一种非稳态气体渗流条件下岩石渗透特性参数计算方法及应用
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摘要
提出了一种非稳态渗流条件下岩石材料气体渗透特性参数的计算方法。首先将气体滑移方程代入非稳态渗流偏微分方程,利用Picard-Newton差分迭代格式建立非稳态渗流方程的数值解。基于此数值解,对非稳态渗流气压变化曲线进行拟合,利用最小二乘原理反算确定最优的绝对渗透率和滑移因子。算例表明,计算稳定收敛,对步长和随机误差不敏感,同时能够准确捕捉渗透性能参数的微小变化。最后,利用该方法成功测试了位于中国高放废物处置首选预选区的甘肃北山坑探设施硐室掌子面花岗岩的气体渗透特性。提出的方法所需输入数据的获取手段简单,核心算法便于数值实现,可以应用于地下工程围岩的气体渗透性能测试。
To test the gas permeability of rock under unsteady flow condition, a new method of calculating the gas permeability was proposed in this paper. Klinkenberg's equation was firstly imported into the partial differential equation of unsteady flow. A numerical solution of this partial differential equation was then generated by using Picard-Newton's difference scheme. Based on this numerical solution, a new method of searching the optimal absolute permeability and slip factor of rock was proposed by fitting the variation of gas pressure under unsteady flow condition with least-square method. The numerical calculation in this method was proven to be stable, convergent and insensitive to step size and random errors, and the slight variation of absolute permeability and slip factor can be successfully captured. Finally, some granite samples from the surrounding rock of the Beishan exploration tunnel, which was located in the pre-selected area for China's high-level radioactive waste disposal, were tested and the absolute gas permeability and slip factor were successfully identified by the proposed method. The input data needed in the proposed method can be easily obtained by simple indoor test and the key algorithm is convenient for numerical realization. Thus it can be applied to the gas permeability test of surrounding rock materials in underground engineering.
To test the gas permeability of rock under unsteady flow condition, a new method of calculating the gas permeability was proposed in this paper. Klinkenberg's equation was firstly imported into the partial differential equation of unsteady flow. A numerical solution of this partial differential equation was then generated by using Picard-Newton's difference scheme. Based on this numerical solution, a new method of searching the optimal absolute permeability and slip factor of rock was proposed by fitting the variation of gas pressure under unsteady flow condition with least-square method. The numerical calculation in this method was proven to be stable, convergent and insensitive to step size and random errors, and the slight variation of absolute permeability and slip factor can be successfully captured. Finally, some granite samples from the surrounding rock of the Beishan exploration tunnel, which was located in the pre-selected area for China's high-level radioactive waste disposal, were tested and the absolute gas permeability and slip factor were successfully identified by the proposed method. The input data needed in the proposed method can be easily obtained by simple indoor test and the key algorithm is convenient for numerical realization. Thus it can be applied to the gas permeability test of surrounding rock materials in underground engineering.
引文
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[11]赵鹏,刘健,陈亮,等.非饱和花岗岩气体相对渗透率试验研究[J].地下空间与工程学报,2017,13(1):57-62.ZHAO Peng,LIU Jian,CHEN Liang,et al.Experimental study on gas relative permeability of unsaturated granite[J].Chinese Journal of Underground Space and Engineering,2017,13(1):57-62.
[12]马利科.高放废物处置库甘肃北山花岗岩围岩长期稳定性研究[D].北京:核工业北京地质研究院,2017:96-105.MA Li-ke.Study on long-term stability of surrounding rock for high-level radioactive waste disposal in Beishan,Gansu[D].Beijing:Beijing Research Institute of Uranium Geology,2017:96-105.
[13]KLINKENBERG L J.The permeability of porous media to liquids and gases[J].Socar Proceedings,1941,2(2):200-213.
[14]FINSTERLE S,PERSOFF P.Determining permeability of tight rock samples using inverse modeling[J].Water Resources Research,1997,33(8):1803-1811.
[15]陈卫忠,杨建平,伍国军,等.低渗介质渗透性试验研究[J].岩石力学与工程学报,2008,27(2):236-243.CHEN Wei-zhong,YANG Jian-ping,WU Guo-jun,et al.Experimental study on permeability in low permeability media[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(2):236-243.
[16]袁光伟,盛志强,杭旭登,等.扩散方程计算方法[M].北京:科学出版社,2015:167-194.YUAN Guang-wei,SHENG Zhi-qiang,HANG Xu-deng,et al.Calculation method of diffusion equation[M].Beijing:Science Press,2015:167-194.
[17]PRESS W H,TEUKOLSKY S A,VETTERLING W T,et al.Numerical recipes in C-the art of scientific computing(second edition)[M].Cambridge:Cambridge University Press,1992:394-444.
[18]SCIPY Community.SCIPY reference guide-release0.12.0[M].Texas:[s.n.],2013:558-559.
[19]WANG J,CHEN L,SU R,et al.The Beishan underground research laboratory for geological disposal of high-level radioactive waste in China:planning,site selection,site characterization and in-situ tests[J].Journal of Rock Mechanics and Geotechnical Engineering,2018,10(3):411-435.
