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作者简介:

孙腾飞(1986-),男,教授,博士,硕士生导师,研究方向为井筒安全技术与管理。E-mail:suntengfei@mail.buct.edu.cn。

通信作者:

孔祥伟(1982-),男,教授,博士,博士生导师,研究方向为井控技术。E-mail:76922591@qq.com。

中图分类号:TE 122.3

文献标识码:A

文章编号:1673-5005(2024)02-0083-09

DOI:10.3969/j.issn.1673-5005.2024.02.009

参考文献 1
苏义脑,路保平,刘岩生,等.中国陆上深井超深井钻完井技术现状及攻关建议[J].石油钻采工艺,2020,42(5):527-542.SU Yinao,LU Baoping,LIU Yansheng,et al.Current status and suggestions for key technologies in the drilling and completion of deep and ultra deep wells on land in China[J].Petroleum Drilling and Production Technology,2020,42(5):527-542.
参考文献 2
薛飞.深井超深井钻井技术现状和发展研究[J].化工管理,2013(22):63.XUE Fei.Research on the current situation and development of deep and ultra deep well drilling technology [J].Chemical Management,2013(22):63.
参考文献 3
吕开河,杜宏艳,孙金声,等.含油钻屑处理技术研究进展与展望[J].中国石油大学学报(自然科学版),2023,47(3):78-86.LÜ Kaihe,DU Hongyan,SUN Jinsheng,et al.Research and development of oily drilling cuttings treatment technologies[J].Journal of China University of Petroleum(Edition of Natural Science),2023,47(3):78-86.
参考文献 4
孙金声,蒋官澄,贺垠博,等.油基钻井液面临的技术难题与挑战[J].中国石油大学学报(自然科学版),2023,47(5):76-89.SUN Jinsheng,JIANG Guancheng,HE Yinbo,et al.Technical difficulties and challenges faced by oil-based drilling fluid[J].Journal of China University of Petroleum(Edition of Natural Science),2023,47(5):76-89.
参考文献 5
梁云栋,何琳,徐荣武,等.高精度液压系统压力波传递速度在线测量试验[J].国防科技大学学报,2022,44(2):195-202.LIANG Yundong,HE Lin,XU Rongwu,et al.High precision hydraulic system pressure wave transmission speed online measurement experiment [J].Journal of National University of Defense Science and Technology,2022,44(2):195-202.
参考文献 6
孔祥伟,林元华,邱伊婕,等.钻井泥浆泵失控/重载引发的波动压力[J].石油学报,2015,36(1):114-119.KONG Xiangwei,LIN Yuanhua,QIU Yijie,et al.Fluctuation pressure caused by uncontrolled/overloaded drilling mud pumps [J].Acta Petrolei Sinica,2015,36(1):114-119.
参考文献 7
VONGVUTHIPORNCHAI S,RAGHAVAN R.Pressure falloff behavior in vertically fractured wells:non-Newtonian power-law fluids [J].SPE Formation Evaluation,1987,2(4):573-589.
参考文献 8
WEISS W W,BALDWIN R W.Planning and implementing a large-scale polymer flood[J].Journal of Petroleum Technology,1985,37(4):720-730.
参考文献 9
李阳,赵清民,薛兆杰.新一代油气开发技术体系构建与创新实践[J].中国石油大学学报(自然科学版),2023,47(5):45-54.LI Yang,ZHAO Qingmin,XUE Zhaojie.Construction and innovative practice of new generation oil and gas development technology system[J].Journal of China University of Petroleum(Edition of Natural Science),2023,47(5):45-54.
参考文献 10
孔祥伟,林元华,何龙,等.一种考虑虚拟质量力的两相压力波速经验模型[J].力学季刊,2015,36(4):611-617.KONG Xiangwei,LIN Yuanhua,HE Long,et al.A two-phase pressure wave velocity empirical model considering virtual mass forces [J].Journal of Mechanics Quarterly,2015,36(4):611-617.
参考文献 11
王刚,刘刚,张悦,等.深水大尺寸井眼钻进钻井液双循环携岩方法[J].中国石油大学学报(自然科学版),2022,46(2):113-120.WANG Gang,LIU Gang,ZHANG Yue,et al.Method of double drilling fluid circulation for cuttings carrying in large-size wellbore during deepwater drilling[J].Journal of China University of Petroleum(Edition of Natural Science),2022,46(2):113-120.
参考文献 12
吕开河,王晨烨,雷少飞,等.裂缝性地层钻井液漏失规律及堵漏对策[J].中国石油大学学报(自然科学版),2022,46(2):85-93.LÜ Kaihe,WANG Chenye,LEI Shaofei,et al.Dynamic behavior and mitigation methods for drilling fluid loss in fractured formations[J].Journal of China University of Petroleum(Edition of Natural Science),2022,46(2):85-93.
参考文献 13
王庆.基于压力信号的气液两相流泄漏检测研究 [D].青岛:中国石油大学(华东),2017.WANG Qing.Research on leakage detection of gas-liquid two phase flow based on pressure signal [D].Qingdao:China University of Petroleum(East China),2017.
参考文献 14
WANG Y,CHENG S Q,ZHANG K D,et al.A comprehensive work flow to characterize waterflood-induced fractures by integrating real-time monitoring,formation test,and dynamic production analysis applied to Changqing Oilfield,China[J].SPE Reservoir Evaluation & Engineering,2018,22(2):692-708.
参考文献 15
DU Q J,PAN G M,HOU J,et al.Study of the mechanisms of streamline-adjustment-assisted heterogeneous combination flooding for enhanced oil recovery for postpolymer-flooded reservoirs [J].Petroleum Science,2019,16(3):606-618.
参考文献 16
刘璞.节流压井井筒压力动态响应分析研究[D].成都:西南石油大学,2017.LIU Pu.Analysis and research on dynamic response of choke and kill wellbore pressure [D].Chengdu:Southwest Petroleum University,2017.
参考文献 17
闫铁,屈俊波,孙晓峰,等.控压钻井回压压力波在井筒中传播的速度和时间规律[J].天然气工业,2017,37(11):77-84.YAN Tie,QU Junbo,SUN Xiaofeng,et al.The velocity and time pattern of backpressure wave propagation in wellbore during controlled pressure drilling[J].Natural Gas Industry,2017,37(11):77-84.
参考文献 18
李红涛.复杂流体介质条件下井筒压力波传播规律研究[D].成都:西南石油大学,2015.LI Hongtao.Study on propagation law of wellbore pressure wave under complex fluid medium conditions [D].Chengdu:Southwest Petroleum University,2015.
参考文献 19
步玉环,景韶瑞,杨恒,等.深水气井测试条件下井筒水合物生成及浅层水合物分解的环空保护液导热系数[J].中国石油大学学报(自然科学版),2023,47(1):81-88.BU Yuhuan,JING Shaorui,YANG Heng,et al.Influence of thermal conductivity of annular protective fluids on wellbore hydrate formation and hydrate decomposition in shallow formation during deep-water drilling and well testing[J].Journal of China University of Petroleum(Edition of Natural Science),2023,47(1):81-88.
参考文献 20
JIA Z C,LI D L,YANG J H,et al.Numerical well test analysis for polymer flooding considering the non-Newtonian behavior [J].Journal of Chemistry,2015,2015:107625.
参考文献 21
孔祥伟,林元华,邱伊婕.控压钻井中三相流体压力波速传播特性[J].力学学报,2014,46(6):887-895.KONG Xiangwei,LIN Yuanhua,QIU Yijie.Pressure wave velocity propagation characteristics of three-phase fluid in controlled pressure drilling wells[J].Journal of Mechanics,2014,46(6):887-895.
参考文献 22
WEI C,CHEN Y.On improving algorithm efficiency of gas-kick simulations toward automated influx management:a robertson differential-algebraic-equation problem approach[J].SPE Drilling & Completion,2021,36(4):943-966.
参考文献 23
孔祥伟,刘祚才,靳彦欣.川渝裂缝性地层自动压井环空多相压力波速特性研究[J].应用数学和力学,2022,43(12):1370-1379.KONG Xiangwei,LIU Zuocai,JIN Yanxin.Study on multiphase pressure wave velocity characteristics of automatic kill annulus in fractured formations in Sichuan and Chongqing [J].Applied Mathematics and Mechanics,2022,43(12):1370-1379.
参考文献 24
孔祥伟,林元华,邱伊婕.控压钻井重力置换与溢流气侵判断准则分析[J].应用力学学报,2015,32(2):317-322,358.KONG Xiangwei,LIN Yuanhua,QIU Yijie.Analysis of judgment criteria for gravity displacement and overflow gas invasion in controlled pressure drilling[J].Journal of Applied Mechanics,2015,32(2):317-322,358.
参考文献 25
YANG W L,YIN H J,ZHONG H Y,et al.Well test analysis of viscoelastic polymer solution[J].Journal of Hydrodynamics,2010,22(1):366-369.
参考文献 26
董长银,甘凌云,赛福拉·地力木拉提,等.深层碳酸盐岩储层泥砂产出与固体控制优化[J].中国石油大学学报(自然科学版),2022,46(5):90-97.DONG Changyin,GAN Lingyun,DILIMULATI·Saifula,et al.Sand production and solid control optimization in deep carbonate reservoirs[J].Journal of China University of Petroleum(Edition of Natural Science),2022,46(5):90-97.
参考文献 27
杨宏伟,张锐尧,李军,等.深水多梯度钻井过滤分离器结构设计与关键参数计算[J].中国石油大学学报(自然科学版),2021,45(6):72-78.YANG Hongwei,ZHANG Ruiyao,LI Jun,et al.Structural design and calculation analysis of key parameters of filter separator during multi-gradient drilling in deep water[J].Journal of China University of Petroleum(Edition of Natural Science),2021,45(6):72-78.
参考文献 28
王雪瑞,孙宝江,王志远,等.考虑温度压力耦合效应的控压固井全过程水力参数计算方法[J].中国石油大学学报(自然科学版),2022,46(2):103-112.WANG Xuerui,SUN Baojiang,WANG Zhiyuan,et al.Calculation method of hydraulic parameters in whole cementing process considering coupling effect of temperature and pressure[J].Journal of China University of Petroleum(Edition of Natural Science),2022,46(2):103-112.
参考文献 29
LIU X S,LI B,YUE Y Q.Transmission behavior of mud-pressure pulse along wellbore[J].Journal of Hydrodynamics,2007,19(2):236-240.
目录contents

