#
Determination of Minimum Miscibility Pressure of CO_{2}–Oil System: A Molecular Dynamics Study

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## Abstract

**:**

_{2}enhanced oil recovery (CO

_{2}-EOR) has become significantly crucial to the petroleum industry, in particular, CO

_{2}miscible flooding can greatly improve the efficiency of EOR. Minimum miscibility pressure (MMP) is a vital factor affecting CO

_{2}flooding, which determines the yield and economic benefit of oil recovery. Therefore, it is important to predict this property for a successful field development plan. In this study, a novel model based on molecular dynamics to determine MMP was developed. The model characterized a miscible state by calculating the ratio of CO

_{2}and crude oil atoms that pass through the initial interface. The whole process was not affected by other external objective factors. We compared our model with several famous empirical correlations, and obtained satisfactory results—the relative errors were 8.53% and 13.71% for the two equations derived from our model. Furthermore, we found the MMPs predicted by different reference materials (i.e., CO

_{2}/crude oil) were approximately linear (R

^{2}= 0.955). We also confirmed the linear relationship between MMP and reservoir temperature (T

_{R}). The correlation coefficient was about 0.15 MPa/K in the present study.

## 1. Introduction

_{2}is the culprit of this phenomenon. CCUS (CO

_{2}capture, utilization, and storage) is a new technology developed from CCS (CO

_{2}capture and storage) that can bring economic benefits while reducing CO

_{2}emissions and alleviating global warming [1]. CO

_{2}enhanced oil recovery (CO

_{2}-EOR) is one of the effective ways of CCUS. The captured CO

_{2}is squeezed into the oil reservoirs that have been exploited, and the interaction between CO

_{2}and crude oil is used to improve the properties of the crude oil, thereby displacing more crude oil from the crust [2]. Research has shown that CO

_{2}-EOR can improve crude oil recovery significantly and extend the life of oil reservoirs [3,4]. Hence, CO

_{2}-EOR has been fundamentally well researched in laboratories and applied in industries as an efficient approach since the 1970s [5].

_{2}-EOR. Under the former condition, CO

_{2}and crude oil can completely integrate into one phase, resulting in a much higher recovery rate than the latter. For the former, there is a minimum pressure above which CO

_{2}and crude oil can be miscible. This minimum pressure value, also called the minimum miscible pressure (MMP), is a vital parameter in the process of CO

_{2}-EOR. Nevertheless, considering the massive influencing factors, the accurate determination of MMP remains a major challenge [6].

_{R}), composition of drive gas (CO

_{2}, H

_{2}S, N

_{2}, and C

_{1}–C

_{5}), molecular weight of C

_{5+}fraction in crude oil (MW

_{c5+}), and the ratio of volatile (C

_{1}and N

_{2}) to intermediate (C

_{2}–C

_{4}, H

_{2}S, and CO

_{2}) in crude oil (Vol./Int.).

_{2}-EOR.

_{2}and crude oil with an obvious phase interface. To mimic the contact between CO

_{2}and crude oil, these molecules were gradually mixed until they were miscible with time evolution by using molecular dynamics. After calculating the ratio of CO

_{2}/crude oil atoms that passed through the initial interface, we found the connection between the ratio value with the miscible state. When the ratio changes from decreasing to stable, it indicates that the system has entered a miscible state, while the pressure corresponding to the inflection point is MMP. Figure 1 is a flow chart that shows all the main steps of modeling. The main objective of this study was to reveal the principle of the MMP formation at the molecular level and provide more feasible ideas for the prediction of the MMP.

## 2. Simulation Method

#### 2.1. Simulation and Force Field

_{2}were generated from Automated Topology Builder and Repository databases [38,39].

^{−5}bar

^{−1}[41]. The time step was 2 fs, and periodic boundary conditions were applied in the XY directions [42]. Walls were set at the top and bottom of the Z-direction in the simulated box to ensure that all atoms passed through the initial interface to achieve the miscibility. Bond lengths were constrained by the LINCS algorithm [43]. During the simulation, van der Waals interactions with the Lennard–Jones potential was cut off at 1.4 nm. Coulomb interaction used the particle-mesh Ewald summation method [44,45]. The Verlet list was updated every 10 steps. The Maxwell–Boltzmann distribution was employed to set the initial atomic velocities of the systems [46]. The trajectories were integrated by the leapfrog Verlet algorithm [47].

