低渗气藏多级压裂水平井产能模型及影响因素
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摘要
多级压裂水平井(MFHW)能大幅度提高低渗气藏的单井产能,提高低渗气藏的开发效益,而准确计算气井产能并分析其影响因素是压裂优化设计、气藏科学开发的基础。为低渗气藏MFHW产能计算建立了一个严格的数学模型,综合运用Laplace变换、叠加原理、积分方程的边界离散求解法、矩阵理论等数学方法成功地对模型进行了求解,并对不同因素影响下的产能进行了定量计算和分析,分析了气层有效厚度、气藏渗透率、压裂缝条数、压裂缝半长、压裂缝导流能力对气井产能的影响,同时也分析了地层流入各条压裂缝流量的差异。研究结果表明,气层有效厚度或气藏渗透率增大时,气井产量几乎呈线性增大;压裂缝条数、压裂缝半长、压裂缝导流能力增大,产量增大,但前期增速快,后期增速慢;地层流入各条压裂缝的流量在早期差别不大,晚期差别明显——端部流量大于中部流量。
Multistage fractured horizontal wells(MFHWs) can greatly improve single well productivity in low permeability reservoirs and improve their development benefits. The accurate calculation of gas well productivity and analysis of related influencing factors are the basis for fracturing optimization and scientific development of gas reservoirs. Herein, a rigorous mathematical model was established for the calculation of MFHW productivity in low permeability reservoirs. Laplace transforms,the superposition principle, boundary discretization method of integral equations, matrix theory, and other mathematical methods were used to successfully solve the proposed model and to perform quantitative calculations and analysis of the production capacity with various influencing factors. The effects on gas well productivity due to the effective thickness of the gas layer,gas reservoir permeability, number of fractures, fracture half-length, and flow conductivity of the fractures were analyzed. The difference in the inflow rate from the stratum to each fracture was also determined. When the effective thickness of the gas layer or the permeability of the gas reservoir increases, the gas well production capacity increases almost linearly. When the number of fractures, fracture half-length, and flow conductivity of the fracture increase, the output increases with an initially higher rate of increase which slows during the later stage. The inflow rate from the stratum to each fracture remains largely unchanged during the early stages, but the difference in the later stage is clear, where the flow rate is greater at the ends compared to that observed in the middle.
Multistage fractured horizontal wells(MFHWs) can greatly improve single well productivity in low permeability reservoirs and improve their development benefits. The accurate calculation of gas well productivity and analysis of related influencing factors are the basis for fracturing optimization and scientific development of gas reservoirs. Herein, a rigorous mathematical model was established for the calculation of MFHW productivity in low permeability reservoirs. Laplace transforms,the superposition principle, boundary discretization method of integral equations, matrix theory, and other mathematical methods were used to successfully solve the proposed model and to perform quantitative calculations and analysis of the production capacity with various influencing factors. The effects on gas well productivity due to the effective thickness of the gas layer,gas reservoir permeability, number of fractures, fracture half-length, and flow conductivity of the fractures were analyzed. The difference in the inflow rate from the stratum to each fracture was also determined. When the effective thickness of the gas layer or the permeability of the gas reservoir increases, the gas well production capacity increases almost linearly. When the number of fractures, fracture half-length, and flow conductivity of the fracture increase, the output increases with an initially higher rate of increase which slows during the later stage. The inflow rate from the stratum to each fracture remains largely unchanged during the early stages, but the difference in the later stage is clear, where the flow rate is greater at the ends compared to that observed in the middle.
