# Quantitative Raman Spectroscopic Determination of the Composition, Pressure, and Density of CO2-CH4 Gas Mixtures

Authors: Ying Chen; I-Ming Chou
Journal: Journal of Spectroscopy
 (2022)

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## Abstract

The Raman spectra for pure CO2 and CH4 gases and their ten gas mixtures were collected at pressures and temperatures ranging from 2 MPa to 40 MPa and room temperature (∼24°C) to 300°C, respectively. A systematic analysis was carried out to establish a methodology for the quantitative determination of the composition, pressure, and density of CO2-CH4 mixtures. The shift in the peak position of the υ1 band for CH4 was sufficiently large to enable the accurate determination of the pressure of pure CH4 and CH4-dominated fluids (>50 mol% CH4). An equation representing the observed relationship of the peak position of the υ1 band of CH4, density, and composition was developed to calculate the density of CO2-CH4 mixtures. The Raman quantification factor F (CH4)/F (CO2) was demonstrated to be near a constant value of 5.048 ± 0.4 and was used to determine the CH4 to CO2 molar ratio in an unknown CO2-CH4‐bearing fluid with high internal pressure (>10 MPa) based on the Raman peak area ratio. The effect of temperature on the variation in Raman spectral parameters was also investigated at temperatures up to 300°C. The results showed that the effect of temperature must be considered when Raman spectral parameters are used to calculate the pressure, density, and composition of CO2-CH4 gas mixtures. Raman spectroscopic analysis results obtained for six samples prepared in fused silica capillary capsules were validated by comparison with the results obtained from microthermometry measurements.


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## Body

## 1. Introduction

Carbon dioxide and methane are two important gaseous components in many geological environments and play important roles during geological processes, such as metamorphic reactions, melting, and deformation [1]. CO2-rich fluid inclusions (FIs) are often found in metamorphic and mantle-derived rocks [2], and occur in close association with many ore deposits [3], such as gold [4], copper [5], and rare Earth element (REE) deposits [6], while CH4-rich FIs are commonly found in sedimentary basins [7, 8], low-grade metamorphic rocks [9], and mid-ocean ridge hydrothermal environments [10, 11]. However, water-free FIs that are approximated by the CO2-CH4 system are common in some metamorphic terranes [12–14]. The information acquired from the composition and density (pressure) of these FIs can be used to help reconstruct the physicochemical conditions under which they and their host minerals are formed [15].Although several analytical techniques can be used to analyze FIs, only microthermometry (MT) and Raman spectroscopy can provide information on both the composition and pressure of individual inclusions [16, 17]. MT is a nondestructive method based on the observation of phase-transition temperatures. When the melting temperature Tm and homogenization temperature Th are known, the VX (molar volume and composition) properties can be directly acquired from the VX diagram [18, 19]. However, the uncertainties in the composition and density obtained from the VX diagram due to the error in Tm and Th (∼±0.1°C) can reach up to ±5 mol% and ±0.09 g·cm−3, respectively [19, 20]. In addition, the microthermometry technique is difficult to apply to small FIs with diameter of <5 μm, low density, and more complex composition [20]. As an alternative to microthermometric measurements, Raman spectroscopy is an extreme useful tool to get quantitative analysis in individual inclusions, partly because it is fast, nondestructive, and high spatial resolution (∼1 μm).Over the past decades, previous studies have been paid more attention to the quantitative analysis of FIs with Raman spectroscopy. Spectral parameters (peak position, peak width, and peak intensity ratio) could be used to determine the pressure, density, and composition of the fluid in FIs. For instance, the concentration of dissolved CH4 or CO2 in water solution has been determined based on their peak area (or height) ratio [21–25], and the pressure (or density) of CH4 can be determined by the peak position of the υ1 band of CH4 [17, 26–33]. In addition, the CO2 density in FIs can be obtained by the measurements of the Fermi diad splitting of CO2 [3, 19, 20, 33–42]. The effect of composition on the Raman spectral parameters of CO2 and CH4 was reported earlier by Seitz et al. [17] with low spectral resolution (∼5 cm−1) [20]. Recently, calibration data for CO2-CH4 mixture and N2-CO2-CH4 mixture have been provided by Le et al. [20] and Sublett et al. [43], respectively. The quantitative relationship between fluid properties (compositions, density, or pressure) and Raman spectral parameters (peak area ratio, peak position, etc.) has to be calibrated carefully with standard samples, since an accurate calibration is fundamental for quantitative measurements.For two Raman-active species, a and b, in a homogeneous phase, their molar ratios can be calculated from their peak areas [44] based on the following equations:(1)AaAb=CaCb×σaσb×ηaηb=CaCb×FaFb,where A is the peak area; C is the concentration; σ is the Raman scattering coefficient; η is the instrumental efficiency factor; and F is the Raman quantification factor [44].Normally, the reported Raman quantification factors for gaseous are relative to N2 [45]. However, the reported values for F (CH4) and F (CO2) among different laboratories are quite different [19, 20, 38, 46]. Considering that two separate experiments are required to obtain F (CH4) and F (CO2), a more practical method is to determine the F (CH4)/F (CO2) ratio; then, the molar ratio of CH4 to CO2 can be obtained directly according to the peak area ratio A (CH4)/A (CO2). In addition, there are only a few Raman spectroscopy calibration data available in the literature for CO2-CH4 mixtures at high temperatures up to 300°C, except for the pure CO2 and CH4 system [30, 33, 37] and N2-CO2-CH4 system [43].In this study, an in situ Raman spectroscopy system combined with a fused silica capillary-high-pressure optical cell (FSC-HPOC) is applied to collect Raman spectra for pure CO2 and CH4 gases and their CO2-CH4 binary mixtures at temperatures ranging from room temperature (∼24°C) to 300°C and pressures up to 40 MPa. The peak position and peak area of the υ1 band of CH4 and the υ1 and 2υ2 bands (Fermi diad) of CO2 are systematically analyzed to establish a methodology for the quantitative determination of the composition, pressure, and density of CO2-CH4 FIs. The purpose of our work is to construct relationships between Raman spectral parameters and composition, pressure, and density with potential applications to the quantitative study of natural CO2-CH4 inclusions. In addition, the effects of temperature on Raman spectral parameters are also investigated. Six synthetic CO2-CH4 FIs, prepared in fused silica capillary capsules (FSCCs), were used to perform both laser Raman and MT studies to validate our established methodology.


## 2. Materials and Methods

### 2.1. High-Pressure Optical Cell

The instruments and procedures are similar to those used in the study of Lu et al. [29] (Figure 1). The experiments were carried out with a capillary high-pressure optical cell (HPOC [47]). Pure CO2 and CH4 gases (99.99%, Jiateng Air Production Inc.) and their ten gaseous mixtures with given compositions (10, 20, 30, 40, 50, 60, 70, 80, 85, and 90 mol% CH4) were investigated systematically. The HPOC was composed of a fused silica capillary with a circular section (Polymicro Technologies, LLC) with an inner (ID) and outer (OD) diameter of 300 μm and 665 μm, respectively, and a length of approximately 25 cm. The gas or gas mixture was loaded into the HPOC and sealed with a column of mercury (∼15 mm long) at one atmospheric pressure. The procedure used for the preparation of the gas samples was described previously in detail [48]. The sample temperature was controlled using a Linkam CAP500 heating-cooling stage. The pressure in the cell was maintained by a water medium in the pressure line and was adjusted using a pressure generator (HiP Model no. 37‐6‐30). The pressure was read using a Setra 204D digital pressure transducer with a Datum 2000™ manometer (69 MPa full scale, accurate to ±0.14% of full scale).Figure 1
Schematic diagram of the experimental system (modified after Lu et al. [29]).


