Chemical Geology 335 (2013) 128–135
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Chemical Geology
journal homepage: www.elsevier.com/locate/chemgeo
Thermodynamic modeling of ternary CH4\H2O\NaCl fluid inclusions
Shide Mao a,⁎, Jiawen Hu b, Dehui Zhang a, Yongquan Li a
a
b
State Key Laboratory of Geological Processes and Mineral Resources, School of Earth Sciences and Resources, China University of Geosciences, Beijing, 100083, China
College of Resources, Shijiazhuang University of Economics, Shijiazhuang 050031, China
a r t i c l e
i n f o
Article history:
Received 11 February 2012
Received in revised form 6 October 2012
Accepted 8 November 2012
Available online 17 November 2012
Editor: Sherwood Lollar
Keywords:
Equation of state
CH4\H2O\NaCl
Fluid inclusion
Microthermometry
Isochore
PVTx data
a b s t r a c t
This paper reports the application of thermodynamic models, including equations of state, to ternary CH4\
H2O\NaCl fluid inclusions. A simple equation describing pressure–temperature–salinity relations on the
CH4 hydrate-liquid-vapor surface has been developed to calculate the NaCl contents (salinities) of inclusions,
where the dissociation pressure of CH4 hydrate coexisting with vapor and liquid at a given temperature is calculated with a pressure equation of pure CH4. The pressure equation is a function of temperature and CH4
Raman peak position shift corrected by Ne lamp. With these relations and the latest CH4 solubility and
PVTx models, a new iterative approach is presented to calculate the CH4 contents of CH4\H2O\NaCl inclusions on the assumption that the bulk molar volume of an inclusion at the melting temperature of CH4
hydrate and at the vapor bubble disappearance (homogenization) temperature are identical. A prominent
merit of this method is that the compositions, molar volumes and homogenization pressures of CH 4\
H2O\NaCl inclusions can be simultaneously obtained without having to use volume fractions of vapor
bubbles at the dissociation temperatures of CH4 hydrates determined based on optical observations or
measurements. The homogenization pressures and isochores of CH4\H2O\NaCl fluid inclusions from
updated models are briefly discussed. The code to estimate PVTx properties of inclusions in the ternary
system CH4\H2O\NaCl, based on microthermometric and Raman data, can be obtained from Chemical
Geology or the corresponding author ([email protected]).
© 2012 Elsevier B.V. All rights reserved.
1. Introduction
Up to now, fluid inclusions represent a powerful tool to estimate the
pressure–temperature conditions and compositions of fluids associated
with various geological processes (Roedder, 1984; Wilkinson, 2001;
Bodnar, 2003). Methane-bearing inclusions are commonly found in
many geological environments, e.g., sedimentary basins (Wang et al.,
2007), MVT and porphyry deposits (Shen et al., 2010), low-grade
metamorphic rocks (Huff and Nabelek, 2007), mid-ocean ridge hydrothermal environments (Kelley and Fruh-Green, 1999; Kelley et al.,
2005), and mafic–ultramafic rocks (Liu and Fei, 2006). Among the
various methane-bearing inclusions, the most typical are the ternary
CH4\H2O\NaCl inclusions. These salt-bearing methane inclusions
contain coexisting H2O\NaCl-rich liquid phase and CH4-rich vapor
phase at room temperatures. On heating they usually homogenize to
liquid by the disappearance of bubble, and they may form CH4 hydrate
and/or ice during cooling. Analysis of the PVTx properties of CH4\H2O\NaCl inclusions requires both experimental data and theoretical
simulations. By combining experimental microthermometric and
Raman analysis, we can obtain the phase-transition temperatures and
bulk compositions of inclusions (Guillaume et al., 2003; Becker et al.,
2010). From thermodynamic models using equations of state (EOS),
⁎ Corresponding author.
E-mail address: [email protected] (S. Mao).
0009-2541/$ – see front matter © 2012 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.chemgeo.2012.11.003
we can calculate the homogenization pressures, molar volumes (or
densities) and isochores of inclusions.