引文
[1] CINCO-LEY H, DOMINGUEZ N. Transient pressure behavior for a well with a finite-conductivity vertical fracture[J]. SPE 6014-PA, 1978. doi:10.2118/6014-PA
[2] RAGHAVAN R, JOSHI S D. Productivity of multiple drainholes or fractured horizontal wells[J]. SPE 21263-PA,1993. doi:10.2118/21263-PA
[3]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. doi:10.7666/d.y1543268LANG Zhaoxin, ZHANG Lihua, CHENG Linsong. Investigation on productivity of fractured horizontal well[J].Journal of University of Petroleum, 1994, 18(2):43-46.doi:10.7666/d.y1543268
[4]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(3):69-71.doi:10.3321/j.issn:0253-2697.2002.02.015NING 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(3):69-71. doi:10.3321/j.issn:-0253-2697.2002.02.015
[5]曾凡辉,郭建春,徐严波,等.压裂水平井产能影响因素[J].石油勘探与开发,2007, 34(4):474-477,482.doi:10.3321/j.issn:1000-0747.2007.04.016ZENG Fanhui, GUO Jianchun, XU Yanbo, et al. Factors affecting production capacity of fractured horizontal wells[J]. Petroleum Exploration and Development,2007,34(4):474-477,482. doi:10.3321/j.issn:1000-0747.2007.04.016
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[8] MUKHERJEE H, ECONOMIDES M. A parametric comparison of horizontal and vertical well performance[J].SPE 18303-PA,1991. doi:10.2118/18303-PA
[9]曾保全,程林松,罗鹏.基于流线模拟的压裂水平井渗流场及产能特征[J].西南石油大学学报(自然科学版),2010, 32(5):109-113. doi:10.3863/j.issn.1674-5086.2010.05.020ZENG Baoquan, CHENG Linsong, LUO Peng. Flow characteristics and productivity of fractured horizontal wells based on streamline simulation[J]. Journal of Southwest Petroleum University(Science&Technology Edition),2010, 32(5):109-113. doi:10.3863/j.issn. 1674-5086.-2010.05.020
[10]张芮菡,张烈辉,卢晓敏,等.低渗透裂缝性油藏压裂水平井产能动态分析[J].科学技术与工程,2014, 14(16):41-48. doi:10.3969/j.issn.1671-1815.2014.16.009ZHANG Ruihan, ZHANG Liehui, LU Xiaomin, et al. Deliverability analysis of fractured horizontal wells in low permeability fractured reservoir[J]. Science Technology and Engineering, 2014, 14(16):41-48. doi:10.3969/j.-issn.1671-1815.2014.16.009
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[12]魏明强,段永刚,方全堂,等.页岩气藏压裂水平井产量递减曲线分析法[J].天然气地球科学,2016, 27(5):898-904. doi:10.11764/j.issn.1672-1926.2016.05.0898WEI Mingqiang, DU AN Yonggang, FANG Quantang, et al. Advanced production decline analytical method for a multi-fractured horizontal well in shale reservoirs[J]. Natural Gas Geoscience, 2016, 27(5):898-904. doi:10.-11764/j.issn.1672-1926.2016.05.0898
[13] WANG Haitao. Performance of multiple fractured horizontal wells in shale gas reservoirs with consideration of multiple mechanisms[J]. Journal of Hydrology, 2014, 510:299-312. doi:10.1016/j.jhydrol.2013.12.019
