Fractal theory-based seepage model of Hershel-Bulkley fluid in porous medium

Authors

YANG Xian, School of Resource, Environment and Safety Engineering, Hunan University of Science and Technology, Xiangtan 411201, China
LU Wei, School of Resource, Environment and Safety Engineering, Hunan University of Science and Technology, Xiangtan 411201, China
JIN Xin, Xi'an Research Institute Co. Ltd., China Coal Technology and Engineering Group Corp., Xi'an 710077, China; School of Geosciences and Info-physics, Central South University, Changsha 410000, ChinaFollow
CHEN Juan, School of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan 411201, China
FENG Xingfa, Chongqing Engineering Co. Ltd., China Coal Technology & Engineering Group Crop., Chongqing 400016, China

Abstract

Slurry is a kind of widely-used engineering fluid. Slurry will seeps into the formation in the process of construction, which has a certain impact on the project. In order to make deeper study on the seepage mechanism of slurry, the formation is simulated as porous medium, the slurry is simulated as Hershel-Bulkley fluid which can more comprehensively reflect its rheological properties, and the seepage model of Hershel-Bulkley fluid in porous medium was established based on Fractal theory. Based on the calculation results of seepage model, the effect of pressure gradient, flow index, consistency coefficient and porosity on the instantaneous average velocity of Hershel-Bulkley fluid in porous medium were analyzed in detail. It is pointed out that the change of velocity has a power exponential relation with the change of pressure gradient, flow index and consistency coefficient, and a binomial relation with the change of porosity. The results provide theory basics for design and construction of slurry grouting in relevant projects.

Keywords

slurry, Hershel-Bulkley fluid, porous medium, fractal theory, seepage model

DOI

10.3969/j.issn.1001-1986.2020.03.018

Recommended Citation

YANG Xian, LU Wei, JIN Xin, et al. (2020) "Fractal theory-based seepage model of Hershel-Bulkley fluid in porous medium," Coal Geology & Exploration: Vol. 48: Iss. 3, Article 19.
DOI: 10.3969/j.issn.1001-1986.2020.03.018
Available at: https://cge.researchcommons.org/journal/vol48/iss3/19

Reference

[1] 莫世扬,杨晓伟,洪元堂,等. 非开挖顶管工艺在公路污水管线下穿工程中应用分析[J]. 公路工程,2019,44(2):151-155. MO Shiyang,YANG Xiaowei,HONG Yuantang,et al. Application analysis of trenchless pipe jacking technology in highway sewage pipeline project[J]. Highway Engineering,2019,44(2):151-155.

[2] 邓利蓉,刘振兴,曹钧,等. 硬岩破碎地层高温钻孔钻进的钻井液实验研究[J]. 煤田地质与勘探,2015,43(4):117-119. DENG Lirong,LIU Zhenxing,CAO Jun,et al. Experiment of drilling fluid used to drill hard fractured complex formation[J]. Coal Geology & Exploration,2015,43(4):117-119.

[3] 侯璐瑶,王奎升,侯世全. 基于宾汉模式的桥梁桩基钻孔泥浆流变特性初步研究[J]. 铁道建筑,2010(6):41-43. HOU Luyao,WANG Kuisheng,HOU Shiquan. Preliminary study on rheological properties of drilling mud from Bingham model to bridge pile foundation[J]. Railway Engineering,2010(6):41-43.

[4] 蔡亮学. 水平定向钻管道穿越回拖过程动态力学特性研究[D]. 东营:中国石油大学(华东),2011. CAI Liangxue. Investigation on dynamics of pipe during pullback in horizontal directional drilling installations[D]. Dongying:China University of Petroleum(East China),2011.

[5] 汪友平,郑秀华,夏柏如,等. 圆管中赫巴流体层流流动规律的研究[J]. 钻井液与完井液,2008,25(1):27-28. WANG Youping,ZHENG Xiuhua,XIA Bairu,et al. Studies of the laminar flow of Herschel-Bulkley fluids in pipes[J]. Drilling Fluid and Completion Fluid,2008,25(1):27-28.

