赫-巴流体在偏心环空中的波动压力计算模型
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摘要
在窄环空间隙中下套管、小井眼钻进、深水钻进和大位移井钻进等作业中,精确的波动压力计算模型是准确预测井底压力的前提。以往利用CFD软件模拟赫-巴流体在偏心环空中流动的波动压力计算方法不仅对计算机性能要求高,而且时间成本高,导致现场应用受限。用窄槽流动模型模拟偏心环空建立了流体流动的物理模型,在稳态层流条件下,结合流体流动的控制方程和赫-巴流体的流变方程,建立了波动压力数学模型和基于自适应辛普森积分与黄金分割理论的数值求解方法,利用室内试验结果对模型的合理性进行了对比验证。结果表明:建立的赫-巴流体在偏心环空中的波动压力数学模型结果准确;采用的数值求解方法精度高、速度快,与室内试验数据对比误差在10%以内,满足现场精度需求;分析了波动压力的影响因素,在管柱处于完全偏心的情况下,波动压力梯度降低为同心环空的50%左右,在窄环空间隙中作业时,应严格限制起下钻的速度。
A precise computational model for surge pressure is the prerequisite to accurately predict the bottom-hole pressure in various drilling operations,including casing in narrow annular space,as well as drilling in slim holes,deep-water and extended-reach wells.Traditional computational methods for surge pressure,which use Calculation Fluids Dynamics(CFD)software to simulate the flow of Herschel-Bulkley fluid in eccentric annuli,require high computer performance and is time costing,resulting in limited field application.A physical model of fluid motion is established using narrow slot flow model to simulate eccentric annulus.Under the condition of steady laminar flow,a mathematical model of surge and swab pressure and analytical solution method based on the golden section method and self-adaptive Simpson integral method are obtained by combining the governing equations of fluid motion and rheology equation of Herschel-Bulkley fluid.The rationality of this model is verified by laboratory test data.The mathematical model for the surge-swab pressure of Herschel-Bulkley fluid in eccentric annulus shows high accuracy and fast computational velocity in terms of numerical method.Compared with the laboratory test data,the error is within the range of±10%,indicating that the model is sufficiently accurate to meet the requirements of field operations.The influence factors of the surge-swab pressure are analyzed.Under the condition of totally eccentric annulus,the gradient of surge pressure decreases to around 50% of that for concentric annulus.The tripping velocity should be strictly limited for operations in the narrow annular space.
A precise computational model for surge pressure is the prerequisite to accurately predict the bottom-hole pressure in various drilling operations,including casing in narrow annular space,as well as drilling in slim holes,deep-water and extended-reach wells.Traditional computational methods for surge pressure,which use Calculation Fluids Dynamics(CFD)software to simulate the flow of Herschel-Bulkley fluid in eccentric annuli,require high computer performance and is time costing,resulting in limited field application.A physical model of fluid motion is established using narrow slot flow model to simulate eccentric annulus.Under the condition of steady laminar flow,a mathematical model of surge and swab pressure and analytical solution method based on the golden section method and self-adaptive Simpson integral method are obtained by combining the governing equations of fluid motion and rheology equation of Herschel-Bulkley fluid.The rationality of this model is verified by laboratory test data.The mathematical model for the surge-swab pressure of Herschel-Bulkley fluid in eccentric annulus shows high accuracy and fast computational velocity in terms of numerical method.Compared with the laboratory test data,the error is within the range of±10%,indicating that the model is sufficiently accurate to meet the requirements of field operations.The influence factors of the surge-swab pressure are analyzed.Under the condition of totally eccentric annulus,the gradient of surge pressure decreases to around 50% of that for concentric annulus.The tripping velocity should be strictly limited for operations in the narrow annular space.
引文
[1]Crespo F E,Ahmed R M,Saasen A.Surge-and-swab pressure predictions for yield-power-law drilling fluids[J].SPE Drilling&Completion,2012,27(4):574-585.
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[3]钟兵,施太和,付建红,等.小井眼侧钻水平井波动压力计算模型[J].西南石油学院学报,1999,21(1):52-55.Zhong Bing,Shi Taihe,Fu Jianhong,et al.Model for computing surge and swab pressures in slim and horizontal holes[J].Journal of Southwest Petroleum Institute,1999,21(1):52-55.
