Research Article  Open Access
Phase Behavior and Physical Parameters of Natural Gas Mixture with
Abstract
The twoflash experiment, constant composition expansion experiment, saturation pressure measurement experiment, and phase transition observation experiment from well bottom hole to well head of four high CO_{2} content natural gas samples were carried out by using the JEFRIPVT apparatus made from DBR Company of Canada. The experimental results show that in the four high CO_{2} content gas samples no phase transitions will take place at temperatures greater than 35°C. In the gasliquid twophase region, saturation pressures, critical pressure, critical temperature, and an integrated PT phase diagram of different CO_{2} 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 CO_{2} content natural gas.
1. Introduction
With the increasing demand of CO_{2} resource, exploration and development of high CO_{2} content gas reservoirs are becoming one part of the future oilgas strategy [1]. Currently, the discovered high CO_{2} 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]. Twentyeight high CO_{2} content gas reservoirs have been discovered in China and they are mainly distributed in oilbearing basins in the east of China, in which the high CO_{2} content natural gas reserve is 20000 × 10^{8} m^{3} in Songliao basin [6]. Furthermore, CO_{2} 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 CO_{2} 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 CO_{2} contents in natural gas [7, 9–14], but seldom focus is directed on the phase behavior of natural gases with high CO_{2} content and the phase behavior of natural gas with high CO_{2} 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 CO_{2} content take place from formation to well head and the physical parameters of high CO_{2} content natural gases for highefficient developing the gas reservoirs with high CO_{2} content.
It is revealed in this paper whether any phase transition in high CO_{2} content natural gases takes place in the exploitation process. The saturation pressures of different CO_{2} content in natural gases at different temperatures are measured by using the DBRPVT apparatus, and the saturation pressures, critical pressures, critical temperatures, and an integrated  phase diagram of different CO_{2} content natural gases are calculated by using the modified PR equation of state and modified 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 CO_{2} content in natural gases on the  phase diagrams and critical points. Furthermore, the variation law and affecting factors of the physical parameters, such as relative volume, factor, formation volume factor, and density of high CO_{2} 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, PengRobinson EOS has been widely used to estimate thermodynamic properties for hydrocarbon systems. It reads [20, 21] aswhere is pressure, is temperature, is the molar volume, is the gas constant, and and are the parameters of the EOS. At constant and , the equation will take the form of a cubic equation in and can be solved for using any standard analytical or numerical technique [22]. The limitations on critical point lead to the following relations for the PREOS parameters [20]:where subscript indicates critical property and is temperature dependent. In this work, we use the new function proposed by Saffari, which is written as [23]
The new functions proposed are exponential functions, each with three adjustable parameters , , and . Since the adjustable parameters determine attractive intermolecular interactions in a pure component system, the values of are compoundspecific 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 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 new function proposed in this work (3) to develop generalized equations in terms of the acentric factor . 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 function proposed by Saffari have been fitted to experimental vapor pressure data, given in Table 1.

And then, the parameters , , and are generalized as a function of acentric factor . 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 squared.
Consequently, the final form of new function with the generalized parameters for natural gas components can be written as
Extending PREOS to mixtures requires replacement of coefficients and by the following van der Waals compositiondependent mixing rules [20]:
The unlikeinteraction parameter, , formed between component and component , can be related to the pure components parameter with an extra fitting coefficient () known as the coupling parameter:
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/T64342000 [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 HP6890 gas chromatography and Shimadzu GC14A 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 CO_{2} in YP9 well, Gas1, Gas2, and Gas3 are, respectively, 21.746 mol%, 10.045 mol%, 55.535 mol%, and 75.323 mol%. The CO_{2} content in natural gas being more than 10 mol% is usually called the high CO_{2} content natural gas [30]. Thus, The four groups of gas samples are all the high CO_{2} content gas samples.
 
Note: gas sample with CO_{2} content of 10.045 mol% is made from YP9 and dry natural gas, and gas sample with CO_{2} 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 mercuryfree high pressure PVT system made by the DBR Company, Canada. A schematic diagram of the corresponding apparatus is given in Figure 4. 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.
The volume of fluid in the PVT cell can be calculated by the internal crosssectional 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 cm^{3}.
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 cm^{3}.
Automatic pump: rated operation pressure is 100 MPa with resolution of 1 Psi, and the range of operation pump volume is 500 cm^{3} with resolution of 0.001 cm^{3}.
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 CO_{2} 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)Twoflash 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) or  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 was repeated at 35°C, 75°C, and 127.5°C, respectively.  relationship experiment was tested at least three times under each temperature and the average value was calculated.(9)Twoflash experiments and CCE experiments were also performed on the other three gas samples by repeating step to step .(10)The gas sample with the highest content of CO_{2} (75.323 mol%) was introduced into the PVT vessel to study whether phase transition in high CO_{2} 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. TwoFlash and CCE Experiments
The results of twoflash experiments are listed in Table 3. 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 factor are calculated by using gas state equation. The gas state equation is expressed as follows [27].

