Science in China Series D: Earth Sciences
© 2007
SCIENCE IN CHINA PRESS
Springer
Effects of salinity on methane gas hydrate system
YANG DingHui1† & XU WenYue2
1
2
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China;
School of Earth & Atmospheric Sciences, Georgia Institute of Technology, Atlanta, GA 30332, USA
Using an approximately analytical formation, we extend the steady state model of the pure methane
hydrate system to include the salinity based on the dynamic model of the methane hydrate system. The
top and bottom boundaries of the methane hydrate stability zone (MHSZ) and the actual methane hydrate zone (MHZ), and the top of free gas occurrence are determined by using numerical methods and
the new steady state model developed in this paper. Numerical results show that the MHZ thickness
becomes thinner with increasing the salinity, and the stability is lowered and the base of the MHSZ is
shifted toward the seafloor in the presence of salts. As a result, the thickness of actual hydrate occurrence becomes thinner compared with that of the pure water case. On the other hand, since lower
solubility reduces the amount of gas needed to form methane hydrate, the existence of salts in seawater can actually promote methane gas hydrate formation in the hydrate stability zone. Numerical
modeling also demonstrates that for the salt-water case the presence of methane within the field of
methane hydrate stability is not sufficient to ensure the occurrence of gas hydrate, which can only form
when the methane concentration dissolved in solution with salts exceeds the local methane solubility
in salt water and if the methane flux exceeds a critical value corresponding to the rate of diffusive
methane transport. In order to maintain gas hydrate or to form methane gas hydrate in marine sediments, a persistent supplied methane probably from biogenic or thermogenic processes, is required to
overcome losses due to diffusion and advection.
methane gas hydrate, solubility, stability of hydrate, salinity, phase equilibrium
Methane gas hydrate (MGH) is an ice-like crystalline
compound of water and gas molecules[1,2] that forms at
low temperature and high pressure when the dissolved
methane concentration exceeds the local solubility[2].
The formation of methane hydrate can extract water and
methane gas reserved in porous media. Under suitable
temperature and pressure conditions liquid water in
pores and methane dissolved in water may transform
into solid hydrate. The formation of solid hydrate can
increase the strength of sediments and result in lowering
porosity and permeability[3]. Reversely, when the gas
hydrate system is not stable, solid hydrate can be decomposed into water and methane. It is stable under
elevated or relatively high pressure and low temperature
conditions such as those found in the marine sediments
along continental margins and permafrost regions[4,5].
The gas hydrate stability depends on the water depth
(pressure) and temperature. Decreasing pressure caused
by lowering the sea level or increasing seawater temperature causes the hydrate dissociation, resulting in the
geologic hazards of seafloor sloping[6] and releasing
“greenhouse” gas (main methane gas) including in hydrate further resulting in the global climate change[7]. In
a word, changes of temperature and pressure cause the
transformation between solid hydrate and methane gas,
which shows a dynamic evolution process of hydrate/
methane.
Studies of MGH in marine sediments have focused on
issues as a potential energy resource, an agent of global
climate change, and a possible role of MGH formation
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Sci China Ser D-Earth Sci | Nov. 2007 | vol. 50 | no. 11 | 1733-1745
www.springerlink.com
Received December 5, 2006; accepted July 4, 2007
doi: 10.1007/s11430-007-0126-5
†
Corresponding author (email: [email protected])
Supported by NSF (USA) (Grant No. OCE-0242163) and partially by the National
Natural Science Foundation of China (Grant No. 40574014)
and dissociation in slope instability and other geologic
hazards[8], and so on. These are all issues of global importance; consequently there have been significant advances in theoretical and laboratory research on MGH
and numerous field studies of MGH in the natural envi―
ronment[9 17]. In recent years the observational data set
on the in situ conditions associated with gas hydrate occurrences has expanded rapidly[12,18]. Many results of
such field-based programs have been a clearer understanding of in situ porosities[12], advective flux rates[11,19],
natural gas hydrate concentration[9,10,20,21], dynamic
process and effects of temperature change on the hydrate
stability[22,23], and hydrate distribution patterns[11,24].
Based on steady state models, some fundamental questions about gas hydrate formation and stability in marine
sediments have also been investigated by Xu and Ruppel[25] and Davie and Buffett[26]. It makes that our understanding of hydrate systems is clearer. However, the
quantitative estimates given by Xu and Ruppel[25] do not
include the effect of salinity on the hydrate system. Actually, it is an important factor for predicting the occurrence, distribution, and evolution of methane gas hydrate
to consider the effect of salinity on the hydrate system in
the seafloor. Therefore, the present study extends the
steady state model suggested by Xu and Ruppel[25] to
include the salinity and presents some numerical results
showing the effects of salinity on the hydrate system.
Addition of simple salts to water previously has been
shown to decrease the stability of gas hydrate such that
for certain pressure ranges the dissociation temperature
is depressed by a constant amount relative to the pure
water system[27,28]. For the pressure range of 2.75―10.0
MPa, at any given pressure, the dissociation temperature
of methane hydrate is depressed by approximately
–1.1℃ relative to the pure methane-pure water system[29]. The phase equilibria of hydrate under conditions
that are relevant to marine environments have been also
studied for three-phase equilibrium between hydrate,
―
free gas, and seawater[29 31]. The conditions for twophase equilibrium between hydrate and salt water were
also investigated by Zatsepina and Buffet[21]. Such conditions are important for determining the deepest depth
of actual occurrence of gas hydrate in marine sediments,
which often coincides with a mark of the bottom simulating reflector (BSR)[9,32] but occurs subtantially deeper
than the bases of the MHZ and the MHSZ in some settings[25]. Consequently, the conditions for three-phase
1734
equilibrium between hydrate, free gas, and salt water are
most important for establishing the stability of methane
gas hydrate in marine sediments.
