Copyright © the author(s). This work is licensed under a Creative Commons Attribution 4.0 International License. DOI: 10.14800/IOGR.1207 Received December 2, 2021; revised March 14, 2022; accepted April 20, 2022. *Corresponding author: dongzz@xsyu.edu.cn 1 Interfacial Characterization and Minimum Miscible Pressure Study of CO2 Flooding Based on Molecular Dynamics Bochao Qu, Xinle Ma, and Zhenzhen Dong*, Xi’an Shiyou University, Xi’an, China Abstract CO2 flooding can not only effectively improve the recovery of oil reservoirs, but also permanently store CO2 underground to alleviate the greenhouse effect. In the process of CO2 flooding, CO2 is injected into the oil reservoirs to affect the properties of crude oil through adsorption on oil interface, which reduces the interfacial tension and the density of the crude oil, thereby enhancing the recovery factor. Conventional core flooding experiments can only observe the oil displacement effect from a macroscopic perspective, but it is difficult to characterize the interface of CO2 flooding from a microscopic perspective. Furthermore, the experiment to obtain the minimum miscible pressure (MMP) usually requires a long time and high cost. In this study, an all-atom molecular dynamics simulation method was used to establish a CO2 model and a crude oil model. Using the CO2 force field of ZHU and the alkane force field of NERD, the interface interaction, interface characteristics, and minimum miscible pressure between CO2 and crude oil were analyzed. The research results show that when CO2 mixes with the crude oil, CO2 accumulates at the interface to form an adsorption layer; with the increase of system pressure, the phase interface and the CO2 adsorption layer gradually become thicken, and the interfacial tension (IFT) between CO2 and crude oil decreases linearly. The addition of the light hydrocarbon component allows CO2 to be more readily miscible with crude oil. At a low pressure, IFT decreases with increasing temperature, while at a high pressure, IFT increases with increasing temperature and MMP increases with increasing temperature as well. The MMP calculated using linear extrapolation of the interfacial tension was in good agreement with the experiment measurements. The main innovations of this study was the use of molecular dynamics analysis to simulate the interfacial properties of a system composed of CO2 and n-alkanes, and it is applicable to apply the simulated MMP in real oilfields.This study can significantly reduce the human, material and financial resources of the experiment in estimating MMP and also provide constructive suggestions on the practical application of CO2 flooding on oil reservoirs. Introduction In domestic and international reservoir development, CO2 flooding can not only enhance oil recovery, but also achieve CO2 sequestration and reduce the greenhouse effect. When the pressure is high enough, the ability of the crude oil to dissolve bitumen and paraffin decreases after CO2 precipitates the lighter mailto:lichen1125@foxmail.com 2 components in the crude oil, and the heavy components precipitate out of the crude oil, the crude oil viscosity decreases significantly and the oil flow ability is improved to achieve the purpose of mixed-phase oil drive. Under certain temperature and pressure conditions, when the crude oil is miscible with CO2, the interfacial tension of the crude oil is eliminated, and the pressure at this point is the minimum miscible pressure (MMP) for CO2 miscible flooding. Therefore, understanding the interfacial properties of processes, such as the dissolution of CO2 into crude oil, is particularly important for CO2 miscible flooding technology. The MMP is the minimum pressure at which the interfacial tension between oil and gas disappears. The most commonly used experiments for determining MMP are the fine tube test method, the bubbler method, and the vanishing interfacial tension method. The fine tube experiments is a standard method widely used and accepted in the petroleum industry to measure MMP and usually the measured MMP is reliable (Elsharkaw1996; Flock and Nouar 1984). Yelling et al. (1980) used sand-filled long fine tubes to simulate the CO2 repulsion process in real reservoirs to determine MMP, and investigated the effect of reservoir temperature and oil compositions on MMP. Nouar and Flock(1984) performed a parameter analysis of the MMP determination using a thin-tube test and suggested that increasing the