地球物理学报

• 中国深部探测地球物理技术与实验研究 • 上一篇    下一篇

含湿孔隙岩石有效热导率的数值分析

刘善琪, 李永兵, 田会全, 刘旭耀, 朱伯靖, 石耀霖   

  1. 中国科学院计算地球动力学重点实验室,中国科学院大学,北京 100049
  • 收稿日期:2012-04-28 修回日期:2012-12-04 出版日期:2012-12-20 发布日期:2012-12-20
  • 通讯作者: 李永兵,男,1973年生,副教授,硕士生导师,矿物学、岩石学、矿床学专业.E-mail:yongbingli@gucas.ac.cn E-mail:yongbingli@gucas.ac.cn
  • 作者简介:刘善琪,女,1987年生,固体地球物理学专业硕士研究生.E-mail:liushanqi10@mails.gucas.ac.cn
  • 基金资助:

    地壳深部探测专项(SinoProbe-07),国家自然科学基金(41174067)和国家科技支撑计划项目(2011BAB03B09)资助.

Numerical simulation on thermal conductivity of wet porous rock

LIU Shan-Qi, LI Yong-Bing, TIAN Hui-Quan, LIU Xu-Yao, ZHU Bo-Jing, SHI Yao-Lin   

  1. Key Laboratory of Computational Geodynamics, CAS, University of Chinese Academy of Sciences, Beijing 100049,China
  • Received:2012-04-28 Revised:2012-12-04 Online:2012-12-20 Published:2012-12-20

摘要:

本文采用有限元方法研究含湿孔隙岩石的有效热导率,即随机划分网格并指定材料性质,建立三维含湿孔隙岩石的有限元模型,模型的上下表面施加不同的温度,侧面绝热,计算出总热流,然后结合上下表面的温度梯度计算出岩石的有效热导率.考虑到单个随机模型不一定具有代表性,对给定的孔隙率和饱和度均生成了200种矿物、水、空气随机分布的岩石模型,进行Monte Carlo实验和统计分析,统计分析结果与前人实验结果吻合良好.数值分析结果表明,孔隙岩石的有效热导率与岩石的孔隙率、饱和度、固体矿物组分及孔隙的分布情况有关,数值计算的误差随着网格数目的增加而减小.此有限元方法可以用来估算岩石的有效热导率,在已知组分性质的多矿物岩石物性计算方面有广阔应用前景.

关键词: 有限元, 多孔介质, 孔隙岩石, 有效热导率, 数值模拟

Abstract:

This paper presents a numerical simulation method to study thermal conductivity of wet porous rock. First, a three-dimensional digital physic model is established by randomly partitioning the rock model and assigning different materials to sub-partitions. Numerical model is in the shape of a cylinder. We impose different temperatures as boundary conditions on the upper and lower surface. The cylindrical surface is adiabatic. The heat flux is obtained by the finite element method, then the effective thermal conductivity of the rock is calculated by combining with the temperature gradient. For a certain porosity and degree of saturation, we adopt an elaborately designed Monte Carlo method to meet the requirement of the random characteristics of grain size, pore space and spatial distribution. Compared with the experimental data, the present model can give fine predictions of the effective thermal conductivity of wet porous rock. We find that the effective thermal properties of the porous rock depends on the type of minerals, the porosity, the degree of saturation and the distribution of pores. The numerical error decreases with the increasing number of grids. This finite element method can be used to compute the effective thermal conductivity and other physical properties of minerals with known components.

Key words: Finite element, Porous media, Porous rock, Effective thermal conductivity, Numerical simulation

中图分类号: 