#### 2.2. Simulation System

_{2}molecules to mimic the supercritical CO

_{2}fluid (333 K, 10 MPa). Energy minimization and 30 ns NVT ensemble simulation enabled the CO

_{2}to reach its equilibrium state. To simulate the contact between CO

_{2}and crude oil, the two boxes were integrated into one rectangular simulation box, and the height of new box in the Z-direction was slightly increased to 11.2 nm to avoid intermolecular overlap, as shown in Figure 2. After that, at least 10 ns NPT ensemble MD simulation was performed.

## 3. Results and Discussion

_{2}was miscible with crude oil, the NPT ensemble achieved equilibrium and the box size remained unchanged. However, the change in the size of the box cannot intuitively reflect the miscibility process. Therefore, we introduced the number density of CO

_{2}/crude oil.

_{2}/crude oil atoms in the upper or lower half of the box should be 50%. In our simulation system, the Z-direction height will not change due to the presence of walls. Therefore, the integral change in the number density in the Z-direction (i.e., the integral bars in Figure 2d) can reflect the change in the size of the box and further reflect the mixing progress. When the system achieves equilibrium, the integral of the number density in Z-direction will also be constant.

#### 3.1. Definition of Initial Miscible Time

_{2}and the crude oil phases just reach the miscible state during their mixing progress, and they can keep the miscible state afterward. The purpose is to ensure that data after this time are miscibility data. We used the CO

_{2}phase as an example to illustrate the calculations. Its number density data were extracted along the Z-direction of the box from 0.5 ns to 10.0 ns every 0.5 ns after the NPT ensemble was run. Hence, there were 20 sets of data in total. We can obtain the number of CO

_{2}atoms in the lower half of the box by integrating the density of CO

_{2}along the Z-direction below the initial interface at each cut-off time. Since CO

_{2}was not distributed in the box below the initial interface at the beginning, the integral values we obtained corresponded to the number of CO

_{2}atoms passing through the initial interface at the cut-off time. More vividly, it is an integral bar in the three-dimensional space of the box along the Z-direction, as shown in Figure 2d.

_{2}atoms passing through the initial interface over time can be plotted. Figure 3 shows the change in the number of CO

_{2}atoms in the lower half of the box at 333 K and 10 MPa: it gradually increased from zero to a stable value (about 49.09), and then tended to be stable. It is worth noting that each molecule always kept in continuous random motion, thus it is normal to have positive and negative fluctuations after miscibility. For the selection of the initial miscibility time, the establishment standard is to find the time when the curve becomes stable and the change is very gentle after the miscibility reference line (i.e., the 49.09 line in Figure 3a). This is also the time when the miscibility has just been achieved. The first-order variance of data with time evolution (Figure 3b) reflects the trend of data changes more intuitively. It should be noted that it is not the “initial miscibility” that is already zero, but the time corresponding to the point relatively close to zero. Based on the situation in Figure 2 and Figure 3, it can be guaranteed that the time at 4 ns: (i) the vertical axis value is already very close to the reference line, and (ii) the curve’s upward trend has slowed down.

_{2}and crude oil were quite similar. Combined with the analyses above, we can preliminarily conclude that 4 ns is the initial miscible time, and is also the time when the CO

_{2}–oil system achieved miscibility.

#### 3.2. Reconfirmation of Initial Miscible Time

#### 3.2.1. Solvent Accessible SURFACE Area (SASA) Analysis

_{2}from 0 ns to 10 ns and went through roughly three processes: (i) At the beginning, SASA increased rapidly and reached the highest point (from C1 to C2); (ii) SASA dropped to the lowest point in a short period of time (from C2 to C3); and (iii) SASA gradually rose to basic stability and attained a state of dynamic balance (from C3 to C4, and the time was after about 4 ns).