    摘要

    考虑相界面雷诺应力、拖拽力、虚拟质量力、气液物性差异等参数,创建井筒多相压力波速及压力响应数学模型,基于超深井环空多相压力波响应图版唯一性,提出压力波响应图版识别超深井气侵位置的新方法;考虑井口气体溢流量、回压、钻井液密度等边界参数,结合差分数学方法对其求解,该方法在超深井 YS1 井(8680 m)验证,压力响应误差小于等于 1. 703 s,计算与实测误差小于等于 6. 15%。结果表明:随回压增大,井筒流体可压缩性减小,井筒压力波速增大,压力响应时间减小;随井口气体溢流量增大,环空空隙率增大,压力波速减小,井筒压力响应时间延长,井口气体溢流量从 0. 83 L/ min 变化至 38. 33 L/ min,井底 8680 m 处压力响应时间从 10. 127 s 增至 36. 643 s,增大了 261. 83%;气侵位置识别结果不仅取决于井口压力及流量传感器准确度,也与压力波响应图版计算准确性有关; 实践证明借助压力波响应图版识别超深井气侵溢流位置的方法可行。

    Abstract

    In this study, considering the parameters of phase interface Reynolds stress, drag force, virtual mass force and gas-liquid physical property difference, a mathematical model of wellbore multiphase pressure wave velocity and pressure response was established, and a new method for identifying the location of gas invasion in ultra-deep wells was proposed based on the uniqueness of the multiphase pressure wave response chart in the wells. In consideration of the boundary parameters, such as wellhead gas overflow rate, backpressure and drilling fluid density, the solution of the model was programed using a differential mathematical method. The new method was verified using the data from an ultra-deep well YS1 (8680 m), with the pressure response error less than 1. 703 s, and the calculation and measurement error less than 6. 15% for predicting the gas invasion location. The results show that, with the increase of the backpressure, the compressibility of wellbore fluid decreases the velocity of wellbore pressure wave increases and the pressure response time decreases. With the increase of the wellhead gas flow rate, the annulus void ratio increases, the pressure wave velocity decreases and the wellbore pressure response time will be prolonged. For instance, when the wellhead gas flow changes from 0. 83 L/ min to 38. 33 L/ min, the pressure response time at 8680 m of the bottom hole can be increased by 261. 83%, from 10. 127 s to 36. 643 s. The results of gas invasion location identification not only depend on the accuracy of wellhead pressure and flow sensors, but also on the calculation accuracy of the pressure wave response chart. This study has proved that identifying the gas invasion location in ultra-deep wells by means of the pressure wave response chart is feasible.

