Investigation of two-phase flow mechanism at pore scale using the phase field method
LIU Xianshan1, 2, SUN Meng1, CAO Yiting1, YANG Wenyuan1, DAI Yuhang1, CHEN Shunshun1, LIU Xinqian1
(1. School of Civil Engineering, Chongqing University, Chongqing 400045, China; 2. State Key Laboratory of Safety and Resilience of Civil Engineering in Mountain Area, Chongqing 400045, China)
Abstract：Regarding the extraction of unconventional shale oil, in-depth investigations of two-phase flow patterns are crucial for describing residual oil content, displacement efficiency, and ultimate recovery. Using a pore-scale rock as a case study, a two-phase flow model has been developed based on phase-field theory and the Navier-Stokes equations to simulate the water-oil two-phase flow process, influenced by pore-throat size and structural wettability under specified flow velocities. The results indicate that variations in pore-throat size inversely correlate with the advancement of the leading-edge positions of the water-oil two-phase interfaces on both sides. It is observed that dominant flow channels form within the pores, with internal flow velocity being inversely proportional to pore size. Moreover, the pressure difference distribution in small-pore-throat structures is considerably greater, while the average pressure change at the inlet gradually diminishes and stabilizes. The stabilization times for both average inlet pressure and leading-edge position are consistent. As the pore-throat size decreases, displacement efficiency within the pores progressively increases, although it deviates from stable displacement. Additionally, variations in pore structure wettability result in the advancement speed of the leading-edge positions being directly proportional to contact angle size, and the central two-phase interface exhibits irregular capillary fingering characteristics; however, final displacement saturation is inversely proportional to contact angle size. Furthermore, the initial pore pressure distribution is uniform, and the pressure gradient at the two-phase interface increases as wettability weakens, particularly with the average pressure change at the inlet gradually diminishing and stabilizing. The advancement speed of the displacement front increases with larger contact angle sizes, and displacement within the pores is significantly influenced by capillary effects, especially for a wetting angle of 30°, leading to an extensive displacement range of the two-phase interface that affects fingering on both sides. These investigations elucidate the water-oil flow mechanism during unconventional shale oil reservoir extraction, providing a scientific basis for optimizing efficient development strategies.
刘先珊1，2*，孙 梦1，曹伊婷1，杨文远1，代宇航1，陈顺顺1，刘新谦1. 基于相场法孔隙介质两相流体流动特性研究[J]. 岩石力学与工程学报, 2026, 45(5): 1461-1476.
LIU Xianshan1, 2, SUN Meng1, CAO Yiting1, YANG Wenyuan1, DAI Yuhang1, CHEN Shunshun1, LIU Xinqian1. Investigation of two-phase flow mechanism at pore scale using the phase field method. , 2026, 45(5): 1461-1476.
[1] 曹博涵. 全球油气勘探开发趋势及对我国油气行业的启示[J]. 当代石油石化，2023，31(1)：31–37.(CAO Bohan. Global oil and gas E&P trend and implications to China[J]. Petroleum and Petrochemical Today，2023，31(1)：31–37.(in Chinese))
[2] 杜金虎，胡素云，庞正炼，等. 中国陆相页岩油类型、潜力及前景[J]. 中国石油勘探，2019，24(5)：560–568.(DU Jinhu，HU Suyun，PANG Zhenglian，et al. The types，potentials and prospects of continental shale oil in China[J]. China Petroleum Exploration，2019，24(5)：560–568.(in Chinese))
[3] ROSS D J K，MARC BUSTIN R. The importance of shale composition and pore structure upon gas storage potential of shale gas reservoirs[J]. Marine and Petroleum Geology，2009，26(6)：916–927.
[4] 邹才能，杨 智，崔景伟，等. 页岩油形成机制、地质特征及发展对策[J]. 石油勘探与开发，2013，40(1)：14–26.(ZOU Caineng，YANG Zhi，CUI Jingwei，et al. Formation mechanism，geological characteristics and development strategy of nonmarine shale oil in China[J]. China Petroleum Exploration，2013，40(1)：14–26.(in Chinese))
[5] LENORMAND R，TOUBOUL E，ZARCONE C. Numerical models and experiments on immiscible displacements in porous media[J]. Journal of Fluid Mechanics. 1988，189：165–187.