The equilibrium methane concentration or solubility
is also important because it determines the minimum
methane concentration needed for hydrate stability. The
gas in solution is limited by the solubility that defines
the minimum methane concentration needed to form
hydrate or represents the maximum concentration of gas
that can be dissolved in salt water under equilibrium
conditions, so that any additional gas is present in the
hydrate phase. Within the stability region of methane gas
hydrate methane solubility increases with both temperature and pressure increasing, and decreases as the salinity increases[20,33,34]. Below the MHSZ, methane solubility increases with decreasing temperature[20,34]. Recently,
Davie et al.[21] suggested a practical method of calculating the solubility profile within the MHSZ in marine
sediments for a given water depth, seafloor temperature
and geothermal gradient. But this method is based on
phase equilibrium calculations of Zatsepina and Buffett[35] and an extension of simple parametric models
into the MHSZ[21]. The extension may produce big errors at the intersection points (the boundaries of the
MHSZ and the MHZ). Our present calculations of solubility at any depths are based on the extension of analytic model suggested by Xu and Ruppel[25], which includes the effects of multi-factors on the solubility. In
other words, the solubility in our present model is
treated as a function of pressure, temperature, and salinity of the liquid solution.
The main purpose of this paper is to investigate the
role of salts in the methane gas hydrate system. For this
we incorporate the salinity into a steady state model for
the formation of hydrate below the seafloor, and then
determine distributions of MHSZ and MHZ and investigate the influence of salinity on the MHSZ and the
MHZ by using the quasi analytical model. Estimates of
the bases of MHSZ and MHZ and the top of free gas in
the pure-methane pure-water and pure-methane saltwater cases are numerically compared. Our calculation
shows that the effect of salinity on the hydrate system is
very significant.
1 Basic theory
1.1 Theoretical time-dependent model
We adapt the model of Xu and Ruppel[25]to incorporate
YANG DingHui et al. Sci China Ser D-Earth Sci | Nov. 2007 | vol. 50 | no. 11 | 1733-1745
3
the influences of salinity on the MGH formation and
stability. For this we consider such a MGH system containing four components, which are methane, salt, water
(subscript w), and solid porous sediment of porosity φ
and permeability k, and five phases: liquid solution, free
gas, solid gas hydrate, solid salt, and solid sediment
(subscript s, density = ρs). Assuming that salt is completely solved in liquid solution, for the case of our consideration the governing equations can be derived from
the thermodynamic model developed by Xu[22], which
are based on the mass conservations (including methane
mass conservation, salt mass conservation, and total
mass conservation) and heat conservation, and be simply
written by[22]
∂ (φρ C )
v
v
v
+ ∇ ⋅ [ql Cl + qg Cg + qh Ch − φ Sl Dc ∇( ρl Cl )] = Qc ,
∂t
(1)
∂ (φρ X )
v
v
+ ∇ ⋅ [ql X l + qh Ch − φ Sl Dx ∇( ρl X l )] = 0 , (2)
∂t
∂ (φρ )
v v
v
+ ∇ ⋅ {ql + qg + qh + φ Sl [ Dw∇ρl +
∂t
( Dc − Dw )∇( ρl Cl ) + ( Dx − Dw )∇( ρl X l )]} = Qc , (3)
∂
v
v
[φρ H + (1 − φ ) ρ s H s ] + ∇ ⋅ (ql H l + qg H g +
∂t
v
v
v
qh H h + qx H x + qs H s − λ∇T ) = 0 ,
sponding phases in our present study.
Using Xu’s notations[22] and assuming that Darcy’s
law describes the conservation of momentum for multiphase fluid flow through oceanic sediments that are
moving downward at a velocity us, the mass fluxes q of
liquid (subscript l ), gas (subscript g), hydrate (subscript
h) and solid sediment phases in eqs. (1)―(4) are given
by
kk ρ
r
r
r
ql = − l l (∇P + ρl g ) + φ Sl ρl us ,
μl
kk g ρ g
r
r
r
qg = −
(∇P + ρ g g ) + φ S g ρ g us ,
μg
and
r
r
r
r
qh = φ Sh ρ h us , qs = (1 − φ ) ρ s us ,
where the vector g is the gravitational acceleration, P
denotes pressure, μl is fluid viscosity, and kl and kg are
the relative permeabilities of the liquid and gas phases,
respectively. The saturations of liquid, gas, salt (subscript x), hydrate satisfy
Sl + S g + S x + S h = 1 ,
which are determined by the phase equilibrium calculation[22].
