低渗气藏多级压裂水平井非稳态流动裂缝设计
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摘要
对于低渗气藏,采用分段压裂水平井技术可以达到经济效益最大化。基于点源函数法和能量守恒方程,建立非稳态气藏渗流与井筒压降耦合模型,刻画气藏介质—裂缝—井筒的流动特征,采用非线性迭代法求解耦合系统,融入平均压缩因数迭代法修正结果。对于某气藏,应用耦合模型设计最优压裂方案,优化单裂缝参数,以单裂缝最优几何形态为基础,优化双裂缝和多裂缝设计方案,包括裂缝位置、条数等。结果表明:相同体积、不同几何形态裂缝的产量差别很大,垂向—水平渗透率比越大,越应减小裂缝的垂向尺寸;固定裂缝几何形态,裂缝位于气藏中部时产量最高;流动早期,裂缝数量的增加使流量提高,随开采进行裂缝数量增加优势逐渐不明显;结合压裂成本、油价等因素,确定多裂缝系统最优裂缝数为3条。耦合模型与数值模拟结果误差在15%以内,验证模型的可靠性,系统化裂缝设计方法为低渗气藏压裂水平井提供指导。
For low-permeability gas reservoir,we adopted multi-fractured horizontal well for economic development.Our research method is to establish a transient flow coupling model for reservoir inflow and wellbore pressure drop for reasonably describing flow mechanism,adopting the potential-superposition-based source function method to establish the reservoir inflow model,selecting appropriate source function,generating analytical solution using Newman product.We derived the basic energy balance equation to establish the wellbore pressure drop model,and got the specific function for horizontal well by adopting the nonlinear iterative method to solve the coupling system.We got the inflow rate from each fracture and the pressure along wellbore,and revised results based on iterative average compressibility factor.Fracture parameters including fracture geometry,location,number are optimized based on optimum single fracture geometry,and the optimum solution for multi-fracture system is obtained.Results show that wellbore inflow is negligible compared with fracture inflow;wellbore pressure drop is non-negligible and has great influence on system production;fractures with same volume but different geometry have great difference on production.The larger the vertical-horizontal permeability ratio,the smaller the fracture height should be controlled.For fracture of fixed geometry,production is highest when locating it in certain range in the central part of the reservoir;production rate is proportional to the number of fractures in early stage,but becomes unobvious as development forwards;for a real gas reservoir,the optimum number of fractures is three.The error between this coupling model and simulation is within 15%,and production curve trends are consistent,demonstrating its reliability.The meaning of this research is the systematic fracture design method,and fast optimum solution for real fields.
For low-permeability gas reservoir,we adopted multi-fractured horizontal well for economic development.Our research method is to establish a transient flow coupling model for reservoir inflow and wellbore pressure drop for reasonably describing flow mechanism,adopting the potential-superposition-based source function method to establish the reservoir inflow model,selecting appropriate source function,generating analytical solution using Newman product.We derived the basic energy balance equation to establish the wellbore pressure drop model,and got the specific function for horizontal well by adopting the nonlinear iterative method to solve the coupling system.We got the inflow rate from each fracture and the pressure along wellbore,and revised results based on iterative average compressibility factor.Fracture parameters including fracture geometry,location,number are optimized based on optimum single fracture geometry,and the optimum solution for multi-fracture system is obtained.Results show that wellbore inflow is negligible compared with fracture inflow;wellbore pressure drop is non-negligible and has great influence on system production;fractures with same volume but different geometry have great difference on production.The larger the vertical-horizontal permeability ratio,the smaller the fracture height should be controlled.For fracture of fixed geometry,production is highest when locating it in certain range in the central part of the reservoir;production rate is proportional to the number of fractures in early stage,but becomes unobvious as development forwards;for a real gas reservoir,the optimum number of fractures is three.The error between this coupling model and simulation is within 15%,and production curve trends are consistent,demonstrating its reliability.The meaning of this research is the systematic fracture design method,and fast optimum solution for real fields.
