Review on mesoscopic flow theory in porous media

ZHU Wei-yao; LI Hua; DENG Qing-jun; MA Qi-peng; LIU Ya-jing

doi:10.13374/j.issn2095-9389.2020.11.30.005

Volume 44 Issue 5

May 2022

Turn off MathJax

Article Contents

Article Navigation > Chinese Journal of Engineering > 2022 > 44(5): 951-962

ZHU Wei-yao, LI Hua, DENG Qing-jun, MA Qi-peng, LIU Ya-jing. Review on mesoscopic flow theory in porous media[J]. Chinese Journal of Engineering, 2022, 44(5): 951-962. doi: 10.13374/j.issn2095-9389.2020.11.30.005

Citation:

ZHU Wei-yao, LI Hua, DENG Qing-jun, MA Qi-peng, LIU Ya-jing. Review on mesoscopic flow theory in porous media[J]. Chinese Journal of Engineering, 2022, 44(5): 951-962. doi: 10.13374/j.issn2095-9389.2020.11.30.005

Citation:

PDF( 1475 KB)

Review on mesoscopic flow theory in porous media

doi: 10.13374/j.issn2095-9389.2020.11.30.005

1.
School of Civil and Resource Engineering, University of Science and Technology Beijing, Beijing 100083, China
2.
First Oil Production Plant, Daqing Oilfield, Daqing 163000, China

More Information

Corresponding author: E-mail: weiyaook@sina.com
Received Date: 2020-11-30
Available Online: 2021-01-20
Publish Date: 2022-05-25

Abstract

Abstract

Porous media are widely found in underground rocks, biomimetic, and engineering materials. However, the current flow theory of fluids (liquid and gas, etc.) is incomplete to study flows in small and complex pores, thus a new theory is urgently needed for studying a large number of fluid flows in porous media. The theory of meso-scale flow in porous media is a “mysterious key” to unlock the flow of nano-micron porous media. At present, a large number of fluid flow problems need an immediate solution in porous media such as shale oil and gas development, soil seepage, human capillary network, and carbon nanotube (CNT). With the advancement of world petroleum engineering technology, unconventional oil and gas reservoirs have become the main areas of development in the petroleum industry. There are a large number of nano-scale pores in unconventional oil and gas reservoirs, and the existing macro-statistical methods of Darcy and non-Darcy percolation cannot reveal the nonlinear flow mechanism and effective production mechanism of fluid in mesopores. Thus, it is urgent to carry out theoretical research on meso-flow in porous media to provide a theoretical basis for unconventional oil and gas development. This paper summarizes the research results in this area, including those of the authors. The current research status of fine and meso flow in porous media is summarized from three aspects: (1) theoretical analysis, (2) experimental research, and (3) numerical model, focusing on key issues such as the relationship and characterization of meso-scale fluid flow interface and micro-mechanical properties, meso–macro network simulation, meso-scale fluid (oil/water, gas/water) flow, meso-dynamic mechanism, and mathematical models. On this basis, the importance of the research on the interface effect and meso-mechanical characteristics of fine and micro-scale fluid flow, the nonlinear flow mechanism of the fine and meso-scale fluids, the construction of a mathematical model reflecting the meso-scale flow under the action of micro-forces, and the formation of a network simulation method are introduced. The study provides certain guiding significance for unconventional oil and gas development processes, revealing the meso-causes affecting flow, clarifying the production mechanism under different conditions, and promoting further development of the discipline of seepage mechanics.
- porous media,
- mesoscopic flow,
- interface effect,
- micro force,
- pore network model

FullText(HTML)

References(98)

