钻井液密度与井壁围岩破坏的关系

钻井液密度与井壁围岩破坏的关系
张广清 陈 勉
(石油大学,北京昌平 102249)
摘要 钻井液密度对井壁围岩的稳定性具有重要的作用。

通过有限元分析,根据Drucker-Prager破坏准则,模拟了井壁剪切破坏的连续过程,并且给出了井壁围岩破坏尺寸与钻井液密度的关系,对于分析钻井液密度对井壁围岩破坏区域的影响提供了定量依据。

计算出的模拟规律与现场观测和实验室内试验结果基本一致。

关键词 有限元分析 井壁稳定 钻井液密度 研究
作者简介 张广清,1975年生。

从事石油工程岩石力学与应用方面的研究工作,在读博士生。

陈勉,1962年生。

教授、博士生导师。

长期以来,井壁稳定问题一直引起钻井界的密切注意,井壁稳定的力学机理可以归结为无限大体内圆孔在复杂载荷作用下的稳定问题。

但是由于地质材料的复杂性[1],如不连续、尺寸效应、不确定性、软弱夹层、流固耦合等等,要准确描述岩石的破坏十分困难,目前甚至还没有一种比较可靠的破坏准则来描述岩石的破坏。

近年来,针对上述不同方面的问题,人们发展了相应的方法,形成了目前岩石力学重要的新的发展方向[2]。

钻井液密度在井壁稳定控制中起着举足轻重的作用,它是在诸多复杂因素中唯一可控的因素。

目前计算井壁稳定的力学模型均假定为等直径井筒,随着钻井液密度的减小,井壁出现剪切破坏。

一般认为剪切破坏发生后,井筒截面形状为椭圆形状,即变形后在地应力和钻井液密度的作用下达到了稳定
随着滤饼质量提高,井壁的稳定性也逐渐提高,简单而言,这是因为,一方面,随着滤饼质量的提高,井壁地层孔隙压力逐渐趋于原状地层的孔隙压力,在正压差钻井条件下,井筒内钻井液液柱压力对井壁地层的支撑作用也逐渐增强,因此,井壁地层抗剪切垮塌的能力也相应提高,地层的坍塌压力降低,井壁稳定性变好;另一方面,随着滤饼质量的提高,在正压差钻井条件下,井壁地层孔隙压力逐渐趋于原状地层的孔隙压力,地层颗粒间的接触应力,即有效应力逐渐增大,岩石抵抗张性破裂的能力增强,地层的破裂压力提高,井壁稳定性变好。

坍塌压力降低和破裂压力提高将扩大钻井 安全 钻井液密度范围,提高井壁稳定性。

滤饼质量好坏对低渗透地层的影响尤其显著。

4 结论
(1)随着滤饼质量变好,井壁周围地层孔隙压力逐渐趋于原始地层孔隙压力,利用线弹性力学分析得到的保持井壁稳定的地层破裂压力提高,坍塌压力降低,井壁的稳定性变好;
(2)随着滤饼质量变差,井壁岩石所受到的径向应力逐渐减小,井筒内钻井液液柱对井壁岩石的支撑作用逐渐减弱,井壁的稳定性逐渐变差;
(3)在相同钻井条件下,与低渗透性地层相比,高渗透性地层由于其孔隙的连通性和渗透性好,钻井压差导致的井壁周围地层孔隙压力也相对较小,但波及范围更宽。

参 考 文 献
[1] 刘向君,罗平亚编著.石油测井与井壁稳定.北京:石油
工业出版社,1999
[2] M clean P J,Wang Y.Predicting the Effects of Pore Pressure
Penetration on the Extent of Wellbore Instability:Application of a Versatile Poro-elas toplas tic Model.SPE28053,1994 [3] 刘向君.井壁力学稳定性原理及影响因素分析.西南石
油学院学报,1995,17(4)
(收稿日期 2001 09 24)
编辑 张振清
平衡状态。

由于实际的钻井作业中钻井液密度的变化不是突然的,剪切破坏发生后认为破坏的岩石部分脱落,从而钻井液作用于新的井壁上。

破坏后形成的井壁一般形状不规则,不再是规则的圆形,一般认为是类似椭圆形状,难于使用弹性力学的解析方法求解。

并且,如果要描述钻井液密度与井壁破坏形状的关系,采用形状不变井筒的假设,会产生较大的误差。

有限元方法尽管存在使用范围上的限制,但由于其它方法正处于发展阶段,因而目前在岩石力学领域还在广泛的应用,文中采用有限元方法对井筒的破坏过程进行模拟,寻求破坏形状与钻井液密度的关系。

J.Rutqvist,P.Digby,O.Stephansson,U.Singh 等人[3]对脆性岩层井壁的连续破坏过程作了研究,采用了有限元程序NFE MP(Singh,1988)进行计算。

在模拟计算中,假定井筒内钻井液密度为无限小接近于零,逐渐增加2个水平主地应力的数值,但保持其比例不变。

岩石破坏后,认为其部分的刚度发生变化,但是没有从井壁上脱落。

这种做法避免了网格的重新定义划分,大大节省了计算分析的时间和计算机资源需求,但是与真实的过程比较起来,差别太大。

采用更为符合实际受力破坏的模型,保持2个水平主地应力的数值不变,并且逐步减小井筒内钻井液密度,在符合破坏准则后认为破坏的岩石部分从井壁脱落。

1 基本假设及计算模型
模拟研究中采用的模型见图1。

考虑到几何形状、载荷和边界条件的对称性,采用四分之一平面模型。

模型结构的边长为100mm,井眼半径为10mm,根据圣维南原理和实际数值计算
表明,这样的模型尺寸可以基本消除边界效应对井筒周围应力分布的影响。

同时,井眼半径和总体模型的尺寸是相对的,可以用于模拟任意直径的实际井眼。

模拟1000m 深度地层的井筒,在2个互相垂直方向施加不等的水平主地应力,分别为26MPa 和18MPa,对应当量钻井液密度分别为2.6g/cm 3和1.8g/c m 3;井筒内表面作用钻井液液柱压力,变化值为16~10MPa,对应当量钻井液密度为1.6~1.0g/cm 3。

