基于有限体积方法的页岩气多段压裂水平井数值模拟
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摘要
为了实现页岩气在多尺度介质中的流动模拟,考虑页岩气在基质—天然微裂缝和人工大尺度压裂缝中的流动特征,建立页岩气多段压裂水平井不稳定渗流数学模型,针对模拟区域采用非结构四面体网格进行网格剖分,基于有限体积方法离散建立页岩气三维渗流数值模型,然后通过顺序求解的方法进行求解,进而模拟页岩气多段压裂水平井的生产动态和储层压力分布变化,并对模拟结果进行分析。研究结果表明:(1)采用所建立的数值模拟计算方法与商业数值模拟软件Eclipse计算的多段压裂水平井产气量基本一致,证实该模型正确、可行;(2)分别采用顺序求解方法和全隐式求解方法计算得到的页岩气水平井产气量虽然在生产初期存在着差异,但随着计算的推进,二者迅速趋于一致,进一步验证了该模型的正确性;(3)尽管解吸气对地层压力具有补充作用,但作用有限,对产气量的影响不大,随着生产时间的延长,解吸气量在产气量中所占比例逐渐上升;(4)确定合理的压裂段数且获得较长的压裂缝长,是页岩气水平井增产改造的核心。结论认为,该研究成果有助于页岩气储层体积压裂的设计以及多段压裂水平井生产动态的预测。
In order to simulate the flowing of shale gas in multi-scale media, we established a mathematical model for the unsteady seepage of multi-stage fractured horizontal wells in shale gas reservoirs in consideration of the flowing characteristics of shale gas in matrix, natural fractures and large-scale artificial fractures. Grid division in the simulation region was carried out by means of nonstructural tetrahedral grid. Then, a 3 D numerical model for the seepage of shale gas was established discretely using finite volume method and solved using sequence solution method. Finally, the production performance of multi-stage fractured horizontal wells in shale gas reservoirs and the reservoir pressure distribution were simulated, and the simulation results were analyzed. And the following research results were obtained. First, the gas production rates of multi-stage fractured horizontal wells calculated by this newly established numerical simulation method are basically consistent with the calculation results by the commercial numerical simulation software Eclipse, which proves that this new model is accurate and feasible. Second, the gas production rates of horizontal wells calculated by the sequential solution method are different from those calculated by the fully implicit solution method in the early production stages, but as the calculation progresses, both of them tend to be consistent, which further verifies the accuracy of this new model. Third, desorbed gas plays a supplementary role to reservoir pressure, but its function is limited, and its effect on gas production is little. As the production goes on, the percentage of desorbed gas increases gradually. Fourth, the key to the stimulation of shale-gas horizontal wells is to determine the number of fractured sections rationally and create longer artificial fractures. In conclusion, the research results are conducive to the design of stimulated reservoir volumes(SRVs) of shale gas reservoirs and the prediction of production performance of multi-stage fractured horizontal wells.
In order to simulate the flowing of shale gas in multi-scale media, we established a mathematical model for the unsteady seepage of multi-stage fractured horizontal wells in shale gas reservoirs in consideration of the flowing characteristics of shale gas in matrix, natural fractures and large-scale artificial fractures. Grid division in the simulation region was carried out by means of nonstructural tetrahedral grid. Then, a 3 D numerical model for the seepage of shale gas was established discretely using finite volume method and solved using sequence solution method. Finally, the production performance of multi-stage fractured horizontal wells in shale gas reservoirs and the reservoir pressure distribution were simulated, and the simulation results were analyzed. And the following research results were obtained. First, the gas production rates of multi-stage fractured horizontal wells calculated by this newly established numerical simulation method are basically consistent with the calculation results by the commercial numerical simulation software Eclipse, which proves that this new model is accurate and feasible. Second, the gas production rates of horizontal wells calculated by the sequential solution method are different from those calculated by the fully implicit solution method in the early production stages, but as the calculation progresses, both of them tend to be consistent, which further verifies the accuracy of this new model. Third, desorbed gas plays a supplementary role to reservoir pressure, but its function is limited, and its effect on gas production is little. As the production goes on, the percentage of desorbed gas increases gradually. Fourth, the key to the stimulation of shale-gas horizontal wells is to determine the number of fractured sections rationally and create longer artificial fractures. In conclusion, the research results are conducive to the design of stimulated reservoir volumes(SRVs) of shale gas reservoirs and the prediction of production performance of multi-stage fractured horizontal wells.
