# Phase Behavior and Physical Parameters of Natural Gas Mixture withCO2

Authors: Dali Hou; Hucheng Deng; Hao Zhang; Kai Li; Lei Sun; Yi Pan
Journal: Journal of Chemistry
 (2015)

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## Abstract

The two-flash experiment, constant composition expansion experiment, saturation pressure measurement experiment, and phase transition observation experiment from well bottom hole to well head of four high CO2 content natural gas samples were carried out by using the JEFRI-PVT apparatus made from DBR Company of Canada. The experimental results show that in the four high CO2 content gas samples no phase transitions will take place at temperatures greater than 35°C. In the gas-liquid two-phase region, saturation pressures, critical pressure, critical temperature, and an integrated P-T phase diagram of different CO2 content natural gases are calculated by using the modified PR equation of state and modified (T) equation proposed by Saffari. The deviations between the saturation pressure calculated by using the model proposed in this study and experimental measured saturation pressure are very small; the average relative error is only 2.86%. Thus, the model can be used to predict the phase equilibrium parameters of high CO2 content natural gas.


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## Body

## 1. Introduction

With the increasing demand of CO2 resource, exploration and development of high CO2 content gas reservoirs are becoming one part of the future oil-gas strategy [1]. Currently, the discovered high CO2 content gas reservoirs in the world are mainly distributed over the Pacific, such as Japan, Indonesia, New Zealand, Philippines, Vietnam, Thailand, Malaysia, Australia, Mexico, America, and Canada [2–5]. Twenty-eight high CO2 content gas reservoirs have been discovered in China and they are mainly distributed in oil-bearing basins in the east of China, in which the high CO2 content natural gas reserve is 20000 × 108 m3 in Songliao basin [6]. Furthermore, CO2 content in Changling, Gudian, Honggang, Shengping, Fangshen, and other gas reservoirs in Jilin oilfield of Songliao basin can even range from 20 mol% to 90 mol% [7–9]. High CO2 content natural gas reservoir is very special and development is very difficult, which mainly reflects in the variation of fluid phase behavior. The research of some scholars at home and abroad focuses on the physical parameters and development index of the CO2 contents in natural gas [7, 9–14], but seldom focus is directed on the phase behavior of natural gases with high CO2 content and the phase behavior of natural gas with high CO2 content is not entirely clear at present [15–19]. Thus, it is one of basic research topics on the experimental measured saturation pressure to determine whether any phase transitions in natural gases with high CO2 content take place from formation to well head and the physical parameters of high CO2 content natural gases for high-efficient developing the gas reservoirs with high CO2 content.It is revealed in this paper whether any phase transition in high CO2 content natural gases takes place in the exploitation process. The saturation pressures of different CO2 content in natural gases at different temperatures are measured by using the DBR-PVT apparatus, and the saturation pressures, critical pressures, critical temperatures, and an integrated P-T phase diagram of different CO2 content natural gases are calculated by using the modified PR equation of state and modified α(T) equation proposed by Saffari. And the deviations between the saturation pressure calculated by using the model proposed in this paper and experimental measured saturation pressure are analyzed. Also revealed in this paper is the influence of different CO2 content in natural gases on the P-T phase diagrams and critical points. Furthermore, the variation law and affecting factors of the physical parameters, such as relative volume, Z-factor, formation volume factor, and density of high CO2 content natural gases are discussed in this paper.


## 2. Theories

By modifying the attractive term in the Redlick–Kwong equation of state, Peng and Robinson were able to enhance the model prediction of experimental data. Since its inception, Peng-Robinson EOS has been widely used to estimate thermodynamic properties for hydrocarbon systems. It reads [20, 21] as(1)P=RTv-b-aTvv+b+bv-b,where P is pressure, T is temperature, v is the molar volume, R is the gas constant, and a(T) and b are the parameters of the EOS. At constant P and T, the equation will take the form of a cubic equation in v and can be solved for v using any standard analytical or numerical technique [22]. The limitations on critical point lead to the following relations for the PR-EOS parameters [20]:(2)aT=aTcαT,aTc=0.45724R2Tc2Pc,b=0.0778RTcPc,where subscript c indicates critical property and α(T) is temperature dependent. In this work, we use the new α-function proposed by Saffari, which is written as [23] (3)αT=exp⁡⁡k1Tr+k2ln⁡⁡Tr+k31-Tr1/2,(4)Tr=TTc.The newα-functions proposed are exponential functions, each with three adjustable parameters k1, k2, and k3. Since the adjustable parameters determine attractive intermolecular interactions in a pure component system, the values of ki are compound-specific and should be optimized for each pure component. In this work, we determine the optimum values of pure component parameters by minimizing the error of vapor pressure predicted by using the modified PR equation of state and modified α(T) equation proposed by Saffari with respect to the experimental values in the temperature range from triple point to critical point [23].And we use the individually optimized parameters of pure components for the newα-function proposed in this work (3) to develop generalized equations in terms of the acentric factor ω. Pure component constants, including critical properties, and vapor pressure data are obtained from Poling et al. [24], Yaws [25], and Smith and Srivastava [26]. The adjustable parameters of the new α-function proposed by Saffari have been fitted to experimental vapor pressure data, given in Table 1.Table 1
Optimized parameters of the newα-function proposed by Saffari (3).
Substance
T
r range
Optimized parameters
k
1
k
2
k
3
CO2
0.72–1
0.0056
0.0881
1.4928
N2
0.52–1
0.0033
−0.0031
0.8180
methane
0.48–1
0.0039
0.0473
0.8514
ethane
0.30–1
0.0047
0.0359
1.0638
propane
0.26–1
0.0050
0.1010
1.3640
i-butane
0.28–1
0.0052
0.0730
1.4200
n-butane
0.33–1
0.0054
0.0780
1.4205
i-pentane
0.25–1
0.0060
0.0885
1.5626
n-pentane
0.31–1
0.0059
0.0872
1.5624
hexane
0.36–1
0.0072
0.1731
1.8759And then, the parametersk1, k2, and k3 are generalized as a function of acentric factor ω. Acentric factor of a pure component is obtained from Poling et al. [24]. Figures 1–3 show the trend of fitted parameters presented in Table 1 versus the acentric factor, as well as a linear fit and the R-squared.Figure 1
Linear trend of fitted parameterk1 of the α-function equation (3).Figure 2
Linear trend of fitted parameterk2 of the α-function equation (3).Figure 3
Linear trend of fitted parameterk3 of the α-function equation (3).Consequently, the final form of newα-function with the generalized parameters for natural gas components can be written as (5)αT=exp⁡⁡k1Tr+k2ln⁡⁡Tr+k31-Tr1/2,k1=0.0113ω+0.0033,k2=0.4106ω-0.0085,k3=3.541ω+0.7532.Extending PR-EOS to mixtures requires replacement of coefficientsa and b by the following van der Waals composition-dependent mixing rules [20]:(6)a=∑in∑jnxixjaij,b=∑jnxibi.The unlike-interaction parameter,aij, formed between component i and component j, can be related to the pure components parameter with an extra fitting coefficient (kij) known as the coupling parameter:(7)aij=1-kijaiaj1/2.


