Wellbore-reservoir coupled simulation study for CO₂ flooding in oil reservoirs

Bujie Ding
China Oilfield Services Limited, Sanhe 065201, China
Huanying Ma
China Oilfield Services Limited, Sanhe 065201, China
Jincang Li
China Oilfield Services Limited, Sanhe 065201, China
Kaifang Jin
China Oilfield Services Limited, Sanhe 065201, China
Tao Zou
China Oilfield Services Limited, Sanhe 065201, China
Hui Zhao
School of Petroleum Engineering, Yangtze University, Wuhan 430100, China; State Key Laboratory of Low-Carbon Catalysis and Carbon Dioxide Utilization, Yangtze University, Wuhan 430100, China
Jiaxu Liu
School of Petroleum Engineering, Yangtze University, Wuhan 430100, China; State Key Laboratory of Low-Carbon Catalysis and Carbon Dioxide Utilization, Yangtze University, Wuhan 430100, China
Siyuan Chen
School of Petroleum Engineering, Yangtze University, Wuhan 430100, China; State Key Laboratory of Low-Carbon Catalysis and Carbon Dioxide Utilization, Yangtze University, Wuhan 430100, China
Xi Ouyang
School of Petroleum Engineering, Yangtze University, Wuhan 430100, China; State Key Laboratory of Low-Carbon Catalysis and Carbon Dioxide Utilization, Yangtze University, Wuhan 430100, China
Xiang Rao
School of Petroleum Engineering, Yangtze University, Wuhan 430100, China; State Key Laboratory of Low-Carbon Catalysis and Carbon Dioxide Utilization, Yangtze University, Wuhan 430100, China; School of Computer Science, Yangtze University, Wuhan 430100, China

Article ID: 4667

Keywords: CO₂ flooding; wellbore-reservoir coupling; tNavigator; high-permeability channel; VFP table

Abstract

CO₂ flooding can simultaneously enhance oil recovery and enable geological carbon storage. This study develops a tNavigator-based coupled wellbore-reservoir CO₂ flooding model to examine tubing-head-to-downhole pressure conversion and early gas breakthrough through a high-permeability channel. A three-dimensional isothermal compositional model represents reservoir flow, while vertical flow performance (VFP) tables constructed using the Beggs-Brill correlation describe wellbore multiphase flow and pressure conversion. The coupled VFP relationships, well flow equations, and reservoir mass-conservation equations are solved using the adaptive implicit method (AIM) implemented in tNavigator, enabling bidirectional interactions among wellbore pressure variation, downhole boundary conditions, and reservoir dynamic parameters. A continuous high-permeability channel between injectors and producers is incorporated to characterize reservoir heterogeneity. Simulations under fixed injection rate and fixed tubing-head pressure conditions are conducted to analyze the influences of injection and production rates, porosity and streak permeability on CO₂ migration and flooding performance. The results show that injection and liquid production rates dominate the inter-well pressure difference and control gas breakthrough. Reservoir porosity primarily governs reservoir storage and pressure buffering capacity, while streak permeability determines CO₂ preferential migration velocity. Under tubing-head pressure constraints, actual injection and production performances are co-regulated by tubing-head pressure limits, wellbore pressure loss and reservoir injectivity/deliverability. The proposed model provides a numerical framework for investigating wellbore-reservoir interactions and gas-channeling risks in heterogeneous reservoirs with high-permeability channels. Quantitative validation against field measurements or controlled experimental data will be undertaken in future work.

Published

2026-08-27

How to Cite

Ding, B., Ma, H., Li, J., Jin, K., Zou, T., Zhao, H., Liu, J., Chen, S., Ouyang, X., & Rao, X. (2026). Wellbore-reservoir coupled simulation study for CO₂ flooding in oil reservoirs. Advances in Differential Equations and Control Processes, 33(3). https://doi.org/10.59400/adecp4667

Download Citation

Issue

Vol. 33 No. 3 (2026): In Progress

Section

Article

This work is licensed under a Creative Commons Attribution 4.0 International License.