[4]付建红,冯剑,陈平,等.深水动态压井钻井井筒压力模拟[J].石油学报,2015,36(2):232-237.Fu Jianhong,Feng Jian,Chen Ping,et al.Simulation on wellbore pressure during dynamic kill drilling in deep water[J].Acta Petrolei Sinica,2015,36(2):232-237.
[5]张波,管志川,张琦.深水油气井开采过程环空压力预测与分析[J].石油学报,2015,36(8):1012-1017.Zhang Bo,Guan Zhichuan,Zhang Qi.Prediction and analysis on annular pressure of deepwater well in the production stage[J].Acta Petrolei Sinica,2015,36(8):1012-1017.
[6]Burkhardt J A.Wellbore pressure surges produced by pipe movement[J].Journal of Petroleum Technology,1961,13(6):595-605.
[7]Schuh F J.Computer makes surge-pressure calculations useful[J].Oil and Gas Journal,1964,62(31):96-104.
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[9]汪海阁,刘希圣,董杰.偏心环空中牛顿流体稳态波动压力近似解[J].石油钻采工艺,1996,18(2):18-21.Wang Haige,Liu Xisheng,Dong Jie.Approximate solution of stable fluctuation pressure of Newtonian fluid in eccentric annular[J].Oil Drilling and Production Technology,1996,18(2):18-21.
[10]鲁港,李晓光,陈铁铮,等.钻井液卡森模式流变参数非线性最小二乘估计新算法[J].石油学报,2008,29(3):470-474.Lu Gang,Li Xiaoguang,Chen Tiezheng,et al.A new method for non-linear least square estimation on rheological parameter in Casson model of drilling fluid[J].Acta Petrolei Sinica,2008,29(3):470-474.
[11]孙玉学,李启明,孔翠龙,等.基于卡森流体的水平井波动压力预测新方法[J].钻井液与完井液,2011,28(2):29-31.Sun Yuxue,Li Qiming,Kong Cuilong,et al.New prediction method on surge pressure in horizontal well basing on Casson fluid[J].Drilling Fluid&Completion Fluid,2011,28(2):29-31.
[12]汪海阁,苏义脑,刘希圣.幂律流体偏心环空波动压力数值解[J].石油学报,1998,19(3):104-109.Wang Haige,Su Yinao,Liu Xisheng.Numerical analysis of steady surge pressure of Power-Law fluid in eccentric annuli[J].Acta Petrolei Sinica,1998,19(3):104-109.
[13]鄢捷年.钻井液工艺学[M].第2版.东营:中国石油大学出版社,2012.Yan Jienian.Drilling fluids technology[M].2nd ed.Dongying:China University of Petroleum Press,2012.
[14]朱云伟.赫-巴流体环空流动的CFD模拟[D].大庆:东北石油大学,2011.Zhu Yunwei.CFD Simulation of Herschel-Bulkley fluid flow in annulus[D].Daqing:Northeast Petroleum University,2011.
[15]魏淑惠,朱云伟,赵艳红.赫-巴流体偏心环空紊流的数值模拟[J].科学技术与工程,2011,11(21):5172-5175.Wei Shuhui,Zhu Yunwei,Zhao Yanhong.Numerical simulation of Herschel-Bulkley fluid turbulence flow in eccentric annulus[J].Science Technology and Engineering,2011,11(21):5172-5175.
[16]王常斌,陈海波,徐洋,等.赫-巴流体同心环空流动的数值模拟[J].科学技术与工程,2011,11(28):6798-6801.Wang Changbin,Chen Haibo,Xu Yang,et al.Numerical simulation of Herschel-Bulkley fluid concentric annulus flow[J].Science Technology and Engineering,2011,11(28):6798-6801.
[17]樊洪海.实用钻井流体力学[M].北京:石油工业出版社,2014.Fan Honghai.Practical drilling fluid mechanics[M].Beijing:Petroleum Industry Press,2014.