## 3. Experiments

### 3.1. Sample

Experimental gas samples were divided into 4 groups: one group was directly taken from surface separator of YP9 well in Jilin gas field, and the other three groups (Gas1, Gas2, and Gas3) were made from YP9 dry natural gas and pure industrial carbon dioxide (purity > 99.99%). The detailed synthetic process refers to SY/T6434-2000 [27]. The initial formation pressure and formation temperature of YP9 well are, respectively, 42.34 MPa and 127.5°C. The components of four groups of gas samples were analyzed by using HP-6890 gas chromatography and Shimadzu GC-14A gas chromatography. The results are shown in Table 2. The critical pressure and temperature [28, 29] of the pure components which are normally presented in natural gas are also listed in Table 2. The contents of CO2 in YP9 well, Gas1, Gas2, and Gas3 are, respectively, 21.746 mol%, 10.045 mol%, 55.535 mol%, and 75.323 mol%. The CO2 content in natural gas being more than 10 mol% is usually called the high CO2 content natural gas [30]. Thus, The four groups of gas samples are all the high CO2 content gas samples.Table 2
Composition of various gas mixtures and the critical properties of the related component.
Components
Gas1
YP9
Gas2
Gas3
P
c
T
c
ω
(mol%)
(mol%)
(mol%)
(mol%)
(MPa)
(K)
CO2
10.045
21.746
55.535
75.323
7.376
304.2
0.225
N2
1.474
2.71
2.056
0.971
3.394
126.2
0.040
C1
84.718
73.604
40.891
23.014
4.600
190.6
0.008
C2
2.973
1.127
0.941
0.422
4.884
305.4
0.098
C3
0.532
0.492
0.235
0.092
4.246
369.8
0.152
iC4
0.064
0.006
0.299
0.034
3.640
408.1
0.176
nC4
0.058
0.301
0.004
0.042
3.800
425.2
0.193
iC5
0.026
0.003
0.005
0.047
3.384
460.4
0.227
nC5
0.052
0.005
0.003
0.033
3.374
469.6
0.251
C6
0.058
0.006
0.031
0.022
2.969
507.4
0.296
Note: gas sample with CO2 content of 10.045 mol% is made from YP9 and dry natural gas, and gas sample with CO2 content of 55.535 mol% or 75.323 mol% is made from YP9 and pure industrial carbon dioxide (purity > 99.99%).


### 3.2. Apparatus

The experimental facility is a mercury-free high pressure PVT system made by the DBR Company, Canada. A schematic diagram of the corresponding apparatus is given in Figure4. It is mainly characterized by the visual observation of experimental phenomena and the specially designed piston in the PVT cell that allows us to precisely measure even minute liquid. The system is mainly made up of a PVT cell, thermostatic air bath, pressure sensor, temperature sensor, flash separator, electronic balance, gasometer, gas chromatography, sample container, automatic pump, and operation control system. Sample container is made from sapphire glass.Figure 4
Schematic diagram of the experimental apparatus.The volume of fluid in the PVT cell can be calculated by the internal cross-sectional area of sapphire glass cylinder multiplied by the height of the fluid, which was measured by the grating altimeter.The physical parameters of main parts are as follows.PVT cells: maximal working pressure is 70 MPa, the highest operating temperature is 200°C, the lowest operating temperature is −100°C, and maximal volume is about 150 cm3.Pressure sensor: It is 0~100 MPa, and precision of pressure control is 1 Psi.Temperature sensor: it is −100~200°C, and precision of temperature control is ±0.1°C.Thermostatic air bath: the highest operation temperature is 200°C and precision of temperature control is ±0.1°C.Sample container: it is 130 cm3.Automatic pump: rated operation pressure is 100 MPa with resolution of 1 Psi, and the range of operation pump volume is 500 cm3 with resolution of 0.001 cm3.Electronic balance: it is 0~500 g, and precision of weight control is 0.001 g.The accuracy of PVT main parts satisfies the phase behavior experimental requirement of the synthetic gas sample with different CO2 content [31].


### 3.3. Experimental Procedures

Experimental procedures are as follows:(1)
Clean PVT vessel and cells; then connect the PVT vessel to cells and evacuate the cells.(2)
Prepare the gas samples, and control and maintain the desired temperature using the constant temperature air bath.(3)
Introduce a test gas about 50 mL (YP9 gas sample) into PVT vessel at the specified temperature and pressure in the oven and keep it for 5 h, and then hold on an hour and measure the gas volume of the PVT vessel.(4)
Two-flash experiment: slightly open the valve between the cells and bleed gas from the PVT vessel into the flash separators, at the same time, and keep the pressure using the automatic pump at formation temperature (127.5°C).(5)
Record the bled gas volumes using the gasometer and remaining gas volumes of PVT vessel.(6)
The bled gas was analyzed using gas chromatograph.(7)
Constant composition expansion experiment (CCE experiment) orP-V relationship experiment: pressure was reduced step by step from initial formation pressure to the limit pressure of the piston movement under the formation temperature. The volumes were recorded when each pressure was stable.(8)
Step(7) was repeated at 35°C, 75°C, and 127.5°C, respectively. P-V relationship experiment was tested at least three times under each temperature and the average value was calculated.(9)
Two-flash experiments and CCE experiments were also performed on the other three gas samples by repeating step(3) to step (8).(10)
The gas sample with the highest content of CO2 (75.323 mol%) was introduced into the PVT vessel to study whether phase transition in high CO2 content natural gas takes place from formation to well head. The experimental temperatures are −10°C and 35°C, respectively.


