“层内爆炸”数值模拟研究
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摘要
“层内爆炸”作为一项低渗透油田开发新技术,在爆炸过程中受多种因素影响产生的裂缝的长度和角度都具有任意性,大大增加了对“层内爆炸”后形成的复杂裂缝进行模拟研究的难度。本文应用有限元法能够比较精确地模拟复杂边界,网格的划分比较灵活的特点,成功实现了对“层内爆炸”后形成的复杂裂缝的合理描述和数值模拟计算。
在有限元法基本原理基础上,将基质和裂缝看作一个渗流系统建立了统一的两相渗流问题的有限元模型。模型中将裂缝处理为直线,并且假设裂缝与基质接触处的压力是连续的。基质的网格剖分采用任意形状的四边形单元,采用等参元对渗流方程在空间上离散,采用向后差分在时间上离散。在此基础上采用元件化的程序设计思想利用Fortran语言编制了有限元法的数值模拟器,得到了稳定的计算结果,解决了利用有限元法求解两相复杂渗流问题稳定性差的难题。
通过与ECLIPSE软件进行算例对比,验证了本文有限元数学模型的准确性和正确性。在此基础上,使用数值模拟器针对“层内爆炸”后形成的复杂裂缝,对裂缝数量、裂缝长度、网缝、任意缝进行了模拟研究,得到了不同裂缝参数下压力分布图及饱和度分布图,研究了不同裂缝参数对油井的动态曲线的影响规律并进行了深入的对比分析,对“层内爆炸”后储层的复杂渗流机理有了深入的认识,为“层内爆炸”技术的现场应用提供了理论指导。
"In-fracture explosion" is a new technology in low-permeability field development. While the process of explosion,the length and angle of fracture are random by the affection of many factor,this increase the difficulty to simulate complex fractures after "In-fracture explosion".Finite Element Method can precise simulate complex boundary and Grid are divided into arbitrary.Reasonable description and simulate to complex fractures after "In-fracture explosion" are successful.
Starting form basic differential equation finite element model of two-phase flow is established based on Finite Element Method theory. In this model, fractures are idealized as lines in two-dimensional. With the assumption of continuity of pressures across the fracture-matrix boundary.The meshes of matrix use the arbitrary shape quadrilateral element. Those equations are dispersed in space by isoparametric element method and in time by using backward difference. A numerical simulator is established by FORTRAN and get steady results.The low steady of simulate two-phase complex problem by Finite Element Method is resolved.
By comparing to example of ECLIPSE software the accuracy and correctness of the finite element mathematical model is verified. On this basic,The influence of four variants to the production performance of fractured well, such as fracture number, fracture length and complicated fracture are simulate by the use of numerical simulator. The pressure field and saturation field are given. The influence of different fracture parameters to production performance curves is deeply analyzed.The complex percolation mechanism after "In-fracture explosion" is deeply understood and can supply theoretical guidance to the pplication in field.
在有限元法基本原理基础上,将基质和裂缝看作一个渗流系统建立了统一的两相渗流问题的有限元模型。模型中将裂缝处理为直线,并且假设裂缝与基质接触处的压力是连续的。基质的网格剖分采用任意形状的四边形单元,采用等参元对渗流方程在空间上离散,采用向后差分在时间上离散。在此基础上采用元件化的程序设计思想利用Fortran语言编制了有限元法的数值模拟器,得到了稳定的计算结果,解决了利用有限元法求解两相复杂渗流问题稳定性差的难题。
通过与ECLIPSE软件进行算例对比,验证了本文有限元数学模型的准确性和正确性。在此基础上,使用数值模拟器针对“层内爆炸”后形成的复杂裂缝,对裂缝数量、裂缝长度、网缝、任意缝进行了模拟研究,得到了不同裂缝参数下压力分布图及饱和度分布图,研究了不同裂缝参数对油井的动态曲线的影响规律并进行了深入的对比分析,对“层内爆炸”后储层的复杂渗流机理有了深入的认识,为“层内爆炸”技术的现场应用提供了理论指导。
"In-fracture explosion" is a new technology in low-permeability field development. While the process of explosion,the length and angle of fracture are random by the affection of many factor,this increase the difficulty to simulate complex fractures after "In-fracture explosion".Finite Element Method can precise simulate complex boundary and Grid are divided into arbitrary.Reasonable description and simulate to complex fractures after "In-fracture explosion" are successful.