[14]林旺,林洪富,刘立峰,等.工程参数对致密油藏压裂水平井产能的影响[J].油气地质与采收率,2017, 24(6):120-126. doi:10.3969/j.issn.1009-9603.2017.06.019LIN Wang, LIN Hongfu, LIU Lifeng, et al. Effect of engineering parameters on fractured horizontal well productivity in tight oil reservoirs[J]. Petroleum Geology and Recovery Efficiency, 2017, 24(6):120-126. doi:10.3969/j.-issn.1009-9603.2017.06.019
[15] BROHI I G, MERHAN P D, AGUILERA R. Modeling fractured horizontal wells as dual-porosity composite reservoirs:Application to tight gas, shale gas and tight oil cases[C]. SPE 144057-MS, 2011. doi:10.2118/144057-MS
[16]姚军,殷修杏,樊冬艳,等.低渗透油藏的压裂水平井三线性流试井模型[J].油气井测试,2011,20(5):1-5.doi:10.3969/j.issn.1004-4388.2011.05.001YAO Jun, YIN Xiuxing, FAN Dongyan, et al. Tri-linear flow well test model of fractured horizontal well in low permeability reservoir[J]. Well Testing,2011,20(5):1-5.doi:10.3969/j.issn. 1004-43 88.2011.05.001
[17] STALGOROVA E, MATTAR L. Practical analytical model to simulate production of horizontal wells with branch fractures[C]. SPE 162515-MS, 2012. doi:10.-2118/162515-MS
[18] STALGOROVA K. Analytical model for unconventional multifractured composite systems[C]. SPE 162516-PA,2013. doi:10.2118/162516-PA
[19]孙志宇,蒲春生,罗明良,等.水平井多级脉冲气体加载压裂及产能评价[J].西南石油大学学报(自然科学版),2008,30(5):104-107.doi:10.3863/j.issn.1000-2634.2008.05.023SUN Zhiyu, PU Chunsheng, LUO Mingliang, et al. Multi-pulse gas load fracturing and deliverability evaluation of horizontal well[J]. Journal of Southwest Petroleum University(Science&Technology Edition),2008, 30(5):104-107. doi:10.3863/j.issn.1000-2634.2008.05.023
[20]王强,童敏,武站国,等.致密火山岩气藏压裂水平井产能预测方法[J].西南石油大学学报(自然科学版),2014,36(4):107-115. doi:10.11885/j.issn.1674-5086.-2013.11.26.04WANG Qiang, TONG Min, WU Zhanguo, et al. An unsteady productivity prediction method of multi-fractured horizontal well in tight volcanic rock reservoir[J]. Journal of Southwest Petroleum University(Science&Technology Edition), 2014, 36(4):107-115. doi:10.11885/j.issn.-1674-5086.2013.11.26.04
[21]曾保全,程林松,李春兰,等.特低渗透油藏压裂水平井开发效果评价[J].石油学报,2010, 31(5):791-796.doi:10.7623/syxb201005015ZENG Baoquan,CHENG Linsong,LI Chunlan,et al.Development evaluation of fractured horizontal wells in ultra-low permeability reservoirs[J]. Acta Petrolei Sinica,2010, 31(5):791-796. doi:10.7623/syxb201005015
[22]廖新维,沈平平.现代试井分析[M].北京:石油工业出版社,2002.LIAO Xinwei, SHEN Pingping. Modern well test analysis[M]. Beijing:Petroleum Industry Press, 2002.
[23] CINCO-LEY H, MENG H Z. Pressure transient analysis of wells with finite conductivity vertical fractures in double porosity reservoirs[C]. SPE 18172-MS, 1988. doi:10.-2118/18172-MS
[24] RAGHAVAN R S, CHEN C C, AGARWAL B. An analysis of horizontal wells intercepted by multiple fractures[C].SPE 27652-PA, 1997. doi:10.2118/27652-PA
[25] CRAIG D P, BLASINGAME T A. Constant-rate drawdown solutions derived for multiple arbitrarily oriented uniform-flux, infinite-conductivity, or finite-conductivity fractures in an infinite-slab reservoir[C]. SPE 100586-MS,2006. doi:10.2118/100586-MS