References

[1]	陶然, 權曉波, 徐建中. 微尺度流動研究中的幾個問題. 工程熱物理學報, 2001, 22(5):575 doi: 10.3321/j.issn:0253-231X.2001.05.015 Tao R, Quan X B, Xu J Z. Several questions in research of micro scale flow. J Eng Thermophys, 2001, 22(5): 575 doi: 10.3321/j.issn:0253-231X.2001.05.015
[2]	陳玉麗, 馬勇, 潘飛, 等. 多尺度復合材料力學研究進展. 固體力學學報, 2018, 39(1):1 Chen Y L, Ma Y, Pan F, et al. Research progress in multi-scale mechanics of composite materials. Chin J Solid Mech, 2018, 39(1): 1
[3]	Zhu W Y, Ma Q P, Song Z Y, et al. The effect of injection pressure on the microscopic migration characteristics by CO₂ flooding in heavy oil reservoirs. Energy Sources Part A, 2019: 1
[4]	朱維耀, 黃延章. 多孔介質對氣-液相變過程的影響. 石油勘探與開發, 1988, 15(1):51 Zhu W Y, Huang Y Z. The effect of porous media on gas-liquid phase behavior. Pet Explor Dev, 1988, 15(1): 51
[5]	Ju Y, Gong W B, Chang W, et al. Effects of pore characteristics on water-oil two-phase displacement in non-homogeneous pore structures: A pore-scale lattice Boltzmann model considering various fluid density ratios. Int J Eng Sci, 2020, 154: 103343 doi: 10.1016/j.ijengsci.2020.103343
[6]	Allen M B III, Behie G A, Trangenstein J A. Multiphase Flow in Porous Media. New York: Springer US, 1988
[7]	Wang Q, Chen X, Jha A N, et al. Natural gas from shale formation?The evolution, evidences and challenges of shale gas revolution in United States. Renewable Sustainable Energy Rev, 2014, 30: 1 doi: 10.1016/j.rser.2013.08.065
[8]	朱維耀, 岳明, 劉昀楓, 等. 中國致密油藏開發理論研究進展. 工程科學學報, 2019, 41(9):1103 Zhu W Y, Yue M, Liu Y F, et al. Research progress on tight oil exploration in China. Chin J Eng, 2019, 41(9): 1103
[9]	王小鋒, 朱維耀, 鄧慶軍, 等. 考慮固液分子作用的多孔介質動態網絡模型. 北京科技大學學報, 2014, 36(2):145 Wang X F, Zhu W Y, Deng Q J, et al. Dynamic network model considering solid-liquid molecule interaction in porous media. J Univ Sci Technol Beijing, 2014, 36(2): 145
[10]	朱維耀, 田英愛, 于明旭, 等. 微圓管中流體的微觀流動機制. 科技導報, 2014, 32(27):23 doi: 10.3981/j.issn.1000-7857.2014.27.003 Zhu W Y, Tian Y A, Yu M X, et al. Mechanism of microscopic fluid flow in microtubes. Sci Technol Rev, 2014, 32(27): 23 doi: 10.3981/j.issn.1000-7857.2014.27.003
[11]	李戰華, 崔海航. 微尺度流動特性. 機械強度, 2001, 23(4):476 doi: 10.3321/j.issn:1001-9669.2001.04.017 Li Z H, Cui H H. Characteristics of micro scale flow. J Mech Strength, 2001, 23(4): 476 doi: 10.3321/j.issn:1001-9669.2001.04.017
[12]	錢曉蓉, 沈宏繼. 微流體動力學研究發展與現狀. 航空精密制造技術, 2005, 41(6):11 doi: 10.3969/j.issn.1003-5451.2005.06.004 Qian X R, Shen H J. Developments on hydrokinetic of microfluidic flow. Aviat Precis Manuf Technol, 2005, 41(6): 11 doi: 10.3969/j.issn.1003-5451.2005.06.004
[13]	Wu P Y, Little W A. Measurement of friction factors for the flow of gases in very fine channels used for microminiature Joule-Thomson refrigerators. Cryogenics, 1983, 23(5): 273 doi: 10.1016/0011-2275(83)90150-9
[14]	Terry S C. A Gas Chromatography System Fabricated on a Silicon Wafer Using Integrated Circuit Technology [Dissertation]. Palo Alto: Stanford University, 1975