[6] 李鑫,高德利,刁斌斌,等. 基于赫巴流体的页岩气大位移水平井裸眼延伸极限分析[J]. 天然气工业,2016,36(10):85-92. LI Xin,GAO Deli,DIAO Binbin,et al. Analysis on the open-hole extension limit of a shale-gas extended-reach horizontal well based on Hershel-Bulkley fluids[J]. Natural Gas Industry,2016,36(10):85-92.

[7] MANDELBROT B B. How long is the coast of britain? statistical self-similarity and fractional dimension[J]. Science,1967,156(3775):636-638.

[8] SPARROW C. The fractal geometry of nature by B. Mandelbrot[J]. Journal of the Royal Statistical Society,1984,147(4):616-618.

[9] AVNIR D,FARIN D,PFEIFER P. Chemistry in non-integer dimensions between two and three. Ⅱ. Fractal surfaces of adsorbents[J]. The Journal of Chemical Physics,1983,79(7):3566-3571.

[10] HANSEN J P,SKJELTORP A T. Fractal pore space and rock permeability implications[J]. Physical Review B Condensed Matter,1988,38(4):2635-2638.

[11] KATZ A J,THOMPSON A H. Fractal sandstone pores:Implications for conductivity and pore formation[J]. Physical Review Letters,1985,54(12):1325-1328.

[12] KROHN C E. Sandstone fractal and euclidean pore volume distributions[J]. Journal of Geophysical Research:Solid Earth,1988,93(B4):3286-3296.

[13] 吴金随. 多孔介质里流动阻力分析[D]. 武汉:华中科技大学,2007. WU Jinsui. Analysis of resistance for flow through porous media[D]. Wuhan:Huazhong University of Science and Technology,2007.

[14] 邹明清. 分形理论的若干应用[D]. 武汉:华中科技大学,2007. ZOU Mingqing. Fractal theory and its applications to porous media, rough surface and thermal contact conductance[D]. Wuhan:Huazhong University of Science and Technology,2007.

[15] YU B M. Fractal character for tortuous stream tubes in porous media[J]. Chinese Physics Letters,2005,22(1):158-160.

[16] XU P,YU B M. Developing a new form of permeability and Kozeny-Carman constant for homogeneous porous media by means of fractal geometry[J]. Advances in Water Resources,2008,31(1):74-81.

[17] LI J H,YU B M. Tortuosity of flow paths through a Sierpinski carpet[J]. Chinese Physics Letters,2011,28(3):117-119.

[18] 员美娟,郁伯铭,郑伟,等. 多孔介质中卡森流体的分形分析[J]. 物理学报,2011,60(2):410-415. YUAN Meijuan,YU Boming,ZHENG Wei,et al. Fractal analysis of Casson fluid flow in porous media[J]. Acta Physica Sinica,2011,60(2):410-415.

[19] 万秀峰. 砂卵石地层水泥-水玻璃复合注浆加固关键技术研究[D]. 长沙:中南大学,2014. WAN Xiufeng. Gordian technique of cement and sodium silicate composite grouting reinforcement in sand gravel strata[D]. Changsha:Central South University,2014.

[20] 周子龙,杜雪明,陈钊,等. 考虑孔隙曲折效应的浆液扩散压力[J]. 中国有色金属学报,2016,26(8):1721-1727. ZHOU Zilong,DU Xueming,CHEN Zhao,et al. Grout dispersion considering effect of pore tortuosity[J]. The Chinese Journal of Nonferrous Metals,2016,26(8):1721-1727.

[21] CRAWFORD J W,MATSUI N. Heterogeneity of the pore and solid volume of soil:Distinguishing a fractal space from its non-fractal complement[J]. Geoderma,1996,73(3/4):183-195.

[22] 黄延章. 低渗透油层渗流机理[M]. 北京:石油工业出版社,1998. HUANG Yanzhang. Seepage mechanism of the low permeability reservoir[M]. Beijing:Petroleum Industry Press,1998.