Thermodynamic modeling of ternary CH4H2ONaCl fluid inclusions

    Thermodynamic modeling of ternary CH 4 -H2 O-NaCl fluid inclusions Shide Mao, Jiawen Hu, Dehui Zhang, Yongquan Li PII: DOI: Reference:

S0009-2541(12)00568-2 doi: 10.1016/j.chemgeo.2012.11.003 CHEMGE 16752

To appear in:

Chemical Geology

Received date: Revised date: Accepted date:

11 February 2012 6 October 2012 8 November 2012

Please cite this article as: Mao, Shide, Hu, Jiawen, Zhang, Dehui, Li, Yongquan, Thermodynamic modeling of ternary CH4 -H2 O-NaCl fluid inclusions, Chemical Geology (2012), doi: 10.1016/j.chemgeo.2012.11.003

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ACCEPTED MANUSCRIPT Thermodynamic modeling of ternary CH4-H2O-NaCl fluid

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inclusions

State Key Laboratory of Geological Processes and Mineral Resources, and School of

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Shide Mao1*, Jiawen Hu2, Dehui Zhang1, Yongquan Li1

China

College of Resources, Shijiazhuang University of Economics, Shijiazhuang 050031,

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2

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Earth Sciences and Resources, China University of Geosciences, Beijing, 100083,

China

*

The corresponding author: ([email protected])

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ACCEPTED MANUSCRIPT Abstract This paper reports the application of thermodynamic models, including equations

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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

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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

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temperature is calculated with a pressure equation of pure CH4. The pressure equation

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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

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approach is presented to calculate the CH4 contents of CH4-H2O-NaCl inclusions on

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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

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are identical. A prominent merit of this method is that the compositions, molar

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volumes and homogenization pressures of CH4-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]).

Keywords: Equation of state, CH4-H2O-NaCl, fluid inclusion, microthermometry, 2

ACCEPTED MANUSCRIPT isochore, PVTx data

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1. Introduction

Up to now, fluid inclusions represent a powerful tool to estimate the

geological

processes

(Bodnar,

2003;

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pressure-temperature conditions and compositions of fluids associated with various Roedder,

1984;

Wilkinson,

2001).

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Methane-bearing inclusions are commonly found in many geological environments,

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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

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hydrothermal environments (Kelley and Fruh-Green, 1999; Kelley et al., 2005), and

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mafic-ultramafic rocks (Liu and Fei, 2006). Among the various methane-bearing inclusions, the most typical are the ternary CH4-H2O-NaCl inclusions. These

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salt-bearing methane inclusions contain coexisting H2O-NaCl-rich liquid phase and

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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 (Becker et al., 2010; Guillaume et al., 2003). From thermodynamic models using equations of state (EOS), we can calculate the homogenization pressures, molar volumes (or densities) and isochores of inclusions.

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ACCEPTED MANUSCRIPT 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

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thermodynamic models, the inclusion compositions must be known. Guillaume et al. (2003) obtained the methane contents using Raman spectroscopy calibrated with

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synthetic fluid inclusions. This approach can be used only when ice-melting temperature and total homogenization temperature are measured. For the

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CH4-H2O-NaCl system, CH4 hydrate is often found at low temperatures and high

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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

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temperature of ice. To calculate the compositions of CH4-H2O-NaCl inclusions,

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Bakker took the observed volume fraction of vapor at the hydrate dissociation temperature as input variable in his calculation softwares (Bakker, 2003; Bakker,

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2009). Although the volume fraction is improved by use of the petrographic

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microscope in conjunction with a spindle-stage (Bakker and Diamond, 2006), this method does not fit to 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 and Bodnar, 2010; Lin et al., 2007; Lu et al., 2008; Lu et al., 2007). 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 ℃, and an empirical pressure equation of methane was established as a function of temperature and CH4 Raman peak position shift:

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P = a0 + ∑ ai (T − 273.15)i +1 + ν ∑ ai (T − 273.15)i−3 i =1

i =3

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5

+ ∑ ai exp(− (2911− ν )

i−8

(1)

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) + ∑∑ bi , j (ν − 2913.46) (T − 273.15) i

i = 2 j =0

T

i =9

j

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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

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pressure error of Eq. (1) is 1.22 bar.

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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

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inclusion can be easily calculated provided temperature and pressure are given. Then,

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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

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and Mao (2006) and PVTx model of Mao et al. (2010), a new iterative algorithm is

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presented to calculate CH4 contents and homogenization properties of ternary CH4-H2O-NaCl inclusions. Finally, the chosen phase-equilibrium and PVTx models of

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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 5

ACCEPTED MANUSCRIPT disappearance of CH4 hydrate. In principle, the dissociation pressures of CH4 hydrates can be calculated from some accurate hydrate equilibrium models (Ballard and Sloan,

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2002, 2004a, 2004b; Diamond, 1994; Duan and Sun, 2006; Jager et al., 2003). However, these models are usually very complicated and uneasy to calculate the

equation is developed here. 10

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salinities of CH4-H2O-NaCl inclusions. For this reason, a simple hydrate dissociation