Starting form basic differential equation finite element model of two-phase flow is established based on Finite Element Method theory. In this model, fractures are idealized as lines in two-dimensional. With the assumption of continuity of pressures across the fracture-matrix boundary.The meshes of matrix use the arbitrary shape quadrilateral element. Those equations are dispersed in space by isoparametric element method and in time by using backward difference. A numerical simulator is established by FORTRAN and get steady results.The low steady of simulate two-phase complex problem by Finite Element Method is resolved.
By comparing to example of ECLIPSE software the accuracy and correctness of the finite element mathematical model is verified. On this basic,The influence of four variants to the production performance of fractured well, such as fracture number, fracture length and complicated fracture are simulate by the use of numerical simulator. The pressure field and saturation field are given. The influence of different fracture parameters to production performance curves is deeply analyzed.The complex percolation mechanism after "In-fracture explosion" is deeply understood and can supply theoretical guidance to the pplication in field.
引文
[1]李道品.低渗透油田开发概论[J].大庆石油地质与开发,1997,16(3):33-37
[2]李道品,罗迪强,刘雨芬.低渗透油田概念及我国处理分布状况.低渗透油气田,1996,1(1):1-7
[3]丁雁生,陈力,张盛宗等.油田层内爆炸处理方法[P].中国专利:CN 1324979A,2001
[4]Watson S C and Benson G R.Liquid Propellant Stimulation of Shallow Appalachian Basin wells[C].SPE 13376,1984
[5]丁雁生,陈力,陈燮等.低渗透油气田“层内爆炸”增产技术研究[J].石油勘探与开发,2001,28(2):90-96,106
[6]Mingyue Cui and Wenwen Shan,Liang Jin,Yansheng Ding,etc.In-Fracture Explosive Hydraulic Fracturing Fluid and Its Rheologieal Study[C].SPE 103807,2006
[7]李传乐,王安仕,李文魁.国外油气井“层内爆炸”增产技术概述及分析[J].石油钻采工艺,2001,23(:)77-78
[8]林英松,刘兆年,秦涛.层内爆炸后储层裂缝分析方法研究[J].断块油气田,2006,13(1):44-46
[9]赵志红,郭建春.层内爆炸压裂技术原理及分析[J].石油天然气学报(江汉石油学院学报),2008,30(2):297-299
[10]Javandel I,Witherspoon P A.Application of the Finite Element Method to Transient Flow in Porous Media[J].SPEJ,Sept.1968:241-252(SPE 2052,Sep.1967)
[11]McMiCHAEL CL,Thomas G W.Reservoir Simulation by Galerkin's Method[C].SPE 3358,1973
[12]Langsrud Qyvind,Computas A Simulation of Two-Phase Flow by Finite Element Method[C].SPE 5725,1976
[13]Spivak A,Price H S,Settari A.Solution of the Equations for Multidimensional,Two-Phase,Immiscible Flow by Variational Methods[J].SPEJ,Feb.1977:27-41(SPE 5723,1977)
