水平井多段压裂非常规裂缝压力动态特征
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摘要
为了解决复杂地层压裂过程中裂缝关于井筒不对称的试井解释问题,通过点源函数基本理论,建立有限导流垂直裂缝试井解释数学模型,利用压降叠加原理获得水平井多段压裂非常规裂缝试井解释模型,采用积分变换获得该模型的半解析解。对压裂裂缝进行数值离散,结合半解析解与杜哈美原理,根据Stehfest数值反演方法绘制考虑井储和表皮效应的井底压力及压力导数曲线。研究表明:该模型总体上划分为井储、双线性流、早期线性流、第一径向流、第二线性流、过渡流和系统径向流阶段;不对称因子主要影响双线性流阶段持续时间的长短;裂缝导流系数主要影响双线性流阶段和早期线性流阶段井底压力及压力导数曲线特征,导流能力越大,双线性流阶段井底压力导数曲线特征越不明显。
To solve the problem of well test interpretation of fracture asymmetry during fracturing in the complicated strata, based on the ba-sic theory of point-source function, a mathematics model for well-test interpretation of finite-conductivity vertical fractures was established,then a well-test interpretation model of the unconventional fracture during multi-staged fracturing in horizontal wells was obtained by usingpressure drop superposition principle, and the semi-analytical solution of the model was obtained with integral transformation. The frac-tures were discredited numerically, and combined with the semi-analytical solution and Duhamel principle, bottom hole pressure and pres-sure derivative curves considering the wellbore storage and skin effects were mapped on the basis of Stehfest numerical inversion. The re-sults showed that the model included wellbore storage stage, bilinear flow stage, early linear flow stage, first radial flow stage, second linearflow stage, transitional flow stage and systematic radial flow stage; asymmetric factor mainly had an influence on time length in the bilinearflow stage; fracture perveance mainly affected the characteristics of downhole pressure and pressure derivative curves in bilinear flow stageand early linear flow stage, and the greater the flow conductivity was, the more unobvious the characteristic of downhole pressure derivativecurves in the bilinear flow stage would be.
To solve the problem of well test interpretation of fracture asymmetry during fracturing in the complicated strata, based on the ba-sic theory of point-source function, a mathematics model for well-test interpretation of finite-conductivity vertical fractures was established,then a well-test interpretation model of the unconventional fracture during multi-staged fracturing in horizontal wells was obtained by usingpressure drop superposition principle, and the semi-analytical solution of the model was obtained with integral transformation. The frac-tures were discredited numerically, and combined with the semi-analytical solution and Duhamel principle, bottom hole pressure and pres-sure derivative curves considering the wellbore storage and skin effects were mapped on the basis of Stehfest numerical inversion. The re-sults showed that the model included wellbore storage stage, bilinear flow stage, early linear flow stage, first radial flow stage, second linearflow stage, transitional flow stage and systematic radial flow stage; asymmetric factor mainly had an influence on time length in the bilinearflow stage; fracture perveance mainly affected the characteristics of downhole pressure and pressure derivative curves in bilinear flow stageand early linear flow stage, and the greater the flow conductivity was, the more unobvious the characteristic of downhole pressure derivativecurves in the bilinear flow stage would be.
引文
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[21]ZAKIAN V.Numercial inversion of Laplace transform[J].Electronics Letters,1970,99(5):47-49
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[24]吕志凯,冀光,位云生,等.致密气藏水平井产能图版及应用[J].特种油气藏,2014,21(6):105-110.LV Zhikai,JI Guang,WEI Yunsheng,et al.Horizontal well production type-curve and its application in tight gas reservoirs[J].Special Oil&Gas Reservoirs,2014,21(6):105-110.
[2]CINCO L H,SAMANIEGO V F,DOMINGUEZ A N.Transient pressure behavior for a well with a finite-conductivity vertical fracture[J].Society of Petroleum Engineers Journal,1978,18(4):253-264.
[3]CINCO L H,MENG H Z.Pressure transient analysis of wells with finite conductivity vertical fractures in double porosity reservoirs[R].SPE 18172,1988.
[4]陈汾君,汤勇,刘世铎,等.低渗致密气藏水平井分段压裂优化研究[J].特种油气藏,2012,19(6):85-89.CHEN Fenjun,TANG Yong,LIU Shiduo,et al.Study on the optimization of staged fracturing of a horizontal well in a tight gas reservoir with low permeability[J].Special Oil&Gas Reservoirs,2012,19(6):85-89.
[5]谷建伟,于秀玲,田同辉,等.致密低渗透气藏压裂水平井产能计算与分析[J].特种油气藏,2016,23(2):77-82.GU Jianwei,YU Xiuling,TIAN Tonghui,et al.Fractured horizontal well productivity forecast and analysis in low-permeability tight gas reservoir[J].Special Oil&Gas Reservoirs,2016,23(2):77-82.
[6]RILEY M F,BRIFHAM W E,HORNE R N.Analytic solutions for elliptical finite-conductivity fractures[R].SPE 22656,1991.