引文
[1]刘振宇,刘洋,贺丽艳,等.人工压裂水平井研究综述[J].大庆石油学院学报,2002,26(4):96-99.LIU Zhenyu,LIU Yang,HE Liyan,et al.Overview of the research of hydraulically fractured horizontal wells[J].Journal of Daqing Petroleum Institute,2002,26(4):96-99.
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[3]吴军来,刘月田.基于PEBI网格加密的水平井分段压裂模拟[J].大庆石油学院学报,2010,34(6):53-57.WU Junlai,LIU Yuetian.Simulation of staged fracturing for horizontal wells based on PEBI grid refinements[J].Journal of Daqing Petroleum Institute,2010,34(6):53-57.
[4]徐春元.裂缝性油气藏离散裂缝数值模拟[D].合肥:中国科学技术大学,2017:83-96.XU Chunyuan.Discrete fracture modeling of fractured reservoirs[D].Hefei:University of Science and Technology of China,2017:83-96.
[5]何易东,任岚,赵金洲,等.页岩气藏体积压裂水平井产能有限元数值模拟[J].断块油气田,2017,24(4):550-556.HE Yidong,REN Lan,ZHAO Jinzhou,et al.Finite element numerical simulation of shale gas production of hydraulically fractured horizontal well with stimulated reservoir volume[J].Fault-Block Oil &Gas Field,2017,24(4):550-556.
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[7]丁一萍,王晓冬,邢静,等.一种压裂水平井产能计算方法[J].特种油气藏,2008,15(2):64-68.DING Yiping,WANG Xiaodong,XING Jing,et al.A method of productivity calculation for fractured horizontal well[J].Special Oil&Gas Reservoirs,2008,15(2):64-68.
[8]郎兆新,张丽华,程林松.压裂水平井产能研究[J].石油大学学报(自然科学版),1994,18(2):43-46.LANG Zhaoxin,ZHANG Lihua,CHENG Linsong.Investigation on productivity of fractured horizontal well[J].Journal of the University of Petroleum(Edition of Natural Science),1994,18(2):43-46.
[9]宁正福,韩树刚,程林松,等.低渗透油气藏压裂水平井产能计算方法[J].石油学报,2002,23(2):68-71.NING Zhengfu,HAN Shugang,CHENG Linsong,et al.Productivity calculation method of fractured horizontal wells in low permeability oil or gas field[J].Acta Petrolei Sinica,2002,23(2):68-71.
[10]郑松青.非均匀分段压裂水平井产能计算[J].东北石油大学学报,2013,37(4):55-59.ZHENG Songqing.Productivity calculation of non-uniform multi-fractured horizontal wells[J].Journal of Northeast Petroleum University,2013,37(4):55-59.
[11]CINCO-LEY H.Transient pressure analysis for fractured wells[J].Journal of Petroleum Technology,1981,33(9):1749-1766.
[12]BROWN M,OZKAN E,RAGHAVAN R,et al.Practical solutions for pressure-transient responses of fractured horizontal wells in unconventional shale reservoirs[J].Reservoir Evaluation &Engineering,2011,14(6):663-676.
[13]STALGOROVA K,MATTAR L.Analytical model for unconventional multifractured composite systems[J].Reservoir Evaluation&Engineering,2013,16(3):246-256.
[14]GUO J C,ZENG J,WANG X,et al.Analytical model for multifractured horizontal wells in heterogeneous shale reservoirs[R].Perth:Asia Pacific Oil &Gas Conference and Exhibition,2016:45-49.
[15]廉培庆,程林松,何理鹏,等.气藏压裂水平井非稳态流动分析[J].计算力学学报,2011,28(4):579-583.LIAN Peiqing,CHENG Linsong,HE Lipeng,et al.Analysis of transient flowing model for fractured horizontal well in gas reservoir[J].Chinese Journal of Computational Mechanics,2011,28(4):579-583.