_{2}and crude oil phases, both gradually achieved the best coexistence state (after C4).

#### 3.2.2. Root Mean Square Deviation (RMSD) Analysis

_{2}/crude oil); and r

_{i}(0) and r

_{i}(t) are the initial position and the position of atom i at time t. Figure 5 displays the RMSD of CO

_{2}/crude oil during NPT ensemble as a function of time. It is interesting to note that CO

_{2}has a higher RMSD value than crude oil at the beginning, which indicates that CO

_{2}has better mobility. From 4 ns to 10 ns, the RMSD of CO

_{2}/crude oil in the box fluctuated with time evolution. Both were gathered around 4 nm of RMSD, which signifies that the system achieved equilibrium after 4 ns.

#### 3.2.3. Interaction Energy Analysis

_{2}and crude oil phases. Interaction energy is a type of non-bonding interaction including long-range Coulomb interaction and short-range van der Waals interaction. As shown in Figure 6, the system was dominated by van der Waals interaction, while Coulomb interaction accounts for only about one-tenth of the former. This is because both CO

_{2}and crude oil are non-polar molecules and do not have forces such as strong hydrogen bonding interaction. The intermolecular forces are mainly dispersive forces. The dispersion forces increased with time evolution, and the van der Waals potential energy and the total intermolecular potential energy increased accordingly.

_{2}and crude oil also reached its maximum and remained dynamically stable. Figure 6 clearly indicates that van der Waals interaction and Coulomb interaction both remained stable after 4 ns.

#### 3.3. Acquisition of MMP

_{2}atoms in the lower half of the box and crude oil atoms in the upper half of the box after 4 ns were taken as the arithmetic mean respectively. It needs to point out that the number of CO

_{2}molecules under different pressures are different for 333 K system (Table S1). In order to reflect the general laws, the ratio of mean value to their respective total number of CO

_{2}and crude oil atoms in the box was calculated. Similarly, the ratio of CO

_{2}/crude oil passing through the initial interface to their respective totals at 333 K for 15 MPa, 20 MPa, 25 MPa, 30 MPa, and 35 MPa were also calculated, as shown in Table 1.

_{2}and 20.21 MPa for crude oil.

#### 3.4. MMP in Different Temperature Systems

_{2}varies greatly at different temperatures and pressures, therefore we computed the number of CO

_{2}molecules under different conditions. The amount of CO

_{2}molecules added to each simulation system are listed in Table S1. Afterward, a summary of initial miscible time in different systems can be obtained according to the methods in Section 3.1 and Section 3.2, as listed in Table 2. Table S2 summarized all the integral values in this study.

_{2}and crude oil atom numbers that passed through the initial interface to their respective totals when they achieved miscibility can be obtained. Consequently, MMP of 343 K, 353 K, 363 K, and 373 K were obtained according to the method described in Section 3.4 by plotting and curve fitting (Figure S2). Table 3 summarizes the results.

#### 3.5. Model Assessment

_{2}/crude oil to T

_{R}, respectively, and obtained two prediction equations (Figure 8). It can be compared with the experimental results to check the predictive performance of the model. Recently, Yu et al. used a combination method of slim-tube experiments and interfacial tension (IFT) to perform MMP measurements on tight oil from the Long Dong region of the Ordos Basin. This method has higher credibility than slim-tube experiments [51]. Afterward, we compared our model with several famous empirical correlations to illustrate its accuracy by employing the experimental method proposed by Yu et al. as the benchmark. Table 4 reports the relative error. Details of these empirical correlations are summarized in Table S3.

_{2}relative error was similar to Alston et al. [53]. The equation proposed by Shokir [54] was based on an alternating conditional expectation algorithm, and had a relative error of 11.89 %. The model of Emera and Sarma [25] can be employed to calculate the MMP of impure CO

_{2}injection, but has poor accuracy. Beyond that, the performances of Cronquist [55], Glaso [56], and Yellig and Metcalfe [57] were also unsatisfactory. The overall results can prove that even if only the influencing factor of T

_{R}is considered, the model proposed in this study had satisfactory prediction accuracy.

