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作者简介:

李军(1971-),男,教授,博士,博士生导师,研究方向为油气井力学与控制工程。E-mail:lijun446@vip.163.com。

通讯作者:

赵超杰(1992-),男,博士研究生,研究方向为井筒完整性、石油地质力学。E-mail:lijunpaper@163.com。

中图分类号:TE122.14

文献标识码:A

文章编号:1673-5005(2021)02-0063-08

DOI:10.3969/j.issn.1673-5005.2021.02.007

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目录contents

    摘要

    威远-长宁页岩气示范区部分区块套管变形率超过 40%,而水力压裂诱发断层滑移是导致套管变形的主要因素之一。 明确水力裂缝诱导下断层的激活机制及滑移量,对页岩气压裂过程中预防套管变形具有重要意义,而目前尚缺乏水力压裂下断层滑移量的理论模型。 基于此,根据断裂力学理论,分析水力裂缝激活断层产生滑移的作用机制,建立水力压裂下断层滑移量计算模型。 应用该模型对威远页岩气水平井威 202X 井进行实例计算,对断层滑移量影响因素进行敏感性分析。 结果表明:断层激活点处的位移量可达 46 mm,与现场实测套管变形数据吻合,验证了该模型的有效性;裂缝内的流体净压力越大,断层滑移量越大;裂缝长度越大,断层滑移量越大;控制压裂泵压和裂缝长度可以有效降低断层滑移量,避免套管严重变形;同时,高水平地应力差异系数、高弹性模量地层的断层滑移更严重;加入可压缩变形材料(陶瓷、玻璃球等)的水泥环能够为大部分断层提供适量滑移空间。

    Abstract

    More than 40% of the casing in production wells has been deformed in Weiyuan-Changning shale gas field, which has a great impact on the development of shale gas. The current field investigation indicates that fault slip induced by hydraulic fracturing could be the main reason for casing deformation. In this paper, the mechanisms of hydraulic fracturing induced fault slip were analyzed, combined with the theory of fracture mechanics, and a calculation model for the fault slip under hydraulic fracturing was established. The calculation results for well Wei202X based on new model show that the fault slip reaches to 46 mm in the activated point of fault. They are in line with the field observation of the fault slip occurred in the shale gas field. The sensitivity study results show that the displacement of fault slip increases with the fracturing fluid pressure and the length of hydraulic fractures. Adequate adjustments of the fracturing pump pressure and the fracture length can reduce the fault slippage, and then avoid serious casing deformation. The faults subjected with high difference of horizontal in-situ stresses and with in rock formation having high elastic modulus will slip with a large displacement once the slippage is activated. The cement sheath with compressible materials(ceramic balls, marble, etc. ) can provide enough space for most of fault slip. The model established in this study can provide a calculation method for fault slip during hydraulic fracturing, which is useful for preventing casing deformation in shale gas wells.

  • 四川威远-长宁页岩气区块经历了多期地质构造运动,断层发育,构造应力强,剪切位移和走滑断层是该区块的主要构造特征[1]。在该区块页岩气井多级压裂过程中套管变形问题突出,超过40%的水平井筒出现严重的套管变形(超过10mm),导致桥塞无法下入[2],改造段数减少,严重威胁了页岩气井的高效、安全、经济开发。基于此,国内外学者开展了大量套管变形机制方面的研究。戴强[3]、田中兰等[4]、Lian等[5]、于浩等[6]、Liu等[7] 指出套管变形是其强度削弱和外载变化共同作用的结果,套管磨损、温度作用等导致套管强度降低,而体积压裂导致局部地应力极端集中使套管应力提升,双重作用致使套管变形。陈朝伟等[8-9]、Kistiansen等[10] 认为压裂过程中压裂液沿天然裂缝或层理面传递,激活天然裂缝滑动, 造成套管剪切变形。郭雪利等[11]、Warpinski等[12]、Zhao等[13] 基于震源机制原理与微地震技术,分析了断层滑移下套管变形机制, 认为断层滑移与套管剪切变形特征相符。国内外研究均指出页岩气压裂引起的断层滑移与套管变形存在密切联系,但是对于压裂过程中断层的激活、滑移量的研究还不够深入,并没有建立断层滑移量与水力压裂之间的定量计算模型。笔者基于断裂力学理论,建立水力裂缝激活断层及滑移量的力学计算模型,并结合现场实例进行计算,与基于套管变形量反演的微断层滑移量进行比较、验证,最后分析压裂泵压、断层性质、地层性质等对断层滑移量的影响。