References

[1]Metz B, Davidson O, de Coninck HC, et al. IPCC Special Report on Carbon Dioxide Capture and Storage. Cambridge University Press; 2005.

[2]Bachu S. CO₂ storage in geological media: Role, means, status and barriers to deployment. Progress in Energy and Combustion Science. 2008; 34(2): 254–273. doi: 10.1016/j.pecs.2007.10.001

[3]Godec ML, Kuuskraa VA, DiPietro P. Opportunities for using anthropogenic CO₂ for enhanced oil recovery and CO₂ storage. Energy & Fuels. 2013; 27(8): 4183–4189. doi: 10.1021/ef302040u

[4]Núñez-López V, Moskal E. Potential of CO₂-EOR for near-term decarbonization. Frontiers in Climate. 2019; 1: 5. doi: 10.3389/fclim.2019.00005

[5]Zhu Y, Wu Z, Ren Y, et al. Unraveling adsorption and pore plugging mechanisms of multi-component shale oil in organic and inorganic nanopores: A molecular dynamics study. Fuel. 2026; 427: 140139. doi: 10.1016/j.fuel.2026.140139

[6]Sikanyika EW, Wu Z, Mbarouk MS, et al. Numerical simulation of the oil production performance of different well patterns with water injection. Energies. 2023; 16(1): 91. doi: 10.3390/en16010091

[7]Zhu Q, Wu K, Guo S, et al. Pore-scale investigation of CO₂-oil miscible flooding in tight reservoir. Applied Energy. 2024; 368: 123439. doi: 10.1016/j.apenergy.2024.123439

[8]Wang Z, Li S, Wei Y, et al. Investigation of oil-based CO₂ foam EOR and carbon mitigation in a 2D visualization physical model: Effects of different injection strategies. Energy. 2024; 313: 133800. doi: 10.1016/j.energy.2024.133800

[9]Rao X. The first application of quantum computing algorithm in streamline-based simulation of water-flooding reservoirs. In: Proceedings of the Abu Dhabi International Petroleum Exhibition and Conference; 4–7 November 2024; Abu Dhabi, United Arab Emirates. doi: 10.2118/221850-MS

[10]Rao X, He X, Kwak H, et al. A hybrid method combining mimetic finite difference and discontinuous Galerkin for two-phase reservoir flow problems. International Journal for Numerical Methods in Fluids. 2025; 97(4): 484–502. doi: 10.1002/fld.5367

[11]Sheng JJ. Enhanced oil recovery in shale reservoirs by gas injection. Journal of Natural Gas Science and Engineering. 2015; 22: 252–259. doi: 10.1016/j.jngse.2014.12.002

[12]Song Z, Song Y, Li Y, et al. A critical review of CO₂ enhanced oil recovery in tight oil reservoirs of North America and China. Fuel. 2020; 276: 118006. doi: 10.1016/j.fuel.2020.118006

[13]Holm LW, Josendal VA. Mechanisms of oil displacement by carbon dioxide. Journal of Petroleum Technology. 1974; 26(12): 1427–1438. doi: 10.2118/4736-PA

[14]Stalkup Jr FI. Miscible Displacement. Society of Petroleum Engineers; 1983.

[15]Orr Jr FM. Theory of Gas Injection Processes. Tie-Line Publications; 2007.

[16]Kumar N, Augusto Sampaio M, Ojha K, et al. Fundamental aspects, mechanisms and emerging possibilities of CO₂ miscible flooding in enhanced oil recovery: A review. Fuel. 2022; 330: 125633. doi: 10.1016/j.fuel.2022.125633

[17]Wang T, Wang L, Meng X, et al. Key parameters and dominant EOR mechanism of CO₂ miscible flooding applied in low-permeability oil reservoirs. Geoenergy Science and Engineering. 2023; 225: 211724. doi: 10.1016/j.geoen.2023.211724

[18]Ren J, Xiao W, Pu W, et al. Characterization of CO₂ miscible/immiscible flooding in low-permeability sandstones using NMR and the VOF simulation method. Energy. 2024; 297: 131211. doi: 10.1016/j.energy.2024.131211

