Jun-Ling Wng , Zi-Ho Song , Lin-Jun Li , Li-Li Yng , Qun-Yun Wng ,I-Ming Chou , Zhi-Yn Pn ,*
a College of Environment, Zhejiang University of Technology, Hangzhou, Zhejiang, 310032, China
b Hangzhou Academy of Environmental Protection, Hangzhou, Zhejiang, 310032, China
c Laboratory for Experimental Study Under Deep-sea Extreme Conditions, Institute of Deep-sea Science and Engineering, Chinese Academy of Sciences,Sanya, Hainan, 572000, China
A B S T R A C T To determine the solubility of CO2 in n-dodecane at T = 303.15-353.15 K, P ≤11.00 MPa, an integrated fused silica capillary and in-situ Raman spectroscopy system was built. The Raman peak intensity ratio(ICO2/IC-H)between the upper band of CO2 Fermi diad(ICO2)and the C-H stretching band of n-dodecane(IC-H)was employed to determine the solubility of CO2 in n-dodecane based on the calibrated correlation equation between the known CO2 molality in n-dodecane and the ICO2/IC-H ratio with R2 = 0.9998. The results indicated that the solubility of CO2 decreased with increasing temperature and increased with increasing pressure. The maximum CO2 molality (30.7314 mol/kg) was obtained at 303.15 K and 7.00 MPa. Finally, a solubility prediction model (lnS = (P - A)/B) based on the relationship with temperature (T in K) and pressure (P in MPa) was developed, where S is CO2 molality, A = - 8× 10-6T2+0.0354T- 8.1605,and B=0.0405T - 10.756.The results indicated that the solubilities of CO2 derived from this model were in good agreement with the experimental data.
Keywords:CO2 solubility n-dodecane Raman spectroscopy Fused silica capillary In-situ
Recently,mitigating climate change by reducing greenhouse gas emissions has become a global focus,and the ability to reduce CO2emissions accordingly has become an urgent task. Carbon capture and storage(CCS)has been widely recognized as a viable method to mitigate carbon emissions (Cormos, 2012; Peng et al., 2013; You et al., 2014; Li et al., 2016; Sun et al., 2017). Among all the storage methods, CO2geological storage has a direct effect on emission reduction and is considered to be the most potential storage method(Leung et al.,2014).Geological storage sites include oil and gas fields, saline aquifers, and deep coal seams (Michael et al.,2010). Injection of CO2in oil and gas fields can not only achieve CO2emission reductions but also enhance oil recovery (EOR) (Liu et al., 2016). Currently, many countries have conducted field tests of CO2flooding in oil fields using mature CO2-EOR technology(Awan et al.,2008;Hill et al.,2013;Lacy et al.,2013;Lv et al.,2015).
The dissolution of CO2in oil can result in oil swelling and viscosity reduction, thereby enhancing oil recovery. CO2solubility data are one of the major parameters to determine the performance of CO2-EOR process (Mosavat et al., 2014). The solubility of CO2in crude or simulated oil (of which the primary components are alkanes) systems at different temperatures and pressures have been investigated previously.Chung et al.(1988)and Henni et al.(1996)employed gas chromatography to analyze the solubility of CO2in heavy oil at temperatures of 297,333 and 391 K and pressures of up to 34.5 MPa, and in n-dodecane at 313, 353, and 393 K and 0-9.6 MPa.Kavousi et al.(2014)studied CO2solubility in heavy oils with different viscosities using the pressure drop method at pressures of 1.73-4.48 MPa and temperatures of 295-305 K.
Previous methods for investigating the solubility of CO2in crude/simulated oil systems at high pressure conditions have been performed primarily with the PVT apparatus (Lay et al., 2006;Nourozieh et al.,2013),equilibrium liquid sampling analysis(Yang et al., 2013), and chromatography (Forte et al., 2011). Although these methods offer distinct advantages,there continue to be some shortcomings.For example,the temperature and pressure ranges of the entire system of the PVT apparatus are limited, and the equilibrium liquid sampling analysis easily changes the original temperature and pressure conditions during the sampling process and upsets the system balance. Analysis of CO2quantity at the equilibrium point is the key to determine the solubility of CO2in crude oil and simulated crude oil. The equilibrium points of these methods generally are judged according to the pressure or the bubble point. It takes plenty of time to reach phase equilibrium because of the higher viscosity of the crude or simulated oil,which leads to an inaccurate judgment of the equilibrium condition in subjective or experimental environments(Mosavat et al.,2014;Han et al., 2015; Gui et al., 2017). In addition, the temperatures and pressures investigated in previous studies frequently have been confined to narrow ranges. Raman spectroscopy is an effective optical analysis method that is noninvasive,sensitive,and fast.(Liu et al.,2012;Belgodere et al.,2015).Therefore,Raman spectroscopy has been used in numerous studies of solubility measurements(e.g., Caumon et al., 2017; Wang et al.,2018).
