aquifers are typically alternated by layers of both coarser and
finer grained sediments, ranging from gravel to clay. To investigate the
effect of such stratification on gas migration, additional simulations
Table 1
Summary of relevant input parameters used for the 17 simulated scenarios in the sensitivity analysis.
Scenario [#]
a
Q
gin
[m
3
.d
−1
]q
w
[m.yr
−1
] Depth [m] Porosity [−]k
h
[m
2
]k
v
[m
2
]P
e
[Pa] λ[m
−1
]S
gr
[−] Note
1 0.1 1 60 0.38 5.3E-11 1.1E-11 1766 1.50 0.01 ‘base case’
2 0.1 060 0.38 5.3E-11 1.1E-11 1766 1.50 0.01
3
b
0.1 060 0.38 5.3E-11 1.1E-11 1766 1.50 0.01 x
iCH4
/x
maxCH4
= 95%
411 60 0.38 5.3E-11 1.1E-11 1766 1.50 0.01
5 0.1 1 60 0.45 7.8E-12 1.6E-12 3924 1.20 0.01 Fine sand
6 0.1 1 60 0.33 2.7E-11 5.4E-12 2256 0.15 0.01 Very fine sand
711060 0.38 5.3E-11 1.1E-11 1766 1.50 0.01
81 100 60 0.38 5.3E-11 1.1E-11 1766 1.50 0.01
910 100 60 0.38 5.3E-11 1.1E-11 1766 1.50 0.01
10 11240 0.38 5.3E-11 1.1E-11 1766 1.50 0.01
11 11480 0.38 5.3E-11 1.1E-11 1766 1.50 0.01
12 0.1 1 60 0.38 5.3E-11 1.1E-11 1766 1.50 0.00
13 0.1 1 60 0.38 5.3E-11 1.1E-11 1766 1.50 0.15
14 0.1 1 60 0.38 5.3E-11 5.3E-11 1766 1.50 0.01 k
h
/k
v
=1
15 0.1 1 60 0.38 5.3E-11 5.3E-12 1766 1.50 0.01 k
h
/k
v
=10
16 0.1 1 60 0.38 5.3E-11 1.1E-11 1766 1.50 0.01 Area inlet: 1 × 1 m
2
17 0.1 1 60 0.38 5.3E-11 1.1E-11 1766 1.50 0.01 Area inlet: 4 × 4 m
2
Bold numbers indicate parameters that are varied with respect to the base case scenario.
a
Volumetric CH
4
flow rate over inlet at atmospheric pressure and 10 °C –due to domain symmetry only half of this flow rate is applied in the model.
b
Initial methane concentration at 95% of the depth-dependent solubility mole fraction (x
iCH4
/x
maxCH4
= 95%).
G. Schout, et al. Journal of Contaminant Hydrology 230 (2020) 103619
4
were carried out based on the hydrogeology observed at two locations
where methane leakage was recently shown to occur. At the first lo-
cation, near the village of Sleen in the east of the Netherlands, gas
migration resulted from a blowout that occurred in 1965 (Schout et al.,
2018). At the second location, in a village called Monster in the west of
the Netherlands, gas migration was detected above a fully decommis-
sioned cut-and-buried gas well (Schout et al., 2019). This leak was more
recently closed offby the responsible operator, in accordance with
Dutch law. Hydrogeologically, these two locations are quite different as
they are situated at opposite ends of the Netherlands (Fig. S2). Hence,
they serve as two distinct case studies used to investigate the effects of
horizontal layering on gas migration. However, it is important to note
here that the goal is not to reproduce exactly the leakage conditions at
these sites, as required information about the depth and magnitude of
the leaks is not known.
Lithological and permeability data were retrieved from the publicly
available national hydrogeological model REGIS II (Vernes and Doorn,
2005). REGIS II divides the subsurface into sandy, complex, and clayey
layers. Complex layers typically consist of successions of more and less
permeable sediments that are taken together as one regional layer. As a
result, they often have a large anisotropy with a much lower vertical
than horizontal permeability. Where not given, anisotropy was assumed
to be 5 for sandy layers and 10 for clay layers. Porosities were assumed
to be 30% for sandy layers, 35% for complex layers, and 40% for clay
layers. The Brooks-Corey pore size distribution index was assumed to be
1.5 for sandy layers, following the experimentally determined value for
the sand used in the base case scenario. Accordingly, a smaller pore size
distribution index was chosen for the clayey (0.75) and for complex
(0.5) layers, reflecting the larger variation in pore sizes that may be
expected for such lithologies. The Leverett J-function (Eq. (7)) was used
to scale the entry pressure based on the ratio between porosity and
permeability. Separate reference values were used for the complex,
sandy and clayey units (Table S1).
=
J
SpSkϕ() () /
wcw(7)
The bedrock at the Sleen site can be considered the top of the Breda
Formation at 126 m depth. The case study modelled after this site was
therefore constructed from this interface up to the surface. At the
Monster location, the thick clay unit below the base of the Maassluis
formation at 231 m depth was considered as the bedrock. Furthermore,
the surficial Holocene deposits (55 m thick) are not included in the
model as REGIS II does not provide data on them. The modelled section
is therefore 176 m thick. The resulting hydrogeological input data used
for both case studies is shown in Fig. 2. For each case two simulations
were carried out, one with a groundwater head gradient of 25 cm.km
−1
and one with 100 cm.km
−1
, on top of the hydrostatic pressure. A flow
rate of 10 m
3
CH
4atm
.d
−
was assumed for all simulations. Otherwise,
the boundary and initial conditions were kept equal to those used in the
sensitivity analysis. The width of the model was extended to 80 m to
avoid gas phase pools below interfaces of entry pressure or permeability
reaching the boundaries of the model. Given the extended size of these
models and the more complex hydrogeology, grid refinement was
slightly reduced to 1 × 1 × 1 m to improve run times.