However, how to determine the compositions of inclusions is still a
tough issue for the studies of CH4\H2O\NaCl inclusions. Before
constructing isochores from thermodynamic models, the inclusion
compositions must be known. Guillaume et al. (2003) obtained the
methane contents using Raman spectroscopy calibrated with synthetic
fluid inclusions. This approach can be used only when ice-melting temperature and total homogenization temperature are measured. For the
CH4-H2O-NaCl system, CH4 hydrate is often found at low temperatures
and high pressures. However, Guillaume et al. (2003) neglect the presence of a clathrate, which increases the salinity of the liquid solution
and therefore decreases the melting temperature of ice. To calculate
the compositions of CH4-H2O-NaCl inclusions, Bakker took the observed
volume fraction of vapor at the hydrate dissociation temperature as
input variable in his calculation softwares (Bakker, 2003, 2009). Although the volume fraction is improved by the use of the petrographic
microscope in conjunction with a spindle-stage (Bakker and Diamond,
2006), this method does not fit the negative-crystal inclusions. In the recent years, Raman spectroscopy methods have been widely used to determine the positions of the Raman methane symmetric stretching
band of CH4-bearing aqueous systems (Lin et al., 2007; Lu et al., 2007,
2008; Lin and Bodnar, 2010). Lin et al. (2007) determined the positions
of the Raman methane symmetric stretching band corrected simultaneously by Ne lamp over the range of 1–650 bar and 0.3–22 °C, and
S. Mao et al. / Chemical Geology 335 (2013) 128–135
an empirical pressure equation of methane was established as a function of temperature and CH4 Raman peak position shift:
P ¼ a0 þ
2
8
X
X
ai ðT−273:15Þiþ1 þ ν ai ðT−273:15Þi−3
i¼1
ð1Þ
i¼9
5 X
5
X
i
j
bi;j ðν−2913:46Þ ðT−273:15Þ
þ
i¼2 j¼0
where P is pressure in bar, T is temperature in K, ν is the measured
Raman peak shift in cm−1, and ai and bi,j are regressed parameters
(Table A1). The standard pressure error of Eq. (1) is 1.22 bar.
In this work, we first develop a simple dissociation pressure equation of methane hydrate as a function of temperature and salinity,
from which the salinity of an inclusion can be easily calculated provided temperature and pressure are given. Then, with the pressure
equation of methane of Lin et al. (2007), the pure CH4 density equation of Setzmann and Wagner (1991), the latest CH4 solubility
model of Duan and Mao (2006) and PVTx model of Mao et al.
(2010), a new iterative algorithm is presented to calculate CH4 contents and homogenization properties of ternary CH4\H2O\NaCl inclusions. Finally, the chosen phase-equilibrium and PVTx models of
CH4\H2O\NaCl system are briefly discussed.
2. Compositions of CH4\H2O\NaCl fluid inclusions
2.1. Salinities of CH4\H2O\NaCl inclusions
The salinities of CH4\H2O\NaCl fluid inclusions are calculated by
using the dissociation temperatures of CH4 hydrates. According to the
Gibbs phase rule, the ternary CH4\H2O\NaCl system has two degrees of freedom on the hydrate-liquid-vapor surface. That is, the
pressure on the hydrate-liquid-vapor surface is a function of salinity
and temperature which can be determined by the disappearance of
CH4 hydrate. In principle, the dissociation pressures of CH4 hydrates
can be calculated from some accurate hydrate equilibrium models
(Diamond, 1994; Ballard and Sloan, 2002, 2004a,2004b; Jager et al.,
2003; Duan and Sun, 2006). However, these models are usually very
complicated and uneasy to calculate the salinities of CH4\H2O\NaCl
inclusions. For this reason, a simple hydrate dissociation equation is
developed here.
5
X
ci T
Table 2
Calculated pressure deviations from experimental data at hydrate–liquid–vapor
equilibria.
References
T (K)
mNaCl
(mol kg−1)
Nd
AAD
(%)
MAD
(%)
(de Roo et al., 1983)
(Dholabhai et al., 1991)
(Jager and Sloan, 2001)
(Maekawa, 2001)
(Kharrat and Dalmazzone,
2003)
261.85–285.98
272.69–279.35
270.66–303.48
274.2–288.2
271.4–284
0–5.43
0.53
0–4.84
0–0.53
0–3.53
32
6
54
37
9
2.24
1.23
4.19
1.96
3.17
4.79
3.09
17.07
4.52
7.75
i¼3
13
X
i−8 þ ai exp −ð2911−νÞ lnP ¼
129
i−1
þ mNaCl
1
10
X
ci T
i−6
2
þ mNaCl
6
15
X
ci T
i−11
ð2Þ
11
phase equilibria. The total average pressure deviation from these experimental data is 2.95%. Figs. 1 and 2 show the comparisons between
the experimental data and model predictions for the binary CH4-H2O
system and the ternary CH4\H2O\NaCl system, respectively. The
dissociation pressures of CH4 hydrates are reproduced by Eq. (2) up
to high pressures within experimental uncertainties, which are also
in good agreement with the results calculated from the accurate
Duan and Sun (2006) model. For the CH4\H2O system, Eq. (2) is
valid for 273–316 K; for CH4\H2O\NaCl system, Eq. (2) is valid for
T ≤ 296 K and mNaCl ≤ 5.5 mol kg −1.
The dissociation temperature of CH4 hydrate can be measured by
microthermometric analysis and the pressure at this temperature can
be calculated by Raman analysis (Lin et al., 2007). Subsequently, the salinity of the liquid phase is defined by Eq. (2). Thus, the salinities of ternary CH4\H2O\NaCl inclusions can be directly calculated from Eq. (2)
with a valid salinity range of 0–5.5 mol kg−1. Fig. 3 shows the relationship of temperature, pressure, salinity and corrected methane Raman
peak shift of ternary CH4\H2O\NaCl inclusions at the hydrate–liquid–
vapor equilibrium. Fig. 4 shows the relation between salinity and dissociation temperature of CH4 hydrate for the ternary CH4\H2O\NaCl
inclusions at different pressures, as well as the salinity deviations arising
from the standard pressure deviation (1.22 bar) from Eq. (1) and the average pressure deviation (2.95%) of Eq. (2). It can be seen from Fig. 4 that
the salinity deviation increases with increasing temperature but decreases with increasing pressure.