[26] STEHFEST H. Algorithm 368:Numerical inversion of Laplace transforms[J]. Communications of the ACM,1970, 13(1):47-49. doi:10.1145/361953.361969
[2] RAGHAVAN R, JOSHI S D. Productivity of multiple drainholes or fractured horizontal wells[J]. SPE 21263-PA,1993. doi:10.2118/21263-PA
[3]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. doi:10.7666/d.y1543268LANG Zhaoxin, ZHANG Lihua, CHENG Linsong. Investigation on productivity of fractured horizontal well[J].Journal of University of Petroleum, 1994, 18(2):43-46.doi:10.7666/d.y1543268
[4]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(3):69-71.doi:10.3321/j.issn:0253-2697.2002.02.015NING 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(3):69-71. doi:10.3321/j.issn:-0253-2697.2002.02.015
[5]曾凡辉,郭建春,徐严波,等.压裂水平井产能影响因素[J].石油勘探与开发,2007, 34(4):474-477,482.doi:10.3321/j.issn:1000-0747.2007.04.016ZENG Fanhui, GUO Jianchun, XU Yanbo, et al. Factors affecting production capacity of fractured horizontal wells[J]. Petroleum Exploration and Development,2007,34(4):474-477,482. doi:10.3321/j.issn:1000-0747.2007.04.016
[6]王海涛,张烈辉,贾永禄.压裂水平井压力动态及流量分布规律[J].大庆石油地质与开发,2009, 28(3):84-88. doi:10.3969/j.issn.1000-3754.2009.03.019WANG Haitao, ZHANG Liehui, JIA Yonglu. Pressure performance and flux distribution law of fractured horizontal well[J]. Petroleum Geology and Oilfield Development in Daqing, 2009, 28(3):84-88. doi:10.3969/j.issn.-1000-3754.2009.03.019
[7] BROWN M, OZKAN E, RAGHAVAN R S, et al. Practical solutions for pressure transient responses of fractured horizontal wells in unconventional reservoirs[C]. SPE 125043-MS, 2009. doi:10.2118/125043-MS
[8] MUKHERJEE H, ECONOMIDES M. A parametric comparison of horizontal and vertical well performance[J].SPE 18303-PA,1991. doi:10.2118/18303-PA
[9]曾保全,程林松,罗鹏.基于流线模拟的压裂水平井渗流场及产能特征[J].西南石油大学学报(自然科学版),2010, 32(5):109-113. doi:10.3863/j.issn.1674-5086.2010.05.020ZENG Baoquan, CHENG Linsong, LUO Peng. Flow characteristics and productivity of fractured horizontal wells based on streamline simulation[J]. Journal of Southwest Petroleum University(Science&Technology Edition),2010, 32(5):109-113. doi:10.3863/j.issn. 1674-5086.-2010.05.020
[10]张芮菡,张烈辉,卢晓敏,等.低渗透裂缝性油藏压裂水平井产能动态分析[J].科学技术与工程,2014, 14(16):41-48. doi:10.3969/j.issn.1671-1815.2014.16.009ZHANG Ruihan, ZHANG Liehui, LU Xiaomin, et al. Deliverability analysis of fractured horizontal wells in low permeability fractured reservoir[J]. Science Technology and Engineering, 2014, 14(16):41-48. doi:10.3969/j.-issn.1671-1815.2014.16.009
[11]张德良.基于非结构网格的页岩气藏多级压裂水平井产能动态研究[D].成都:西南石油大学,2016.ZHANG Deliang. The transient productivity research of multi-stage fractured horizontal wells in shale based on unstructured grids[D]. Chengdu:Southwest Petroleum University, 2016.