[15]	Harley J C, Huang Y F, Bau H H, et al. Gas flow in micro-channels. J Fluid Mech, 1995, 284: 257 doi: 10.1017/S0022112095000358
[16]	Ho C M, Tai Y C. Micro-electro-mechanical-systems (MEMS) and fluid flows. Annu Rev Fluid Mech, 1998, 30(1): 579 doi: 10.1146/annurev.fluid.30.1.579
[17]	Barajas A M, Panton R L. The effects of contact angle on two-phase flow in capillary tubes. Int J Multiph Flow, 1993, 19(2): 337 doi: 10.1016/0301-9322(93)90007-H
[18]	Triplett K A, Ghiaasiaan S M, Abdel-Khalik S I, et al. Gas-liquid two-phase flow in microchannels Part I: Two-phase flow patterns. Int J Multiph Flow, 1999, 25(3): 377 doi: 10.1016/S0301-9322(98)00054-8
[19]	鄧慶軍, 朱維耀, 王小鋒, 等. 多孔介質中微觀力的作用及滲流模型. 北京科技大學學報, 2014, 36(4):415 Deng Q J, Zhu W Y, Wang X F, et al. Seepage model considering micro forces in porous media. J Univ Sci Technol Beijing, 2014, 36(4): 415
[20]	Koplik J, Banavar J R, Willemsen J F. Molecular dynamics of fluid flow at solid surfaces. Phys Fluids A, 1989, 1(5): 781
[21]	Zhu W Y, Li B B, Liu Y J, et al. Solid-liquid interfacial effects on residual oil distribution utilizing three-dimensional micro network models. Energies, 2017, 10(12): 2059 doi: 10.3390/en10122059
[22]	Cai Q, Buts A, Seaton N A, et al. A pore network model for diffusion in nanoporous carbons: Validation by molecular dynamics simulation. Chem Eng Sci, 2008, 63(13): 3319 doi: 10.1016/j.ces.2008.03.032
[23]	Wang S, Feng Q, Javadpour F, et al. Multiscale modeling of shale apparent permeability: an integrated study of molecular dynamics and pore network model // SPE Annual Technical Conference and Exhibition. San Antonio, 2017: SPE-187286-MS
[24]	李軼凡. 低表面張力液體下的粗糙表面固液界面邊界滑移的研究[學位論文]. 哈爾濱: 哈爾濱工業大學, 2018 Li Y F. Study on Boundary Slip at the Solid-Liquid Interface of the Rough Surfaces Immersed in Liquids with Low Surface Tension [Dissertation]. Harbin: Harbin Institute of Technology, 2018
[25]	Hubbert M K. Darcy’s law and the field equations of the flow of underground fluids. Int Assoc Sci Hydrol Bull, 1957, 2(1): 222
[26]	Allen M B. Basic Mechanics of Oil Reservoir Flows. New York: Springer Press, 1988
[27]	Hu G Q, Li D Q. Multiscale phenomena in microfluidics and nanofluidics. Chem Eng Sci, 2007, 62(13): 3443 doi: 10.1016/j.ces.2006.11.058
[28]	Civan F. A triple-mechanism fractal model with hydraulic dispersion for gas permeation in tight reservoirs // SPE International Petroleum Conference and Exhibition in Mexico. Villahermosa, 2002: SPE-74368-MS
[29]	Roy S, Raju R, Chuang H F, et al. Modeling gas flow through microchannels and nanopores. J Appl Phys, 2003, 93(8): 4870 doi: 10.1063/1.1559936
[30]	李戰華, 鄭旭. 微納米尺度流動實驗研究的問題與進展. 實驗流體力學, 2014, 28(3):1 doi: 10.11729/syltlx20140018 Li Z H, Zheng X. The problems and progress in the experimental study of micro/nano-scale flow. J Exp Fluid Mech, 2014, 28(3): 1 doi: 10.11729/syltlx20140018