[18]李琪,王再兴,沈黎阳,等.基于改进黄金分割法的钻井液流变模式优选[J].钻井液与完井液,2016,33(1):57-62.Li Qi,Wang Zaixing,Shen Liyang,et al.Optimization of drilling fluid rheology pattern using improved golden section method[J].Drilling Fluid&Completion Fluid,2016,33(1):57-62.
[19]郭宇建.起下钻工况下井筒压力波动计算模型及实验研究[D].北京:中国石油大学,2014.Guo Yujian,Research on calculation models and experiment of surge-swab pressure while tripping[D].Beijing:China University of Petroleum,2014.
[20]Crespo F,Ahmed R.A simplified surge and swab pressure model for yield power law fluids[J].Journal of Petroleum Science and Engineering,2013,101:12-20.
[21]郭宇健,李根生,宋先知,等.基于赫巴流体的偏心环空波动压力数值模拟[J].石油机械,2014,42(3):5-9.Guo Yujian,Li Gensheng,Song Xianzhi,et al.Herschel-Buckley fluid-based numerical simulation of eccentric annular fluctuating pressure[J].China Petroleum Machinery,2014,42(3):5-9.
[22]张晋凯,李根生,郭宇健.钻井液流变模式的优选与评价[J].科学技术与工程,2013,13(26):7619-7623.Zhang Jinkai,Li Gensheng,Guo Yujian.Optimization and evaluation on drilling fluid rheological model[J].Science Technology and Engineering,2013,13(26):7619-7623.
[23]汪海阁,苏义脑.管柱运动过程中钻井液粘附系数计算[J].钻采工艺,1996,19(6):64-66.Wang Haige,Su Yinao.Calculation of drilling fluid adhesion coefficient during the process of drilling string movement[J].Drilling&Production Technology,1996,19(6):64-66.
[2]Srivastav R,Enfis M S,Crespo F E,et al.Surge and swab pressures in horizontal and inclined wells[R].SPE152662,2012.
[3]钟兵,施太和,付建红,等.小井眼侧钻水平井波动压力计算模型[J].西南石油学院学报,1999,21(1):52-55.Zhong Bing,Shi Taihe,Fu Jianhong,et al.Model for computing surge and swab pressures in slim and horizontal holes[J].Journal of Southwest Petroleum Institute,1999,21(1):52-55.
[4]付建红,冯剑,陈平,等.深水动态压井钻井井筒压力模拟[J].石油学报,2015,36(2):232-237.Fu Jianhong,Feng Jian,Chen Ping,et al.Simulation on wellbore pressure during dynamic kill drilling in deep water[J].Acta Petrolei Sinica,2015,36(2):232-237.
[5]张波,管志川,张琦.深水油气井开采过程环空压力预测与分析[J].石油学报,2015,36(8):1012-1017.Zhang Bo,Guan Zhichuan,Zhang Qi.Prediction and analysis on annular pressure of deepwater well in the production stage[J].Acta Petrolei Sinica,2015,36(8):1012-1017.
[6]Burkhardt J A.Wellbore pressure surges produced by pipe movement[J].Journal of Petroleum Technology,1961,13(6):595-605.
[7]Schuh F J.Computer makes surge-pressure calculations useful[J].Oil and Gas Journal,1964,62(31):96-104.
[8]李启明.适于水平井的波动压力预测新模型研究[D].大庆:东北石油大学,2011.Li Qiming.Research on a new prediction model of surge pressure appropriated to horizontal well[D].Daqing:Northeast Petroleum University,2011.
[9]汪海阁,刘希圣,董杰.偏心环空中牛顿流体稳态波动压力近似解[J].石油钻采工艺,1996,18(2):18-21.Wang Haige,Liu Xisheng,Dong Jie.Approximate solution of stable fluctuation pressure of Newtonian fluid in eccentric annular[J].Oil Drilling and Production Technology,1996,18(2):18-21.
[10]鲁港,李晓光,陈铁铮,等.钻井液卡森模式流变参数非线性最小二乘估计新算法[J].石油学报,2008,29(3):470-474.Lu Gang,Li Xiaoguang,Chen Tiezheng,et al.A new method for non-linear least square estimation on rheological parameter in Casson model of drilling fluid[J].Acta Petrolei Sinica,2008,29(3):470-474.