[12]魏明强,段永刚,方全堂,等.页岩气藏压裂水平井产量递减曲线分析法[J].天然气地球科学,2016, 27(5):898-904. doi:10.11764/j.issn.1672-1926.2016.05.0898WEI Mingqiang, DU AN Yonggang, FANG Quantang, et al. Advanced production decline analytical method for a multi-fractured horizontal well in shale reservoirs[J]. Natural Gas Geoscience, 2016, 27(5):898-904. doi:10.-11764/j.issn.1672-1926.2016.05.0898
[13] WANG Haitao. Performance of multiple fractured horizontal wells in shale gas reservoirs with consideration of multiple mechanisms[J]. Journal of Hydrology, 2014, 510:299-312. doi:10.1016/j.jhydrol.2013.12.019
[14]林旺,林洪富,刘立峰,等.工程参数对致密油藏压裂水平井产能的影响[J].油气地质与采收率,2017, 24(6):120-126. doi:10.3969/j.issn.1009-9603.2017.06.019LIN Wang, LIN Hongfu, LIU Lifeng, et al. Effect of engineering parameters on fractured horizontal well productivity in tight oil reservoirs[J]. Petroleum Geology and Recovery Efficiency, 2017, 24(6):120-126. doi:10.3969/j.-issn.1009-9603.2017.06.019
[15] BROHI I G, MERHAN P D, AGUILERA R. Modeling fractured horizontal wells as dual-porosity composite reservoirs:Application to tight gas, shale gas and tight oil cases[C]. SPE 144057-MS, 2011. doi:10.2118/144057-MS
[16]姚军,殷修杏,樊冬艳,等.低渗透油藏的压裂水平井三线性流试井模型[J].油气井测试,2011,20(5):1-5.doi:10.3969/j.issn.1004-4388.2011.05.001YAO Jun, YIN Xiuxing, FAN Dongyan, et al. Tri-linear flow well test model of fractured horizontal well in low permeability reservoir[J]. Well Testing,2011,20(5):1-5.doi:10.3969/j.issn. 1004-43 88.2011.05.001
[17] STALGOROVA E, MATTAR L. Practical analytical model to simulate production of horizontal wells with branch fractures[C]. SPE 162515-MS, 2012. doi:10.-2118/162515-MS
[18] STALGOROVA K. Analytical model for unconventional multifractured composite systems[C]. SPE 162516-PA,2013. doi:10.2118/162516-PA
[19]孙志宇,蒲春生,罗明良,等.水平井多级脉冲气体加载压裂及产能评价[J].西南石油大学学报(自然科学版),2008,30(5):104-107.doi:10.3863/j.issn.1000-2634.2008.05.023SUN Zhiyu, PU Chunsheng, LUO Mingliang, et al. Multi-pulse gas load fracturing and deliverability evaluation of horizontal well[J]. Journal of Southwest Petroleum University(Science&Technology Edition),2008, 30(5):104-107. doi:10.3863/j.issn.1000-2634.2008.05.023
[20]王强,童敏,武站国,等.致密火山岩气藏压裂水平井产能预测方法[J].西南石油大学学报(自然科学版),2014,36(4):107-115. doi:10.11885/j.issn.1674-5086.-2013.11.26.04WANG Qiang, TONG Min, WU Zhanguo, et al. An unsteady productivity prediction method of multi-fractured horizontal well in tight volcanic rock reservoir[J]. Journal of Southwest Petroleum University(Science&Technology Edition), 2014, 36(4):107-115. doi:10.11885/j.issn.-1674-5086.2013.11.26.04
[21]曾保全,程林松,李春兰,等.特低渗透油藏压裂水平井开发效果评价[J].石油学报,2010, 31(5):791-796.doi:10.7623/syxb201005015ZENG Baoquan,CHENG Linsong,LI Chunlan,et al.Development evaluation of fractured horizontal wells in ultra-low permeability reservoirs[J]. Acta Petrolei Sinica,2010, 31(5):791-796. doi:10.7623/syxb201005015
[22]廖新维,沈平平.现代试井分析[M].北京:石油工业出版社,2002.LIAO Xinwei, SHEN Pingping. Modern well test analysis[M]. Beijing:Petroleum Industry Press, 2002.
[23] CINCO-LEY H, MENG H Z. Pressure transient analysis of wells with finite conductivity vertical fractures in double porosity reservoirs[C]. SPE 18172-MS, 1988. doi:10.-2118/18172-MS
[24] RAGHAVAN R S, CHEN C C, AGARWAL B. An analysis of horizontal wells intercepted by multiple fractures[C].SPE 27652-PA, 1997. doi:10.2118/27652-PA
[25] CRAIG D P, BLASINGAME T A. Constant-rate drawdown solutions derived for multiple arbitrarily oriented uniform-flux, infinite-conductivity, or finite-conductivity fractures in an infinite-slab reservoir[C]. SPE 100586-MS,2006. doi:10.2118/100586-MS
[26] STEHFEST H. Algorithm 368:Numerical inversion of Laplace transforms[J]. Communications of the ACM,1970, 13(1):47-49. doi:10.1145/361953.361969