3. Results
First, an assessment of the potential for methane retention in the
subsurface is briefly presented, and the relative magnitude of forces
relevant to methane migration for the unconsolidated aquifers under
study. Then, the results of the sensitivity analysis are presented, fol-
lowed by the results of hydrogeologically layered case studies.
3.1. Dimensional analysis of methane retention and migration
Within the range of temperature and pressure considered in this
study, that result from a maximum depth of 480 m below water table,
methane aqueous solubility and gas phase density increase from 31 to
1112 mg.L
−1
and 0.69 to 32.3 kg.m
−3
, respectively (Fig. S3). While
methane mass density as a gas phase is much greater than its solubility
at equal depths, the mass stored in the aqueous phase is roughly equal
at gas phase saturations of 4% (Fig. 3). For gas saturations exceeding
4%, retention in the gas phase starts to rapidly exceed aqueous reten-
tion. At a gas saturation of 4% and a depth of 60 m below the water
table, the cumulative storage in both phases is ~0.2 kg.m
−3
(Fig. 3). In
comparison, the flow rate in our base case scenario is 0.1 m
3
CH
4atm
.d
−1
, equal to a methane mass flow rate of 0.07 kg.d
−1
or flux of
~0.02 kg.m
−2
.d
−1
(given the inlet area of 4 m
2
). Therefore, at this
depth, it would require 10 days to saturate 1 m
3
of aquifer with me-
thane, assuming a gas saturation of 4%. Although this is just a first
approximation, which notably does not take into account the replen-
ishment of available groundwater for methane to dissolve in due to
groundwater flow, it confirms that there is indeed potential for sub-
surface methane retention to significantly affect the monitorability of
gas migration originating at depth.
Following the definitions in Kopp (2009) a dimensional analysis of
the balance of forces in the system was carried out. Preliminary testing
showed that for the gas migration velocities encountered in our sensi-
tivity analysis, viscous forces were insignificant compared to both
gravity and capillary forces. Hence, the system is characterized by the
dimensionless Bond number:
==
−
Bo capillary forces
gravitational forces
p
ρρgl()
cr
wg
cr (8)
where p
cr
and l
cr
are the critical pressure and length, respectively, and g
is the gravity constant (9.81 m.s
−2
). The critical pressure is defined as
the capillary pressure drop over the saturation front length and is
therefore roughly equal to entry pressure. Typically, for advection-
driven flow systems, the critical length is taken to be equal to the length
of the saturation front width (Kopp, 2009). When assuming a critical
length equal to the discretization length (0.5 m), capillary forces equal
gravitational forces for entry pressure values of 5 kPa (Fig. S4). This
shows that for the three sands considered in the sensitivity analysis,
which have a maximum entry pressure of 3.9 kPa (Table 1), gravita-
tional forces likely dominate. However, the complex and clayey layers
in the hydrogeologically layered case studies have a maximum entry
pressure of 7.8 kPa (Fig. 2). Depending on the actual width of the sa-
turation front, capillary forces likely exceed gravitational forces for
these clayey sediments.
3.2. Sensitivity analysis
3.2.1. Retention by CH
4
dissolution
In the base case scenario (Table 1) the upward, buoyancy-driven
migration of the gas plume from the base of the simulated aquifer to its
top (60 m interval) takes 1.65 years (Fig. 4a and Table 2). Due to the
coarse grain size and relatively low methane flux, migration is mostly
vertical and the gas phase stays within the column overlying the inlet
boundary. This observation is in line with the findings of the dimen-
sional analysis, and confirms that gravitational forces indeed dominate
in this case. Maximum gas phase saturations remain low at only 2.4%.
As the gas phase migrates, the surrounding water column is saturated
throughout, and methane saturated groundwater is advectively trans-
ported away from the gas phase plume, allowing more gaseous methane
to be dissolved (Fig. 5). Migration time reduces to 1.14 years when the
Darcy velocity in the aquifer is reduced to zero (scenario 2) and just
0.35 years if in addition the initial concentration of methane
throughout the aquifer is raised from 0 to 95% of the solubility (sce-
nario 3). Therefore, methane dissolution, from the bottom to the top of
a 60 m thick sandy aquifer with a groundwater Darcy velocity of only
1 m.yr
−1
, causes the migration of a 0.1 m
3
CH
4atm
.d
−1
leak to occur
G. Schout, et al. Journal of Contaminant Hydrology 230 (2020) 103619
5
1.3 years more slowly than it would have without dissolution.
The difference in results of the first three scenarios is more pro-
nounced when looking at the percentage of inflowing methane that
exits the model through the top boundary (Q
out
/Q
in
). For scenario 3,
Q
out
/Q
in
reaches 82% in a year and goes to 100% after approximately
5 years (Fig. 4a). Ultimately, this fraction even slightly exceeds 100% as
some of the initially dissolved methane also passes through the top
boundary (Fig. 4a). For scenario 2, when both the initial methane
concentration and groundwater velocity are zero, Q
out
/Q
in
increases
gradually with time to 91% after 20 years. The remaining 9% is trapped
in the aquifer by dissolution and subsequent diffusion away from the
gas phase plume. With time, this fraction would steadily increase fur-
ther as the aquifer saturates with methane and the rate of diffusion
slows down. However, for the base case scenario these outcomes are
entirely different, as Q
out
/Q
in
stabilizes after 4 years when just 10% of
the imposed methane flow rate migrates on through the top boundary.
