## 4 Conclusions  
This paper presents a multiscale compositional numerical simulation method that incorporates capillary forces in phase equilibrium calculations. A one-dimensional model is used for validation, demonstrating the method's accuracy and advancement in analyzing the impact of capillary forces on phase equilibrium and tight oil recovery.  
1. Phase behavior in tight oil reservoirs is influenced by pore size and capillary forces, which traditional equations of state fail to capture in nanopores. This paper introduces capillary forces into traditional equations of state and compositional numerical simulations, improving phase equilibrium calculations using MRST.
2. To enhance iterative solution efficiency, a sequential solution format is employed, leveraging the parallel advantages of the improved multiscale finite volume method for pressure equation resolution. Numerical validation with a one-dimensional model confirms that this method enhances solution efficiency without compromising accuracy.
3. Using the proposed multiscale compositional simulation method, the impact of capillary forces on phase equilibrium and tight oil recovery is analyzed. Sensitivity analysis shows that smaller pore radii lead to more pronounced capillary effects, with a decrease in bubble point and dew point lines, and an increase in calculation iterations. For tight oil recovery, capillary forces generally result in higher cumulative oil production and improved recovery rates for heavy components. Capillary effects  
Figure 14: Oil saturation distribution at different stages across various scenarios.  
Figure 15: Oil saturation distribution focusing on the cell marked by a red star in Figure 9 at different stages across various scenarios.  
lower bubble point pressure, suppress gas stripping and increase oil saturation while decreasing gas saturation.
* Compared to traditional numerical simulators, the proposed multiscale compositional method, which accounts for capillary forces, better characterizes phase behavior in tight oil reservoirs. This approach is significant for PVT simulation, development of numerical simulations, and forecasting development strategies in tight oil reservoirs.  
In summary, the proposed model advances numerical simulation research for tight oil reservoirs, though several challenges remain. First, this study examines the reservoir-scale impact of capillary forces on phase behavior under an instantaneous equilibrium assumption, without addressing nanopore kinetic limitations and complex flow mechanisms. Second, large-scale physical experiments could help overcome the validation constraints of commercial simulators. Finally, although MATLAB Reservoir Simulation Toolbox (MRST 2024b) offer significant community and ecosystem potential, incorporating additional open-source high-performance components may further promote the development of large-scale 3D tight oil reservoir simulators.  
Conceptualization, J.W. and S.W.; methodology, J.W.; software, W.C.; validation, L.W., J.W., and S.W.; formal analysis, R.Z.; investigation, W.C. and H.Y.; resources, Q.S.; data curation, L.W. and H.Y.; writing--original draft preparation, J.W.; writing--review and editing, Q.S.; visualization, R.Z.; supervision, S.W.; project administration, S.W.; funding acquisition, S.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (Grant No. 5237405 and U24B2037), the Science and Technology Project of China National Petroleum Corporation (2021 ZG12, 2023D)[8405).  
Not applicable.  
Data Availability Statement: Data are contained within the article.  
The authors would like to sincerely thank those who have contributed to this research.  
[PERSON] was employed by PetroChina Company Limited. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.