埋地管道小泄漏模型及数值求解
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摘要
随着全国范围的天然气管网逐渐形成,管道运行安全管理的重要性日益突出。在气体单相渗流理论的基础上,结合高速非达西渗流理论,建立了埋地管道发生穿孔小泄漏后在土壤中渗流的数学模型。利用有限体积法对控制方程做离散,以三对角阵(TD-MA)和交替方向隐式线迭代法(ADI)对离散方程进行求解。结合实验研究,得到了适用于地表土壤的高速非达西渗流系数经验公式和土壤变形压力修正公式。采用该修正公式计算得到的压力分布与实验结果吻合较好,证明了数值模型的正确性。
Several long-distance transporting pipelines have been constructed in the past ten years to meet the rapid increasing demand and usage of natural gases in China.Along with the construction of West-East China and Sichuan to eastern China long-distance natural gas transporting pipelines,a national-wide gas pipeline network has taken shape.Therefore,safety management of pipelines has gained more and more attention.A mathematic model for the natural gas porous flow in soil after the underground pipeline small leakage was established based on theories of the single-phase porous flow and high-speed non-Darcy porous flow.A finite volumetric method was applied to making controlling equations discrete and these discrete equation were solved with the tridiagonal matrix(TDMA) and the alternating direction implicit(ADI).An empirical equation applicable to the high-speed non-Darcy seepage coefficient of surface soil and a pressure-modifier formula of soil deformation were derived through a comparison of experimental data with numerical simulation results.The pressure distribution acquired by the calculation with the empirical equation was in a good agreement with experiment results,which proves the correctness of the numerical model.
Several long-distance transporting pipelines have been constructed in the past ten years to meet the rapid increasing demand and usage of natural gases in China.Along with the construction of West-East China and Sichuan to eastern China long-distance natural gas transporting pipelines,a national-wide gas pipeline network has taken shape.Therefore,safety management of pipelines has gained more and more attention.A mathematic model for the natural gas porous flow in soil after the underground pipeline small leakage was established based on theories of the single-phase porous flow and high-speed non-Darcy porous flow.A finite volumetric method was applied to making controlling equations discrete and these discrete equation were solved with the tridiagonal matrix(TDMA) and the alternating direction implicit(ADI).An empirical equation applicable to the high-speed non-Darcy seepage coefficient of surface soil and a pressure-modifier formula of soil deformation were derived through a comparison of experimental data with numerical simulation results.The pressure distribution acquired by the calculation with the empirical equation was in a good agreement with experiment results,which proves the correctness of the numerical model.
引文
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[2]王玉梅,郭书平.国外天然气管道事故分析[J].油气储运,2000,19(7):5-10.Wang Yumei,Guo Shuping.Accidental analysis on abroad natural gas pipelines[J].Oil&Gas Storage and Transportation,2000,19(7):5-10.
[3]张宇,靳世久,何静菁,等.基于动态压力信号的管道泄漏特征提取方法研究[J].石油学报,2010,31(2):338-342.Zhang Yu,Jin Shijiu,He Jingjing,et al.Extraction method for pipeline leakage feature based on dynamic pressure signal[J].Acta Petrolei Sinica,2010,31(2):338-342.
[4]帅健,王晓霖,牛双会.基于C/S网络模式的管道完整性管理系统[J].石油学报,2010,31(2):327-332.Shuai Jian,Wang Xiaolin,Niu Shuanghui.A pipeline integrity management system based on Client/Server mode[J].Acta Pe-trolei Sinica,2010,31(2):327-332.
[5]霍春勇,董玉华,余大涛,等.长输管线气体泄漏率的计算方法研究[J].石油学报,2004,25(1):101-105.Huo Chunyong,Dong Yuhua,Yu Datao,et al.Estimation of acci-dental gas release flow rate in long transmission pipelines[J].Acta Petrolei Sinica,2004,25(1):101-105.
[6]国辉.我国城市天然气管道事故统计及分析[J].安全、健康和环境,2008,8(4):6-8.Guo Hui.Statistics and analysis for accidents from natural gas pipelines in cities in China[J].Safety Health&Environment,2008,8(4):6-8.