This shows that dissolution in combination with advective transport
exerts a much stronger control on gas migration than dissolution with
diffusive transport, even for groundwater with a Darcy velocity of only
1 m.yr
−1
.
3.2.2. Impact of methane flow rate
The relative impact of dissolutive retention is significantly reduced
when increasing the methane flow rate through the inlet by a factor of
10, from 0.1 to 1 m
3
CH
4atm
.d
−1
(scenario 4). While maximum gas
phase saturations increased to 4.6%, migration is still primarily vertical
and migration time reduced from 1.65 year in the base case scenario to
just 0.16 year (Table 2). Therefore, a smaller fraction of migration
methane can be dissolved and retained in the aquifer, given that the
groundwater velocity was kept equal, and Q
out
/Q
in
stabilizes after just
2 years at 85% compared to 4 years and 10% in the base case scenario
(Fig. 4a).
3.2.3. Impact of sand properties
Due to the smaller permeability, larger entry pressure and smaller
pore size distributions of the finer grained sands simulated in scenarios
5 and 6 (Table 1), gas phase propagation patterns are changed con-
siderably with respect to the base case (Fig. 5). Particularly for the case
of a very fine sand (scenario 6), with a 10 times smaller pore size
Fig. 2. Hydrogeological input data used for construction of the two layered case studies. In the permeability plot, the solid line (‘k
v
’) and dashed line (‘k
h
’) show the
vertical and horizontal permeability, respectively. In the Darcy velocity plot, the solid line (‘q
25
’) and dashed line (‘q
100
’) show the modelled Darcy velocities resulting
from the cases with groundwater head gradients of 25 and 100 cm.km
−1
, respectively.
Fig. 3. Potential mass density of methane as a gas phase (green lines) or in the
aqueous phase (blue lines) as a function of depth, for three different values of
the gas phase saturation (S
g
). Temperature is based on a thermal gradient of
31.3 °C km
−1
and a porosity of 38% was assumed, equal to that of the base case
scenario. (For interpretation of the references to colour in this figure legend, the
reader is referred to the web version of this article.)
G. Schout, et al. Journal of Contaminant Hydrology 230 (2020) 103619
6
distribution index (0.15 versus 1.5 in the base case), the gaseous plume
becomes more rounded (Fig. 5a). This also leads to some minor up-
stream migration of the gas phase, and is the result of an increase in
capillary force, which acts in all directions equally, relative to the
gravitational force, which acts only vertically upwards. In the fine sand
case (scenario 5), both vertical and horizontal permeabilities are ~7
times lower than in the base case. Due to this increased resistance to
flow, the maximum gas phase saturation becomes higher than in the
base case: 3.0% versus 2.4%. The gas phase can be seen to migrate
slightly along with groundwater flow in both scenarios with finer
average grain sizes (Fig. 5b). Ultimately, the change in shape and de-
creased speed of upward propagation allows more methane to be dis-
solved in both cases, given that Darcy velocities were kept equal. This
causes the gas phase propagation to stagnate at 6.5 m and 18.5 m below
the top of the model domain for the fine sand and the very fine sand
cases, respectively (Table 2). Hence, Q
out
/Q
in
remains 0. The distance
with which methane has been transported at the base of the model is
28 m in the base case scenario, 24 m in scenario 5 and 34 m in scenario
6, calculated from the inlet at x = 42 m to where the concentration
equals half that of the solubility at 60 m depth (204 mg.L
−1
). The
difference between these distances is caused by the differences in por-
osity, resulting in varying effective groundwater velocities. It should be
noted that due to diffusion, the distance where methane concentrations
are sufficiently large to be readily detected in groundwater samples
(~0.1 mg.L
−1
) is almost twice as large (Fig. 5b).
3.2.4. Impact of groundwater flow velocity
Gas migration resulting from a 1 m
3
CH
4atm
.d
−1
flow rate is not
impacted greatly when raising groundwater velocity from 1 to
10 m.yr
−1
(scenarios 4 and 7). Migration time increases from 0.16 to
0.25 year and Q
out
/Q
in
is reduced from 85% to 76% (Table 2). How-
ever, when groundwater velocity is further increased to 100 m.yr
−1
(scenario 8), the gas plume movement is severely impacted and mi-
gration stagnates at 53.5 m below the top of the aquifer, having moved
up just 6.5 m (Fig. 4b). The impact of a 100 m.yr
−1
groundwater flow
velocity was also assessed for an even higher methane flow rate of
10 m
3
CH
4atm
.d
−1
(scenario 10). The higher flow rate results in larger
maximum gas saturations (6.2%) and much more rapid gas phase
Fig. 4. Vertical propagation of the gas phase plume (left) and fraction of inflowing methane that exits (Q
out
/Q
in
) the domain through the top boundary (right).
Results for scenarios 1–4 are shown in figure a, scenarios 4, 7, 8 and 9 in figure b, and scenarios 4, 10 and 11 in figure c. Lines are labelled according to the
corresponding scenario numbers in Table 1, with simulated variations with respect to the base case indicated in figure legends.