  • 近年由于石油及天然气勘探开发的需要,超深井钻井井位增加,钻井技术也随之迅速发展[1-5]。据不完全统计,目前世界上已钻成 8 000 m 以上超深井 15 口,其中美国 6 口、前苏联 2 口、挪威 1 口、奥地利 1 口、原民主德国 1 口、中国 4 口。 2015 年中国石油塔里木油田克深 902 井完钻,实现 8 000 m 钻井的成功突破[6-10]; 中国石化完成 2018 年度亚洲第 1 深井川深 1 井,完井井深为 8 690 m; 2019 年中国石油勘探完成轮探 1 井完钻井深达 8 882 m,打破了川深 1 井的纪录。 2022 年 6 月双鱼 001-H6 井以 9 010 m 井深顺利完钻,在成功突破 9 000 m 的同时创造了截止 2022 年亚洲陆上最深气井纪录[11-17]。将井深 4 500~6 000 m 的钻井定位为“深井”,6 000~9 000 m 为“超深井”,超深井具有埋深大、高温、高压、高含硫化氢等特点,由于地层破碎、溶孔发育、地层出现多套压力体系等客观原因[18-21],易发生气体溢流,由于超深井井底压力呈现高温、高压等特点,气体在井底处于高度压缩状态,一旦发生气体溢流,井底气侵位置较难掌握,工程师处理气体溢流周期较长,从而延误了施工进度。目前超深井尚无有效快速识别气侵位置方法,多数只局限于井口气侵量的监测,无法满足深井高效处理气体溢流的需要[22-28]。笔者考虑气侵位置、溢流量、井口回压等参数,基于多相压力波响应图版唯一性,绘制不同溢流量、回压、井深等条件下的压力波图版,创新性的提出基于压力波图版法识别超深井气侵位置方法。由于井下气侵量不易监测,从井口回压、气体溢流量等可监测参数入手,采用差分计算井筒多相流参数,可为多相压力波响应图版制定提供基础参数,达到匹配识别井底气侵位置的目的,为超深井气侵位置识别提供理论基础。

  • 1 多相压力波响应模型建立

  • 模型建立:①建立井筒多相流动模型; ②基于多相流动参数建立井筒多相压力波速数学模型; ③求解相应井筒深度压力响应时间; ④利用压力响应图版匹配溢流发生位置。

  • 图1 为压力波响应图版法识别气侵位置设备示意图。设备使用前,输入井身结构数据、钻井液物性、井口气体物性等基础参数,借助双流体模型绘制不同井口参数条件下的井筒压力波速图版、压力响应图版,结合实时监测的井口气体流量、井口回压及温度等,匹配压力波响应图版,达到识别具体气侵位置的目的。

  • 图1 压力波响应图版法识别气侵位置设备示意图

  • Fig.1 Schematic diagram of equipment for identifying gas invasion location using pressure wave response chart method

  • 1.1 井筒多相流动数学模型建立

  • 取井筒中多相流一微元控制体,井筒气液两相连续方程为

  • Ak ρkφkt+Ak ρkφkvks=0.
    (1)
  • 式中,A 为环空截面积,m 2; s 为环空长度,m; φk 为气或钻井液相的体积分数,%; ρk 为气或钻井液相密度,g / cm 3; vk 为气或钻井液相速度,m / s; k 为气或钻井液相; t 为时间,s。

  • 井筒控制体气液两相运动方程为

  • Ak ρkφkvkt+Ak ρkφkvk2s+Agk ρkφk+(Ap)s+Apf=0.
    (2)
  • 式中,g 为重力加速度,m / s 2; pf 为摩阻梯度,MPa /m; p 为压力,MPa。

  • 对井筒气液两相连续方程差分得

  • Aρgvsgi+1n+1-Aρgvsgin+1Δs=Aρgφgin2Δt+Aρgφgi+1n2Δt-Aρgφgin+1-Aρgφgi+1n+12Δt.
    (3)
  • 式中,φg 为空隙率; vsg 为气相表观速度,m / s。

  • 整理式(3)得

  • Avsli+1n+1-Avslin+1Δs=Aφ1in+Aφ1i+1n-Aφ1in+1-Aφ1i+1n+12Δt.
    (4)
  • 式中,Δs 为控制体长度,m; vsl 为钻井液相表观速度,m / s; φl 为持液率,%; Δt 为微元时间,s。

  • 对井筒多相流控制体气液两相运动方程差分得

  • (Ap)i+1n+1-(Ap)in+1=K1+K2+K3+K4.
    (5)
  • 其中

  • K1=Δs2ΔtAρ1vsl+ρgvsgin+Aρ1vsl+ρgvsgi+1n-Aρ1vss+ρgvsgin+1+Aρ1vsl+ρgvsgi+1n+1, K2=Aρ1vsl2φ1+ρgvsg2φgin+1-Aρ1vsl2φ1+ρgvsg2φggi+1n+1, K3=-gΔs2Aρ1in+1+Aρli+1n+1, K4=-Δs2Apsfrin+1+Apsfri+1n+1.

  • 式中,ρl 为混相密度,kg / m 3

  • 1.2 井筒双流体数学模型建立

  • 井筒气液双流体连续方程为

  • tφkρk+xφkρkvk=0.
    (6)
  • 井筒气液双流体动量方程为

  • tφkρkvk+xφkρkvk2=-xφkρk+xφkτfrk+τRek+Mki-4τkD.
    (7)
  • 式中,τfrk 为气或钻井液相剪切力,N/ m 2; τRek 为气/ 液相雷诺应力,N/ m 2; Mki 为气或钻井液相界面动量交换,N/ m 3; τk 为气或钻井液相管壁剪切力,N/ m 2; D 为环空有效直径,m。

  • k 为气相时,界面动量交换量方程为

  • Mgi=-Mndli-Mdli+τffri+τReiφ1x+φσsx+φpgx-p1x.
    (8)
  • 式中,pg 为气相压力,MPa; Mndli 为液相非拖拽力动量交换,N/ m 3; pl 为液相压力,MPa; Mdli 为液相拖拽力的动量交换,N/ m 3; τReli 为液相界面雷诺应力,N; τfrli 为液相界面剪切力,N/ m 2; σs 为表面张力,N/ m 2