The change in Raman peak intensity(peak height or peak area)ratio between two species in a fluid reflects variations in their relative quantities. For example, Wang et al. (2019) and Guo et al.(2014) demonstrated that the ratio between the upper band of CO2Fermi diad and the O-H stretching band of water in homogenous solutions could be used to determine the solubility of CO2in water at various pressure-temperature conditions. Similarly, the ratio between the upper band of CO2Fermi diad and the C-H stretching band of n-dodecane enables quantification of CO2solubility in n-dodecane.
In this study,to determine the solubility of CO2in n-dodecane at temperatures of 303.15-335.50 K and pressures up to 11.0 MPa,an integrated fused silica capillary and in-situ Raman spectroscopy system was built (Pan et al., 2013a, 2013b; Wang et al., 2017a,2017b). n-dodecane, one of the primary components of crude oil,was used as a simulated oil in this experiment. The physical properties of n-dodecane (ρ = 753 kg/m3,μ = 1.36 cp at 298.15 K,and atmospheric pressure)are similar to those of light crude oil(Bei et al.,2018).The Raman spectra of the system with CO2dissolved in n-dodecane are presented in Fig.1. It shows that the main Raman peaks (2800-3000 cm-1) of n-dodecane do not coincide with the CO2Fermi diad upper band (1385 cm-1) and its minor peaks at
Fig.1. Raman spectra of CO2, n-dodecane, and fused silica capillary (FSC).
1250-1500 cm-1do not block the upper Fermi diad band of CO2at 1385 cm-1.Therefore,any influence of the peaks of the n-dodecane at 1250-1500 cm-1to the intensity of the upper Fermi diad band of CO2at 1385 cm-1can be ignored. In this study, the ratio between the upper band of CO2Fermi diad and the C-H stretching band of n-dodecane(ICO2/IC-H)was used to determine the CO2solubility in n-dodecane,based on the calibrated correlation equation between the known CO2molality in n-dodecane and theICO2/IC-Hratio.Finally, a CO2solubility model based on its relationship with temperature and pressure was developed.
Technologies, LLC (Phoenix, AZ, USA) with an outer diameter of 665 μm and inner diameter of 300 μm. All of the valves and highpressure stainless-steel tubes were purchased from the Nantong Huaxing Petroleum Instrument Co., Ltd. (Nantong,Jiangsu, China).
An experimental setup was built to measure the solubility of CO2in n-dodecane at 303.15-353.15 K and up to 11.00 MPa(Fig.2).The apparatus primarily consisted of a fused silica capillary (FSC) and the balance kettle observation window, combined with a heatingcooling stage (CAP500, Linkam Scientific Instruments, Tadworth,UK), a confocal Raman spectrometer (Horiba JobinYvon, HR800,HORIBA FRANCE,Palaiseau,France),a horizontal phase equilibrium kettle with a magnetic stirrer, a manual pressure pump (JY-80,Jiangsu,China),a 70.00 MPa pressure sensor,a magnetic circulating pump,and a quantitative pump(30.00 MPa full scale).A circulation line was formed by the FSC connected to a circulating pump and a phase equilibrium kettle with an electric heating jacket, which could adjust the temperature of the fluid in the kettle. Controlled the temperature within the FSC utilizing a heating-cooling stage in conjunction with a digital temperature controller (accurate to 0.1 K). The pressure of the phase equilibrium kettle was adjusted using a manual pressure pump connected to a pressure transducer(70.00 MPa full scale,accurate to±0.25%FS)and an electric heater connected to a digital temperature controller (accurate to 0.1 K).Measurements of pressures in the quantitative pump were achieved by using a pressure transducer(30.00 MPa full scale,accurate to±0.25% FS).