2 ln P = ∑ ciT i−1 + mNaCl ∑ ciT i−6 + mNaCl ∑ ciT i−11

1

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(2)

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where P is the hydrate dissociation pressure in bar, T is temperature in K, mNaCl is

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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;

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Dholabhai et al., 1991; Jager and Sloan, 2001; Kharrat and Dalmazzone, 2003;

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Maekawa, 2001) reviewed by Duan and Sun (2006). Table 2 shows the deviations of Eq. (2) from the experimental data of hydrate-liquid-vapor phase equilibria. The total

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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 6

ACCEPTED MANUSCRIPT 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

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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

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shows the relationship of temperature, pressure, salinity and corrected methane Raman peak shift of ternary CH4-H2O-NaCl inclusions at the hydrate-liquid-vapor

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equilibrium. Fig. 4 shows the relation between salinity and dissociation temperature

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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)

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from Eq. (1) and the average pressure deviation (2.95%) of Eq. (2). It can be seen

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from Fig. 4 that the salinity deviation increases with increasing temperature but decreases with increasing pressure.

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In fact, when CH4 hydrates in an inclusion dissolves, liquid and vapor bubble

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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. 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

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ACCEPTED MANUSCRIPT 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

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Raman shifts of C-H symmetric stretching band near zero pressure must be measured at different dissociation temperatures of CH4 hydrates. Therefore, the pressure

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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

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inclusions.

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2.2 CH4 contents of CH4-H2O-NaCl inclusions

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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

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the ice-melting temperatures and total homogenization temperatures. If a

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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

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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:

x

bulk

 ϕ ⋅ y ( CH 4 ) (1 − ϕ vap ) ⋅ x ( CH 4 )   ϕ vap 1 − ϕ vap  ⋅ + + ( CH 4 ) =  vap    Vm,vap Vm,vap Vm,liq Vm,liq   

−1

(3) where x bulk (CH 4 ) 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 (CH 4 ) and x(CH 4 ) are the mole fractions of CH4 in the vapor phase and liquid phase at the hydrate-liquid-vapor equilibrium temperature, respectively, Vm,vap and

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ACCEPTED MANUSCRIPT are the molar volumes of vapor phase and liquid phase at the

Vm,liq

hydrate-liquid-vapor equilibrium temperature, respectively. Because the water content

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of vapor phase is very low at the disappearance temperature of CH4 hydrate (which is generally below 20 ℃), y (CH 4 ) ≈ 1.0 is used in Eq. (3) below 20 ℃.

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x(CH 4 ) 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

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and Mao (2006). Vm,vap in Eq. (3) is a function of temperature and pressure and is

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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

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temperature, pressure and composition ( mNaCl and x(CH 4 ) ), which can be calculated

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from the general PVTx model (Mao et al., 2010). Combining ϕvap , Vm,vap and Vm,liq ,

equation: bulk m

ϕ 1 − ϕ vap =  vap +  Vm,vap Vm,liq 

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V

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the bulk molar volume Vmbulk of the inclusion can be calculated from the following

  

−1

(4)

In the above calculation for determining the CH4 contents of CH4-H2O-NaCl inclusions, ϕvap is an input variable, whose values are obtained from experimental measurements. The relative accuracy of estimated volume fraction ϕ vap 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 9

ACCEPTED MANUSCRIPT homogenization into the liquid phase. One prominent merit of this method is that the compositions, molar volumes and homogenization pressures of CH4-H2O-NaCl

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inclusions can be obtained simultaneously without using optical volume fractions of vapor bubbles at the dissociation temperatures of CH4 hydrates. The whole calculation

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is based on a bisection algorithm, whose main steps are summarized as follows: Step 1: Input the dissociation temperature of methane hydrate on the

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hydrate-liquid-vapor equilibrium surface ( THLV ), the corrected Raman peak shift of

(1)

to

calculate

the

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vapor methane ( ν ), and the total homogenization temperature Th (total) ，then use Eq. dissociation

pressure

of

methane

hydrate

on

the

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hydrate-liquid-vapor equilibrium surface ( PHLV ).

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Step 2: Calculate salinity ( mNaCl ) from Eq. (2) with the input THLV and the calculated PHLV from Eq. (1).

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Step 3: Calculate x(CH 4 ) with THLV , PHLV and mNaCl from the methane

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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(CH 4 ) from the PVTx model (Mao et al., 2010). Step 5: Calculate the maximal volume fraction ϕ vap (max) at THLV by Th (total) . Because the maximal applicable pressure of the methane solubility model (Duan and Mao, 2006) is 2000 bar, ϕ vap (max) is calculated from Eq. (3), where the maximal methane content is from the Duan and Mao (2006) model with Th (total) ,

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ACCEPTED MANUSCRIPT mNaCl and 2000 bar. Step 6: Assume initial volume fraction of vapor bubble ϕ vap1 = 0 , final volume

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fraction of vapor bubble ϕ vap2 = ϕ vap (max) , ϕvap = (ϕvap1 + ϕvap2 ) / 2 , and calculate x bulk (CH 4 ) and Vmbulk from Eqs. (3) and (4). Then, use a bisection method to

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calculate the total homogenization pressure Ph (total) with Th (total) , mNaCl and

x bulk (CH 4 ) from the methane solubility model (Duan and Mao, 2006). Finally,

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calculate the bulk molar volume Vmcal with Th (total) , Ph (total) , mNaCl and

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x bulk (CH 4 ) from the PVTx model (Mao et al., 2010). Generally, Vmcal is not equal to Vmbulk . Therefore, the initial value of ϕvap and the calculated x bulk (CH 4 ) and

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Ph (total) are not right because the molar volume of fluid inclusion is constant during heating.