G. Schout, et al. Journal of Contaminant Hydrology 230 (2020) 103619
7
migration, as the top of the aquifer was reached in 0.06 years. However,
Q
out
/Q
in
stabilized at just 2%. This shows that even large gaseous flow
rates can be severely impacted by dissolutive retention, in spite of a
very rapid upward migration of the gas phase.
3.2.5. Impact of aquifer depth
The depth of the aquifer was increased 4 and 8 times in scenarios 11
and 12, respectively, resulting in an increased depth of the base of the
aquifer of 240 m and 480 m depth (aquifer thickness remains 60 m).
Simulations were run with a methane flow rate of 1 m
3
CH
4atm
.d
−1
, and
are thus compared to that of scenario 4 (Table 1). The average methane
solubility over the resulting depth intervals is 4.8 and 8.6 times higher
than in the base case scenario, and the average gas phase density in-
creases 5.3 and 10.9 times (Fig. S3). Both aqueous and gaseous
Table 2
Percentage of inflowing methane that exits through the top boundary of the model (Q
out
/Q
in
) with increasing time, for the 17 scenarios (Table 1) considered in the
sensitivity analysis.
Scenario [#] Time to top aquifer [yrs] max depth gas plume [m] Q
out
/Q
in
[%]
0.25 [yrs] 0.5 [yrs] 1 [yrs] 2 [yrs] 3 [yrs] 5 [yrs] 7.5 [yrs] 10 [yrs] 15 [yrs] 20 [yrs]
1 1.65 –0.0 0.0 0.0 4.6 8.8 9.9 10.1 10.1 10.2 10.2
2 1.14 –0.0 0.0 0.0 55.5 68.7 80.9 85.4 87.7 90.1 91.4
3 0.35 –0.1 42.7 82.1 93.4 96.8 99.3 100.5 101.2 102.1 102.7
4 0.16 –47.3 72.9 82.9 84.7 85.0 85.1 85.1 85.1 85.2 85.2
5 Not reached 6.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
6 Not reached 18.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
7 0.25 –0.0 68.0 73.5 74.9 75.3 75.4 75.5 75.5 75.5 75.5
8 Not reached 53.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
9 0.06 –2.1 2.2 2.2 2.2 2.2 2.3 2.4 2.4 2.4 2.4
10 0.70 –0.0 0.0 25.4 42.8 44.7 45.1 45.2 45.2 45.2 45.2
11 1.45 –0.0 0.0 0.0 10.8 15.3 16.4 16.6 16.6 16.4 16.1
12 1.09 –0.0 0.0 0.0 13.1 15.4 15.5 15.5 15.6 15.6 15.6
13 Not reached 4 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
14 0.80 –0.0 0.0 11.4 21.9 23.2 23.3 23.3 23.4 23.5 23.5
15 3.19 –0.0 0.0 0.0 0.0 0.0 2.0 2.2 2.2 2.3 2.3
16 1.12 –0.0 0.0 0.0 16.8 19.0 19.6 19.7 19.7 19.8 19.8
17 Not reached 17 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
Fig. 5. Cross sections of the gas phase saturation (green) and dissolved CH
4
mass concentration (blue) after simulated times of 1 year (a) and 10 years (b). Results are
shown for the case of a coarse sand, fine sand and very fine sand, corresponding to scenarios 1, 5 and 6 (Table 1). Vertical dashed lines indicate the relative position of
the CH
4
inlet boundary at the base of the model at 60 m depth. (For interpretation of the references to colour in this figure legend, the reader is referred to the web
version of this article.)
G. Schout, et al. Journal of Contaminant Hydrology 230 (2020) 103619
8
retention capacity is therefore greatly increased at these depths and
model outcomes are indeed significantly changed, as migration time to
the top of the aquifer increased from 0.16 year to 0.7 year at 240 m
depth and 1.45 year at 480 m depth (Table 2). By extension, Q
out
/Q
in
stabilized later and decreased from 85% to 45% at 240 m depth and to
16% at 480 m depth (Fig. 4).
3.2.6. Impact of the residual gas saturation
In scenario 12 the residual gas saturation was lowered to 0%.
Migration time to the top of the aquifer decreased to 1.09 years, com-
pared to 1.65 years in the base case scenario. Q
out
/Q
in
increased from
10 to 16%. This shows that even very small variations in residual gas
saturation impact gas retention and migration. In scenario 13 the re-
sidual gas saturation was raised to 15%. As the residual gas saturation
acts as a sort of threshold value, below which flow cannot start, this
causes gas phase saturations to become much larger than in the base
case scenario, and thus more gas is stored in the porous medium.
Migration of the gas phase plume slows down considerably and had
nearly stagnated after 20 years of simulation at a depth of 4 m below
the top of the aquifer (Table 2).
3.2.7. Impact of anisotropy
Variations in anisotropy were modelled by raising the vertical per-
meability to equal the horizontal permeability in scenario 14 (k
h
/
k
v
= 1) and lowering it to 1/10th of the horizontal permeability in
scenario 15 (k
h
/k
v
= 10, Table 1). The expected higher and lower gas
migration speed results in the gas reaching the top of the aquifer in only
0.80 years for the lower anisotropy case and in 3.19 years in the higher
anisotropy case, compared to 1.65 in the base case scenario (Table 2).
In turn, the change in gas migration velocity affects the amount of
methane that is dissolved and Q
out
/Q
in
after 20 years of leakage
changes to 24% and 2% for scenarios 14 and 15, respectively.