Under the formation conditions one has
Under the standard conditions one has
is the formation pressure; is the gas volume under the formation conditions; is the deviation factor under the formation conditions; is the formation temperature; is the number of moles; is the gas general constant, 8.3147 MPa·cm^{3}·mol^{−1}·K^{−1}; is the atmospheric pressure, and it is usually approximately equal to 0.101325 MPa; is the gas volume under the standard conditions; is the deviation factor under the standard conditions, and it is usually approximately equal to 1; is the standard temperature, and it is usually approximately equal to 20°C.
Relative densities are calculated by using the following [27]:
is the gas molecular weight; is the air molecular weight, and it is usually approximately equal to 28.97 g/mol.
We can draw the conclusion from Table 3 that the density, molecular weight, and relative density increase with increasing CO_{2} content in natural gas, while the formation volume factor and factor decrease with increasing CO_{2} content in natural gas.
CCE experiment was performed to draw the relative volume, factor, formation volume factor, and density under the grading pressure. And the results are shown from Figures 5–12.
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 Figures 5–7 that the relative volume and formation volume factor of high CO_{2} 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 CO_{2} content natural gases decrease with increasing pressure at isothermal conditions. The effects of temperature and pressure on the experimental factors for YP9 gas sample are shown in Figure 8. It can be seen clearly form Figure 8 that 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 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 CO_{2} Content
Experimental relative volumes, formation volume factors, and densities of different CO_{2} 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 CO_{2} content in natural gas at 127.5°C isothermal and constant pressure conditions, but they do not change insignificantly. The effects of CO_{2} content in natural gas on the experimental factors of different CO_{2} content natural gases are shown in Figure 12. It can be seen from Figure 12 that factor decreases with increasing CO_{2} 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 CO_{2} Content on  Diagram
In order to test and draw the  phase diagram of the high CO_{2} content natural gas, we have tested saturation pressures of the high CO_{2} 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 C_{6} on the basis of the fixed binary interaction coefficients in the process of calculation; the calculated results are also shown in Table 4. C_{6} has several isomers; the critical parameters are not fixed, so we choose the critical parameters of C_{6} as adjustable parameters to fit the saturation pressure of different CO_{2} content natural gases. The fixed binary interaction coefficients are given in Table 6 and the critical parameters (critical temperatures and critical pressures) of C_{6} are given in Table 7. It can be seen from Table 7 that the higher the CO_{2} content, the higher the critical temperature, the lower the critical pressure, and the heavier the system (different CO_{2} 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 CO_{2} 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  phase diagram of the high CO_{2} content natural gas. Consider
 
Note: “/” shows that no saturation pressure is measured and calculated. 



 diagrams and critical points of different CO_{2} content natural gases in the gasliquid twophase region were drawn using (1) to (7); the calculated results are shown in Figures 13 and 14. And  diagrams and critical points of pure methane and pure CO_{2} in Figures 13 and 14 refer to the experimental data from the literature [33, 34]. In Figure 13, the vaporliquid critical locus exits in the pure CH_{4} critical point extending continuously toward the CO_{2} critical point [35]. Threephase loci originating from triplepoint of pure CO_{2} ends in the triplepoint of CH_{4} [35]. Here, we only consider the gasliquid twophase region, because it is found in the process of calculation that the model proposed in this study is only applied to calculate the gasliquid phase equilibrium, while it is not applied to calculate the gassolid, liquidsolid, and gasliquidsolid phase equilibrium. We can draw the conclusion from Figures 13 and 14 that as CO_{2} content in natural gas increases, the twophase envelope moves right and twophase 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 CO_{2} is about 55.535 mol%. The closer the distribution ratio of CH_{4} and CO_{2}, the larger the twophase region. Furthermore, comparing the contents of CH_{4} and CO_{2}, as one component becomes more predominant, the  diagram tends to approach the vapor pressure curve ( diagram of one component) of the major component. The critical pressure of natural gas with high CO_{2} content increases with increasing CO_{2} content in natural gas when CO_{2} content in natural gas is below 55.535 mol%, while the critical pressure of high CO_{2} content natural gas decreases with increasing CO_{2} content in natural gas when CO_{2} content in natural gas is above 55.523 mol%. But the critical temperature constantly increases with increasing CO_{2} content in natural gas.
4.3. Phase Transition Observation Experiment
It can be seen from Section 4.2 that the critical temperature increases with increasing CO_{2} content in natural gas. And in order to facilitate reducing the temperature, we chose the gas sample with CO_{2} 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 CO_{2} 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 CO_{2} 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 gasliquid phase transition happens from bottom hole to well head.
5. Conclusions
Conclusions are as follows:(1)For the four high CO_{2} 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 gasliquid 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 conditions 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, and 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 and factors of four gas samples decrease with increasing CO_{2} 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 CO_{2} 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 CO_{2} content natural gas.(6)In the gasliquid twophase region, as CO_{2} content in natural gas increases, the twophase envelope moves right and twophase 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 CO_{2} content is about 55.535 mol%.
Conflict of Interests
Here, all the authors solemnly declare that there is no conflict of interests regarding the publication of this paper.
Acknowledgments
The authors wish to acknowledge anonymous reviewers for constructive comments and suggestions for improving this paper. The authors also wish to thank the anonymous Associate Editor for his handling of the paper and additional suggestions. This work was supported by National Science and Technology Major Project of China (no. 2011ZX050160052) and a grant from the National Natural Science Foundation of China (no. 50604011).
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Copyright © 2015 Dali Hou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.