## 3.1. Sample

Experimental gas samples were divided into 4 groups: one group was directly taken from surface separator of YP9 well in Jilin gas field, and the other three groups (Gas1, Gas2, and Gas3) were made from YP9 dry natural gas and pure industrial carbon dioxide (purity > 99.99%). The detailed synthetic process refers to SY/T6434-2000 [27]. The initial formation pressure and formation temperature of YP9 well are, respectively, 42.34 MPa and 127.5°C. The components of four groups of gas samples were analyzed by using HP-6890 gas chromatography and Shimadzu GC-14A gas chromatography. The results are shown in Table 2. The critical pressure and temperature [28, 29] of the pure components which are normally presented in natural gas are also listed in Table 2. The contents of CO2 in YP9 well, Gas1, Gas2, and Gas3 are, respectively, 21.746 mol%, 10.045 mol%, 55.535 mol%, and 75.323 mol%. The CO2 content in natural gas being more than 10 mol% is usually called the high CO2 content natural gas [30]. Thus, The four groups of gas samples are all the high CO2 content gas samples.Table 2
Composition of various gas mixtures and the critical properties of the related component.
Components
Gas1
YP9
Gas2
Gas3
P
c
T
c
ω
(mol%)
(mol%)
(mol%)
(mol%)
(MPa)
(K)
CO2
10.045
21.746
55.535
75.323
7.376
304.2
0.225
N2
1.474
2.71
2.056
0.971
3.394
126.2
0.040
C1
84.718
73.604
40.891
23.014
4.600
190.6
0.008
C2
2.973
1.127
0.941
0.422
4.884
305.4
0.098
C3
0.532
0.492
0.235
0.092
4.246
369.8
0.152
iC4
0.064
0.006
0.299
0.034
3.640
408.1
0.176
nC4
0.058
0.301
0.004
0.042
3.800
425.2
0.193
iC5
0.026
0.003
0.005
0.047
3.384
460.4
0.227
nC5
0.052
0.005
0.003
0.033
3.374
469.6
0.251
C6
0.058
0.006
0.031
0.022
2.969
507.4
0.296
Note: gas sample with CO2 content of 10.045 mol% is made from YP9 and dry natural gas, and gas sample with CO2 content of 55.535 mol% or 75.323 mol% is made from YP9 and pure industrial carbon dioxide (purity > 99.99%).


## 3.2. Apparatus

The experimental facility is a mercury-free high pressure PVT system made by the DBR Company, Canada. A schematic diagram of the corresponding apparatus is given in Figure4. It is mainly characterized by the visual observation of experimental phenomena and the specially designed piston in the PVT cell that allows us to precisely measure even minute liquid. The system is mainly made up of a PVT cell, thermostatic air bath, pressure sensor, temperature sensor, flash separator, electronic balance, gasometer, gas chromatography, sample container, automatic pump, and operation control system. Sample container is made from sapphire glass.Figure 4
Schematic diagram of the experimental apparatus.The volume of fluid in the PVT cell can be calculated by the internal cross-sectional area of sapphire glass cylinder multiplied by the height of the fluid, which was measured by the grating altimeter.The physical parameters of main parts are as follows.PVT cells: maximal working pressure is 70 MPa, the highest operating temperature is 200°C, the lowest operating temperature is −100°C, and maximal volume is about 150 cm3.Pressure sensor: It is 0~100 MPa, and precision of pressure control is 1 Psi.Temperature sensor: it is −100~200°C, and precision of temperature control is ±0.1°C.Thermostatic air bath: the highest operation temperature is 200°C and precision of temperature control is ±0.1°C.Sample container: it is 130 cm3.Automatic pump: rated operation pressure is 100 MPa with resolution of 1 Psi, and the range of operation pump volume is 500 cm3 with resolution of 0.001 cm3.Electronic balance: it is 0~500 g, and precision of weight control is 0.001 g.The accuracy of PVT main parts satisfies the phase behavior experimental requirement of the synthetic gas sample with different CO2 content [31].


## 3.3. Experimental Procedures

Experimental procedures are as follows:(1)
Clean PVT vessel and cells; then connect the PVT vessel to cells and evacuate the cells.(2)
Prepare the gas samples, and control and maintain the desired temperature using the constant temperature air bath.(3)
Introduce a test gas about 50 mL (YP9 gas sample) into PVT vessel at the specified temperature and pressure in the oven and keep it for 5 h, and then hold on an hour and measure the gas volume of the PVT vessel.(4)
Two-flash experiment: slightly open the valve between the cells and bleed gas from the PVT vessel into the flash separators, at the same time, and keep the pressure using the automatic pump at formation temperature (127.5°C).(5)
Record the bled gas volumes using the gasometer and remaining gas volumes of PVT vessel.(6)
The bled gas was analyzed using gas chromatograph.(7)
Constant composition expansion experiment (CCE experiment) orP-V relationship experiment: pressure was reduced step by step from initial formation pressure to the limit pressure of the piston movement under the formation temperature. The volumes were recorded when each pressure was stable.(8)
Step(7) was repeated at 35°C, 75°C, and 127.5°C, respectively. P-V relationship experiment was tested at least three times under each temperature and the average value was calculated.(9)
Two-flash experiments and CCE experiments were also performed on the other three gas samples by repeating step(3) to step (8).(10)
The gas sample with the highest content of CO2 (75.323 mol%) was introduced into the PVT vessel to study whether phase transition in high CO2 content natural gas takes place from formation to well head. The experimental temperatures are −10°C and 35°C, respectively.