采用平面六节点三角形单元,为平面应变问题。

假设地层岩石材料为各向同性且均匀,根据试验测试的结果,弹性模量取为15GPa,泊松比为0.25,粘聚力为8MPa,内摩擦角为30 。

计算模型采用弹塑性材料假设。

应力计算由ANSYS55完成。

2 破坏条件
对于不同的问题,破坏的含义不同,比如:达到弹性极限;失去抵抗能力;稳定性等等。

并且实际的破坏过程十分复杂,根据试验观察和理论分析[4],岩石的破坏过程分为:弹性阶段、塑性阶段、微裂纹产生发展、岩体裂片的产生。

实际结果表明,破碎区岩体裂片是否脱离岩体以及残余强度的大小对井壁围岩的稳定性影响较大,并且将弹性理论和假定井壁围岩全部为弹性状态来作为稳定性的依据,这种做法过于保守。

目前在岩石力学中,存在大量的破坏判别条件[5],并且每隔一段时间就有新的破坏条件提出,但是使用较为广泛的仍然是Mhor -Column 条件、Drucker-Prager 条件以及完全根据试验结果提出的Hoek-Brown 条件,文中采用Drucker-Prager 条件。

Drucker-Prager 条件当量应力
e =3 m +
12
{s}T [M ]{s
}12
(1)
其中
m =1
3( x
+ y + z )(2) =2sin 3(3-sin )(3) y =
6c cos 3(3-sin )
(4)
式(1)~(4)中, m 为平均应力;{s}为偏应力; 为材料系数;[M]为系数矩阵; 为材料的内摩擦角;c 材料粘聚力; y 为材料屈服参数。

这样Drucker-Prager 条件的屈服破坏准则,可以表示为
F =3 m +
1
2
{s}T [M ]{
s}12
- y =0(5)
在计算出应力场之后,定义一应力比值
N =
e y
(6)
如果N 不小于1,表明塑性变形发生,否则认为
材料处于弹性状态。

3 计算结果
根据Drucker-Prager 破坏准则判断发生破坏的岩石部分,将破坏的岩石部分去掉,保持2个水平主
地应力不变,将减小后的钻井液密度施加于新产生的井筒表面上,重新划分单元,再计算判断,依此类推,直至钻井液密度到1.0g/c m 3
为止,见图2。

为分析井筒内钻井液密度与井筒破坏形状的关系,每次计算后,取出包括径向和环向破坏区域的尺寸,见表1、图3。

根据计算结果,发现适当地降低钻井液密度,虽然井径扩大率有所增大,但井壁仍然保持稳定,有利于相邻地层或夹层的疏松或高渗地层的低密度钻井液钻井。

表1 破坏区域的参数
钻井液密度/g cm -3
井眼半径长轴
/mm 破坏区角度
/( )井径扩大率
/%1.610.2577.66 2.571.510.46015.09 4.601.410.70922.097.091.311.11428.8511.141.211.47733.6814.771.111.82036.2118.201.0
12.116
37.88
21.
16
4 结论及进一步的问题
(1)通过逐步减小钻井液密度,得出井筒破坏形状的逐步发展过程,井壁岩石在平行最小地应力方向发生剪切破坏,井筒在这一方向尺寸变大,为近似的椭圆形状,这一点与井下成像观测和室内试验结果一致。

(2)得到了井筒破坏形状和钻井液密度的关系,基本上为抛物线关系。

由于是数值模拟,无法反映井筒内钻井液密度的连续变化;钻井液密度的变化的幅度越小,模拟的结果越可信,但计算工作量会因此而急剧增加。

考虑2方面的因素,文中的钻井液密度的变化幅度为1.0g/cm 3。

另外,该研究目前仅限于直井井眼中,并且为平面问题,对于斜井井眼、水平井井眼,以及三维问题,需要进一步进行研究。

参 考 文 献
[1] T illard D J,King M S.General Report:Mechanical Behavior
of Rocks and Rock Masses Discontinuities at Great Dep th.Rock at Great Depth,M aury &Fourmaintraux (eds),1990:1235~1241
[2] Glaser S D,Doolin D M.New Directions in Rock Mechanics
-report on a Forum Sponsored by the American Rock Me chanics Association.International Journal of Rock Mechanics and M ining Sciences,37(2000):683~698
[3] Rutqvist J,Digby P,Stephansson O,Singh U.Simulation of
Borehole Breakouts with a Damage M aterial Model.Rock at Great Depth,Maury &Fourmaintraux (eds),1990:1439~1445
[4] Germanovich L N,Dyskin A V.Fracture Mechanisms and
Instabili ty of Opening in Compression.International Journal of Rock M echanics and M i ning Sciences,37(2000):263~284[5] 郑颖人,沈珠江.岩土塑性力学原理.北京:中国人民解
放军后勤工程学院,1984:57~72
(收稿日期 2001 12 03)
编辑 张振清
15
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82。