In fact, when CH4 hydrates in an inclusion dissolves, liquid and vapor
bubble remain, and the salinity calculated from Eq. (2) is the content of
NaCl in liquid phase. Because the contents of water and NaCl in the
vapor bubble are low at low temperatures, the salinity calculated from
Eq. (2) approximately represents the bulk salinity of an inclusion. This
method of combing pressure of fluid inclusion obtained from Raman
spectroscopic analysis and measured clathrate melting temperature to
determine the salinity of a fluid inclusion is similar to the method described by Fall et al. (2011) for the H2O\CO2\NaCl inclusions.
800
700
600
P (bar)
where P is the hydrate dissociation pressure in bar, T is temperature
in K, mNaCl is the molality of NaCl, and ci's are parameters (Table 1)
regressed with the same weight from reliable experimental hydrate–liquid–vapor data (de Roo et al., 1983; Dholabhai et al., 1991;
Jager and Sloan, 2001; Maekawa, 2001; Kharrat and Dalmazzone,
2003) reviewed by Duan and Sun (2006). Table 2 shows the deviations of Eq. (2) from the experimental data of hydrate–liquid–vapor
AAD: average absolute deviations calculated from Eq. (2); MAD: maximal absolute
deviations calculated from Eq. (2); Nd: number of data points.
Table 1
Parameters of Eq. (2).
500
de Roo et al. (1983)
Jager and Sloan (2001)
Maekawa (2001)
Kharrat and Dalmazzone (2003)
This study
Duan and Sun (2006)
400
300
Parameter
Value
Parameter
Value
200
c1
c2
c3
c4
c5
c6
c7
c8
0.25494028D+04
−0.31751341D+02
0.14596120D+00
−0.29275456D−03
0.21606982D−06
−0.34240283D+04
0.47693085D+02
−0.24925194D+00
c9
c10
c11
c12
c13
c14
c15
0.57920308D−03
−0.50485929D−06
0.40044909D+03
−0.54933907D+01
0.28186500D−01
−0.64079832D−04
0.54436180D−07
100
0
275
280
285
290
295
300
305
T (K)
Fig. 1. P–T conditions of the hydrate–liquid–vapor phase equilibria in the binary
CH4\H2O system.
130
S. Mao et al. / Chemical Geology 335 (2013) 128–135
a
5
NaCl
(mol.kg-1) =5.43 4.69
3.53
4
de Roo et al. (1983)
Dholabhai et al. (1991)
Maekawa (2001)
This study
Duan and Sun (2006)
140
120
0.53
100
P (bar)
100 bar
200 bar
300 bar
2.27
mNaCl(mol.kg-1)
m
80
3
2
1
60
0
40
275
20
260
265
270
275
280
m
NaCl
(mol.kg-1) =4.84 3.54 2.08 1.13
Jager and Sloan (2001)
This study
Duan and Sun (2006)
700
600
290
295
285
b
800
285
THLV
T (K)
P (bar)
280
Kharrat and Dalmazzone (2003)
Fig. 4. Relationship between salinity and dissociation temperature of CH4 hydrate for
the ternary CH4\H2O\NaCl fluid inclusions: THLV is the dissociation temperature of
CH4 hydrate with coexisting liquid and vapor, and mNaCl is the salinity in mol kg−1.
The vertical short bars stand for the salinity deviations arising from the standard pressure deviation (1.22 bar) from Eq. (1) and the average pressure deviation (2.95%) of
Eq. (2).
hydrates. Therefore, the pressure equation of Lu et al. (2007) is not
used in this work, but the equation of Lin et al. (2007), together with
Eq. (2), is used to determine the salinities of CH4\H2O\NaCl inclusions.
500
400
2.2. CH4 contents of CH4\H2O\NaCl inclusions
300
200
100
265
270
275
280
285
290
295
300
T (K)
Fig. 2. P–T conditions of the hydrate-liquid-vapor phase equilibria in the ternary CH4H2O\NaCl system: (a) low temperatures and low pressures and (b) low temperatures
and high pressures.
It should be noted that Lu et al. (2007) also presented a unified pressure equation of methane as a function of measured Raman shifts of
C\H symmetric stretching band in the methane vapor phase near
room temperature. If this equation is applied to calculate the dissociation pressures of CH4 hydrates in CH4\H2O\NaCl inclusions, the
Raman shifts of C\H symmetric stretching band near zero pressure
must be measured at different dissociation temperatures of CH4
350
300
3
4
5
0 2912
1
2
PHLV (bar)
250
2913
200
2914
150
2915
100
2916
50
2917
0
Salinity in mol.kg
-1
-1
Corrected Raman peak shift of CH4 in cm
275
280
285
290
295
THLV (K)
Fig. 3. Relationship between THLV, PHLV, salinity and corrected methane Raman peak
shift of the ternary CH4\H2O\NaCl fluid inclusions: THLV and PHLV are the dissociation
temperature and pressure of CH4 hydrate at the hydrate–liquid–vapor equilibrium,
respectively.