  • k 为液相时,界面动量交换量方程为

  • Mli=Mndli+Mdli+pliφ1x-τfrli+τReiφlx.
    (9)
  • 式中,pli 为液相拖拽力引起的压力,MPa。

  • 非拖拽力引起的界面动量交换量方程为

  • Mndli=cvmφgρ1avm-0.1φgρ1ururx-0.1ρ1ur2φgx.
    (10)
  • 式中,cvm 为虚拟质量力系数; αvm 为虚拟质量加速度,m / s 2; ur 为气相滑脱速度,m / s。

  • 拖拽力引起动量界面交换量方程为

  • Mdli=38cDrρ1φgur2.
    (11)
  • 式中,r 为气泡直径,m; cD 为拖拽力系数。

  • 1.3 井筒多相压力响应数学模型建立

  • 井筒多相压力响应时间方程为

  • tHi=i Hici,in.
    (12)
  • 式中,tHi)为井筒中第 i 网格管长的压力响应时间,s; Hi 为井筒中 i 网格长度,m; ci 为井筒中第 i 网格管长的压力波速,m / s。

  • 在气液双流体中沿井筒返回的压力波传输时间为

  • T1=i Hi/ci,in.
    (13)
  • 式中,T1 为在气液双流体中沿井筒返回的压力波传播时间,s。

  • 在单相钻井液中沿井筒返回的压力波传播的时间为

  • T2=i Hi/c,in.
    (14)
  • 式中,T2 为在单相钻井液中沿井筒返回的压力波传播的时间,s; c 为压力波在不含气的单相钻井液中传播速度,m / s。

  • 计算出的压力波返回时差为

  • ΔT=T1-T2.
    (15)
  • 式中,ΔT 为计算出的压力波返回时差,s。

  • Tc-T1-T2<δ.
    (16)
  • 式中,Tc 为压力传感器检测到压力波返回时差,s; δ为气侵漏点计算精度,m。

  • H=i Hi,in.
    (17)
  • 式中,H 为气侵位置以上井段长度,m。

  • 2 模型求解及验证

  • 2.1 模型求解

  • 井筒气侵位置识别计算流程如图2 所示,具体步骤如下:

  • (1)对井筒划分 n 个单元网格,将第 i 个井筒网格(t 时刻)气相密度、黏度、压力等参数视为恒定,t = 0 时刻作为压力波速求解的初始边界条件。

  • 图2 井筒气侵位置识别计算流程

  • Fig.2 Calculation flow for identifying location of gas invasion in wellbore

  • (2)可通过差分方法确定第 t = i+1 个网格气相偏差因子、气相密度、气相黏度、井筒压力、温度、空隙率等物性参数。

  • (3)考虑每个网格初始井筒多相流动参数,结合流体数学模型求解每个井筒网格气相压力波速。

  • (4)根据各网格压力波速,求取各网格的压力响应时间,同时对每个网格压力响应时间相加,可得到求取点的地面压力响应时间,得到多相压力波响应图版。

  • (5)计算出气侵位置与压力波时差之间的对应关系,计算的两个压力传感器检测到压力波在两条路径中传播的时间差与迭代计算出的压力响应之间的差值,若满足精度要求,则结束运算,此时可得到井筒气侵位置; 反之,进入下一个网格,重复上述步骤至满足精度要求。

  • 2.2 模型验证

  • 通过求解环空双流模型,得到不同工况下井筒压力波速。由于压力波速的计算是影响压力波响应图版绘制准确度的关键因素,对压力为 30 MPa 条件下的模型计算结果与前人试验实测的压力波速[29]进行对比,如图3 所示。模型计算结果与前人试验测试数据具有一致性。

  • 图3 模型计算结果与前人试验实测压力波速对比

  • Fig.3 Model calculation results compared with previous experimental measured pressure wave velocity

  • 3 YS1 井压力波特性及溢流位置预测

  • 由于 YS1 井井身 8 680 m 属于特深层井,该井配置了回压测量装置,可以验证测试模型的准确性,因此选用 YS1 井作为实例井。 2022 年开展 YS1 井五开现场井的验证,图4 为现场压力波响应测试关键设备,井眼直径 Φ165.1 mm,尾管直径 Ф139.7 mm,该井目的层位为灯影组,井深为 8 680 m。

  • 图4 现场压力波响应测试关键设备

  • Fig.4 Key equipment for on-site pressure wave response testing

  • 图5 为 YS1 井井底压力响应测试井身结构示意图。现场试验使用主要测试设备包括压力传感器、温度传感器、泵冲传感器、节流阀位指示器及科里奥利流量计等装置,整个试验过程历时 98.2 h,设备和软件运转正常,数据采集、传输及时可靠、压力波信号提取到位。

  • YS1 井五开 8 680 m 井深处,钻井液密度为2 100 kg / m 3、气体相对密度为 0.65、套压 0.5 MPa、井口气体流量为 3.33 L / min、气体黏度为 1.14 × 10-5 Pa·s; 钻杆弹性模量为 2. 07×10 11 Pa、粗糙度为 1.54×10-7 m、泊松比为 0.3; 地表温度为 298 K、地温梯度为 0. 025℃ / m。

  • 图5 YS1 井井底压力响应测试井身结构示意图

  • Fig.5 Schematic diagram of well YS1 bottom-hole pressure response testing wellbore structure

  • 图6 为现场试验测试压力响应时间与模型计算结果对比。由图6 可得:井深 8 680 m 时,回压为 0.1 MPa 时,实测和计算井底压力响应分别为 33. 023 和 31. 09 s,误差小于等于 5.97%; 回压为 0.5 MPa 时,实测和计算井底压力响应分别为 27.703 和 26. 00 s,误差小于等于 6.15%。

  • 图6 压力响应时间现场试验数据对比

  • Fig.6 Comparison of on-site test data for pressure response time

  • 3.1 井口回压对空隙率、压力波速和压力响应时间的影响

  • 图7 为回压对井筒空隙率、压力波速及压力响应时间的影响。由图7 可以看出:当回压增大时,相当于在密闭井筒中整体增大压力,使井筒中的多相流体可压缩性减小,因此井筒空隙率呈现减小趋势,井筒压力波速增大,压力响应时间减小; 由于流体在井底承受高压,回压的加载对井底压力波速的影响较小。当井深大于等于 6 600 m 且井口回压大于等于 1.5 MPa 时,压力波速趋于恒定,这是由于当压力增大到一定极值时,气体可压缩性变小的缘故,气液两相压力波速趋于液相压力波速,其最大值趋于钻井液相压力波速; 随着井口回压的增大,井底接收到的压力响应时间呈减小趋势,井底压力响应时间主要受井筒压力波速的影响,井口回压的增大,增大了压力传递速度,从而使井底压力响应时间减小。