## 4. Results and Discussion

### 4.1. Two-Flash and CCE Experiments

The results of two-flash experiments are listed in Table3. Formation volumes (under the formation conditions) and ground volumes (under the standard conditions) are the experimental measurements, and density, molecular weight, formation volume factor, and Z-factor are calculated by using gas state equation. The gas state equation is expressed as follows [27].Table 3
Results from two-flash experiments for different CO2 contents in natural gas.
Parameters
Gas1
YP9
Gas2
Gas3
Formation volume/Vt (cm3)
2.97
3.951
3.762
6.676
Ground volume/Vsc (cm3)
850
1135
1155
2160
Formation volume factor/Bgt
0.003496
0.003481
0.003257
0.003091
Z-factor/Zt
1.0702
1.0663
0.9885
0.9295
Gas density/ρt (kg/m3)
230.00
268.51
398.75
494.13
(under the formation conditions)
Molecular weight/M (g/mol)
19.85
22.49
30.55
35.92
Relative density/γg
0.6853
0.7763
1.0545
1.2398Under the formation conditions one has(8)PtVt=nRZtTt.Under the standard conditions one has(9)PscVsc=nRZscTsc.P
t is the formation pressure; Vt is the gas volume under the formation conditions; Zt is the deviation factor under the formation conditions; Tt is the formation temperature; n is the number of moles; R is the gas general constant, 8.3147 MPa·cm3·mol−1·K−1; Psc is the atmospheric pressure, and it is usually approximately equal to 0.101325 MPa; Vsc is the gas volume under the standard conditions; Zsc is the deviation factor under the standard conditions, and it is usually approximately equal to 1; Tsc is the standard temperature, and it is usually approximately equal to 20°C.Relative densities are calculated by using the following [27]:(10)γg=MMair.M is the gas molecular weight; Mair is the air molecular weight, and it is usually approximately equal to 28.97 g/mol.We can draw the conclusion from Table3 that the density, molecular weight, and relative density increase with increasing CO2 content in natural gas, while the formation volume factor and Z-factor decrease with increasing CO2 content in natural gas.CCE experiment was performed to draw the relative volume,Z-factor, formation volume factor, and density under the grading pressure. And the results are shown from Figures 5–12.Figure 5
Variation of the relative volume of YP9 gas sample with pressure under different temperatures.Figure 6
Variation of the formation volume factor of YP9 gas sample with pressure under different temperatures.Figure 7
Variation of the gas density of YP9 gas sample with pressure under different temperatures.Figure 8
Variation of theZ-factor of YP9 gas sample with pressure under different temperatures.Figure 9
Variation of the relative volume of different CO2 content natural gas samples with pressure at 127.5°C.Figure 10
Variation of the volume factor of different CO2 content natural gas samples with pressure at 127.5°C.Figure 11
Variation of the gas density of different CO2 content natural gas samples with pressure at 127.5°C.Figure 12
Variation of theZ-factor of different CO2 content natural gas samples with pressure at 127.5°C.


#### 4.1.1. Effect of Temperature

The effect of temperature on the physical properties of YP9 gas sample was, respectively, tested under the formation temperature (127.5°C), the temperature in the well (75°C), and the ground temperature (35°C). It can be seen from Figures5–7 that the relative volume and formation volume factor of high CO2 content natural gases increase with increasing temperature under constant pressure, while the density of gas decreases with increasing temperature under constant pressure. And the relative volume and formation volume factor of high CO2 content natural gases decrease with increasing pressure at isothermal conditions. The effects of temperature and pressure on the experimental Z-factors for YP9 gas sample are shown in Figure 8. It can be seen clearly form Figure 8 that Z-factor decreases with increasing pressure at lower pressure range, that is, less than 18 MPa, while it increases with increasing pressure at higher pressures, that is, higher than 18 MPa. And the Z-factor decreases with decreasing temperature and a greater decrease can be observed in a pressure range from about 15 MPa to 22 MPa [32].


#### 4.1.2. Effect of CO2 Content

Experimental relative volumes, formation volume factors, and densities of different CO2 content natural gases are shown from Figures 9–11. It can be seen clearly from Figures 9–11 that relative volume and formation volume factor decrease with increasing CO2 content in natural gas at 127.5°C isothermal and constant pressure conditions, but they do not change insignificantly. The effects of CO2 content in natural gas on the experimental Z-factors of different CO2 content natural gases are shown in Figure 12. It can be seen from Figure 12 that Z-factor decreases with increasing CO2 content in natural gas at 127.5°C isothermal and constant pressure conditions. And the dependence of the pressure follows the same trends as mentioned in Figure 5.