If CH4 hydrate is not observed at low temperatures, the method of
Guillaume et al. (2003) can be used to calculate the CH4 contents of
CH4\H2O\NaCl inclusions with the ice-melting temperatures and
total homogenization temperatures. If a CH4\H2O\NaCl inclusion is
not a negative-crystal inclusion and the volume fraction of vapor bubble
at the disappearance temperature of CH4 hydrate is well measured by
the improved approach of Bakker and Diamond (2006), the following
equation can be used to calculate CH4 content of the CH4\H2O\NaCl
fluid inclusion:
bulk
x
0
1
!−1
1−φvap ⋅xðCH4 Þ
φvap ⋅yðCH4 Þ
φvap
1−φvap
@
A
ðCH4 Þ ¼
þ
þ
⋅
V m;vap
V m;liq
V m;vap
V m;liq
ð3Þ
where x bulk(CH4) is the total mole fraction of CH4 in the inclusion, φvap is
the volume fraction of vapor bubble at the disappearance temperature
of CH4 hydrate, y(CH4) and x(CH4) are the mole fractions of CH4 in the
vapor phase and liquid phase at the hydrate-liquid-vapor equilibrium
temperature, respectively, Vm,vap and Vm,liq are the molar volumes of
vapor phase and liquid phase at the hydrate–liquid–vapor equilibrium
temperature, respectively. Because the water content of vapor phase
is very low at the disappearance temperature of CH4 hydrate (which
is generally below 20 °C), y(CH4) ≈ 1.0 is used in Eq. (3) below 20 °C.
x(CH4) is a function of temperature, pressure and salinity, which
can be calculated by combining Eqs. (1) and (2) and the methane solubility model of Duan and Mao (2006). Vm,vap in Eq. (3) is a function
of temperature and pressure and is calculated from equation of state
of pure methane (Setzmann and Wagner, 1991) due to the negligible
contents of water and NaCl in vapor. Vm,liq in Eq. (3) is a function of
temperature, pressure and composition (mNaCl and x(CH4)), which
can be calculated from the general PVTx model (Mao et al., 2010).
bulk
Combining φvap, Vm,vap and Vm,liq, the bulk molar volume Vm
of the
inclusion can be calculated from the following equation:
bulk
Vm
¼
φvap
V m;vap
þ
1−φvap
V m;liq
!−1
ð4Þ
S. Mao et al. / Chemical Geology 335 (2013) 128–135
131
In the above calculation for determining the CH4 contents of CH4H2O\NaCl inclusions, φvap is an input variable, whose values are
obtained from experimental measurements. The relative accuracy of estimated volume fraction φvap is ±4% if the improved method (Bakker
and Diamond, 2006) is used. This approach has been used for the binary
CH4\H2O fluid inclusions (Mao et al., 2011), but it is time-consuming.
In order to solve the above issue, an iterative approach is presented
to calculate the CH4 contents of CH4\H2O\NaCl inclusions on the prerequisite that molar volumes of inclusions by the disappearance of CH4
hydrate equal to those by the total homogenization into the liquid
phase. One prominent merit of this method is that the compositions,
molar volumes and homogenization pressures of CH4\H2O\NaCl inclusions can be obtained simultaneously without using optical volume
fractions of vapor bubbles at the dissociation temperatures of CH4 hydrates. The whole calculation is based on a bisection algorithm, whose
main steps are summarized as follows:
Step 1 Input the dissociation temperature of methane hydrate on the
hydrate–liquid–vapor equilibrium surface (THLV), the corrected
Raman peak shift of vapor methane (ν), and the total homogenization temperature Th(total),then use Eq. (1) to calculate the
dissociation pressure of methane hydrate on the hydrateliquid-vapor equilibrium surface (PHLV).
Step 2 Calculate salinity (mNaCl) from Eq. (2) with the input THLV and
the calculated PHLV from Eq. (1).
Step 3 Calculate x(CH4) with THLV, PHLV and mNaCl from the methane
solubility model of Duan and Mao (2006).
Step 4 Calculate Vm,vap with THLV and PHLV from the equation of state of
Setzmann and Wagner (1991), where the vapor is approximated as pure CH4; at the same time, calculate Vm,liq with THLV, PHLV,
mNaCl and x(CH4) from the PVTx model (Mao et al., 2010).
Step 5 Calculate the maximal volume fraction φvap(max) at THLV by
Th(total). Because the maximal applicable pressure of the
methane solubility model (Duan and Mao, 2006) is 2000 bar,
φvap(max) is calculated from Eq. (3), where the maximal methane content is from the Duan and Mao (2006) model with
Th(total), mNaCl and 2000 bar.
