基于量纲分析和达西定律的地下化学爆炸气体泄漏规律
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摘要
针对周围是均匀岩石介质的地下化学爆炸,研究爆炸后爆室内气体的泄漏规律.利用量纲分析,得到影响气体泄漏时间的主要物理量,包括气体动力学粘度、爆室内超压、围岩孔隙率及围岩厚度的平方与渗透率的比值等,并初步给出它们之间的函数关系.然后基于达西定律,推导计算气体泄漏时间的解析公式.得到的气体泄漏时间计算公式与通过量纲分析得到的定性函数关系式完全相符,二者从不同的角度对同一问题给出了相容的结果.可为地下化学爆炸气体泄漏的理论分析和规律性研究提供研究思路和工具,为地下爆炸有关的工程估算提供参考依据.
For underground chemical explosions in a cavity surrounded by uniform rock media, regularity of gas leakage was studied. Firstly, with method of dimensional analysis, influence physical quantities of gas leakage time, such as gas dynamic viscosity, overpressure of cavity, porosity of surrounding rock and ratio of the square of surrounding rock's thickness to permeability, were obtained. Qualitative functional relation of these quantities was proposed. Then, on the basis of Darcy's law, analytical formula for gas leakage time was derived. It agrees well with the qualitative functional relation derived with dimensional analysis method. Namely, two functions derived from totally different ways are highly compatible with each other. The method proposed is an enlightening idea and an efficient technique for theoretical analysis and regularity research of underground explosions gas leakage. It provides references for engineering estimation.
For underground chemical explosions in a cavity surrounded by uniform rock media, regularity of gas leakage was studied. Firstly, with method of dimensional analysis, influence physical quantities of gas leakage time, such as gas dynamic viscosity, overpressure of cavity, porosity of surrounding rock and ratio of the square of surrounding rock's thickness to permeability, were obtained. Qualitative functional relation of these quantities was proposed. Then, on the basis of Darcy's law, analytical formula for gas leakage time was derived. It agrees well with the qualitative functional relation derived with dimensional analysis method. Namely, two functions derived from totally different ways are highly compatible with each other. The method proposed is an enlightening idea and an efficient technique for theoretical analysis and regularity research of underground explosions gas leakage. It provides references for engineering estimation.
引文
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[2] HE Congge,FAN Zifei,XU Anzhu,et al.Calculation of water breakthrough time in well patterns of ultra-low permeability reservoir[J].Chinese Journal of Computational Physics,2016,33(2):190-196.
[3] LIU Hailong.Pressure dynamic analysis of vertical well flow with partial penetration fractures[J].Chinese Journal of Computational Physics,2016,33(3):322-332.
[4] LIU Huapu,LIU Huiqing,WANG Jing.Nonlinear percolation law in low permeability fissure cave reservoir with fractal dimension[J].Chinese Journal of Computational Physics,2018,35(1):55-63.
[5] TRAVIS B J,BIRDSELL K H.TRACR3D:A model of flow and transport in porous media-model description and user’s manual[R].DE91010691,1984.
[6] NITAO J J.User’s manual for the USNT module of the NUFT code[R].Version 2.0,UCRL-MA-130653,1998.
[7] WANG Tieliang,ZHANG Jianxin,CAO Yuan.A dual porosity mathematical model of gas transportation on underground detonation[J].Chinese Journal of Applied Mechanics,2011,28(6):565-569.
[8] WANG Tieliang,ZHANG Jianxin,HUANG Liuxing,et al.Numerical simulation of gas and aerosol migration in porous media[J].Chinese Journal of Computational Physics,2005,22(5):407-411.
[9] WANG Tieliang,TIAN Zhou,WANG Zhanjiang,et al.Regularity of gas leakage from scaled underground chemical explosions[J].Chinese Journal of Computational Physics,2013,30(2):209-213.
[10] TAN Qingming.Dimensional analysis[M].Hefei:Press of University of Science and Technology of China,2005.
[11] BUCKINGHAM E.On Physically similar systems:Illustrations of the use of dimensional analysis[J].Physical Review,1914,4(4):345-376.
[12] TAYLOR G I.The formation of a blast wave by a very intense explosion I:Theoretical discussion[J].Proceedings of the Royal Society of London,Series A:Mathematical and Physical Sciences,1950,201(1065):159-174.
[13] TAYLOR G I.The formation of a blast wave by a very intense explosion II:The atomic explosion of 1945[J].Proceedings of the Royal Society of London,Series A:Mathematical and Physical Sciences,1950,201(1065):175-186.
[14] ZHONG Wei.The numerical calculations for chemical reaction kinetics of confined explosions [D].Xi’an:Northwest Institute of Nuclear Technology,2012.
[15] ZHONG Wei,TIAN Zhou.Calculation of quasi-static pressure for confined explosions considering chemical reactions under isobaric assumption[J].Explosion and Shock Waves,2013,33(4):375-380.
[16] ZHONGG Wei,TIAN Zhou.Numerical calculation of quasi-static pressures of confined explosions considering chemical reactions kinetic of detonation products[J].Explosion and Shock Waves,2013,33(S1):78-83.
[17] WANG Tieliang,WANG Zhanjiang,LU Qiang,et al.Experimental research on gas leakage from chemical explosion in rock[J].Explosion and Shock Waves,2014,34(6):754-758.
[18] WANG Tieliang,CAO Yuan,ZHANG Jianxin.Numerical simulation of cavity pressure and temperature in underground detonation[J].Chinese Journal of Computational Physics,2011,28(5):713-718.