Fig. 2. Schematic diagram of the CO2 + n-dodecane solubility measurement system.1 to 13 are high-pressure valves. FSC = fused silica capillary.
Fig. 3. Variation in the Raman peak intensity ratio of the CO2 + n-dodecane system with time (T = 293.15 K, P = 6.67 MPa, xCO2 = 0.1071 mol/kg).
Fig. 4. The change in the CO2 + n-dodecane Raman peak intensity ratio with time under different CO2 concentrations at 303.15 K.
Fig. 5. Changes in the CO2-saturated solution during heating and depressurization (a) →(d), and cooling and pressurization (e) →(h) in a FSC.
Fig. 6. Three positions for Raman spectroscopic measurements in the CO2-saturated solution in a FSC.
The procedure for measuring the solubility of CO2in n-dodecane at different temperatures and pressures followed two steps: (1)determination of the relationship between the known CO2molality and the Raman peak intensity ratio of the upper band of CO2and ndodecane in a homogeneous CO2/n-dodecane system; and (2)measurement of the Raman peak intensity of the upper band of CO2and n-dodecane in a CO2-saturated CO2/n-dodecane system.
The procedures for the first step included the following:(1)Valve 11 was opened,and a certain amount of n-dodecane was fed into the phase equilibrium kettle using the liquid sampler at roomtemperature(about 293.15 K).Then,the valve was closed;(2)Valves 2, 4,and 8 were opened, and the quantitative CO2, which was estimated in advance,was charged into the quantitative pump,and then the three valves were closed.The CO2was pressed into the cell using the quantitative pump, and valves 9 and 10 were successively opened and closed.During this step,a pressure transducer was used to measure the initial and final pressures,and a digital temperature controller was used to measure the initial and final temperatures.The void volume of the quantitative pump and the pipe gap between the quantitative pump and the phase equilibrium kettle was known.Thus, using the Peng-Robinson equation to calculate the amount of CO2which was injected into the system(accurate to±0.13%);(3)The mixture was slowly compressed to 30.00 MPa using a manual pressure pump that was connected to the phase equilibrium kettle.The stirring device was used for several hours to accelerate the CO2dissolution; (4) The circulating pump was turned on for approximately 30 min to ensure the homogeneity of the solution in the circulation line,and then it was turned off.The Raman spectrum of a homogeneous CO2/n-dodecane solution was collected;(5)Repeated step (4) until the deviation of the Raman peak intensity ratio between the upper band of CO2Fermi diad and the C-H stretching band of the n-dodecane from previous measurement could be neglected, proving that the system had reached dissolution equilibrium; (6) The temperature or pressure was changed using the same procedures to ensure that the system reached dissolution
equilibrium,and the Raman spectra of the solution were collected at different pressures and temperatures. (7) The CO2molality was changed, and repeated steps (2)-(6); (8) The experiment was repeated to obtain the Raman spectra of the CO2-containing homogeneous solution under different pressures and at temperatures of 303.15-353.15 K.The CO2molality was plotted versus the Raman peak intensity ratio of the CO2/n-dodecane solution, and the equation of the calibrated line was obtained.
The procedures for measuring the Raman peak intensity ratio of CO2and n-dodecane and judging the phase equilibrium in the saturated CO2/n-dodecane system are the same as those for the homogeneous CO2/n-dodecane system. After reaching phase equilibrium, some bubbles appeared as the temperature of the system was increased or as the pressure was decreased in the saturated CO2/n-dodecane system. The Raman peak intensities of the upper band of CO2Fermi diad and the C-H stretching band of the n-dodecane under different temperature-pressure conditions(303.15-353.15 K,0-15.00 MPa)were determined for the solution near the CO2bubbles(approximately 100 μm from the edge of the CO2bubbles),and the Raman peak intensity ratios were calculated.
In the experiment,a JY/Horiba LabRam HR800 system equipped with a frequency-doubled Nd:YAG 531.95 nm laser with 20 mW of output laser power to collect the Raman spectra was employed.In addition,a charge coupled device(CCD)detector(multichannel,air cooled) was utilized to analyze the CO2+ n-dodecane system in situ. Under various temperature-pressure conditions, the Raman spectra of the system in the range of 1100-4000 cm-1were collected to obtain the peak intensity ratio of the CO2Fermi diad upper band to the C-H stretching band of the n-dodecane. The acquisition time was 20 s with two accumulations.The Raman peak intensity ratio of each group of temperature-pressure-composition(T-P-x) conditions was measured five times and the average value was invoked as the experimental datum.