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Step 7: Go to step 6 and modify the values of ϕ vap1 or ϕ vap2 by a bisection

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algorithm until the calculated Vmcal equals to Vmbulk . Under this condition, ϕ vap is

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right and the calculated x bulk (CH 4 ) , Ph (total) and Vmcal 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 condition is | Vmcal − Vmbulk |< 10 −5 cm 3 ⋅ 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.

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ACCEPTED MANUSCRIPT 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

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the total mass of an inclusion is identical at 22 ℃ and the total homogenization temperature. In their model, salinity is an input variable, the pressure at 22 ℃ is

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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

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homogenization pressure and density of aqueous phase are calculated from the model

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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

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PHLV from Eq. (1) with input Raman shift (Lin et al., 2007), CH4 density (or molar

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volume) of vapor phase is calculated from the equation of Setzmann and Wagner (1991) NIST recommends, homogenization pressure is calculated from the model of

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Duan and Mao (2006), and the molar volume of aqueous phase is calculated from the

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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

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ACCEPTED MANUSCRIPT homogenization temperatures are above 523 K, the homogenization pressures will be calculated by extrapolating the solubility model. Fig. 6 shows the relation of Ph and

Th

(homogenization

temperature)

T

pressure)

of

the

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CH4-H2O-NaCl inclusions homogenizing to liquid phase at given compositions,

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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

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Ph at low temperatures.

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Experimental solubility data of methane in aqueous NaCl solutions are scarce at temperatures above 523 K. Lamb et al. (1996, 2002) determined the approximate

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phase relations of CH4-H2O-NaCl system at 1000 and 2000 bar and 300-600 ℃

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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

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of the ternary system between 641 and 800 K with pressures up to 2500 bar. McGee et

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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 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

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ACCEPTED MANUSCRIPT 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,

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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

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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

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uncertainties. The volumetric model can predict the molar volumes of the ternary

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CH4-H2O-NaCl fluids with a large temperature-pressure-composition region: 273-1273 K, 1-5000 bar, 0-1 xCH 4 (mole fraction of CH4) and 0-1 xNaCl (mole fraction of

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NaCl). Hence, this updated PVTx model of Mao et al. (2010) is used to calculate the

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isochores and molar volumes of the CH4-H2O-NaCl fluid inclusions. Fig. 7 shows the isochores calculated from the volumetric model of Mao et al. (2010), where the

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bubble point curves are calculated from the methane solubility model of Duan and

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Mao (2006). It can be seen that the isochores of liquids can be approximated as straight lines at high temperatures.

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),

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ACCEPTED MANUSCRIPT ν

(corrected Raman peak shift of CH4), Th (total) (total homogenization

temperature). The other parameters, such as PHLV (dissociation pressure of CH4

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hydrate at THLV ), mNaCl (salinity of inclusion), x(CH 4 ) (mole fraction of CH4 in liquid phase at THLV ), Vm,vap (molar volume of vapor phase at THLV ), Vm,liq (molar

x bulk (CH 4 )

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volume of liquid phase at THLV ), ϕ vap (volume fraction of vapor phase at THLV ), (bulk mole fraction of CH4 in the inclusion),

Ph (total) (total

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homogenization pressure), Vmbulk (bulk molar volume of inclusion), as well as

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isochore (temperature-pressure relation) can be calculated. Table 3 gives an example for the thermodynamic calculation of a CH4-H2O-NaCl inclusion finally

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cm-1, Th (total) = 500 K.

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homogenizing to liquid phase, where the input parameters THLV = 285 K, ν = 2915

It is worthy of note that the software of Bakker (2003) can also be used to

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calculate thermodynamic properties of CH4-H2O-NaCl inclusions at given THLV and

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PHLV , but the calculated PHLV at given THLV and mNaCl deviates significantly from the experimental data with high 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

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ACCEPTED MANUSCRIPT close to experimental accuracy, much better than the results from Bakker (2003) (Fig 2).

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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

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CH4-H2O system by synthetic fluid inclusions. THLV and Th (total) of some CH4-H2O inclusions with certain compositions were measured by Lin (2005).

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Therefore, the calculated bulk compositions can be compared with these experimental

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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

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calculated results are listed in Table 4, where the calculated bulk contents of CH4 in

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inclusions are in agreement well with the experimental results at x bulk (CH 4 ) <0.02, above which the deviations increase with CH4 contents. Because the total

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homogenization temperatures are beyond the valid range of the Duan and Mao (2006)

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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 (CH 4 ) >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.

