基于分形反常扩散的体积压裂水平井渗流新模型
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摘要
体积压裂后在压裂区内形成形态异常复杂的缝网,常规建立在欧几里得几何基础上渗流模型难以准确反映多重强非均质性介质内的流动特点。基于分形和反常扩散理论,考虑体积压裂区2个方向的流动,建立了水平井复合三线性流反常扩散的理论模型,并用分数阶微分进行数值求解,通过与欧几里得空间的模型对比,验证了新模型的正确性。采用新模型计算分析了体积压裂水平井压力动态响应及特殊流动特征的影响因素,结果表明:与常规三线性流模型相比,新模型拟压力导数曲线上窜流特征出现的时间更早,说明气体在考虑双向流动的裂缝区流动更迅速;反常扩散效应增加了流动阻力并造成特征流动阶段出现时间延迟,反常扩散指数越大,气体流动孔道的连通性越差,压降越大;天然裂缝分形维数影响井筒储存之后的所有流动阶段,而基质分形维数的效应只出现在裂缝和基质窜流之后的阶段。新模型能准确描述体积压裂改造区渗流的复杂性,有助于完善体积压裂水平井试井解释模型和提高生产动态分析精度。
Complicated network is formed in the stimulated reservoir volume, the conventional percolating model on the basis of Euclidean geometry cannot accurately reflect the multiple flow characteristics of the strong heterogeneity within the medium. Based on the fractal and anomalous diffusion theory, considering the flow in the two directions of the volume fractured zone, the theoretical model of the anomalous diffusion was established for the horizontal well with composite three linear flow and solved numerically by fractional order derivative, compared with Euclidean space model, the correctness of the new model was verified, the pressure dynamic response and influencing factors of the special flow characteristics for the SRV horizontal well were analyzed with the help of the new model. The results show that compared with the conventional three linear flow model, the upper interporosity flow characteristics appear more earlier on the pseudo-pressure derivative curve of the new model, this indicates that the gas flows more faster in the fracture zone considering the bidirectional flow; the anomalous diffusion effect increases the flow resistance and causes the characteristic flow stage delayed, the larger the anomalous diffusion index is, the worse the connectivity of the gas flow channel and the greater the pressure drop will be; the fractal dimension of the natural fracture affects all flow stages after the wellbore storage, while the effect of the matrix fractal dimension only appears at the stage after the interporosity flow between the fracture and matrix. The new model can accurately describe the complexity of the percolation in the volumetric fractured zone, and help to improve the SRV horizontal well test interpreting model and enhance the precision of the production performance analysis.
Complicated network is formed in the stimulated reservoir volume, the conventional percolating model on the basis of Euclidean geometry cannot accurately reflect the multiple flow characteristics of the strong heterogeneity within the medium. Based on the fractal and anomalous diffusion theory, considering the flow in the two directions of the volume fractured zone, the theoretical model of the anomalous diffusion was established for the horizontal well with composite three linear flow and solved numerically by fractional order derivative, compared with Euclidean space model, the correctness of the new model was verified, the pressure dynamic response and influencing factors of the special flow characteristics for the SRV horizontal well were analyzed with the help of the new model. The results show that compared with the conventional three linear flow model, the upper interporosity flow characteristics appear more earlier on the pseudo-pressure derivative curve of the new model, this indicates that the gas flows more faster in the fracture zone considering the bidirectional flow; the anomalous diffusion effect increases the flow resistance and causes the characteristic flow stage delayed, the larger the anomalous diffusion index is, the worse the connectivity of the gas flow channel and the greater the pressure drop will be; the fractal dimension of the natural fracture affects all flow stages after the wellbore storage, while the effect of the matrix fractal dimension only appears at the stage after the interporosity flow between the fracture and matrix. The new model can accurately describe the complexity of the percolation in the volumetric fractured zone, and help to improve the SRV horizontal well test interpreting model and enhance the precision of the production performance analysis.
引文
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[13]郭柏灵,蒲学科,黄凤辉.分数阶偏微分方程及其数值解[M].北京:科学出版社,2011.GUO Bailing,PU Xueke,HUANG Fenghui.Frational partial differential equations and their numerical solutions[M].Beijing:Science Press,2011.
[14]BROWN M L,BROWN.Analytical trilinear pressure transient model for multiply fractured horizontal wells in tight shale reservoirs[D].Colorado:Colorado School of Mines,2009.