The details of how to determine the molality of CO2(x) have been reported in our previous study (Wang et al., 2019). Raman peak intensity (height) ratio (λ) was calculated using Eq. (1).
whereICO2is the Raman peak intensity (height) of the CO2Fermi diad upper band,IC-His the Raman peak intensity (height) of the C-H stretching band of the n-dodecane, and the baseline is subtracted during the calculation.
The prerequisite for determining the solubility of CO2in ndodecane is the phase equilibrium of the CO2+n-dodecane system.Confocal Raman spectroscopy can be utilized to quantitatively monitor the concentration of gases in aqueous solutions because the band intensity of an active Raman species is proportional to its concentration in a fluid (Han et al., 2015; Wang et al., 2017a).Therefore, in this study, the peak intensity ratio of CO2Fermi diad upper band to the C-H stretching band of n-dodecane was employed to verify whether the system reached thermodynamic equilibrium under a particularT-P-xcondition.
3.1.1. Phase equilibrium determination of the CO2+n-dodecane system during homogenization
After feeding quantitative CO2into cells at room temperature,Raman spectroscopy was used to track the Raman peak intensity of the CO2and the n-dodecane in the FSC in real time and calculated the peak intensity ratio to understand the mass transfer of CO2in the system. Variation in the Raman peak intensity ratio of the CO2+ n-dodecane with time at 293 K and 6.67 MPa is shown in Fig. 3. It can be seen that the Raman peak intensity ratio was relatively high during the preliminary stage, but it decreased rapidly after the stirring device was turned on. During continuous stirring of the fluid,the CO2gradually dissolved in the n-dodecane,and the Raman peak intensity ratio increased and finally stabilized around 68 h, indicating the system had nearly reached phase equilibrium.
After the system reached the phase equilibrium for this sample fluid with knownxCO2,the temperature of the system was adjusted and the Raman peak intensity of the system was measured at a newT-Pcondition. While the deviation of the obtained Raman peak intensity ratio from the previous measurement was negligible, it can be considered that the system has reached phase equilibrium at this time. Fig. 4 shows that the time required to reach the phase equilibrium was approximately 7 h at 303.15 K for CO2concentrations of 0.1071-0.2469 mol/kg.
3.1.2. Phase equilibrium determination of a CO2-saturated solution
While increasing the system temperature or decreasing the system pressure from the CO2-saturated equilibriumT-Pcondition,bubbles could be formed in the CO2+ n-dodecane system due to the amount of available CO2is more than the solubility value.Fig.5 shows the formation and growth of CO2bubble(s) during heating and decompression (a→d), and the shrinkage of a CO2bubble during cooling and pressurization (e→h). By adjusting the system to a specific temperature and pressure,the size of the bubbles in the CO2+ n-dodecane system can be observed under a microscope.When the sizes of bubbles did not change within 1 h, in order to further ensure the phase equilibrium of the system,Raman spectra at positions 1,2,and 3 were collected (Fig.6) and the Raman peak intensity ratios of the upper band of CO2Fermi diad and the C-H stretching band of n-dodecane were calculated. Results, listed in Table 2 for threeT-Pconditions,show that the system had reached phase equilibrium.
Table 1 CAS registry number, source,mass fraction purity and molecular weight of the chemicals used in this work.
Table 2 Raman peak intensity ratios of the CO2 + n-dodecane system at three positions in the FSC under three different temperature-pressure conditions.
Table 3 The Raman peak intensity ratio of the CO2 + n-dodecane system for the same CO2 molality and different temperature-pressure conditions.a.
To confirm the feasibility of the method,the peak intensities at position 2 were continuously tracked every 20 min for 2 h after phase equilibrium was reached to determine whether the phase balance was reached in this state. As shown in Fig. 7, the Raman spectra of the CO2+n-dodecane system were acquired at position 2 at 333.15 K and 5.55 MPa from 0 to 120 min, and the peak intensity ratios were found to be 0.2247, 0.2278, 0.2309,0.2313,and 0.2315. The variations in the peak intensity ratio became increasingly smaller as time went on,which were negligible during these times.
Fig. 7. Raman spectra of the CO2 + n-dodecane system at 333.15 K and 5.55 MPa from 0 to 120 min after phase equilibrium was reached.