[14]Dalen Vilgeir.Simplified Finite-Element Models for Reservoir Flow Problems[C].SPE 7196,1979
[15]Young Larry C.A Finite-Element Method for Reservoir Simulation[C].SPE 7413,1981
[16]Masato Tauchia,Kazuo Kohda,Yutaka Suzukawa.A Well Model for Finite Element Reservoir Simulators[C].SPE 12936,1984
[17]Peters E J,Kasap E.Simulation of Unstable Miscible Displacements by Finite Eliment Method[C].SPE 15597,1986
[18]Bhatia K S,Advani S H,Lee J K.Finite Element Representation of Two-Phase Fluid Flow Through a Naturally Fractured Reservoir[C].SPE 19069,1989
[19]Peter A Forsyth.A Control-Volume,Finite-Element Method for Local Mesh Refinement in Thermal Reservoir Simulation[C].SPE 18415,1990
[20]Nobuo Morita.Transient Finite Element Code:A Versatile Tool for Well Performance Analyses[C].SPE 25878,1993
[21]Murzenko V V.Finite Element Method for Steady Fluid Flow in Reservoir Containing a Fracture[C].SPE 26306,1994
[22]Jong Gyun Kim,Milind D Deo.Finite Element,Discrete-Fracture Model for Multiphase Flow in Porous Media[J].AICHE Journal,2000,46(6):1120-1130
[23]袁益让,王文洽.关于油水两相渗流平面弹性驱动问题的有限元方法[J].石油学报,1980,1(4):65-76
[24]袁益让.二相渗流数值模拟的一类有限元格式及其理论分析[J].科学通报,1984,4:193-197
[25]袁益让.油、水二相渗流驱动问题的变网格有限元方法及其理论分析[J].中国科学,1986,A(2):135-148
[26]梁栋.两项渗流问题特征混合元数值模拟方法[J].中国科学,1991,A(5):478-485
[27]张子香,宋洪才,范江.两维两相不稳定渗流变分有限元数值模拟方法[J].石油学报,1992,13(3):79-86
[28]宋洪才,张继芬,王江.油藏数值模拟中的变分有限元方法[J].大庆石油学院学报,1996,20(3):97-101
[29]宋洪才,张继芬,王江.变分有限元数值模拟理论分析[J].大庆石油学院学报,1996,20(3):102-104
[30]程林松,郎兆新.水平井油—水两相渗流的有限元方法[J].水动力学研究与进展,1995,10(3):309-314
[31]周竹眉,郎兆新.水平井油藏数值模拟的有限元方法[J].水动力学研究与进展,1996,11(3):261-270
[32]程林松,李春兰,郎兆新.裂缝性底水油藏水平井三维油水两相有限元数值模拟方法[J].石油勘探与开发,1998,25(2):41-45
[33]程林松,李春兰,郎兆新.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):26-27,33
[34]谢海兵,马远乐,桓冠仁等.非结构网格油藏数值模拟方法研究[J].石油学报,2001,22(1):63-66
[35]蒋廷学,郎兆新,单文文.低渗透油藏压裂井动态预测的有限元方法[J].石油学报,2002,23(5):53-58
[36]刘振宇.有限元法在油藏渗流中的理论和应用[D].大庆:大庆石油学院博士学位论文,2003
[37]刘振宇,翟云芳.油藏数值模拟的有限元模型,第十六届全国水动力学研讨会文集[C],2002
[38]郑宪宝.人工裂缝井生产动态模拟研究[D].大庆:大庆石油学院硕士学位论文,2006
[39]李文娟.复杂裂缝条件下的渗流机理研究[D].大庆:大庆石油学院硕士学位论文,2007
[40]李金东.不规则人工压裂井网的数值模拟研究[D].大庆石油学院硕士学位论文,2008
[41]练章华,孟英峰,童敏.二维有限元热流模型在射孔完井中的应用研究[J].天然气工业,2000,20(4):49-53
[42]练章华,孟英峰,童敏.射孔完井有限元模拟的建立及网格划分[J].西南石油学院学报,2000,22(2):46-49
[43]向晓丽,张玺.有限元技术在预测储层孔隙度、渗透率中的应用[J].油气采收率技术,1999,6(2):49-60
[44]黄蔚,刘迎曦,周承芳.三维无压渗流场的有限元算法研究[J].水力学报,2001,6:33-36
[45]陈洁,李尧臣.三维多孔介质中应力与渗流的摄动—有限元分析[J].上海铁道大学学报,1999,20(10):6-10