[16]王家航,王晓冬,董文秀,等.非均质油藏多段压裂水平井不稳态压力分析半解析方法[J].东北石油大学学报,2017,41(5):90-99.WANG Jiahang,WANG Xiaodong,DONG Wenxiu,et al.Semi-analytical approach to model pressure transients of multiple-fractured horizontal wells in heterogeneous reservois[J].Journal of Northeast Petroleum University,2017,41(5):90-99.
[17]董广为,陈志海,廉培庆.考虑非均质定压边界油藏的复杂结构井产量计算新方法[C]//陕西石油协会.2014油气藏监测与管理国际会议论文集.北京:中国学术期刊电子出版社,2014:157-166.DONG Guangwei,CHEN Zhihai,LIAN Peiqing.Calculation method on complex-structure well rate in heterogeneous reservoirs with constant pressure boundary[C]//Shaanxi Petroleum Society.2014ICRSM.Beijing:China Academic Journal Electronic Publishing House,2014:157-166.
[18]GRINGARTEN A C,RAMEY H J.The use of source and green's functions in solving unsteady-flow problems in reservoirs[J].SPEJ,1973,13(5):285-296.
[19]HILL A D,ZHU D,ECONOMIDES M J.Multilateral wells[M].Houston:Society of Petroleum Engineers,2008:84-85.
[20]杨兆中,陈倩,李小刚,等.鄂尔多斯盆地低渗透致密砂岩气藏水平井分段多簇压裂布缝优化研究[J].油气地质与采收率,2019,26(3):120-126.YANG Zhaozhong,CHEN Qian,LI Xiaogang,et al.Optimization of multi-cluster staged fracturing for horizontal well in low-permeability tight sandstone gas reservoir,Ordos Basin[J].Petroleum Geology and Recovery Efficiency,2019,26(3):120-126.
[2]黄亮,宁正福,石军太,等.低渗致密气藏压裂水平井产能预测新方法[J].大庆石油地质与开发,2017,36(2):160-166.HUANG Liang,NING Zhengfu,SHI Juntai,et al.A new method of the productivity prediction for the fractured horizontal wells in low-permeability tight gas reservoirs[J].Petroleum Geology &Oilfield Development in Daqing,2017,36(2):160-166.
[3]吴军来,刘月田.基于PEBI网格加密的水平井分段压裂模拟[J].大庆石油学院学报,2010,34(6):53-57.WU Junlai,LIU Yuetian.Simulation of staged fracturing for horizontal wells based on PEBI grid refinements[J].Journal of Daqing Petroleum Institute,2010,34(6):53-57.
[4]徐春元.裂缝性油气藏离散裂缝数值模拟[D].合肥:中国科学技术大学,2017:83-96.XU Chunyuan.Discrete fracture modeling of fractured reservoirs[D].Hefei:University of Science and Technology of China,2017:83-96.
[5]何易东,任岚,赵金洲,等.页岩气藏体积压裂水平井产能有限元数值模拟[J].断块油气田,2017,24(4):550-556.HE Yidong,REN Lan,ZHAO Jinzhou,et al.Finite element numerical simulation of shale gas production of hydraulically fractured horizontal well with stimulated reservoir volume[J].Fault-Block Oil &Gas Field,2017,24(4):550-556.
[6]GUO Boyun,YU Xiance,KHOSHGAHDAM M.A simple analytical model for predicting productivity of multifractured horizontal wells[J].Reservoir Evaluation &Engineering,2009,12(6):119-125.
[7]丁一萍,王晓冬,邢静,等.一种压裂水平井产能计算方法[J].特种油气藏,2008,15(2):64-68.DING Yiping,WANG Xiaodong,XING Jing,et al.A method of productivity calculation for fractured horizontal well[J].Special Oil&Gas Reservoirs,2008,15(2):64-68.