Fig. 8. The relationship between CO2 molality and the Raman peak intensity ratio between the upper band of CO2 Fermi diad and n-dodecane derived from spectra collected from homogeneous CO2/n-dodecane solutions.
After reaching phase equilibrium in a homogeneous CO2system,Raman spectroscopy was used to measure the peak intensity ratio of the system at different pressures and temperatures.As shown in Table 3,for the same CO2molality and temperatures,the changes in the Raman peak intensity ratio of the system with increasing pressure were very slight, with standard deviations of less than 0.0015, which were negligible. Thus, pressure had little effect on the peak intensity ratio. According to Table 4, the Raman peak intensity ratio of the system slightly decreased with increasing temperature at a constant CO2concentration and constant pressure, but the standard deviation of the peak intensity ratio from
303.15 to 353.15 K was less than 0.0007 for eachxCO2, which indicated that the temperature also had little effect on the peak intensity ratio. As a result, the peak intensity ratio of the homogeneous solution did not depend on temperature and pressure within the range of these experimental conditions.Therefore,the linear relationship between the CO2molality and the CO2+ndodecane Raman intensity ratio does not need to consider the effect of temperature and pressure.
In this experiment, the average value of the Raman peak intensity ratio of the CO2+ n-dodecane system at the same CO2molality and under design temperature conditions was used to establish a correlation equation for CO2molality.As shown in Fig.8(the data see Table S1), there was a positive correlation(R2= 0.9998) between the CO2molality and the Raman peak intensity ratio of the CO2+ n-dodecane system. The correlation equation is as following:
Table 4 Raman peak intensity ratio of a homogeneous solution at different temperatures and CO2 molality.
Table 5 Raman peak intensity ratio and solubility of the CO2 in n-dodecane at 303.15-353.15 K and 1.00-11.00 MPaa.
Fig. 9. Raman peak intensity ratios of the CO2 + n-dodecane system at 303.15-353.15 K and 1.00-11.00 MPa.
where λ is the peak intensity ratio of the CO2+n-dodecane system;andxis the molality of CO2(mol/kg).
Fig.10. Solubility of CO2 in n-dodecane at 303.15-353.15 K and 1.00-11.00 MPa.
Fig.11. Comparison of the CO2 solubilities in n-dodecane obtained in this study with those reported previously.
The solubility of the system based on the peak intensity ratio of the system under different temperature and pressure conditions in the saturated solution could be calculated from the relationship between the CO2molality and the peak intensity ratio of the CO2+ n-dodecane (Eq. (2)). At temperatures of 303.15-353.15 K and pressures of 1.00-11.00 MPa,the Raman spectra of CO2and ndodecane in CO2-saturated solution were collected, and the peak intensity ratios were calculated (shown in Table 5 and plotted in Fig. 9). The reproducibility of peak intensity ratio is characterized by relative standard deviation,which ranges from 0.23%to 0.90%,it proved that samples were appropriate to be analyzed by this method with satisfactory results in our works.
As shown in Fig.10,the solubility of the CO2-saturated solution decreased with increasing temperature and increased with increasing pressure.The maximum solubility obtained in this study is 30.7314 mol/kg at 303.15 K and 7.00 MPa.
According to Fig.10,the CO2solubility in n-dodecane gradually increased with increasing pressure and decreased with increasing temperature. At lower pressure, CO2had a weaker solubility in ndodecane, and the solubility increased nearly linearly with increasing pressure. As the pressure increased, the distance between the CO2and the n-dodecane molecule decreased,and the interaction force increased and gradually approached the force between the n-dodecane molecules, causing the CO2solubility to increase (Yang et al., 2013). In particular, the CO2solubility in ndodecane-rich liquid phase changes significantly for pressures and temperatures close to the critical pressure and temperature of pure CO2. For example, the pressure increased from 1.08 MPa to 5.03 MPa at 303.15 K, whereas the solubility increased only from 0.6331 mol/kg to 7.9775 mol/kg.In addition,the pressure increased from 5.03 MPa to 7.00 MPa, whereas the solubility increased dramatically from 7.9775 mol/kg to 30.7314 mol/kg.This indicated that the CO2+n-dodecane system reached the miscible phase with increasing pressure, thereby making the solubility value change significantly with increasing pressure(Lashkarbolooki et al.,2017).In contrast, at lower pressure, the CO2solubility in n-dodecane decreased with increasing temperature.The temperature increased from 303.15 to 353.15 K at 5.03 MPa,resulting in a decrease in the solubility of CO2in n-dodecane from 7.9775 mol/kg to 1.6270 mol/kg. Studies have shown that increasing temperature can increase the distance between the CO2and alkane molecules, reduce their interactions, enhance the Brownian motion of the CO2molecules,and allow the CO2molecules to escape from the liquid phase,which reduces the CO2solubility (Yang et al., 2012).