5. Conclusions Based on the assumption that the bulk molar volume of a fluid inclusion keeps

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ACCEPTED MANUSCRIPT 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

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this approach, the inclusion salinity (NaCl content) is calculated from a simple empirical equation on the CH4 hydrate-liquid-vapor equilibrium surface, where the

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dissociation pressure of CH4 hydrate coexisting with vapor and liquid at given temperature is calculated with a pressure equation of pure CH4 fluid, whose

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independent variables are temperature and CH4 Raman peak position shift corrected

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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

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volume fractions, bulk CH4 contents, molar volumes and homogenization pressures of

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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

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time, the intensive properties of individual coexisting phases can also be obtained in

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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.

Acknowledgements: 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

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ACCEPTED MANUSCRIPT Projects of Replaced Resources in Crisis Mines.

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Appendix A

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Parameters of Eq. (1) are in Table A1. The source code of the program

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associated with this article can be found in the online version at Chemical Geology.

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References

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Bakker, R.J., 2003. Package Fluids 1. Computer programs for analysis of fluid inclusion data and for modelling bulk fluid properties. Chemical Geology, 194,

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3-23.

Bakker, R.J., 2009. Package FLUIDS. Part 3: correlations between equations of state,

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thermodynamics and fluid inclusions. Geofluids, 9(1), 63-74.

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Bakker, R.J. ,Diamond, L.W., 2006. Estimation of volume fractions of liquid and

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vapor phases in fluid inclusions, and definition of inclusion shapes. American Mineralogist, 91, 635-657.

Ballard, A.L. ,Sloan, E.D., 2002. The next generation of hydrate prediction: I. Hydrate standard states and incorporation of spectroscopy. Fluid Phase Equilibria, 194-197(0), 371-383. Ballard, A.L. ,Sloan, E.D., 2004a. The next generation of hydrate prediction: Part III. Gibbs energy minimization formalism. Fluid Phase Equilibria, 218(1), 15-31. Ballard, L. ,Sloan, E.D., 2004b. The next generation of hydrate prediction IV: A comparison of available hydrate prediction programs. Fluid Phase Equilibria,

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ACCEPTED MANUSCRIPT 216(2), 257-270. Becker, S.P., Eichhubl, P., Laubach, S.E., Reed, R.M., Lander, R.H. ,Bodnar, R.J.,

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2010. A 48 m.y. history of fracture opening, temperature and fluid pressure: Cretaceous Travis Peak Formation, East Texas basin. Bulletin of the

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Geological Society of America, 122(7/8), 1081-1093.

Bodnar, R.J., 2003. Introduction to fluid inclusions In I. Samson, A. Anderson, & D.

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Canada, Short Course, 32, 1-8.

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Marshall, eds. Fluid Inclusions: Analysis and Interpretation. Mineral. Assoc.

de Roo, J.L., Peters, C.J., Lichtenthaler, R.N. ,Diepen, G.A.M., 1983. Occurrence of

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methane hydrate in saturated and unsaturated solutions of sodium chloride and

651-657.

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water in dependence of temperature and pressure. AIChE Journal, 29,

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Dholabhai, P.D., Englezos, P., Kalogerakis, N. ,Bishnoi, P.R., 1991. Equilibrium for

Methane

Hydrate

Formation

in

Aqueous

Mixed

AC

Conditions

Electrolyte-Solutions. Canadian Journal of Chemical Engineering, 69(3), 800-805.

Diamond, L.W., 1994. Salinity of Multivolatile Fluid Inclusions Determined from Clathrate Hydrate Stability. Geochimica et Cosmochimica Acta, 58(1), 19-41. Duan, Z. ,Mao, S., 2006. A thermodynamic model for calculating methane solubility, density and gas phase composition of methane-bearing aqueous fluids from 273 to 523 K and from 1 to 2000 bar. Geochimica et Cosmochimica Acta, 70(13), 3369-3386.

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ACCEPTED MANUSCRIPT Duan, Z., Moller, N. ,Weare, J.H., 1992. An equation of state for the CH4-CO2-H2O system: I Pure systems for 0 to 1000 0C and 0 to 8000 bar. Geochimica et

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Cosmochimica Acta, 56, 2605-2617.

Duan, Z.H. ,Sun, R., 2006. A model to predict phase equilibrium of CH4 and CO2

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clathrate hydrate in aqueous electrolyte solutions. American Mineralogist, 91, 1346-1354.

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Fall, A., Tattitch, B. ,Bodnar, R.J., 2011. Combined microthermometric and Raman

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spectroscopic technique to determine the salinity of H2O-CO2-NaCl fluid inclusions based on clathrate melting. Geochimica et Cosmochimica Acta,

ED

75(4), 951-964.

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Guillaume, D., Teinturier, S., Dubessy, J. ,Pironon, J., 2003. Calibration of methane analysis by Raman spectroscopy in H2O-NaCl-CH4 fluid inclusions. Chemical

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Geology, 194(1-3), 41-49.

