考虑启动压力梯度的复合气藏不稳定压力动态分析
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摘要
低渗透气藏的渗流过程中存在启动压力梯度,导致其渗流机理比常规气藏更加复杂。其次,在低渗透气藏开发过程中由于酸化、压裂或气藏本身的特点,会使得气藏近井区和远井区的岩石及流体性质存在差异,形成复合气藏。因此,建立了考虑启动压力梯度的复合气藏水平井不稳定渗流模型,使用Laplace变换、正交变换等方法获得了该模型的无量纲解析解。在此基础上,研究了启动压力梯度、水平段长度、内外区流度比和内区半径对复合气藏水平井不稳定压力动态特征的影响。结果表明,考虑启动压力梯度的复合气藏水平井的压力动态曲线可划分为纯井储阶段、井储后的过渡阶段、早期垂向径向流阶段、中期线性流阶段、内区拟径向流阶段、内外区拟径向流过渡阶段和外区拟径向流阶段。启动压力梯度越大,压力动态曲线后期上翘幅度越大;水平段长度越大,压力动态曲线位置越低;内外区流度比越大,压力动态曲线位置越高;内区半径越大,内区拟径向流阶段持续时间越长。研究结果丰富了低渗透复合气藏不稳定渗流的相关理论,为更好地认识气藏渗流规律和气藏的科学高效开发提供了理论依据。
The existence of threshold pressure gradient in the flow process of low permeability gas reservoirs makes its flow mechanism more complicated than that of the conventional gas reservoirs.Moreover,due to acidizing,fracturing and some inherent features of gas reservoirs during the development of low-permeability gas reservoirs,there are some differences in the rock and fluid properties between the near wellbore areas and far-from-wellbore areas,resulting in the formation of composite gas reservoirs.Therefore,the paper establishes a unsteady flow model considering the threshold pressure gradient for horizontal wells in composite reservoirs,and obtains dimensionless analytical solutions of the model by using complex mathematical methods such as Laplace transformation and orthogonal transformation.Based on which,the influences of threshold pressure gradient,horizontal section length,mobility ratio and inner radius on the dynamic characteristics of the unsteady pressure in horizontal wells in the composite reservoirs are also studied.The results show that the pressure response type curves of the proposed model can be divided into 7 stages such as wellbore storage stage,transitional flow stage after wellbore storage,early vertical radial flow stage,mid-term linear flow stage,inner-zone pseudo-radial flow stage,transitional flow stage from inner zone to outer zone and outer-zone pseudo-radial flow stage.The higher the threshold pressure gradient,the larger the up-warping amplitude of the pressure response type curve;the longer the horizontal section length,the lower the position of the type curve;the bigger the mobility ratio,the higher the position of the type curve;the larger the inner zone radius,the longer the duration of inner-zone pseudo-radial flow stage will be.This research enriches the theories related to unsteady flow in low-permeability composite gas reservoirs,and provides a theoretical basis for a better understanding of the flow characteristics and for efficient development of gas reservoirs.
The existence of threshold pressure gradient in the flow process of low permeability gas reservoirs makes its flow mechanism more complicated than that of the conventional gas reservoirs.Moreover,due to acidizing,fracturing and some inherent features of gas reservoirs during the development of low-permeability gas reservoirs,there are some differences in the rock and fluid properties between the near wellbore areas and far-from-wellbore areas,resulting in the formation of composite gas reservoirs.Therefore,the paper establishes a unsteady flow model considering the threshold pressure gradient for horizontal wells in composite reservoirs,and obtains dimensionless analytical solutions of the model by using complex mathematical methods such as Laplace transformation and orthogonal transformation.Based on which,the influences of threshold pressure gradient,horizontal section length,mobility ratio and inner radius on the dynamic characteristics of the unsteady pressure in horizontal wells in the composite reservoirs are also studied.The results show that the pressure response type curves of the proposed model can be divided into 7 stages such as wellbore storage stage,transitional flow stage after wellbore storage,early vertical radial flow stage,mid-term linear flow stage,inner-zone pseudo-radial flow stage,transitional flow stage from inner zone to outer zone and outer-zone pseudo-radial flow stage.The higher the threshold pressure gradient,the larger the up-warping amplitude of the pressure response type curve;the longer the horizontal section length,the lower the position of the type curve;the bigger the mobility ratio,the higher the position of the type curve;the larger the inner zone radius,the longer the duration of inner-zone pseudo-radial flow stage will be.This research enriches the theories related to unsteady flow in low-permeability composite gas reservoirs,and provides a theoretical basis for a better understanding of the flow characteristics and for efficient development of gas reservoirs.
