多孔介质的渗透性能表征了流体在多孔介质内流动的难易程度,对流体在多孔介质内的流动过程具有重要影响。本文回顾了近年来多孔介质渗透性能研究的方法、模型、成果和应用,尤其阐述了近年来的研究热点,分形理论在多孔介质渗透性能研究中的应用进展。研究表明,多孔介质的渗透性能由孔隙率、迂曲度、孔隙半径、分形维数、比表面积以及流体性质等共同决定,并不是某一参数的单值函数,而是由众多参数共同作用的复合函数。分形理论在描述不规则、具有分形特征的多孔介质渗透性能方面发挥了重要作用。 The permeability of porous media characterizes the difficulty of fluid flow in porous media. It has an important influence on the flow of fluid in a porous medium. This paper reviews the methods, models, results and applications of porous media permeability studies in recent years, especially the recent research hotspots, the application development of fractal theory in porous media per-meability research. The results show that the permeability of porous media is determined by the combination of porosity, tortuosity, pore radius, fractal dimension, specific surface area and fluid properties. It is not a single-valued function of a parameter, but a composite function that interacts with many parameters. Fractal theory plays an important role in describing the permeability of porous media with irregular and fractal features.
多孔介质,渗透性能,孔隙结构,分形理论, Porous Media Permeability Pore Structure Fractal Theory多孔介质渗透性能的研究进展
实验直接测量的结果一般表示为包含有一个或者多个经验常数的函数表达式。其中经验常数也叫做拟合常数,通常无实际的物理意义,并且由实验的精度和人为确定,缺乏准确性和一致性。比如雷树业 [13] 等在研究颗粒床层的渗流规律时,在试验中得到了颗粒床层渗透率的经验表达式如式(3),该式含有三个无实际意义物理参数(也叫经验参数),且该只适用于 d = 0.1 ~ 0.45 mm ,具有一定的局限性。
K e = 2 D T − 2 D f n − 1 n 2 ∅ L 1 − D T ( 1 + 3 n ) D T ( n D T − n D f ) n − 1 ( 2 − D f r max 1 + D T ) ( D T − n D f + 3 n ) ( 1 − ∅ ) [ 1 − ( τ min τ max ) ( D T / n ) − D f ] n − 1 (8)
式中, K e 、DT、Df、n、r、 τ 、 λ max 依次分别为等效渗透率、迂曲度分形维数、孔隙面积分形维数、幂律指数、孔隙半径、迂曲度、最大孔隙直径。
巩剑南,王启立,杨娜娜,于鸣泉. 多孔介质渗透性能的研究进展Research Progress on Permeability of Porous Media[J]. 渗流力学进展, 2019, 09(02): 9-16. https://doi.org/10.12677/APF.2019.92002
参考文献ReferencesSasaki, A., Aiba, S. and Fukuda, H. (1987) A Study on the Thermophysical Properties of a Soil. Journal of Heat Transfer, 109, 232-237. <br>https://doi.org/10.1115/1.3248048Jeong, N. (2010) Advanced Study about the Permeability for Micro-Porous Structures Using the Lattice Boltzmann Method. Transport in Porous Media, 83, 271-288. <br>https://doi.org/10.1007/s11242-009-9438-6何映颉. 纳米孔隙对页岩气吸附扩散的分子模拟研究[D]: [硕士学位论文]. 成都: 西南石油大学, 2017.胡冉, 陈益峰, 万嘉敏, 等. 超临界CO2-水两相流与CO2毛细捕获: 微观孔隙模型实验与数值模拟研究[J]. 力学学报, 2017, 49(3):638-648.Lee, S.L. and Yang, J.H. (1997) Modeling of Darcy-Forchheimer Drag for Fluid Flow across a Bank of Circular Cylinders. International Journal of Heat and Mass Transfer, 40, 3149-3155.