length of the thin-tube could result in more accurate MMP values. However, the fine tube test is very expensive and time consuming (Zhang and Gu 2015). The bubble-lift method is an relative cheap and fast method for determining MMP. The movement of CO2 bubbles in oil is observed through a high-pressure window, and the oil-gas miscible state is determined by the change in appearance of the bubbles as they move at different pressures. However, the method relies on human observations and is subjective (Elsharkaw 1996; Dong 2001). The vanishing interfacial tension method was used to determine the interfacial tension between the injected gas and oil at constant temperature and pressure, and the pressure at which the interfacial tension is zero is obtained by extrapolation, i.e. the MMP (Rao 1997; Rao and Lee 2002; 2003). Ayirala and Rao demonstrated that the MMP determined using the vanishing interfacial tension method was similar to that was determined by the fine tube experiment and the bubble lifter method. The experiment results clearly supported that the use of vanishing interfacial tension for the rapid and economical determination of MMP (Ayirala and Rao 2011). Due to the complex composition of crude oil, there are too many influencing factors if the properties of the system composed of CO2 and crude oil are studied directly in the CO2 flooding process. Therefore, researchers generally take the major components of oil to represent crude oil, such as n-alkanes, cycloalkanes aromatic hydrocarbons, etc. Shaver et al. (2001) experimentally measured the phase fraction, phase density and interfacial tension of CO2 and n-decane in the pressure range of 1~13MPa at 344 K. Hsu et al.(1985) measured the oil composition, oil density, and interfacial tension of CO2 and n-butane system at the temperature of 319K~378K until the pressure achieved the MMP. Spee and Schneider (1991) measured the change of oil composition with pressure in a CO2/dodecane system and CO2/1,8-octanediol system at 393 K and 10~100 MPa. In recent years, molecular simulations have been widely applied to study the CO2 and crude oil systems. Makimura et al. (2012) investigated two characteristics of CO2-EOR based on molecular simulations, including interfacial properties and phase equilibrium. Neyt et al. (2011) used Gibbs Ensemble Monte Carlo and two-phase Monte Carlo to calculate the interfacial tension between CO2 and water, the interfacial tension between CO2 and n-butane system. The calculated results were in good agreement with the experiment results. Müller et al .(2009) used molecular dynamics to calculate the oil composition, oil density, interfacial tension and interfacial structure of n-hexane and n-decane system, CO2 and n-decane system, and ethane and n-eicosane system. The simulation results agreed well with the experiments. De 3 Lara et al. (2012) used molecular dynamics to investigate the interfacial properties of brine/light oil, CO2/light oil, N2/ light oil and CH4/light oil systems. They showed that the CO2/light oil system had the advantage of lower interfacial tension and enhancing diffusion of CO2 in the oil phase. The diffusion coefficients of n-alkanes from methane to tetradecane in CO2 at infinite dilution were calculated by Feng et al. (2013). The results obtained from the simulations were reliable. Compared to experimental methods, molecular simulations can be used to calculate the interfacial tension between CO2 and crude oil, to reveal the interfacial properties of CO2 and oil, and to observe microscopic mixing processes. These are difficult or impossible to be observed and measured using experimental methods. In addition, molecular dynamics simulations can be used to predict the interfacial properties of CO2 and oil with low cost and fast calculation time. In this study, the molecular dynamics simulation method was proposed to study the miscibility characteristics of injected CO2 and oil in a block of Yanchang Oilfield. The paper is structured as follows: Section 2 describes the proposed methodology in details, including force field and MMP calculation methods; Section 3 describes the model used for the molecular simulations; Section 4 presents the main results of the study. Methodology Force Field. The potential energy function describing the forces interacting between atoms in a system is called the force field. Constructing an accurate potential energy function for a system is an important step in molecular dynamics