  • 图7 井口回压对井筒空隙率、压力波速及压力响应时间的影响

  • Fig.7 Influence of wellhead backpressure on wellbore voidage, pressure wave velocity and pressure response time

  • 3.2 井口气体溢流量对空隙率、压力波速和压力响应时间的影响

  • 井口气体溢流量对井筒空隙率、压力波速及压力响应时间的影响如图8 所示。井底气体沿井筒运移至井口过程中,井筒压力逐渐减小,使多相流的压缩性增大,从而空隙率呈增大趋势。随气侵量增大,环空空隙率增大,使整个环空气体体积增大,井筒中多相流体的可压缩性增大,压力波速减小,从而压力响应时间增大。

  • 图8 井口气体溢流量对井筒空隙率、压力波速及压力响应时间的影响

  • Fig.8 Influence of wellhead gas overflow on wellbore voidage, pressure wave velocity and pressure response time

  • 当井口气体溢流量为 0.83 L / min 时,井深 100 m 同井底 8 680 m 比较,空隙率从 36.744% 减至 0. 011%,减小 99.97%; 当井口气体溢流量为 38.33 L / min 时,井深 100 m 同井底 8 680 m 比较,空隙率从 96.642%减至 1.668%,减小 98.24%。当井口气体溢流量为 0.83 L/ min 时,压力波速在井深区间[0,4 000 m]增大幅度较大,当井深 D>4000 m 时,压力波速变化趋于平缓。当井口气体溢流量为 38.33 L/ min 时,井筒多相压力波速呈线性增大趋势。

  • 随着井口气体溢流量的增大,井底压力响应时间呈增大趋势。井口气体溢流量从 0.83 L / min 增至 38.33 L / min,井深 4 000 m 压力响应时间从 6.362 s 增大至 30.498 s,增大了 379.38%。相同井口气体溢流量增量,井深的变化对压力响应时间的影响较为敏感,井底 8 680 m 压力响应时间从 10.127 s 增大至 36.643 s,增大了 261.83%。

  • 3.3 井底气侵量为 2.3 L/ s 时溢流量和空隙率的变化规律

  • 图9 为井底气侵量为 2.3 L / s 时井口回压对溢流量的影响,图10 为气侵位置(井底气侵量为 2.3 L / s)对空隙率的影响。相同的井底气侵量,随着井深的增大,井口气体量大幅增大,井筒空隙率也呈增大趋势。当井深 D = 8 680 m 时,井底出气量为 2.3 L / s,当气体运移至井口时,井口气体溢流量为 2 365.79 L / s,这是由于井底压力较井口压力增大数百倍,导致井底气体运移至井口时,气体体积膨胀 1 028.6 倍。

  • 图9 井底气侵量为 2.3 L/ s 时井口回压对溢流量的影响

  • Fig.9 Influence of wellhead backpressure on overflow flow rate when bottom-hole gas influx rate being 2.3 L/ s

  • 3.4 气侵位置对井筒多相压力波速及压力响应时间的影响

  • 图11 为气侵位置对井筒多相压力波速及压力响应时间图版的影响。井筒压力响应时间变化的实质受气液两相介质可压缩性影响,当气体可压缩性小时,井筒气液两相压力响应时间短。在井口附近或井筒深度较小(D≤500 m)处,井筒气体的可压缩性较大,从而井筒气液两相的压力响应时间大幅增加。相同的井底气侵量,井深从 500 m 变化至 8 680 m,压力响应时间从 6.605 s 增至 37. 087 s,增加 461.49%。

  • 图10 井底气侵量为 2.3 L/ s 时气侵位置对空隙率的影响

  • Fig.10 Influence of gas influx location on void ratio when bottom-hole gas influx rate being 2.3 L/ s

  • 图11 气侵位置对井筒多相压力波速及压力响应时间图版的影响

  • Fig.11 Influence of different well depths on multiphase pressure wave velocity and pressure response time chart

  • 3.5 YS1 井气侵位置预测

  • 表1 为预测 YS1 井气侵位置数据。随着气侵量的增大预测误差呈减小趋势。采用环空水力学模型对各参数进行龙格库塔迭代,得出环空中不同网格的环空空隙率的分布、波速响应时间、气侵位置与压力波响应时间之间存在的一一对应关系,用本文中建立的预测气侵位置的方法,可计算得到相应预测井深,预测气侵位置与实测值具有一致性。

  • 表1 预测 YS1 井气侵位置数据

  • Table1 Predicted well YS1 gas invasion location data

  • 4 结论

  • (1)针对超深井气体溢流复杂工况,创建了井筒多相压力波速及压力响应数学模型,提出了压力波响应图版识别超深井气侵位置的新方法。考虑气相压缩性、气相压力波速、井深等因素的数学模型,具有精度高、预测速度快的优点,不仅适用于超深井,也适用于中浅井。

  • (2)随井深的增大,井口气体量大幅增大,井筒空隙率也呈增大趋势; 随井口回压的增大,井底接收到的压力响应时间呈减小趋势; 随气侵量增大,环空空隙率增大,使整个环空气体体积增大,井筒中多相流体的可压缩性增大,压力波速减小,从而压力响应时间增大。

  • (3)压力波响应图版法识别气侵位置准确性不仅依靠监测设备的准确性,也依靠压力波速计算的准确度,在井口监测出压力反射波,从而计算出压力响应时间; 压力波响应图版不仅可以预测气侵发生位置,还可以指导控压钻井节流阀动作时间间隔、多相波动压力计算等。

  • 参考文献

    • [1] 苏义脑,路保平,刘岩生,等.中国陆上深井超深井钻完井技术现状及攻关建议[J].石油钻采工艺,2020,42(5):527-542.SU Yinao,LU Baoping,LIU Yansheng,et al.Current status and suggestions for key technologies in the drilling and completion of deep and ultra deep wells on land in China[J].Petroleum Drilling and Production Technology,2020,42(5):527-542.

    • [2] 薛飞.深井超深井钻井技术现状和发展研究[J].化工管理,2013(22):63.XUE Fei.Research on the current situation and development of deep and ultra deep well drilling technology [J].Chemical Management,2013(22):63.