[15]彭涛,黄时祯,仝可佳,等.裂缝性页岩气藏渗流特征与压力动态分析[J].复杂油气藏,2016,9(2):63-67.PENG Tao,HUANG Shizhen,TONG Kejia,et al.Pressure transient analysis of fractured shale gas flow and seepage characteristics[J].Complex Hydrocarbon Reservoirs,2016,9(2):63-67.
[2]程林松,李春兰,郎兆林.裂缝油藏三维油,水两相渗流的有限元方法[J].大庆石油地质与开发,1998,17(1):26-27.CHENG Linsong,LI Chunlan,LANG Zhaolin.A finite element method for 3D oil & water two-phase seepage flow in a naturally fractured reservoir[J].Petroleum Geology & Oilfield Development in Daqing,1998,17(1):26-27.
[3]黄延章.低渗透油层非线性渗流特征[J].特种油气藏,1997,4(1):9-14.HUANG Yanzhang.Nonlinear percolation feature in low permeability reservoir[J].Special Oil & Gas Reservoirs,1997,4 (1):9-14.
[4]WANG Wendong,SHAHVALI M,SU Yuliang.A semi-analytical fractal model for production from tight oil reservoirs with hydraulically fractured horizontal wells[J].Fuel,2015,158(15):612-618.
[5]丁道权.分形致密气藏压裂水平井压力动态研究[D].北京:中国石油大学,2016.DING Daoquan.Dynamic study on horizontal well pressure of fractal and tight gas reservoir fracturing[D].Beijing :China University of Petroleum,2016.
[6]苏丽娟.分数阶扩散方程的几种数值解法[D].青岛:山东大学,2010.SU Lijuan.Several numerical solutions of fractional diffusion equations[D].Qingdao:Shandong University,2010.
[7]刘艳芹.分数阶反常扩散方程及其解[D].济南:山东大学,2006.LIU Yanqin.The fractional anomalous diffusion equation and its solutions[D].Jinan:Shandong University,2006.
[8]辛厚文.分形介质反应动力学[M].上海:上海科技教育出版社,1997.XIN Houwen.Reaction Kinetics in Fractal Media[M].Shanghai:Shanghai Science and Technology Education Press,1997.
[9]李树松,段永刚,陈伟,等.压裂水平井多裂缝系统的试井分析[J].大庆石油地质与开发,2006,25(3):67-69.LI Shusong,DUAN Yonggang,CHEN Wei,et al.Well testing analysis of fractured horizontal well[J].Petroleum Geology & Oilfield Development in Daqing,2006,25 (3):67-69
[10]陈科洛,张廷山,陈晓慧,等.页岩微观孔隙模型构建:以滇黔北地区志留系龙马溪组页岩为例[J].石油勘探与开发,2018,45(3):396-405.CHEN Keluo,ZHANG Yanshan,CHEN Xiaohui,et al.Model construction of micro-pores in shale:A case study of Silurian Longmaxi Formation shale in Dianqianbei area,SW China[J].Petroleum Exploration and Development,2018,45(3):396-405.
[11]温庆志,蒲春生,曲占庆,等.低渗透、特低渗透油藏非达西渗流整体压裂优化设计[J].油气地质与采收率,2009,16(6):102-104.WEN Qingzhi,PU Chunsheng,QU Zhanqing,et al.Integral fracturing optimization design of non-Darcy flows in low and ultra-low permeability oil reservoirs[J].Petroleum Geology and Recovery Efficiency,2009,16 (6):102-104.
[12]马春晓,尹洪军,唐鹏飞,等.基于有限元的压裂水平井渗流场分析[J].大庆石油地质与开发,2015,34(2):90-94.MA Chunxiao,YIN Hongjun,TANG Pengfei,et al.Seepage field analysis of the fractured horizontal well by finite element method [J].Petroleum Geology & Oilfield Development in Daqing,2015,34 (2):90-94.
[13]郭柏灵,蒲学科,黄凤辉.分数阶偏微分方程及其数值解[M].北京:科学出版社,2011.GUO Bailing,PU Xueke,HUANG Fenghui.Frational partial differential equations and their numerical solutions[M].Beijing:Science Press,2011.
[14]BROWN M L,BROWN.Analytical trilinear pressure transient model for multiply fractured horizontal wells in tight shale reservoirs[D].Colorado:Colorado School of Mines,2009.
[15]彭涛,黄时祯,仝可佳,等.裂缝性页岩气藏渗流特征与压力动态分析[J].复杂油气藏,2016,9(2):63-67.PENG Tao,HUANG Shizhen,TONG Kejia,et al.Pressure transient analysis of fractured shale gas flow and seepage characteristics[J].Complex Hydrocarbon Reservoirs,2016,9(2):63-67.
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