Step 6 Assume initial volume fraction of vapor bubble φvap1 = 0, final
volume fraction of vapor bubble φvap2 = φvap(max), φvap =
bulk
(φvap1 + φvap2)/2, and calculate x bulk(CH4) and Vm
from
Eqs. (3) to (4). Then, use a bisection method to calculate the
total homogenization pressure Ph(total) with Th(total),
mNaCl and x bulk(CH4) from the methane solubility model
(Duan and Mao, 2006). Finally, calculate the bulk molar volcal
ume Vm
with Th(total), Ph(total), mNaCl and x bulk(CH4) from
cal
the PVTx model (Mao et al., 2010). Generally, Vm
is not
bulk
equal to Vm
. Therefore, the initial value of φvap and the calculated x bulk(CH4) and Ph(total) are not right because the
molar volume of fluid inclusion is constant during heating.
Step 7 Go to step 6 and modify the values of φvap1 or φvap2 by a biseccal
bulk
tion algorithm until the calculated Vm
equals to Vm
. Under
this condition, φvap is right and the calculated x bulk(CH4),
cal
Ph(total) and Vm
represent the bulk content of methane, total
homogenization pressure and bulk molar volume, respectively.
Fig. 5 shows the flow chart of the algorithm, whose convergence
cal
bulk
condition is |Vm
− Vm
| b 10 −5 cm3 ⋅ mol−1.
If a fluid inclusion can be represented by the binary CH4\H2O system and finally homogenize to liquid phase, the needed input parameters are only THLV and Th(total). In this case, the calculation can be
simplified: in Step 1, PHLV is calculated from Eq. (2) with mNaCl = 0;
step 2 becomes unnecessary and is omitted; and the other steps are
the same as those of the ternary CH4\H2O\NaCl system.
Becker et al. (2010) also presented an iterative method to determine the CH4 content of a CH4\H2O\NaCl inclusion. Their method is
based on the assumption that the total mass of an inclusion is identical
at 22 °C and the total homogenization temperature. In their model,
bulk
Fig. 5. A bisection algorithm for calculating xbulk(CH4), Ph(total) and Vm
of the CH4\
H2O\NaCl fluid inclusion at given THLV, methane Raman peak shift ν and Th(total):
xbulk(CH4) is the bulk mole fraction of CH4 in the inclusion, Ph(total) is the total homogbulk
enization pressure, Vm
is the bulk molar volume of the inclusion, THLV is the dissociation temperature of CH4 hydrate at the hydrate-liquid-vapor equilibrium, and
Th(total) is the total homogenization temperature.
salinity is an input variable, the pressure at 22 °C is calculated from
the equation of Lin et al. (2007) as in this work, the CH4 density of
vapor phase is calculated from the equation of state of Duan et al.
(1992), and the homogenization pressure and density of aqueous
phase are calculated from the model of Duan and Mao (2006). In this
work, salinity is not an input parameter, but calculated from a simple
equation developed here using input THLV and calculated PHLV from
Eq. (1) with input Raman shift (Lin et al., 2007), CH4 density (or
molar volume) of vapor phase is calculated from the equation of
Setzmann and Wagner (1991) NIST recommends, homogenization
pressure is calculated from the model of Duan and Mao (2006), and
the molar volume of aqueous phase is calculated from the model of
Mao et al. (2010) that covers a wider valid T–P-xNaCl range. Therefore,
these models used in this study should be the optimal models till
now, and the bisection algorithm is also different from that of Becker
et al. (2010).
3. Homogenization pressures and isochores of CH4\H2O\NaCl
fluid inclusions
In this work, the homogenization pressures of CH4\H2O\NaCl inclusions are calculated from the methane solubility model (Duan and
Mao, 2006) whose valid T − P − mNaCl range is 273–523 K, 1–2000 bar
and 0–6 mol kg−1. Therefore, if homogenization temperatures are
above 523 K, the homogenization pressures will be calculated by extrapolating the solubility model. Fig. 6 shows the relation of Ph
132
S. Mao et al. / Chemical Geology 335 (2013) 128–135
(homogenization pressure) and Th (homogenization temperature) of
the CH4\H2O\NaCl inclusions homogenizing to liquid phase at given
compositions, where Ph generally increases slowly with increasing Th
at the beginning, then decreases slowly, and finally increases rapidly,
and most Ph–Th curves have a maximal Ph at low temperatures.
Experimental solubility data of methane in aqueous NaCl solutions
are scarce at temperatures above 523 K. Lamb et al. (1996, 2002) determined the approximate phase relations of CH4\H2O\NaCl system at
1000 and 2000 bar and 300-600 °C using synthetic fluid inclusions,
but their results are only reported in the form of graphs. Krader and
Franck (1987) determined the PVTx data along phase boundaries of
the ternary system between 641 and 800 K with pressures up to
2500 bar. McGee et al. (1981) reported 23 solubility data of methane
in aqueous NaCl solutions, which cover a T − P − mNaCl range of
484.65–565.45 K, 110.2–179.8 bar and 0.91–4.28 mol kg−1. It is evident that the future measurements of solubility of methane in aqueous
NaCl solutions should focus on temperatures above 523 K and pressures
above 200 bar so that a better thermodynamic model (either equation
a
of state or methane solubility model) covering a much wider T − P −
mNaCl range can be developed to calculate homogenization pressures
of CH4-H2O-NaCl inclusions with the above iterative approach.