### 2.2. Fused Silica Capillary Capsule

Fused silica capillary capsules (FSCCs; 300μm OD, 100 μm ID, and approximately 1.0 cm long) were constructed to contain the CO2-CH4 mixture gas using the sample-loading system of Chou et al. [47], and they were used for verification of our quantitative Raman spectroscopic analyses of the CO2-CH4 system. First, the line was flushed twice with one gas (CH4 or CO2) after placing under vacuum. Then, gas at a pressure of slightly lower than 0.2 MPa was loaded into the line and silica tube, and the closed end of the tube was immersed in liquid nitrogen to form liquid or solid CH4/CO2. Second, the system was evacuated, while the closed end was still immersed in liquid nitrogen, and the silica tube was then pressurized with another gas (CO2 or CH4). Third, the system was evacuated again, and the open end of the tube was sealed with a hydrogen flame in vacuum, while the closed end remained immersed in liquid nitrogen. A higher loading concentration in CO2-CH4 mixture was obtained for the gas loaded first. Even though CO2-CH4 gas mixtures with known proportions could also be loaded directly into the FSC tubes, we found that their proportions changed slightly due to the different freezing temperature while freezing.


### 2.3. Microthermometry Analyses of FSCC Samples

Microthermometric analyses of the FSCC samples were carried out using a Linkam CAP500 heating-cooling stage under the Olympus microscope in the laser Raman spectroscopic system. The temperature was calibrated with the triple points of H2O (±0°C) and CO2 (−56.6°C) and was accurate to ±0.1°C. In the present study, measurements of the phase changes were carried out only below room temperature. The system was cooled rapidly at a rate of 10°C/min to −180°C, and after holding for 10 minutes, it was then heated at a rate of 10°C/min. The heating rate was reduced to 0.3°C/min at a temperature of approximately 5°C below the phase transition point to precisely determine the temperature of the phase changes. The same rates were used for heating-cooling cycling. The CO2-CH4 system shows three phases at low temperatures: solid CO2, liquid, and vapor. Two phase transition temperatures can be measured during heating from −180°C to room temperature: the final melting temperature of solid CO2 (Tm) and the L-V homogenization temperature (Th) for the disappearance of the liquid phase or vapor bubble [49]. The measured values for Tm and Th were then used to calculate the composition and density of the FSCC samples based on the VX diagram of Thiery et al. [18].


### 2.4. Collection and Calibration of Raman Spectra

Raman spectra were acquired using a JY/Horiba LabRam HR Evolution Raman system equipped with a 532.06 nm (frequency-doubled Nd: YAG) laser, an SLWD 50× Olympus objective with a numerical aperture of 0.35, and an 1800 groove/mm grating with a spectral resolution of approximately 0.65 cm−1 or a 600 groove/mm grating with a spectral resolution of approximately 2 cm−1. Approximately 20 mW of laser light was focused onto the center of the horizontal tube to generate Raman signals during the measurement.Raman spectra for CO2 and CH4 are shown in Figure 2. CO2 has five Raman bands, including the Fermi diad of CO2 between 1200 and 1400 cm−1 (the lower band at ∼1285 cm−1 and the upper band at ∼1388 cm−1), two hot bands flanking the Fermi diad at ∼1265 and 1409 cm−1, and a weak CO2 band at 1370.0 cm−1 due to the isotopic splitting of 13CO2 [37]. CH4 has four Raman bands: the asymmetric bending overtone band (2υ4 at ∼2580 cm−1), the C-H symmetric stretching band (υ1 at ∼2917 cm−1), the asymmetric stretching band (υ3 at ∼3020 cm−1), and the asymmetric bending overtone band (2υ2 at ∼3070 cm−1) [50]; the other three bands have an intensity that is ∼2% of that of the υ1 band. In this study, only the Fermi diad and hot bands of CO2 and υ1 band of CH4 (approximately 2917 cm−1) were investigated.Figure 2
Raman spectrum of the CO2-CH4 mixture showing the Raman lines for CO2 and CH4. The top left insert shows the detailed spectrum of CO2 containing Fermi diad bands, two hot bands, 13CO2, and the spectrum for benzonitrile. The two marked peaks for benzonitrile (1192.6 and 1598.9 cm−1) were used to calibrate the CO2 Fermi diad splitting. The right insert shows the C-H symmetric υ1 band of CH4 and Ne emission lines at 2836.976 cm−1, 2933.916 cm−1, and 3008.127 cm−1. The Ne emission lines at 2836.976 cm−1 and 2933.916 cm−1 bracket the υ1 band of CH4 and were used to calibrate the CH4υ1 peak position.As shown in Figure2, the 600 groove/mm grating, with a lower spectral resolution but wider spectral range, was used for collecting spectra in multiple windows ranging between 1000 cm−1 and 3200 cm−1 to cover the peaks of the Fermi diad of CO2 and CH4. In addition, spectra employing the 1800 groove/mm grating with a high spectral resolution were also collected in two single windows to obtain precise peak positions. One window ranged between 1170 cm−1 and 1620 cm−1, which covers the Fermi diad of CO2 (1200∼1400 cm−1), and two well-established reference peaks of benzonitrile (1192.6 and 1598.9 cm−1) was used to calibrate the Fermi diad of CO2. The other window ranged between 2718 cm−1 and 3075 cm−1, which covers the CH4 peak at approximately 2917 cm−1; neon lines at 626.649 nm (2836.976 cm−1) and 630.479 nm (2933.916 cm−1) were selected to calibrate the peak position of CH4 [30].The measured spectra with single windows for CO2 and CH4 were fitted with the program PeakFit v4.12 (AISN Software Inc.) using Gaussian–Lorentzian functions without smoothing or baseline correction before peak‐fitting procedures. The real peak positions of CO2 and CH4 were derived from the following relations:(2)υreal−1192.6υm−Benzm1=1598.9−1192.6Benzm2−Benzm1,(3)υreal−2836.976υm−Nem1=2933.916−2836.976Nem2−Nem1,where ʋreal is the real position of the upper and lower bands of the Fermi diad of CO2 in equation (2) and the C-H symmetric stretching band (υ1) of CH4 in equation (3); ʋm is the measured peak position of CO2 or CH4; Benzm1 and Benzm2 are the two reference peaks of benzonitrile; and Nem1 and Nem2 are the measured wavenumbers of the two reference neon lines.The Raman peak area ratio (PAR) of the upper band of the Fermi diad of CO2 to the C-H symmetric stretching band (υ1) of CH4 was determined by the software GRAMS/AI (Thermo Galactic). Three spectra were collected at each set P-T condition.


## 2.1. High-Pressure Optical Cell

The instruments and procedures are similar to those used in the study of Lu et al. [29] (Figure 1). The experiments were carried out with a capillary high-pressure optical cell (HPOC [47]). Pure CO2 and CH4 gases (99.99%, Jiateng Air Production Inc.) and their ten gaseous mixtures with given compositions (10, 20, 30, 40, 50, 60, 70, 80, 85, and 90 mol% CH4) were investigated systematically. The HPOC was composed of a fused silica capillary with a circular section (Polymicro Technologies, LLC) with an inner (ID) and outer (OD) diameter of 300 μm and 665 μm, respectively, and a length of approximately 25 cm. The gas or gas mixture was loaded into the HPOC and sealed with a column of mercury (∼15 mm long) at one atmospheric pressure. The procedure used for the preparation of the gas samples was described previously in detail [48]. The sample temperature was controlled using a Linkam CAP500 heating-cooling stage. The pressure in the cell was maintained by a water medium in the pressure line and was adjusted using a pressure generator (HiP Model no. 37‐6‐30). The pressure was read using a Setra 204D digital pressure transducer with a Datum 2000™ manometer (69 MPa full scale, accurate to ±0.14% of full scale).Figure 1
Schematic diagram of the experimental system (modified after Lu et al. [29]).


## 2.2. Fused Silica Capillary Capsule

Fused silica capillary capsules (FSCCs; 300μm OD, 100 μm ID, and approximately 1.0 cm long) were constructed to contain the CO2-CH4 mixture gas using the sample-loading system of Chou et al. [47], and they were used for verification of our quantitative Raman spectroscopic analyses of the CO2-CH4 system. First, the line was flushed twice with one gas (CH4 or CO2) after placing under vacuum. Then, gas at a pressure of slightly lower than 0.2 MPa was loaded into the line and silica tube, and the closed end of the tube was immersed in liquid nitrogen to form liquid or solid CH4/CO2. Second, the system was evacuated, while the closed end was still immersed in liquid nitrogen, and the silica tube was then pressurized with another gas (CO2 or CH4). Third, the system was evacuated again, and the open end of the tube was sealed with a hydrogen flame in vacuum, while the closed end remained immersed in liquid nitrogen. A higher loading concentration in CO2-CH4 mixture was obtained for the gas loaded first. Even though CO2-CH4 gas mixtures with known proportions could also be loaded directly into the FSC tubes, we found that their proportions changed slightly due to the different freezing temperature while freezing.