### 4.2. Effect of CO2 Content on P-T Diagram

In order to test and draw theP-T phase diagram of the high CO2 content natural gas, we have tested saturation pressures of the high CO2 content natural gases at different temperatures (−60°C, −50°C, −40°C, −30°C, −20°C, −10°C, and 0°C) based on the above CCE experimental test methods. The test results are shown in Table 4. At the same time, saturation pressures at the corresponding conditions are calculated by using (1) to (7), and the tested saturation pressures are fitted by adjusting critical parameters (critical temperature and critical pressure) of C6 on the basis of the fixed binary interaction coefficients in the process of calculation; the calculated results are also shown in Table 4. C6 has several isomers; the critical parameters are not fixed, so we choose the critical parameters of C6 as adjustable parameters to fit the saturation pressure of different CO2 content natural gases. The fixed binary interaction coefficients are given in Table 6 and the critical parameters (critical temperatures and critical pressures) of C6 are given in Table 7. It can be seen from  Table 7 that the higher the CO2 content, the higher the critical temperature, the lower the critical pressure, and the heavier the system (different CO2 content natural gas). And we compare the saturation pressure calculated by using the model proposed in this paper with the experimental measured saturation pressure; the deviations between the saturation pressure calculated by using the model proposed in this paper and experimental measured saturation pressure are shown in Table 5. The absolute relative error (11) and the average absolute relative error (12) are used to express the deviation between the saturation pressure calculated by using the model proposed in this paper and the experimental measured saturation pressure. We can draw the conclusion from Table 5 that the temperatures are colder, the absolute relative error is greater, and the higher the CO2 content in natural gas, the greater the absolute relative error. The average relative errors of Gas1, YP9, Gas2, and Gas3 are 1.62%, 2.03%, 3.29%, and 3.38%, respectively. Overall, the deviations between the saturation pressure calculated by using the model proposed in this paper and experimental measured saturation pressure are very small; the average relative error of all the gas samples is 2.86%. So it shows that the model can be used to predict the P-T phase diagram of the high CO2 content natural gas. Consider(11)ARE (%)=∑i=1NCal-ExpExpi×100,(12)AARE (%)=1N∑i=1NCal-ExpExpi×100.Table 4
Saturation pressure calculated by using the model proposed in this paper and experimental measured saturation pressure.
Parameters
Gas1
YP9
Gas2
Gas3
Calculated value
Measured value
Calculated value
Measured value
Calculated value
Measured value
Calculated value
Measured value
(MPa)
(MPa)
(MPa)
(MPa)
(MPa)
(MPa)
(MPa)
(MPa)
Saturation pressure (−60°C)
6.21
6.05
6.28
6.11
4.88
4.62
/
/
Saturation pressure (−50°C)
6.75
6.68
7.05
6.92
5.69
5.51
3.99
3.75
Saturation pressure (−40°C)
6.08
6.01
6.88
6.98
6.48
6.66
4.68
4.45
Saturation pressure (−30°C)
/
/
/
/
7.32
7.15
5.42
5.65
Saturation pressure (−20°C)
/
/
/
/
8.13
8.45
6.23
6.35
Saturation pressure (−10°C)
/
/
/
/
8.48
8.65
7.08
6.95
Saturation pressure (0°C)
/
/
/
/
/
/
7.85
8.02
Note: “/” shows that no saturation pressure is measured and calculated.Table 5
The deviations between the saturation pressure calculated by using the model proposed in this paper and experimental measured saturation pressure.
Parameters
Gas1
Gas1
YP9
YP9
Gas2
Gas2
Gas3
Gas3
Total
ARE, %
AARE, %
ARE, %
AARE, %
ARE/%
AARE/%
ARE/%
AARE/%
AARE/%
Saturation pressure (−60°C)
2.64
1.62
2.78
2.03
5.63
3.29
/
3.38
2.86
Saturation pressure (−50°C)
1.05
1.88
3.27
6.40
Saturation pressure (−40°C)
1.16
1.43
2.70
5.17
Saturation pressure (−30°C)
/
/
2.38
4.07
Saturation pressure (−20°C)
/
/
3.79
1.89
Saturation pressure (−10°C)
/
/
1.97
1.87
Saturation pressure (0°C)
/
/
/
2.12Table 6
Binary interaction parameters (kij) and mixing rules for the model proposed in this study.
Components
CO2
N2
C1
C2
C3
iC4
nC4
iC5
nC5
C6
CO2
0
−0.02
0.103
0.130
0.135
0.130
0.130
0.125
0.125
0.150
N2
−0.02
0
0.031
0.042
0.091
0.095
0.095
0.095
0.095
0.120
C1
0.103
0.031
0
0.003
0.009
0.016
0.015
0.021
0.021
0.025
C2
0.13
0.042
0.003
0
0.002
0.005
0.005
0.009
0.009
0.012
C3
0.135
0.091
0.009
0.002
0
0.001
0.001
0.003
0.003
0.005
iC4
0.13
0.095
0.016
0.005
0.001
0
0.000
0.000
0.000
0.001
nC4
0.13
0.095
0.015
0.005
0.001
0.000
0
0.001
0.001
0.001
iC5
0.125
0.095
0.021
0.009
0.003
0.000
0.001
0
0.000
0.000
nC5
0.125
0.095
0.021
0.009
0.003
0.000
0.001
0.000
0
0.000
C6
0.15
0.12
0.025
0.012
0.005
0.001
0.001
0.000
0.000
zeroTable 7
The critical parameters (critical temperature and critical pressure) of C6.
Sample
Critical temperature, °C
Critical pressure, MPa
Gas1
235.95
2.934
YP9
242.45
2.889
Gas2
255.65
2.776
Gas3
268.95
2.740P-T diagrams and critical points of different CO2 content natural gases in the gas-liquid two-phase region were drawn using (1) to (7); the calculated results are shown in Figures 13 and 14. And P-T diagrams and critical points of pure methane and pure CO2 in Figures 13 and 14 refer to the experimental data from the literature [33, 34]. In Figure 13, the vapor-liquid critical locus exits in the pure CH4 critical point extending continuously toward the CO2 critical point [35]. Three-phase loci originating from triple-point of pure CO2 ends in the triple-point of CH4 [35]. Here, we only consider the gas-liquid two-phase region, because it is found in the process of calculation that the model proposed in this study is only applied to calculate the gas-liquid phase equilibrium, while it is not applied to calculate the gas-solid, liquid-solid, and gas-liquid-solid phase equilibrium. We can draw the conclusion from Figures 13 and 14 that as CO2 content in natural gas increases, the two-phase envelope moves right and two-phase region becomes narrower. And critical point of natural gas moves to upper right (reaching a maximum), and finally it moves to lower right. The maximum critical pressure is 8.49 MPa when CO2 is about 55.535 mol%. The closer the distribution ratio of CH4 and CO2, the larger the two-phase region. Furthermore, comparing the contents of CH4 and CO2, as one component becomes more predominant, the P-T diagram tends to approach the vapor pressure curve (P-T diagram of one component) of the major component. The critical pressure of natural gas with high CO2 content increases with increasing CO2 content in natural gas when CO2 content in natural gas is below 55.535 mol%, while the critical pressure of high CO2 content natural gas decreases with increasing CO2 content in natural gas when CO2 content in natural gas is above 55.523 mol%. But the critical temperature constantly increases with increasing CO2 content in natural gas.Figure 13
CalculatedP-T phase diagrams and measured saturation pressure of natural gas with different CO2 contents.Figure 14
Variation curve of the critical points of natural gas with different CO2 contents.