<br>https://doi.org/10.1016/S0017-9310(96)00347-XKoponen, A., Kataja, M. and Timonen, J. (1997) Permeability and Effec-tive Porosity of Porous Media. Physical Review E, 56, 3319-3325. <br>https://doi.org/10.1103/PhysRevE.56.3319王启立. 石墨多孔介质成孔逾渗机理及渗透率研究[D]: [博士学位论文]. 徐州: 中国矿业大学, 2011.Levec, J., Sáez, A.E. and Carbonell, R.G. (2010) The Hydrodynamics of Trickling Flow in Packed Beds. Part II: Experimental Observations. AIChE Journal, 32, 369-380. <br>https://doi.org/10.1002/aic.690320303Wang, T.J., Wu, C.H. and Lee, L.J. (2010) In-Plane Permeability Measurement and Analysis in Liquid Composite Molding. Polymer Composites, 15, 278-288. <br>https://doi.org/10.1002/pc.750150406Chen, Z.Q., Cheng, P. and Zhao, T.S. (2000) An Experimental Study of Two Phase Flow and Boiling Heat Transfer in Bi-Dispersed Porous Channels. International Communications in Heat and Mass Transfer, 27, 293-302.
<br>https://doi.org/10.1016/S0735-1933(00)00110-XLee, Q.F. (2002) Fluid Flow through Packed Columns of Cooked Wood Chips.Mcgregor, R. (2010) The Effect of Rate of Flow on Rate of Dyeing II—The Mechanism of Fluid Flow through Textiles and its Significance in Dyeing. Coloration Technology, 81, 429-438.
<br>https://doi.org/10.1111/j.1478-4408.1965.tb02615.x雷树业. 颗粒床孔隙率与渗透率的关系[J]. 清华大学学报(自然科学版), 1998, 38(5): 76-79.Adler, P.M. and Thovert, J.F. (1998) Real Porous Media: Local Geometry and Macroscopic Proper-ties. Applied Mechanics Reviews, 51, 537-585. <br>https://doi.org/10.1115/1.3099022Al-Raoush, R. and Alshibli, K.A. (2006) Distribution of Local Void Ratio in Porous Media Systems from 3D X-Ray Microtomography Images. Physica A: Statistical Mechanics and Its Applications, 361, 441-456.
<br>https://doi.org/10.1016/j.physa.2005.05.043Mostaghimi, P., Blunt, M.J. and Bijeljic, B. (2013) Computations of Absolute Permeability on Micro-CT Images. Mathematical Geosciences, 45, 103-125. <br>https://doi.org/10.1007/s11004-012-9431-4Raeini, A.Q., Blunt, M.J. and Bijeljic, B. (2014) Direct Simulations of Two-Phase Flow on Micro-CT Images of Porous Media and Upscaling of Pore-Scale Forces. Advances in Water Resources, 74, 116-126.
<br>https://doi.org/10.1016/j.advwatres.2014.08.012冯周, 刘瑞林, 应海玲, 等. 岩心CT扫描图像分割计算缝洞孔隙度与测井资料处理结果对比研究[J]. 石油天然气学报, 2011, 33(4): 100-104.宋晓夏, 唐跃刚, 李伟, 等. 基于显微CT的构造煤渗流孔精细表征[J]. 煤炭学报, 2013, 38(3): 435-440.谢淑云, 何治亮, 钱一雄, 等. 基于岩石CT图像的碳酸盐岩三维孔隙组构的多重分形特征研究[J]. 地质学刊, 2015, 39(1): 46-54.姚艳斌, 刘大锰, 蔡益栋, 等. 基于NMR和X-CT的煤的孔裂隙精细定量表征[J]. 中国科学: 地球科学, 2010, 40(11): 1598-1607.王宇, 李晓, 阙介民, 等. 基于CT图像灰度水平的孔隙率计算及应用[J]. 水利学报, 2015, 46(3): 357-365.李建胜, 王东, 康天合. 基于显微CT试验的岩石孔隙结构算法研究[J]. 岩土工程学报, 2010, 32(11): 1703-1708.吕洪志, 陆云龙, 崔云江, 等. 改进的孔隙模型评价流体性质与裂缝孔隙度[J]. 应用声学, 2016, 35(4): 351-356.Hirono, T., Takahashi, M. and Nakashima, S. (2003) In Situ Visualization of Fluid Flow Image within Deformed Rock by X-Ray CT. Engineering Geology, 70, 37-46. <br>https://doi.org/10.1016/S0013-7952(03)00074-7Pierret, A., Capowiez, Y., Belzunces, L. and Moran, C.J. (2002) 3D Re-construction and Quantification of Macropores Using X-Ray Computed Tomography and Image Analysis. Geoderma, 106, 247-271.
<br>https://doi.org/10.1016/S0016-7061(01)00127-6Carman, P.C. (1939) Permeability of Saturated Sands, Soils and Clays. Journal of Agricultural Science, 29, 262-273.