## 2.3. Microthermometry Analyses of FSCC Samples

Microthermometric analyses of the FSCC samples were carried out using a Linkam CAP500 heating-cooling stage under the Olympus microscope in the laser Raman spectroscopic system. The temperature was calibrated with the triple points of H2O (±0°C) and CO2 (−56.6°C) and was accurate to ±0.1°C. In the present study, measurements of the phase changes were carried out only below room temperature. The system was cooled rapidly at a rate of 10°C/min to −180°C, and after holding for 10 minutes, it was then heated at a rate of 10°C/min. The heating rate was reduced to 0.3°C/min at a temperature of approximately 5°C below the phase transition point to precisely determine the temperature of the phase changes. The same rates were used for heating-cooling cycling. The CO2-CH4 system shows three phases at low temperatures: solid CO2, liquid, and vapor. Two phase transition temperatures can be measured during heating from −180°C to room temperature: the final melting temperature of solid CO2 (Tm) and the L-V homogenization temperature (Th) for the disappearance of the liquid phase or vapor bubble [49]. The measured values for Tm and Th were then used to calculate the composition and density of the FSCC samples based on the VX diagram of Thiery et al. [18].


## 2.4. Collection and Calibration of Raman Spectra

Raman spectra were acquired using a JY/Horiba LabRam HR Evolution Raman system equipped with a 532.06 nm (frequency-doubled Nd: YAG) laser, an SLWD 50× Olympus objective with a numerical aperture of 0.35, and an 1800 groove/mm grating with a spectral resolution of approximately 0.65 cm−1 or a 600 groove/mm grating with a spectral resolution of approximately 2 cm−1. Approximately 20 mW of laser light was focused onto the center of the horizontal tube to generate Raman signals during the measurement.Raman spectra for CO2 and CH4 are shown in Figure 2. CO2 has five Raman bands, including the Fermi diad of CO2 between 1200 and 1400 cm−1 (the lower band at ∼1285 cm−1 and the upper band at ∼1388 cm−1), two hot bands flanking the Fermi diad at ∼1265 and 1409 cm−1, and a weak CO2 band at 1370.0 cm−1 due to the isotopic splitting of 13CO2 [37]. CH4 has four Raman bands: the asymmetric bending overtone band (2υ4 at ∼2580 cm−1), the C-H symmetric stretching band (υ1 at ∼2917 cm−1), the asymmetric stretching band (υ3 at ∼3020 cm−1), and the asymmetric bending overtone band (2υ2 at ∼3070 cm−1) [50]; the other three bands have an intensity that is ∼2% of that of the υ1 band. In this study, only the Fermi diad and hot bands of CO2 and υ1 band of CH4 (approximately 2917 cm−1) were investigated.Figure 2
Raman spectrum of the CO2-CH4 mixture showing the Raman lines for CO2 and CH4. The top left insert shows the detailed spectrum of CO2 containing Fermi diad bands, two hot bands, 13CO2, and the spectrum for benzonitrile. The two marked peaks for benzonitrile (1192.6 and 1598.9 cm−1) were used to calibrate the CO2 Fermi diad splitting. The right insert shows the C-H symmetric υ1 band of CH4 and Ne emission lines at 2836.976 cm−1, 2933.916 cm−1, and 3008.127 cm−1. The Ne emission lines at 2836.976 cm−1 and 2933.916 cm−1 bracket the υ1 band of CH4 and were used to calibrate the CH4υ1 peak position.As shown in Figure2, the 600 groove/mm grating, with a lower spectral resolution but wider spectral range, was used for collecting spectra in multiple windows ranging between 1000 cm−1 and 3200 cm−1 to cover the peaks of the Fermi diad of CO2 and CH4. In addition, spectra employing the 1800 groove/mm grating with a high spectral resolution were also collected in two single windows to obtain precise peak positions. One window ranged between 1170 cm−1 and 1620 cm−1, which covers the Fermi diad of CO2 (1200∼1400 cm−1), and two well-established reference peaks of benzonitrile (1192.6 and 1598.9 cm−1) was used to calibrate the Fermi diad of CO2. The other window ranged between 2718 cm−1 and 3075 cm−1, which covers the CH4 peak at approximately 2917 cm−1; neon lines at 626.649 nm (2836.976 cm−1) and 630.479 nm (2933.916 cm−1) were selected to calibrate the peak position of CH4 [30].The measured spectra with single windows for CO2 and CH4 were fitted with the program PeakFit v4.12 (AISN Software Inc.) using Gaussian–Lorentzian functions without smoothing or baseline correction before peak‐fitting procedures. The real peak positions of CO2 and CH4 were derived from the following relations:(2)υreal−1192.6υm−Benzm1=1598.9−1192.6Benzm2−Benzm1,(3)υreal−2836.976υm−Nem1=2933.916−2836.976Nem2−Nem1,where ʋreal is the real position of the upper and lower bands of the Fermi diad of CO2 in equation (2) and the C-H symmetric stretching band (υ1) of CH4 in equation (3); ʋm is the measured peak position of CO2 or CH4; Benzm1 and Benzm2 are the two reference peaks of benzonitrile; and Nem1 and Nem2 are the measured wavenumbers of the two reference neon lines.The Raman peak area ratio (PAR) of the upper band of the Fermi diad of CO2 to the C-H symmetric stretching band (υ1) of CH4 was determined by the software GRAMS/AI (Thermo Galactic). Three spectra were collected at each set P-T condition.


## 3. Results and Discussion

### 3.1. Determination of the Pressure of the CO2-CH4 Gas Mixtures

The calibrated peak positions for the CH4υ1 peak and the lower and upper members of the CO2 Fermi diad and the Fermi diad splittings for all samples at room temperature and various pressures collected in HPOC are listed in Table S1 and S2 (Supplemental material) and shown in Figure 3. Figure 3(a) shows the peak positions for the υ1 peak of CH4 in pure CH4 and ten CO2-CH4 mixtures as a function of total pressure; the addition of CO2 can affect the peak position of CH4; however, the dominant factor affecting the peak position of CH4 is the total fluid pressure, which is in agreement with the result of Seitz et al. [17]. A leap in υ1 peak position for CH4 in Figure 3(a) is evident for CO2-rich mixtures at low pressure. For the 10 mol% CH4-90 mol% CO2 mixture, this abrupt shift in the peak position in response to pressure represents the liquid-vapor phase transition. The 30% CH4-70% CO2 mixture, however, remains supercritical (but near-critical) at room temperature [17].Figure 3
Raman peak positions for the CH4υ1 peak (a) and the lower (b) and upper (c) members of the CO2 Fermi diad and the Fermi diad splitting (d) for different CO2-CH4 gaseous mixtures at room temperature as a function of pressure.
(a)(b)(c)(d)The lower and upper members of the Fermi diad peaks for CO2 and Fermi diad splitting for CO2 in CO2-CH4 mixtures as a function of pressure are presented in Figures 3(b)–3(d), respectively. The peak shift with pressure from 2 MPa to 40 MPa is much greater for the lower Fermi diad member (∼5 cm−1) than for the upper Fermi diad member (∼3 cm−1). Thus, the peak position of the lower Fermi diad member is a more sensitive monitor of fluid pressure, which are consistent with previous studies [41]. However, the peak position of the lower Fermi diad member is also more sensitive to composition. Indeed, the Fermi diad splitting (Δ, the separation between bands in the Fermi diad) of CO2 has been previously used to determine the pressure or density of CO2 in FIs [37, 40]. Our results show that at 2 MPa, Δ is nearly identical (∼102.76 cm−1) for any composition, while at higher pressures, the effect of the gas mixture composition becomes more obvious, which is similar to that observed for CO2 mixed with N2 and CH4 [19, 20]. Therefore, we can draw the same conclusion with previous studies [17, 20] that the Δ for CO2 is not only a function of pressure but also a function of the composition of the CO2-CH4 gas mixture (Figure 3(d)).As mentioned above, it can be concluded that the CH4υ1 peak could be the most suitable parameter for the pressure determination, although there is an abrupt shift in the CH4 peak positions due to the existence of the liquid-vapor transition in CO2-rich mixtures. As shown in Figure 4, different laboratories have their own calibration curves for the CH4 peak position-pressure relationship. It can be ascribed to different measurement conditions, including excitation wavelength, the numerical aperture of the objective, the slit width, and the groove density of grating. However, all six data sets collected from the literature for pure CH4 and from this study for CH4-rich mixture have similar relations between peak position and pressure, which are almost parallel to each other but with different intercepts at zero pressure, indicating that systematic discrepancies may exist among these data sets. Fortunately, these discrepancies can be eliminated by choosing D as a variable (Figure 5), where D = υp − υ0, the difference between the peak positions at elevated pressure (υp) and near-zero pressure (υ0) (in this study, υ0 = 2917.924 cm−1 for <0.1 MPa). The same treatment was successfully demonstrated for pure CH4 many years ago by Lu et al. [29]. Our data (CH4-rich mixtures with CH4 ≥ 50 mol% and pure CH4) at room temperature agree with previous studies [17, 27, 29, 51] for pure CH4 (Figure 5). After fitting the data obtained from the six sources, the relation between D (in cm−1) and pressure P (in MPa) can be described by the following equation:(4)D=2.6953×10−8P5−5.0314×10−6P4+3.1297×10−4P3−5.1191×10−3P2−1.9752×10−1P,with R2 (squared correlation coefficient) = 0.9972. The uncertainty (1σ) in the calculated pressure was ±1.1 MPa. This equation could be used to correlate P with D in other laboratories and calculate the pressure (≤70 MPa) of CH4-rich mixtures (CH4 ≥ 50 mol%) with the measured peak position of the CH4υ1 band near room temperature, as long as υ0 is known for the particular Raman spectrometer.Figure 4
Raman peak position of C-H symmetric stretching band (υ1) of CH4 from six available data sets as a function of pressure.Figure 5
The P-D relationship determined in this study compared with other published values at near room temperature. Note that the original data of Jager’s Colorado School of Mines are cited from Lu et al. [29].