1.2 An approximate steady state model
(4)
where eqs. (1)―(3) describe the conservations of mass
for methane gas, salt mass, and total mass for the gas
hydrate system, respectively, and eq. (4) represents the
conservation of heat energy. Dc, Dx and Dw in eqs. (1)―
(3) are the diffusivities of methane, salt, and water in
liquid solution, respectively. Qc represents the rate of in
situ methane production, λ is effective thermal conductivity, and Sl denotes the liquid saturation. ρ, C, X, and H
denote the composite density, concentration, salinity, and
enthalpy, respectively. The vector q with subscripts l, g, h,
x, and s are the fluxes of liquid, free gas, hydrate, salt,
and solid sediment, respectively. Variables C (concentration), ρ (density), X (salinity), and H (enthalpy) with
subscripts l (liquid), g (gas), h (hydrate), x (salt), and s
(sediment) are the properties of individual phases (liquid
solution, free gas, solid gas hydrate, salt, and solid
sediment). For example, Hl, Hg, Hs, Hx, and Hh represent
enthalpies of liquid, gas, solid sediment, salt, and hydrate, respectively. Similarly, we can define other variables with subscripts. These variables are either constants or functions of P, T, and salinity of the corre-
Time-dependent equations stated above show that the
hydrate and bubble volumes evolve into steady states
after approximately several million years. For the onedimensional case steady state solutions can be obtained
by integrating the time-dependent equations (1) ― (4)
from t = 0 for a sufficiently long time. But the treatment
in computational efficiency is low. Substantial improvements are possible if the problem is reformulated
to solve directly for the steady state. One method is the
approximate analytical method under some suitable assumptions, and the other is the discretization method
such as finite-difference and finite-element methods in
which we first discretize eqs. (1)―(4) and then solve the
resulting finite-difference equations. We note that the
goal of this paper is to gain fundamental physical insights into the effects of salinity on the natural gas hydrate systems in natural environments through the application of a simple model. For this like Xu and Ruppel’s work[25] we assume that the hydrate system is
steady under certain boundary conditions and salts are
completely dissolved into liquid. At the same time, we
also assume that the amount of hydrate and salt in pore
YANG DingHui et al. Sci China Ser D-Earth Sci | Nov. 2007 | vol. 50 | no. 11 | 1733-1745
1735
space is sufficiently small that the liquid phase occupies
almost the entire available porosity, and the advective
and diffusive effects of solid hydrate are negligible.
Following the treatment suggested by Xu and Ruppel[25],
with these assumptions the governing equations for the
one-dimensional system reduce approximately from eqs.
(1)―(4) to
qf = −
k ρl ⎛ dP
⎞
+ ρl g ⎟ = constant,
⎜
μl ⎝ dz
⎠
(5)
dT
= constant,
(6)
dz
dCl
,
(7)
qm = q f Cl − φ Dc ρl Sl
dz
where Cl0 is specific heat capacity of liquid water, Cl is
concentration of methane, qf and qe stand for constant
fluxes of total fluid mass and energy in all regions below
the seafloor, respectively. Sl equals 1 based on our previous assumptions, and qm represents depth-dependent
methane flux, which is a subsection function. In other
words, below the base of the MHZ, qm is a constant
given by the corresponding boundary condition. In the
region above the top of the MHZ, qm reduces to a constant and equals the flux qmT at the top of the MHZ. And
qm is not a constant within the MHZ.
qe = q f Cl 0T − λ
1.3 Hydrate stability and actual zone of hydrate
occurrence
(i) Locations of MHSZ boundaries. The phase boundaries for methane gas hydrate have been determined experimentally for pure water[2] and salt-water[29] systems.
In theory, the intersection of the local geotherm with gas
hydrate stability constraints defined the base of the gas
hydrate zone. However, in dynamic systems, the positions of the MHSZ boundaries depend on the flux of
various system components and must be written as functions of the mass and energy transport[25]. In other words,
we first determine the actual geotherm via the approximate model in section 1.2 and then solve the intersection
of the geotherm with hydrate stability constraints to get
the position of the MHSZ. For the steady state system,
integrating to eqs. (5) and (6), we can obtain the following expressions[25]:
⎧
⎛ qe − q f Cl 0T0 ⎞
λ
ln ⎜
⎪z = −
⎟,
q f Cl 0 ⎜⎝ qe − q f Cl 0T ⎟⎠
⎪
⎨
λ
⎪
qf = 0
⎪ z = − q (T − T0 ),
e
⎩
1736
qf ≠ 0
(8)
and these relations between pressure and temperature
⎧
⎛ qe − q f Cl 0T0 ⎞
⎛ q f μl
⎞ λ
+ ρl g ⎟
ln ⎜
⎪ P = P0 + ⎜
⎟,
⎪
⎝ k ρl
⎠ q f Cl 0 ⎜⎝ qe − q f Cl 0T ⎟⎠
⎪
qf ≠ 0
(9)
⎨
⎪
⎪ P = P + ρl g λ (T − T ),
qf = 0
0
0
⎪
qe
⎩
where P0 and T0 are seafloor pressure and temperature,
respectively.
When eq. (9) is coupled with methane hydrate stability curves that are treated as a function of pressure and
salinity and is regressed from the data obtained using the
CSMHYD software[2] (Appendix), the pressure PT (and
PB) and temperature TT (and TB) at both the top and base
of the MHSZ can be determined. We can determine the
locations of the MHSZ by substituting the values of TT
and TB into (8), respectively.
(ii) Top and bottom of MHZ. The locations of MHZ
boundaries can be determined by solving the intersections of the solubility curve with concentration curve for
the steady state system. Within the MHZ solubility or
the dissolved methane mass fraction can be written as a
function of pressure and temperature[35]. Above the top
of the MHZ, integrating (7) with the seafloor boundary
condition Cl (z = 0) = C0 from the top of MHZ to the
seafloor, we can determine the top depth of the MHZ as
follows:
⎧
φ D ρ ⎛ qmT − q f C0 ⎞
⎪ zT = − c l ln ⎜
⎟, qf ≠ 0
⎜ qmT − q f Csl ( zT ) ⎟
qf
⎪
⎝
⎠
(10)
⎨
φ Dc ρl
⎪
[Csl ( zT ) − C0 ],
qf = 0
⎪ zT = − q
mT
⎩
where C0 is the concentration of methane at the seafloor
boundary, Csl (zT) is the solubility of methane at the top
boundary (zT) of the MHZ. From the computational expression stated above we can see that eq. (10) is the
same as Xu and Ruppel’s results[25] for the pure-water
case except that the solubility (Csl (zT)) in eq. (10) is
calculated as a function of pressure, temperature, and
salinity of liquid solution. The above intersection point
(top of the MHZ) (zT) of the solubility and methane
concentration curves yields[25]
dCl ( zT ) dCsl ( zT )
=
,
(11)
Cl ( zT ) = Csl ( zT ),
dz
dz
so from (7) we have
dCsl ( zT )
.
