椭圆形井筒破裂压力预测模型
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摘要
水力压裂是油气藏增产的一项重要技术手段,准确预测破裂压力是水力压裂成功的关键。目前的破裂压力预测模型假设井筒为圆形,但测井数据表明井筒为椭圆形。因此,运用复变函数理论和弹性力学理论,推导出椭圆形井筒井周应力场计算解析表达式,建立椭圆形井筒破裂压力预测模型,通过公式蜕化和数值计算检验证明本文模型的正确性。分析椭圆长短轴比和地应力差对破裂压力的影响,研究表明:(1)以我国西部地区某井为例,本文模型计算的破裂压力与现场实际的误差在4%以内;受井筒形状的影响,最小水平地应力方向有应力集中效应,裂缝沿着该方向起裂。(2)当长短轴比较大时,裂缝在最小水平地应力方向起裂,将会发生近井筒裂缝弯曲现象;当长短轴比较小时,小范围的井壁坍塌会引起破裂压力有较大提升。(3)平衡曲线有y(28)ax(10)1的表达形式,当参数点落在区域I内时,破裂压力受地应力差影响大,井筒沿着最大水平地应力方向起裂;当参数点落在区域II内时,破裂压力受井筒形状影响大,井筒沿着最小水平地应力方向起裂;当参数点落在平衡线及其附近区域时,井筒各个方向的破裂压力相近,井筒内多裂缝同时起裂。
Hydraulic fracturing is an important technique to increase the production of oil and gas reservoirs. The prediction of breakdown pressure accurately is the key to the success of hydraulic fracturing. The current prediction model of breakdown pressure assumes that the wellbore is circular,but the wellbore is actually elliptical according to the log data. The complex function theory and the theory of elasticity are therefore used to derive the analytical stress field around the elliptical wellbore and a prediction model for the breakdown pressure of an elliptical wellbore is established. The correctness of the model is verified through formula deduction and numerical calculation. The influence of the ratio of major axis to minor axis and the difference of in-situ stress on the breakdown pressure are analyzed. A well in western China was studied as an example. The error of breakdown pressure calculated with this model is within 4%. The stress concentration due to the influence of wellbore shape occurs in the direction of minimum horizontal stress and fractures initiate along this direction. When the ratio of major axis to minor axis is large,fractures initiate along the direction of minimum horizontal stress and fracture bending occur near the wellbore. When the ratio is small,the collapse of small area of well wall leads to drastic increasing in breakdown pressure. The equilibrium curve has an expression of y(28)ax(10)1. When the point of the parameter falls in zone I,the breakdown pressure is greatly influenced by the difference of in-situ stress,and the wellbore fractures initiate along the direction of maximum horizontal stress. When it falls in zone II,the breakdown pressure is greatly influenced by the shape of the wellbore,and the wellbore fractures initiate along the direction of minimum horizontal stress. When it falls on the balance line and its adjacent area,the breakdown pressure is close in different directions of the wellbore,and the multiple fractures initiate in the wellbore at the same time.
Hydraulic fracturing is an important technique to increase the production of oil and gas reservoirs. The prediction of breakdown pressure accurately is the key to the success of hydraulic fracturing. The current prediction model of breakdown pressure assumes that the wellbore is circular,but the wellbore is actually elliptical according to the log data. The complex function theory and the theory of elasticity are therefore used to derive the analytical stress field around the elliptical wellbore and a prediction model for the breakdown pressure of an elliptical wellbore is established. The correctness of the model is verified through formula deduction and numerical calculation. The influence of the ratio of major axis to minor axis and the difference of in-situ stress on the breakdown pressure are analyzed. A well in western China was studied as an example. The error of breakdown pressure calculated with this model is within 4%. The stress concentration due to the influence of wellbore shape occurs in the direction of minimum horizontal stress and fractures initiate along this direction. When the ratio of major axis to minor axis is large,fractures initiate along the direction of minimum horizontal stress and fracture bending occur near the wellbore. When the ratio is small,the collapse of small area of well wall leads to drastic increasing in breakdown pressure. The equilibrium curve has an expression of y(28)ax(10)1. When the point of the parameter falls in zone I,the breakdown pressure is greatly influenced by the difference of in-situ stress,and the wellbore fractures initiate along the direction of maximum horizontal stress. When it falls in zone II,the breakdown pressure is greatly influenced by the shape of the wellbore,and the wellbore fractures initiate along the direction of minimum horizontal stress. When it falls on the balance line and its adjacent area,the breakdown pressure is close in different directions of the wellbore,and the multiple fractures initiate in the wellbore at the same time.