### 3.2. Determination of the Density of CO2-CH4 Gas Mixtures

The pressure of the CO2-CH4 gas mixtures of known composition at room temperature (∼24°C) was converted to density using the GERG-2008 EoS (equation of state), which is a new wide-range EoS for natural gases and other mixtures of 21 natural gas components [52]. The variations in D and Δ within CO2-CH4 gas mixtures as a function of density and composition are plotted in Figure 6. The results show that D decreases with increasing CH4 concentration and density of the gas mixture, whereas Δ increases with elevated CO2 concentration and density. The maximum value of the variation in Δ is quite small (<∼3 cm−1) compared to that for D (<∼6 cm−1) over the same density range (0∼1 g/cm3). Thus, given an analytical uncertainty of ±0.01 cm−1 for the measurement of the peak position, D will generally provide the most precise estimate of density. Therefore, the experimental data for D in CO2-CH4 gas mixtures were fitted to the following equation by polynomial regression analysis (using the software 1stOpt):(5)ρ=a00+a10×CCH4+a01×D+a20×CCH42+a11×CCH4×D+a02×D2+a30×CCH43+a21×CCH42×D+a12×CCH4×D2+a03×D3+a31×CCH43×D+a22×CCH42×D2+a13×CCH4×D3+a04×D4.Figure 6
The variation inD (a) and Δ (b) within CO2-CH4 gas mixtures as a function of density and composition. D = υp − υ0 is the difference between the υ1 peak positions of CH4 at elevated pressure (υp) and near-zero pressure (υ0); Δ represents the separation between bands in the Fermi diad of CO2.
(a)(b)The fitted coefficients for equation (5) are listed in Table 1, and the root-mean-square error of equation (5) is 0.012 g/cm3 with an R2 of 0.997. This equation can be used to calculate the density of CH4-CO2 mixtures with the measured peak position of the CH4υ1 band near room temperature.Table 1
The fitting parameters for equation (5).
a000.0458578972a100.0070465891a01−0.0367435722a20−0.3041825424a11−0.0208569183a020.0264438359a300.2888501741a21−0.0290891828a12−0.0400853154a030.0014973436a310.0879585851a220.0270909951a130.0002772730a040.0000945387


### 3.3. Determination ofF (CH4)/F (CO2)

The ratio of the peak areas of theυ1 band of CH4 and the upper Fermi diad member of CO2 (A (CH4)/A (CO2)) for CO2-CH4 mixtures increases with pressure below 10 MPa and then maintains the same levels at higher pressures (Table 2), indicating that it is an advantageous to use the ratios of the peak area of the υ1 band of CH4 and the upper Fermi diad member of CO2 for quantitative determinations of the fluid composition in CO2-CH4 mixtures [17].Table 2
TheF (CH4)/F (CO2) in ten CO2-CH4 gaseous mixtures at room temperature and pressures up to 40 MPa.
P (MPa)XCH4 (mol%)aA (CH4)/ A (CO2)F (CH4)/ F (CO2)2100.4313.87850.4454.006100.4494.043200.4534.074300.4454.008400.4464.010Avg.0.4484.0312200.9943.97851.0374.147101.0784.314201.0554.219301.0594.235401.0634.250Avg.1.0594.2352301.7634.11451.8524.322101.8904.409201.9304.504301.9254.491401.9194.477Avg.1.9254.4912402.8734.30952.9764.463103.0214.531203.0214.531303.0274.540403.0444.565Avg.3.0304.5452504.6984.69854.7884.788104.9284.928204.8364.836304.6584.658404.6914.691Avg.4.7284.7282606.6434.42956.9194.613107.0724.714207.1654.777307.1764.784407.1984.799Avg.7.1804.78727011.9455.119512.4925.3541011.9745.1322012.9285.5413012.6165.4074012.5255.368Avg.12.6905.43028018.1704.542518.5414.6351018.8084.7022019.4274.8573019.6524.9134019.5164.879Avg.19.5314.88328527.0754.778528.3084.9961028.1294.9642028.7815.0793028.8215.0864028.6065.048Avg.28.7365.07129039.8124.424541.3454.5941042.1734.6862046.2085.1343045.4965.0554044.9504.994Avg.45.5515.061aA is the Raman peak area.According to equation (1), if F (CH4)/F (CO2) has been determined by the known A (CH4)/A (CO2) and C (CH4)/C (CO2), then it can be used to determine the molar ratio of CH4 to CO2 in an unknown CO2-CH4‐bearing fluid from the Raman peak area ratio. F (CH4)/F (CO2) in ten CO2-CH4 gaseous mixtures were calculated based on equation (1) and listed in Table 2. Within a given CO2-CH4 gaseous mixture, the F (CH4)/F (CO2) value rises at low pressures and remains constant (within analytical uncertainty) above 10 MPa (Table 2), which is in agreement with the previous work of Seitz et al. [17]. Therefore, the F (CH4)/F (CO2) values obtained at 20 MPa, 30 MPa, and 40 MPa were averaged and considered as the general F (CH4)/F (CO2) value of this mixture. It can be found that the general F (CH4)/F (CO2) value varies somewhat with different gaseous mixtures. Figure 7 shows a good linear relationship between the molar ratio (C (CH4)/C (CO2)) and peak area ratio (A (CH4)/A (CO2)) with an R2 of 0.9995. The slope shows a value of 5.048, which represents the F (CH4)/F (CO2) ratio based on equation (1). The uncertainty in the average values of F (CH4)/F (CO2) is ±0.4, which in turn can lead to an average error in the composition up to ±1.4 mol% CH4.Figure 7
The linear relationship between the molar ratio (C (CH4)/C (CO2)) and the Raman peak area ratio (A (CH4)/A (CO2)) at room temperature.Table3 shows a comparison of our results with those obtained in six previous studies. The results show that F (CH4)/F (CO2) is quite different among different laboratories. Our value is in agreement with four previous results [17, 19, 20, 53]. Seitz et al. [17] stated that the variation in F (CH4)/F (CO2) is not significant within their analytical uncertainty, and the average value of F (CH4)/F (CO2) determined in five different CO2-CH4 mixtures at 20 MPa is 5.16 ± 0.18. Le et al. [19, 20] reported the F (CH4) and F (CO2) (relative to N2) to be 7.73 ± 0.16 and 1.40 ± 0.03, respectively, yielding an F (CH4)/F (CO2) ratio of 5.52 ± 0.16. They also argued that the difference between different concentrations is not significant for the measured composition of the gas mixtures. Wopenka and Pasteris [44] obtained an average F (CH4)/F (CO2) of 4.4 ± 0.15 in a variety of CO2-CH4-bearing gas mixtures at low pressure (≤1.6 MPa). Qiu et al. [32] determined a F (CH4) of 6.420 ± 0.104 and a F (CO2) of 1.690 ± 0.042 in a CH4-CO2-CO-N2 mixture with a molar ratio of 1 : 1 : 1 : 2 from 10 MPa to 60 MPa, yielding an F (CH4)/F (CO2) ratio of 3.80 ± 0.10.Table 3
Comparison ofF (CH4)/F (CO2) in this study with previous works.
This studyRef. [17]Ref. [19, 20]Ref. [32]Ref. [44]Ref. [53]Ref. [54]λ (nm)532.07514.5514.5532514.5514.5514Pressure (MPa)2–40200.5–601–60<1.60.15, 10Temperature (°C)24223222——22C (CH4)/C (CO2)0.11∼90.11∼90.11∼91——0.43∼2.33F (CH4)/F (CO2)5.05 ± 0.45.16 ± 0.185.52 ± 0.163.8 ± 0.14.40 ± 0.155.0511.12