引文
[1]黄婷.基于多尺度流动机理的页岩气藏压裂井渗流理论研究[D].成都:西南石油大学,2016.Huang Ting.Research on seepage theory of fractured wells in shale gas reservoir based on multi-scale flow mechanisms[D].Chengdu:Southwest Petroleum University,2016
[2]Kucuk F&Sawyer WK.Transient flow in naturally fractured reservoirs and its application to devonian gas shales[C]//Paper9397-MS presented at the SPE Annual Technical Conference and Exhibition,21-24 September 1980,Dallas,Texas,USA.
[3]Bumb AC&McKee CR.Gas-well testing in the presence of desorption for coalbed methane and devonian shale[J].SPE Formation Evaluation,1988,3(1):179-185.
[4]Carlson ES&Mercer JC.Devonian shale gas production:Mechanisms and simple models[J].Journal of Petroleum Technology,1991,43(4):476-482.
[5]Swami V.Shale gas reservoir modeling:From nanopores to laboratory[C]//Paper 163065-STU presented at the SPE Annual Technical Conference and Exhibition,8-10 October 2012,San Antonio,Texas,USA.
[6]Saputelli L,Lopez C,Chacon A&Soliman M.Design optimization of horizontal wells with multiple hydraulic fractures in the Bakken Shale[C]//Paper 167770 presented at the SPE/EAGEEuropean Unconventional Resources Conference and Exhibition,25-27 February 2014,Vienna,Austria.
[7]Rubin B.Accurate simulation of Non Darcy flow in stimulated fractured shale reservoirs[C]//Paper 132093-MS presented at the SPE Western Regional Meeting,27-29 May 2010,Anaheim,California,USA.
[8]Klimkowski?&Nagy S.Key factors in shale gas modeling and simulation[J].Archives of Mining Sciences,2014,59(4):987-1004.
[9]Mirzaei M&Cipolla CL.A workflow for modeling and simulation of hydraulic fractures in unconventional gas reservoirs[C]//Paper 153022-MS presented at the SPE Middle East Unconventional Gas Conference and Exhibition,23-25 January 2012,Abu Dhabi,UAE.
[10]赵金洲,任岚,沈骋,李勇明.页岩气储层缝网压裂理论与技术研究新进展[J].天然气工业,2018,38(3):1-14.Zhao Jinzhou,Ren Lan,Shen Cheng&Li Yongming.Latest research progresses in network fracturing theories and technologies for shale gas reservoirs[J].Natural Gas Industry,2018,38(3):1-14.
[11]姚军,王子胜,张允,黄朝琴.天然裂缝性油藏的离散裂缝网络数值模拟方法[J].石油学报,2010,31(2):284-288Yao Jun,Wang Zisheng,Zhang Yun&Huang Chaoqin.Numerical simulation method of discrete fracture network for naturally fractured reservoirs[J].Acta Petrolei Sinica,2010,31(2):284-288.
[12]Hoteit H&Firoozabadi A.Compositional modeling of discretefractured media without transfer functions by the discontinuous galerkin and mixed methods[J].SPE Journal,2006,11(3):341-352.
[13]Moinfar A,Narr W,Hui MH,Mallison BT&Lee SH.Comparison of discrete-fracture and dual-permeability models for multiphase flow in naturally fractured reservoirs[C]//Paper 142295-MS presented at the SPE Reservoir Simulation Symposium,21-23 February 2011,The Woodlands,Texas,USA.