[6] ZHANG C，OOSTROM M，WIETSMA T W，et al. Influence of viscous and capillary forces on immiscible fluid displacement：Pore-scale experimental study in a water-wet micromodel demonstrating viscous and capillary fingering[J]. Energy and Fuels，2011，25(8)：3 493–3 505.
[7] 朱维耀，陈 震，尚新春. 非常规油气藏多场耦合渗流理论研究进展[J]. 工程科学学报，2023，45(6)：1 045–1 056.(ZHU Weiyao，CHEN Zhen，SHANG Xinchun. Multiphysical field coupling in unconventional oil and gas reservoirs[J]. Chinese Journal of Engineering，2023，45(6)：1 045–1 056.(in Chinese))
[8] WEI H，ZHU X，LIU X，et al. Pore-scale study of drainage processes in porous media with various structural heterogeneity[J]. International Communications in Heat and Mass Transfer，2022，132(0)：105914.
[9] ZHAO Y，XI R，YANG L，et al. Influence of two-phase displacement characteristics on the storage efficiency and security of geological carbon storage[J]. Geoenergy Science and Engineering，2023，226：211773.
[10] 魏鹳举，胡 冉，廖 震，等. 湿润性对孔隙介质两相渗流驱替效率的影响[J]. 力学学报，2021，53(4)：1 008–1 017.(WEI Guanju，HU Ran，LIAO Zhen，et al. Effects of wettability on displacement efficiency of two-phase flow in porous media[J]. Chinese Journal of Theoretical and Applied Mechanics，2021，53(4)：1 008–1 017.(in Chinese))
[11] COTTIN C，BODIGUEL H，COLIN A. Drainage in two-dimensional porous media：From capillary fingering to viscous flow[J]. Physical Review E，2010，82(4)：046315.
[12] GONG W，LIU J. Effect of wettability heterogeneity on water-gas two-phase displacement behavior in a complex pore structure by phase-field model[J]. Energies，2022，15(20)：7 658.
[13] BHARDWAJ S，DALAL A，MUKHERJEE P P. Mesoscale understanding of capillarity driven two-phase flow in a packed bed architecture[J]. International Journal of Heat and Mass Transfer，2019，136：116–127.
[14] LAN T，HU R，YANG Z，CHEN Y F. A pore filling-based model to predict quasi-static displacement patterns in porous media with pore size gradient[J]. Frontiers in Physics，2022，10：993398.
[15] SHAN F，CHAI Z，SHI B，et al. The optimal displacement of immiscible two-phase fluids in a pore doublet[J]. Physics of Fluids，2023，35(5)：053332.
[16] TANG H，JIA C，LU H，et al. Numerical simulation of residual oil distribution characteristic of carbonate reservoir after water flooding[J]. Frontiers in Earth Science，2024，12：1395483.
[17] 谢驰宇，张建影，王沫然. 多相非牛顿流体驱替过程的格子Boltzmann模拟[J]. 计算物理，2016，33(2)：147–155.(XIE Chiyu，ZHANG Jianying，WANG Moran. Lattice boltzmann modeling of non-newtonian multiphase fluid displacement[J]. Chinese Journal of Computational Physics，2016，33(2)：147–155.(in Chinese))
[18] GUEYFFIER D，LI J，NADIM A，et al. Volume-of-fluid interface tracking with smoothed surface stress methods for three-dimensional flows[J]. Journal of Computational Physics，1999，152(2)：423–456.