calculations. In general, molecular force fields mainly include bond stretching potential energy, bond angle bending potential energy, dihedral angle distortion potential energy, and non-bonding potential energy. Non-bonding potential energy includes van der Waals potential energy and Coulomb electrostatic potential energy. Force fields have been developed for each system and are basically suitable for molecular dynamics simulation studies in various fields. Different force fields include different atom types, so before selecting a force field one should first check the list of atom types for the force field and whether the force field covers the atom types in the simulated system. The available CO2 molecular force fields are mainly divided into a rigid force field containing the TraPPE force field, a semi-flexible force field with the EPM2 force field and a flexible force field with the ZHU force field (Potoff and Siepmann 2001; Harris and Yung 1995; Zhu 2009). The molecular force fields of n-alkanes can be divided into two categories: joint atomic force fields and all-atomic force fields. Joint atomic force fields are those that equate CH3 and CH2 of n-alkanes as one atom, such as OPLS-UA, TraPPE-UA and NERD (Jorgensen 1984; Martin and Siepmann 1998; Nath 1998). All-atomic force fields are those all atoms expressed in n-alkanes explicitly, such as OPLS-AA and CHARMM (Jorgensen 1996; Price 2001; Davis 2008). The ZHU force field was proposed by Zhu et al. (2009), which can accurately predict the saturated gas-liquid phase density, critical point properties, while taking into account the molecular structure properties of supercritical CO2, and is therefore suitable for the simulation of systems containing supercritical CO2. The calculated gas-liquid equilibrium curves from the NERD force field are in good agreement with experimental data for both shorter chain alkanes and longer chain alkanes (Müller 2009; Nath 1998). Therefore, the ZHU CO2 force field and the NERD n-alkane force field were used in this study. The NERD molecular force field defines the total potential energy function of an alkane as shown in Eq. 1. 4 �total = bonds ��� � 2 ��� − ���� 2 + ������ ���� � 2 ���� − ����0� 2 + ��ℎ�������0 + �1 1 + ���� +� �2 1 − ��� 2� + �3 1 + ��� 3� + ���������4���� ��� ��� 12 − ��� ��� 6 + ���� 4��0����� .............................................(1) The ZHU CO2 force field function takes the form shown in Eq. 2. �total = bonds ��� � 2 ��� − ���� 2 + ������ ���� � 2 ���� − ����0� 2 + ���������4���� ��� ��� 12 − ��� ��� 6 + ���� 4��0����� ,...............................................(2) Van der Waals interactions between atoms describe the interactions between atoms that are caused by non-covalent and non-hydrostatic forces that attract or repel each other. The Lennard-Jones potential function is a function that describes the Van der Waals interactions between atoms and has the form shown in Eq. 3. ��� ��� = 4��� ��� ��� 12 − ��� ��� 6 .............................................................................................................(3) The sums between the different atoms are obtained by means of a mixing rule, the common Lorentz-Berthelot mixing rule, as shown in Eq. 4 and 5, respectively. ��� = ��+�� 2 ,...............................................................................................................................................................................(4) ��� = ����...............................................................................................................................................(5) Simulation method. In this study, Lammps molecular simulation software was used for the simulations. During the molecular dynamics (MD) simulations, periodic boundary conditions were used, the equations of motion were solved for integration using the Velocity-verlet method. The long-range force electrostatic interactions used the particle-particle-particle-mesh (PPPM) summation method with an accuracy of 1.0×10-4. The non-bonded van der Waals forces used the 12-6 Lennar-Jones potential function with a truncation radius of 2 nm and a time step of 1 fs. The temperature coupling was performed using the Nosé-Hoover algorithm. The entire simulation time was 10 ns of relaxation time, 30 ns of calculation time, with data collected at 0.1 ps intervals. Finally, the IFT of the system was calculated. There are many ways to obtain the MMP, the most common ones are to calculate