3.2.8. Impact of the area over which the influx occurs
The results of earlier simulations and the dimensional analysis de-
monstrate that for the flow rates considered in this study and parameter
values typical of sandy aquifers, buoyancy driven, vertical gas migra-
tion dominates. As a consequence, the degree of dissolutive retention is
not only related to the groundwater velocity, flow rate, and sediment
properties, but also depends on the area of the inlet. This determines
the leakage flux (L
3
.L
−2
.d
−1
) and hence the amount of water that is
available for methane to dissolve in. To investigate the importance of
this effect, the inlet boundary size was reduced from 2 × 2 m
2
to 1 × 1
m
2
in scenario 16, while keeping Q
in
equal. Upward migration velocity
increased considerably and gas reached to the top of the aquifer in
1.12 years while Q
out
/Q
in
after 20 years increased to 20%, compared
1.65 years and 10% in the base case. When increasing the inlet area to
4×4m
2
(scenario 17), migration velocity was significantly reduced
such that stagnation occurred at 17 m below the top of the aquifer
(Table 2).
3.3. Layered case studies based on real sites
3.3.1. Case study 1: Sleen site
The modelling domain of the first case study consists of a simplified
hydrogeology with 7 main layers, cumulatively 126 m thick (Fig. 2).
The lowest layer is characterized by a high anisotropy factor of 125 (k
h
/
k
v
) and low vertical permeability of 4.2∙10
−14
m
2
. This complex layer is
overlain by 5 sandy sections with slightly varying permeabilities. No-
tably, the third layer from the bottom is a coarse sand and has the
highest horizontal permeability of 1.1∙10
−10
m
2
. The sandy units are
only interbedded by a 1 m thick complex layer with a low vertical
permeability from 1 to 2 m depth. Two scenarios were carried out using
this parametrization, one with a constant head gradient of 0.25 m.km
−1
and the other with 1 m.km
−1
. Given the constant head gradient,
groundwater velocities in the coarse sandy layer are highest, with Darcy
velocities of 8.6 and 34.2 m.yr
−1
in the first and second scenario, re-
spectively (Fig. 2).
The low k
v
in the highly anisotropic bottom layer causes significant
lateral spreading of the methane plume to occur, with gas phase sa-
turations greater than 6% close to the inlet. In the 0.25 m.km
−1
head
gradient scenario, this spreading occurs more or less symmetrically in
each direction (Fig. 6). In the 1.00 m.km
−1
scenario the plume is tilted
more strongly in the direction of groundwater flow. Gas migration
through this 49 m thick layer takes roughly 3.2 years in both scenarios.
In comparison, migration through the remaining 77 m thick modelling
domain occurs in only 1.9 years in the first scenario (Table S2). Dis-
solution of gaseous methane in the horizontally flowing groundwater is
highly significant, as evidenced by the stagnation of the gas phase
plume in the high permeability coarse sand layer in the 1.00 m.km
−1
scenario (Fig. 6). The high groundwater velocities here, combined with
the lateral spreading of the methane plume that occurs in the under-
lying layers, causes the 10 m
3
CH
4atm
.d
−1
flow rate to be completely
dissolved once the plume reaches a depth of around 52 m. In the
0.25 m.km
−1
scenario, Q
out
/Q
in
stabilizes after 20 years at 41% (Table
S2). The radius of the gaseous plume at the top of the simulated section
(which in this case represents the groundwater table) reaches a max-
imum value of around 20 m, and is slightly elongated in the direction of
groundwater flow.
3.3.2. Case study 2: Monster site
Similar to the first case study, the lowest layer of the second case
study consists of a complex unit with a low vertical permeability and
high anisotropy. However, the overlying stratigraphy is notably dif-
ferent than in the first case study and is characterized by the presence of
5 low permeability, high entry pressure clay layers that alternate the
Fig. 6. Gas phase saturation and dissolved CH
4
mass concentration after 6 years
of a 10 m
3
CH
4atm
.d
−
1 leakage rate for the first case study site (‘Sleen’). Top
figures shows the results of the scenario with a head gradient of 0.25 m.km
−1
,
lower figure for the scenario with a head gradient of 1 m.km
−1
. Horizontal
dashed lines delineate the different hydrogeological layers (Fig. 2), with darker
shaded layers representing the clayey and complex layers that have a higher
entry pressure and a lower permeability than the sandy layers.
G. Schout, et al. Journal of Contaminant Hydrology 230 (2020) 103619
9
sandy aquifers (Fig. 2). Particularly the first and second clay layers from
the bottom, at depths of 155–143 m and 119–110 m, have much lower
vertical permeabilities (~4∙10
−15
m
2
). Accordingly, they are also as-
signed higher entry pressures (~7.8 kPa) than the sandy units, and the
values considered in the sensitivity analysis. The sandy aquifers are also
slightly less permeable than in the first case study, resulting in Darcy
velocities of ~0.7 m.yr
−1
and ~2.7 m.yr
−1
for the low and high head
gradient scenario's, respectively. The modelled section is 176 m thick,
and the top of the model is at 55 m depth. Gas migrating through the
top boundary would enter the overlying Holocene deposits, which were
not considered in our simulations.
