Study of phase and physical property changes during gas lift injection of high CO2‐content associated gas in the offshore M oil field

The gas lift in the offshore M field will be performed with high CO2‐content associated gas, but the change of wellbore temperature and pressure during the injection process will lead to the change of phase and physical parameters of associated gas, which has a great impact on the design of gas lift. To ensure the smooth implementation of gas lift in the offshore M field, this paper conducts a study on the physical parameters of associated gas considering the change of CO2 phase state. We obtained the density, viscosity, compression factor, constant pressure specific heat capacity, thermal conductivity, and Joule Thomson coefficient at each temperature and pressure by Hysys calculation, and regression analysis to obtain the regression model of the physical parameters; finally, the regression model was compared with the flash experiment and Hysys calculation results. The results show that the CO2 phase change has a large influence on the physical parameters; R2 > 0.8, which indicates that the regression model has sufficient reliability; the results of the comparison show that the empirical formulas of all physical properties have sufficient accuracy and superiority except Joule–Thomson coefficients. In addition, the empirical formula of the Joule–Thomson coefficient also has good accuracy and superiority at the pressure not exceeding 22 MPa. The study of phase changes and physical parameters of associated gas with high CO2 content provides a basis for subsequent gas lift design in the offshore M field and multiphase flow calculations in the wellbore during the gas lift. Although this study is only applicable to this sample, it also provides a feasible research method for other samples.