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Huff, T.A. ,Nabelek, P.I., 2007. Production of carbonic fluids during metamorphism of graphitic pelites in a collisional orogen - An assessment from fluid inclusions. Geochimica Et Cosmochimica Acta, 71(20), 4997-5015.

Jager, M.D., Ballard, A.L. ,Sloan, E.D., 2003. The next generation of hydrate prediction: II. Dedicated aqueous phase fugacity model for hydrate prediction. Fluid Phase Equilibria, 211(1), 85-107. Jager, M.D. ,Sloan, E.D., 2001. The effect of pressure on methane hydration in pure water and sodium chloride solutions. Fluid Phase Equilibria, 185(1-2), 89-99. Kelley, D.S. ,Fruh-Green, G.L., 1999. Abiogenic methane in deep-seated mid-ocean

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ACCEPTED MANUSCRIPT ridge environments: Insights from stable isotope analyses. Journal of Geophysical Research-Solid Earth, 104(B5), 10439-10460.

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Kelley, D.S., Karson, J.A., Fruh-Green, G.L., Yoerger, D.R., Shank, T.M., Butterfield, D.A., Hayes, J.M., Schrenk, M.O., Olson, E.J., Proskurowski, G., Jakuba, M.,

SC

Bradley, A., Larson, B., Ludwig, K., Glickson, D., Buckman, K., Bradley, A.S., Brazelton, W.J., Roe, K., Elend, M.J., Delacour, A., Bernasconi, S.M., Lilley,

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M.D., Baross, J.A., Summons, R.T. ,Sylva, S.P., 2005. A serpentinite-hosted

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ecosystem: The lost city hydrothermal field. Science, 307(5714), 1428-1434. Kharrat, M. ,Dalmazzone, D., 2003. Experimental determination of stability

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conditions of methane hydrate in aqueous calcium chloride solutions using

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high pressure differential scanning calorimetry. Journal of Chemical Thermodynamics, 35(9), 1489-1505.

CE

Krader, T. ,Franck, E.U., 1987. The ternary systems H2O-CH4-NaCl and

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H2O-CH4-CaCl2 to 800 K and 250 MPa. Berichte der Bunsen-Gesellschaft für Physikalische Chemie, 91, 627-634.

Lamb, W.M., Mcshane, C.J. ,Popp, R.K., 2002. Phase relations in the CH4-H2O-NaCl system at 2 kbar, 300 to 600°C as determined using synthetic fluid inclusions. Geochimica et Cosmochimica Acta, 66(22), 3971-3986. Lamb, W.M., Popp, R.K. ,Boockoff, L.A., 1996. The determination of phase relations in the CH4-H2O-NaCl system at 1 kbar, 400 to 600°C using synthetic fluid inclusions. Geochimica et Cosmochimica Acta, 60(11), 1885-1897. Lin, F., 2005. Experimental study of the PVTX properties of the system H2O-CH4,

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ACCEPTED MANUSCRIPT Doctor thesis, Faculty of the Virginia Polytechnic Institute and State University.

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Lin, F. ,Bodnar, R.J., 2010. Synthetic fluid inclusions XVIII: Experimental determination of the PVTX properties of H2O-CH4 to 500 0C, 3 kbar and

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XCH4≤4 mol.%. Geochimica et Cosmochimica Acta, 74(11), 3260-3273. Lin, F., Bodnar, R.J. ,Becker, S.P., 2007. Experimental determination of the Raman

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CH4 symmetric stretching band position from 1-650 bar and 0.3-22 ℃:

71(15), 3746-3756.

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Application to fluid inclusion studies. Geochimica et Cosmochimica Acta,

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Liu, W. ,Fei, P.X., 2006. Methane-rich fluid inclusions from ophiolitic dunite and

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post-collisional mafic-ultramafic intrusion: The mantle dynamics underneath the Palaeo-Asian Ocean through to the post-collisional period. Earth and

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Planetary Science Letters, 242(3-4), 286-301.

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Lu, W., Chou, I.M. ,Burruss, R.C., 2008. Determination of methane concentrations in water in equilibrium with sI methane hydrate in the absence of a vapor phase by in situ Raman spectroscopy. Geochimica et Cosmochimica Acta, 72(2), 412-422. Lu, W., Chou, I.M., Burruss, R.C. ,Song, Y., 2007. A unified equation for calculating methane vapor pressures in the CH4-H2O system with measured Raman shifts. Geochimica et Cosmochimica Acta, 71(16), 3969-3978. Maekawa, T., 2001. Equilibrium conditions for gas hydrates of methane and ethane mixtures in pure water and sodium chloride solution. Geochemical Journal,

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ACCEPTED MANUSCRIPT 35(1), 59-66. Mao, S., Duan, Z., Hu, J. ,Zhang, D., 2010. A model for single-phase PVTx properties

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of CO2-CH4-C2H6-N2-H2O-NaCl fluid mixtures from 273 to 1273 K and from 1 to 5000 bar. Chemical Geology, 275(3-4), 148-160.