[7]TIAN D,LU J,NGUYEN H,et al.Evaluation of fracture asymmetry of finite conductivity fractured wells[J].Journal of Energy Resources Technology,2010,132(1):11-17.
[8]BERUMEN S,TIABB D,RODRIGUEZA F.Constant rate solutions for a fractured well with an asymmetric fracture[J].Journal of Petroleum Science and Engineering,2000,25(1):49-58.
[9]LUO W J.Preseeure transient analysis of multiwing fractures connected to a vertical wellbore[R].SPE 171556,2015.
[10]WANG L,WANG X.Type curves analysis for asymmetrically fractured wells[J].Journal of Energy Resources Technology,2014,136(2):1-8.
[11]熊健,刘海上,赵长虹,等.低渗透气藏不对称垂直裂缝井产能预测[J].油气地质与采收率,2013,20(6):76-79.XIONG Jian,LIU Haishang,ZHAO Changhong,et al.Study on productivity of asymmetrical vertical fracture well in low-permeability gas reservoirs[J].Petroleum Geology and Recovery Efficiency,2013,20(6):76-79.
[12]曹宝军,李相方,姜子杰,等.压裂火山岩气井不对称裂缝产能模型研究[J].天然气工业,2009,29(8):79-81.CAO Baojun,LI Xiangfang,JIANG Zijie,et al.A research on the asymmetric fracture productivity models for fracturing volcanic gas wells[J].Natural Gas Industry,2009,29(8):79-81.
[13]王本成,贾永禄,李友全,等.多段压裂水平井试井模型求解新方法[J].石油学报,2013,34(6):1 151-1 158.WANG Bencheng,JIA Yonglu,LI Youquan,et al.A new solution of well test model for multistage fractured horizontal wells[J].Acta Petrolei Sinica,2013,34(6):1 151-1 158.
[14]李龙龙,姚军,李阳,等.分段多簇压裂水平井产能计算及其分布规律[J].石油勘探与开发,2014,41(4):457-462.LI Longlong,YAO Jun,LI Yang,et al.Productivity calculation and distribution of staged multi-cluster fractured horizontal wells[J].Petroleum Exploration and Development,2014,41(4):457-462.
[15]OZKAN E,RAGHAVAN R.New solutions for well-test-analysis problems:part 1-analytical considerations[J].SPE Formation Evaluation,1991,6(3):359-368.
[16]OZKAN E,RAGHAVAN R.New solutions for well-test-analysis problems:part 2-computional considerations[J].SPE Formation Evaluation,1991,6(3):369-378.
[17]GUO J J,WANG H T,ZHANG L H.Transient pressure and production dynamics of multi-stage fractured horizontal wells in shale gas reservoirs with stimulated reservoir volume[J].Journal of Atural Gas Science and Engineering,2016,35(1):425-443.
[18]TIAN Q,LIU P H.Pressure transient analysis of non-planar asymmetric fractures connected to vertical wellbores in hydrocarbon reservoirs[J].Intenational Journal of Hydrogen Energy,2017,42(29):18 146-18 155.
[19]包劲青,刘合,张广明,等.分段压裂裂缝扩展规律及其对导流能力的影响[J].石油勘探与开发,2014,41(2):281-289.BAO Jinqing,LIU He,ZHANG Guangming,et al.Fracture propagation laws in staged hydraulic fracturing and their effects on fracture conductivities[J].Petroleum Exploration and Development,2014,41(2):281-289.
[20]王晓冬,罗万静,侯晓春,等.矩形油藏多段压裂水平井不稳态压力分析[J].石油勘探与开发,2014,41(1):74-94.WANG Xiaodong,LUO Wanjing,HOU Xiaochun,et al.Transient pressure analysis of multiple-fractured horizontal wells in boxed reservoirs[J].Petroleum Exploration and Development,2014,41(1):74-94.
[21]ZAKIAN V.Numercial inversion of Laplace transform[J].Electronics Letters,1970,99(5):47-49
[22]江涛,王玉根,张修明,等.在页岩气试井分析中Bessel函数溢出问题的解决方法[J].天然气工业,2017,37(6):42-45.JIANG Tao,WANG Yugen,ZHANG Xiuming,et al.Solution to the numerical overflow of Bessel functions in the analysis of shale gas well testing[J].Natural Gas Industry,2017,37(6):42-45.
[23]任龙,苏玉亮,郝永卯,等.基于改造模式的致密油藏体积压裂水平井动态分析[J].石油学报,2015,36(10):1 272-1 280.REN Long,SU Yuliang,HAO Yongmao,et al.Dynamic analysis of SRV-fractured horizontal wells in tight oil reservoirs based on stimulated patterns[J].Acta Petrolei Sinica,2015,36(10):1 272-1 280.
[24]吕志凯,冀光,位云生,等.致密气藏水平井产能图版及应用[J].特种油气藏,2014,21(6):105-110.LV Zhikai,JI Guang,WEI Yunsheng,et al.Horizontal well production type-curve and its application in tight gas reservoirs[J].Special Oil&Gas Reservoirs,2014,21(6):105-110.