As in the first case study, the complex unit at the base of the model
causes substantial lateral spreading (Fig. 7). After around 3 years, the
migrating gas phase encounters the first clay layer which results in
significant gas phase pooling. Invasion of the clay layer only occurs
after gaseous saturations exceed 6%. At that saturation, the combined
capillary and gravitational forces were large enough to overcome the
entry pressure barrier. In the low head gradient scenario, this gaseous
pool grows to saturations exceeding 10% and a diameter of roughly
70 m. In the high head gradient scenario, less pooling occurs due to the
larger amount of methane that is already dissolved in the underlying
units. However, the pool is more extensive in the direction of
groundwater flow. Similar behavior is observed at the 2nd clay layer,
but entry pressures assigned to the remaining three clay layers were not
sufficient to cause significant pooling. In the low head gradient sce-
nario, the gas phase plume reaches the top of the modelled domain after
16.2 years. Even at the end of the 50 year simulation time, Q
out
/Q
in
had
not fully stabilized reaching a value of 46.3% (Table S2). Due to the
relatively slow upward migration, pooling of gas below the clay layers,
and low groundwater velocities in the clay layers, the dissolved me-
thane plume takes on a pine tree-like shape (Fig. 7). In the high head
gradient scenario, gas phase migration stagnates at 103 m depth, or
48 m below the top of the modelling domain. Notably, the center of the
gaseous plume at that depth can be seen to have shifted by roughly
30 m in the direction of groundwater flow. This is caused by the im-
posed hydraulic gradient, which results in slightly lower water pres-
sures downstream. Given that the entry pressure is defined as P
e
=P
g
-
P
l
, the migrating gas will preferentially invade cells those cells and the
plume shifts in the direction of groundwater flow.
4. Discussion
4.1. Upward migration and retention of methane gas
For the simulated homogeneous sandy aquifers and leakage flow
rates up to 1 m
3
CH
4atm
.d
−1
, gas migration was shown to be primarily
buoyancy driven and vertical (Fig. 5), as expected based on an analysis
of the relative magnitude of gravitational and capillary forces (Fig. S4),
and as observed by other researchers for weakly isotopic sandy porous
media (Klazinga et al., 2019). A limited amount of up or down gradient
flow of gas only occurred for two simulations with more fine grained
sediment properties (Fig. 5), due to their lower vertical permeability
and an increase in capillary forces. Gas phase saturations remained low
and reached up to around 5%, depending on the imposed flow rate and
permeability. At these saturations, the potential mass storage of me-
thane in the aqueous phase is either larger than or equal to the storage
in the gaseous phase (Fig. 3), even without considering the additional
dissolution capacity with groundwater flow.
Gaseous retention has been shown to be significant in simulations of
methane migrating from gas reservoirs towards shallow aquifers, when
assuming large residual gas saturations of up to 30% (Kissinger et al.,
2013). However, there is little consensus on appropriate values to use
for simulating gas migration through unconsolidated aquifers. While
Klazinga et al. (2019) used a single value of 10%, Rice et al. (2018)
chose a negligibly small value, arguing that gas cannot be trapped
during processes with strictly increasing gaseous saturations (i.e. drai-
nage), which is the case in our numerical simulations. However, gas
migration through real-world, heterogeneous sediments is likely to be a
more dynamic process. As a result, intermittent periods of imbibition
may still occur, particularly when leakage at the leakage point is not
entirely continuous. In spite of this uncertainty, model outcomes
showed relatively little sensitivity to a change in residual gas saturation
from 1% to 0% (scenario 12, Table 2), because gas migration is more
strongly controlled by retention in the aqueous phase at those con-
centrations. On the contrary, an imposed residual saturation of 15%
exerted a strong control on upward gas migration leading to a much
more slowly developing gas plume (scenario 13, Table 2).
4.2. Retention of methane by dissolution
The sensitivity analysis showed that dissolutive retention of me-
thane in unconsolidated sedimentary aquifers can play a major role in
limiting upward gas migration. Even low groundwater flow velocities
(1 m.yr
−1
) resulted in significant methane retention (Fig. 4a). On the
contrary, retention was negligible in the absence of groundwater flow.
This shows that it is primarily driven by advective transport of dis-
solved methane away from the gas phase plume, rather than diffusive
transport. Hence, retention is proportional to the groundwater velocity
Fig. 7. Gas phase saturation and dissolved CH
4
mass concentration after
15 years of a 10 m
3
CH
4atm
.d
−
1 leakage rate for the second case study site
(‘Monster’). Top figures show the results of the scenario with a head gradient of
0.25 m.km
−1
, lower figures for the scenario with a head gradient of 1 m.km
−1
.
Horizontal dashed lines delineate the different hydrogeological layers (Fig. 2),
with darker shaded layers representing the clayey and complex layers that have
a higher entry pressure and a lower permeability than the sandy layers.
G. Schout, et al. Journal of Contaminant Hydrology 230 (2020) 103619
10
and methane solubility. The effect of retention on methane migration
was therefore also much less significant for a simulation where the
initial aqueous CH
4
concentration was raised to 95% solubility. In this
scenario, migration time through the 60 m thick aquifer was just
0.35 years, compared to 1.65 years in the base case with fully un-
saturated groundwater (Fig. 4a). This also highlights that upward me-
thane gas migration can be more rapid in areas with pre-occurring
concentrations of dissolved methane. However, natural methane con-
centrations near solubility are rarely found in shallow groundwater. As
an example, the methane solubility at just 60 m depth below the water
table (~200 mg.L
−1
, Fig. S3) already exceeds the maximum con-
centration ever observed in Dutch shallow groundwater (~120 mg.L
−1
,
Cirkel et al., 2015). Hence, dissolutive retention can still be significant
even for locations with relatively high methane concentrations.