### 4.3. Phase Transition Observation Experiment

It can be seen from Section4.2 that the critical temperature increases with increasing CO2 content in natural gas. And in order to facilitate reducing the temperature, we chose the gas sample with CO2 content of 75.323 mol% as the research object. The result of phase transition observation experiment is shown in Figures 15 and 16. We can draw the conclusion that phase transition of gas sample with CO2 content of 75.323 mol% does not take place as pressure decreases from 42.34 MPa to 5 MPa at 35°C isothermal conditions, while phase transition of gas sample with CO2 content of 75.323 mol% takes place as pressure decreases from 42.34 MPa to 5 MPa at −10°C isothermal conditions. The phase transition process is shown in the red dotted line part in Figure 16. The state of natural gas changes from the original transparent state into the mist. The testing results of phase transition observation experiment consist with the calculation results and testing results in Section 4.2 and, for the four gas samples, no phase transitions will take place at temperatures greater than 35°C. It also suggests that phase transition does not also take place at 75°C isothermal conditions and at 125°C isothermal conditions. It is illustrated that in the four gas samples no gas-liquid phase transition happens from bottom hole to well head.Figure 15
Phase transition of high CO2 content natural gas samples (75.323 mol%) in the process of pressure drawdown at 35°C.Figure 16
Phase transition of high CO2 content natural gas sample (75.323 mol%) in the process of pressure drawdown at −10°C.


## 4.1. Two-Flash and CCE Experiments

The results of two-flash experiments are listed in Table3. Formation volumes (under the formation conditions) and ground volumes (under the standard conditions) are the experimental measurements, and density, molecular weight, formation volume factor, and Z-factor are calculated by using gas state equation. The gas state equation is expressed as follows [27].Table 3
Results from two-flash experiments for different CO2 contents in natural gas.
Parameters
Gas1
YP9
Gas2
Gas3
Formation volume/Vt (cm3)
2.97
3.951
3.762
6.676
Ground volume/Vsc (cm3)
850
1135
1155
2160
Formation volume factor/Bgt
0.003496
0.003481
0.003257
0.003091
Z-factor/Zt
1.0702
1.0663
0.9885
0.9295
Gas density/ρt (kg/m3)
230.00
268.51
398.75
494.13
(under the formation conditions)
Molecular weight/M (g/mol)
19.85
22.49
30.55
35.92
Relative density/γg
0.6853
0.7763
1.0545
1.2398Under the formation conditions one has(8)PtVt=nRZtTt.Under the standard conditions one has(9)PscVsc=nRZscTsc.P
t is the formation pressure; Vt is the gas volume under the formation conditions; Zt is the deviation factor under the formation conditions; Tt is the formation temperature; n is the number of moles; R is the gas general constant, 8.3147 MPa·cm3·mol−1·K−1; Psc is the atmospheric pressure, and it is usually approximately equal to 0.101325 MPa; Vsc is the gas volume under the standard conditions; Zsc is the deviation factor under the standard conditions, and it is usually approximately equal to 1; Tsc is the standard temperature, and it is usually approximately equal to 20°C.Relative densities are calculated by using the following [27]:(10)γg=MMair.M is the gas molecular weight; Mair is the air molecular weight, and it is usually approximately equal to 28.97 g/mol.We can draw the conclusion from Table3 that the density, molecular weight, and relative density increase with increasing CO2 content in natural gas, while the formation volume factor and Z-factor decrease with increasing CO2 content in natural gas.CCE experiment was performed to draw the relative volume,Z-factor, formation volume factor, and density under the grading pressure. And the results are shown from Figures 5–12.Figure 5
Variation of the relative volume of YP9 gas sample with pressure under different temperatures.Figure 6
Variation of the formation volume factor of YP9 gas sample with pressure under different temperatures.Figure 7
Variation of the gas density of YP9 gas sample with pressure under different temperatures.Figure 8
Variation of theZ-factor of YP9 gas sample with pressure under different temperatures.Figure 9
Variation of the relative volume of different CO2 content natural gas samples with pressure at 127.5°C.Figure 10
Variation of the volume factor of different CO2 content natural gas samples with pressure at 127.5°C.Figure 11
Variation of the gas density of different CO2 content natural gas samples with pressure at 127.5°C.Figure 12
Variation of theZ-factor of different CO2 content natural gas samples with pressure at 127.5°C.


### 4.1.1. Effect of Temperature

The effect of temperature on the physical properties of YP9 gas sample was, respectively, tested under the formation temperature (127.5°C), the temperature in the well (75°C), and the ground temperature (35°C). It can be seen from Figures5–7 that the relative volume and formation volume factor of high CO2 content natural gases increase with increasing temperature under constant pressure, while the density of gas decreases with increasing temperature under constant pressure. And the relative volume and formation volume factor of high CO2 content natural gases decrease with increasing pressure at isothermal conditions. The effects of temperature and pressure on the experimental Z-factors for YP9 gas sample are shown in Figure 8. It can be seen clearly form Figure 8 that Z-factor decreases with increasing pressure at lower pressure range, that is, less than 18 MPa, while it increases with increasing pressure at higher pressures, that is, higher than 18 MPa. And the Z-factor decreases with decreasing temperature and a greater decrease can be observed in a pressure range from about 15 MPa to 22 MPa [32].


### 4.1.2. Effect of CO2 Content

Experimental relative volumes, formation volume factors, and densities of different CO2 content natural gases are shown from Figures 9–11. It can be seen clearly from Figures 9–11 that relative volume and formation volume factor decrease with increasing CO2 content in natural gas at 127.5°C isothermal and constant pressure conditions, but they do not change insignificantly. The effects of CO2 content in natural gas on the experimental Z-factors of different CO2 content natural gases are shown in Figure 12. It can be seen from Figure 12 that Z-factor decreases with increasing CO2 content in natural gas at 127.5°C isothermal and constant pressure conditions. And the dependence of the pressure follows the same trends as mentioned in Figure 5.