SC

Mao, S., Duan, Z., Zhang, D., Shi, L., Chen, Y. ,Li, J., 2011. Thermodynamic modeling of binary CH4-H2O fluid inclusions. Geochimica et Cosmochimica

NU

Acta, 75(20), 5892-5902.

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McGee, K.A., Susak, N.J., Sutton, A.J. ,Haas, J.L., 1981. The solubility of methane in sodium chloride brines. United States Department of the Interior Geological

ED

Survey Open-File Report 81-1294: 42.

PT

Roedder, E., 1984. Fluid inclusions. Reviews in Minerlogy,12, Mineralogy Society of America, Washington.

CE

Setzmann, U. ,Wagner, W., 1991. A new equation of state and tables of

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thermodynamic properties for methane covering the range from the melting line to 625 K at pressures up to 1000 MPa. Journal of Physical and Chemical Reference Data, 20(6), 1061-1155.

Shen, P., Shen, Y.C., Wang, J.B., Zhu, H.P., Wang, L.J. ,Meng, L., 2010. Methane-rich fluid evolution of the Baogutu porphyry Cu-Mo-Au deposit, Xinjiang, NW China. Chemical Geology, 275(1-2), 78-98. Wang, P.J., Hou, Q.J., Wang, K.Y., Chen, S.M., Cheng, R.H., Liu, W.Z. ,Li, Q.L., 2007. Discovery and significance of high CH4 primary fluid inclusions in reservoir volcanic rocks of the Songliao Basin, NE China. Acta Geologica

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ACCEPTED MANUSCRIPT Sinica-English Edition, 81(1), 113-120. Wilkinson, J.J., 2001. Fluid inclusions in hydrothermal ore deposits. Lithos, 55(1-4),

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CE

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229-272.

24

ACCEPTED MANUSCRIPT Tables Table 1: Parameters of equation (2) Value

Parameter

Value

c1

0.25494028D+04

c9

0.57920308D-03

c2

-0.31751341D+02

c10

c3

0.14596120D+00

c11

c4

-0.29275456D-03

c12

-0.54933907D+01

c5

0.21606982D-06

c13

0.28186500D-01

c6

-0.34240283D+04

c14

-0.64079832D-04

c7

0.47693085D+02

c15

0.54436180D-07

c8

-0.24925194D+00

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T

Parameter

-0.50485929D-06

AC

CE

PT

ED

MA

NU

SC

0.40044909D+03

25

ACCEPTED MANUSCRIPT Table 2: Calculated pressure deviations from experimental data at hydrate-liquid-vapor equilibria References

mNaCl

T (K)

Nd 32 6 54 37 9

RI P

261.85-285.98 272.69-279.35 270.66-303.48 274.2-288.2 271.4-284

SC

(de Roo et al., 1983) (Dholabhai et al., 1991) (Jager and Sloan, 2001) (Maekawa, 2001) (Kharrat and Dalmazzone, 2003)

T

-1

(mol·kg ) 0-5.43 0.53 0-4.84 0-0.53 0-3.53

AAD (%) 2.24 1.23 4.19 1.96 3.17

MAD (%) 4.79 3.09 17.07 4.52 7.75

AC

CE

PT

ED

MA

NU

AAD: average absolute deviations calculated from equation (2); MAD: maximal absolute deviations calculated from equation (2); Nd: number of data points.

26

ACCEPTED MANUSCRIPT Table 3: Calculated results for a CH4-H2O-NaCl fluid inclusion (V+L L→L) Isochore (P-T relation)

ν = 2915 cm-1

T (K)

Th (total) = 500 K

500

1300.18

PHLV = 110.95 bar

525

1746.83

mNaCl = 0.844 mol·kg-1

575

2660.98

Vm,vap = 172.32 cm3·mol-1 600

3125.31

MA

625

3592.53

ϕvap = 0.1197

650

4061.28

x bulk (CH 4 ) = 0.01584

675

4530.33

Ph (total) = 1300.18 bar

700

4999.08

Vmbulk = 20.13 cm3·mol-1

725

5466.61

ED

Vm,liq = 17.97 cm3·mol-1

PT CE

T

2200.93

NU

550

x(CH 4 ) = 0.00188

Output variables

P (bar)

RI P

SC

Input variables

THLV = 285 K

AC

Note: The parameters THLV , ν , Th (total) , PHLV , mNaCl , x(CH 4 ) , Vm,vap , Vm,liq , ϕvap ,

x bulk (CH 4 ) ,

Ph (total)

bulk

and Vm

are defined in Section 4; “V+L → L” denotes

homogenization to liquid by the disappearance of vapor bubble.

27

ACCEPTED MANUSCRIPT Table 4: Calculated and experimental results for the synthetic CH4-H2O fluid

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

Ph (total) (bar)

x bulk (CH 4 ) (cal)

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)

RI P

633.25

ϕvap

SC

273.65

PHLV (bar)

NU

x bulk (CH 4 ) (exp)

MA

THLV (K) Th (total) (K)

T

inclusions (V+L L→L)

ED

Note: The meanings of THLV , Th (total) , PHLV , ϕvap and Ph (total) are defined in Section 4,

x bulk (CH 4 ) (exp) is the experimental bulk mole fraction of CH4 from (Lin, 2005),

PT

x bulk (CH 4 ) (cal) is the calculated bulk mole fraction of CH4 from the iterative method in this

CE

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

AC

homogenization to liquid by the disappearance of vapor bubble.