(12)
qmT = q f Csl ( zT ) − φ Dc ρl Sl
dz
YANG DingHui et al. Sci China Ser D-Earth Sci | Nov. 2007 | vol. 50 | no. 11 | 1733-1745
Knowing methane solubility Csl and its derivative at z
= zT, the position of the top of the MHZ can be calculated from (10) for the steady state system. In practical
calculations, we can calculate iteratively to determine zT
by using eqs. (10) and (12).
The base of the MHZ (zB) may often be shallower
than the base of the MHSZ (MHSZB) due to the dependence of the MHZ base on the rate of methane supply[25]. At the location of the base of the MHZ (MHZB),
the following relations are satisfied by
dCl ( z B ) dCsl ( z B )
=
,
Cl ( z B ) = Csl ( z B ),
dz
dz
qm = qmB ,
(13)
so we have
dCsl ( z B )
.
(14)
qm = qmB = q f Csl ( z B ) − φ Dc ρl Sl
dz
Knowing the methane flux qm at the boundary, the
location of the MHZB can be determined iteratively using (14). Using (12) and (14) together yields the thickness of the MHZ, which depends obviously on a combination of the rates of fluid flux qf, energy flux qe, methane flux qm, salinity, and the water depth at the seafloor.
For a given rate of fluid flux, increasing methane flux qm
results in a thicker MHZ up to the critical point, which
occurs when the MHZB coincides with the MHSZB for
a pure-methane and pure-water system[25]. For the puremethane and saltwater system we shall further show the
results for the critical flux in subsection 2.4.
2 Numerical results
The basic theory stated above can be used to derive the
relations between the MHSZ, the MHZ and these parameters such as the rates of fluid flux qf, energy flux qe,
methane flux qm, the salinity, the water depth at the seafloor, and so on. In this section, numerical results are
used further to demonstrate the influence of different
parameters such as salinity, water depth, energy flux,
and methane flux on the MGH system with saltwater.
Following Xu and Ruppel[25], we here use observational
data to constrain the physical parameters given in section 1. Table 1 lists the physical properties of the hydrate
system used in our present calculations. These parameters coincide basically with those of the standard MGH
system. Some values in Table 1 have been chosen to
crudely represent those that might be applied to marine
systems like the Blake Ridge[25].
Table 1
Physical parameters used in calculations
Symbol
g
Parameter
Value
Units
9.81
m s−2
gravitational acceleration
T0
temperature at seafloor
3
℃
us
sedimentation rate
0
m s−1
φ
porosity
Dm
methane diffusivity in seawater
0.5
1.3×10−9
−8
kg m−1 s−1
kg kg-1
C0
methane concentration at seafloor
1×10
qf
total mass flux
1×10−8
kg m−2 s−1
qe
total energy flux
30―60
mW m−2
qh
total hydrate flux
0
kg m−2 s−1
Qc
rate of methane gas production
0
kg m−3 s−1
k
permeability
1×10−14
m2
λ
ρl
bulk thermal conductivity
1.0
W m−1 K−1
density of liquid-phase fluid
1024
kg m−3
Cl0
specific heat capacity of fluids
4.18
kJ kg−1 K−1
μl
viscosity
8.87×10−4
kg m−1 s−1
X
salinity
0.035
kg kg−1
2.1 Effects of salinity on the MHSZ
On the basis of the approximate steady state model
given in section 1, the previous calculations[25] included
only effects of various parameters such as the rates of
energy flux qe, methane flux qm, and the water depth at
the seafloor on the MHSZ and do not account for the
influence of salinity on the MHSZ. We investigate effects of salinity on the MGH system. By including salinity, the methane hydrate stability is a function of pressure and salinity, which is obtained by the regressed
method from these data obtained[2] (see Appendix).
Effects of salinity are shown in Figure 1 using the
constant salinity S = 0.035 kg/kg that is comparable to
that of seawater. For comparison, the top and base of the
MHSZ for the pure-water pure-methane case are also
shown in Figure 1. Figure 1 shows that the MHSZB
(MHSZB-1) for the pure-methane seawater case (Stabiliy-1) is shallower than that base (MHSZB-2) for the
pure-methane pure-water case (Stabillity-2), which is
identical with previous results[20,30,36,37]. In other words,
water in marine gas hydrate systems contains dissolved
salts, which reduces the stability of gas hydrate. The
shallower MHSZB results in the shallower MHZB in
gas hydrate systems with salts (MHZB-1) compared
with that in pure-methane pure-water systems (MHZB-2)
(see Figure 2).
Figure 2 shows effects of salinity on the bases of
MHSZ and MHZ, and the top of the free gas zone
(GAST). Comparison between the pure-methane sea-
YANG DingHui et al. Sci China Ser D-Earth Sci | Nov. 2007 | vol. 50 | no. 11 | 1733-1745
1737
the MGH system with salts are shallower than those for
the pure-methane pure-water system, and shoal as the
salinity increases.