## 4.1.1. Effect of Temperature

The effect of temperature on the physical properties of YP9 gas sample was, respectively, tested under the formation temperature (127.5°C), the temperature in the well (75°C), and the ground temperature (35°C). It can be seen from Figures5–7 that the relative volume and formation volume factor of high CO2 content natural gases increase with increasing temperature under constant pressure, while the density of gas decreases with increasing temperature under constant pressure. And the relative volume and formation volume factor of high CO2 content natural gases decrease with increasing pressure at isothermal conditions. The effects of temperature and pressure on the experimental Z-factors for YP9 gas sample are shown in Figure 8. It can be seen clearly form Figure 8 that Z-factor decreases with increasing pressure at lower pressure range, that is, less than 18 MPa, while it increases with increasing pressure at higher pressures, that is, higher than 18 MPa. And the Z-factor decreases with decreasing temperature and a greater decrease can be observed in a pressure range from about 15 MPa to 22 MPa [32].


## 4.1.2. Effect of CO2 Content

Experimental relative volumes, formation volume factors, and densities of different CO2 content natural gases are shown from Figures 9–11. It can be seen clearly from Figures 9–11 that relative volume and formation volume factor decrease with increasing CO2 content in natural gas at 127.5°C isothermal and constant pressure conditions, but they do not change insignificantly. The effects of CO2 content in natural gas on the experimental Z-factors of different CO2 content natural gases are shown in Figure 12. It can be seen from Figure 12 that Z-factor decreases with increasing CO2 content in natural gas at 127.5°C isothermal and constant pressure conditions. And the dependence of the pressure follows the same trends as mentioned in Figure 5.


## 4.2. Effect of CO2 Content on P-T Diagram

In order to test and draw theP-T phase diagram of the high CO2 content natural gas, we have tested saturation pressures of the high CO2 content natural gases at different temperatures (−60°C, −50°C, −40°C, −30°C, −20°C, −10°C, and 0°C) based on the above CCE experimental test methods. The test results are shown in Table 4. At the same time, saturation pressures at the corresponding conditions are calculated by using (1) to (7), and the tested saturation pressures are fitted by adjusting critical parameters (critical temperature and critical pressure) of C6 on the basis of the fixed binary interaction coefficients in the process of calculation; the calculated results are also shown in Table 4. C6 has several isomers; the critical parameters are not fixed, so we choose the critical parameters of C6 as adjustable parameters to fit the saturation pressure of different CO2 content natural gases. The fixed binary interaction coefficients are given in Table 6 and the critical parameters (critical temperatures and critical pressures) of C6 are given in Table 7. It can be seen from  Table 7 that the higher the CO2 content, the higher the critical temperature, the lower the critical pressure, and the heavier the system (different CO2 content natural gas). And we compare the saturation pressure calculated by using the model proposed in this paper with the experimental measured saturation pressure; the deviations between the saturation pressure calculated by using the model proposed in this paper and experimental measured saturation pressure are shown in Table 5. The absolute relative error (11) and the average absolute relative error (12) are used to express the deviation between the saturation pressure calculated by using the model proposed in this paper and the experimental measured saturation pressure. We can draw the conclusion from Table 5 that the temperatures are colder, the absolute relative error is greater, and the higher the CO2 content in natural gas, the greater the absolute relative error. The average relative errors of Gas1, YP9, Gas2, and Gas3 are 1.62%, 2.03%, 3.29%, and 3.38%, respectively. Overall, the deviations between the saturation pressure calculated by using the model proposed in this paper and experimental measured saturation pressure are very small; the average relative error of all the gas samples is 2.86%. So it shows that the model can be used to predict the P-T phase diagram of the high CO2 content natural gas. Consider(11)ARE (%)=∑i=1NCal-ExpExpi×100,(12)AARE (%)=1N∑i=1NCal-ExpExpi×100.Table 4
Saturation pressure calculated by using the model proposed in this paper and experimental measured saturation pressure.
Parameters
Gas1
YP9
Gas2
Gas3
Calculated value
Measured value
Calculated value
Measured value
Calculated value
Measured value
Calculated value
Measured value
(MPa)
(MPa)
(MPa)
(MPa)
(MPa)
(MPa)
(MPa)
(MPa)
Saturation pressure (−60°C)
6.21
6.05
6.28
6.11
4.88
4.62
/
/
Saturation pressure (−50°C)
6.75
6.68
7.05
6.92
5.69
5.51
3.99
3.75
Saturation pressure (−40°C)
6.08
6.01
6.88
6.98
6.48
6.66
4.68
4.45
Saturation pressure (−30°C)
/
/
/
/
7.32
7.15
5.42
5.65
Saturation pressure (−20°C)
/
/
/
/
8.13
8.45
6.23
6.35
Saturation pressure (−10°C)
/
/
/
/
8.48
8.65
7.08
6.95
Saturation pressure (0°C)
/
/
/
/
/
/
7.85
8.02
Note: “/” shows that no saturation pressure is measured and calculated.Table 5
The deviations between the saturation pressure calculated by using the model proposed in this paper and experimental measured saturation pressure.
Parameters
Gas1
Gas1
YP9
YP9
Gas2
Gas2
Gas3
Gas3
Total
ARE, %
AARE, %
ARE, %
AARE, %
ARE/%
AARE/%
ARE/%
AARE/%
AARE/%
Saturation pressure (−60°C)
2.64
1.62
2.78
2.03
5.63
3.29
/
3.38
2.86
Saturation pressure (−50°C)
1.05
1.88
3.27
6.40
Saturation pressure (−40°C)
1.16
1.43
2.70
5.17
Saturation pressure (−30°C)
/
/
2.38
4.07
Saturation pressure (−20°C)
/
/
3.79
1.89
Saturation pressure (−10°C)
/
/
1.97
1.87
Saturation pressure (0°C)
/
/
/
2.12Table 6
Binary interaction parameters (kij) and mixing rules for the model proposed in this study.
Components
CO2
N2
C1
C2
C3
iC4
nC4
iC5
nC5
C6
CO2
0
−0.02
0.103
0.130
0.135
0.130
0.130
0.125
0.125
0.150
N2
−0.02
0
0.031
0.042
0.091
0.095
0.095
0.095
0.095
0.120
C1
0.103
0.031
0
0.003
0.009
0.016
0.015
0.021
0.021
0.025
C2
0.13
0.042
0.003
0
0.002
0.005
0.005
0.009
0.009
0.012
C3
0.135
0.091
0.009
0.002
0
0.001
0.001
0.003
0.003
0.005
iC4
0.13
0.095
0.016
0.005
0.001
0
0.000
0.000
0.000
0.001
nC4
0.13
0.095
0.015
0.005
0.001
0.000
0
0.001
0.001
0.001
iC5
0.125
0.095
0.021
0.009
0.003
0.000
0.001
0
0.000
0.000
nC5
0.125
0.095
0.021
0.009
0.003
0.000
0.001
0.000
0
0.000
C6
0.15
0.12
0.025
0.012
0.005
0.001
0.001
0.000
0.000
zeroTable 7
The critical parameters (critical temperature and critical pressure) of C6.
Sample
Critical temperature, °C
Critical pressure, MPa
Gas1
235.95
2.934
YP9
242.45
2.889
Gas2
255.65
2.776
Gas3
268.95
2.740P-T diagrams and critical points of different CO2 content natural gases in the gas-liquid two-phase region were drawn using (1) to (7); the calculated results are shown in Figures 13 and 14. And P-T diagrams and critical points of pure methane and pure CO2 in Figures 13 and 14 refer to the experimental data from the literature [33, 34]. In Figure 13, the vapor-liquid critical locus exits in the pure CH4 critical point extending continuously toward the CO2 critical point [35]. Three-phase loci originating from triple-point of pure CO2 ends in the triple-point of CH4 [35]. Here, we only consider the gas-liquid two-phase region, because it is found in the process of calculation that the model proposed in this study is only applied to calculate the gas-liquid phase equilibrium, while it is not applied to calculate the gas-solid, liquid-solid, and gas-liquid-solid phase equilibrium. We can draw the conclusion from Figures 13 and 14 that as CO2 content in natural gas increases, the two-phase envelope moves right and two-phase region becomes narrower. And critical point of natural gas moves to upper right (reaching a maximum), and finally it moves to lower right. The maximum critical pressure is 8.49 MPa when CO2 is about 55.535 mol%. The closer the distribution ratio of CH4 and CO2, the larger the two-phase region. Furthermore, comparing the contents of CH4 and CO2, as one component becomes more predominant, the P-T diagram tends to approach the vapor pressure curve (P-T diagram of one component) of the major component. The critical pressure of natural gas with high CO2 content increases with increasing CO2 content in natural gas when CO2 content in natural gas is below 55.535 mol%, while the critical pressure of high CO2 content natural gas decreases with increasing CO2 content in natural gas when CO2 content in natural gas is above 55.523 mol%. But the critical temperature constantly increases with increasing CO2 content in natural gas.Figure 13
CalculatedP-T phase diagrams and measured saturation pressure of natural gas with different CO2 contents.Figure 14
Variation curve of the critical points of natural gas with different CO2 contents.