## 3.1. Determination of the Pressure of the CO2-CH4 Gas Mixtures

The calibrated peak positions for the CH4υ1 peak and the lower and upper members of the CO2 Fermi diad and the Fermi diad splittings for all samples at room temperature and various pressures collected in HPOC are listed in Table S1 and S2 (Supplemental material) and shown in Figure 3. Figure 3(a) shows the peak positions for the υ1 peak of CH4 in pure CH4 and ten CO2-CH4 mixtures as a function of total pressure; the addition of CO2 can affect the peak position of CH4; however, the dominant factor affecting the peak position of CH4 is the total fluid pressure, which is in agreement with the result of Seitz et al. [17]. A leap in υ1 peak position for CH4 in Figure 3(a) is evident for CO2-rich mixtures at low pressure. For the 10 mol% CH4-90 mol% CO2 mixture, this abrupt shift in the peak position in response to pressure represents the liquid-vapor phase transition. The 30% CH4-70% CO2 mixture, however, remains supercritical (but near-critical) at room temperature [17].Figure 3
Raman peak positions for the CH4υ1 peak (a) and the lower (b) and upper (c) members of the CO2 Fermi diad and the Fermi diad splitting (d) for different CO2-CH4 gaseous mixtures at room temperature as a function of pressure.
(a)(b)(c)(d)The lower and upper members of the Fermi diad peaks for CO2 and Fermi diad splitting for CO2 in CO2-CH4 mixtures as a function of pressure are presented in Figures 3(b)–3(d), respectively. The peak shift with pressure from 2 MPa to 40 MPa is much greater for the lower Fermi diad member (∼5 cm−1) than for the upper Fermi diad member (∼3 cm−1). Thus, the peak position of the lower Fermi diad member is a more sensitive monitor of fluid pressure, which are consistent with previous studies [41]. However, the peak position of the lower Fermi diad member is also more sensitive to composition. Indeed, the Fermi diad splitting (Δ, the separation between bands in the Fermi diad) of CO2 has been previously used to determine the pressure or density of CO2 in FIs [37, 40]. Our results show that at 2 MPa, Δ is nearly identical (∼102.76 cm−1) for any composition, while at higher pressures, the effect of the gas mixture composition becomes more obvious, which is similar to that observed for CO2 mixed with N2 and CH4 [19, 20]. Therefore, we can draw the same conclusion with previous studies [17, 20] that the Δ for CO2 is not only a function of pressure but also a function of the composition of the CO2-CH4 gas mixture (Figure 3(d)).As mentioned above, it can be concluded that the CH4υ1 peak could be the most suitable parameter for the pressure determination, although there is an abrupt shift in the CH4 peak positions due to the existence of the liquid-vapor transition in CO2-rich mixtures. As shown in Figure 4, different laboratories have their own calibration curves for the CH4 peak position-pressure relationship. It can be ascribed to different measurement conditions, including excitation wavelength, the numerical aperture of the objective, the slit width, and the groove density of grating. However, all six data sets collected from the literature for pure CH4 and from this study for CH4-rich mixture have similar relations between peak position and pressure, which are almost parallel to each other but with different intercepts at zero pressure, indicating that systematic discrepancies may exist among these data sets. Fortunately, these discrepancies can be eliminated by choosing D as a variable (Figure 5), where D = υp − υ0, the difference between the peak positions at elevated pressure (υp) and near-zero pressure (υ0) (in this study, υ0 = 2917.924 cm−1 for <0.1 MPa). The same treatment was successfully demonstrated for pure CH4 many years ago by Lu et al. [29]. Our data (CH4-rich mixtures with CH4 ≥ 50 mol% and pure CH4) at room temperature agree with previous studies [17, 27, 29, 51] for pure CH4 (Figure 5). After fitting the data obtained from the six sources, the relation between D (in cm−1) and pressure P (in MPa) can be described by the following equation:(4)D=2.6953×10−8P5−5.0314×10−6P4+3.1297×10−4P3−5.1191×10−3P2−1.9752×10−1P,with R2 (squared correlation coefficient) = 0.9972. The uncertainty (1σ) in the calculated pressure was ±1.1 MPa. This equation could be used to correlate P with D in other laboratories and calculate the pressure (≤70 MPa) of CH4-rich mixtures (CH4 ≥ 50 mol%) with the measured peak position of the CH4υ1 band near room temperature, as long as υ0 is known for the particular Raman spectrometer.Figure 4
Raman peak position of C-H symmetric stretching band (υ1) of CH4 from six available data sets as a function of pressure.Figure 5
The P-D relationship determined in this study compared with other published values at near room temperature. Note that the original data of Jager’s Colorado School of Mines are cited from Lu et al. [29].


## 3.2. Determination of the Density of CO2-CH4 Gas Mixtures

The pressure of the CO2-CH4 gas mixtures of known composition at room temperature (∼24°C) was converted to density using the GERG-2008 EoS (equation of state), which is a new wide-range EoS for natural gases and other mixtures of 21 natural gas components [52]. The variations in D and Δ within CO2-CH4 gas mixtures as a function of density and composition are plotted in Figure 6. The results show that D decreases with increasing CH4 concentration and density of the gas mixture, whereas Δ increases with elevated CO2 concentration and density. The maximum value of the variation in Δ is quite small (<∼3 cm−1) compared to that for D (<∼6 cm−1) over the same density range (0∼1 g/cm3). Thus, given an analytical uncertainty of ±0.01 cm−1 for the measurement of the peak position, D will generally provide the most precise estimate of density. Therefore, the experimental data for D in CO2-CH4 gas mixtures were fitted to the following equation by polynomial regression analysis (using the software 1stOpt):(5)ρ=a00+a10×CCH4+a01×D+a20×CCH42+a11×CCH4×D+a02×D2+a30×CCH43+a21×CCH42×D+a12×CCH4×D2+a03×D3+a31×CCH43×D+a22×CCH42×D2+a13×CCH4×D3+a04×D4.Figure 6
The variation inD (a) and Δ (b) within CO2-CH4 gas mixtures as a function of density and composition. D = υp − υ0 is the difference between the υ1 peak positions of CH4 at elevated pressure (υp) and near-zero pressure (υ0); Δ represents the separation between bands in the Fermi diad of CO2.
(a)(b)The fitted coefficients for equation (5) are listed in Table 1, and the root-mean-square error of equation (5) is 0.012 g/cm3 with an R2 of 0.997. This equation can be used to calculate the density of CH4-CO2 mixtures with the measured peak position of the CH4υ1 band near room temperature.Table 1
The fitting parameters for equation (5).
a000.0458578972a100.0070465891a01−0.0367435722a20−0.3041825424a11−0.0208569183a020.0264438359a300.2888501741a21−0.0290891828a12−0.0400853154a030.0014973436a310.0879585851a220.0270909951a130.0002772730a040.0000945387