2.2 Effects of salinity on the MHZ
Figure 1 Comparison of effects of salinity on the MHSZ between MGH
systems with salts and without salts for an assumed seafloor pressure
corresponding to 2800 m water depth. Curves stability-1 and stability-2
represent the stability temperatures for gas hydrate systems with salts and
without salts, respectively, and curves MHSZB-1 and MHSZB-2 show the
bases of the MHSZ for the saltwater and pure-water systems, respectively.
Figure 2 Comparison of depths versus salinity between the MHZB and
the MHSZB and the top of the free gas zone for the pure-methane saltwater and pure-methane pure-water systems, which the depths are calculated
as a function of salinity X for the constant methane flux qm = 2.7×10−11 kg
s−1 m−2 and energy flux 40 mW m−2 at the water depth of 2700 m. Where
dashed curves MHZB-1, MHSZB-1, and GAST-1 represent the bases of
the MHZ and the MHSZ, the top of the free gas zone for the saltwater
system, respectively, and solid curves MHZB-2, MHSZB-2, and GAST-2
represent the bases of the MHZ and the MHSZ, and the top of the free gas
zone for the pure-water system, respectively.
water and pure-methane pure-water cases shown in Figure 2 indicates that the MHSZB for the MGH system
with salts is generally shallower than that of the puremethane pure-water case except for salinity equal to
zero, and the degree of MHSZ deepening increases with
decreasing salinity. This trend can also be observed on
depths below seafloor (mbsf) versus salinity curves
given in Figure 2, where the MHZB and the GAST for
1738
In order to understand the effects of salinity on the top
and base of the MHZ, we chose the same model parameters as those given in Table 1. In fact, from Figure 2
we have seen the influence of salinity on the MHZ. In
the following we give again more numerical results to
further demonstrate the effect of salinity on gas hydrate
systems.
Figure 3 shows that the thickness of the MHZ depends on a combination of the rates of energy flux qe,
methane flux qm, salinity, and the water depth at the seafloor for the pure-methane seawater hydrate system. For
a given rate of fluid flux, increasing methane flux results
in a thicker MHZ up to the critical point denoted by the
attainment of constant MHZ thickness in Figure 3. This
critical point occurs when the MHZB instantaneously
coincides with the MHSZB and the GAST. Beyond the
critical point, further increases in methane flux rate will
not produce a thicker MHZ (see Figure 3). This is identical with results given by Xu and Ruppel for the puremethane pure-water system[25]. Figure 3 also shows that
for constant rates of fluid and methane fluxes increasing
energy flux produce a thinner MHZ.
For comparisons, Figure 4 shows the thickness of the
MHZ for the gas hydrate systems with salts (lines 1 and
3) and without salts (lines 2 and 4). In Figure 4 the bases
of the MHZ for the hydrate system with salts shown by
lines 1 and 3 are shallower than those for the hydrate
system without salts shown by lines 2 and 4. This suggests that the presence of salts reduces the thickness of
the MHZ. The tendency is also shown in Figure 2 and is
identical with previous results[20,29].
In order to further illustrate the influence of salinity
on the thickness of the MHZ, Figure 5 presents changes
of thickness of MHZ with salinity. For given rates of
fluid flux and methane flux, increasing salinity results in
a thinner MHZ up to the critical depth that the base and
the top of the MHZ become coincident in Figure 5. The
critical salinity, which results in no gas hydrate to form
within the MGH zone, decreases with increasing energy
flux. For a given salinity, the top of the actual hydrate
occurrence tends to a shallower location as the heat flux
increases, and the salinity does not affect the top of the
MHZ, as shown in Figure 5.
YANG DingHui et al. Sci China Ser D-Earth Sci | Nov. 2007 | vol. 50 | no. 11 | 1733-1745
Figure 3 The top and base of the MHZ as a function of methane flux rates at constant water depths of (a) 1000 m, (b) 2000 m, and (c) 3000 m at the
seafloor, assuming a constant fluid flux rate of 10−8 kg s−1 m−2 (about 0.3 mm a−1). Where three curves located at the top in (a), (b), and (c) show the top of
the MHZ while three curves located at the bottom show the base of the MHZ, corresponding to heat flux rates of 50, 40, and 30 mW m−2, respectively.
Figure 4 Comparison of the thickness of the MHZ between gas hydrate
systems with salts (lines 1 and 3) and without salts (lines 2 and 4). The
thickness is calculated as a function of the methane flux qm for constant
energy fluxes of 40 and 30 mW m−2 at the water depth of 1000 m.
Figure 5 Influence of salinity on the top and the base of the actual zone
of gas hydrate occurrence (MHZ) for the total methane flux qm = 1×10−11
kg s−1 m−2 and constant energy fluxes of 50, 40, and 30 mW m−2 at the
water depth of 2000 m.
2.3 Effects of salinity on the top of free gas
Free gas is present in the deeper sediments, while gas
hydrate occurs at shallower depths when the gas con-
centration exceeds the solubility[20,25]. For methane flux
rates lower than the critical value the GAST is not coincident with the bases of the MHZ/MHSZ, and the MHZ
YANG DingHui et al. Sci China Ser D-Earth Sci | Nov. 2007 | vol. 50 | no. 11 | 1733-1745
1739
is separated from the free gas zone by a layer of sediment containing neither gas hydrate nor free gas[25].
Figure 2 has shown the relationships between the GAST
and the bases of the MHZ/MHSZ. From Figure 2 we can
see that the free gas zone exists deeper than both the
MHZ and the MHSZ, and the GAST shoals gradually
with the salinity increasing. We can also observe that the
GAST for the pure-methane saltwater case is shallower
than that of the pure-methane pure-water case except for
the limit case of salinity equal to zero. In the following
example presented in this subsection, we would like to
use the same calculation method stated previously to
investigate the effects of salinity on the GAST for different energy fluxes.