[31]	Wang J L, Song H Q, Zhu W Y, et al. Flow characteristics and a permeability model in nanoporous media with solid-liquid interfacial effects. Interpretation, 2017, 5(1): SB1 doi: 10.1190/INT-2016-0009.1
[32]	Keenan J H, Neumann E P. Measurements of friction in a pipe for subsonic and supersonic flow of air. J Appl Mech, 1946, 13(2): A91 doi: 10.1115/1.4009532
[33]	Pfitzner J. Poiseuille and his law. Anaesthesia, 1976, 31(2): 273 doi: 10.1111/j.1365-2044.1976.tb11804.x
[34]	張雪齡, 朱維耀, 蔡強, 等. 考慮固壁作用力的微可壓縮流體納微米圓管流動分析. 北京科技大學學報, 2014, 36(5):569 Zhang X L, Zhu W Y, Cai Q, et al. Analysis of weakly compressible fluid flow in nano /micro-size circular tubes considering solid wall force. J Univ Sci Technol Beijing, 2014, 36(5): 569
[35]	Bonaccurso E, Butt H J, Craig V S. Surface roughness and hydrodynamic boundary slip of a Newtonian fluid in a completely wetting system. Phys Rev Lett, 2003, 90(14): 144501 doi: 10.1103/PhysRevLett.90.144501
[36]	Shen W J, Song F Q, Hu X, et al. Experimental study on flow characteristics of gas transport in micro- and nanoscale pores. Sci Rep, 2019, 9: 10196 doi: 10.1038/s41598-019-46430-2
[37]	Ou J, Rothstein J P. Direct velocity measurements of the flow past drag-reducing ultrahydrophobic surfaces. Phys Fluids, 2005, 17(10): 103606 doi: 10.1063/1.2109867
[38]	Pak T, Butler I B, Geiger S, et al. Droplet fragmentation: 3D imaging of a previously unidentified pore-scale process during multiphase flow in porous media. PNAS, 2015, 112(7): 1947 doi: 10.1073/pnas.1420202112
[39]	王渝明, 龐顏民, 楊樹鋒, 等. 基于啟動壓力梯度的低滲透砂巖儲層分類研究. 高校地質學報, 2005, 11(4):617 doi: 10.3969/j.issn.1006-7493.2005.04.019 Wang Y M, Pang Y M, Yang S F, et al. Study on classification of low-permealility sandstone reservoirs based on the starting pressure gradient. Geol J China Univ, 2005, 11(4): 617 doi: 10.3969/j.issn.1006-7493.2005.04.019
[40]	Jerauld G R, Salter S J. The effect of pore-structure on hysteresis in relative permeability and capillary pressure: Pore-level modeling. Transp Porous Media, 1990, 5(2): 103 doi: 10.1007/BF00144600
[41]	McDougall S R, Sorbie K S. The impact of wettability on waterflooding: Pore-scale simulation. SPE Reserv Eng, 1995, 10(3): 208 doi: 10.2118/25271-PA
[42]	Wang C, Nguyen N T, Wong T N, et al. Investigation of active interface control of pressure driven two-fluid flow in microchannels. Sens Actuators A, 2007, 133(2): 323 doi: 10.1016/j.sna.2006.06.034
[43]	Datta S S, Ramakrishnan T S, Weitz D A. Mobilization of a trapped non-wetting fluid from a three-dimensional porous medium. Phys Fluids, 2014, 26(2): 022002 doi: 10.1063/1.4866641
[44]	Arif M, Mahmoud M, Zhang Y H, et al. X-ray tomography imaging of shale microstructures: A review in the context of multiscale correlative imaging. Int J Coal Geol, 2021, 233: 103641 doi: 10.1016/j.coal.2020.103641