the number of CO2 and alkanes that cross the phase interface at the same temperature and different pressures as a percentage of the total number of CO2 and alkanes, and to obtain the MMP when the number of ratios drops to a stable pressure. There are also methods to obtain the MMP by the disappearance of interfacial tension. In this study, the MMP was obtained by the disappearance of interfacial tension, as the method has a clear definition of parameters. When the interfacial tension is zero, the interface between the two phases disappears, then the two phases can completely become a miscible phase. The Gibbs interfacial tension equation was used to calculate the variation of the two-phase interfacial tension with pressure, from which MMP is indirectly calculated. The specific expression is given as Eq. 6. � = 1 2 0 �� �� � − �� � ��� = 1 2 ��� − ���+��� 2 ��,..........................................................................(6) where γ is the interfacial tension, and �� � and �� � represents the normal and tangential pressures, ��� is the amount on the diagonal of the pressure tensor, and �� is the length in the z-direction of the simulated system. 5 Modeling. The force field parameters for this study are shown in Table 1. The initial systems of two cases are given in Figure 1, with a oil (liquid phase) in the middle and CO2 (gas phase) in the two side. The oil phase consists of alkanes of different chain lengths, depending on the case. For the CO2/n-decane system, the oil contains 800 n-decane molecules. The system pressure was varied with the number of CO2 molecules in the gas phase on both sides. The size of the simulated system was taken to be 5×5×30 nm3. Table 1—Force field parameters. Atom σ(nm) εij(KJ/mol) CT_CH3 0.3910 0.8647 CT_CH2 0.3930 0.3808 C 0.2800 0.23397 O 0.3028 0.66824 Bond r0(nm) kb(kJ/(mol/nm2) ) CH3_CH2 0.1540 80235.0280 CH2_CH2 0.1540 80235.0280 C-O 0.1162 60000.0000 Angle θ0(deg) Kθ（kJ/mol/rad2) CH3_CH2—CH2 114 519.657 CH2_CH2—CH2 114 519.657 C-O-C 180 110.000 Torsion V0（kJ/mol) V1（kJ/mol) V2（kJ/mol) V3（kJ/mol) CH3_CH2—CH2—CH2 0.0000 5.9038 -1.1339 13.1590 CH2_CH2—CH2—CH2 0.0000 5.9038 -1.1339 13.1590 (a) Case 1 (b) Case 2 Figure 1—Initial structure of the two systems. 6 Results and Discussion Interfacial Tension and MMP. The disappearance of interfacial tension method was used in the MD simulation to indirectly calculate the MMP of CO2 with n-decane at 334K. Because Shaver (2001) experimentally measured the phase fraction, phase density and interfacial tension of CO2 and n-decane in the pressure range of 1~13MPa at 344 K, the simulation results in this section are compared with the experimental values. As shown in Figure 2(a), the calculated IFTs by this work were in very good agreement with Shaver (2001) method. The interfacial tension decreases with increasing pressure and displays a linear relationship, which indicates that the interface between CO2 and alkane becomes increasingly blurred and gradually tends to a miscible phase. In addition, the linear relationship enables a reliable extrapolation to obtain the pressure when the interfacial tension is zero. Thus, the MMP was determined to be 11.89 MPa when IFT equal 0. The estimated MMP is very close to that measured MMP (12.74 MPa) by Shaver et al (2001). As can be seen from Figure 2(b), the relationship between interfacial tensions and pressure obtained by Müller and Mejía (2009) using the EPM2 CO2 model and the NERD n-decane model were in good agreement with the experiments. Mejia et al. (2014) used coarse-grained molecular model to simulate CO2/n-decane system. But the estimated interfacial tensions were slightly higher than the measured values. The estimated IFTs by this work agreed well with the measured values. Therefore, ZHU CO2 model and the NERD n-alkane model used in this paper are an effective, convenient and low-cost method for predicting the MMP for CO2 and alkane systems compared to coarse-grained simulations. (a) (b) Figure 2—Interfacial tension between carbon dioxide and n-decane with pressure. To validate the effectiveness of the proposed method in estimating MMP, the proposed method was compared to the empirical formulas. The comparison results are shown in Table 2. The National Petroleum Council (NPC) empirical equation estimates MMP roughly, mainly by using API and temperature as parameters, and obtains results with large errors. Yellig and Metcalfe (1980) proposed a method to predict MMP according to the temperature, which is one of the most common methods. The temperature is the only parameter in the formula: ���=1833.7217+2.2518055(T-460)+0.01800674(T-460)2 − 103949.93 �−460 ......................................