#### 3.6. Comparison of MMP Predicted by CO_{2} and Crude Oil

_{2}and crude oil can be compared. It is more intuitive to reflect the data in Table 3 to Figure 9. In Figure 9, the blue line represents the curve whose analytical formula is y = x, and the red line is the fitting curve for the data. It can be found that the MMPs predicted by CO

_{2}and crude oil were approximately linear (R

^{2}= 0.955). Furthermore, in the same simulation system, the MMP values obtained from different reference materials (CO

_{2}/crude oil) were not identical as there was a slight difference between them (i.e., an included angle of about 8°).

#### 3.7. Relationships between T_{R} and MMP

_{R}) is usually regarded as one of the most important factors affecting MMP [58]. Exploring the influence of T

_{R}on MMP is the core of many studies (such as the fitting of empirical formula). Recently, Zheng et al. [59] proposed a novel oil droplet volume measurement method (ODVM) to measure the multiple contact minimum miscibility pressure (MCMMP) and first contact miscibility pressure (FCMP) in the CO

_{2}/n-hexadecane (C

_{16}H

_{34}) and CO

_{2}/liquid paraffin systems. Their experimental data showed that the measured MMP values of two CO

_{2}–oil systems increased linearly with T

_{R}. Furthermore, Mostafa et al. found that the MMP is a linear function of temperature with a slope of 0.15 MPa/K [60].

_{R}and MMP can be identified in the principle of miscibility because it is not affected by other external objective factors. As shown in Figure 8, for both CO

_{2}and crude oil, the change in T

_{R}and MMP basically conformed to a linear relationship, thus a fairly good fitting result can be obtained by using the first-order linear equation. This is because the increase in T

_{R}can effectively reduce the solubility of CO

_{2}in crude oil, which is not conducive to the mixing progress of CO

_{2}and crude oil, ultimately leading to the increase in MMP. During the temperature range (333–373 K), it is a linear change with a slope of 0.15 MPa/K and 0.12 MPa/K and consistent with the experimental results.

## 4. Conclusions

_{2}–oil system was developed. The model characterized the miscible state by calculating the ratio of both CO

_{2}and crude oil atoms that passed through the initial interface to their respective totals. These ratio values dropped rapidly and fluctuated after a certain value with the increase in pressure at a fixed T

_{R}. The value is the MMP of T

_{R}. In comparison with conventional prediction approaches, the present work proposed a straightforward model to simulate the complex miscibility of CO

_{2}and crude oil, and the miscible principle was clarified at the molecular scale.

- (1)
- The molecular scale mixing progress of CO
_{2}and crude oil was investigated in principle for the first time, and the research process was not affected by other external objective factors. Results showed that the ratio of CO_{2}/crude oil atoms that passed through the initial interface to their respective totals was always the same when the system was miscible. The proposed model had good prediction capabilities. - (2)
- In the process of the simulation, the SASA, RMSD, and interaction energy of CO
_{2}/crude oil changed obviously, thus they can be used as criteria of miscibility between both phases. - (3)
- The MMP predicted by CO
_{2}of the CO_{2}–oil system were 20.31 MPa, 21.08 MPa, 22.12 MPa, 24.43 MPa, and 26.25 MPa at temperatures of 333 K, 343 K, 353 K, 363 K, and 373 K, respectively, and MMPs predicted by crude oil were 20.21 MPa, 20.89 MPa, 22.36 MPa, 23.84 MPa, and 24.52 MPa at the same temperatures. The two sets of data had a linear relationship. - (4)
- MMP and reservoir temperature (T
_{R}) had a linear relationship in the present work, and the slope was about 0.15 MPa/K, which are in agreement with theoretical analyses and literature results.