Besides groundwater velocity and initial methane concentrations,
model outcomes indicate a strong control of the sediment properties
and the magnitude of the leak, as they determine the velocity and di-
mensions of the upward migrating gas phase. For a given groundwater
velocity, a more dilute or more slowly migrating gas plume allows for a
larger fraction of the total flux to dissolve. Sediment properties that
limit upward migration include the vertical permeability, the residual
gas saturation, and the capillary pressure-saturation and relative per-
meability relations. Using the Brooks-Corey model, the latter two are
defined by the capillary entry pressure and the pore size distribution
index. Indeed, for two simulated scenarios with sediment properties
associated with more finely grained sediments (D50 0.16 and 0.09 mm,
compared to 0.61 mm in the base case), methane migration resulting
from a 0.1 m
3
CH
4atm
.d
−1
flow rate stagnated entirely due to the
complete dissolution of the migrating gas plume at depth (Fig. 5).
Model outcomes also show that the dimension of the inlet over
which the leakage is imposed also has a strong influence. Here, we
assumed that gas migrated into the model domain over a 2 × 2 m
2
area,
and that the origin of the leak was somewhere below the bottom of the
model domain, for example caused by gas circumvention or SCP-in-
duced leakage (Fig. 1). This also explains why retention was greatly
enhanced in two simulated case studies where the sandy aquifers where
alternated by sediment beds of lower permeability (Fig. 2). Besides
their greater thickness and depth, such layers cause significant
spreading of the gaseous plume to occur, which in turn enhances dis-
solutive retention significantly (Figs. 6 and 7). Flow rates of 10 m
3
CH
4atm
.d
−1
were either completely dissolved, causing migration to
stagnate well below the top of the modelled domain, or took several
decades to fully develop (Table S2). Significant lateral spreading of
migrating methane was also shown to occur for SCP-induced leakage
originating in a low permeable shale below a shallow aquifer (Rice
et al., 2018). In such conditions, our results show that more permeable
overlying layers can become strong barriers to upward migration due to
dissolutive retention. Conversely, the impact of dissolutive retention
would be much smaller when methane migration is focused through
high permeable pathways such as faults or fractures.
As methane solubility is strongly depth dependent (Fig. S3), dis-
solutive retention is likely to be even more significant when gas mi-
gration occurs at greater depths than those considered in this study.
However, the effect of increasing solubility due to increasing pressures
may be counteracted somewhat by increasing salinities, which decrease
methane solubility. Also, groundwater is generally more stagnant at
depth than in surficial aquifers. As shown in this work, dissolutive re-
tention is limited in the absence of groundwater flow. The complex
interaction of these processes, and their effect on the fate of gas mi-
gration occurring at depths greater than those considered in this study
(up to 480 mbgl), would be a relevant subject for further research.
4.3. Gaseous pooling and permeability clay layers to gas migration
While significant gas phase pooling occurred below the low
permeable clay layers (k
v
up to minimum of 4∙10
−15
m
2
,P
e
up to
7.8 kPa) in the 2nd case study, they were ultimately permeable to the
migrating gas (Fig. 7). Invasion of a higher entry pressure layer requires
a large enough gas accumulation in the underlying layer such that the
combined capillary and gravitational forces exceed the entry pressure
barrier. For large enough entry pressure values and horizontal barriers,
such conditions would not be obtained as the accumulating gas pool
spreads out laterally into a thin, pancake like shape. High resolution
permeability measurements have shown that thin, low permeability
clay lenses can be present within larger clayey formations, with per-
meabilities that are orders of magnitude lower than the average per-
meability of the unit (Rogiers et al., 2014). Given their low perme-
ability and presumably higher entry pressure, these lenses would likely
act as impermeable barriers to gas phase flow, essentially turning the
entire formation into a cap rock. However, the ubiquity and lateral
extent of these lenses is poorly understood. Therefore, further research
into how heterogeneity of clay deposits impacts gas migration would be
required.
4.4. Continuum modelling of gas migration
The low observed saturations call into question whether the injected
gas actually forms a continuous phase, and hence whether the widely-
used Darcy's law approach is applicable for modelling gas migration
through unconsolidated aquifers. Air sparging experiments have shown
that, for unconsolidated sediments, the injected gas phase migrates as
continuous gaseous channels when grain sizes are ≤1 mm. For larger
grain sizes the flow pattern gradually changes to discontinuous bubble
flow (Brooks et al., 1999). The grain sizes considered in this study fall in
the former category, and hence channel flow may be expected to
dominate, although the flow type is also dependent on the flux size.
Furthermore, whether such migration takes the form of a dendritic
network of small channels or a smaller amount of larger gas channels is
poorly understood (Brooks et al., 1999). Continuous dewatered chan-
nels through which the gas phase dominantly migrates also occurred in
the field experiments of gas migration by Cahill et al. (2018). Observed
dissolved methane concentrations below theoretical solubility were
attributed to this flow pattern, as the available contact area over which
mass transfer between phases can occur is smaller, and the collected
groundwater samples aggregate both water that has been in contact
with a gas channel and water that has not.