28

ACCEPTED MANUSCRIPT

Table A1: Parameters of equation (1) Value

Parameter

Value

a0

8.53515960e+04

b2,2

1.71860770e-02

a1

1.48902115e+02

b2,3

a2

-2.39432404e+00

b3,1

a3

-2.92469763e+01

b3,3

a4

5.67346889e-04

a5

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T

Parameter

-4.35004018e-04

-2.36973068e-04 5.66663153e-05

-5.11679055e-02

b3,5

-1.83240413e-06

a6

8.33155475e-04

b4,0

-7.10236339e-02

a7

-7.43167336e-07

b4,1

3.52327035e-02

a8

1.62131106e-08

b4,4

-8.65562143e-06

2.16322623e+02

b4,5

3.28159643e-07

a10

-1.70322954e+02

b5,1

-2.186084013e-03

a11

2.69206173e+02

a12

-1.89548748e+02

a13

5.80742203e+01

AC

PT

CE

a9

MA

b3,4

ED

NU

SC

-1.28299852e-01

Note: The parameters bi , j not listed in the table are zero.

29

ACCEPTED MANUSCRIPT Figures and captions

T

Fig. 1: P-T conditions of the hydrate-liquid-vapor phase equilibria in the binary

RI P

CH4-H2O system.

SC

Fig. 2: P-T conditions of the hydrate-liquid-vapor phase equilibria in the ternary CH4-H2O-NaCl system: (a) Low temperatures and low pressures, (b) Low

NU

temperatures and high pressures.

MA

Fig. 3: Relationship between THLV , PHLV , salinity and corrected methane Raman

ED

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

CE

PT

equilibrium, respectively.

Fig. 4: Relationship between salinity and dissociation temperature of CH4

AC

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).

Fig. 5: A bisection algorithm for calculating x bulk (CH 4 ) , Ph (total) and Vmbulk of the CH4-H2O-NaCl fluid inclusion at given THLV , methane Raman peak shift ν and Th (total) : x bulk (CH 4 ) is the bulk mole fraction of CH4 in the inclusion, 30

ACCEPTED MANUSCRIPT Ph (total) is the total homogenization pressure, Vmbulk is the bulk molar volume of the THLV

is the dissociation temperature

at the

is the total homogenization

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hydrate-liquid-vapor equilibrium, and Th (total)

of CH4 hydrate

T

inclusion,

temperature.

SC

Fig. 6: Isopleths of the CH4-H2O-NaCl fluid mixtures: (a) mNaCl = 1 mol·kg-1, (b)

NU

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

MA

homogenization temperature, and “V+L→L” denotes homogenization to liquid by the

ED

disappearance of bubble.

Fig. 7: Isochores of the CH4-H2O-NaCl fluid mixtures at x bulk (CH 4 ) = 0.001: (a)

PT

mNaCl = 1 mol·kg-1 and mCH 4 = 0.05657 mol·kg-1, (b) mNaCl = 2 mol·kg-1 and

CE

mCH 4 = 0.05757 mol·kg-1, (c) mNaCl = 3 mol·kg-1 and mCH 4 = 0.05857 mol·kg-1, (d)

AC

mNaCl = 4 mol·kg-1 and mCH 4 = 0.05957 mol·kg-1, (e) mNaCl = 5 mol·kg-1 and mCH 4 = 0.06057 mol·kg-1. x bulk (CH 4 ) 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 Vmbulk is

cm3 ⋅ mol−1 .

31

ACCEPTED MANUSCRIPT

800

400

SC

P (bar)

500

RI P

600

T

de Roo et al. (1983) Jager and Sloan (2001) Maekawa (2001) Kharrat and Dalmazzone (2003) This study Duan and Sun (2006)

700

300

100 0 280

285

290

MA

275

NU

200

Fig. 1

AC

CE

PT

ED

T (K)

32

295

300

305

ACCEPTED MANUSCRIPT

-1

mNaCl(mol⋅kg ) = 5.43 de Roo et al. (1983) Dholabhai et al. (1991) Maekawa (2001) This study Duan and Sun (2006)

120

2.27

RI P

100 P (bar)

3.53

T

140

4.69

80

SC

60

0.53

40 20 260

NU

Kharrat and Dalmazzone (2003)

265

270

275

280

285

T (K)

MA

a

-1

700

3.54

2.08 1.13

Jager and Sloan (2001) This study Duan and Sun (2006)

PT

600

mNaCl(mol⋅kg ) = 4.84

ED

800

400

CE

P (bar)

500

300

AC

200 100

b

265

270

275

280

285

T (K)

