考虑流动电位的微米/纳米毛细管单相渗流模式
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摘要
流体在多孔介质中流动时,由于固-液界面扩散双电层的存在,流体的流动会产生流动电位现象,而流动电位会反过来对流体在多孔介质中的流动造成影响。从微米和纳米尺度,利用圆形、正方形和三角形截面毛细管模型,采用有限元数值求解方法,研究了在不同毛细管尺寸下,流动电位对毛细管单相流体渗流模式的影响,得到了考虑流动电位情况下不同尺寸三角形截面毛细管传导率和其形状因子的关系,并研究了在不同毛细管尺寸条件下,考虑流动电位对流体流动的影响后外加压力梯度与流体流量之间的关系。研究结果表明,由于流动电位对流体流动的影响,当毛细管尺寸与扩散双电层厚度相当时,流动电位会对流体在毛细管中的流动产生显著影响,流体的流动阻力增加,毛细管传导率减小,但是毛细管中的流体流量与压力梯度仍然保持线性关系。
Due to the presence of electric double layer at the solid-liquid interface,fluid flow in porous media can give rise to streaming potential which in turn influences the fluid flow.In this study,the impact of streaming potential on fluid flow is investigated at the micro-/nanoscale by resolving different sizes of capillary models of circular,square,and triangular cross sections using finite element numerical method.The relationships between conductivities in triangular capillaries of different sizes and their corresponding shape factors are examined by considering streaming potential.Additionally,the relationship between flow rate in capillaries of different sizes and their external pressure gradients are investigated.Results show that streaming potential strongly impacts fluid flow in capillaries when the size of the capillary is comparable to the thickness of the electric double layer.Due to the impact of streaming potential,flow resistance of the fluid increases while the conductivities in capillaries decrease.However,the relationship between flow rate and pressure gradient in capillaries remains linear.
Due to the presence of electric double layer at the solid-liquid interface,fluid flow in porous media can give rise to streaming potential which in turn influences the fluid flow.In this study,the impact of streaming potential on fluid flow is investigated at the micro-/nanoscale by resolving different sizes of capillary models of circular,square,and triangular cross sections using finite element numerical method.The relationships between conductivities in triangular capillaries of different sizes and their corresponding shape factors are examined by considering streaming potential.Additionally,the relationship between flow rate in capillaries of different sizes and their external pressure gradients are investigated.Results show that streaming potential strongly impacts fluid flow in capillaries when the size of the capillary is comparable to the thickness of the electric double layer.Due to the impact of streaming potential,flow resistance of the fluid increases while the conductivities in capillaries decrease.However,the relationship between flow rate and pressure gradient in capillaries remains linear.
引文
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[17]Mason G,Morrow N R.Capillary behavior of a perfectly wetting liquid in irregular triangular tubes[J].Journal of Colloid and Interface Science,1991,141(1):262-274.
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[20]Revil A,Glover P W J.Nature of surface electrical conductivity in natural sands,sandstones,and clays[J].Geophysical Research Letters,1998,25(5):691-694.
[21]Alkafeef S F,Alajmi A F.Streaming potentials and conductivities of reservoir rock cores in aqueous and non-aqueous liquids[J].Colloids and Surfaces A:Physicochemical and Engineering Aspects,2006,289(1/3):141-148.
[22]Alkafeef S F,Alajmi A F.The electrical conductivity and surface conduction of consolidated rock cores[J].Journal of Colloid and Interface Science,2007,309(2):253-261.
[2]杨建,康毅力,李前贵,等.致密砂岩气藏微观结构及渗流特征[J].力学进展,2008,38(2):229-236.Yang Jian,Kang Yili,Li Qiangui,et al.Characters of microstructure and percolation in tight sandstone gas reservoirs[J].Advances in Mechanics,2008,38(2):229-236.
[3]Handwerger D A,Suarez-Rivera R,Vaughn K I,et al.Improved petrophysical core measurements on tight shale reservoirs using retort and crushed samples[R].SPE147456,2011.