引文
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[16]李军,陈勉,张辉,等.不同地应力条件下水泥环形状对套管应力的影响[J].天然气工业,2004,24(8):50–52.(LI Jun,CHEN Mian,ZHANG Hui,et al.Influence of cement sheath shape on casing stress under different ground stress conditions[J].Natural Gas Industry,2004,24(8):50–52.(in Chinese))
[17]孙晓锋,刘禹铭,李波,等.椭圆井眼井壁稳定性研究[J].化工设计通讯,2016,42(5):139–142.(SUN Xiaofeng,LIU Yuming,LI Bo,et al.The effects of the wellbore pressure on damaged wellbore stability[J].Chemical Engineering Design Communications,2016,42(5):139–142.(in Chinese))
[18]徐力群,石祥超,孟英峰,等.气体钻井椭圆井眼应力分布规律研究[J].钻采工艺,2016,39(1):42–45.(XU Liqun,SHI Xiangchao,MENG Yingfeng,et al.Analysis on the stress distribution of elliptic borehole in gas drilling[J].Drilling and Production Technology,2016,39(1):42–45.(in Chinese))
[19]王光钦.弹性力学[M].北京:中国铁道出版社,2008:257–285.(WANG Guangqin.Elastic mechanics[M].Beijing:China Railway Publishing House,2008:257–285.(in Chinese))
[20]范天佑.断裂理论基础[M].北京:科学出版社,2003:20–29.(FAN Tianyou.Foundation of fracture theory[M].Beijing:Science Press,2003:20–29.(in Chinese))
[2]李小刚,易良平,杨兆中.横观各向同性地层水平井井壁拟三维应力场计算模型[J].岩石力学与工程学报,2017,36(6):1 452–1 459.(LI Xiaogang,YI Liangping,YANG Zhaozhong.A pseudo three-dimensional stress model of horizontal bore well in transversely isotropic formation[J].Chinese Journal of Rock Mechanics and Engineering,2017,36(6):1 452–1 459.(in Chinese))
[3]HUBBERT M K,WILLIS D G W.Mechanics of hydraulic fracturing[J].Developments in Petroleum Science,1972,210(7):369–390.
[4]HAIMSON B,FAIRHURST C.Initiation and extension of hydraulic fractures in rocks[J].Society of Petroleum Engineers Journal,1967,7(3):310–318.
[5]YEW C H,LI Y.Fracturing of a deviated well[J].SPE Production Engineering,1988,3(4):429–437.
[6]EATON B A.Fracture gradient prediction and its application in oilfield operations[J].Journal of Petroleum Technology,1969,21(10):1 353–1 360.