[46]许俊,胡显波,邹忠平.送风支管传热的有限元分析[J].钢铁技术,2006,2:5-7
[47]李辉平,赵国群,牛山廷等.基于有限元和最优化方法的淬火冷却过程反传热分析[J].金属学报,2006,41(2):167-172
[48]Bo Lu,Tareq M.Alshaalan and Mary F.Wheeler.Iteratively Coupled Reservoir Simulation for Multiphase Flow[C].SPE 110114,2007
[49]Jong Gyun Kim and Milind D.Deo.Comparison of the Performance of a Discrete Fracture Multiphase Model With Those Using Conventional Methods[C].SPE 51928,1999
[50]Yi-Kun Yang,and M.D.Deo.Full-Tensor Multiphase Flow Simulations With Applications to Upscaling and Discrete-Fracture Models[C].SPE 66348,2001
[51]Kebaili A L,Thomas G W.A Two-Phases Coning Model Using Alternating Direction Galerkin Procedure[C].SPE 5724,1976
[2]李道品,罗迪强,刘雨芬.低渗透油田概念及我国处理分布状况.低渗透油气田,1996,1(1):1-7
[3]丁雁生,陈力,张盛宗等.油田层内爆炸处理方法[P].中国专利:CN 1324979A,2001
[4]Watson S C and Benson G R.Liquid Propellant Stimulation of Shallow Appalachian Basin wells[C].SPE 13376,1984
[5]丁雁生,陈力,陈燮等.低渗透油气田“层内爆炸”增产技术研究[J].石油勘探与开发,2001,28(2):90-96,106
[6]Mingyue Cui and Wenwen Shan,Liang Jin,Yansheng Ding,etc.In-Fracture Explosive Hydraulic Fracturing Fluid and Its Rheologieal Study[C].SPE 103807,2006
[7]李传乐,王安仕,李文魁.国外油气井“层内爆炸”增产技术概述及分析[J].石油钻采工艺,2001,23(:)77-78
[8]林英松,刘兆年,秦涛.层内爆炸后储层裂缝分析方法研究[J].断块油气田,2006,13(1):44-46
[9]赵志红,郭建春.层内爆炸压裂技术原理及分析[J].石油天然气学报(江汉石油学院学报),2008,30(2):297-299
[10]Javandel I,Witherspoon P A.Application of the Finite Element Method to Transient Flow in Porous Media[J].SPEJ,Sept.1968:241-252(SPE 2052,Sep.1967)
[11]McMiCHAEL CL,Thomas G W.Reservoir Simulation by Galerkin's Method[C].SPE 3358,1973
[12]Langsrud Qyvind,Computas A Simulation of Two-Phase Flow by Finite Element Method[C].SPE 5725,1976
[13]Spivak A,Price H S,Settari A.Solution of the Equations for Multidimensional,Two-Phase,Immiscible Flow by Variational Methods[J].SPEJ,Feb.1977:27-41(SPE 5723,1977)
[14]Dalen Vilgeir.Simplified Finite-Element Models for Reservoir Flow Problems[C].SPE 7196,1979
[15]Young Larry C.A Finite-Element Method for Reservoir Simulation[C].SPE 7413,1981
[16]Masato Tauchia,Kazuo Kohda,Yutaka Suzukawa.A Well Model for Finite Element Reservoir Simulators[C].SPE 12936,1984
[17]Peters E J,Kasap E.Simulation of Unstable Miscible Displacements by Finite Eliment Method[C].SPE 15597,1986
[18]Bhatia K S,Advani S H,Lee J K.Finite Element Representation of Two-Phase Fluid Flow Through a Naturally Fractured Reservoir[C].SPE 19069,1989
[19]Peter A Forsyth.A Control-Volume,Finite-Element Method for Local Mesh Refinement in Thermal Reservoir Simulation[C].SPE 18415,1990