| INTRODUCTION
Gas lift is the most commonly used artificial lift method, [1][2][3][4][5] which helps lift oil with nitrogen or natural gas from the well, [6][7][8] and has significant advantages for the extraction and development of oil fields rich in associated gas. It has a wide range of adaptability to the production of oil wells and is easy to operate and manage. [9][10][11] At present, gas lift gas is mainly nitrogen and natural gas. Only in 1994, the El Trapial oil field in central Argentina's Neuquen province, and in 2008, 12 the Xu Shen 5 well in China's Daqing oil field was implemented with CO 2 gas lift. 13 Although the two CO 2 gas lifts achieved some success, a large amount of CO 2 gas injected into the wellbore dissolved in oil and water to carbonate the oil and water, which has large corrosion on the oil casing, and the corrosion of the gas and water surface is more serious, resulting in high maintenance costs later, so it is not promoted. 14 The offshore M oil field is planned to use the gas lift to recover oil. However, the CO 2 content of the selfproduced gas in the block is as high as 36.68% and will continue to increase as the wells produce, reaching 57.67% CO 2 by 2040. Despite the high CO 2 content of the self-produced gas, the cost of gas transportation in the offshore field is high, and the decision was made to use high CO 2 -content gas as the source of gas lift, taking into account the economic and anticorrosion situation.
Phase changes occur with wellbore temperature and pressure changes during gas lift injection of high CO 2content gas, and the phase changes will lead to changes in the physical parameters of the injected gas. 15 In gas lift design, calculation of the pressure profile is critical for designing the gas injection volume, injection point, and production. 16 Changes in the physical parameters of high CO 2 -content gas can cause changes in the wellbore pressure profile, making gas lift design difficult. Therefore, it is necessary to investigate the variation pattern of the physical parameters of high CO 2 -content gas considering the phase change.
The study of gas phase characteristics in oil and gas fields began in the 1940s with the study of hightemperature and high-pressure physical parameters of natural gas. [17][18][19][20] Nowadays, with the rapid development of the natural gas industry, gas phase characteristics have become one of the hot topics for research. 21,22 At present, the research on gas phase characteristics is mainly divided into the experimental method, 23 graphical plate method, 24 empirical formula method, 25 equation of state method, 26 and intelligent algorithm. 27 The experimental determination method has the advantages of higher accuracy and smaller error, but the experimental equipment is more demanding, time-consuming and costly. However, the workload of the experimental method to determine the physical parameters of gas mixtures considering phase changes is huge. For this reason, we consider the use of Hysys to calculate the physical parameters of the gas mixture combined with the experimental method of verification. 28,29 Hysys provides a powerful physical properties calculation package, which is based on data from the worldrenowned physical properties data system, and is useful in cases where measured physical properties are not available. 30 A key problem is the selection of Hysys calculation model. Considering the quantitative relationship of components in the gas and liquid phases when the phase state changes, it depends on the equation of state, gas-liquid equilibrium equation, and equilibrium condensation equation. Therefore, the physical parameters of mixed gas can be calculated through the coupling of these three groups of equations.
In this paper, the physical parameters (deviation factor, viscosity, density, constant pressure specific heat capacity, thermal conductivity, and Joule-Thomson coefficient) of high CO 2 -content gas were calculated by using Hysys software with the gas mixture state equation, gas-liquid phase equilibrium equation and equilibrium condensation equation as the calculation models, analyzing the variation law of physical parameters under phase change, and obtaining the empirical model of physical parameters by regression analysis. Finally, the reliability and superiority of the empirical formula is verified by comparing the deviation factors with the empirical model under some temperature and pressure conditions obtained from flash tests and the calculation results of Hysys with the empirical formula in a larger pressure range. It provides a theoretical basis for the subsequent gas lift design and the calculation of multiphase flow in the wellbore during the gas lift process in the offshore M oilfield, and is of obvious value for the practical application in the production of the offshore M oilfield. There are many equations to calculate the state of a gas, but the equation of state of the cubic type is still commonly used. 31 The Peng-Robinson (PR) equation, 32 which can calculate the phase equilibrium and volumetric properties of the mixed system, is chosen, and its equation is as follows: In the above equation: where T ri = T/T c is the contrast pressure, ω i is the eccentricity factor of component i or monomeric gas I, P ci is the critical pressure of component i or monomeric gas I, T ci is the critical temperature of component i or onomeric gas i. For multicomponent systems the following relationships exist. Equation:   The cubic equation for solving the deviation factor can be expressed by the following equation: In the above equation A m and B m can be expressed by Equation (11) and Equation (12), respectively.
m m (12) 2. Gas-liquid phase equilibrium equation Gas-liquid equilibrium calculations are based on the concept of phase equilibrium. The coexistence of more than two phases is considered to reach phase equilibrium if there is no transfer of any substance between the phases on a macroscopic scale for a long time. Under certain temperature and pressure conditions, the composition of the two phases of a system in gas-liquid equilibrium is constant. When the pressure or temperature in the system changes, the original phase equilibrium is disrupted, and the system will reach a new equilibrium state under this new pressure or temperature, and then the two-phase composition has its new value. Therefore, a specific gas-liquid equilibrium system can be quantitatively described by pressure, temperature, and composition of the system substances.
In a system in gas-liquid two-phase equilibrium, the ratio of the molar fraction of a component in the gas and liquid phases is called the phase equilibrium constant of the component, expressed as K i , that is, where K i is the phase equilibrium constants for component i, x i is the Molar fraction of component i in the liquid phase, y i is the Molar fraction of component i in the gas phase. It can be seen that the phase equilibrium constant is not a constant, it varies with the pressure, temperature, and composition of the system. Thermodynamically, to determine whether the gas and liquid phases in the system are in equilibrium, in addition to the pressure and temperature of the gas phase being equal to the pressure and temperature of the liquid phase, there is another important criterion: in the gas and liquid equilibrium system at the same pressure and temperature, the degree of escape of each component in the gas and liquid phases must be equal. 33,34 where f iV , f iL are the fugacity of component i in the gas phase and liquid phase, respectively. The above equation shows that phase equilibrium can be reached only when the fugacity of component I is equal in both gas and liquid phases. Therefore, to determine whether a system has reached phase equilibrium, the above two defining equations can be used.
The fugacity of component I in the gas phase is equal to the product of the fugacity of pure component (monomer) i in the gas phase and the molar fraction of component i in the gas phase at the same pressure and temperature; the fugacity of component i in the liquid phase is equal to the product of the fugacity of pure component (monomer) i in the liquid phase and the molar fraction of component i in the liquid phase at the same pressure and temperature.
where f iV 0 is the fugacity of the pure component i in the gas phase at the system equilibrium pressure and temperature, f iL 0 is the fugacity of pure component i in the liquid phase at the equilibrium pressure, and temperature of the system, y i , x i is the Molar fraction of component i in the gas and liquid phases. Thus, from the phase equilibrium criterion (14) Equation (17) can be obtained.
Up to this point, the phase equilibrium constant can be expressed in terms of fugacity.
where P is the balancing system pressure,  = In the equation: (20) In the actual calculation, the deviation factor of the mixture is first found using the selected equation of state, and then the fugacity equation is used to find the gas and liquid phase fugacity of each component, and finally, the phase equilibrium constant of each component at equilibrium is obtained.