[8]郎兆新,张丽华,程林松.压裂水平井产能研究[J].石油大学学报(自然科学版),1994,18(2):43-46.LANG Zhaoxin,ZHANG Lihua,CHENG Linsong.Investigation on productivity of fractured horizontal well[J].Journal of the University of Petroleum(Edition of Natural Science),1994,18(2):43-46.
[9]宁正福,韩树刚,程林松,等.低渗透油气藏压裂水平井产能计算方法[J].石油学报,2002,23(2):68-71.NING Zhengfu,HAN Shugang,CHENG Linsong,et al.Productivity calculation method of fractured horizontal wells in low permeability oil or gas field[J].Acta Petrolei Sinica,2002,23(2):68-71.
[10]郑松青.非均匀分段压裂水平井产能计算[J].东北石油大学学报,2013,37(4):55-59.ZHENG Songqing.Productivity calculation of non-uniform multi-fractured horizontal wells[J].Journal of Northeast Petroleum University,2013,37(4):55-59.
[11]CINCO-LEY H.Transient pressure analysis for fractured wells[J].Journal of Petroleum Technology,1981,33(9):1749-1766.
[12]BROWN M,OZKAN E,RAGHAVAN R,et al.Practical solutions for pressure-transient responses of fractured horizontal wells in unconventional shale reservoirs[J].Reservoir Evaluation &Engineering,2011,14(6):663-676.
[13]STALGOROVA K,MATTAR L.Analytical model for unconventional multifractured composite systems[J].Reservoir Evaluation&Engineering,2013,16(3):246-256.
[14]GUO J C,ZENG J,WANG X,et al.Analytical model for multifractured horizontal wells in heterogeneous shale reservoirs[R].Perth:Asia Pacific Oil &Gas Conference and Exhibition,2016:45-49.
[15]廉培庆,程林松,何理鹏,等.气藏压裂水平井非稳态流动分析[J].计算力学学报,2011,28(4):579-583.LIAN Peiqing,CHENG Linsong,HE Lipeng,et al.Analysis of transient flowing model for fractured horizontal well in gas reservoir[J].Chinese Journal of Computational Mechanics,2011,28(4):579-583.
[16]王家航,王晓冬,董文秀,等.非均质油藏多段压裂水平井不稳态压力分析半解析方法[J].东北石油大学学报,2017,41(5):90-99.WANG Jiahang,WANG Xiaodong,DONG Wenxiu,et al.Semi-analytical approach to model pressure transients of multiple-fractured horizontal wells in heterogeneous reservois[J].Journal of Northeast Petroleum University,2017,41(5):90-99.
[17]董广为,陈志海,廉培庆.考虑非均质定压边界油藏的复杂结构井产量计算新方法[C]//陕西石油协会.2014油气藏监测与管理国际会议论文集.北京:中国学术期刊电子出版社,2014:157-166.DONG Guangwei,CHEN Zhihai,LIAN Peiqing.Calculation method on complex-structure well rate in heterogeneous reservoirs with constant pressure boundary[C]//Shaanxi Petroleum Society.2014ICRSM.Beijing:China Academic Journal Electronic Publishing House,2014:157-166.
[18]GRINGARTEN A C,RAMEY H J.The use of source and green's functions in solving unsteady-flow problems in reservoirs[J].SPEJ,1973,13(5):285-296.
[19]HILL A D,ZHU D,ECONOMIDES M J.Multilateral wells[M].Houston:Society of Petroleum Engineers,2008:84-85.
[20]杨兆中,陈倩,李小刚,等.鄂尔多斯盆地低渗透致密砂岩气藏水平井分段多簇压裂布缝优化研究[J].油气地质与采收率,2019,26(3):120-126.YANG Zhaozhong,CHEN Qian,LI Xiaogang,et al.Optimization of multi-cluster staged fracturing for horizontal well in low-permeability tight sandstone gas reservoir,Ordos Basin[J].Petroleum Geology and Recovery Efficiency,2019,26(3):120-126.