[45]	鄧慶軍. 大慶油田薩中開發區特高含水期微觀剩余油成因及動用機制研究[學位論文]. 大慶: 東北石油大學, 2015 Deng Q J. Microscale Occurence and Recovery Mechanism of Remaining Oil in Sazhong Area at Extra-High Water Cut Stage of Daqing Field [Dissertation]. Daqing: Northeast Petroleum University, 2015
[46]	Xiong Q R, Baychev T G, Jivkov A P. Review of pore network modelling of porous media: Experimental characterisations, network constructions and applications to reactive transport. J Contam Hydrol, 2016, 192: 101 doi: 10.1016/j.jconhyd.2016.07.002
[47]	Fatt I. The network model of porous media. Trans AIME, 1956, 207(1): 144 doi: 10.2118/574-G
[48]	Dullien F A L, Lai F S Y, MacDonald I F. Hydraulic continuity of residual wetting phase in porous media. J Colloid Interface Sci, 1986, 109(1): 201 doi: 10.1016/0021-9797(86)90295-X
[49]	Zhang X L, Shi Y T, Kuang S Y, et al. Microscale effects of Bingham-plastic liquid behavior considering electroviscous effects in nano- or microsized circular tubes. Phys Fluids, 2019, 31(2): 022001 doi: 10.1063/1.5068774
[50]	張雪齡, 鄺頌雅, 師渝滔, 等. 致密油納微米孔隙介質非線性滲流特性研究進展. 中國海上油氣, 2019, 31(4):102 Zhang X L, Kuang S Y, Shi Y T, et al. Research progress on the nonlinear seepage characteristics of tight oil in nano-micron porous media. China Offshore Oil Gas, 2019, 31(4): 102
[51]	Xie C Y, Xu K, Mohanty K, et al. Nonwetting droplet oscillation and displacement by viscoelastic fluids. Phys Rev Fluids, 2020, 5(6): 063301 doi: 10.1103/PhysRevFluids.5.063301
[52]	王金勛, 吳曉東, 楊普華, 等. 孔隙網絡模型法計算氣液體系吸吮過程相對滲透率. 天然氣工業, 2003, 23(3):8 doi: 10.3321/j.issn:1000-0976.2003.03.003 Wang J X, Wu X D, Yang P H, et al. Calculating the imbibition relative permeability of a gas-liquid system by pore scale network model. Nat Gas Ind, 2003, 23(3): 8 doi: 10.3321/j.issn:1000-0976.2003.03.003
[53]	韓強, 屈展, 葉正寅. 頁巖多尺度力學特性研究現狀. 應用力學學報, 2018, 35(3):564 Han Q, Qu Z, Ye Z Y. Research status of shale multi-scale mechanical properties. Chin J Appl Mech, 2018, 35(3): 564
[54]	馬勇軍, 王瑞飛. 超低滲淺層砂巖油藏儲層非線性滲流模型. 斷塊油氣田, 2017, 24(4):514 Ma Y J, Wang R F. Non-linear seepage models for sandstone reservoirs of ultra-low permeability and shallow layers. Gas Field, 2017, 24(4): 514
[55]	馬銓崢, 楊勝來, 王君如, 等. 基于啟動壓力梯度的致密油藏非線性滲流模型. 石油化工高等學校學報, 2020, 33(1):36 doi: 10.3969/j.issn.1006-396X.2020.01.007 Ma Q Z, Yang S L, Wang J R, et al. Non-linear seepage model of tight reservoir based on threshold pressure gradient. J Petrochem Univ, 2020, 33(1): 36 doi: 10.3969/j.issn.1006-396X.2020.01.007
[56]	鄧佳. 頁巖氣儲層多級壓裂水平井非線性滲流理論研究[學位論文]. 北京: 北京科技大學, 2015 Deng J. Nonlinear Seepage Theory of Multistage Fractured Horizontal Wells for Shale Gas Reservoirs [Dissertation]. Beijing: University of Science and Technology Beijing, 2015
[57]	黃延章. 低滲透油層非線性滲流特征. 特種油氣藏, 1997, 4(1):9 Huang Y Z. Nonlinear percolation feature in low permeability reservoir. Gas Reservoirs, 1997, 4(1): 9
[58]	姚約東, 葛家理. 低滲透油層非達西滲流規律的研究. 新疆石油地質, 2000, 21(3):213 doi: 10.3969/j.issn.1001-3873.2000.03.010 Yao Y D, Ge J L. Study on non-darcy flow pattern in low permeability oil reservoir. Xinjiang Pet Geol, 2000, 21(3): 213 doi: 10.3969/j.issn.1001-3873.2000.03.010