(7) As can be seen from Table 2, the results of the NPC empirical formula approach are poor. The molecular simulation used in this study has a higher prediction accuracy than the Yellig-Metcalfe model. 7 It indicates that the empirical formula has certain limitations, such as the composition of different oil fields, the composition of the injected gas, and the range of working conditions. Thus, the results obtained by the empirical formulas are difficult to be generalized. In contrast, the working conditions of the molecular simulation method proposed in this study is easy to set, and the calculated values agree well with the experimental values, so it has a wider applications. Table 2—Comparisons between the proposed method and the empirical formulas. MMP from experiment (MPa) NPC Yellig-Metcalfe (1980) This study 12.74 MMP (MPa) Error (%) MMP (MPa) Error (%) MMP (MPa) Error (%) 10.69 2.05 13.78 1.04 11.89 0.85 Phase Interface Properties. The phase interface properties of CO2 and n-decane systems, such as interfacial structure and interfacial thickness, are difficult or impossible to be measured by experiments. However, molecular dynamics has the advantage of being intuitive and convenient for this purpose. In this section, the mixing process, interfacial structure and interfacial thickness of the CO2 and n-decane system at 344 K were investigated. The dynamic mixing process of the CO2/n-decane system at 344 K are shown in Figure 3. A small amount of decane molecules were extracted by CO2 and moved towards the CO2 phase, and the phase interface gradually disappeared; a large number of CO2 molecules formed clusters around the decane molecules, and the two gradually miscible, and finally the phase interface disappeared and reached the mixed-phase state after 40ns. (a) 0ns (b) 5ns (c) 15ns 8 (d) 30ns (e) 40ns CO2, n-decane Figure 3—CO2/n-decane mixed-phase microscopic processes. The variation of the gas-liquid phase density with pressure for the CO2 and n-decane system at 344 K is shown in Figure 4. As the pressure of the system increases, the system in the liquid phase area gradually expands, the gas-liquid phase density also increases and the phase interface gradually becomes thicker. Figure 4—Variation of gas-liquid phase density with pressure of CO2/n-decane system. The density distribution of CO2 and n-decane in the system at different pressures is shown in Figure 5. As the pressure of the system increases, the density of n-decane decreases and the density of CO2 increases. Part of the CO2 in the system gathered at the interface to form a CO2 adsorption layer, and the adsorption layer gradually became thicker as the pressure increased, which surface more and more CO2 gathered at the interface as the pressure increased. 9 (a)2.72MPa (b)4.51MPa (c)5.91MPa (d)7.06MPa (e)8.1MPa (f)9.09MPa (g)9.76MPa Figure 5—Density distribution of components of CO2/n-decane system at different pressures. 10 Base on the above analytical simulations, a mixture of n-decane and n-hexane was used to replace the oil from the Yanchang field and the MMP was determined. The results are shown in Figure 6, which shows an MMP of 11.4 MPa at 344 K. And the effect of the oil components on the MMP can also be illustrated with Figure 6, which shows that the addition of n-hexane has a significant effect on the MMP of n-decane and CO2. The addition of n-hexane makes the MMP decrease, because the light hydrocarbon components can be extracted from oil phase by CO2, when CO2 contacts with the oil, while the light components originally were dissolved in the oil. As a result, it makes CO2 become hydrocarbon rich. The enriched CO2 then contacts with the oil to further extract the light components. The process repeats until CO2 extracts enough alkanes. In contrast, when n-hexane is dissolved in the oil to contain more light components, so CO2 can be more easier to extract enough light hydrocarbons to accelerate enrichment and make CO2 be more easy miscible with the oil. Figure 6—Effect of oil composition on MMPs. The Effects of Temperature on MMP. It has been proven by numerous experiments that reservoir temperature has a significant effect on MMP and it is an important variable affecting MMP (Zolghadr 2013). The variation of MMP