[14]任岚,林然,赵金洲,荣莽,陈建达.页岩气水平井增产改造体积评价模型及其应用[J].天然气工业,2018,38(8):47-56.Ren Lan,Lin Ran,Zhao Jinzhou,Rong Mang&Chen Jianda.Astimulated reservoir volume(SRV)evaluation model and its application to shale gas well productivity enhancement[J].Natural Gas Industry,2018,38(8):47-56.
[15]Schepers KC,Gonzalez RJ,Koperna GJ&Oudinot AY.Reservoir modeling in support of shale gas exploration[C]//Paper 123057-MS presented at the Latin American and Caribbean Petroleum Engineering Conference,31 May-3 June 2009,Cartagena de Indias,Colombia.
[16]Dehghanpour H&Shirdel M.A triple porosity model for shale gas reservoirs[C]//Paper 149501-MS presented at the Canadian Unconventional Resources Conference,15-17 November 2011,Calgary,Alberta,Canada.
[17]Wu YS,Moridis G,Bai B&Zhang K.A multi-continuum model for gas production in tight fractured reservoirs[C]//Paper 118944-MS presented at the SPE Hydraulic Fracturing Technology Conference,19-21 January 2009,The Woodlands,Texas,USA.
[18]张烈辉,张芮菡,蒋和煦,孔玲,佘娟.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,Kong Ling&She Juan.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.
[19]Aboaba AL&Cheng Y.Estimation of fracture properties for a horizontal well with multiple hydraulic fractures in gas shale[R].SPE Eastern Regional Meeting,13-15 October 2010,Morgantown,West Virginia,USA.
[20]Wang K,Liu H,Luo J,Wu KL&Chen ZX.A comprehensive model coupling embedded discrete fractures,multiple interacting continua,and geomechanics in shale gas reservoirs with multiscale fractures[J].Energy&Fuels,2017,31(8):7758-7776.
[21]方文超,姜汉桥,李俊键,王青,Killough J,李林凯,等.致密储集层跨尺度耦合渗流数值模拟模型[J].石油勘探与开发,2017,44(3):415-422.Fang Wenchao,Jiang Hanqiao,Li Junjian,Wang Qing,Killough J,Li Linkai,et al.A numerical simulation model for multi-scale flow in tight oil reservoirs[J].Petroleum Exploration and Development,2017,44(3):415-422
[22]Caumon G,Collon-Drouaillet P,Veslud de Carlier Le C,Viseur S&Sausse J.Surface-based 3D modeling of geological structures[J].Mathematical Geosciences,2009,41(8):927-945.
[23]Juanes R,Samper J&Molinero J.A general and efficient formulation of fractures and boundary conditions in the finite element method[J].International Journal for Numerical Methods in Engineering,2002,54(12):1751-1774.
[24]Moukalled F,Mangani L&Darwish M.The finite volume method in computational fluid dynamics[M].Zürich:Springer International Publishing Switzerland,2016.
[25]C?engel Y A.Heat and mass transfer:A practical approach[M].New York:McGraw-Hill,2007.
[26]Patankar SV.Numerical heat transfer and fluid flow[M].Washington,DC:Hemisphere Publishing Corp,1980.
[27]Darwish M&Moukalled F.A new approach for building bounded skew-upwind schemes[J].Computer Methods in Applied Mechanics&Engineering,1996,129(3):221-233.
[28]Spekreijse S.Multigrid solution of monotone second-order discretizations of hyperbolic conservation laws[J].Mathematics of Computation,1987,49(179):135-155.
[29]Barth T&Jespersen D.The design and application of upwind schemes on unstructured meshes[C]//27th Aerospace Sciences Meeting,9-12 January 1989,Reno,Nevada,USA.
[30]Leonard BP.The ULTIMATE conservative difference scheme applied to unsteady one-dimensional advection[J].Computer Methods in Applied Mechanics and Engineering,1991,88(1):17-74.
[31]Incropera FP,Dewitt DP,Bergman TL&Lavine AS.Fundamentals of heat and mass transfer[M].Hoboken:John Wiley&Sons,2007.