引文
[1]杨学云,张学婧,蒋国斌,等.启动压力梯度影响下低渗透气藏水平井产能模型的建立[J].特种油气藏,2010,17(1):85-87.YANG Xueyun,ZHANG Xuejing,JIANG Guobin,et al.Horizontal well deliverability model of low permeability gas reservoirs considering threshold pressure gradient[J].Special Oil&Gas Reservoirs,2010,17(1):85-87.
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[6]魏漪,宋新民,冉启全,等.致密油藏压裂水平井非稳态产能预测模型[J].新疆石油地质,2014,35(1):67-72.WEI Yi,SONG Xinmin,RAN Qiquan,et al.An unstable productivity prediction model for fractured horizontal well in tight oil reservoirs[J].Xinjiang Petroleum Geology,2014,35(1):67-72.
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[8]欧阳伟平,张冕,刘曰武,等.基于三参数非线性渗流的致密气藏数值试井分析[J].天然气地球科学,2016,27(11):2 030-2 036.OUYANG Weiping,ZHANG Mian,LIU Yuewu,et al.Numerical well test analysis of tight gas reservoirs based on the three parameter nonlinear seepage[J].Natural Gas Geoscience,2016,27(11):2 030-2 036.
[9]刘化普,刘慧卿,王敬.缝洞型三重介质油藏分形渗流规律[J].新疆石油地质,2017,38(2):204-208.LIU Huapu,LIU Huiqing,WANG Jing.Fractal percolation law in fractured-vuggy triple medium reservoirs[J].Xinjiang Petroleum Geology,2017,38(2):204-208.
[10]曹丽娜,李晓平,罗诚,等.裂缝性低渗气藏水平井不稳定产量递减探讨[J].西南石油大学学报(自然科学版),2017,39(3):103-110.CAO Lina,LI Xiaoping,LUO Cheng,et al.Investigation of unstable production decline in fractured low-permeability gas reservoir horizontal wells[J].Journal of Southwest Petroleum University(Science&Technology Edition),2017,39(3):103-110.
[11]张小龙,杨志兴.启动压力梯度对低渗气藏不稳定渗流特征的影响[J].油气井测试,2018,27(3):7-13.ZHANG Xiaolong,YANG Zhixing.Lmpacts of start-up pressure gradient on features of transient seepage flow in low-permeability gas reservoirs[J].Well Testing,2018,27(3):7-13.
[12]武治岐,王厚坤,王睿.裂缝性致密油藏体积压裂水平井压力动态分析[J].新疆石油地质,2018,39(3):333-339.WU Zhiqi,WANG Houkun,WANG Rui.Pressure behavior analysis of volume fracturing in horizontal wells in fractured tight oil reservoirs[J].Xinjiang Petroleum Geology,2018,39(3):333-339.
[13]KUCHUK F J,HABASHY T M,TORRES-VERDIN C.A nonlinear approximation for the pressure behavior of heterogeneous reservoirs[J].SPE Journal,1996,1(3):229-242.
[14]FLAVIO M,ERDAL O,HOSSEIN K.A semianalytical approach to model pressure transients in heterogeneous reservoirs[J].SPE Reservoir Evaluation&Engineering,2010,13(2):341-358.
[15]蔡明金,张福祥,杨向同,等.碳酸盐岩洞穴型储层试井解释新模型[J].特种油气藏,2014,21(2):98-101.CAI Mingjin,ZHANG Fuxiang,YANG Xiangtong,et al.New model of well test interpretation in cavernous carbonate reservoirs[J].Special Oil&Gas Reservoirs,2014,21(2):98-101.
[16]姜瑞忠,郜益华,孙召勃,等.双重介质复合油藏偏心井试井分析[J].新疆石油地质,2016,37(3):327-331.JIANG Ruizhong,GAO Yihua,SUN Zhaobo,et al.Off-center well test analysis for composite dual porosity reservoirs[J].Xinjiang Petroleum Geology,2016,37(3):327-331.
[17]张烈辉,张芮菡,蒋和煦,等.低渗透复合油藏压力动态有限元理论分析[J].西南石油大学学报(自然科学版),2016,38(4):1-8.ZHANG Liehui,ZHANG Ruihan,JIANG Hexu,et al.Theoretical analysis of low permeability composite reservoir using finite element method[J].Journal of Southwest Petroleum University(Science&Technology Edition),2016,38(4):1-8.