## 3.3. Determination ofF (CH4)/F (CO2)

The ratio of the peak areas of theυ1 band of CH4 and the upper Fermi diad member of CO2 (A (CH4)/A (CO2)) for CO2-CH4 mixtures increases with pressure below 10 MPa and then maintains the same levels at higher pressures (Table 2), indicating that it is an advantageous to use the ratios of the peak area of the υ1 band of CH4 and the upper Fermi diad member of CO2 for quantitative determinations of the fluid composition in CO2-CH4 mixtures [17].Table 2
TheF (CH4)/F (CO2) in ten CO2-CH4 gaseous mixtures at room temperature and pressures up to 40 MPa.
P (MPa)XCH4 (mol%)aA (CH4)/ A (CO2)F (CH4)/ F (CO2)2100.4313.87850.4454.006100.4494.043200.4534.074300.4454.008400.4464.010Avg.0.4484.0312200.9943.97851.0374.147101.0784.314201.0554.219301.0594.235401.0634.250Avg.1.0594.2352301.7634.11451.8524.322101.8904.409201.9304.504301.9254.491401.9194.477Avg.1.9254.4912402.8734.30952.9764.463103.0214.531203.0214.531303.0274.540403.0444.565Avg.3.0304.5452504.6984.69854.7884.788104.9284.928204.8364.836304.6584.658404.6914.691Avg.4.7284.7282606.6434.42956.9194.613107.0724.714207.1654.777307.1764.784407.1984.799Avg.7.1804.78727011.9455.119512.4925.3541011.9745.1322012.9285.5413012.6165.4074012.5255.368Avg.12.6905.43028018.1704.542518.5414.6351018.8084.7022019.4274.8573019.6524.9134019.5164.879Avg.19.5314.88328527.0754.778528.3084.9961028.1294.9642028.7815.0793028.8215.0864028.6065.048Avg.28.7365.07129039.8124.424541.3454.5941042.1734.6862046.2085.1343045.4965.0554044.9504.994Avg.45.5515.061aA is the Raman peak area.According to equation (1), if F (CH4)/F (CO2) has been determined by the known A (CH4)/A (CO2) and C (CH4)/C (CO2), then it can be used to determine the molar ratio of CH4 to CO2 in an unknown CO2-CH4‐bearing fluid from the Raman peak area ratio. F (CH4)/F (CO2) in ten CO2-CH4 gaseous mixtures were calculated based on equation (1) and listed in Table 2. Within a given CO2-CH4 gaseous mixture, the F (CH4)/F (CO2) value rises at low pressures and remains constant (within analytical uncertainty) above 10 MPa (Table 2), which is in agreement with the previous work of Seitz et al. [17]. Therefore, the F (CH4)/F (CO2) values obtained at 20 MPa, 30 MPa, and 40 MPa were averaged and considered as the general F (CH4)/F (CO2) value of this mixture. It can be found that the general F (CH4)/F (CO2) value varies somewhat with different gaseous mixtures. Figure 7 shows a good linear relationship between the molar ratio (C (CH4)/C (CO2)) and peak area ratio (A (CH4)/A (CO2)) with an R2 of 0.9995. The slope shows a value of 5.048, which represents the F (CH4)/F (CO2) ratio based on equation (1). The uncertainty in the average values of F (CH4)/F (CO2) is ±0.4, which in turn can lead to an average error in the composition up to ±1.4 mol% CH4.Figure 7
The linear relationship between the molar ratio (C (CH4)/C (CO2)) and the Raman peak area ratio (A (CH4)/A (CO2)) at room temperature.Table3 shows a comparison of our results with those obtained in six previous studies. The results show that F (CH4)/F (CO2) is quite different among different laboratories. Our value is in agreement with four previous results [17, 19, 20, 53]. Seitz et al. [17] stated that the variation in F (CH4)/F (CO2) is not significant within their analytical uncertainty, and the average value of F (CH4)/F (CO2) determined in five different CO2-CH4 mixtures at 20 MPa is 5.16 ± 0.18. Le et al. [19, 20] reported the F (CH4) and F (CO2) (relative to N2) to be 7.73 ± 0.16 and 1.40 ± 0.03, respectively, yielding an F (CH4)/F (CO2) ratio of 5.52 ± 0.16. They also argued that the difference between different concentrations is not significant for the measured composition of the gas mixtures. Wopenka and Pasteris [44] obtained an average F (CH4)/F (CO2) of 4.4 ± 0.15 in a variety of CO2-CH4-bearing gas mixtures at low pressure (≤1.6 MPa). Qiu et al. [32] determined a F (CH4) of 6.420 ± 0.104 and a F (CO2) of 1.690 ± 0.042 in a CH4-CO2-CO-N2 mixture with a molar ratio of 1 : 1 : 1 : 2 from 10 MPa to 60 MPa, yielding an F (CH4)/F (CO2) ratio of 3.80 ± 0.10.Table 3
Comparison ofF (CH4)/F (CO2) in this study with previous works.
This studyRef. [17]Ref. [19, 20]Ref. [32]Ref. [44]Ref. [53]Ref. [54]λ (nm)532.07514.5514.5532514.5514.5514Pressure (MPa)2–40200.5–601–60<1.60.15, 10Temperature (°C)24223222——22C (CH4)/C (CO2)0.11∼90.11∼90.11∼91——0.43∼2.33F (CH4)/F (CO2)5.05 ± 0.45.16 ± 0.185.52 ± 0.163.8 ± 0.14.40 ± 0.155.0511.12


## 4. Influence of Temperature on the Raman Spectral Parameters

To study the influence of temperature on the Raman spectra measured for CO2-CH4 gas mixtures, HPOC was used to collect Raman spectra for five CO2-CH4 gas mixtures (10 mol% CH4, 30 mol% CH4, 50 mol% CH4, 70 mol% CH4, and 90 mol% CH4) ranging from room temperature to 300°C and from 2 MPa to 40 MPa. The pressures and temperatures of the CO2-CH4 gas mixtures of known composition were converted to density using the GERG-2008 EoS.


### 4.1. Influence of Temperature on the Relationship between Peak Position and Pressure/Density for CO2-CH4 Gas Mixtures

The peak positions of theυ1 band of CH4 and Fermi diad splitting (Δ) of CO2 for pure CH4 or CO2 gas and their five CO2-CH4 gas mixtures at various temperatures and pressures are listed in Table S3 (Supplemental material) and shown in Figures 8 and 9. As shown in Figure 8, as the temperature increases at constant pressure, the peak positions of the υ1 band of CH4 and Fermi diad splitting (Δ) of CO2 for the five CO2-CH4 gas mixtures shift to higher and lower wavenumbers, respectively. The results show that the effect of temperature on the peak positions of CH4 and CO2 in the mixed system has the same trend as demonstrated previously for the pure CH4 or CO2 system [30, 33, 37] and N2-CO2-CH4 system [43]. The pressure-induced change in the shift decreases at higher temperatures (Figure 8). Additionally, at room temperature, there is an abrupt shift in the measured position of CH4 and CO2 resulting from the phase transition, but this shift vanishes at higher temperatures (above 100°C). At the same pressure and temperature, υCH4 and Δ in the gas mixtures are shifted to lower wavenumbers compared with the values in the pure system (Figures 9(a) and 9(b)), which have also been reported in previous studies [17, 20]. However, in the N2-CO2-CH4 system, υCH4 is located at higher wavenumbers relative to the pure system at the same P-T conditions [43]. Figure 10 presents the variation in υCH4 and Δ as a function of density, composition, and temperature. The difference in density is notable at various temperatures. Taking 10 mol% CH4 at 40 MPa as an example, the density and Raman shift of υCH4 at 24°C are 0.902 g/cm3 and 2912.03 cm−1, respectively, and at 300°C, they are 0.338 g/cm3 and 2914.0 cm−1, respectively. In conclusion, the effect of temperature must be considered when Raman shifts are used to calculate the pressure or density of CO2-CH4 gas mixtures.Figure 8
Effect of temperature on the Raman peak positions of (a) theυ1 band of CH4 and (b) Fermi diad splitting of CO2 (Δ) for five CO2-CH4 gas mixtures as a function of pressure.
(a)(b)Figure 9
Effect of temperature on the Raman peak positions of (a) theυ1 band of CH4 for pure CH4 and 10 mol% CH4 and (b) Fermi diad splitting of CO2 (Δ) for pure CO2 and 10 mol% CH4 as a function of pressure.
(a)(b)Figure 10
Effect of temperature on the variation of (a) theυ1 band of CH4 and (b) Fermi diad splitting of CO2 (Δ) as a function of the density of CO2-CH4 mixtures.
(a)(b)Effect of temperature on the variation of (a) theυ1 band of CH4 and (b) Fermi diad splitting of CO2 (Δ) as a function of the density of CO2-CH4 mixtures.The relationship between the molar ratio and peak area ratio (average values above 10 MPa) is plotted at different temperatures in Figure12 and listed in Table 4. This indicates that F (CH4)/F (CO2) increases with increasing temperature, and the peak area ratio obtained at high temperatures is not suitable for determining the composition at room temperature because it could lead to an overestimation of the molar ratio of CH4/CO2. Therefore, the temperature effect must be considered when CH4 to CO2 peak area ratios are used to calculate the fluid composition in CO2-CH4 mixtures.Figure 11
Relationship between the CH4 to CO2 peak area ratio and pressure at 50 mol% CH4-50 mol% CO2 mixture and temperatures ranging from 24°C to 300°C.Figure 12
Raman peak area ratio between CH4 and CO2 as a function of their molar ratio at different temperatures.Table 4
The fitting parameters for equation (1) at different temperatures.
Temperature (°C)24100150200250300F (CH4)/F (CO2)5.0485.47705.88466.1476.21196.4383R20.99950.99890.99900.99870.99770.9983