## 4.3. Phase Transition Observation Experiment

It can be seen from Section4.2 that the critical temperature increases with increasing CO2 content in natural gas. And in order to facilitate reducing the temperature, we chose the gas sample with CO2 content of 75.323 mol% as the research object. The result of phase transition observation experiment is shown in Figures 15 and 16. We can draw the conclusion that phase transition of gas sample with CO2 content of 75.323 mol% does not take place as pressure decreases from 42.34 MPa to 5 MPa at 35°C isothermal conditions, while phase transition of gas sample with CO2 content of 75.323 mol% takes place as pressure decreases from 42.34 MPa to 5 MPa at −10°C isothermal conditions. The phase transition process is shown in the red dotted line part in Figure 16. The state of natural gas changes from the original transparent state into the mist. The testing results of phase transition observation experiment consist with the calculation results and testing results in Section 4.2 and, for the four gas samples, no phase transitions will take place at temperatures greater than 35°C. It also suggests that phase transition does not also take place at 75°C isothermal conditions and at 125°C isothermal conditions. It is illustrated that in the four gas samples no gas-liquid phase transition happens from bottom hole to well head.Figure 15
Phase transition of high CO2 content natural gas samples (75.323 mol%) in the process of pressure drawdown at 35°C.Figure 16
Phase transition of high CO2 content natural gas sample (75.323 mol%) in the process of pressure drawdown at −10°C.


## 5. Conclusions

Conclusions are as follows:(1)
For the four high CO2 content gas samples, no phase transitions will take place at temperatures greater than 35°C. It is illustrated that in the four gas samples no gas-liquid phase transition happens from bottom hole to well head.(2)
Relative volume and formation volume factor of four gas samples in this paper decrease with increasing pressure at isothermal conditions, while densities of four gas samples increase with increasing pressure at isothermal conditions. At isothermal conditionsZ-factors of four gas samples decrease with increasing pressure at lower pressure range, that is, less than 18 MPa, while they increase with increasing pressure at higher pressure range, that is, higher than 18 MPa.(3)
Relative volumes, formation volume factors, andZ-factors of four gas samples increase with increasing temperature at constant pressure conditions, while densities of four gas samples decrease with increasing temperature at constant pressure.(4)
Formation volume factors andZ-factors of four gas samples decrease with increasing CO2 content in natural gas at isothermal and constant pressure conditions, but relative volumes and volume factors do not change insignificantly. And densities of four gas samples increase with increasing CO2 content in natural gas at isothermal and constant pressure conditions.(5)
The deviations between the saturation pressure calculated by using the model proposed in this paper and experimental measured saturation pressure are very small; the average relative error is only 2.86%. Thus, the model can be used to predict the saturation pressure of high CO2 content natural gas.(6)
In the gas-liquid two-phase region, as CO2 content in natural gas increases, the two-phase envelope moves right and two-phase region becomes narrower. And critical point of natural gas proposed in this paper moves to upper right (reaching a maximum) and then moves to lower right. The maximum critical pressure is 8.49 MPa when CO2 content is about 55.535 mol%.



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*Source: 873718-2015-04-19.xml*