三重介质压裂气藏椭圆流非稳态产能模型
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摘要
天然气藏经水力压裂后产生藏改造体积(SRV),SRV内的气藏性质与原始储层存在很大的差异,水力压裂每一阶段的SRV可简化为水力裂缝附近的一个椭圆形区域。由于三重介质气藏为各向异性储层,与经典的径向流模型相比,椭圆流模型对于三重介质气藏的优化开发至关重要。通过建立一个新的压裂井复合椭圆流模型来分析考虑SRV的三重介质气藏产能变化,模型内外椭圆区均为三重介质,高流动能力的内区用来表征SRV,基质和裂缝间的窜流视为非稳态。使用Mathieu函数、拉普拉斯变换和Stehfest数值反演算法等求解数学模型,之后绘制无因次典型曲线,并对模型进行验证。典型曲线的特征显示模型存在13个流动阶段,将基质与裂缝间非稳态与拟稳态窜流进行比较,并分析了井筒半径、SRV半径、流度比和储容比等相关敏感参数对产能的影响。
The stimulated reservoir volume(SRV)is generated after hydraulic fracturing,and the gas reservoir properties in SRV are different from those in original formation.SRV can be simplified to an elliptical shape region around hydraulic fracture at each stage of hydraulic fracturing.Since the triple medium gas reservoir is an anisotropic formation,compared to classical radial flow model,the elliptical flow model is essential for the optimal development of triple medium gas reservoirs.A new composite elliptical flow model of fracturing wells is established to analyze the production performance of triple medium gas reservoirs considering SRV.The inner and outer elliptical regions of the model both are triple media,and the inner region with high flow capacity is used to characterize SRV.The cross flow between matrix and fractures is considered as unsteady flow.The elliptical flow model is solved using the Mathieu function,Laplacian variation and Stehfest numerical inversion algorithm.The dimensionless typical curves are plotted and the model is verified.According to the characteristics of type curves,there are thirteen flow regimes.The unsteady cross flow between matrix and fractures is compared with the pseudo-steady cross flow.The influences of relevant parameters on productivity are analyzed,such as wellbore radius,SRV radius,mobility ratio and storativity ratio.
The stimulated reservoir volume(SRV)is generated after hydraulic fracturing,and the gas reservoir properties in SRV are different from those in original formation.SRV can be simplified to an elliptical shape region around hydraulic fracture at each stage of hydraulic fracturing.Since the triple medium gas reservoir is an anisotropic formation,compared to classical radial flow model,the elliptical flow model is essential for the optimal development of triple medium gas reservoirs.A new composite elliptical flow model of fracturing wells is established to analyze the production performance of triple medium gas reservoirs considering SRV.The inner and outer elliptical regions of the model both are triple media,and the inner region with high flow capacity is used to characterize SRV.The cross flow between matrix and fractures is considered as unsteady flow.The elliptical flow model is solved using the Mathieu function,Laplacian variation and Stehfest numerical inversion algorithm.The dimensionless typical curves are plotted and the model is verified.According to the characteristics of type curves,there are thirteen flow regimes.The unsteady cross flow between matrix and fractures is compared with the pseudo-steady cross flow.The influences of relevant parameters on productivity are analyzed,such as wellbore radius,SRV radius,mobility ratio and storativity ratio.
引文
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[14]Wang H,Liao X,Zhao X.Study of tight oil reservoir flow regimes in different treated horizontal well[J].Journal of the Energy Institute,2015,88(2):198-204.
[15]Zhao Y L,Zhang L H,Luo J X,et al.Performance of fractured horizontal well with stimulated reservoir volume in tight gas reservoir[J].Journal of Hydrology,2014,512:447-456.
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[17]Wang Yanyan,Wang Weihong,Hu Xiaohu,et al.Pressure dynamic analysis model of MFHW in induced permeability field[J].Natural Gas Geoscience,2017,28(5):785-791.王妍妍,王卫红,胡小虎.诱导渗透率场中压裂水平井压力动态分析模型[J].天然气地球科学,2017,28(5):785-791.