[59]	楊清立, 楊正明, 王一飛, 等. 特低滲透油藏滲流理論研究. 鉆采工藝, 2007, 30(6):52 doi: 10.3969/j.issn.1006-768X.2007.06.019 Yang Q L, Yang Z M, Wang Y F, et al. Study on flow theory in ultra-low permeability oil reservoir. Drill Prod Technol, 2007, 30(6): 52 doi: 10.3969/j.issn.1006-768X.2007.06.019
[60]	鄧英爾, 劉慈群. 低滲油藏非線性滲流規律數學模型及其應用. 石油學報, 2001, 22(4):72 doi: 10.3321/j.issn:0253-2697.2001.04.014 Deng Y E, Liu C Q. Mathematical model of nonlinear flow law in low permeability porous media and its application. Acta Petrolei Sin, 2001, 22(4): 72 doi: 10.3321/j.issn:0253-2697.2001.04.014
[61]	黃延章, 楊正明, 何英, 等. 低滲透多孔介質中的非線性滲流理論. 力學與實踐, 2013, 35(5):1 doi: 10.6052/1000-0879-13-165 Huang Y Z, Yang Z M, He Y, et al. Nonlinear porous flow in low permeability porous media. Mech Eng, 2013, 35(5): 1 doi: 10.6052/1000-0879-13-165
[62]	Vinay G, Wachs A, Agassant J F. Numerical simulation of weakly compressible Bingham flows: The restart of pipeline flows of waxy crude oils. J Non Newton Fluid Mech, 2006, 136(2-3): 93 doi: 10.1016/j.jnnfm.2006.03.003
[63]	向大平, 鄧小剛, 毛枚良. 低馬赫數流動數值模擬方法的研究. 空氣動力學學報, 2002, 20(4):373 doi: 10.3969/j.issn.0258-1825.2002.04.001 Xiang D P, Deng X G, Mao M L. Study on a novel method for low Mach number flows computation. Acta Aerodyn Sin, 2002, 20(4): 373 doi: 10.3969/j.issn.0258-1825.2002.04.001
[64]	向大平, 鄧小剛, 毛枚良. 微可壓縮模型(SCM)與可壓縮NS方程數值計算對比研究. 空氣動力學學報, 2005, 23(2):195 doi: 10.3969/j.issn.0258-1825.2005.02.012 Xiang D P, Deng X G, Mao M L. Study of slightly compressible model (SCM) and compressible N-S equations on low Mach number flow computation. Acta Aerodyn Sin, 2005, 23(2): 195 doi: 10.3969/j.issn.0258-1825.2005.02.012
[65]	劉慈群. 非牛頓流體的廣義Maxwell模型及其解. 力學與實踐, 1995, 17(2):21 Liu C Q. Generalized Maxwell Model of Non-Newtonian Fluid and Its Solution. Mech Pract, 1995, 17(2): 21
[66]	黃耀英, 沈振中, 吳中如. 不同應力分量下廣義開爾文模型粘性系數探討. 應用力學學報, 2007, 24(4):588 doi: 10.3969/j.issn.1000-4939.2007.04.019 Huang Y Y, Shen Z Z, Wu Z R. Generalized kelvin model under different stress state. Chin J Appl Mech, 2007, 24(4): 588 doi: 10.3969/j.issn.1000-4939.2007.04.019
[67]	栗雪娟, 歐陽潔, 蔣濤, 等. 模擬微可壓粘彈性流體的WCCBSSU方法. 計算力學學報, 2011, 28(4):590 doi: 10.7511/jslx201104017 Li X J, Ouyang J, Jiang T, et al. A WCCBSSU method for solving weakly compressible visco-elastic flow problems. Chin J Comput Mech, 2011, 28(4): 590 doi: 10.7511/jslx201104017
[68]	Venerus D C. Laminar capillary flow of compressible viscous fluids. J Fluid Mech, 2006, 555: 59 doi: 10.1017/S0022112006008755
[69]	劉學利, 彭小龍, 杜志敏, 等. 油水兩相流Darcy-Stokes模型. 西南石油大學學報, 2007, 29(6):89 Liu X L, Peng X L, Du Z M, et al. Oil water two phases flow darcy-strokes mode. J Southwest Pet Univ, 2007, 29(6): 89
[70]	萬釗. 微可壓縮模型預處理求解方法研究[學位論文]. 綿陽: 中國空氣動力研究與發展中心, 2010 Wan Z. Preconditioning Technique in Slighly Compressible Model [Dissertation]. Mianyang: China Aerodynamics Research and Development Center, 2010