    • [3] 吕开河,杜宏艳,孙金声,等.含油钻屑处理技术研究进展与展望[J].中国石油大学学报(自然科学版),2023,47(3):78-86.LÜ Kaihe,DU Hongyan,SUN Jinsheng,et al.Research and development of oily drilling cuttings treatment technologies[J].Journal of China University of Petroleum(Edition of Natural Science),2023,47(3):78-86.

    • [4] 孙金声,蒋官澄,贺垠博,等.油基钻井液面临的技术难题与挑战[J].中国石油大学学报(自然科学版),2023,47(5):76-89.SUN Jinsheng,JIANG Guancheng,HE Yinbo,et al.Technical difficulties and challenges faced by oil-based drilling fluid[J].Journal of China University of Petroleum(Edition of Natural Science),2023,47(5):76-89.

    • [5] 梁云栋,何琳,徐荣武,等.高精度液压系统压力波传递速度在线测量试验[J].国防科技大学学报,2022,44(2):195-202.LIANG Yundong,HE Lin,XU Rongwu,et al.High precision hydraulic system pressure wave transmission speed online measurement experiment [J].Journal of National University of Defense Science and Technology,2022,44(2):195-202.

    • [6] 孔祥伟,林元华,邱伊婕,等.钻井泥浆泵失控/重载引发的波动压力[J].石油学报,2015,36(1):114-119.KONG Xiangwei,LIN Yuanhua,QIU Yijie,et al.Fluctuation pressure caused by uncontrolled/overloaded drilling mud pumps [J].Acta Petrolei Sinica,2015,36(1):114-119.

    • [7] VONGVUTHIPORNCHAI S,RAGHAVAN R.Pressure falloff behavior in vertically fractured wells:non-Newtonian power-law fluids [J].SPE Formation Evaluation,1987,2(4):573-589.

    • [8] WEISS W W,BALDWIN R W.Planning and implementing a large-scale polymer flood[J].Journal of Petroleum Technology,1985,37(4):720-730.

    • [9] 李阳,赵清民,薛兆杰.新一代油气开发技术体系构建与创新实践[J].中国石油大学学报(自然科学版),2023,47(5):45-54.LI Yang,ZHAO Qingmin,XUE Zhaojie.Construction and innovative practice of new generation oil and gas development technology system[J].Journal of China University of Petroleum(Edition of Natural Science),2023,47(5):45-54.

    • [10] 孔祥伟,林元华,何龙,等.一种考虑虚拟质量力的两相压力波速经验模型[J].力学季刊,2015,36(4):611-617.KONG Xiangwei,LIN Yuanhua,HE Long,et al.A two-phase pressure wave velocity empirical model considering virtual mass forces [J].Journal of Mechanics Quarterly,2015,36(4):611-617.

    • [11] 王刚,刘刚,张悦,等.深水大尺寸井眼钻进钻井液双循环携岩方法[J].中国石油大学学报(自然科学版),2022,46(2):113-120.WANG Gang,LIU Gang,ZHANG Yue,et al.Method of double drilling fluid circulation for cuttings carrying in large-size wellbore during deepwater drilling[J].Journal of China University of Petroleum(Edition of Natural Science),2022,46(2):113-120.

    • [12] 吕开河,王晨烨,雷少飞,等.裂缝性地层钻井液漏失规律及堵漏对策[J].中国石油大学学报(自然科学版),2022,46(2):85-93.LÜ Kaihe,WANG Chenye,LEI Shaofei,et al.Dynamic behavior and mitigation methods for drilling fluid loss in fractured formations[J].Journal of China University of Petroleum(Edition of Natural Science),2022,46(2):85-93.

    • [13] 王庆.基于压力信号的气液两相流泄漏检测研究 [D].青岛:中国石油大学(华东),2017.WANG Qing.Research on leakage detection of gas-liquid two phase flow based on pressure signal [D].Qingdao:China University of Petroleum(East China),2017.

    • [14] WANG Y,CHENG S Q,ZHANG K D,et al.A comprehensive work flow to characterize waterflood-induced fractures by integrating real-time monitoring,formation test,and dynamic production analysis applied to Changqing Oilfield,China[J].SPE Reservoir Evaluation & Engineering,2018,22(2):692-708.

    • [15] DU Q J,PAN G M,HOU J,et al.Study of the mechanisms of streamline-adjustment-assisted heterogeneous combination flooding for enhanced oil recovery for postpolymer-flooded reservoirs [J].Petroleum Science,2019,16(3):606-618.

    • [16] 刘璞.节流压井井筒压力动态响应分析研究[D].成都:西南石油大学,2017.LIU Pu.Analysis and research on dynamic response of choke and kill wellbore pressure [D].Chengdu:Southwest Petroleum University,2017.

    • [17] 闫铁,屈俊波,孙晓峰,等.控压钻井回压压力波在井筒中传播的速度和时间规律[J].天然气工业,2017,37(11):77-84.YAN Tie,QU Junbo,SUN Xiaofeng,et al.The velocity and time pattern of backpressure wave propagation in wellbore during controlled pressure drilling[J].Natural Gas Industry,2017,37(11):77-84.

    • [18] 李红涛.复杂流体介质条件下井筒压力波传播规律研究[D].成都:西南石油大学,2015.LI Hongtao.Study on propagation law of wellbore pressure wave under complex fluid medium conditions [D].Chengdu:Southwest Petroleum University,2015.

    • [19] 步玉环,景韶瑞,杨恒,等.深水气井测试条件下井筒水合物生成及浅层水合物分解的环空保护液导热系数[J].中国石油大学学报(自然科学版),2023,47(1):81-88.BU Yuhuan,JING Shaorui,YANG Heng,et al.Influence of thermal conductivity of annular protective fluids on wellbore hydrate formation and hydrate decomposition in shallow formation during deep-water drilling and well testing[J].Journal of China University of Petroleum(Edition of Natural Science),2023,47(1):81-88.

    • [20] JIA Z C,LI D L,YANG J H,et al.Numerical well test analysis for polymer flooding considering the non-Newtonian behavior [J].Journal of Chemistry,2015,2015:107625.

    • [21] 孔祥伟,林元华,邱伊婕.控压钻井中三相流体压力波速传播特性[J].力学学报,2014,46(6):887-895.KONG Xiangwei,LIN Yuanhua,QIU Yijie.Pressure wave velocity propagation characteristics of three-phase fluid in controlled pressure drilling wells[J].Journal of Mechanics,2014,46(6):887-895.