[18]Obuto T S,Ertekin T.A composite system solution in elliptic flow geometry[J].SPE Formation Evaluation,1987,2(3):227-238.
[19]Zhang Q,Su Y L,Wang W D,et al.Performance analysis of fractured wells with elliptical SRV in shale reservoirs[J].Journal of Natural Gas Science and Engineering,2017,45:380-390.
[20]Ma Kuiqian,Gao Yihua,Sun Zhaobo.Well test model of triple media composite reservoir based on elliptic flow[J].FaultBlock Oil&Gas Field,2017,24(1):63-68.马奎前,郜益华,孙召勃.三重介质复合油藏椭圆流试井模型[J].断块油气田,2017,24(1):63-68.
[21]Xie J,Yang C D,Gupta N,et al.Integration of shale-gas-production data and microseismic for fracture and reservoir properties with the fast marching method[J].SPE Journal,2015,20(2):347-359.
[22]Brown M,Ozkan E,Raghavan R,et al.Practical solutions for pressure-transient responses of fractured horizontal wells in tight shale reservoirs[J].SPE Reservoir Evaluation Engineering,2011,14(6):663-676.
[23]Jia Y L,Fan X Y,Nie R S,et al.Flow modeling of well test analysis for porous-vuggy carbonate reservoirs[J].Transport in Porous Media,2013,97(2):253-279.
[24]McLachlan N W.Theory and Application of Mathieu Functions[M].Oxford:Oxford University Press,1951:10-57.
[25]Van Everdingen A F,Hurst W.The application of the Laplace transformation to flow problems in reservoirs[J].Journal of Petroleum Technology,1949,1(12):305-324.
[26]Stehfest H.Algorithm 368numerical inversion of Laplace transforms[J].Communication of the ACM,1970,13(1):47-49.
[2]Zhang Yitang,Liu Ciqun.Further study on the approximate solution of the elliptical flow model for wells with vertical fractures[J].Acta Petrolei Sinica,1996,17(4):71-77.张义堂,刘慈群.垂直裂缝井椭圆流模型近似解的进一步研究[J].石油学报,1996,17(4):71-77.
[3]Luo Tianyu,Zhao Jinzhou,Guo Jianchun.Elliptical flow method to calculate productivity of gas wells after fracturing[J].Natural Gas Industry,2005,25(10):94-96.罗天雨,赵金洲,郭建春.求取压裂后气井产能的椭圆流方法[J].天然气工业,2005,25(10):94-96.
[4]Zhang L H,Zhang X T,Wang Y,et al.A study on elliptical gas flow in tri-porosity gas reservoirs[J].Transport in Porous Media,2011,87(3):777-791.
[5]Kucuk F,Brigham W E.Transient flow in elliptical systems[J].SPE Journal,1979,19(6):401-410.
[6]Riley M F,Brigham W E,Horne R N.Analytic solutions for elliptical finite-conductivity fractures[C]//paper 22656-MSpresented at the SPE 66th Annual Technical Conference and Exhibition,USA:Dallas,TX,1991:6-9.
[7]Amini S,Ilk D,Blasingame T A.Evaluation of the elliptical flow period for hydraulically-fractured wells in tight gas sands-theoretical aspects and practical considerations[C]//paper 106308-MS presented at the SPE Hydraulic Fracturing Technology Conference,USA:College Station,TX,2007:29-31.
[8]Cheng Y M,Lee W J,Mcvay D A.A new approach for reliable estimation of hydraulic fracture properties in tight gas wells[J].SPE Reservoir Evaluation Engineering,2009,2(12):254-262.
[9]Escobar F H,Ghisays-Ruiz A,Bonilla L F.New model for elliptical flow regime in hydraulically-fractured vertical wells in homogeneous and naturally-fractured systems[J].APRNJournal of Engineering and Applied Sciences,2014,9(9):1629-1636.