[18]刘启国,金吉焱,贵富,等.存在直线断层的复合模型试井曲线特征研究[J].西南石油大学学报(自然科学版),2017,39(4):113-118.LIU Qiguo,JIN Jiyan,GUI Fu,et al.Characteristics of well test curves corresponding to a combined reservoir with linear faults[J].Journal of Southwest Petroleum University(Science&Technology Edition),2017,39(4):113-118.
[19]WANG M,FAN Z,XING G,et al.Rate decline analysis for modeling volume fractured well production in naturally fractured reservoirs[J].Energies,2018,11(1):1-21.
[20]VAN-EVERDINGEN A F,HURST W.The application of the Laplace transformation to flow problem in reservoirs[J].Journal of Petroleum Technology,1949,1(12):305-324.
[21]吴小庆.数学物理方程及其应用[M].北京:科学出版社,2008:50-52.WU Xiaoqing.Equation and application of mathematical physics[M].Beijing:Science Press,2008:50-52.
[22]胡俊坤.水驱气藏水平井产能评价及不稳定渗流理论研究[D].成都:西南石油大学,2013.HU Junkun.Study on deliverability evaluation and transient seepage theory of horizontal wells in water drive gas reservoirs[D].Chengdu:Southwest Petroleum University,2013.
[23]刘式适.特殊函数[M].北京:气象出版社,2002:386-427.LIU Shishi.Special functions[M].Beijing:Meteorological Press,2002:386-427.
[24]段志文.数学物理方程与特殊函数[M].北京:高等教育出版社,2008:119-128.DUAN Zhiwen.Equations of mathematical physics&special functions[M].Beijing:Higher Education Press,2008:119-128.
[2]杨仁锋,姜瑞忠,孙君书,等.低渗透油藏非线性微观渗流机理[J].油气地质与采收率,2011,18(2):90-93.YANG Renfeng,JIANG Ruizhong,SUN Junshu,et al.Study on nonlinear flow mechanism in low permeability porous medium[J].Petroleum Geology and Recovery Efficiency,2011,18(2):90-93.
[3]姜瑞忠,李林凯,徐建春,等.低渗透油藏非线性渗流新模型及试井分析[J].石油学报,2012,33(2):264-268.JIANG Ruizhong,LI Linkai,XU Jianchun,et al.A nonlinear mathematical model for low-permeability reservoirs and well-testing analysis[J].Acta Petrolei Sinica,2012,33(2):264-268.
[4]冯青.低渗透气藏非线性渗流试井理论研究[D].成都:西南石油大学,2013.FENG Qing.Study on well test theory of nonlinear seepage in low permeability gas reservoir[D].Chengdu:Southwest Petroleum University,2013.
[5]赵益忠,程远方,刘钰川,等.启动压力梯度对低渗透油藏微观渗流及开发动态的影响[J].油气地质与采收率,2013,20(1):67-69.ZHAO Yizhong,CHENG Yuanfang,LIU Yuchuan,et al.Study on influence of start-up pressure gradient to micro-seepage in low permeability reservoirs and development trends[J].Petroleum Geology and Recovery Efficiency,2013,20(1):67-69.
[6]魏漪,宋新民,冉启全,等.致密油藏压裂水平井非稳态产能预测模型[J].新疆石油地质,2014,35(1):67-72.WEI Yi,SONG Xinmin,RAN Qiquan,et al.An unstable productivity prediction model for fractured horizontal well in tight oil reservoirs[J].Xinjiang Petroleum Geology,2014,35(1):67-72.
[7]RENYI C,LING C,MA Y Z,et al.Characteristics of unsteady flow in porous media while considering threshold pressure gradient with Green’s function[J].Journal of Central South University,2016,23(1):201-208.
[8]欧阳伟平,张冕,刘曰武,等.基于三参数非线性渗流的致密气藏数值试井分析[J].天然气地球科学,2016,27(11):2 030-2 036.OUYANG Weiping,ZHANG Mian,LIU Yuewu,et al.Numerical well test analysis of tight gas reservoirs based on the three parameter nonlinear seepage[J].Natural Gas Geoscience,2016,27(11):2 030-2 036.
[9]刘化普,刘慧卿,王敬.缝洞型三重介质油藏分形渗流规律[J].新疆石油地质,2017,38(2):204-208.LIU Huapu,LIU Huiqing,WANG Jing.Fractal percolation law in fractured-vuggy triple medium reservoirs[J].Xinjiang Petroleum Geology,2017,38(2):204-208.