## Supplementary Materials

_{2}molecules added in different systems. Table S2: Integrated values of CO

_{2}and crude oil at different temperatures. Table S3: Summarization of some famous empirical correlations.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Sample Availability

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**Figure 1.**Flowchart of proposed MMP prediction model. (i) Construction of the simulation system, (ii) Extracting number density data after MD simulation, (iii) Determination of initial miscible time, (iv) Reconfirmation of initial miscible time, (v) Processing data from initial miscible time to the end, (vi) Processing data from P1 to P6 at T, (vii) Acquisition of MMP.

**Figure 2.**Construction of the simulation system. (

**a**) CO

_{2}phase. (

**b**) Crude oil phase. (

**c**) Initial simulation box. (

**d**) Integral of CO

_{2}/crude oil molecules passing through the initial phase interface.

**Figure 3.**The number of CO

_{2}atoms passing through the initial interface (

**a**) and its first–order variance (

**b**) with time evolution (333 K, 10 MPa).

**Table 1.**The ratio of CO

_{2}and crude oil atoms passing through the initial interface to their respective totals.

CO_{2} | Crude Oil | |
---|---|---|

10 MPa | 0.0292 | 0.0300 |

15 MPa | 0.0231 | 0.0236 |

20 MPa | 0.0219 | 0.0221 |

25 MPa | 0.0216 | 0.0217 |

30 MPa | 0.0204 | 0.0207 |

35 MPa | 0.0205 | 0.0208 |

333 K | 343 K | 353 K | 363 K | 373 K | |
---|---|---|---|---|---|

10 MPa | 4.0 | 5.0 | 3.5 | 4.0 | 3.0 |

15 MPa | 4.5 | 6.0 | 3.5 | 3.0 | 2.5 |

20 MPa | 4.5 | 5.0 | 4.0 | 3.0 | 3.0 |

25 MPa | 4.0 | 3.5 | 4.0 | 3.0 | 3.5 |

30 MPa | 3.5 | 4.0 | 4.0 | 3.0 | 4.0 |

35 MPa | 4.5 | 4.0 | 4.5 | 3.5 | 4.0 |

CO_{2} | Crude Oil | |
---|---|---|

333 K | 20.31 | 20.21 |

343 K | 21.08 | 20.89 |

353 K | 22.12 | 22.36 |

363 K | 24.43 | 23.84 |

373 K | 26.25 | 24.52 |

**Table 4.**Summary of MMP (MPa) and relative error predicted by experimental and different empirical correlations.

Model | Number of Parameters | Predicted MMP (MPa) | Relative Error (%) |
---|---|---|---|

Yu et al. [51] | - | 22.75 | - |

CO_{2} (this study) | 1 | 19.63 | 13.71 |

Crude Oil (this study) | 1 | 20.81 | 8.53 |

Lee [52] | 1 | 20.84 | 8.32 |

Alston et al. [53] | 4 | 19.72 | 13.22 |

Shokir [54] | 8 | 20.03 | 11.89 |

Emera and Sarma [25] | 2 | 30.11 | 32.44 |

Cronquist [55] | 3 | 26.59 | 16.96 |

Glaso [56] | 2 | 27.60 | 21.41 |

Yellig and Metcalfe [57] | 1 | 16.55 | 27.18 |

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**MDPI and ACS Style**

Li, D.; Xie, S.; Li, X.; Zhang, Y.; Zhang, H.; Yuan, S.
Determination of Minimum Miscibility Pressure of CO_{2}–Oil System: A Molecular Dynamics Study. *Molecules* **2021**, *26*, 4983.
https://doi.org/10.3390/molecules26164983

**AMA Style**

Li D, Xie S, Li X, Zhang Y, Zhang H, Yuan S.
Determination of Minimum Miscibility Pressure of CO_{2}–Oil System: A Molecular Dynamics Study. *Molecules*. 2021; 26(16):4983.
https://doi.org/10.3390/molecules26164983

**Chicago/Turabian Style**

Li, Ding, Shuixiang Xie, Xiangliang Li, Yinghua Zhang, Heng Zhang, and Shiling Yuan.
2021. "Determination of Minimum Miscibility Pressure of CO_{2}–Oil System: A Molecular Dynamics Study" *Molecules* 26, no. 16: 4983.
https://doi.org/10.3390/molecules26164983