  • P314
[1]杨淑贞, 张文仁, 沈显杰. 孔隙岩石热导率的饱水试验研究. 岩石学报, 1986, 2(4): 83-91. Yang S Z, Zhang W R, Shen X J. Experimental research on the thermal conductivity of water-saturated porous rocks. Acta Petrologica Sinica (in Chinese), 1986, 2(4): 83-91.
[2]Bear J著. 李竞生, 陈崇希译. 多孔介质流体动力学. 北京: 中国建筑工业出版社, 1983. Bear J. Translated by Li J Z, Chen C X. Dynamics of Fluids in Porous Media (in Chinese). Beijing: China Architecture and Building Press, 1983.
[3]李大心. 国外岩石热导率的研究动向. 地质科技情报, 1985, 4(2): 12-20. Li D X. Research trends of thermal conductivity of rocks abroad. Geological Science and Technology Information (in Chinese), 1985, 4(2): 12-20.
[4]Miller M N. Bounds for effective electrical, thermal, and magnetic properties of heterogeneous materials. Mathematical Physics, 1969, 12(10): 1988-2004.
[5]Carbonell R G, Whitaker S. Heat and mass transfer in porous media. //Proceedings of the NATO Advanced Study Institute on Mechanics of Fluids in Porous Media. Newark, USA, 1982; 121-198.
[6]Hadley G R. Thermal conductivity of packed metal powders. Int. J. Heat and Mass Transfer, 1986, 29(6): 909-920.
[7]Kaviany M. Principle of Heat Transfer in Porous Media. New York: Springer-Verlag, 1995.
[8]Katz A J, Thompson A H. Fractal sandstone pores: implications for conductivity and pore formation. Physical Review Letters, 1985, 54(12): 1325-1328.
[9]Thompson A H, Katz A J, Krohn C E. The microgeometry and transport properties of sedimentary rock. Advances in Physics, 1987, 36(5): 625-694.
[10]李小川, 施明恒, 张东辉. 非均匀多孔介质中导热过程. 东南大学学报(自然科学版), 2005, 35(5): 761-766. Li X C, Shi M H, Zhang D H. Heat conduction process in non-uniform porous media. Journal of Southeast University (Natural Science Edition) (in Chinese), 2005, 35(5): 761-766.
[11]Bogaty H, Hollies N R S, Milton H M. Some thermal properties of fabrics: Part Ⅰ. The effect of arrangement. Text. Res. J., 1957, 27(6): 445-449.
[12]Hollies N R S, Bogarty H. Some thermal properties of fabrics Part Ⅱ. The effect of water content. Text. Res. J., 1965, 35(2): 187-190.
[13]Singh A K, Singh R, Chaudhary D R. Heat conduction through moist soils at different temperatures. Pramana, 1988, 31(6): 523-528.
[14]Pande R N, Kumar V, Chaudhary D R. Thermal conduction in a homogeneous two-phase system. Pramana, 1984, 22(1): 63-70.
[15]Pande R N, Chaudhary D R. Thermal conduction through loose and granular two-phase materials at normal pressure. Pramana, 1984, 23(5): 599-605.
[16]Zhang H F, Ge X S, Ye H. Effectiveness of the heat conduction reinforcement of particle filled composites. Modelling Simul. Mater. Sci. Eng., 2005, 13(3): 401-412.
[17]Zhang H F, Ge X S, Ye H. Randomly mixed model for predicting the effective thermal conductivity of moist porous media. J. Phys. D: Appl. Phys., 2006, 39(1): 220-226.
[18]Zhang H F, Ge X S, Ye H, et al. Heat conduction and heat storage characteristics of soils. Applied Thermal Engineering, 2007, 27(2-3): 369-373.