Construction of isochores along which the trapped fluids in minerals evolve is the final goal to inclusion researchers. Experimental
data for the iso-Th lines approximated as isochores are not reported
for the CH4\H2O\NaCl system. Therefore, the predictive PVTx
models should be the best choice to calculate the isochores of fluid inclusions. For the CH4\H2O\NaCl fluid system, the PVTx model developed recently by Mao et al. (2010) is established on the basis of the
Helmholtz energy and can reproduce the molar volumes and densities within or close to experimental uncertainties. The volumetric
model can predict the molar volumes of the ternary CH4\H2O\NaCl
fluids with a large temperature-pressure-composition region: 273–
1273 K, 1–5000 bar, 0–1 xCH4 (mole fraction of CH4) and 0–1 xNaCl
(mole fraction of NaCl). Hence, this updated PVTx model of Mao et
al. (2010) is used to calculate the isochores and molar volumes of
the CH4\H2O\NaCl fluid inclusions. Fig. 7 shows the isochores
b
150
150
CH4+H2O+NaCl
bulk
x
CH4+H2O+NaCl
(CH4) = 0.001
-1
mNaCl = 2 molkg
-1
mNaCl = 1 mol kg
x
100
(CH4) = 0.001
0.00075
50
100
Ph (bar)
Ph (bar)
bulk
0.00075
0.00050
50
0.00050
0.00025
0.00025
V+L→ L
0.00010
V+L→ L
0.00010
0
0
300
350
400
450
500
550
300
600
350
400
Th (K)
450
500
550
600
Th (K)
d
c
350
200
bulk
x
CH4+H2O+NaCl
(CH4) = 0.001
bulk
300
-1
x
CH4+H2O+NaCl
(CH4) = 0.001
mNaCl = 3 mol kg
-1
Ph (bar)
Ph (bar)
mNaCl = 4 mol kg
250
150
0.00075
100
0.00050
50
200
0.00025
V+L→ L
0.00010
0.00075
150
100
0.00050
50
0.00025
V+L→ L
0.00010
0
0
300
350
400
450
500
550
300
600
350
400
Th (K)
e
CH4+H2O+NaCl
)=
(CH 4
m NaCl = 5 molkg
x
bulk
400
350
500
550
600
0.00075
-1
01
0.0
300
Ph (bar)
450
Th (K)
250
200
150
0.00050
100
50
0.00025
V+L→ L
0.00010
0
300
350
400
450
500
550
600
Th (K)
Fig. 6. Isopleths of the CH4\H2O\NaCl fluid mixtures: (a) mNaCl = 1 mol kg−1, (b) mNaCl = 2 mol kg−1, (c) mNaCl = 3 mol kg−1, (d) mNaCl = 4 mol kg−1, and (e) mNaCl = 5 mol kg−1.
mNaCl is the molality of NaCl, Ph is homogenization pressure, Th is homogenization temperature, and “V + L → L” denotes homogenization to liquid by the disappearance of bubble.
S. Mao et al. / Chemical Geology 335 (2013) 128–135
calculated from the volumetric model of Mao et al. (2010), where the
bubble point curves are calculated from the methane solubility model
of Duan and Mao (2006). It can be seen that the isochores of liquids
can be approximated as straight lines at high temperatures.
(dissociation pressure of CH4 hydrate at THLV), mNaCl (salinity of inclusion), x(CH4) (mole fraction of CH4 in liquid phase at THLV), Vm,vap
(molar volume of vapor phase at THLV), Vm,liq (molar volume of liquid
phase at THLV), φvap (volume fraction of vapor phase at THLV),
x bulk(CH4) (bulk mole fraction of CH4 in the inclusion), Ph(total)
bulk
(total homogenization pressure), and Vm
(bulk molar volume of inclusion), as well as isochore (temperature–pressure relation) can be
calculated. Table 3 gives an example for the thermodynamic calculation of a CH4\H2O\NaCl inclusion finally homogenizing to liquid
phase, where the input parameters THLV = 285 K, ν = 2915 cm −1,
Th(total) = 500 K.