[4]杨峰,宁正福,胡昌蓬,等.页岩储层微观孔隙结构特征[J].石油学报,2013,34(2):301-311.Yang Feng,Ning Zhengfu,Hu Changpeng,et al.Characterization of microscopic pore structures in shale reservoirs[J].Acta Petrolei Sinica,2013,34(2):301-311.
[5]Yang Feng,Ning Zhengfu,Liu Huiqing.Fractal characteristics of shales from a shale gas reservoir in the Sichuan Basin,China[J].Fuel,2014,115:378-384.
[6]秦积舜,李爱芬.油层物理学[M].东营:中国石油大学出版社,2003.Qin Jishun,Li Aifen.Physical Properties of Petroleum Reservoir[M].Dongying:China University of Petroleum Press,2003.
[7]Grahame D C.The electrical double layer and the theory of elec-trocapillarity[J].Chemical Reviews,1947,41(3):441-501.
[8]Kirby B J,Hasselbrink Jr.EF.Zeta potential of microfluidic substrates:1.Theory,experimental techniques,and effects on separations[J].Electrophoresis,2004,25(2):187-202.
[9]于华,关继腾,陈辉,等.储层岩石流动电位频散特性的数学模拟[J].地球物理学报,2013,56(2):676-687.Yu Hua,Guan Jiteng,Chen Hui,et al.Mathematical simulation on the frequency dispersion characteristics of the streaming potential in reservoir rocks[J].Chinese Journal of Geophysics,2013,56(2):676-687.
[10]Widom B.Statistical mechanics:a concise introduction for chemists[M].Cambridge:Cambridge University Press,2002.
[11]Revil A,Pezard P A,Glover P W J.Streaming potential in porous media:1.Theory of the zeta potential[J].Journal of Geophysical Research:Solid Earth,1999,104(B9):20021-20031.
[12]Revil A,Schwaeger H,Cathles L M,et al.Streaming potential in porous media:2.Theory and application to geothermal systems[J].Journal of Geophysical Research:Solid Earth,1999,104(B9):20033-20048.
[13]Tandon V,Bhagavatula S K,Nelson W C,et al.Zeta potential and electroosmotic mobility in microfluidic devices fabricated from hydrophobic polymers:1.The origins of charge[J].Electrophoresis,2008,29(5):1092-1101.
[14]署恒木,仝兴华.工程有限单元法[M].东营:中国石油大学出版社,2002.Shu Hengmu,Tong Xinghua.Engineering finite element method[M].DongYing:China University of Petroleum Press,2002.
[15]Rice C L,Whitehead R.Electrokinetic flow in a narrow cylindrical capillary[J].The Journal of Physical Chemistry,1965,69(11):4017-4024.
[16]姚军,赵秀才.数字岩心及孔隙级渗流模拟理论[M].北京:石油工业出版社,2010.Yao Jun,Zhao Xiucai.Digital core and pore-scale modeling of fluid flow in porous media[M].Beijing:Petroleum Industry Press,2010.
[17]Mason G,Morrow N R.Capillary behavior of a perfectly wetting liquid in irregular triangular tubes[J].Journal of Colloid and Interface Science,1991,141(1):262-274.
[18]Patzek T.Verification of a complete pore network simulator of drainage and imbibition[R].SPE71310,2001.
[19]Valvatne P H,Blunt M J.Predictive pore-scale modeling of twophase flow in mixed wet media[J].Water Resources Research,2004,40(7):W07406.
[20]Revil A,Glover P W J.Nature of surface electrical conductivity in natural sands,sandstones,and clays[J].Geophysical Research Letters,1998,25(5):691-694.
[21]Alkafeef S F,Alajmi A F.Streaming potentials and conductivities of reservoir rock cores in aqueous and non-aqueous liquids[J].Colloids and Surfaces A:Physicochemical and Engineering Aspects,2006,289(1/3):141-148.
[22]Alkafeef S F,Alajmi A F.The electrical conductivity and surface conduction of consolidated rock cores[J].Journal of Colloid and Interface Science,2007,309(2):253-261.