  • 1 模型建立

  • 页岩气水平井压裂过程中,水力裂缝拓展延伸, 改变局部地应力场,从而改变断层力学平衡,激活断层,产生走滑剪切位移。因此分析水力压裂对断层滑移的影响,需要首先分析水力裂缝拓展导致的局部应力场变化;然后,结合尖端诱导应力场作用下断层的力学状态,以判断断层是否被激活并发生滑移; 进而计算水力裂缝拓展导致诱导局部态下断层滑移量。

  • 1.1 水力裂缝诱导下断层界面应力场

  • 假设水力裂缝、断层均为理想均质刚性平面,遵守线弹性力学准则,且断层无限远边界无明显滑移。

  • 建立三维空间坐标系(x,y,z),如图1所示,其中x轴、y轴、z轴分别与主地应力 σhσHσv 一致。红色虚线框为内置断层面,其法向矢量为P1¯=n1,n2,n3;蓝色长轴为水平井筒,其平行与x轴;蓝色实线框为水力裂缝面,其垂直于最小主应力方向,即x轴方向,其法向矢量为P2¯=(1,0,0),水力裂缝与微断层的夹角为

  • β=arccosP1¯P2¯
    (1)
  • 式中,β 为水力裂缝与断层间的夹角,(°)。

  • 图1 断层面、水力裂缝面空间位置示意图

  • Fig.1 Schematic diagram of spatial position of fault plane and hydraulic fracture surface

  • 取同时垂直于水力裂缝和微断层的1个平面P 3,该平面满足平面应变,如图2所示,该平面法向矢量为P3¯=0,l1,-n1n2l2

  • 在平面P 3 上,以水平井筒轴向为x′轴,裂缝延伸方向为y′轴,水力裂缝与微断层的交线与 σv 的夹角满足:

  • α=arccosP1¯×P2¯(1,0,0)
    (2)
  • 故在该平面上:

  • σy'=σHcos2α+σvsin2α
    (3)
  • 式中,σyP3 平面上y′轴方向的主应力,MPa;σH 为水平最大主应力,MPa;σh 为最小水平主应力, MPa;σv 为垂向地应力,MPa。

  • 水力裂缝主裂缝是拉伸型裂缝,模型中假设主裂缝拓展逼近断层。根据断裂力学理论[14],可以求解水力裂缝尖端区域应力场。根据应力场线性叠加原理将水力裂缝尖端应力场与远场地应力场叠加后得

  • σxx=σh-KI2πrcosθ21+sinθ2-sin3θ2,σyy=σy'-KI2πrcosθ21-sinθ2-sin3θ2,τxy=-KI2πrsinθ2cos3θ2cosθ2
    (4)
  • 其中

  • KI=Δpπa

  • 式中,σxx 为x轴方向的正应力,MPa;σyy 为y轴方向的正应力,MPa;τxy 为剪应力,MPa;KI 为第一类应力强度因子;a为裂缝半长,m;Δp 为裂缝内净拉应力即缝内流体压力与最小水平地应力之差,MPa; r 为断层处某点距裂缝尖端的距离,m;θ 为断层处某点在以裂缝尖端为原点处的极坐标下角度,(°)。

  • 图2 水力裂缝与断层在P3平面位置示意图

  • Fig.2 Schematic diagram of hydraulic fractures and faults in P3plane

  • 利用坐标转换,可以得到断层界面处的剪切应力与正应力为

  • τ=σxx-σyycosπ2-βsinπ2-β+τxycos2π2-β-sin2π2-β
    (5)
  • σ=σxxsin2π2-β+σyycos2π2-β+2τxysin2π2-β-cosπ2-β.
    (6)
  • 考虑水力裂缝在无限接近断层时,压裂流体应该已经渗入断层中,则断层界面主应力 σtrue 变为