[7]黄荣樽.水力压裂裂缝的起裂和扩展[J].石油勘探与开发,1981,8(5):62–74.(HUANG Rongzun.Initiation and extension of hydraulic fracturing[J].Journal of Petroleum Exploration and Development,1981,8(5):62–74.(in Chinese))
[8]李传亮,孔祥言.油井压裂过程中岩石破裂压力计算公式的理论研究[J].石油钻采工艺,2000,22(2):54–56.(LI Chuanliang,KONG Xiangyan.A theoretical study on rock breakdown pressure calculation equations of fracturing process[J].Oil Drilling and Production Technology,2000,22(2):54–56.(in Chinese))
[9]郭建春,曾凡辉,赵金洲.酸损伤射孔井储集层破裂压力预测模型[J].石油勘探与开发,2011,38(2):221–227.(GUO Jianchun,ZENG Fanhui,ZHAO Jinzhou.A model for predicting reservoir fracturing pressure of perforated wells after acid damage[J].Petroleum Exploration and Development,2011,38(2):221–227.(in Chinese))
[10]赵金洲,任岚,胡永全,等.裂缝性地层射孔井破裂压力计算模型[J].石油学报,2012,33(5):841–845.(ZHAO Jinzhou,REN Lan,HU Yongquan,et al.A calculation model of breakdown pressure for perforated wells in fractured formations[J].Acta Petrolei Sinica,2012,33(5):841–845.(in Chinese))
[11]刘合,兰中孝,王素玲,等.水平井定面射孔条件下水力裂缝起裂机制[J].石油勘探与开发,2015,42(6):794–800.(LIU He,LAN Zhongxiao,WANG Suling,et al.Hydraulic fracture initiation mechanism in the definite plane perforating technology of horizontal well[J].Petroleum Exploration and Development,2015,42(6):794–800.(in Chinese))
[12]GOUGH D I,BELL J S.Stress orientations from borehole wall fractures with examples from Co.[J].Canadian Journal of Earth Sciences,1982,19(7):1 358–1 370.
[13]ZOBACK M D,BARTON C A,BRUDY M,et al.Determination of stress orientation and magnitude in deep wells[J].International Journal of Rock Mechanics and Mining Sciences,2003,40(7/8):1 049–1 076.
[14]赵凯,韩继勇,许永华.定向井井径扩大率计算模型及影响因素分析[J].断块油气田,2016,23(5):638–642.(ZHAO Kai,HAN Jiyong,XU Yonghua.Borehole diameter enlargement ratio calculation model of directional wells and influence factors analysis[J].Fault-Block Oil and Gas Field,2016,23(5):638–642.(in Chinese))
[15]李军,陈勉,张广清,等.易坍塌地层椭圆形井眼内套管应力的有限元分析[J].中国石油大学学报:自然科学版,2004,28(2):45–48.(LI Jun,CHEN Mian,ZHANG Guangqing,et al.Analysis on stress distribution of casing in sloughing formation with finite element method[J].Journal of the University of Petroleum:Natural Science,2004,28(2):45–48.(in Chinese))
[16]李军,陈勉,张辉,等.不同地应力条件下水泥环形状对套管应力的影响[J].天然气工业,2004,24(8):50–52.(LI Jun,CHEN Mian,ZHANG Hui,et al.Influence of cement sheath shape on casing stress under different ground stress conditions[J].Natural Gas Industry,2004,24(8):50–52.(in Chinese))
[17]孙晓锋,刘禹铭,李波,等.椭圆井眼井壁稳定性研究[J].化工设计通讯,2016,42(5):139–142.(SUN Xiaofeng,LIU Yuming,LI Bo,et al.The effects of the wellbore pressure on damaged wellbore stability[J].Chemical Engineering Design Communications,2016,42(5):139–142.(in Chinese))
[18]徐力群,石祥超,孟英峰,等.气体钻井椭圆井眼应力分布规律研究[J].钻采工艺,2016,39(1):42–45.(XU Liqun,SHI Xiangchao,MENG Yingfeng,et al.Analysis on the stress distribution of elliptic borehole in gas drilling[J].Drilling and Production Technology,2016,39(1):42–45.(in Chinese))
[19]王光钦.弹性力学[M].北京:中国铁道出版社,2008:257–285.(WANG Guangqin.Elastic mechanics[M].Beijing:China Railway Publishing House,2008:257–285.(in Chinese))
[20]范天佑.断裂理论基础[M].北京:科学出版社,2003:20–29.(FAN Tianyou.Foundation of fracture theory[M].Beijing:Science Press,2003:20–29.(in Chinese))