<br>https://doi.org/10.1017/S0021859600051789Kaviany, M. (1995) Principles of Heat Transfer in Porous Media. Springer Press, Berlin.
<br>https://doi.org/10.1007/978-1-4612-4254-3Mourzenko, V.V., Thovert, J.F. and Adler, P.M. (2018) Conductivity and Transmissivity of a Single Fracture. Transport in Porous Media, 123, 235-256. <br>https://doi.org/10.1007/s11242-018-1037-yMourzenko, V.V., Thovert, J.F. and Adler, P.M. (1999) Percolation and Con-ductivity of Self-Affine Fractures. Physical Review E, 59, 4265-4284. <br>https://doi.org/10.1103/PhysRevE.59.4265Zheng, B. and Ju-Hua, L.I. (2015) A New Fractal Permeability Model for Porous Media Based on Kozeny-Carman Equation. Journal of Natural Gas Geoscience, 26, 193-198.Carman, P.C. (1937) Fluid Flow through Granular Beds. Chemical Engineering Research and Design, 75, S32-S48.
<br>https://doi.org/10.1016/S0263-8762(97)80003-2Rumpf, H. and Gupte, A.R. (1975) The Influence of Porosity and Grain Size Distribution on the permeability Equation of Porous Flow. Nasa Sti/Recon Technical Report, 75, 367-375.Pape, H., Clauser, C. and Iffland, J. (2000) Variation of Permeability with Porosity in Sandstone Diagenesis Interpreted with a Fractal Pore Space Model. Pure Applied Geophysics, 157, 603-619. <br>https://doi.org/10.1007/PL00001110Rodriguez, E., Giacomelli, F. and Vazquez, A. (2004) Permeability-Porosity Relationship in RTM for Different Fiberglass and Natural Reinforcements. Journal of Composite Materials, 38, 259-268.
<br>https://doi.org/10.1177/0021998304039269Succi, S., Benzi, R., Calí, A. and Vergassola, M. (1992) The Lattice Boltzmann Equation. Physics Reports, 222, 187-203.Koplik, J., Redner, S. and Wilkinson, D. (1988) Transport and Dispersion in Random Networks with Percolation Disorder. Physical Review A, 37, 2619-2636. <br>https://doi.org/10.1103/PhysRevA.37.2619Blunt, M. and King, P. (1991) Relative Permeabilities from Two- and Three-Dimensional Pore-Scale Network Modelling. Transport in Porous Media, 6, 407-433. <br>https://doi.org/10.1007/BF00136349Mandelbrot, B.B. (1982) The Fractal Geometry of Nature. Freeman Press, San Francisco, CA.Perfect, E., Mclaughlin, N.B., Kay, B.D. and Topp, G.C. (1996) An Improved Fractal Equation for the Soil Water Retention Curve. Water Resources Research, 32, 281-287. <br>https://doi.org/10.1029/95WR02970Hunt, A.G. (2004) Percolative Transport in Fractal Porous Media. Chaos, Solitons & Fractals, 19, 309-325.
<br>https://doi.org/10.1016/S0960-0779(03)00044-4Adler, P.M. (1996) Transports in Fractal Porous Media. Journal of Hy-drology, 187, 195-213.
<br>https://doi.org/10.1016/S0022-1694(96)03096-XAdler, P.M. (1985) Transport Processes in Fractals—I. Conductivity and Permeability of a Leibniz Packing in the Lubrication Limit. International Journal of Multiphase Flow, 11, 91-108. <br>https://doi.org/10.1016/0301-9322(85)90007-2Yu, B. and Lee, L.J. (2000) A Simplified in-Plane Permeability Model for Textile Fabrics. Polymer Composites, 21, 660-685. <br>https://doi.org/10.1002/pc.10221Pitchumani, R. and Ramakrishnan, B. (1999) A Fractal Geometry Model for Evaluating Permeabilities of Porous Preforms Used in Liquid Composite Molding. International Journal of Heat and Mass Transfer, 42, 2219-2232.
<br>https://doi.org/10.1016/S0017-9310(98)00261-0陈永平, 施明恒. 基于分形理论的多孔介质渗透率的研究[J]. 清华大学学报, 2000, 40(12): 94-97.郁伯铭, 邹明清. 用分形一蒙特卡罗方法预测多孔介质的渗透率[J]. 中国科学技术大学学报, 2004, 34(8): 286-291.