Equilibrium condensation equation
The process by which the gas mixture is cooled to a certain pressure and temperature and reaches gas-liquid equilibrium is called equilibrium condensation. 35 The proportion of the liquid phase formed by condensation to the raw material feed F is called the condensation rate or liquefaction rate. There is this relationship between them.
where F is the total traffic, kmol/h, L is the flow rate of liquid phase products, kmol/h, V is the flow rate of gas phase products, kmol/h, e is the condensation rate or liquefaction rate. The material balance is followed between the feed of raw gas and the output of the liquid and gas phases, as shown in Figure 1.
For any component i, the relationship that exists for the equilibrium condensation process is shown in Equation (23) F I G U R E 1 Schematic diagram of equilibrium gasification or condensation where z i , x i , y i are the molar fractions of component i in the feed, liquid phase, and gas phase, respectively. If F = 1 kmol/h, then the above equation can be written as Equation (24).
At condenser pressure and temperature, if the gas and liquid phases reach phase equilibrium, the result obtained by substituting y Kx = i i into Equation (23) according to the phase destruction criterion is shown in Equation (25) x When the gas and liquid phases reach equilibrium, Referring to the schematic diagram of equilibrium condensation in Figure 1, the known conditions for equilibrium condensation calculation are the mass flow F of feed, the molar composition Zi of feed mixture, the pressure P, and temperature T for condensation calculation. The quantities to be solved are the phase equilibrium constant K i of each component, the molar composition y i and x i of the gas-liquid phase of each component, and the flow L and V of gas-liquid products under the condensation pressure and temperature.
The calculation is performed using either of the equilibrium condensation Equations (20) and (22), as in Equation (20), and expressed in functional form.
Solving Equation (23) can be done by Newton's iterative method.
The calculation process is as follows: 1. Assign initial values to K i For a given condensing pressure and temperature (i.e., K i ), the initial value of the equilibrium constant can be obtained from the following empirical Willson equation. (31) where ω i is the eccentricity factor of component I, T ri is the comparison temperature for the given conditions, P ri is the comparative pressure under the given conditions. 2. If the gas-liquid phase is in equilibrium, there must be a liquefaction rate e (0 < e < 1) such that f(e) = 0. Therefore, assuming an initial value of e, this e value is obtained from Equation (29); 3. Substitute the e value back into Equation (23) or (24) to obtain the composition of the liquid and gas phases x i , y i ; 4. From the density equation, the deviation factors Z V , Z L (or the densities ρ V , ρ L of the gas and liquid phases) are obtained for the gas and liquid phases; 5. Then calculate the fugacity coefficients φ iV and φ iL for the gas phase and liquid phase from Equation (17)  6. Check if the thermodynamic phase equilibrium conditions are met; 7. Finally, other physical parameters are calculated.
If the given schedule accuracy requirement is not met, a new phase balance condition is calculated.
Repeat Steps 2-6 until the phase equilibrium condition is satisfied. Figure 2 shows the calculation process.

| Flash evaporation experiment
The experimental equipment is a PVT analyzer ( Figure 3A), which mainly includes a PY-2 high-temperature and high-pressure dispenser, HSB-1 high-pressure displacement pump, PVT cylinder, flash separator, and gas meter. The experimental gas components were provided by M oilfield and formulated by Sichuan Dingbiao Technology Co. The specific gas components are shown in Table 1.
The experimental process is as follows, and the flash evaporation experiment is shown in Figure 4.
1. Clean and dry the PVT cylinder, test the temperature and pressure of the instrument, and record the atmospheric temperature and pressure; 2. Prepare gas sample; 3. Transfer the gas sample to a PVT cylinder, and record the volume of the gas sample; 4. Adjust the temperature and pressure of the PVT cylinder to the target value, and record the volume of the gas sample after 1 h of stabilization; The formula for the deviation factor is shown in Equation (35).
where Z f is the deviation factor under experimental temperature and pressure conditions, P f is the experimental pressure, T f is the experimental temperature, P m is the atmospheric pressure, T m is the room temperature, V 1 , V 2 , V m is the volumes of the gas before and after flashing under experimental conditions and the volume of the gas at room temperature and pressure, respectively.
3 | RESULTS AND DISCUSSION

| Density
The surface of density variation with temperature and pressure and the variation of density with temperature for different pressure conditions are shown in Figure 5. It can be seen from the figure that the density surface extends smoothly with temperature and pressure, and the density decreases with the increase of temperature and increases with the increase of pressure. The regression model of density is shown in Equation (36), with R 2 = 0.997. The fitted surface is shown in Figure 6A, and the fitted surface is almost the same as the density change surface. Some temperatures and pressures were selected, and the corresponding densities were calculated using empirical formulas and compared with the Hysys results, which are shown in Figure 6B and Table 2. Figure 6B shows that the data of the empirical formula and Hysys are closer, and Table 2 shows that the errors of both are within 20%. The curves, scatter plots and relative errors show that the model is relatively accurate and can be applied to practical engineering calculations.