[20]Nobuo Morita.Transient Finite Element Code:A Versatile Tool for Well Performance Analyses[C].SPE 25878,1993
[21]Murzenko V V.Finite Element Method for Steady Fluid Flow in Reservoir Containing a Fracture[C].SPE 26306,1994
[22]Jong Gyun Kim,Milind D Deo.Finite Element,Discrete-Fracture Model for Multiphase Flow in Porous Media[J].AICHE Journal,2000,46(6):1120-1130
[23]袁益让,王文洽.关于油水两相渗流平面弹性驱动问题的有限元方法[J].石油学报,1980,1(4):65-76
[24]袁益让.二相渗流数值模拟的一类有限元格式及其理论分析[J].科学通报,1984,4:193-197
[25]袁益让.油、水二相渗流驱动问题的变网格有限元方法及其理论分析[J].中国科学,1986,A(2):135-148
[26]梁栋.两项渗流问题特征混合元数值模拟方法[J].中国科学,1991,A(5):478-485
[27]张子香,宋洪才,范江.两维两相不稳定渗流变分有限元数值模拟方法[J].石油学报,1992,13(3):79-86
[28]宋洪才,张继芬,王江.油藏数值模拟中的变分有限元方法[J].大庆石油学院学报,1996,20(3):97-101
[29]宋洪才,张继芬,王江.变分有限元数值模拟理论分析[J].大庆石油学院学报,1996,20(3):102-104
[30]程林松,郎兆新.水平井油—水两相渗流的有限元方法[J].水动力学研究与进展,1995,10(3):309-314
[31]周竹眉,郎兆新.水平井油藏数值模拟的有限元方法[J].水动力学研究与进展,1996,11(3):261-270
[32]程林松,李春兰,郎兆新.裂缝性底水油藏水平井三维油水两相有限元数值模拟方法[J].石油勘探与开发,1998,25(2):41-45
[33]程林松,李春兰,郎兆新.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):26-27,33
[34]谢海兵,马远乐,桓冠仁等.非结构网格油藏数值模拟方法研究[J].石油学报,2001,22(1):63-66
[35]蒋廷学,郎兆新,单文文.低渗透油藏压裂井动态预测的有限元方法[J].石油学报,2002,23(5):53-58
[36]刘振宇.有限元法在油藏渗流中的理论和应用[D].大庆:大庆石油学院博士学位论文,2003
[37]刘振宇,翟云芳.油藏数值模拟的有限元模型,第十六届全国水动力学研讨会文集[C],2002
[38]郑宪宝.人工裂缝井生产动态模拟研究[D].大庆:大庆石油学院硕士学位论文,2006
[39]李文娟.复杂裂缝条件下的渗流机理研究[D].大庆:大庆石油学院硕士学位论文,2007
[40]李金东.不规则人工压裂井网的数值模拟研究[D].大庆石油学院硕士学位论文,2008
[41]练章华,孟英峰,童敏.二维有限元热流模型在射孔完井中的应用研究[J].天然气工业,2000,20(4):49-53
[42]练章华,孟英峰,童敏.射孔完井有限元模拟的建立及网格划分[J].西南石油学院学报,2000,22(2):46-49
[43]向晓丽,张玺.有限元技术在预测储层孔隙度、渗透率中的应用[J].油气采收率技术,1999,6(2):49-60
[44]黄蔚,刘迎曦,周承芳.三维无压渗流场的有限元算法研究[J].水力学报,2001,6:33-36
[45]陈洁,李尧臣.三维多孔介质中应力与渗流的摄动—有限元分析[J].上海铁道大学学报,1999,20(10):6-10
[46]许俊,胡显波,邹忠平.送风支管传热的有限元分析[J].钢铁技术,2006,2:5-7
[47]李辉平,赵国群,牛山廷等.基于有限元和最优化方法的淬火冷却过程反传热分析[J].金属学报,2006,41(2):167-172
[48]Bo Lu,Tareq M.Alshaalan and Mary F.Wheeler.Iteratively Coupled Reservoir Simulation for Multiphase Flow[C].SPE 110114,2007
[49]Jong Gyun Kim and Milind D.Deo.Comparison of the Performance of a Discrete Fracture Multiphase Model With Those Using Conventional Methods[C].SPE 51928,1999
[50]Yi-Kun Yang,and M.D.Deo.Full-Tensor Multiphase Flow Simulations With Applications to Upscaling and Discrete-Fracture Models[C].SPE 66348,2001
[51]Kebaili A L,Thomas G W.A Two-Phases Coning Model Using Alternating Direction Galerkin Procedure[C].SPE 5724,1976