[10]Clarkson C R.Production data analysis of tight gas wells:review of theory and best practices[J].International Journal of Coal Geology,2013,109:101-146.
[11]Guo T K,Zhang S C,Qu Z Q,et al.Experimental study of hydraulic fracturing for shale by stimulated reservoir volume[J].Fuel,2014,128:373-380.
[12]Cipolla C L,Lolon E P,Erdle J C,et al.Reservoir modeling in shale-gas reservoirs[J].SPE Reservoir Evaluation Engineering,2010,13(4):638-653.
[13]Zhao Haifeng,Jiang Di,Shi Jun.Fluid mechanics and rock fracture kinetics of fracture mesh system in tight sand gas reservoirs[J].Natural Gas Geoscience,2016,27(2):346-351.赵海峰,蒋迪,石俊.致密砂岩气藏缝网系统渗流力学和岩石断裂动力学[J].天然气地球科学,2016,27(2):346-351.
[14]Wang H,Liao X,Zhao X.Study of tight oil reservoir flow regimes in different treated horizontal well[J].Journal of the Energy Institute,2015,88(2):198-204.
[15]Zhao Y L,Zhang L H,Luo J X,et al.Performance of fractured horizontal well with stimulated reservoir volume in tight gas reservoir[J].Journal of Hydrology,2014,512:447-456.
[16]Wen Qingzhi,Gao Jinjian,Li Yang,et al.Analysis of the factors of influencing stimulated volume of shale reservoir volume fracturing[J].Journal of Xi'an Shiyou University:Natural Science Edition,2014,29(6):58-64.温庆志,高金剑,李扬,等.页岩气储层SRV影响因素分析[J].西安石油大学学报:自然科学版,2014,29(6):58-64.
[17]Wang Yanyan,Wang Weihong,Hu Xiaohu,et al.Pressure dynamic analysis model of MFHW in induced permeability field[J].Natural Gas Geoscience,2017,28(5):785-791.王妍妍,王卫红,胡小虎.诱导渗透率场中压裂水平井压力动态分析模型[J].天然气地球科学,2017,28(5):785-791.
[18]Obuto T S,Ertekin T.A composite system solution in elliptic flow geometry[J].SPE Formation Evaluation,1987,2(3):227-238.
[19]Zhang Q,Su Y L,Wang W D,et al.Performance analysis of fractured wells with elliptical SRV in shale reservoirs[J].Journal of Natural Gas Science and Engineering,2017,45:380-390.
[20]Ma Kuiqian,Gao Yihua,Sun Zhaobo.Well test model of triple media composite reservoir based on elliptic flow[J].FaultBlock Oil&Gas Field,2017,24(1):63-68.马奎前,郜益华,孙召勃.三重介质复合油藏椭圆流试井模型[J].断块油气田,2017,24(1):63-68.
[21]Xie J,Yang C D,Gupta N,et al.Integration of shale-gas-production data and microseismic for fracture and reservoir properties with the fast marching method[J].SPE Journal,2015,20(2):347-359.
[22]Brown M,Ozkan E,Raghavan R,et al.Practical solutions for pressure-transient responses of fractured horizontal wells in tight shale reservoirs[J].SPE Reservoir Evaluation Engineering,2011,14(6):663-676.
[23]Jia Y L,Fan X Y,Nie R S,et al.Flow modeling of well test analysis for porous-vuggy carbonate reservoirs[J].Transport in Porous Media,2013,97(2):253-279.
[24]McLachlan N W.Theory and Application of Mathieu Functions[M].Oxford:Oxford University Press,1951:10-57.
[25]Van Everdingen A F,Hurst W.The application of the Laplace transformation to flow problems in reservoirs[J].Journal of Petroleum Technology,1949,1(12):305-324.
[26]Stehfest H.Algorithm 368numerical inversion of Laplace transforms[J].Communication of the ACM,1970,13(1):47-49.