In the numerical calculation, we similarly chose the
physical parameters given in Table 1. The predicting
results for the GAST are shown in Figure 6 for two gas
hydrate systems with and without salts. In Figure 6 lines
1, 3, and 5 (solid lines) correspond to energy fluxes of
50, 40, and 30 mW m−2 for the gas hydrate system with
salts, while lines 2, 4, and 6 (dashed lines) corresponding to the three cases represent the tops of the MHZ for
the pure-methane pure-water system. Figure 6 shows for
different energy fluxes that the GAST in the gas hydrate
system with salts is shifted upward as compared to that
in the gas hydrate system without salts. This suggests
that the presence of salts increases the thickness of the
free gas zone if the abundance of gas in marine sediments can be provided. From Figure 2 we also have the
same conclusion.
2.4 Critical rates of methane supply
The MHZB does not coincide with the MHSZB in the
pure-methane pure-water system[25]. For the gas hydrate
setting with salts, similar conclusion can be obtained. In
fact, the MHZB is only equivalent to the MHSZB when
methane mass flux qm exceeds a critical value that produces a concentration excess of methane solubility in
salt water within all MHSZ. Figure 7 shows the results
of calculations to determine this critical methane flux
value as a function of water depth at the seafloor and
various fluid fluxes of qf for the given energy flux 40
mW m-2. The result shown in Figure 7 demonstrates that
the critical methane flux rate necessary for the MHZB to
coincide with the MHSZB is strongly dependent on the
total fluid flux. The critical methane flux rate increases
with increasing the water depth (or pressure) at seafloor,
and the slope of critical methane flux rate profile also
gradually becomes larger with increasing the fluid flux
rate. Figure 7 also shows numerically that marine sediments characterized by high advection rates require a
high rate of methane supply if the actual hydrate occurrence is to extend to the MHSZB. This result has important implications for assessment of the resource potential
of methane gas hydrate deposits in marine sediments.
Figure 7 Critical methane flux qm for the MHZB to coincide with the
MHSZB, which is calculated as a function of water depth (or pressure) at
seafloor. The four curves correspond to the fluid flux rates of 2 mm/a, 1.4
mm/a, 0.8 mm/a, and 0.3 mm/a, respectively.
2.5 Effects of salinity on the solubility and saltwater
system
Figure 6 Comparison of the top of the free gas zone between gas hydrate systems with salts (lines 1, 3, and 5) and without salts (lines 2, 4, and
6), the top boundaries are calculated as a function of the methane flux qm
for constant energy fluxes of 50, 40, and 30 mW m-2 at the water depth of
2000 m.
1740
The existence of salts in pore water shifts the MHSZB to
shallower depths, which is shown in Figure 1, and
causes a small reduction in the solubility of methane[33].
Changes in methane solubility have been calculated by
YANG DingHui et al. Sci China Ser D-Earth Sci | Nov. 2007 | vol. 50 | no. 11 | 1733-1745
Table 2
Comparison of depths (m) of base and top of the MHSZ, the MHZ, and the free gas zone for the saltwater (case 1) and pure-water (case 2) cases
Top of the MHZ
Base of the MHZ
Base of the MHSZ
Top of the free gas zone
Case 1
112.30
382.92
407.77
415.74
Case 2
112.31
369.07
425.78
554.23
Zatsepina and Buffett[20] using 0.6-mol solution of NaCl
that is approximately equivalent to 0.035 kg/kg. Their
calculations for the solubility show that a linear dependence on the salinity X. Recently, Davie et al.[21]
suggested a calculation formula of the solubility as
Csl (T , P, X ) = (1 − β X )Cslpure (T , P) .
(15)
Cslpure (T , P) is the solubility at the base of the MHSZ in
the pure water case, which is calculated by two steps.
The solubility at the conditions of three-phase equilibrium is first approximated by a linear function of temperature and pressure and then extended this solubility
into the MHSZ using simple parametric equations[21].
The calculation may produce big errors for the solubility
Cslpure (T , P) at the intersection points. In this paper,
calculations of the solubility at any depths are based on
the steady state model presented in subsection 1.2,
which is treated as a function of pressure, temperature,
and salinity of the liquid solution. The computational
steps are given as follows:
We first calculate the solubility at any depths from the
MHSZB to the seafloor, using the following formula:
Csl (T , P) = d exp(a + b ln P + c ln 2 P) × exp[α (T − Ts )] ,
(16)
where Ts is the stability temperature for the saltwater
case, and coefficients of a = −26.7534, b = 1.9848, c =
−0.0448, d = 0.8904, and α = 0.07 are determined by
―
using experimental data[34,38 40]. And then we modify
the solubility by using the following formula:
⎧(1 − β% X )Csl (T , P),
X < X0
⎪⎪
Csl (T , P, X ) = ⎨(1 − 0.0058β% )Csl (T , P) ≈ 0.9Csl (T , P),
⎪
X ≥ X0
(17)
⎪⎩
where β% = 17.094 is determined from the results given
by Zatsepina and Buffett[20], and X0 = 0.0058 kg/kg is
approximately equivalent to 0.1 mol.