[71]	張雪齡. 考慮液—固界面作用的微可壓縮流體的滲流理論研究[學位論文]. 北京: 北京科技大學, 2015 Zhang X L. Percolation Theory Research of Weakly Compressible Fluid Flow Considering Wall-Liquid Interaction [Dissertation]. Beijing: University of Science and Technology Beijing, 2015
[72]	Liu C, Li Z G. Flow regimes and parameter dependence in nanochannel flows. Phys Rev E, 2009, 80(3): 036302 doi: 10.1103/PhysRevE.80.036302
[73]	Yang C, Li D Q. Electrokinetic effects on pressure-driven liquid flows in rectangular microchannels. J Colloid Interface Sci, 1997, 194(1): 95 doi: 10.1006/jcis.1997.5091
[74]	朱維耀, 王亞震, 岳明, 等. 考慮空間位形力作用的微米軟顆粒溶液微圓管流動規律. 工程科學學報, 2019, 41(10):1266 Zhu W Y, Wang Y Z, Yue M, et al. Micro circular pipe flow in micron-sized soft particle solution considering the effect of spatial configuration force. Chin J Eng, 2019, 41(10): 1266
[75]	龍運前, 朱維耀, 劉啟鵬, 等. 納微米聚合物顆粒分散體系微孔濾膜流動特征. 西南石油大學學報(自然科學版), 2015, 37(6):144 Long Y Q, Zhu W Y, Liu Q P, et al. Flow characteristics of nano/micron-sized polymer particles aqueous solution through microporous membrane. J Southwest Pet Univ Sci Technol, 2015, 37(6): 144
[76]	朱維耀, 馬千, 鄧佳, 等. 納微米級孔隙氣體流動數學模型及應用. 北京科技大學學報, 2014, 36(6):709 Zhu W Y, Ma Q, Deng J, et al. Mathematical model and application of gas flow in nano-micron pores. J Univ Sci Technol Beijing, 2014, 36(6): 709
[77]	Hazlett R D. Simulation of capillary-dominated displacements in microtomographic images of reservoir rocks. Transp Porous Media, 1995, 20(1-2): 21 doi: 10.1007/BF00616924
[78]	Coles M E, Hazlett R D, Spanne P, et al. Pore level imaging of fluid transport using synchrotron X-ray microtomography. J Petroleum Sci Eng, 1998, 19(1-2): 55 doi: 10.1016/S0920-4105(97)00035-1
[79]	Joshi M Y. A Class of Stochastic Models for Porous Media[Dissertation]. Lawrence: University of Kansas, 1974.
[80]	Quiblier J A. A new three-dimensional modeling technique for studying porous media. J Colloid Interface Sci, 1984, 98(1): 84 doi: 10.1016/0021-9797(84)90481-8
[81]	徐模. 數字巖心及孔隙網絡模型的構建方法研究[學位論文]. 成都: 西南石油大學, 2017 Xu M. Method of Digital Core Construction and Pore Network Extraction[Dissertation]. Chengdu: Southwest Petroleum University, 2017
[82]	Hazlett R D. Statistical characterization and stochastic modeling of pore networks in relation to fluid flow. Math Geol, 1997, 29(6): 801 doi: 10.1007/BF02768903
[83]	趙秀才, 姚軍, 陶軍, 等. 基于模擬退火算法的數字巖心建模方法. 高校應用數學學報A輯, 2007, 22(2):127 doi: 10.3969/j.issn.1000-4424.2007.02.001 Zhao X C, Yao J, Tao J, et al. A method of constructing digital core by simulated annealing algorithm. Appl Math A J Chin Univ (Sera), 2007, 22(2): 127 doi: 10.3969/j.issn.1000-4424.2007.02.001
[84]	Hidajat I, Rastogi A, Singh M, et al. Transport properties of porous media reconstructed from thin-sections. SPE J, 2002, 7(1): 40 doi: 10.2118/77270-PA
[85]	Wu K J, Dijke M I J, Couples G D, et al. 3D stochastic modelling of heterogeneous porous media-applications to reservoir rocks. Transp Porous Media, 2006, 65(3): 443 doi: 10.1007/s11242-006-0006-z