[7]张建国,雷光伦,张艳玉.油气层渗流力学[M].东营:石油大学出版社,1998.Zhang Jianguo,Lei Guanglun,Zhang Yanyu.Permeation fluid mechanics of hydrocarbon reservoir[M].Dongying:The Press of the University of Petroleum,China,1998.
[8]Forchheimer P.Wasserbewegung durch Boden[J].Z.Vere-ines deutscher Ingenieure,1901,45:1782-1788.
[9]Cornell D,Katz D L.Flow of gases through consolidated porous media[J].Industrial and Engineering Chemistry,1953,45(10):21-45.
[10]Geertsma J.Estimating the coefficient of inertial resistanee in fluid flow through porous media[J].SPE Journal,1974,14(5):445-450.
[11]Frederick D C,Gravers R M.New correlations to predict Non-Darcy flow coefficients at immobile and mobile water saturation[R].SPE28451,1994.
[12]Fevang C,Whitson C H.Modeling gas-condensate well deliver-ability[R].SPE30714,1995.
[13]马婧,程时清.高速非达西气井渗流模型及压力曲线特征[J].石油钻探技术,2009,37(4):28-31.Ma Jing,Cheng Shiqing.High velocity Non-Darcy flow model and pressure distribution[J].Petroleum Drilling Techniques,2009,37(4):28-31.
[14]康晓东,李相方,程时清.考虑流动边界影响的气井非达西效应评价[J].中国石油大学学报:自然科学版,2006,30(1):82-85.Kang Xiaodong,Li Xiangfang,Cheng Shiqing.Evaluation of non-Darcy flow effect in gas well considering influence of flow bound-ary[J].Journal of China University of Petroleum:Edition of Nat-ural Science,2006,30(1):82-85.
[15]康晓东,李相方,郝伟.气井高速非达西流动附加压降计算公式的修正[J].油气井测试,2004,13(5):4-5.Kang Xiaodong,Li Xiangfang,Hao Wei.Pressure drop calcula-tion of Non Darcy flow at high velocity for gas well[J].Well Testing,2004,13(5):4-5.
[16]陶文铨.数值传热学[M].西安:西安交通大学出版社,2001.Tao Wenquan.Numerical heat transfer[M].Xi’an:Xi’an Jiao-tong University Press,2001.
[17]陆金甫,关治.偏微分方程数值解法[M].北京:清华大学出版社,2004.Lu Jinfu,Guan Zhi.Numerical solution of partial differential e-quations[M].Beijing:Thinghua University Press,2004.
[18]陶同康.堤坝非稳定渗流试验研究与计算[J].岩土工程学报,1981,3(1):81-93.Tao Tongkang.Experiment study and computation of unsteady seepage in embankment dams[J].Chinese Journal of Geotechni-cal Engineering,1981,3(1):81-93.
[19]严飞,詹美礼,速宝玉.堤坝非饱和渗流模型实验[J].岩土工程学报,2004,26(2):296-298.Yan Fei,Zhan Meili,Su Baoyu.Model test on unsaturated seep-age of dike[J].Chinese Journal of Geotechnical Engineering,2004,26(2):296-298.
[20]付俊峰.基于水头饱和度分布的双变量土坝渗流研究[D].大连:大连理工大学,2009.Fu Junfeng.The research of seepage flow through dam based on the distributions of waterhead and saturation[D].Dalian:Dalian University of Technology,2009.
[21]杨乐巍.土壤气相抽提(SVE)现场实验研究[D].天津:天津大学,2006.Yang Lewei.Field study of soil vapor extraction(SVE)[D].Tianjin:Tianjin University,2006.
[22]刘晓旭,钟兵,胡勇,等.低渗透气藏气体渗流机理实验[J].天然气工业,2008,28(4):130-132.Liu Xiaoxu,Zhong Bing,Hu Yong,et al.Experiment on gas seepage mechanism in low-permeability gas reservoirs[J].Natu-ral Gas Industry,2008,28(4):130-132.
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