It is worthy of note that the software of Bakker (2003) can also be
used to calculate thermodynamic properties of CH4\H2O\NaCl inclusions at given THLV and PHLV, but the calculated PHLV at given THLV and
mNaCl deviates significantly from the experimental data with high
4. Calculation program of CH4\H2O\NaCl fluid inclusions
The composition equation, the methane solubility model and the
updated volumetric model of the CH4\H2O\NaCl system have been
programmed in Fortran95 language. The source code of the program
can be obtained from Chemical Geology or the corresponding author
([email protected]). In this program, input variables are THLV (dissociation temperature of CH4 hydrate at hydrate–liquid–vapor equilibrium), ν (corrected Raman peak shift of CH4), Th(total) (total
homogenization temperature). The other parameters, such as PHLV
a
b
26
24
5000
4000
4000
3000
2000
400
0
4
600
800
1000
-1
mNaCl = 2 mol kg
-1
mCH = 0.05657 mol kg
Bubble point curve
CH4+H2O+NaCl
1000
-1
mNaCl = 1 mol kg
-1
mCH = 0.05757 mol kg
Bubble point curve
4
1200
400
600
T (K)
19
20 21 22
d
26
24
5000
4000
4000
3000
2000
CH4+H2O+NaCl
1000
mNaCl = 3 mol kg
1200
21
22
23
24
CH4+H2O+NaCl
-1
mNaCl = 4 mol kg
0
4
1000
20
2000
-1
800
19
3000
mCH = 0.05857 mol kg
600
1000
1000
-1
400
v m = 18
6000
5000
Bubble point curve
800
T (K)
P (bar)
P (bar)
vm = 18
6000
0
26
3000
2000
CH4+H2O+NaCl
1000
c
24
28
5000
0
20 21 22
19
v m = 18
6000
28
P (bar)
P (bar)
19 20 21 22
vm = 18
6000
133
-1
mCH = 0.05957 mol kg
Bubble point curve
4
1200
400
600
T (K)
800
1000
T (K)
e
v m =18
6000
19
20
21
22
23
24
5000
P (bar)
4000
3000
2000
CH4+H2O+NaCl
1000
-1
mNaCl = 5 mol kg
0
-1
mCH = 0.06057 molkg
Bubble point curve
4
400
600
800
1000
T (K)
Fig. 7. Isochores of the CH4\H2O\NaCl fluid mixtures at x
(CH4) = 0.001: (a) mNaCl = 1 mol kg−1 and mCH4 ¼ 0:05657 mol kg−1, (b) mNaCl = 2 mol kg−1 and
mCH4 ¼ 0:05757 mol kg−1, (c) mNaCl = 3 mol kg−1 and mCH4 ¼ 0:05857 mol kg−1, (d) mNaCl = 4 mol kg−1 and mCH4 ¼ 0:05957 mol kg−1, (e) mNaCl = 5 mol kg−1 and
mCH4 ¼ 0:06057 mol kg−1. xbulk(CH4) is the bulk mole fraction of CH4. mNaCl and mCH4 are the molalities of NaCl and CH4, respectively. The bubble point curves are calculated
from the CH4 solubility model of Duan and Mao (2006), the isochores are calculated from the PVTx model of Mao et al. (2010), and the unit of Vm is cm3 mol−1.
bulk
134
S. Mao et al. / Chemical Geology 335 (2013) 128–135
salinities and those of Eq. (2). For example, compared with experimental data of Jager and Sloan (2001) with mNaCl = 4.836 mol kg−1, the average absolute deviation of calculated pressure from Eq. (2) and from
the software of Bakker (2003) is 4.52% and 31.18%, respectively. The
big pressure deviations from Bakker (2003) may be caused by the
used Pitzer equations whose parameters are not valid for the ternary
CH4\H2O\NaCl system with high salinities. Duan and Sun (2006) developed a methane clathrate phase-equilibrium model based on Pitzer
theory and refit the Pitzer parameters by experimental data, and the
calculated pressures are close to experimental accuracy, much better
than the results from Bakker (2003) (Fig. 2).
As a special case, the approach above can be testified with experimental data of the binary CH4\H2O system from Lin (2005), who
studied the PVTx properties of CH4\H2O system by synthetic fluid inclusions. THLV and Th(total) of some CH4\H2O inclusions with certain
compositions were measured by Lin (2005). Therefore, the calculated
bulk compositions can be compared with these experimental data.
Here PHLV is directly calculated from Eq. (2) with mNaCl = 0, then we
use the above iterative method to calculate the bulk compositions of
CH4\H2O inclusions. The calculated results are listed in Table 4,
where the calculated bulk contents of CH4 in inclusions are in agreement well with the experimental results at x bulk(CH4) b 0.02, above
which the deviations increase with CH4 contents. Because the total
homogenization temperatures are beyond the valid range of the
Duan and Mao (2006) model, the extrapolation of the solubility
model is used in the whole calculation, but the calculated results
are still in reasonable agreement with the experimental results at
x bulk(CH4) > 0.02. In addition, the software of Bakker (2003) is also
used to calculate the PHLV and the corresponding properties of
CH4\H2O inclusions by the iterative method (Table 4). It can be
seen that the calculated results are very close to those of this work.
Table 4
Calculated and experimental results for the synthetic CH4\H2O fluid inclusions
(V + L → L).