[86]	胡雪濤, 李允. 隨機網絡模擬研究微觀剩余油分布. 石油學報, 2000, 21(4):46 doi: 10.3321/j.issn:0253-2697.2000.04.009 Hu X T, Li Y. Study of microcosmic distribution of residual oil with stochastic simulation in networks. Acta Petrolei Sin, 2000, 21(4): 46 doi: 10.3321/j.issn:0253-2697.2000.04.009
[87]	Blunt M J, Jackson M D, Piri M, et al. Detailed physics, predictive capabilities and macroscopic consequences for pore-network models of multiphase flow. Adv Water Resour, 2002, 25(8-12): 1069 doi: 10.1016/S0309-1708(02)00049-0
[88]	徐守余, 李紅南. 儲集層孔喉網絡場演化規律和剩余油分布. 石油學報, 2003, 24(4):48 doi: 10.3321/j.issn:0253-2697.2003.04.011 Xu S Y, Li H N. Evolvement of reservoir pore-throat-net and remaining oil distribution. Acta Petrolei Sin, 2003, 24(4): 48 doi: 10.3321/j.issn:0253-2697.2003.04.011
[89]	王克文, 孫建孟, 關繼騰, 等. 聚合物驅后微觀剩余油分布的網絡模型模擬. 中國石油大學學報(自然科學版), 2006, 30(1):72 Wang K W, Sun J M, Guan J T, et al. Network model modeling of microcosmic remaining oil distribution after polymer flooding. J China Univ Pet Ed Nat Sci, 2006, 30(1): 72
[90]	姚軍, 陶軍, 李愛芬. 利用三維隨機網絡模型研究油水兩相流動. 石油學報, 2007, 28(2):94 doi: 10.3321/j.issn:0253-2697.2007.02.018 Yao J, Tao J, Li A F. Research on oil-water two-phase flow using 3D random network model. Acta Petrolei Sin, 2007, 28(2): 94 doi: 10.3321/j.issn:0253-2697.2007.02.018
[91]	張鵬偉, 胡黎明, Jay N Meegoda, 等. 基于巖土介質三維孔隙結構的兩相流模型. 巖土工程學報, 2020, 42(1):37 Zhang P W, Hu L M, Meegoda J, et al. Two-phase flow model based on 3D pore structure of geomaterials. Chin J Geotech Eng, 2020, 42(1): 37
[92]	閆偉超, 孫建孟. 微觀剩余油研究現狀分析. 地球物理學進展, 2016, 31(5):2198 doi: 10.6038/pg20160544 Yan W C, Sun J M. Analysis of research present situation of microscopic remaining oil. Prog Geophys, 2016, 31(5): 2198 doi: 10.6038/pg20160544
[93]	王芳芳, 胡海光, 何志雄. 剩余油形成機理與賦存狀態研究綜述. 廣東化工, 2013, 40(3):66 doi: 10.3969/j.issn.1007-1865.2013.03.033 Wang F F, Hu H G, He Z X. Remaining oil forming mechanism of occurrence research. Guangdong Chem Ind, 2013, 40(3): 66 doi: 10.3969/j.issn.1007-1865.2013.03.033
[94]	Li T X, Song H Q, Wang J L, et al. An analytical method for modeling and analysis gas-water relative permeability in nanoscale pores with interfacial effects. Int J Coal Geol, 2016, 159: 71 doi: 10.1016/j.coal.2016.03.018
[95]	Chatenever A, Calhoun J C Jr. Visual examinations of fluid behavior in porous media?part I. J Pet Technol, 1952, 4(6): 149 doi: 10.2118/135-G
[96]	Templeton C C. A study of displacements in microscopic capillaries. J Pet Technol, 1954, 6(7): 37 doi: 10.2118/307-G
[97]	黃延章. 微觀滲流實驗力學及其應用. 北京: 石油工業出版社, 2001 Huang Y Z. Experimental Mechanics of Microscopic Seepage and its Application. Beijing: Petroleum industry press, 2001
[98]	Zhang X L, Zhu W Y, Cai Q, et al. Compressible liquid flow in nano- or micro-sized circular tubes considering wall–liquid Lifshitz–van der Waals interaction. Phys Fluids, 2018, 30(6): 062002 doi: 10.1063/1.5023291