| Deviation factor
The surface of the deviation factor with temperature and pressure and the variation of the deviation factor with temperature for different pressure conditions are shown in Figure 7. From the figure, we can see that the deviation factor surface extends smoothly with temperature and pressure, and the deviation factor increases with the increase in temperature. When the temperature is lower than the critical temperature, and the pressure is lower than the critical pressure, the deviation factor decreases with the increase of pressure, and when the pressure is higher than the critical pressure, the deviation factor increases with the increase of pressure; when the temperature is higher than the critical temperature, the deviation factor decreases with the increase of pressure regardless of the relationship between the pressure and the critical pressure. This is due to the fact that below the critical pressure, both gas and liquid phases exist in the component, and above the critical pressure, only the liquid phase exists, and the pressure has the opposite trend on the gas-liquid deviation factor. As the temperature enters the critical temperature, the gas mixture changes from the liquid phase above the critical pressure to the supercritical state, which is close to the gas phase, and the trend of deviation factor changes with increasing pressure is reversed. The regression model for the deviation factor is shown in Equation 37, with R 2 = 0.995. The fitted surface is shown in Figure 8A, and the scatter plots of the calculated results with the Hysys data are shown in Figure 8B. Table 3 shows the comparison of the relative errors between the empirical formula and Hysys. The surface plots and scatter plots of Hysys, and the empirical formula almost overlap, and the relative errors between them are within 20%, which indicates that the model is more accurate.

| Viscosity
The surface of viscosity variation with temperature and pressure and the variation of viscosity with temperature for different pressure conditions are shown in Figure 9. From Figure 9A, it can be seen that the viscosity decreases in a certain temperature and pressure range in a "precipitous" manner. From Figure 9B, it can be seen that the viscosity increases with the increase of pressure and decreases with the increase of temperature, and there is an obvious inflection point in the curve of viscosity with temperature when it is higher than the critical pressure. This is mainly due to the opposite effect of temperature on the viscosity of the liquid and gas phases. When the temperature increases, the viscosity of the liquid phase decreases, while the viscosity of the gas phase increases. Below the critical pressure, the viscosity decreases and then increases with temperature due to the coexistence of gas and liquid, and the higher the pressure, the larger the volume share of the liquid phase, and the more obvious this trend. When the temperature is higher than the critical temperature, the nature of the supercritical state is close to the nature of the gas phase, and the transition from the pure liquid phase to the supercritical state leads to an inflection point of the curve and a "cliff" of the surface.
The regression model for viscosity is shown in Equation 38 with R 2 = 0.973, and the fitted surface is shown in Figure 10A. The fitted surface is shown in Figure 8A, and the scatter plots of the calculated results with the Hysys data are shown in Figure 10B. Table 4 shows the comparison of the relative errors between the empirical formula and Hysys. The empirical formulas almost overlap with Hysys' surface plots, the scatter plot trends are consistent, the data points are similar, and the relative error between them is within 20%, which indicates the high accuracy of the model.

| Constant pressure-specific heat capacity
The curves of constant pressure-specific heat capacity with temperature and pressure and the variation of constant pressure-specific heat capacity with temperature for different pressure conditions are shown in Figure 11. From Figure 11, it can be seen that the constant pressure-specific heat capacity surface extends smoothly with temperature and pressure, and the constant pressurespecific heat capacity decreases first with the increase of temperature and then increases. When the temperature is lower than the critical temperature and the pressure is lower than the critical pressure, the constant pressure specific heat capacity increases with the increase of pressure, and when the pressure is higher than the critical pressure, the constant pressure specific heat capacity decreases with the increase of pressure, when the temperature is higher than the critical temperature, regardless of the relationship between the pressure and the critical pressure, the constant pressure specific heat capacity increases with the increase of pressure. The reason is similar to the effect of temperature and pressure on the deviation factor, both due to the opposite trend of temperature and pressure on the gas-liquid influence and the nature of the transformation of the liquid phase into the supercritical state. The regression model of constant pressure-specific heat capacity is shown in Equation (39) with R 2 = 0.828, which satisfies the requirements of engineering analysis. The fitted surface is shown in Figure 12A, and the scatter plots of the calculated results with the Hysys data are shown in Figure 12B. Table 5 shows the comparison of the relative errors between the empirical formula and Hysys. The graphs show a slight difference between the Hysys and empirical formulations, but in most cases, their relative errors are within 20%. Relative errors greater than 20% are found in the temperature range of 60-100°C, which indicates that the

| Thermal conductivity
The surface of thermal conductivity with temperature and pressure and the variation of thermal conductivity with temperature for different pressure conditions are shown in Figure 13. Similar to viscosity, the thermal conductivity surface has an obvious "cliff" where the thermal conductivity increases with pressure and decreases and then increases with temperature, and there is an obvious inflection point in the viscosity versus temperature curve above the critical pressure, which is caused by the transformation of the liquid phase into a supercritical state.
The regression model of thermal conductivity is shown in Equation (40) with R 2 = 0.961. The fitted surface is shown in Figure 14A, and the scatter plots of the calculated results with the Hysys data are shown in Figure 14B. Table 6 shows the comparison of the relative errors between the empirical formula and Hysys. The surface plots and scatter plots of Hysys, and the empirical formula almost overlap, and the relative errors between them are within 20%, which indicates that the model is more accurate.

