底部钻具组合上切点边界条件的正确性

传统底部钻具组合上切点边界条件的正确性
李子丰 李同林
(中国地质大学工程学院,湖北武汉 430074)
摘要 传统的底部钻具组合受力分析的上切点处的边界条件表达为:1.与下井壁接触;2.转角与井眼轴线的一致;3.曲率与井眼轴线的一致。

该表达方法已经采用了多年,应用效果良好。

近来,有文章否定该边界条件,文中例证了传统底部钻具组合上切点边界条件的正确性。

关键词 底部钻具组合 钻柱力学 边界条件 上切点
作者简介 李子丰,1962年生。

主要从事油气井杆管柱力学研究工作,现任教授、博士生导师。

李同林, 1955年生。

现为副教授。

下部钻具力学分析是井眼轨道控制技术的基础。

理论和实践都证明,上切点以上的钻柱对钻头的受力和变形影响很小,为了提高计算速度,可将钻柱从上切点处断开,忽略上切点以上钻柱对下部钻具受力和变形的影响。

关于上切点处边界条件的表述,已经基本成熟,并在理论计算的过程中得到了成功的应用[1~5]。

该切点处的边界条件可以表述为(1)钻柱与下井壁接触;(2)钻柱转角与井眼轴线的一致;(3)钻柱曲率与井眼轴线的一致。

参考文献[6]提出将钻柱曲率与井眼轴线的一致改换为钻柱内的剪力为零。

举例证明了传统的底部钻具上切点边界条件的正确性,并指出了在切点处钻柱内的剪力不为零。

1 传统的钻柱上切点边界条件
(1)钻柱与下井壁接触;(2)钻柱转角与井眼轴线的一致;(3)钻柱曲率与井眼轴线的一致。

在二维井眼中表达为
U n(L n)=X n+
D W-d n
2
U n(L n)=X n
U n(L n)=X n
(1)
中起下,必须使用外径较小的泥浆马达,如钻 216mm井眼时,只能使用外径 121mm的泥浆马达而不是 171mm的泥浆马达,这样在钻较深或较硬地层时将会造成输出功率不够,导致机械钻速下降或马达过载,所以必须提高泥浆马达的输出功率。

参 考 文 献
[1] Richard E,Leturno.Drilling with Casin g and Retrievable
Drilling P5271472,1993-12
[2] Bob Tessari.Casing Drilling-A Revolutionary Approach to
Reducing Well Costs.SPE52789
[3] B ob Tessari.Drilling with Casing Promises M ajor Benefits.Oil
&Gas Journal,1999-05
[4] A Breakthrough to Lowering Drillin g Costs.Tesco Corporation
Brochure,2000
[5] Garret Madell.Casing Drilli ng-An Innovative Approach to
Reducing Drilling Costs.C ADE/CAODC Spring Drilling Con-
ference,Calgary,Canada,1999-04
[6] Skinazi E.Develop ment of a Casing/Drilling System Improves
the Drilling Process.SPE62780
[7] Brian Tarr.Casing-While-Drilling:The Next Step Change
in Well Construction.World Oil,1999-10
[8] Tessari R M.A Revolutionary Approach to Reducing Well
Costs.16th World Petroleum Congress,Calgary,Canada,
2000-03
[9] Jose C,De Leon Mojarro.Drilling with Casing:The Mexican
T echnique Uses the Casing as a Drillpipe.SPE59055 [10] Robin Goodale.Systems Make Casing Drilling Viable.T he
American Oil&Gas Reporter,2000-09
(收稿日期 2001-09-12)
编辑 薛改珍
n 为第n 段钻柱的长度;U n 为第n 段钻柱的位移函数;D W 为井径;d n 为第n 段钻柱外径。

2 传统的边界条件的最简单算例
为了简捷地理解上述边界条件的正确性。

以光钻铤底部钻具组合自由放置在水平井眼中为例,见图1。

图1 光钻铤底部钻具组合在水平井眼中示意图
图1中,粗实线代表钻柱,承受横向载荷q ;A 点为钻头,此处为铰支,支撑力为R A ;B 点为切点,支撑力为R B ;AB 的长度为L ,此段钻柱悬空;BC 段钻柱躺在井壁下侧。

在lU 坐标系中,钻柱的边界条件为
U(0)=0U (0)=0
U(L )=D W -d n
2U (L )=0U (L )=0
(2)
由(2)可以推导出A 、B 两点的弯矩为
M A =M B =0
(3)
式中,M A 为A 点的弯矩,M B 为B 点的弯矩。

利用
(3),并列平衡方程,可以求得
R A =R B =qL
2
(4) 其实,对于AB 段钻柱来讲,就是承受均匀横向载荷的简支梁,只不过是其长度可以随支撑力的增加而增长而已。

这与可以用1个量程10kg 的秤,利用简支梁原理,称20kg 的均匀杆状物体一样。

3 用 钻柱内的剪力为零 取代 钻柱曲率与
井眼轴线的一致 存在的问题
在示意图的情况下,如果切点处钻柱的剪力为零,即R B =0,则可以导出R A =qL ,M B =q L 2/2;而在BC 段的钻柱躺在井壁下侧,弯矩恒为零;弯矩在B 点两侧产生量值为qL 2/2的突变;此处没有增加
外力矩,也不是固定端。

在该处弯矩不可能产生突变。

从另外一个角度再看,如果钻柱刚度增大,L 将不断增长,B 点不断接近C 点,当达到C 点时,变成普通教材中的简支梁。

M B =q L 2/2显然不对,此时M B =0;R A =q L ,R B =0也不对,此时R A =R B =q L /2。

4 结论
传统的底部钻具组合受力分析的上切点处边界条件的表达方式是正确的。

不能用 钻柱内的剪力为零 取代 钻柱曲率与井眼轴线的一致 。

参 考 文 献
[1] 李子丰.油气井杆管柱力学.北京:石油工业出版社,
1996
[2] 李子丰,马兴瑞,黄文虎.钻柱力学基本方程及应用.力
学学报,1995,27(4):406~414
[3] Li Zifeng,Ma Xingri,Huan g Wenhu,and Liu Xisheng.A
3D Analysis of a Bottomhole Assembly Under Large Deflec -tion.SPE Drilling &Completion,1996,11(2):104~110[4] 李子丰,赵新瑞,赵德云.通用下部钻具三维小挠度静
力分析的数学模型及应用.工程力学,2000,17(6):121
~129
[5] 白家祉,苏义脑.井斜控制理论与实践.北京:石油工业
出版社,1990
[6] 宋执武,高德利.确定底部钻具组合上切点位置的新观
点.石油钻采工艺,2001,23(5):9~11
(收稿日期 2001-11-09)
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