  • σtrue =σ-pf
    (7)
  • 式中,pf 为水力裂缝内的净流体压力,MPa。

  • 将式(5)、(7)代入Coulomb-Navier准则[15],判断在水力裂缝影响下断层是否发生滑移,

  • τ=C+λσtrue
    (8)
  • 式中,C 为断层界面处初始内聚力,MPa;λ 为断层界面处内摩擦系数(压裂液的润滑作用下,内摩擦系数降低)。

  • 1.2 滑移状态下断层位移场

  • 若断层发生滑移,则需要克服内聚力与内摩擦力,水力裂缝形成后断层界面的有效剪应力为

  • Δτ=τ-C+μσtrue
    (9)
  • 如图3所示,以断层中点为原点,断层走向为x轴,垂直走向为y轴,建立平面坐标系,断层长度为2L,假设断层两尖端为永久闭合,即尖端处为刚性约束。

  • 图3 断层滑移受力分析

  • Fig.3 Fault slip force analysis

  • 微断层的运动状态为剪切滑移,可以视为滑移型裂缝,结合断裂力学基础,可知其Westergaard应力函数[16]应选用如下形式:

  • φ=-yReZ-
    (10)
  • 可以得到应力分量表达式为

  • σx=2ImZ+yReZ',σy=-yReZ',τxy=ReZ-yImZ'.
    (11)
  • 式中,Z'=dZdz为导数;Z-=Zdz为一次积分式。

  • 代入本构方程可以得到位移分量表达式为

  • u=1+μEk+12ImZ-+yReZv=1+μE1-k2ReZ-+yImZ,k=3-μ1+μ.
    (12)
  • 式中,μ 为地层泊松比;E 为地层弹性模量,GPa;u为断层在x方向位移量;v为断层在y方向位移量。

  • 通过以上推导可知,求应力和位移不需要找出应力函数,只需选择 Z,并使其满足边界条件:y=0,-L<x<L 时,剪应力为 τ;y=0,x趋近无穷时,剪应力为0。

  • 选取 Z(x)为

  • Z(x)=τxx2-L2
    (13)
  • 而后将坐标原点移到右端点,并用极坐标( r′, θ′)表示可得

  • Zr',θ'=KII2πr'cosθ'2-isinθ'2.
    (14)
  • 其中

  • KII=ΔτπL

  • 将式(14)代入位移分量表达式可以得到断层界面处某点的位移表达式为

  • u=KΠ4μr'2π(2k+3)sinθ'2+sin3θ'2,v=KΠ4μr'2π(2-2k)-cos3θ'2,k=3-μ1+μ.
    (15)
  • 水力压裂过程中断层会发生多次滑移,故断层滑移总量等于多次位移量叠加:

  • D=in ui2+νi2
    (16)
  • 式中,D 为断层总滑移量;i为断层被激活的事件数。

  • 2 实例计算与验证

  • 威202X井,水平井眼方向150°,最大水平主应力67MPa,最小水平主应力50MPa,垂向地应力58MPa。根据直井取心观察确定,龙马溪组发育有一组微断层,方向是30°,即水力裂缝面与微断层面的夹角为60°,根据地震资料解释该断层长度约为80m。页岩抗拉强度为2MPa,微断层面的内聚力为0.3MPa,内摩擦系数为0.6。压裂作业泵压为60~75MPa(即裂缝缝内流体净压力约为10MPa)。该井在压裂第10、11、12段时,微地震监测发现井筒下方数据出现异常点,在压裂第13段时,桥塞无法下入,说明套管发生了变形,根据通井测试可知套管变形量为33.7mm [9]。利用上述模型计算水力裂缝逼近断层时断层的滑移量,结果如图4所示。