The CO2solubilities in n-dodecane obtained in this study were compared with those reported previously (Fig.11). Our CO2solubility data were basically consistent with the experimental data of Henni et al. (1996) and Brain Bufkin (1986) at pressures below 4.00 MPa.However,at higher pressures,our data show higher CO2solubility than those published in the literature,except at 353.15 K.The reasons of lower solubility may be that the system did not reach phase equilibrium while analyzing the results during their experiments.Another reason may be that previous studies need to extract sample fluids, which may disrupt the original equilibrium condition of the system,lead to the escape of CO2. In addition,the CO2solubility becomes more sensitive to the changes of pressure and temperature when theP-Tconditions are near the critical point of CO2.
Fig.12. Comparison of the experimental values of CO2 solubility in n-dodecane with those calculated from a model.
In CO2-EOR technology, CO2solubility is one of the most important factors required to improve oil recovery. Because of a lack of experimental data for CO2solubility in a wider range of temperatures and pressures, semi-empirical models often have been adopted in previous studies(Tsuji et al.,2004)to predict CO2solubility in organic liquids. Jou and Mather (2005) fitted a CO2solubility model based on experimental data, as shown in Eq. (3).
wherePis the pressure(MPa);Sis the CO2solubility(mol/kg);andAandBare functions of the temperatureT.
The model is relatively simple and suitable for predicting the solubility of CO2in different solvents.Fornari et al.(2009),Paninho et al. (2013), and Howlader et al. (2017) used this model to determine the solubility of CO2in organic liquids, such as ethyl lactate and triglycerides. The prediction results were in good agreement with the experimental results.Therefore,this model was also used in this work to predict the solubility of CO2in n-dodecane.
In this study, the model developed by Jou and Mather (2005)was improved, as shown in Eq. (4). First, the experimental CO2solubilities were fitted with pressure,P,under isothermal conditions.Then,based on the improved model,the relationships amongA,B,andTwere obtained,as shown in Eqs.(5)and(6).Thus,the CO2solubility correlation model obtained by correlating the temperature and pressure was determined to be as following:
The CO2solubility calculated using the prediction model(Fig.12)were consistent with the experimental data,and the mean average percentage error between the experimental and calculated data was within 4.0%. Therefore, the model can be expanded in future work to predict the CO2solubility in a wider range of temperatures and pressures.
In this study, to determine the solubility of CO2in n-dodecane under near-critical and supercritical conditions(T= 303.15-353.15 K,P≤11.00 MPa), an integrated fused silica capillary and in-situ Raman spectroscopy system was built. The calculated Raman peak intensity ratio was used to qualitatively and quantitatively analyze the CO2and its concentrations. The relationship between the known CO2molality in the n-dodecane and the Raman intensity ratio,ICO2/IC-H, was used to establish the correlation equation.Subsequently,the CO2solubility of the system was calculated by incorporating the measuredICO2/IC-Hratio into the correlation equation. The maximum CO2solubility(30.7314 mol/kg)was obtained at 303.15 K and 7.00 MPa.Finally,a solubility correlation model (lnS= (P-A)/B) based on the relationship between temperature and pressure was developed. The CO2solubility data can be extended using the model equation to provide an empirical correlation and experimental data for the CO2-EOR technology. This is a promising method for the determination of CO2solubility in organic liquids under supercritical conditions of CO2,provided the occasionally encountered interference of fluorescence on Raman signals can be effectively reduced.
Declaration of competing interest
The authors declare no competing financial interests.
Acknowledgment
This work was supported by the National Key Research and Development Program of China(2019YFE0117200)and the Natural Science Foundation of China (41977304). We thank the editors of Petroleum Science and the reviewers, whose constructive comments improve the paper.
Appendix A. Supplementary data
Supplementary data to this article can be found online at https://doi.org/10.1016/j.petsci.2022.06.014.