[32]樊冬艳,姚军,孙海,曾慧.考虑多重运移机制耦合页岩气藏压裂水平井数值模拟[J].力学学报,2015,47(6):906-915.Fan Dongyan,Yao Jun,Sun Hai&Zeng Hui.Numerical simulation of multi-fractured horizontal well in shale gas reservoir considering multiple gas transport mechanisms[J].Chinese Journal of Theoretical and Applied Mechanics,2015,47(6):906-915
[2]Kucuk F&Sawyer WK.Transient flow in naturally fractured reservoirs and its application to devonian gas shales[C]//Paper9397-MS presented at the SPE Annual Technical Conference and Exhibition,21-24 September 1980,Dallas,Texas,USA.
[3]Bumb AC&McKee CR.Gas-well testing in the presence of desorption for coalbed methane and devonian shale[J].SPE Formation Evaluation,1988,3(1):179-185.
[4]Carlson ES&Mercer JC.Devonian shale gas production:Mechanisms and simple models[J].Journal of Petroleum Technology,1991,43(4):476-482.
[5]Swami V.Shale gas reservoir modeling:From nanopores to laboratory[C]//Paper 163065-STU presented at the SPE Annual Technical Conference and Exhibition,8-10 October 2012,San Antonio,Texas,USA.
[6]Saputelli L,Lopez C,Chacon A&Soliman M.Design optimization of horizontal wells with multiple hydraulic fractures in the Bakken Shale[C]//Paper 167770 presented at the SPE/EAGEEuropean Unconventional Resources Conference and Exhibition,25-27 February 2014,Vienna,Austria.
[7]Rubin B.Accurate simulation of Non Darcy flow in stimulated fractured shale reservoirs[C]//Paper 132093-MS presented at the SPE Western Regional Meeting,27-29 May 2010,Anaheim,California,USA.
[8]Klimkowski?&Nagy S.Key factors in shale gas modeling and simulation[J].Archives of Mining Sciences,2014,59(4):987-1004.
[9]Mirzaei M&Cipolla CL.A workflow for modeling and simulation of hydraulic fractures in unconventional gas reservoirs[C]//Paper 153022-MS presented at the SPE Middle East Unconventional Gas Conference and Exhibition,23-25 January 2012,Abu Dhabi,UAE.
[10]赵金洲,任岚,沈骋,李勇明.页岩气储层缝网压裂理论与技术研究新进展[J].天然气工业,2018,38(3):1-14.Zhao Jinzhou,Ren Lan,Shen Cheng&Li Yongming.Latest research progresses in network fracturing theories and technologies for shale gas reservoirs[J].Natural Gas Industry,2018,38(3):1-14.
[11]姚军,王子胜,张允,黄朝琴.天然裂缝性油藏的离散裂缝网络数值模拟方法[J].石油学报,2010,31(2):284-288Yao Jun,Wang Zisheng,Zhang Yun&Huang Chaoqin.Numerical simulation method of discrete fracture network for naturally fractured reservoirs[J].Acta Petrolei Sinica,2010,31(2):284-288.
[12]Hoteit H&Firoozabadi A.Compositional modeling of discretefractured media without transfer functions by the discontinuous galerkin and mixed methods[J].SPE Journal,2006,11(3):341-352.
[13]Moinfar A,Narr W,Hui MH,Mallison BT&Lee SH.Comparison of discrete-fracture and dual-permeability models for multiphase flow in naturally fractured reservoirs[C]//Paper 142295-MS presented at the SPE Reservoir Simulation Symposium,21-23 February 2011,The Woodlands,Texas,USA.
[14]任岚,林然,赵金洲,荣莽,陈建达.页岩气水平井增产改造体积评价模型及其应用[J].天然气工业,2018,38(8):47-56.Ren Lan,Lin Ran,Zhao Jinzhou,Rong Mang&Chen Jianda.Astimulated reservoir volume(SRV)evaluation model and its application to shale gas well productivity enhancement[J].Natural Gas Industry,2018,38(8):47-56.