THLV
(K)
Th(total)
(K)
xbulk(CH4)
(exp)
PHLV
(bar)
φvap
Ph(total)
(bar)
xbulk(CH4)
(cal)
273.65
633.25
0.0277
276.85
585.95
0.0167
278.75
589.05
0.0233
280.45
592.95
0.0287
276.15
543.75
0.0107
281.55
554.65
0.0230
28.39
(27.84)
37.15
(37.97)
44.55
(45.80)
53.01
(54.32)
34.88
(35.46)
59.62
(60.77)
0.4841
(0.4839)
0.3263
(0.3264)
0.3354
(0.3356)
0.3469
(0.3470)
0.2360
(0.2360)
0.2552
(0.2550)
275.27
(273.21)
246.06
(250.14)
283.14
(289.98)
328.63
(336.27)
231.21
(234.94)
390.83
(400.24)
0.0232
(0.0227)
0.0164
(0.0168)
0.0204
(0.0210)
0.0254
(0.0260)
0.0103
(0.0105)
0.0193
(0.0197)
Note: The meanings of THLV, Th(total), PHLV, φvap and Ph(total) are defined in Section 4,
xbulk(CH4) (exp) is the experimental bulk mole fraction of CH4 from (Lin, 2005),
xbulk(CH4) (cal) is the calculated bulk mole fraction of CH4 from the iterative method
in this work, PHLV values in parentheses are calculated from Bakker (2003) and the
other values in parentheses are calculated from the iterative method in this work,
and “V + L → L” denotes homogenization to liquid by the disappearance of vapor
bubble.
of CH4\H2O\NaCl inclusions by a bisection algorithm without use of
optical volume fractions of vapor phase at the dissociation temperatures of CH4 hydrates. At the same time, the intensive properties of individual coexisting phases can also be obtained in the calculation. The
calculated salinities, homogenization pressures, homogenization volumes, isopleths and isochores can be used to interpret the P–T conditions of relevant geological processes and the microthermometric and
Raman data of CH4\H2O\NaCl inclusions.
5. Conclusions
Acknowledgements
Based on the assumption that the bulk molar volume of a fluid inclusion keeps constant during heating and cooling, an iterative approach is
presented to calculate the CH4 contents of the CH4\H2O\NaCl fluid inclusions finally homogenizing to liquid. In this approach, the inclusion
salinity (NaCl content) is calculated from a simple empirical equation
on the CH4 hydrate–liquid–vapor equilibrium surface, where the dissociation pressure of CH4 hydrate coexisting with vapor and liquid at
given temperature is calculated with a pressure equation of pure CH4
fluid, whose independent variables are temperature and CH4 Raman
peak position shift corrected by Ne lamp. These relations and relevant
phase equilibrium and PVTx models of the CH4\H2O\NaCl fluids are
combined together to simultaneously calculate the vapor volume fractions, bulk CH4 contents, molar volumes and homogenization pressures
We thank professors Robert J. Bodnar and Ronald J. Bakker for
their constructive suggestions. This work is supported by the funds
(41173072, 90914010, 41172118) awarded by the National Natural
Science Foundation of China, and the fund (20109903) awarded by
Chinese Management Office of Ore Prospecting Projects of Replaced
Resources in Crisis Mines.
Appendix A
Parameters of Eq. (1) are in Table A1. The source code of the program associated with this article can be found in the online version at
Chemical Geology.
Table 3
Calculated results for a CH4\H2O\NaCl fluid inclusion (V + L →L).
Input variables
Output variables
THLV = 285 K
Isochore (P–T
relation)
ν = 2915 cm-1
T (K)
P (bar)
Th(total) = 500 K
500
1300.18
PHLV = 110.95 bar
mNaCl = 0.844 mol kg−1
x(CH4) = 0.00188
Vm,vap = 172.32 cm3 mol−1
Vm,liq = 17.97 cm3 mol−1
φvap = 0.1197
xbulk(CH4) = 0.01584
Ph(total) = 1300.18 bar
bulk
Vm
= 20.13 cm3 mol−1
525
550
575
600
625
650
675
700
725
1746.83
2200.93
2660.98
3125.31
3592.53
4061.28
4530.33
4999.08
5466.61
Note: The parameters THLV, ν, Th(total), PHLV, mNaCl, x(CH4), Vm,vap, Vm,liq, φvap,
bulk
xbulk(CH4), Ph(total) and Vm
are defined in Section 4; “V+ L →L” denotes
homogenization to liquid by the disappearance of vapor bubble.
Parameters of Eq. (1).
Parameter
Value
Parameter
Value
a0
a1
a2
a3
a4
a5
a6
a7
a8
a9
a10
a11
a12
a13
8.53515960e+04
1.48902115e+02
−2.39432404e+00
−2.92469763e+01
5.67346889e−04
−5.11679055e−02
8.33155475e−04
−7.43167336e−07
1.62131106e−08
2.16322623e+02
−1.70322954e+02
2.69206173e+02
−1.89548748e+02
5.80742203e+01
b2,2
b2,3
b3,1
b3,3
b3,4
b3,5
b4,0
b4,1
b4,4
b4,5
b5,1
1.71860770e−02
−4.35004018e−04
−1.28299852e−01
−2.36973068e−04
5.66663153e−05
−1.83240413e−06
−7.10236339e−02
3.52327035e−02
−8.65562143e−06
3.28159643e−07
−2.186084013e−03
Note: The parameters bi,j not listed in the table are zero.
S. Mao et al. / Chemical Geology 335 (2013) 128–135
Appendix B. Supplementary data
Supplementary data to this article can be found online at http://
dx.doi.org/10.1016/j.chemgeo.2012.11.003.
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