页岩气储层压裂水平井非线性渗流模型
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摘要
水平井+体积压裂技术已经成为目前高效高速开发页岩气藏的主要技术手段。针对页岩储层存在的吸附扩散效应和应力敏感效应以及流体的滑脱效应和高速紊流效应,建立了水平井多级压裂复合渗流模型,并获得了其在Laplace空间的解析解;通过Stefest数值反演和Duhamel原理,得到了考虑井筒储集效应和表皮效应影响下的实空间无因次产量模型,从而绘制了无因次产能模型图版并进行了产能影响因素敏感性分析。根据实践应用结果显示,模型能够预测水平井产量并具有更高的预测精度。研究结果表明:页岩气藏压裂水平井产能可划分为三个渗流区域和五个流动阶段,前期由裂缝线性流占主导地位,产量高但递减速度快;中期由天然裂缝供气,是处于基质和裂缝供气的过渡阶段;后期由基质线性流占主导地位,产量低但递减缓慢。启动压力梯度对水平井前期产量影响较大,而储层应力敏感性对后期产量影响较大。模型为认识体积压裂水平井复杂渗流规律、预测页岩气藏压裂水平井产能、评价压裂效果以及优化水平井压裂参数提供了有效的科学依据和理论支撑。
The technology of multi-fractured horizontal well is the one of the most effective and efficient methods to develop shale gas reservoir. Referring to absorption/diffusion effect,stress sensitivity effect in shale formation and slippage effect,a compound flow model of multi-fractured horizontal well was built and its analytic solution in Laplace space was also obtained. Using Stefest numerical reversion technology and Duhamel principle,taking wellbore storage and skin effect into consideration,a non-dimensional productivity model in real space was built and its solution was resolved,thus drawing standard template of non-dimensional productivity model and carrying out sensitive analysis of influencing factors. According to the consequences of realistic application,this model can predict real productivity of a multi-fractured horizontal well and the forecast accuracy is high enough to solve real problem.The results show that production of multi-fractured horizontal well in shale gas can be divided into three seepage zones and five stages. In the first stage when linear flow in artificial fractures is dominant,production relatively high whereas the decline rate is also high; in the middle stage when linear flow in nature fractures or micro-fractures is dominant,production and decline rate are both decreasing; in the final stage when linear flow in matrix is predominant,production period long with low production rate. Foundation for learning complicated seepage law of multifractured horizontal well was built,forecasting productivity of multi-fractured horizontal well in shale gas reservoir,revaluating result of artificial fracturing and optimizing fracturing parameters of horizontal well.
The technology of multi-fractured horizontal well is the one of the most effective and efficient methods to develop shale gas reservoir. Referring to absorption/diffusion effect,stress sensitivity effect in shale formation and slippage effect,a compound flow model of multi-fractured horizontal well was built and its analytic solution in Laplace space was also obtained. Using Stefest numerical reversion technology and Duhamel principle,taking wellbore storage and skin effect into consideration,a non-dimensional productivity model in real space was built and its solution was resolved,thus drawing standard template of non-dimensional productivity model and carrying out sensitive analysis of influencing factors. According to the consequences of realistic application,this model can predict real productivity of a multi-fractured horizontal well and the forecast accuracy is high enough to solve real problem.The results show that production of multi-fractured horizontal well in shale gas can be divided into three seepage zones and five stages. In the first stage when linear flow in artificial fractures is dominant,production relatively high whereas the decline rate is also high; in the middle stage when linear flow in nature fractures or micro-fractures is dominant,production and decline rate are both decreasing; in the final stage when linear flow in matrix is predominant,production period long with low production rate. Foundation for learning complicated seepage law of multifractured horizontal well was built,forecasting productivity of multi-fractured horizontal well in shale gas reservoir,revaluating result of artificial fracturing and optimizing fracturing parameters of horizontal well.