### 4.2. Effect of Temperature on the Raman Peak Area for CO2-CH4 Gas Mixtures

The ratios of the peak area of theυ1 band of CH4 and the upper Fermi diad of CO2 for the 50 mol% CH4-50 mol% CO2 (CCH4/CCO2 = 1 : 1) mixture are plotted at different temperatures as a function of pressure in Figure 11. The results show that the A (CH4)/A (CO2) rises steeply with increasing pressure up to 10 MPa and then becomes approximately constant at higher pressures, ranging from 4.7 at 24°C to 7.0 at 300°C.


### 4.3. Effect of Temperature on the Hot Band of CO2 for CO2-CH4 Gas Mixtures

Earlier studies have confirmed that the intensity of CO2 hot bands increases with increasing temperature [37, 55, 56] and assessed the possibility of using the CO2 hot band as a thermometer [57, 58]. In this study, we examined the relationship between the peak area ratio between the upper hot band (υH,B+) and the upper Fermi diad member (υII) with temperature, pressure, and composition. Figure 13 shows that the peak area ratio between the upper hot band and the upper Fermi domain is a sensitive function of temperature, and almost independent of composition and pressure. This indicates that the CO2 hot band can be used as a thermometer in the CO2-CH4 gas mixtures.Figure 13
(a) Raman peak area ratio between the upper hot band and the upper Fermi domain versus temperature at 20 MPa for different CO2-CH4 mixtures. (b) Raman peak area ratio between the upper hot band and the upper Fermi domain versus temperature at 70% CH4-30% CO2 and different pressures.
(a)(b)


## 4.1. Influence of Temperature on the Relationship between Peak Position and Pressure/Density for CO2-CH4 Gas Mixtures

The peak positions of theυ1 band of CH4 and Fermi diad splitting (Δ) of CO2 for pure CH4 or CO2 gas and their five CO2-CH4 gas mixtures at various temperatures and pressures are listed in Table S3 (Supplemental material) and shown in Figures 8 and 9. As shown in Figure 8, as the temperature increases at constant pressure, the peak positions of the υ1 band of CH4 and Fermi diad splitting (Δ) of CO2 for the five CO2-CH4 gas mixtures shift to higher and lower wavenumbers, respectively. The results show that the effect of temperature on the peak positions of CH4 and CO2 in the mixed system has the same trend as demonstrated previously for the pure CH4 or CO2 system [30, 33, 37] and N2-CO2-CH4 system [43]. The pressure-induced change in the shift decreases at higher temperatures (Figure 8). Additionally, at room temperature, there is an abrupt shift in the measured position of CH4 and CO2 resulting from the phase transition, but this shift vanishes at higher temperatures (above 100°C). At the same pressure and temperature, υCH4 and Δ in the gas mixtures are shifted to lower wavenumbers compared with the values in the pure system (Figures 9(a) and 9(b)), which have also been reported in previous studies [17, 20]. However, in the N2-CO2-CH4 system, υCH4 is located at higher wavenumbers relative to the pure system at the same P-T conditions [43]. Figure 10 presents the variation in υCH4 and Δ as a function of density, composition, and temperature. The difference in density is notable at various temperatures. Taking 10 mol% CH4 at 40 MPa as an example, the density and Raman shift of υCH4 at 24°C are 0.902 g/cm3 and 2912.03 cm−1, respectively, and at 300°C, they are 0.338 g/cm3 and 2914.0 cm−1, respectively. In conclusion, the effect of temperature must be considered when Raman shifts are used to calculate the pressure or density of CO2-CH4 gas mixtures.Figure 8
Effect of temperature on the Raman peak positions of (a) theυ1 band of CH4 and (b) Fermi diad splitting of CO2 (Δ) for five CO2-CH4 gas mixtures as a function of pressure.
(a)(b)Figure 9
Effect of temperature on the Raman peak positions of (a) theυ1 band of CH4 for pure CH4 and 10 mol% CH4 and (b) Fermi diad splitting of CO2 (Δ) for pure CO2 and 10 mol% CH4 as a function of pressure.
(a)(b)Figure 10
Effect of temperature on the variation of (a) theυ1 band of CH4 and (b) Fermi diad splitting of CO2 (Δ) as a function of the density of CO2-CH4 mixtures.
(a)(b)Effect of temperature on the variation of (a) theυ1 band of CH4 and (b) Fermi diad splitting of CO2 (Δ) as a function of the density of CO2-CH4 mixtures.The relationship between the molar ratio and peak area ratio (average values above 10 MPa) is plotted at different temperatures in Figure12 and listed in Table 4. This indicates that F (CH4)/F (CO2) increases with increasing temperature, and the peak area ratio obtained at high temperatures is not suitable for determining the composition at room temperature because it could lead to an overestimation of the molar ratio of CH4/CO2. Therefore, the temperature effect must be considered when CH4 to CO2 peak area ratios are used to calculate the fluid composition in CO2-CH4 mixtures.Figure 11
Relationship between the CH4 to CO2 peak area ratio and pressure at 50 mol% CH4-50 mol% CO2 mixture and temperatures ranging from 24°C to 300°C.Figure 12
Raman peak area ratio between CH4 and CO2 as a function of their molar ratio at different temperatures.Table 4
The fitting parameters for equation (1) at different temperatures.
Temperature (°C)24100150200250300F (CH4)/F (CO2)5.0485.47705.88466.1476.21196.4383R20.99950.99890.99900.99870.99770.9983


## 4.2. Effect of Temperature on the Raman Peak Area for CO2-CH4 Gas Mixtures

The ratios of the peak area of theυ1 band of CH4 and the upper Fermi diad of CO2 for the 50 mol% CH4-50 mol% CO2 (CCH4/CCO2 = 1 : 1) mixture are plotted at different temperatures as a function of pressure in Figure 11. The results show that the A (CH4)/A (CO2) rises steeply with increasing pressure up to 10 MPa and then becomes approximately constant at higher pressures, ranging from 4.7 at 24°C to 7.0 at 300°C.