[2]杨伟,王雪亮,马成荣.国内外地下储气库现状及发展趋势[J].油气储运,2007,26(6):15-19.YANG Wei,WANG Xue-liang,MA Cheng-rong.Underground gas storage-status quo and development worldwide,OGST[J].Oil&Gas Storage,2007,26(6):15-19.
[3]谢健,魏宁,吴礼舟,等.CO2地质封存泄露研究进展[J].岩土力学,2017,38(增刊1):181-188.XIE Jian,WEI Ning,WU Li-zhou,et al.Progress in leakage study of geological CO2 storage[J].Rock and Soil Mechanics,2017,38(Suppl.1):181-188.
[4]陈祥胜,李银平,尹洪武,等.多夹层盐矿地下储气库气体渗漏评价方法[J].岩土力学,2018,39(1):11-20.CHEN Xiang-sheng,LI Yin-ping,YIN Hong-wu,et al.Gas leakage assessment method of underground gas storage in multi-interlayer salt mine[J].Rock and Soil Mechanics,2018,39(1):11-20.
[5]邹才能,董大忠,王社教,等.中国页岩气形成机理、地质特征及资源潜力[J].石油勘探与开发,2010,37(6):641-653.ZOU Cai-neng,DONG Da-zhong,WANG She-jiao,et al.Geological characteristics,formation mechanism and resource potential of shale gas in China[J].Petroleum Exploration and Development,2010,37(6):641-653.
[6]HO C K,WEBB S W.Gas transport in porous media[M].Dordrecht:Springer,2006:5-26.
[7]DANA E,SKOCZYLAS F.Gas relative permeability and pore structure of sandstones[J].International Journal of Rock Mechanics&Mining Sciences,1999,36(5):613-625.
[8]BRACE W F,WALSH J B,FRANGOS W T.Permeability of granite under high pressure[J].Journal of Geophysical Research,1968,73(6):2225-2236.
[9]贾朝军,王环玲,徐卫亚,等.地下水封洞库围岩气体渗透特性及滑脱效应研究[J].工程力学,2015,32(8):50-57.JIA Chao-jun,WANG Huan-ling,XU Wei-ya,et al.Study on gas permeation and slippage effects in rock mass of underground water-sealed cave[J].Engineering Mechanics,2015,32(8):50-57.
[10]胡少华,陈益峰,周创兵.北山花岗岩渗透特性试验研究与细观力学分析[J].岩石力学与工程学报,2014,33(11):2200-2209.HU Shao-hua,CHEN Yi-feng,ZHOU Chuang-bing.Laboratory test and mesomechanical analysis of permeability variation of Beishan granite[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(11):2200-2209.
[11]赵鹏,刘健,陈亮,等.非饱和花岗岩气体相对渗透率试验研究[J].地下空间与工程学报,2017,13(1):57-62.ZHAO Peng,LIU Jian,CHEN Liang,et al.Experimental study on gas relative permeability of unsaturated granite[J].Chinese Journal of Underground Space and Engineering,2017,13(1):57-62.
[12]马利科.高放废物处置库甘肃北山花岗岩围岩长期稳定性研究[D].北京:核工业北京地质研究院,2017:96-105.MA Li-ke.Study on long-term stability of surrounding rock for high-level radioactive waste disposal in Beishan,Gansu[D].Beijing:Beijing Research Institute of Uranium Geology,2017:96-105.
[13]KLINKENBERG L J.The permeability of porous media to liquids and gases[J].Socar Proceedings,1941,2(2):200-213.
[14]FINSTERLE S,PERSOFF P.Determining permeability of tight rock samples using inverse modeling[J].Water Resources Research,1997,33(8):1803-1811.
[15]陈卫忠,杨建平,伍国军,等.低渗介质渗透性试验研究[J].岩石力学与工程学报,2008,27(2):236-243.CHEN Wei-zhong,YANG Jian-ping,WU Guo-jun,et al.Experimental study on permeability in low permeability media[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(2):236-243.
[16]袁光伟,盛志强,杭旭登,等.扩散方程计算方法[M].北京:科学出版社,2015:167-194.YUAN Guang-wei,SHENG Zhi-qiang,HANG Xu-deng,et al.Calculation method of diffusion equation[M].Beijing:Science Press,2015:167-194.
[17]PRESS W H,TEUKOLSKY S A,VETTERLING W T,et al.Numerical recipes in C-the art of scientific computing(second edition)[M].Cambridge:Cambridge University Press,1992:394-444.
[18]SCIPY Community.SCIPY reference guide-release0.12.0[M].Texas:[s.n.],2013:558-559.
[19]WANG J,CHEN L,SU R,et al.The Beishan underground research laboratory for geological disposal of high-level radioactive waste in China:planning,site selection,site characterization and in-situ tests[J].Journal of Rock Mechanics and Geotechnical Engineering,2018,10(3):411-435.
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