with temperature for the CO2/n-decane system is shown in Figure 7. At a low pressure, IFT decreases with increasing temperature. But at a high pressure, IFT increases with increasing temperature and MMP increases with increasing temperature. This is because the density of CO2 is controlled by temperature and pressure. As can be seen in Figure 8, at a constant pressure, the density of CO2 decreases with increasing temperature, leading to a decrease in the solubility of CO2 and in the extraction ability of light hydrocarbons. Thus, to give CO2 sufficient solubility to achieve a mixed phase, it is necessary to increase the density of CO2 by increasing pressure, so the MMP increases with increasing temperature. 11 Figure 7—Effect of temperature on MMPs. Figure 8—The density distribution of CO2/n-decane at 4.5 MPa. Conclusions In this paper, we simulated the phase density and interfacial tension of the CO2 and n-decane system at 334 K under different pressures using molecular dynamics methods, analyzed the interfacial characteristics of the system, and investigated the effect of the addition of hexane on the minimum miscibility pressure of the CO2 and n-decane system, and the main conclusions are as follows. 1. The MMP of CO2 with n-decane at 334 K was predicted to be 11.89 MPa using the molecular simulation method, which has the advantage of being less costly and more efficient than the experimental methods, and the prediction is more realistic and reliable than the theoretical equations. 2. The proposed molecular dynamics simulation displayed the mixing process of CO2/n-decane system. In the process, CO2 is dissolved into n-decane, while n-decane is continuously extracted by CO2. The interface between CO2 and n-decane gradually disappears and the interfacial tension gradually decreases, and finally reaches the miscible state. 12 3. As the pressure of the system increases, the thickness of the phase interface between CO2 and n-decane increases, and the CO2 adsorption layer on the interface also gradually becomes thicker, and the density of n-decane decreases with the increase of pressure, while the density of CO2 is the opposite. 4. When a certain amount of hexane is dissolved to the system of CO2 and n-decane, the MMP of the system decreases. At a low pressure, the IFT decreases with increasing temperature; while at a high pressure, both the IFT and MMP increases with increasing temperature. Conflicts of Interest The author(s) declare that they have no conflicting interests. References Ayirala, S.C. and Rao, D.N. 2011. Comparative Evaluation of a New Gas/Oil Miscibility-Determination Technique. J Can Pet Technol 50(2):71–81. Davis J. E., Warren G. 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Zhang, K. and Gu, Y. 2015. Two Different Technical Criteria for Determining the Minimum Miscibility Pressures (MMPs) From the Slim-Tube and Coreflood Tests. Fuel 161(1): 146-156. Zhu, A., Zhang, X., Liu, Q., et al. 2009. A Fully Flexible Potential Model for Carbon Dioxide. Chinese. J. Chem. Eng. 17(2): 268-272. Zolghadr, A., Escrochi, M., and Ayatollahi, S. 2013. Temperature and Composition Effect on CO2 Miscibility by Interfacial Tension Measurement. J. Chem. Eng. Data. 58(5): 1168-1175. Bochao Qu, is a master candidate in Petroleum Engineering department at Xi’an Shiyou University. He has focused his research in areas involving reservoir simulation, well testing, and production analysis. Tian holds a BS degree in Petroleum Engineering from Xi’an Shiyou University. Xinle Ma, is a master candidate in Petroleum Engineering department at Xi’an Shiyou University. He has focused his research in areas involving reservoir simulation, well testing, and production analysis. Tian holds a BS degree in Petroleum Engineering from Xi’an Shiyou University. Zhenzhen Dong is a Professor in the Petroleum Engineering Department at Xi’an Shiyou University. She worked as a reservoir engineer with Schlumberger from 2012 to 2016. Her research interests include unconventional resources/reserves estimates, reservoir simulation, well testing, and production analysis. 14 Dong holds a bachelor’s degree in mathematics from Northeast Petroleum University, China; a master’s degree in petroleum engineering from Research Institute of Petroleum Exploration and Development, China; and a PhD degree in petroleum engineering from Texas A&M University. Abstract Introduction Methodology Results and Discussion Conclusions Conflicts of Interest References