  • 由图4可知,当断层面与水力裂缝面的夹角为60°时,断层激活点处(即水力裂缝与天然断层的相交点,断层在该点首先被激活发生滑移) 的位移量可达46mm,而后随着距离激活点的距离变大而下降,在距离断层激活点约30m处,其滑移量为33mm,即断层滑移量(距断层激活点30m内)为33~46mm。计算得到的该处断层滑移量与实际井筒变形量在同一数量级,且差值较小。考虑到井筒与断层激活点间的距离变化,及断层滑移量与套管变形量的差距,计算结果较符合实际,验证了本模型的准确性。

  • 此外,也可以从计算结果看出,断层面与裂缝面的夹角对断层的状态及滑移量影响明显。当其夹角超过70°时,断层不会滑移,而夹角为51°时,断层最大滑移量可达10cm。

  • 图4 不同断层与裂缝夹角下断层滑移量分布

  • Fig.4 Distribution of fault slip under different angle between fault and fracture

  • 3 断层滑移量影响因素敏感性

  • 由模型中变量参数分析可知,断层滑移量与水力裂缝的长度、缝内流体净压力、断层面的内聚力与内摩擦系数、地层弹性参数及地应力等参数密切相关,故进行影响因素敏感性分析。

  • 3.1 压裂施工

  • 3.1.1 水力裂缝尖端流体净压力

  • 压裂时泵压能够直接影响水力裂缝内流体压力,水力裂缝内的流体压力会显著影响裂缝尖端局部应力场,从而影响断层的活动状态。不同裂缝内流体净压力(裂缝内流体压力与最小水平地应力之差)下断层滑移量变化如图5所示。可见,裂缝内的流体净压力对断层滑移量影响显著,随裂缝内流体净压力增大,断层滑移量增加;裂缝内的流体净压力低于8MPa时断层不会发生滑移。

  • 3.1.2 水力裂缝长度

  • 水力裂缝的长度影响局部地应力场的范围及极值,进而改变附近断层的受力状态。不同水力裂缝长度下断层滑移量变化如图6所示。由图6可见, 断层的滑移量随水力裂缝长度变大而增加,且增加的速率逐渐变大。目前页岩气井压裂裂缝半长约为100m,当裂缝尖端与断层相互连通时,断层滑移量可达85mm,即使在距断层30m处其滑移量也超过40mm,足以造成套管变形而无法下入标准井下工具。故在断层发育区域可以适当优化水力裂缝的长度,以降低断层滑移下套管变形概率。

  • 图5 不同裂缝内流体净压力下断层滑移量变化

  • Fig.5 Distribution of fault slip under different net pressure of fluid in fracture

  • 图6 不同水力裂缝长度下断层滑移量变化

  • Fig.6 Distribution of fault slip under different length of fracture

  • 3.2 断层特征

  • 3.2.1 断层长度

  • 水力裂缝影响下不同长度的断层滑移量变化如图7所示。由图7(a)可知,在水力裂缝影响下不同长度的断层的滑移量分布规律一致,即在激活点滑移量最大,而后变小,且在断层末端趋于0。由图7(b)可知,两者均随断层半长而增加,且为类抛物线关系。在长断层处两者之间的差值越大,说明长断层界面的位移滑移量变化更大。可以推断,断层长度越长,断层滑移量越大,即套管变形概率及变形量越大。

  • 3.2.2 断层面初始内聚力

  • 断层滑移需要克服断层初始内聚力及断层界面上的摩擦力,故断层界面的内聚力会影响断层滑移量。断层面内聚力对断层滑移量的影响如图8所示。由图8可以看出,断层的滑移量随断层界面内聚力增加而减小,且随着内聚力增加,其对断层滑移量的影响逐渐变弱,在距离激活点位置越远处作用越弱。此外,当断层界面内聚力超过2MPa时断层不会发生滑移。