    • [22] WEI C,CHEN Y.On improving algorithm efficiency of gas-kick simulations toward automated influx management:a robertson differential-algebraic-equation problem approach[J].SPE Drilling & Completion,2021,36(4):943-966.

    • [23] 孔祥伟,刘祚才,靳彦欣.川渝裂缝性地层自动压井环空多相压力波速特性研究[J].应用数学和力学,2022,43(12):1370-1379.KONG Xiangwei,LIU Zuocai,JIN Yanxin.Study on multiphase pressure wave velocity characteristics of automatic kill annulus in fractured formations in Sichuan and Chongqing [J].Applied Mathematics and Mechanics,2022,43(12):1370-1379.

    • [24] 孔祥伟,林元华,邱伊婕.控压钻井重力置换与溢流气侵判断准则分析[J].应用力学学报,2015,32(2):317-322,358.KONG Xiangwei,LIN Yuanhua,QIU Yijie.Analysis of judgment criteria for gravity displacement and overflow gas invasion in controlled pressure drilling[J].Journal of Applied Mechanics,2015,32(2):317-322,358.

    • [25] YANG W L,YIN H J,ZHONG H Y,et al.Well test analysis of viscoelastic polymer solution[J].Journal of Hydrodynamics,2010,22(1):366-369.

    • [26] 董长银,甘凌云,赛福拉·地力木拉提,等.深层碳酸盐岩储层泥砂产出与固体控制优化[J].中国石油大学学报(自然科学版),2022,46(5):90-97.DONG Changyin,GAN Lingyun,DILIMULATI·Saifula,et al.Sand production and solid control optimization in deep carbonate reservoirs[J].Journal of China University of Petroleum(Edition of Natural Science),2022,46(5):90-97.

    • [27] 杨宏伟,张锐尧,李军,等.深水多梯度钻井过滤分离器结构设计与关键参数计算[J].中国石油大学学报(自然科学版),2021,45(6):72-78.YANG Hongwei,ZHANG Ruiyao,LI Jun,et al.Structural design and calculation analysis of key parameters of filter separator during multi-gradient drilling in deep water[J].Journal of China University of Petroleum(Edition of Natural Science),2021,45(6):72-78.

    • [28] 王雪瑞,孙宝江,王志远,等.考虑温度压力耦合效应的控压固井全过程水力参数计算方法[J].中国石油大学学报(自然科学版),2022,46(2):103-112.WANG Xuerui,SUN Baojiang,WANG Zhiyuan,et al.Calculation method of hydraulic parameters in whole cementing process considering coupling effect of temperature and pressure[J].Journal of China University of Petroleum(Edition of Natural Science),2022,46(2):103-112.

    • [29] LIU X S,LI B,YUE Y Q.Transmission behavior of mud-pressure pulse along wellbore[J].Journal of Hydrodynamics,2007,19(2):236-240.

  • 参考文献

    • [1] 苏义脑,路保平,刘岩生,等.中国陆上深井超深井钻完井技术现状及攻关建议[J].石油钻采工艺,2020,42(5):527-542.SU Yinao,LU Baoping,LIU Yansheng,et al.Current status and suggestions for key technologies in the drilling and completion of deep and ultra deep wells on land in China[J].Petroleum Drilling and Production Technology,2020,42(5):527-542.

    • [2] 薛飞.深井超深井钻井技术现状和发展研究[J].化工管理,2013(22):63.XUE Fei.Research on the current situation and development of deep and ultra deep well drilling technology [J].Chemical Management,2013(22):63.

    • [3] 吕开河,杜宏艳,孙金声,等.含油钻屑处理技术研究进展与展望[J].中国石油大学学报(自然科学版),2023,47(3):78-86.LÜ Kaihe,DU Hongyan,SUN Jinsheng,et al.Research and development of oily drilling cuttings treatment technologies[J].Journal of China University of Petroleum(Edition of Natural Science),2023,47(3):78-86.

    • [4] 孙金声,蒋官澄,贺垠博,等.油基钻井液面临的技术难题与挑战[J].中国石油大学学报(自然科学版),2023,47(5):76-89.SUN Jinsheng,JIANG Guancheng,HE Yinbo,et al.Technical difficulties and challenges faced by oil-based drilling fluid[J].Journal of China University of Petroleum(Edition of Natural Science),2023,47(5):76-89.

    • [5] 梁云栋,何琳,徐荣武,等.高精度液压系统压力波传递速度在线测量试验[J].国防科技大学学报,2022,44(2):195-202.LIANG Yundong,HE Lin,XU Rongwu,et al.High precision hydraulic system pressure wave transmission speed online measurement experiment [J].Journal of National University of Defense Science and Technology,2022,44(2):195-202.

    • [6] 孔祥伟,林元华,邱伊婕,等.钻井泥浆泵失控/重载引发的波动压力[J].石油学报,2015,36(1):114-119.KONG Xiangwei,LIN Yuanhua,QIU Yijie,et al.Fluctuation pressure caused by uncontrolled/overloaded drilling mud pumps [J].Acta Petrolei Sinica,2015,36(1):114-119.

    • [7] VONGVUTHIPORNCHAI S,RAGHAVAN R.Pressure falloff behavior in vertically fractured wells:non-Newtonian power-law fluids [J].SPE Formation Evaluation,1987,2(4):573-589.

    • [8] WEISS W W,BALDWIN R W.Planning and implementing a large-scale polymer flood[J].Journal of Petroleum Technology,1985,37(4):720-730.

    • [9] 李阳,赵清民,薛兆杰.新一代油气开发技术体系构建与创新实践[J].中国石油大学学报(自然科学版),2023,47(5):45-54.LI Yang,ZHAO Qingmin,XUE Zhaojie.Construction and innovative practice of new generation oil and gas development technology system[J].Journal of China University of Petroleum(Edition of Natural Science),2023,47(5):45-54.

    • [10] 孔祥伟,林元华,何龙,等.一种考虑虚拟质量力的两相压力波速经验模型[J].力学季刊,2015,36(4):611-617.KONG Xiangwei,LIN Yuanhua,HE Long,et al.A two-phase pressure wave velocity empirical model considering virtual mass forces [J].Journal of Mechanics Quarterly,2015,36(4):611-617.