[19]Wang M R, Wang J L, Pan N, et al. Three-dimensional effect on the effective thermal conductivity of porous media. Phys. D: Appl. Phys., 2007, 40(1): 260-265.
[20]Tiak D, Delkumburewatte G B. The influence of moisture content on the thermal conductivity of a knitted structure. Measurement Science and Technology, 2007, 18(5): 1304-1314.
[21]Aurangzeb, Maqsood A. Modeling of the effective thermal conductivity of consolidated porous media with different Saturants: A test case of Gabbro rocks. International Journal of Thermophysics, 2007, 28(4): 1371-1386.
[22]景惠敏. 数值模拟在地震海啸、港口风浪等地学问题上的应用. 北京: 中国科学院研究生院地球科学学院, 2011. Jing H M. Numerical simulation applied in evaluation of tsunami and wave hazard in a harbor (in Chinese). Beijing: College of Earth Science, Graduate University of Chinese Academy of Sciences, 2011.
[23]王勖成. 有限单元法. 北京: 清华大学出版社, 2003. Wang X C. Finite Element Method (in Chinese). Beijing: Tsinghua University Press, 2003.
[24]Bouguerra A. Prediction of effective thermal conductivity of moist wood concrete. J. Phys. D: Appl. Phys., 1999, 32(12): 1407-1414.
[25]Vermia L S, Shrotriya A K, Singh R, et al. Prediction and measurement of effective thermal conductivity of three phase systems. J. Phys. D: Appl. Phys., 1991, 24(9): 1515-1526.
[26]Somerton W H. Thermal Properties and Temperature Related Behavior of Rock/Fluid Systems. New York: Elsevier, 1992.
[27]Zhu B J, Cheng H H, Qiao Y C, et al. Porosity and permeability evolution and evaluation in anisotropic porosity multiscale-multiphase-multicomponent structure. Chinese Science Bulletin, 2012, 57(4): 320-327.
[1] 黄晞桐;宋海斌;关永贤;耿明会;王亚龙. 基于流体动力学数值模拟的海水层反射地震研究[J]. 地球物理学报, 2018, 61(7): 2892-2904.
[2] 徐世刚;刘洋. 基于优化有限差分和混合吸收边界条件的三维VTI介质声波和弹性波数值模拟[J]. 地球物理学报, 2018, 61(7): 2950-2968.
[3] 徐凯军;李猛. 基于自适应有限元的复电阻率法2.5维复杂构造电磁场模拟[J]. 地球物理学报, 2018, 61(7): 3102-3111.
[4] 柯灝;吴敬文;李斐;王泽民;张胜凯;赵建虎. 基于潮波运动三维数值模拟的海洋连续深度基准面建立方法研究[J]. 地球物理学报, 2018, 61(6): 2220-2226.
[5] 孙云强;罗纲. 青藏高原东北缘地震时空迁移的有限元数值模拟[J]. 地球物理学报, 2018, 61(6): 2246-2264.
[6] 姚琪;徐锡伟;邢会林;程佳;江国焰;马未宇;刘杰;杨文. 2015年尼泊尔地震三维发震构造及地震危险性研究[J]. 地球物理学报, 2018, 61(6): 2332-2343.
[7] 吴建鲁;吴国忱. 频率域声-弹耦合地震波波动方程有限差分方法[J]. 地球物理学报, 2018, 61(6): 2396-2408.
[8] 皮娇龙;滕吉文;刘有山. 地震槽波的数学-物理模拟初探[J]. 地球物理学报, 2018, 61(6): 2481-2493.
[9] 陈汉波;李桐林;熊彬;王恒;张镕哲;李少朋. 基于微增模型的海洋可控源电磁法三维非结构化矢量有限元数值模拟[J]. 地球物理学报, 2018, 61(6): 2560-2577.
[10] 曹晓月;殷长春;张博;黄鑫;刘云鹤;蔡晶. 面向目标自适应有限元法的带地形三维大地电磁各向异性正演模拟[J]. 地球物理学报, 2018, 61(6): 2618-2628.
[11] 师皓宇;马念杰;马骥. 龙门山断裂带形成过程及其地应力状态模拟[J]. 地球物理学报, 2018, 61(5): 1817-1823.
[12] 赵由佳;张国宏;单新建;尹昊;屈春燕. 考虑地形起伏和障碍体破裂的汶川地震强地面运动数值模拟[J]. 地球物理学报, 2018, 61(5): 1853-1862.
[13] 尹力;罗纲. 有限元数值模拟龙门山断裂带地震循环的地壳变形演化[J]. 地球物理学报, 2018, 61(4): 1238-1257.
[14] 白帆;陈祖安;白武明. 地幔柱与岩石圈相互作用过程中熔融问题的数值模拟[J]. 地球物理学报, 2018, 61(4): 1341-1351.
[15] 董超;焦立果;张怀;程惠红;石耀霖. 外核黏性对地磁场发电机数值模型的影响[J]. 地球物理学报, 2018, 61(4): 1366-1377.
浏览
全文


摘要

被引

  分享   
  讨论   
No Suggested Reading articles found!