*3.7. Relationships between T<sup>R</sup> and MMP*

However, the real situation of each oil reservoir varies, and the composition of injected gases is also different in EOR, so it is meaningless and almost impossible to obtain the accurate relationship between each influence factor and MMP. For a certain influencing factor, we can explore the qualitative relationship between the factor and MMP. Oil reservoir temperature (TR) is usually regarded as one of the most important factors affecting MMP [58]. Exploring the influence of T<sup>R</sup> 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 CO2/n-hexadecane (C16H34) and CO2/liquid paraffin systems. Their experimental data showed that the measured MMP values of two CO2–oil systems increased linearly with TR. Furthermore, Mostafa et al. found that the MMP is a linear function of temperature with a slope of 0.15 MPa/K [60].

The modeling method of this study shows that the relationship between T<sup>R</sup> 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<sup>2</sup> and crude oil, the change in T<sup>R</sup> 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<sup>R</sup> can effectively reduce the solubility of CO<sup>2</sup> in crude oil, which is not conducive to the mixing progress of CO<sup>2</sup> 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**

In this paper, a novel molecular dynamics-based model to determine minimum miscible pressure of CO2–oil system was developed. The model characterized the miscible

state by calculating the ratio of both CO<sup>2</sup> 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 TR. The value is the MMP of TR. In comparison with conventional prediction approaches, the present work proposed a straightforward model to simulate the complex miscibility of CO<sup>2</sup> and crude oil, and the miscible principle was clarified at the molecular scale.

Based on the above studies, the newly proposed model is believed to be reliable for the prediction of MMP. However, there still remain some distinctions when compared to the real situation, which may have a certain impact on the prediction [61]. We have begun to adjust the model to enhance its application. For example, we plan to introduce silica slab and asphaltenes to mimic the real situation of crust and heavy oil, respectively. To sum up, the following conclusions can be drawn:


**Supplementary Materials:** The following are available online. Figure S1: The number of crude oil atoms passing through the initial interface. Figure S2: Acquisition of MMP in different systems. Table S1: The number of CO<sup>2</sup> molecules added in different systems. Table S2: Integrated values of CO<sup>2</sup> and crude oil at different temperatures. Table S3: Summarization of some famous empirical correlations.

**Author Contributions:** Conceptualization, D.L. and H.Z.; methodology, D.L., H.Z. and S.Y.; software, D.L.; validation, D.L., H.Z. and S.Y.; formal analysis, D.L. and H.Z.; investigation, D.L.; resources, S.X., X.L., Y.Z. and S.Y.; data curation, D.L.; writing—original draft preparation, D.L.; writing—review and editing, D.L., H.Z. and S.Y.; visualization, D.L.; supervision, H.Z.; project administration, S.X., X.L. and Y.Z.; funding acquisition, S.Y. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research project was funded by the financial support from the National Science Foundation of China (No. 21573130) and the Youth Innovation Group of Shandong University (No. 2020QNQT018).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study is available upon reasonable request.

**Conflicts of Interest:** The authors declare no conflict of interest.

**Sample Availability:** Samples of the compounds are not available from the authors.