引文
1郭小哲,周长沙.页岩气储层压裂水平井三线性渗流模型研究[J].西南石油大学学报(自然科学版),2016,38(2):86-94Guo Xiaozhe,Zhou Changsha.The trilinear seepage model for fractured horizontal well in shale gas reservoir[J].Journal of Southwest Petroleum University(Science&Technology Edition),2016,38(2):86-94
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4沈瑞,胡志明,高树生,等.页岩基质中甲烷传质输运产能计算模型[J].科学技术与工程,2017,17(4):55-59Shen Rui,Hu Zhiming,Gao Shusheng,et al.Methane production and mass transport calculation model in shale matrix[J].Science Technology and Engineering,2017,17(4):55-59
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6 Cui X,Bustin A M M,Bustin R M.Measurement of gas permeability and diffusivity of tight reservoir rocks:different approaches and their applications[J].Geofluids,2009,9(3):208-223
7 Bear J.Dynamics of fluids in porous media[M].New York:Dover Publications,1988
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9吴克柳,李相方,陈掌星.页岩气纳米孔气体传输模型.石油学报,2015,36(7):837-889Wu Keliu,Li Xiangfang,Cheng Zhangxing.Micro-scale effects of gas transport in organic nanopores of shale gas reservoirs[J].Natural Gas Industry,2015,36(7):837-889
10 Klinkenberg L J.The permeability of porous media to liquids and gases[J].Socar Proceedings,1941,2(2):200-213
11杨峰,宁正福,胡昌蓬,等.页岩储层微观孔隙结构特征[J].石油学报,2013,34(2):301-311Yang Feng,Ning Zhengfu,Hu Changpeng,et al.Characterization of microscopic pore structures in shale reservoirs[J].Acta Petroleum Sinica,2013,34(2):301-311
12韩辉,李大华,马勇,等.四川盆地东北地区下寒武统海相页岩气成因:来自气体组分和碳同位素组成的启示[J].石油学报,2013,34(3):453-459Han Hui,Li Dahua,Ma Yong,et al.The origin of marine shale gas in the northeastern Sichuan Basin,China:Implications from chemical composition and stable carbon isotope of desorbed gas[J].Acta Petroleum Sinica,2013,34(3):453-459
13姚军,李爱芬.单孔隙介质渗流问题的统一解[J].水动力学研究与进展(A辑),1999,14(3):317-324Yao Jun,Li Aifen.General solutions for seepage flow in single porous medium[J].Journal of Hydrodynamics(Ser A),1999,14(3):317-324
14同登科,陈钦雷.关于Laplace数值反演Stefest方法的一点注记[J].石油学报,2001,22(6):91-92Tong Dengke,Chen Qinlei.A note of Laplace numerical inversion for Stefest model[J].Acta Petrolei Sinica,2001,22(6):91-92
15 Stehfest H.Remark on algorithm 368 numerical inversion of Laplace transforms[J].Communications of ACM,1970,13(10):624-625
16王志刚.涪陵页岩气藏勘探开发重大突破与启示[J].石油与天然气地质,2015,36(1):1-6Wang Zhigang.Breakthrough of fueling shale gas exploration and development and its application[J].Oil&Gas Geology,2015,36(1):1-6
17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):107-115Wang 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
18林拓,张金川,李博,等.湘西北常页1井下寒武统牛蹄塘组页岩气聚集条件及含气特征[J].石油学报,2014,35(5):839-846Lin Tuo,Zhang Jinchuan,Li Bo,et al.Shale gas accumulation conditions and gas-bearing properties of the lower Cambrian Niutitang formation in well Changeye 1,northwestern Hunan[J].Acta Petroleum Sinica,2014,35(5):839-846
19袁俊亮,邓金根,张定宇,等.页岩气储层可压裂性评价技术[J].石油学报,2013,34(3):523-528Yuan Junliange,Deng Jingen,Zhang Dingyu,et al.Fracability evaluation of shale-gas reservoirs[J].Acta Petroleum Sinica,2013,34(3):523-528
2 EIA.Annual energy outlook 2013 early release overview[J/OL].[2012-12-05]https://www.eia.gov/outlooks/archive/aeo13/