Figure 8 shows the comparison of the relationship
among the MHZ, the MHSZ, and the free gas zone for
two cases of including simultaneously effects of salinity
(X = 0.025 kg/kg) on both the stability and the solubility
(case 1) and X = 0 (case 2). Labels 1 and 2 shown in
Figure 8 correspond to these results of cases 1 and 2,
respectively. For comparison, the locations of top and
base of the MHZ and the MHSZ, and the location of the
GAST for two cases are also listed in Table 2. From Table 2 and Figure 8 (left) we clearly see that the MHZB
(MHZB-1) for case 1 is deeper than that of case 2
(MHZB-2). It demonstrates that accounting for the influence of salinity on both the solubility and the stability
(case 1) results in more thickness of the MHZ as compared with the pure-water case (case 2), but the GAST
(GAST-1) for case 1 becomes shallower than that of the
pure-water (GAST-2). Figure 8 also shows that the
MHSZB does not coincide with the MHZB because upward flux of methane (qm) does not exceed the critical
value for the saltwater system. The free gas zone only
exists at depths for which the concentration of methane
Cl exceeds methane solubility Csl below the MHSZB
(Figure 8). Figure 8 shows that the free gas zone lies
below the MHSZB and is separated from the MHSZ by
an intervening layer of sediment lacking both gas hydrate and free gas for every case. The intervening layer
between the MHSZB (MHSZB-1) and the GAST
(GAST-1) for the pure-methane system with salts (case 1)
is thinner that for the pure-methane pure-water system
(case 2) (see Figure 8). This may be a significant implication to explain why the MHSZB in many situations
coincides with the GAST because the salinity affects
simultaneously both the stability and the solubility in
natural marine environments.
On one hand, in Figure 8 (right) or Figure 1 the stability curve (stability-1) for cases 1 shifting toward to
the low temperature demonstrates that the salinity depresses the temperature to form gas hydrate in marine
sediments. The physical meaning is that the existence of
salts depresses the stability of gas hydrate. As a result,
the position of the MHZB is shallower than that of the
pure-water system (see Figure 4) as we only account the
influence of salinity on the pure-methane saltwater system. On the other hand, the salinity decreases the solubility from theoretical formulae (15) and (17) further
resulting in the reduction of the minimum methane concentration needed to form hydrate. So when considering
YANG DingHui et al. Sci China Ser D-Earth Sci | Nov. 2007 | vol. 50 | no. 11 | 1733-1745
1741
Figure 8 Comparison of effects of salinity on the MHZ, the MHSZ, and the free gas zone between methane gas hydrate systems with constant salinity
2.5% and without salts for the constant methane flux rate of qm = 2.71×10−11 kg s−1 m−2 and an assumed seafloor pressure corresponding to 3000 m water
depth. Where curves C1 and S1 represent the methane concentration and the solubility including simultaneously effects of salinity on both the stability and
the solubility in natural marine environments, and curves C2 and S2 show the methane concentration and the solubility for the methane gas hydrate without
salts. Below the MHSZ the solubility is approximated by a constant solubility equal to the solubility at the base of the MHSZ. Curves MHZB-1 and
MHZB-2 show the bases of the MHZ for two cases, while GAST-1 and GAST-2 present the tops of the free gas zone for two cases, respectively. Stability-1
and MHSZB-1, stability-2 and MHSZB-2 show the stability curves and bases of the MHSZ for the gas hydrate systems with salts and without salts, respectively.
simultaneously effects of salinity on both the stability
and the solubility, our numerical results (Figures 8 (left)
and 9 in the following) show that the salinity increases
actually the thickness of the MHZ within the MHSZ
although the MHSZB for the saltwater case is shallower
than that for the pure-water case.
In order to further investigate the effect of salinity on
pure-methane saltwater system under this case of simultaneously considering influences of salinity on both hydrate stability and solubility, in the final example the
model parameters are chosen by the total energy flux qe
= 60 mW m−2, total methane flux qm = 2.71 mW m-2,
seafloor temperature T0 = 2 (℃), seafloor depth of 3050
m, and the salinity from 0.6 % to 20 %. Rest parameters
are listed in Table 1. The numerical results are displayed
in Figure 9, where the solid and dashed curves represent
the bases of MHZ and MHSZ, and the GAST for the
pure-water and saltwater cases, respectively.
Figure 9 shows that the MHSZB and the GAST for
the saltwater case are shallower than those for the purewater case in the chosen range of salinity and shoal with
1742
Figure 9 Relationships of depths versus salinity among the MHZB, and
the MHSZB, and the GAST for the pure-methane saltwater system including simultaneous effects of salinity on both the hydrate stability and
the solubility and for the pure-methane pure-water system, of which
depths are calculated as a function of salinity X for the constant methane
flux qm = 2.71×10−11 kg s−1 m−2, energy flux 60 mW m-2, and seafloor
temperature T0 = 2 0C at the water depth of 3050 m. Dashed curves
MHZB-1, MHSZB-1, and GAST-1 represent the MHZB, the MHSZB, and
the GAST for the saltwater system, respectively, and solid curves
MHZB-2, MHSZB-2, and GAST-2 show the MHZB, the MHSZB, and the
GAST for the pure-water system, respectively.
YANG DingHui et al. Sci China Ser D-Earth Sci | Nov. 2007 | vol. 50 | no. 11 | 1733-1745
increasing the salinity, and relationships of MHZB between the pure-water and saltwater cases is different in
different salinity range. In other words, the MHZB for
the pure-methane saltwater system is deeper than that
for the pure-methane pure-water system as the salinity is
smaller than about 3.5% in the chosen range of salinity,
whereas it is shallower than that for the pure-methane
pure-water case when the salinity is greater than 3.5%.
The numerical experiment also illustrates that for the
marine sediments with salts the MHSZB may be shallower than the predicted MHZB by the pure-water
model when the salinity greater than 6.3% and the top of
free gas may be shallower than the MHZB for the
pure-water system as the salinity over 7.3%. Meanwhile,
from Figure 9 we can observe that for the saltwater system the MHSZB is near to the GAST as compared with
the pure-water system.