[19] 姜水生，赵万东，张 莹，等. 孔隙尺度下超临界CO2驱水两相流数值模拟[J]. 化工进展，2017，36(11)：3 955–3 962.(JIANG Shuisheng，ZHAO Wandong，ZHANG Ying，et al. Pore-scale two-phase numerical simulation of supercritical carbon dioxide displacement of water[J]. Chemical Industry and Engineering Progress，2017，36(11)：3 955–3 962.(in Chinese))
[20] 杨永飞，王金雷，王建忠，等. 基于VOF方法的超临界二氧化碳——水两相流动孔隙尺度数值模拟[J]. 天然气工业，2023，43(3)：69–77.(YANG Yongfei，WANG Jinlei，WANG Jianzhong，et al. Pore-scale numerical simulation of supercritical CO2-brine two-phase flow based on VOF method[J]. Natural Gas Industry，2023，43(3)：69–77.(in Chinese))
[21] 魏祥祥，冯其红，张先敏，等. 基于VOF方法的水驱油藏孔隙尺度剩余油分布状态研究[J]. 计算物理，2021，38(5)：573–584.(WEI Xiangxiang，FENG Qihong，ZHANG Xianmin，et al. Distribution of remaining oil in water flooding at pore scale：volume of fluid method[J]. Chinese Journal of Computational Physics，2021，38(5)：573–584.(in Chinese))
[22] 赵玉龙，周厚杰，李洪玺，等. 基于水平集方法的低渗砂岩数字岩心气水两相渗流模拟[J]. 计算物理，2021，38(5)：585–594.(ZHAO Yulong，ZHOU Houjie，LI Hongxi，et al. Gas-water two-phase flow simulation of low-permeability sandstone digital rock：Level-set method[J]. Chinese Journal of Computational Physics，2021，38(5)：585–594.(in Chinese))
[23] ZHU G，YAO J，LI A，et al. Pore-scale investigation of carbon dioxide-enhanced oil recovery[J]. Energy and Fuels，2017，31(5)：5 324–5 332.
[24] 左伟芹，崔佩雯，刘彦伟，等. 基于相场法的非等温气–水两相驱替特征研究[J]. 力学学报，2025，57(1)：261–272.(ZUO Weiqin，CUI Peiwen，LIU Yanwei，et al. Characterisation of non-isothermal gas-water displacement based on the phase field method[J]. Chinese Journal of Theoretical and Applied Mechanics，2025，57(1)：261–272.(in Chinese))
[25] ROKHFOROUZ M R，AKHLAGHI AMIRI H A. Effects of grain size and shape distribution on pore-scale numerical simulation of two-phase flow in a heterogeneous porous medium[J]. Advances in Water Resources，2019，124：84–95.
[26] SHEN J. Modeling and numerical approximation of two-phase incompressible flows by a phase-field approach[M]. Singapore：Multiscale Modeling and Analysis for Materials Simulation，2012：147–195.
[27] HUANG H，LU X Y. Relative permeabilities and coupling effects in steady-state gas-liquid flow in porous media：A lattice boltzmann study[J]. Physics of Fluids，2009，21(9)：092104.
[28] 王 雷，窦之林，林 涛，等. 缝洞型油藏注水驱油可视化物理模拟研究[J]. 西南石油大学学报：自然科学版，2011，33(2)：121–124.(WANG Lei，DOU Zhilin，LIN Tao，et al. Study on the visual modeling of water flooding in carbonate fracture-cavity reservoir[J]. Journal of Southwest Petroleum University：Science and Technology，2011，33(2)：121–124.(in Chinese))
[29] ZACHAROUDIOU I，BOEK E S. Capillary filling and haines jump dynamics using free energy lattice boltzmann simulations[J]. Advances in Water Resources，2016，92：43–56.
[30] 刘先珊，孙 梦，郑志伟，等.复杂孔隙介质两相驱替模式及驱替效率研究[J]. 岩土力学，2025，46(8)：2 363–2 375.(LIU Xianshan，SUN Meng，ZHENG Zhiwei，et al. Modes and efficiency of two-phase displacement flow in complex pores[J]. Rock and Soil Mechanics，2025，46(8)：2 363–2 375.(in Chinese))
[31] PAK T，RABBANI H S，RAEINI A Q，et al. Effects of the pore morphology on multiphase fluid displacement in porous media—A high-resolution modeling investigation[J]. ACS Omega，2023，8(4)：3 889–3 895.
[32] CHEN K，LIU P，WANG W，et al. Effects of capillary and viscous forces on two-phase fluid displacement in the microfluidic model[J]. Energy and Fuels，2023，37(22)：17 263–17 276.
2026, Vol. 45 