[19]Song R, Tang Y, Wang Y, et al. Pore-scale numerical simulation of CO₂-oil two-phase flow: A multiple-parameter analysis based on phase-field method. Energies. 2023; 16(1): 82. doi: 10.3390/en16010082

[20]Chi J, Ju B, Wang J, et al. A novel numerical simulation of CO₂ immiscible flooding coupled with viscosity and starting pressure gradient modeling in ultra-low permeability reservoir. Frontiers of Earth Science. 2023; 17: 884–898. doi: 10.1007/s11707-023-0085-y

[21]Rao X, He X, Xu Y, et al. Numerical simulation of carbon dioxide flooding in fractured reservoirs using generic projection-based embedded discrete fracture model. Physics of Fluids. 2024; 36(10): 106601. doi: 10.1063/5.0225059

[22]Rao X, Luo C, He X, et al. An efficient quantum neural network model for prediction of carbon dioxide (CO₂) sequestration in saline aquifers. In: Proceedings of the Abu Dhabi International Petroleum Exhibition and Conference; 4–7 November 2024; Abu Dhabi, United Arab Emirates. doi: 10.2118/222257-MS

[23]Peng DY, Robinson DB. A new two-constant equation of state. Industrial & Engineering Chemistry Fundamentals. 1976; 15(1): 59–64. doi: 10.1021/i160057a011

[24]Coats KH. An equation of state compositional model. Society of Petroleum Engineers Journal. 1980; 20(5): 363–376. doi: 10.2118/8284-PA

[25]Nghiem LX, Fong DK, Aziz K. Compositional modeling with an equation of state. Society of Petroleum Engineers Journal. 1981; 21(6): 687–698. doi: 10.2118/9306-PA

[26]Young LC, Stephenson RE. A generalized compositional approach for reservoir simulation. Society of Petroleum Engineers Journal. 1983; 23(5): 727–742. doi: 10.2118/10516-PA

[27]Beggs HD, Brill JP. A study of two-phase flow in inclined pipes. Journal of Petroleum Technology. 1973; 25(5): 607–617. doi: 10.2118/4007-PA

[28]Hasan AR, Kabir CS, Wang X. Development and application of a wellbore/reservoir simulator for testing oil wells. Society of Petroleum Engineers Formation Evaluation. 1997; 12(3): 182–188. doi: 10.2118/29892-PA

[29]da Silva DVA, Jansen JD. A review of coupled dynamic well-reservoir simulation. IFAC-PapersOnLine. 2015; 48(6): 236–241. doi: 10.1016/j.ifacol.2015.08.037

[30]Peng L, Han G, Chen Z, et al. Dynamically coupled reservoir and wellbore simulation research in two-phase flow systems: A critical review. Processes. 2022; 10(9): 1778. doi: 10.3390/pr10091778

[31]Abdelaal M, Zeidouni M. Coupled wellbore-reservoir modelling to evaluate CO₂ injection rate distribution over thick multilayer storage zones. International Journal of Greenhouse Gas Control. 2023; 129: 103987. doi: 10.1016/j.ijggc.2023.103987

[32]Zamani N, Oldenburg CM, Solbakken J, et al. CO₂ flow modeling in a coupled wellbore and aquifer system: Details of pressure, temperature, and dry-out. International Journal of Greenhouse Gas Control. 2024; 132: 104067. doi: 10.1016/j.ijggc.2024.104067

[33]Tavagh Mohammadi B, Jahanbani Ghahfarokhi A, Grimstad AA. A review of modeling approaches for CO₂ injection into depleted gas reservoirs: Coupling transient wellbore and reservoir dynamics. International Journal of Greenhouse Gas Control. 2025; 145: 104406. doi: 10.1016/j.ijggc.2025.104406

[34]Koval EJ. A method for predicting the performance of unstable miscible displacement in heterogeneous media. Society of Petroleum Engineers Journal. 1963; 3(2): 145–154. doi: 10.2118/450-PA