## 4.3. Effect of Temperature on the Hot Band of CO2 for CO2-CH4 Gas Mixtures

Earlier studies have confirmed that the intensity of CO2 hot bands increases with increasing temperature [37, 55, 56] and assessed the possibility of using the CO2 hot band as a thermometer [57, 58]. In this study, we examined the relationship between the peak area ratio between the upper hot band (υH,B+) and the upper Fermi diad member (υII) with temperature, pressure, and composition. Figure 13 shows that the peak area ratio between the upper hot band and the upper Fermi domain is a sensitive function of temperature, and almost independent of composition and pressure. This indicates that the CO2 hot band can be used as a thermometer in the CO2-CH4 gas mixtures.Figure 13
(a) Raman peak area ratio between the upper hot band and the upper Fermi domain versus temperature at 20 MPa for different CO2-CH4 mixtures. (b) Raman peak area ratio between the upper hot band and the upper Fermi domain versus temperature at 70% CH4-30% CO2 and different pressures.
(a)(b)


## 5. Application to FSCC Samples

To verify the accuracy of the Raman quantitative analysis methods described above, six synthetic FIs in FSCC samples with unknown relative molar proportions of the components, total pressure, and density were prepared, and the results of microthermometric measurements for these samples were compared with laser Raman (LRM) spectroscopic data. Each FSCC sample was analyzed by MT to determine the melting temperatureTm and the homogenization temperature Th, and they were used to calculate the composition and density of the fluid inclusion based on the VX diagram of Thiery et al. [18]. The total pressures were determined from MT using the GERG-2008 EoS. The selected FSCC samples were also analyzed three times with Raman spectroscopy. The average values of the CH4 to CO2 peak area ratio (A (CH4)/A (CO2)) and peak position of CH4 (υCH4) were used to calculate the composition, pressure, and density through equations (1), (4), and (5). A comparison of the results obtained by LRM and MT is listed in Table 5 and plotted in Figure 14. The uncertainty for 1σ is also provided, and the procedure used for calculating the uncertainty propagation is the same as that reported by Le et al. [19].Table 5
Comparison of the results obtained from Raman spectroscopy and microthermometry.
No.Raman resultsaMicrothermometry resultsbDifferencecA (CH4)/A (CO2)υCH4 (cm−1)XRaman mol% CH4PRaman (MPa)ρRaman (g·cm−3)Pcal1 (MPa)ρcal1 (g·cm−3)Tm (°C)Th (°C)XMicroth mol% CH4ρMicroth (g·cm−3)Pcal2 (MPa)ΔX mol%ΔP (MPa)Δρ (g·cm−3)S.131.821±0.7652911.342±0.00686.6±0.150.2±0.80.345±0.00348.80.349−79.5−89.187.5±0.80.364±0.00559.6±1.1−0.9−9.4−0.019S.224.901±0.0532911.644±0.02983.1±0.542.2±1.20.342±0.00641.30.345−75.3−83.182.5±1.20.398±0.00661.1±0.80.6−18.9−0.056S.312.214±0.4872913.341±0.02370.8±1.522.4±0.80.284±0.01320.70.301−67.4−44.670.7±0.80.286±0.00120.9±0.10.11.5−0.002S.44.907±0.0362911.464±0.00849.3±1.346.8±0.90.569±0.01243.20.582−65.6−59.849.0±1.30.631±0.01062.8±0.30.3−16.0−0.062S.53.573±0.0242911.469±0.00841.4±1.946.7±0.80.636±0.01744.80.643−64.8−64.243.5±1.10.677±0.01264.3±3.0−2.1−17.6−0.041S.61.495±0.00112911.811±0.00422.8±2.138.6±0.70.766±0.01737.30.772−61.7−24.820.9±1.00.795±0.01139.9±1.41.9−1.3−0.029aXRaman, PRaman, and ρRaman are determined from equations (1), (4), and (5) based on A (CH4)/A (CO2) and υCH4; Pcal1 is the pressure calculated from XRaman and ρRaman using the GERG-2008 EoS; ρcal1 is the density calculated from XRaman and PRaman using the GERG-2008 EoS. bXMicroth and ρMicroth are obtained from the VX diagram of Thiery et al. [18] based on Tm and Th; Pcal2 is the pressure calculated from XMicroth and ρMicroth using the GERG-2008 EoS. cΔX = XRaman − XMicroth. ΔP = PRaman − Pcal2. Δρ = ρRaman − ρMicroth. Note that all data are measured at room temperature (∼24°C), and the uncertainty is provided for 1σ.Figure 14
Comparison of (a) mol% CH4, (b) pressure, and (c) density of CO2-CH4 mixtures in FSCCs based on laser Raman (LRM) and microthermometry (MT) data. Note that the pressure (b) and density (c) calculated by GERG-2008 EoS are based on XRaman and ρRaman, and XRaman and PRaman, respectively.
(a)(b)(c)For the LRM data, average errors in the values of mol% CH4, pressure, and density, based on the differences between these three sets of analyses on the same FSCC samples and the best-fitted equations (1), (4), and (5), are ±1.2 mol%, ±0.9 MPa, and ±0.011 g·cm−3, respectively. For the MT data, the uncertainty in ±0.1°C of the heating-cooling stage for Tm and Th and an error in graphic reading arising from the VX diagram can result in average errors of ±1.0 mol% in composition and ±0.008 g/cm3 in density, which can lead to an average error of ±1.1 MPa in pressure, as determined from the GERG-2008 EoS.Overall, for the same FSCC samples, there is a very good agreement between the mol% CH4 derived from LRM and MT analyses (Table 5, Figure 14(a)). The largest difference in mol% CH4 is 2.1 mol%. The densities derived from LRM analysis are slightly smaller than those obtained from MT analysis, and the difference is within 0.062 g/cm3 (Figure 14(c)). However, there is a large deviation between the pressure derived from LRM analysis and MT analysis (Figure 14(b)). To investigate the reason for the large deviation, the pressure (Pcal1) calculated from XRaman and ρRaman and the density (ρcal1) calculated from XRaman and PRaman using the GERG-2008 EoS are also obtained (Table 5, Figures 14(b) and 14(c)), and they are very close to the values for PRaman and ρRaman obtained directly using equations (4) and (5), respectively. The results show that our calibration equations could provide reasonable estimates for the composition, pressure, and density of fluid inclusions. Therefore, it is reasonable to believe that this deviation is derived from the deviation of density and composition between LRM analysis and MT analysis. Incredibly, the slight deviation in density and composition can lead to such a large deviation in pressure. For example, a small difference between the composition of 0.6 mol% CH4 and the density of 0.056 g/cm3 can lead to a pressure deviation of up to 18.9 MPa (Table 5, Figure 14(b)). Although the uncertainty in the MT analysis is slightly better than that derived from the LRM analysis in this work, Raman spectroscopy is still a powerful tool for fluid inclusion investigations. In addition, for the analyses of natural fluid inclusions, MT may not be more efficient than LRM analysis in some cases, such as small inclusions (<5 μm) and inclusions with poor optical properties (color, contrast, etc.) or the formation of clathrates [20]. It is worth noting that when analyzing natural fluid inclusions in anisotropic host minerals by using Raman spectroscopy, it must be placed at crystal extinction position to eliminate the effect of birefringence of the host mineral on the composition of the gas phase of fluid inclusions, as suggested by Caumon et al. [59].


## 6. Conclusion

This study investigated the Raman spectral parameters (peak position and peak area) for CO2-CH4 mixtures at pressures up to 40 MPa and temperatures up to 300°C. The variation in each spectral parameter as a function of fluid pressure, density, temperature, and composition was discussed. The peak position of the υ1 band for CH4 can be used to determine the pressure of pure CH4 and CH4-dominated fluids (>50 mol% CH4). The relationships for the peak position of the υ1 band for CH4, density, and composition were established and used to calculate the densities for CO2-CH4 mixtures. The Raman quantification factor F (CH4)/F (CO2) was found to remain almost constant (5.048 ± 0.4) with varying pressure/density and composition, and, therefore, was used for the determination of the CH4 to CO2 molar ratio for fluids with high internal pressures (>10 MPa) based on the Raman peak area ratio. The effects of temperature on the variations in Raman spectral parameters were first investigated at temperatures up to 300°C, and these effects should not be ignored when Raman spectral parameters are used to calculate the pressure, density, and composition of CO2-CH4 gas mixtures. The results of our Raman spectroscopic measurements for six FSCC samples agree very well with those derived from MT analyses and, thus, verify our methodology for the quantitative determination of composition, pressure, and density of CO2-CH4 mixtures.



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