Fig. 2

33

290

295

300

ACCEPTED MANUSCRIPT

350 3

4

5

RI P

2913

200

2914

150 2915

100 2916

50

275

-1

Salinity in mol⋅kg -1 Corrected Raman peak shift of CH4 in cm

280

NU

2917

0

SC

PHLV (bar)

250

T

300

02912

1

2

285

MA

THLV (K)

AC

CE

PT

ED

Fig. 3

34

290

295

ACCEPTED MANUSCRIPT

5

100 bar 200 bar 300 bar

T

RI P

3 2

SC

-1

mNaCl(mol⋅ kg )

4

1

275

280

NU

0

285

Fig. 4

AC

CE

PT

ED

MA

THLV

35

290

295

ACCEPTED MANUSCRIPT

RI P

T

St ar t

SC

Input THLV , ν and Th (total)

Calculate PHLV , mNaCl , x(CH 4 ),

NU

Vm,vap , Vm,liq and ϕvap (max)

MA

Initial ϕvap1 =0, ϕvap2 =ϕvap (max),

ϕvap =(ϕvap1 +ϕvap2 )/2

ED

Calculate x bulk (CH 4 ), Vmbulk ,

PT

Ph (total) and Vmcal

Modify ϕvap1 or ϕvap2

AC

CE

by bisection

No

Vmcal −Vmbulk =0? Yes Calculated x bulk (CH 4 ), Ph (total),

ϕvap and Vmcal are correct

E nd

Fig. 5

36

ACCEPTED MANUSCRIPT

150

150 CH4+H2O+NaCl

CH4+H2O+NaCl

bulk

x

(CH4) = 0.001

-1

mNaCl = 2 mol⋅kg

-1

mNaCl = 1 mol⋅kg

100

0.00075

50

0.00075

0.00050

50

0.00050

0.00025

0.00025

V+L→L

0.00010

0

350

400

a

450

500

550

V+L→L

0.00010

0 300

T

Ph (bar)

(CH4) = 0.001

RI P

x

100

Ph (bar)

bulk

600

300

Th (K)

350

400

450

500

550

600

Th (K)

SC

b

CH4+H2O+NaCl

bulk

x

NU

350

200

-1

mNaCl = 3 mol⋅kg

Ph (bar)

MA

100 0.00050

0.00025

350

400

450 Th (K)

550

0.00075

150 100

0.00050

50

0.00025

300

350

d

bulk

0.00075

-1

mNaCl = 5 mol⋅kg

0.0

250

01

Ph (bar)

)= (C H 4

CE

CH4+H2O+NaCl

x

300

200 150

0.00050

100 50

0.00025

V+L→L

0.00010

0 300 e

350

400

450 Th (K)

Fig. 6

37

500

400

450 Th (K)

400 350

V+L→L

0.00010

600

PT

c

500

-1

mNaCl = 4 mol⋅kg

0

ED

300

(CH4) = 0.001

200

V+L→L

0.00010

AC

Ph (bar)

0.00075

0

x

250

150

50

CH4+H2O+NaCl

bulk

300

(CH4) = 0.001

550

600

500

550

600

ACCEPTED MANUSCRIPT

19

vm = 18

6000

20 21

22

24

26

2000 CH4+H2O+NaCl

22

24

26

2000 1000

-1

mNaCl = 1 mol⋅kg

-1

mCH = 0.05657 mol⋅kg

Bubble point curve

0

4

600

800

1000

1200

400

19

20

21

22

26

24

NU

vm = 18

6000

600

-1

mCH = 0.05757 mol⋅kg 4

1000

1200

T (K)

vm = 18

6000

5000

-1

mNaCl = 2 mol⋅kg

800

b

T (K)

a

CH4+H2O+NaCl

Bubble point curve

SC

400

T

3000

RI P

P (bar)

P (bar)

4000

3000

1000

19

20

21

22

23

24

5000

3000 2000

4000

P (bar)

MA

4000

CH4+H2O+NaCl

1000

-1

mNaCl = 3 mol⋅kg

3000 2000 CH4+H2O+NaCl

1000 -1

ED

mNaCl = 4 mol⋅kg

-1

0

mCH = 0.05857 mol⋅kg

Bubble point curve

-1

mCH = 0.05957 mol⋅kg

Bubble point curve

4

400

600

c

800

1000

PT

T (K)

P (bar)

CE

6000

AC

P (bar)

21

5000

4000

0

20

28

5000

0

19

vm = 18

6000

28

4

1200

vm = 18

400

600

d

20

19

21

22

23

24

5000 4000 3000 2000 CH4+H2O+NaCl

1000 -1

mNaCl = 5 mol⋅ kg

0

-1

mCH = 0.06057 mol⋅kg

Bubble point curve

4

400 e

600

800 T (K)

Fig. 7

38

800 T (K)

1000

1000

ACCEPTED MANUSCRIPT Highlights An iterative approach is presented to calculate CH4 content of CH4-H2O-NaCl

RI P

T

inclusion

Salinity of CH4-H2O-NaCl inclusion is calculated from a simple empirical equation

AC

CE

PT

ED

MA

NU

SC

Volume fraction and homogenization pressure can be obtained with this method

39