[11]孙玉学,李启明,孔翠龙,等.基于卡森流体的水平井波动压力预测新方法[J].钻井液与完井液,2011,28(2):29-31.Sun Yuxue,Li Qiming,Kong Cuilong,et al.New prediction method on surge pressure in horizontal well basing on Casson fluid[J].Drilling Fluid&Completion Fluid,2011,28(2):29-31.
[12]汪海阁,苏义脑,刘希圣.幂律流体偏心环空波动压力数值解[J].石油学报,1998,19(3):104-109.Wang Haige,Su Yinao,Liu Xisheng.Numerical analysis of steady surge pressure of Power-Law fluid in eccentric annuli[J].Acta Petrolei Sinica,1998,19(3):104-109.
[13]鄢捷年.钻井液工艺学[M].第2版.东营:中国石油大学出版社,2012.Yan Jienian.Drilling fluids technology[M].2nd ed.Dongying:China University of Petroleum Press,2012.
[14]朱云伟.赫-巴流体环空流动的CFD模拟[D].大庆:东北石油大学,2011.Zhu Yunwei.CFD Simulation of Herschel-Bulkley fluid flow in annulus[D].Daqing:Northeast Petroleum University,2011.
[15]魏淑惠,朱云伟,赵艳红.赫-巴流体偏心环空紊流的数值模拟[J].科学技术与工程,2011,11(21):5172-5175.Wei Shuhui,Zhu Yunwei,Zhao Yanhong.Numerical simulation of Herschel-Bulkley fluid turbulence flow in eccentric annulus[J].Science Technology and Engineering,2011,11(21):5172-5175.
[16]王常斌,陈海波,徐洋,等.赫-巴流体同心环空流动的数值模拟[J].科学技术与工程,2011,11(28):6798-6801.Wang Changbin,Chen Haibo,Xu Yang,et al.Numerical simulation of Herschel-Bulkley fluid concentric annulus flow[J].Science Technology and Engineering,2011,11(28):6798-6801.
[17]樊洪海.实用钻井流体力学[M].北京:石油工业出版社,2014.Fan Honghai.Practical drilling fluid mechanics[M].Beijing:Petroleum Industry Press,2014.
[18]李琪,王再兴,沈黎阳,等.基于改进黄金分割法的钻井液流变模式优选[J].钻井液与完井液,2016,33(1):57-62.Li Qi,Wang Zaixing,Shen Liyang,et al.Optimization of drilling fluid rheology pattern using improved golden section method[J].Drilling Fluid&Completion Fluid,2016,33(1):57-62.
[19]郭宇建.起下钻工况下井筒压力波动计算模型及实验研究[D].北京:中国石油大学,2014.Guo Yujian,Research on calculation models and experiment of surge-swab pressure while tripping[D].Beijing:China University of Petroleum,2014.
[20]Crespo F,Ahmed R.A simplified surge and swab pressure model for yield power law fluids[J].Journal of Petroleum Science and Engineering,2013,101:12-20.
[21]郭宇健,李根生,宋先知,等.基于赫巴流体的偏心环空波动压力数值模拟[J].石油机械,2014,42(3):5-9.Guo Yujian,Li Gensheng,Song Xianzhi,et al.Herschel-Buckley fluid-based numerical simulation of eccentric annular fluctuating pressure[J].China Petroleum Machinery,2014,42(3):5-9.
[22]张晋凯,李根生,郭宇健.钻井液流变模式的优选与评价[J].科学技术与工程,2013,13(26):7619-7623.Zhang Jinkai,Li Gensheng,Guo Yujian.Optimization and evaluation on drilling fluid rheological model[J].Science Technology and Engineering,2013,13(26):7619-7623.
[23]汪海阁,苏义脑.管柱运动过程中钻井液粘附系数计算[J].钻采工艺,1996,19(6):64-66.Wang Haige,Su Yinao.Calculation of drilling fluid adhesion coefficient during the process of drilling string movement[J].Drilling&Production Technology,1996,19(6):64-66.