3 Discussion and conclusions
These factors such as temperature, pressure, salt, sedimentation rate, source of methane supply, and so on affect strongly the formation and dissociation of gas hydrate in marine sediments. Many studies have demonstrated that the temperature, pressure, and salinity are
the most important factors for the formation and the stability of gas hydrate[20,21,29,33,34,41]. When salinity decreases, MGH may be dissolved into seawater, whereas
more MGH may be formed as a result of the decrease in
solubility that occurs when the salinity increases[20,21].
Effects of salinity on the stability also result in affecting
to form gas hydrate because the presence of salts in marine gas hydrate systems depresses the stability of gas
hydrate[20,29,36,37]. Although the obtained results have
made great progress in study about the role of salts in
marine gas hydrate systems, no quantitative links between the gas hydrate and the salinity, which is based on
the extension of the quasi-steady state model suggested
by Xu and Ruppel[25], were established in these studies.
In this study, we incorporate the salinity into a steady
state model presented in subsection 1.2 to establish the
links between the gas hydrate system and the salinity,
and to investigate the influences of salinity on the MGH
stability and the actual gas hydrate occurrence in marine
sediments. By including the salinity into a unified model,
the methane hydrate stability is a function of pressure
and salinity, which is obtained by the regressed method
from these data obtained by Sloan[2] (see Appendix). The
methane solubility is determined by (16) and (17), and
temperature and pressure in (16) and (17) are calculated
by the steady state model presented in subsection 1.2.
We apply our calculations to determining the bases of
the MHSZ and the MHZ, and the GAST for the puremethane saltwater system. Numerical results indicate
that the MHSZB for the pure-methane saltwater case is
shallower than that base for the pure-methane pure-water case, while the top of the MHZ is independence of
the salinity (Figures 5 and 8) but depends on the energy
flux and shoals with increasing the energy flux (Figures
3―6). The shallower MHSZB may result in the shallower MHZB in gas hydrate systems with salts when we
only account to the effect of salinity on the stability. The
salinity decreases directly the thickness of the MHZ as
shown in Figures 2 and 4. Changes in salinity can
strongly affect the formation of actual methane gas hydrate. Increasing salinity decreases the thickness of the
MHZ and increases the thickness of the free gas zone if
the abundance of gas in marine sediments can be provided (Figures 2 and 9). Measured salinity profiles, in
conjunction with the depth of MHZ and MHSZ, provide
a complementary constraint on the quantity and distribution of hydrate and free gas in the sediments.
On one hand, the salinity reduces the stability of gas
hydrate system (see Figures 1 and 8) further resulting in
the shallower MHZB as compared with the pure- methane pure-water case (Figures 2 and 4). On the other hand,
since the salinity lowers the methane solubility from (17)
further resulting in the reduction of the amount of gas
required to form hydrate, the presence of salts in natural
settings may actually promote hydrate formation within
the MHSZ. Speaking more details, the MHZB for the
pure-methane saltwater system is deeper than that for
the pure-water case as the salinity is smaller than 3.5%,
whereas it is shallower than that for the pure-water case
when the salinity is greater than 3.5% (Figure 9). It suggests that we can estimate the position of the MHZ from
the predicted results by the pure-water model and the
salinity of the marine sediment. The curves (Figure 9),
indicating that the MHSZB and the GAST change with
salinities, show that the MHSZB for the saltwater system may be shallower than the predicted MHZB by the
pure-water model when the salinity greater than 6.3%
and the GAST may be shallower than the MHZB for the
pure-water system as the salinity is over 7.3%. Besides,
the MHSZB of the saltwater system is near to the GAST
as compared with the pure-water system (Figures 8 and
YANG DingHui et al. Sci China Ser D-Earth Sci | Nov. 2007 | vol. 50 | no. 11 | 1733-1745
1743
9). This is why the GAST is near or equal to the bases of
the MHSZ/MHZ in many practical marine sediments
because there exists salt in real marine sediments and the
salinity increases the MHZB and decreases the GAST.
Our numerical results also reveal an obvious explanation for the disparity in the depths to the MHZB, the
MHSZB, and the GAST shown in Figures 8 and 9.
When the methane solubility is a function of independence of salinity treated approximately as Xu and Ruppel[25], for certain methane flux rates a free gas zone
could develop far below the MHSZB and be separated
from the MHZB by a zone of marine sediments containing neither free gas nor gas hydrate. However, when
incorporating the effect of salinity on the methane solubility into calculations of the solubility, we find that the
thickness of the separated zone between the MHSZB
and the GAST becomes thinner (see Figures 8 and 9).
Appendix: Stability function
When we consider the influence of salinity on the MGH
system, the methane hydrate stability is treated as a
function of pressure and salinity and is obtained by regressing from data obtained using the CSMHYD software[2] as follows:
Tstability = A( X ) ln P + B ( X ) ln 2 P + C ( X ) ln 3 P , (A1)
in which
A(X) = 12.6223−60.66X+1078.90X2−11080.07X3
+61534.87X4−185885.18X5+231861.14X6,
B(X) = −2.0780+32.43X−740.52X2+8506.69X3
−53994.43X4+175167.33X5-216507.56X6,
C(X) = 0.3418−5.51X+154.32 X2−1985.04 X3
+13855.28 X4−46685.56 X5+58554.43 X6,
where X denotes the salinity and P is pressure. If X = 0,
then Tstability denotes the stability temperature (Tpw) for
the pure water case.
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