[15]Schepers KC,Gonzalez RJ,Koperna GJ&Oudinot AY.Reservoir modeling in support of shale gas exploration[C]//Paper 123057-MS presented at the Latin American and Caribbean Petroleum Engineering Conference,31 May-3 June 2009,Cartagena de Indias,Colombia.
[16]Dehghanpour H&Shirdel M.A triple porosity model for shale gas reservoirs[C]//Paper 149501-MS presented at the Canadian Unconventional Resources Conference,15-17 November 2011,Calgary,Alberta,Canada.
[17]Wu YS,Moridis G,Bai B&Zhang K.A multi-continuum model for gas production in tight fractured reservoirs[C]//Paper 118944-MS presented at the SPE Hydraulic Fracturing Technology Conference,19-21 January 2009,The Woodlands,Texas,USA.
[18]张烈辉,张芮菡,蒋和煦,孔玲,佘娟.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,Kong Ling&She Juan.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.
[19]Aboaba AL&Cheng Y.Estimation of fracture properties for a horizontal well with multiple hydraulic fractures in gas shale[R].SPE Eastern Regional Meeting,13-15 October 2010,Morgantown,West Virginia,USA.
[20]Wang K,Liu H,Luo J,Wu KL&Chen ZX.A comprehensive model coupling embedded discrete fractures,multiple interacting continua,and geomechanics in shale gas reservoirs with multiscale fractures[J].Energy&Fuels,2017,31(8):7758-7776.
[21]方文超,姜汉桥,李俊键,王青,Killough J,李林凯,等.致密储集层跨尺度耦合渗流数值模拟模型[J].石油勘探与开发,2017,44(3):415-422.Fang Wenchao,Jiang Hanqiao,Li Junjian,Wang Qing,Killough J,Li Linkai,et al.A numerical simulation model for multi-scale flow in tight oil reservoirs[J].Petroleum Exploration and Development,2017,44(3):415-422
[22]Caumon G,Collon-Drouaillet P,Veslud de Carlier Le C,Viseur S&Sausse J.Surface-based 3D modeling of geological structures[J].Mathematical Geosciences,2009,41(8):927-945.
[23]Juanes R,Samper J&Molinero J.A general and efficient formulation of fractures and boundary conditions in the finite element method[J].International Journal for Numerical Methods in Engineering,2002,54(12):1751-1774.
[24]Moukalled F,Mangani L&Darwish M.The finite volume method in computational fluid dynamics[M].Zürich:Springer International Publishing Switzerland,2016.
[25]C?engel Y A.Heat and mass transfer:A practical approach[M].New York:McGraw-Hill,2007.
[26]Patankar SV.Numerical heat transfer and fluid flow[M].Washington,DC:Hemisphere Publishing Corp,1980.
[27]Darwish M&Moukalled F.A new approach for building bounded skew-upwind schemes[J].Computer Methods in Applied Mechanics&Engineering,1996,129(3):221-233.
[28]Spekreijse S.Multigrid solution of monotone second-order discretizations of hyperbolic conservation laws[J].Mathematics of Computation,1987,49(179):135-155.
[29]Barth T&Jespersen D.The design and application of upwind schemes on unstructured meshes[C]//27th Aerospace Sciences Meeting,9-12 January 1989,Reno,Nevada,USA.
[30]Leonard BP.The ULTIMATE conservative difference scheme applied to unsteady one-dimensional advection[J].Computer Methods in Applied Mechanics and Engineering,1991,88(1):17-74.
[31]Incropera FP,Dewitt DP,Bergman TL&Lavine AS.Fundamentals of heat and mass transfer[M].Hoboken:John Wiley&Sons,2007.
[32]樊冬艳,姚军,孙海,曾慧.考虑多重运移机制耦合页岩气藏压裂水平井数值模拟[J].力学学报,2015,47(6):906-915.Fan Dongyan,Yao Jun,Sun Hai&Zeng Hui.Numerical simulation of multi-fractured horizontal well in shale gas reservoir considering multiple gas transport mechanisms[J].Chinese Journal of Theoretical and Applied Mechanics,2015,47(6):906-915