[10]曹丽娜,李晓平,罗诚,等.裂缝性低渗气藏水平井不稳定产量递减探讨[J].西南石油大学学报(自然科学版),2017,39(3):103-110.CAO Lina,LI Xiaoping,LUO Cheng,et al.Investigation of unstable production decline in fractured low-permeability gas reservoir horizontal wells[J].Journal of Southwest Petroleum University(Science&Technology Edition),2017,39(3):103-110.
[11]张小龙,杨志兴.启动压力梯度对低渗气藏不稳定渗流特征的影响[J].油气井测试,2018,27(3):7-13.ZHANG Xiaolong,YANG Zhixing.Lmpacts of start-up pressure gradient on features of transient seepage flow in low-permeability gas reservoirs[J].Well Testing,2018,27(3):7-13.
[12]武治岐,王厚坤,王睿.裂缝性致密油藏体积压裂水平井压力动态分析[J].新疆石油地质,2018,39(3):333-339.WU Zhiqi,WANG Houkun,WANG Rui.Pressure behavior analysis of volume fracturing in horizontal wells in fractured tight oil reservoirs[J].Xinjiang Petroleum Geology,2018,39(3):333-339.
[13]KUCHUK F J,HABASHY T M,TORRES-VERDIN C.A nonlinear approximation for the pressure behavior of heterogeneous reservoirs[J].SPE Journal,1996,1(3):229-242.
[14]FLAVIO M,ERDAL O,HOSSEIN K.A semianalytical approach to model pressure transients in heterogeneous reservoirs[J].SPE Reservoir Evaluation&Engineering,2010,13(2):341-358.
[15]蔡明金,张福祥,杨向同,等.碳酸盐岩洞穴型储层试井解释新模型[J].特种油气藏,2014,21(2):98-101.CAI Mingjin,ZHANG Fuxiang,YANG Xiangtong,et al.New model of well test interpretation in cavernous carbonate reservoirs[J].Special Oil&Gas Reservoirs,2014,21(2):98-101.
[16]姜瑞忠,郜益华,孙召勃,等.双重介质复合油藏偏心井试井分析[J].新疆石油地质,2016,37(3):327-331.JIANG Ruizhong,GAO Yihua,SUN Zhaobo,et al.Off-center well test analysis for composite dual porosity reservoirs[J].Xinjiang Petroleum Geology,2016,37(3):327-331.
[17]张烈辉,张芮菡,蒋和煦,等.低渗透复合油藏压力动态有限元理论分析[J].西南石油大学学报(自然科学版),2016,38(4):1-8.ZHANG Liehui,ZHANG Ruihan,JIANG Hexu,et al.Theoretical analysis of low permeability composite reservoir using finite element method[J].Journal of Southwest Petroleum University(Science&Technology Edition),2016,38(4):1-8.
[18]刘启国,金吉焱,贵富,等.存在直线断层的复合模型试井曲线特征研究[J].西南石油大学学报(自然科学版),2017,39(4):113-118.LIU Qiguo,JIN Jiyan,GUI Fu,et al.Characteristics of well test curves corresponding to a combined reservoir with linear faults[J].Journal of Southwest Petroleum University(Science&Technology Edition),2017,39(4):113-118.
[19]WANG M,FAN Z,XING G,et al.Rate decline analysis for modeling volume fractured well production in naturally fractured reservoirs[J].Energies,2018,11(1):1-21.
[20]VAN-EVERDINGEN A F,HURST W.The application of the Laplace transformation to flow problem in reservoirs[J].Journal of Petroleum Technology,1949,1(12):305-324.
[21]吴小庆.数学物理方程及其应用[M].北京:科学出版社,2008:50-52.WU Xiaoqing.Equation and application of mathematical physics[M].Beijing:Science Press,2008:50-52.
[22]胡俊坤.水驱气藏水平井产能评价及不稳定渗流理论研究[D].成都:西南石油大学,2013.HU Junkun.Study on deliverability evaluation and transient seepage theory of horizontal wells in water drive gas reservoirs[D].Chengdu:Southwest Petroleum University,2013.
[23]刘式适.特殊函数[M].北京:气象出版社,2002:386-427.LIU Shishi.Special functions[M].Beijing:Meteorological Press,2002:386-427.
[24]段志文.数学物理方程与特殊函数[M].北京:高等教育出版社,2008:119-128.DUAN Zhiwen.Equations of mathematical physics&special functions[M].Beijing:Higher Education Press,2008:119-128.