[35]Luo J, Hou Z, Feng G, et al. Effect of reservoir heterogeneity on CO₂ flooding in tight oil reservoirs. Energies. 2022; 15(9): 3015. doi: 10.3390/en15093015

[36]Khan MY, Mandal A. The impact of permeability heterogeneity on water-alternating-gas displacement in highly stratified heterogeneous reservoirs. Journal of Petroleum Exploration and Production Technology. 2022; 12(3): 871–897. doi: 10.1007/s13202-021-01347-3

[37]Li J, Cui C, Wu Z, et al. Study on the migration law of CO₂ miscible flooding front and the quantitative identification and characterization of gas channeling. Journal of Petroleum Science and Engineering. 2022; 218: 110970. doi: 10.1016/j.petrol.2022.110970

[38]Zhang L, Li C, Zhang Y, et al. CO₂-EOR and storage in a low-permeability oil reservoir: Optimization of CO₂ balanced displacement from lab experiment to numerical simulation. Geoenergy Science and Engineering. 2024; 243: 213325. doi: 10.1016/j.geoen.2024.213325

[39]Li Z, Xu T, Tian H, et al. The impacts of reservoir heterogeneities on the CO₂-enhanced oil recovery process—A case study of Daqingzijing Block in Jilin Oilfield, China. Energies. 2024; 17(23): 6128. doi: 10.3390/en17236128

[40]Zhang YQ, Yang SL, Bi LF, et al. A technical review of CO₂ flooding sweep-characteristics research advance and sweep-extend technology. Petroleum Science. 2025; 22(1): 255–276. doi: 10.1016/j.petsci.2024.09.005

Early fault signals of the rolling bearing in the rotor are weak and present the characteristics of non-periodic and non-stationary; it is more difficult to carry out fault diagnosis on it. In this regard, this paper proposes a weak rolling bearing fault diagnosis algorithm based on whale optimization algorithm, simplistic geometry mode decomposition, and maximum correlated kurtosis deconvolution (WOA-SGMD-MCKD). Firstly, the vibration signal of the rotor platform is obtained, and the Symmetric Geometric Mode Decomposition (SGMD) is used to reconstruct the vibration signal. To obtain the best decomposition effect of the SGMD and overcome modal aliasing, the Whale Optimization Algorithm (WOA) is used to optimize the embedding dimension. Secondly, for the reconstructed vibration signal, the Maximum Correlated Kurtosis Deconvolution (MCKD) is used to extract its impulse component, and the WOA is used to optimize the filter length and deconvolution period of the MCKD so that the frequency envelope spectrum of the vibration signal can be obtained, which can provide the basis for the fault diagnosis of rolling bearings. Finally, the effectiveness and feasibility of the algorithm proposed are verified by a non-periodic and non-stationary simulation platform and rotor maneuvering platform in this paper.

Numerical solution of a 3D mathematical model for the progression of tumor angiogenic factor in a tissue

In this work, the movement of tumor angiogenic factor in a three-dimensional tissue is obtained by the Method of Lines. This method transforms a partial differential equation into a system of ordinary differential equations together with the initial and boundary conditions. The more the number of lines is increased, the more the accuracy of the method increases. This method results in very accurate numerical solutions for linear and non-linear problems in contrast with other existing methods. We present Matlab-generated figures, which are the movement of tumor angiogenic factor in porous medium and explain the biological importance of this progression. The computer codes are also provided.

Mathematical modelling and controllability analysis of fractional order coal mill pulverizer model

This paper investigates the controllability of nonlinear dynamical systems and their applications, with a focus on fractional-order systems and coal mill models. A novel theorem is proposed, providing sufficient conditions for controllability, including constraints on the steering operator and nonlinear perturbation bounds. The theorem establishes the existence of a contraction mapping for the nonlinear operator, enabling effective control strategies for fractional systems. The methodology is demonstrated through rigorous proof and supported by an iterative algorithm for controller design. Additionally, the controllability of a coal mill system represented as a nonlinear differential system, is analyzed. The findings present new insights into the interplay of fractional dynamics and nonlinear systems, offering practical solutions for real-world control problems.