  • 图7 水力裂缝影响下不同长度的断层滑移量变化

  • Fig.7 Distribution of fault slip for different length faults

  • 图8 断层面内聚力对断层滑移量的影响

  • Fig.8 Effect of cohesion of fault on fault slip

  • 3.2.3 断层面内摩擦系数

  • 大部分断层面的内摩擦系数为0.4~0.8 [17],图9为断层面内摩擦系数对断层滑移量的影响规律曲线。断层滑移量随内摩擦系数增加而减小,且两者间呈线性关系。在距离断层激活点位置远的位置, 内摩擦系数的影响逐渐变弱。当内摩擦系数超过0.75时断层不会发生滑移。

  • 图9 断层面内摩擦系数对断层滑移量的影响

  • Fig.9 Effect of internal friction coefficient of fault on fault slip

  • 3.3 地层特征

  • 地层水平地应力差异系数、弹性模量、泊松比对断层滑移量的影响如图10所示。

  • 威远-长宁区块页岩地层受构造运动影响,水平方向地应力存在明显差异,可以用水平地应力差异系数K h 表征[18],即Kh=σH-σhσH。而由所建立的断层滑移量计算模型可知,水平地应力差异系数与断层滑移量有着密切联系。

  • 由图10(a)可知,断层滑移量随水平地应力差异系数增加而增加,且水平地应力差异系数对于断层滑移量的影响在越靠近断层激活点位置而越明显。高水平地应力差异系数下断层滑移量与低水平地应力差异系数下的滑移量相比,两者差值可到达15mm。统计资料表明,相比美国Barnett页岩气田[19-20],中国威远-长宁、威荣等[21] 页岩区块地应力差异系数与更大,而页岩区块的高水平地应力差异系数加剧了断层滑移,故中国威远-长宁、威荣页岩区块套管变形更加严重。

  • 图10 地层水平地应力差异系数、弹性模量、泊松比对断层滑移量的影响

  • Fig.10 Effect of difference coefficient of horizontal in-site stress, elastic modulus, Poisson̍s ratio in formation on fault slip

  • 断层滑移的本质是通过地层的弹性变形,形成新的应力平衡,根据应力-应变本构关系,可知地层弹性参数会影响断层滑移量。图10(b)表明,断层滑移量随地层弹性模量变大而增加,且变化随弹性模量变大而明显。当地层弹性模量达到30GPa时, 断层激活点处的滑移量接近10cm,距断层激活点30m处的滑移量也超过4cm,均可造成严重的套管变形。此外,根据岩石脆性与力学参数关系[22],可知高弹性模量地层其脆性指数偏高,即地层脆性段套管变形更严重,这一规律与现场统计结果相符。

  • 整体上,地层泊松比对断层滑移量的影响不明显[23],而低泊松比(高脆性)下断层滑移量高。

  • 由敏感性分析可知,压裂施工参数的优化,地层物性参数及断层构造的精确识别都能够有效降低断层滑移量。但是实际生产作业中,上述因素的精确识别与优化非常困难[24],须对井筒结构本身进行优化,以有效避免断层滑移造成的套管变形。在水泥浆中加入可压缩变形材料(如陶瓷小球、玻璃空心球等),固化形成水泥环。当断层滑移时,井壁会挤压水泥环,而可压缩变形材料被挤压产生变形,为地层滑移岩体提供了空间,而减少了套管变形。大多数状态下(即不同的压裂施工、地层与断层参数)断层的滑移量为2~6cm,而加入可压缩变形材料形成的水泥环可以提供适量的变形空间,故通过预留断层滑移空间降低套管变形量可行且有效。

  • 4 结论

  • (1)断层滑移量随裂缝内的流体净压力、裂缝长度变大而增加,控制压裂泵压、裂缝长度可以有效降低断层滑移量,避免套管严重变形。

  • (2)断层的尺度、内聚力、内摩擦系数等参数与其滑移量关系密切,对低内聚力、低内摩擦系数的断层,在压裂改造中需要予以重视。

  • (3)高水平地应力差异系数、高弹性模量地层的断层滑移会加剧,压裂改造应避开该类断层。

  • (4)在水泥浆中加入可压缩变形材料(如陶瓷球、玻璃球)能够为断层滑移提供适量空间,可以有效降低套管变形。

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