| Joule-Thomson coefficient
The surface of the Joule-Thomson coefficient with temperature and pressure and the variation of the Joule-Thomson coefficient with temperature for different pressure conditions are shown in Figure 15. From Figure 15, it can be seen that the Joule-Thomson coefficient surface extends smoothly with temperature and pressure and decreases with increasing pressure, and the Joule-Thomson coefficient changes from decreasing with increasing temperature to increasing first and then decreasing with increasing temperature as the pressure increases. This is due to the fact that as the pressure increases, the volume fraction of the liquid phase of the gas mixture increases and the temperature increases, the Joule-Thomson coefficient of the gas phase decreases while the Joule-Thomson coefficient of the liquid phase increases. The regression model of the Joule-Thomson coefficient is shown in Equation (41), and the R 2 = 0.901, which indicates that the model is more accurate. The fitted surface is shown in Figure 16A, and  Figure 16B. Table 7 shows the comparison of the relative errors between the empirical formula and Hysys. The results show that the empirical formula and the data plot of Hysys are similar, and the relative error shows that the error between them is generally within 20%, and the error is larger only at the temperature of 0°C and pressure of 10 MPa, which indicates that the empirical model has high accuracy and can be used for engineering applications.

| Verification of empirical formula
The deviation factors obtained by flashing experiments at different temperature and pressure conditions are compared with the results of Hysys calculations, which can reflect to a certain extent the credibility of Hysys in the calculation of all physical parameters. The comparison results are shown in Table 8.
As can be seen from Table 8, the experimental results of deviation factors in different temperature and pressure ranges are closer to the calculated results of Hysys, and the relative errors vary in the range of 0.52%-4.71%, indicating that the calculated results of Hysys have a high degree of confidence and can be used for subsequent analysis and design.

| Comparison of empirical formulae with the results of Hsysy calculations
To further investigate the reliability of the fitted empirical formulas, we compared the empirical formulas with the results calculated by Hysys in a larger pressure range. Hysys was calculated for temperatures from 30°C to 130°C and pressures of 22, 26, and 30 MPa in that order. Tables 9 and 10 and Figure 17 show the results of the comparison. From the tables, it can be seen that the relative errors of density, deviation factor, viscosity, constant pressure specific heat capacity, and thermal conductivity are less than 20%, and in most cases are less than 10%. This error satisfies the general engineering requirement of less than 20%, which shows the sufficient accuracy and superiority of these empirical formulas. In addition, we found that the relative error between the empirical formula of the Joule-Thomson coefficient and the calculated result of Hysys varies greatly with the rise of temperature and pressure, and the relative error is generally greater than 20% when the pressure is 24-30 MPa. Therefore, it can be considered that the empirical formula of Joule-Thomson is not applicable to the case of pressure greater than 22 MPa, while at pressure ≤22 MPa, an error of less than 20% indicates that the empirical formula still has sufficient reliability.

| CONCLUSION
In this study, the gas state equation, gas-liquid phase equilibrium equation, and equilibrium condensation equation were used as computational models, and the physical parameters of the gas mixture were obtained by Hysys calculations, and the following conclusions were obtained 1. The variation of the phase state of the gas mixture has a significant influence on the physical parameters, which is attributed to the variation of the gas-liquid composition and the different degrees of influence of temperature and pressure on the gas-liquid. 2. The computational models for each physical parameter were obtained using regression analysis. The R 2 of the model and the comparison with Hysys and experimental data show sufficient accuracy and superiority of the empirical formulations of the model except for the Joule-Thomson coefficient. In addition, the empirical formulations of Joule-Thomson coefficients also have good accuracy and superiority for pressures not exceeding 22 MPa. 3. By studying the change rule of physical parameters considering the phase state change of high CO 2content gas, provides a theoretical basis for the subsequent gas lift design and the calculation of multiphase flow in the wellbore during a gas lift in offshore M oilfield and has obvious value for the practical application of offshore M oilfield production. Although this study is only applicable to this sample, it also provides a research case for other samples.