    • [11] 王刚,刘刚,张悦,等.深水大尺寸井眼钻进钻井液双循环携岩方法[J].中国石油大学学报(自然科学版),2022,46(2):113-120.WANG Gang,LIU Gang,ZHANG Yue,et al.Method of double drilling fluid circulation for cuttings carrying in large-size wellbore during deepwater drilling[J].Journal of China University of Petroleum(Edition of Natural Science),2022,46(2):113-120.

    • [12] 吕开河,王晨烨,雷少飞,等.裂缝性地层钻井液漏失规律及堵漏对策[J].中国石油大学学报(自然科学版),2022,46(2):85-93.LÜ Kaihe,WANG Chenye,LEI Shaofei,et al.Dynamic behavior and mitigation methods for drilling fluid loss in fractured formations[J].Journal of China University of Petroleum(Edition of Natural Science),2022,46(2):85-93.

    • [13] 王庆.基于压力信号的气液两相流泄漏检测研究 [D].青岛:中国石油大学(华东),2017.WANG Qing.Research on leakage detection of gas-liquid two phase flow based on pressure signal [D].Qingdao:China University of Petroleum(East China),2017.

    • [14] WANG Y,CHENG S Q,ZHANG K D,et al.A comprehensive work flow to characterize waterflood-induced fractures by integrating real-time monitoring,formation test,and dynamic production analysis applied to Changqing Oilfield,China[J].SPE Reservoir Evaluation & Engineering,2018,22(2):692-708.

    • [15] DU Q J,PAN G M,HOU J,et al.Study of the mechanisms of streamline-adjustment-assisted heterogeneous combination flooding for enhanced oil recovery for postpolymer-flooded reservoirs [J].Petroleum Science,2019,16(3):606-618.

    • [16] 刘璞.节流压井井筒压力动态响应分析研究[D].成都:西南石油大学,2017.LIU Pu.Analysis and research on dynamic response of choke and kill wellbore pressure [D].Chengdu:Southwest Petroleum University,2017.

    • [17] 闫铁,屈俊波,孙晓峰,等.控压钻井回压压力波在井筒中传播的速度和时间规律[J].天然气工业,2017,37(11):77-84.YAN Tie,QU Junbo,SUN Xiaofeng,et al.The velocity and time pattern of backpressure wave propagation in wellbore during controlled pressure drilling[J].Natural Gas Industry,2017,37(11):77-84.

    • [18] 李红涛.复杂流体介质条件下井筒压力波传播规律研究[D].成都:西南石油大学,2015.LI Hongtao.Study on propagation law of wellbore pressure wave under complex fluid medium conditions [D].Chengdu:Southwest Petroleum University,2015.

    • [19] 步玉环,景韶瑞,杨恒,等.深水气井测试条件下井筒水合物生成及浅层水合物分解的环空保护液导热系数[J].中国石油大学学报(自然科学版),2023,47(1):81-88.BU Yuhuan,JING Shaorui,YANG Heng,et al.Influence of thermal conductivity of annular protective fluids on wellbore hydrate formation and hydrate decomposition in shallow formation during deep-water drilling and well testing[J].Journal of China University of Petroleum(Edition of Natural Science),2023,47(1):81-88.

    • [20] JIA Z C,LI D L,YANG J H,et al.Numerical well test analysis for polymer flooding considering the non-Newtonian behavior [J].Journal of Chemistry,2015,2015:107625.

    • [21] 孔祥伟,林元华,邱伊婕.控压钻井中三相流体压力波速传播特性[J].力学学报,2014,46(6):887-895.KONG Xiangwei,LIN Yuanhua,QIU Yijie.Pressure wave velocity propagation characteristics of three-phase fluid in controlled pressure drilling wells[J].Journal of Mechanics,2014,46(6):887-895.

    • [22] WEI C,CHEN Y.On improving algorithm efficiency of gas-kick simulations toward automated influx management:a robertson differential-algebraic-equation problem approach[J].SPE Drilling & Completion,2021,36(4):943-966.

    • [23] 孔祥伟,刘祚才,靳彦欣.川渝裂缝性地层自动压井环空多相压力波速特性研究[J].应用数学和力学,2022,43(12):1370-1379.KONG Xiangwei,LIU Zuocai,JIN Yanxin.Study on multiphase pressure wave velocity characteristics of automatic kill annulus in fractured formations in Sichuan and Chongqing [J].Applied Mathematics and Mechanics,2022,43(12):1370-1379.

    • [24] 孔祥伟,林元华,邱伊婕.控压钻井重力置换与溢流气侵判断准则分析[J].应用力学学报,2015,32(2):317-322,358.KONG Xiangwei,LIN Yuanhua,QIU Yijie.Analysis of judgment criteria for gravity displacement and overflow gas invasion in controlled pressure drilling[J].Journal of Applied Mechanics,2015,32(2):317-322,358.

    • [25] YANG W L,YIN H J,ZHONG H Y,et al.Well test analysis of viscoelastic polymer solution[J].Journal of Hydrodynamics,2010,22(1):366-369.

    • [26] 董长银,甘凌云,赛福拉·地力木拉提,等.深层碳酸盐岩储层泥砂产出与固体控制优化[J].中国石油大学学报(自然科学版),2022,46(5):90-97.DONG Changyin,GAN Lingyun,DILIMULATI·Saifula,et al.Sand production and solid control optimization in deep carbonate reservoirs[J].Journal of China University of Petroleum(Edition of Natural Science),2022,46(5):90-97.

    • [27] 杨宏伟,张锐尧,李军,等.深水多梯度钻井过滤分离器结构设计与关键参数计算[J].中国石油大学学报(自然科学版),2021,45(6):72-78.YANG Hongwei,ZHANG Ruiyao,LI Jun,et al.Structural design and calculation analysis of key parameters of filter separator during multi-gradient drilling in deep water[J].Journal of China University of Petroleum(Edition of Natural Science),2021,45(6):72-78.

    • [28] 王雪瑞,孙宝江,王志远,等.考虑温度压力耦合效应的控压固井全过程水力参数计算方法[J].中国石油大学学报(自然科学版),2022,46(2):103-112.WANG Xuerui,SUN Baojiang,WANG Zhiyuan,et al.Calculation method of hydraulic parameters in whole cementing process considering coupling effect of temperature and pressure[J].Journal of China University of Petroleum(Edition of Natural Science),2022,46(2):103-112.

    • [29] LIU X S,LI B,YUE Y Q.Transmission behavior of mud-pressure pulse along wellbore[J].Journal of Hydrodynamics,2007,19(2):236-240.

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