As this process is not captured in our simulations, the resulting
amount of dissolution may be overestimated. On the other hand, me-
chanical dispersion was not included in our simulations. Excluding
dispersion actually leads to an underestimation of the dissolutive ca-
pacity, as dispersion would spread out both the gas phase and the
dissolved methane more rapidly, allowing for more contact with the
water and quicker transport of dissolved methane away from the gas
phase plume. Ultimately, the suitability of continuum models for
modelling gas migration should be further analyzed through re-
production of experimental results. A promising experimental method
which could be employed for this purpose was recently published by
Van De Ven and Mumford (2018), who injected gaseous CO
2
at the
bottom of a 2D flow cell and used pH as a proxy to visually track dis-
solved CO
2
concentrations. Reproducing such experiments with nu-
merical simulation would be a good model validation strategy.
4.5. Implications for methane monitoring
From this study a number of important implications for monitoring
of gas migration and leakages in the vicinity of oil and gas wells can be
derived. Notably, surficial expressions of gas leakage originating at
depth in unconsolidated sedimentary basins may take several years to
manifest in settings dominated by relatively coarse grained sands, and
may take at least up to several decades when migrating gas also en-
counters interbedded low permeable layers. Surficial detection of
leaking oil and gas wellbores may therefore only become possible long
G. Schout, et al. Journal of Contaminant Hydrology 230 (2020) 103619
11
after the onset of leakage, and potentially after wells have already been
abandoned. This is particularly relevant as in many oil and gas jur-
isdictions decommissioned wells are cut and buried below the ground
surface (Davies et al., 2014;Schout et al., 2019), in which case direct
measurements of well integrity failure at the wellhead are no longer
possible. Furthermore, for example in the Netherlands there are cur-
rently no regulations in place that require operators to monitor the
locations of gas wells for extensive periods post-decommissioning.
Relying on surficial flux measurements or near-surface groundwater
wells may lead to the underestimation of the actual occurrence and
magnitude of gas leakage, and groundwater contamination at depth
may remain unnoticed. Hence, measuring dissolved gas molecular and
isotopic compositions in groundwater wells in close proximity to po-
tential leakage points is likely a more reliable method. When surface
expressions do occur, the dissolution of methane may still be such that
measured fluxes at the surface only represent a fraction of the flow rate
at the leakage point. Lastly, our simulations show that regional
groundwater flow may cause the center of a migrating gas plume to be
transported several tens of meters downstream from the well before
reaching the surface. Recent field studies have employed search radii of
15 m (Schout et al., 2019) and 20 m (Forde et al., 2019) from the co-
ordinates of gas wells when carrying out surficial flux measurements.
While likely suitable in most cases, widening the investigated area in
the direction of groundwater flow may need to be considered de-
pending on the conditions.
5. Conclusions
Oil and gas well failure leading to gas migration in the subsurface
poses both an environmental and safety hazard. Effective mitigation of
these hazards and the proper assessment of their impact is reliant on the
successful detection and quantification of leaks. In this study, upward
methane migration through unconsolidated aquifers was analyzed
using two-phase, two-component (H
2
O and CH
4
) numerical simulations
in DuMu
x
. Results show that the retention of migrating methane due to
dissolution into laterally flowing groundwater can become significant
at groundwater Darcy velocities as low as 1 m.yr
−1
. Retention was
shown to be dependent on a complex interaction between the lateral
groundwater velocity, the depth of the leak, and the velocity and shape
of the upwardly migrating gas plume. The latter is in turn a function of
the leakage flux and sediment properties (permeability, capillary
pressure-saturation and relative permeability relations, and residual gas
saturation). Across a range of conditions representative of un-
consolidated aquifers and leak sizes up to 1 m
3
CH
4atm
.d
−1
, the time it
took before the gas plume propagated through to the top of the mod-
elled domain varied from less than 2 months to 5 years. In some sce-
narios, the total methane leakage rate was dissolved and transported
laterally, causing the gas plume to stagnate at depth.
Subsurface methane retention was even more pronounced in addi-
tional simulations of migration through stratified sequences based on
the hydrogeological conditions at two leaking gas wells in the
Netherlands, consisting of a number of alternating sedimentary units
ranging in grain size from clays to coarse sands. Under such conditions,
depending on the imposed groundwater head gradient, flow rates of up
to 10 m
3
CH
4atm
.d
−1
were either entirely retained in subsurface or took
several decades to fully develop. Not only the presence of fine grained
and low permeable layers formed barriers to upward gas migration, but
also high permeable sands with large groundwater velocities. These
allow for a larger dissolutive capacity, particularly when the migrating
gas phase has been spread out laterally by underlying low permeability
units. Overall, the results of this study show that for the most commonly
observed methane leakage rates (0.1–10 m
3
.d
−1
), unconsolidated
aquifer systems with lateral groundwater flow can retain significant
amounts of migrating methane due to dissolution. Consequently, re-
sulting atmospheric methane emissions above such leaks may be de-
layed with decades after the onset of leakage, significantly reduced or
prevented entirely. Therefore, groundwater contamination and future
explosion hazards may go unnoticed.
Declaration of Competing Interest
None
Acknowledgements
This work is part of the research program ‘Shale Gas and Water’
with project number 859.14.001, which is financed by the Netherlands
Organization for Scientific Research (NWO). We thank the German
Research Foundation (DFG) for providing financial support for a visit to
Stuttgart University in March of 2019 through the SFB1313, project
number 327154368. Furthermore, we thank Dennis Gläser of Stuttgart
University for extensive assistance with setting up the DuMu
x
simula-
tions and many helpful discussions about numerical simulation of
multiphase flow and transport in general.
Appendix A. Supplementary data
Supplementary data to this article can be found online at https://
doi.org/10.1016/j.jconhyd.2020.103619.
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