3郭伟.四川威远区块页岩水平井产量差异分析[J].科学技术与工程,2018,18(1):228-233Guo Wei.Differentiation analysis on shale gas production of the horizontal wells in Sichuan Block[J].Science Technology and Engineering,2018,18(1):228-233
4沈瑞,胡志明,高树生,等.页岩基质中甲烷传质输运产能计算模型[J].科学技术与工程,2017,17(4):55-59Shen Rui,Hu Zhiming,Gao Shusheng,et al.Methane production and mass transport calculation model in shale matrix[J].Science Technology and Engineering,2017,17(4):55-59
5 Lee S T,Brockenbrough J R.A new approximate analytic solution for finite-conductivity vertical fractures[J].SPE Formation Evaluation,1986,1(1):75-88
6 Cui X,Bustin A M M,Bustin R M.Measurement of gas permeability and diffusivity of tight reservoir rocks:different approaches and their applications[J].Geofluids,2009,9(3):208-223
7 Bear J.Dynamics of fluids in porous media[M].New York:Dover Publications,1988
8葛洪魁,申颖浩,宋岩,等.页岩纳米孔隙气体流动的滑脱效应[J].天然气工业,2014,34(7):46-54Ge Hongkui,Shen Yinghao,Song Yan,et al.Slippage effect of shale gas flow in nanoscale pores[J].Natural Gas Industry,2014,34(7):46-54
9吴克柳,李相方,陈掌星.页岩气纳米孔气体传输模型.石油学报,2015,36(7):837-889Wu Keliu,Li Xiangfang,Cheng Zhangxing.Micro-scale effects of gas transport in organic nanopores of shale gas reservoirs[J].Natural Gas Industry,2015,36(7):837-889
10 Klinkenberg L J.The permeability of porous media to liquids and gases[J].Socar Proceedings,1941,2(2):200-213
11杨峰,宁正福,胡昌蓬,等.页岩储层微观孔隙结构特征[J].石油学报,2013,34(2):301-311Yang Feng,Ning Zhengfu,Hu Changpeng,et al.Characterization of microscopic pore structures in shale reservoirs[J].Acta Petroleum Sinica,2013,34(2):301-311
12韩辉,李大华,马勇,等.四川盆地东北地区下寒武统海相页岩气成因:来自气体组分和碳同位素组成的启示[J].石油学报,2013,34(3):453-459Han Hui,Li Dahua,Ma Yong,et al.The origin of marine shale gas in the northeastern Sichuan Basin,China:Implications from chemical composition and stable carbon isotope of desorbed gas[J].Acta Petroleum Sinica,2013,34(3):453-459
13姚军,李爱芬.单孔隙介质渗流问题的统一解[J].水动力学研究与进展(A辑),1999,14(3):317-324Yao Jun,Li Aifen.General solutions for seepage flow in single porous medium[J].Journal of Hydrodynamics(Ser A),1999,14(3):317-324
14同登科,陈钦雷.关于Laplace数值反演Stefest方法的一点注记[J].石油学报,2001,22(6):91-92Tong Dengke,Chen Qinlei.A note of Laplace numerical inversion for Stefest model[J].Acta Petrolei Sinica,2001,22(6):91-92
15 Stehfest H.Remark on algorithm 368 numerical inversion of Laplace transforms[J].Communications of ACM,1970,13(10):624-625
16王志刚.涪陵页岩气藏勘探开发重大突破与启示[J].石油与天然气地质,2015,36(1):1-6Wang Zhigang.Breakthrough of fueling shale gas exploration and development and its application[J].Oil&Gas Geology,2015,36(1):1-6
17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):107-115Wang 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
18林拓,张金川,李博,等.湘西北常页1井下寒武统牛蹄塘组页岩气聚集条件及含气特征[J].石油学报,2014,35(5):839-846Lin Tuo,Zhang Jinchuan,Li Bo,et al.Shale gas accumulation conditions and gas-bearing properties of the lower Cambrian Niutitang formation in well Changeye 1,northwestern Hunan[J].Acta Petroleum Sinica,2014,35(5):839-846
19袁俊亮,邓金根,张定宇,等.页岩气储层可压裂性评价技术[J].石油学报,2013,34(3):523-528Yuan Junliange,Deng Jingen,Zhang Dingyu,et al.Fracability evaluation of shale-gas reservoirs[J].Acta Petroleum Sinica,2013,34(3):523-528