基于最优裂缝导流能力的水平井压裂后生产指数预测新方法A new prediction method for postfracturing productivity index of horizontal well based on optimal fracture conductivity
纪国法,王晓燕,南晨阳,刘文涛,刘进
JI Guofa,WANG Xiaoyan,NAN Chenyang,LIU Wentao,LIU Jin
摘要(Abstract):
生产指数是水平井压裂后生产能力评价的重要指标,目前非常规油气水平井压裂后产能预测方法较复杂,参数较多,需进一步优化设计。基于统一压裂设计理论的支撑剂指数法,借用支撑裂缝流动效率优化无因次裂缝导流能力及无因次生产指数,采用多元线性回归方法建立了水平井长度、裂缝半长、裂缝条数、井控边界、储层厚度5种因素影响下的最优无因次裂缝导流能力及无因次生产指数计算模型。结果表明:利用新建模型回归的最优无因次裂缝导流能力多元线性方程决定系数R2为0.933,回归的无因次生产指数多元线性方程决定系数R2为0.980,平均相对误差均小于5%,与传统预测方法相比,精度有了明显的提高。敏感性分析结果表明,生产指数与水平井长度、裂缝条数、裂缝半长和储层厚度呈正相关,与矩形渗流区域长度呈负相关,其中与裂缝条数的关联性最强。研究成果对快速实现非常规油气水平井压裂后产能准确预测、经济评价和施工参数优化都具有重要意义。
Productivity index is an important index for evaluating postfracturing productivity of horizontal wells. Current methods of postfracturing productivity prediction for unconventional oil and gas horizontal wells are complex with many parameters and need further optimization. Based on proppant index method of unified fracture design theory, dimensionless fracture conductivity and dimensionless productivity index are optimized with the help of propped fracture flow efficiency, and the optimal dimensionless fracture conductivity and dimensionless production index calculation model influenced by 5 factors of horizontal well length, fracture half-length, number of fractures, well controlled boundary and reservoir thickness is established by using multiple linear regression method. The results show that new-established model in this paper gets regressed determination coefficient R2 =0.933 of multi-linear equation of optimal dimensionless fracture conductivity, and determination coefficient R2=0.980 of multi-linear equation of regression dimensionless productivity index, with average relative error of <5%, and compared with traditional prediction methods,the accuracy is improved obviously. Sensitivity analysis shows that productivity index is positively correlated with the length of horizontal wells, the number of fractures, half-length of fractures and reservoir thickness, and negatively correlated with the length of rectangular seepage area, with the most correlation with the number of fractures. The research provides much significance for rapid realization of accurate productivity prediction, economic evaluation and operation parameters optimization of unconventional oil and gas horizontal wells after fracturing.
关键词(KeyWords):
水平井;分段压裂;裂缝导流能力;统一压裂设计;生产指数
horizontal well;multi-stage fracturing;fracture conductivity;unified fracture design;productivity index
基金项目(Foundation): 国家自然科学基金项目“基于分形理论及多尺度方法的页岩体积改造压裂液滤失机理研究”(51804042);; 油气资源勘探技术教育部重点实验室(长江大学)青年创新团队项目“页岩气水平井重复压裂关键技术”(PI2021-04);; 非常规油气省部共建创新中心(长江大学)开放基金项目“考虑页岩弱结构面的人工裂缝穿层延展机理研究”(UOG2022-38)
作者(Author):
纪国法,王晓燕,南晨阳,刘文涛,刘进
JI Guofa,WANG Xiaoyan,NAN Chenyang,LIU Wentao,LIU Jin
DOI: 10.19597/j.issn.1000-3754.202211044
参考文献(References):
- [1]杨智,邹才能.论常规-非常规油气有序“共生富集”:兼论常规-非常规油气地质学理论技术[J].地质学报,2022, 96(5):1635-1653.YANG Zhi, ZOU Caineng. Orderly “symbiotic enrichment” of conventional&unconventional oil and gas:Discussion on theory and technology of conventional&unconventional petroleum geology[J]. Acta Geologica Sinica,2022,96(5):1635-1653.
- [2] KANFAR M S,WATTENBARGER R A. Comparison of empirical decline curve methods for shale wells[R]. SPE 162648,2012.
- [3] RUSHING J A., PEREGO A D, SULLIVAN R B, et al. Estimating reserves in tight gas sands at HP/HT reservoir conditions:Use and misuse of an arps decline curve methodology[R]. SPE109625,2007.
- [4]李浩楠,师耀利,姚振华,等.玛18井区低渗透砂砾岩油藏水平井优化设计及产能预测[J].特种油气藏,2021,28(6):83-90.LI Haonan,SHI Yaoli,YAO Zhenhua,et al. Design optimization and productivity prediction of horizontal wells in low-permeability conglomerate reservoir in Well Block Ma18[J]. Special Oil&Gas Reservoirs,2021,28(6):83-90.
- [5] YU W,TAN X,ZUO L,et al. A new probabilistic approach for uncertainty quantification in well performance of shale gas reservoirs[J]. SPE Journal,2016,21(6):2038-2048.
- [6] KUPPE F,SETTARI A. A practical method for determining the productivity of multi-fractured horizontal wells[J]. Journal of Canadian Petroleum Technology,1998,37(10):68-81.
- [7]贾成业,贾爱林,何东博,等.页岩气水平井产量影响因素分析[J].天然气工业,2017,37(4):80-88.JIA Chengye,JIA Ailin,HE Dongbo,et al. Key factors influencing shale gas horizontal well production[J]. Natural Gas Industry,2017,37(4):80-88.
- [8]金萍,王献,张尚明,等.致密砂岩油藏高速通道压裂裂缝导流能力影响因素分析[J].断块油气田,2022,29(2):234-238.JIN Ping,WANG Xian,ZHANG Shangming,et al. Influencing factors of fracture conductivity in high-speed channel fracturing in tight sandstone reservoir[J]. Fault-Block Oil&Gas Field,2022,29(2):234-238.
- [9] VALKO P, ECONOMIDES M J. Hydraulic fracture mechanics[M]. Chichester:John Wiley&Sons Inc,1995.
- [10] BELLARBY J. Well completion design[M]. Amsterdam:Elsevier Science,2009.
- [11]杨兆中,廖梓佳,李小刚,等.非均布导流下页岩气藏压裂水平井产量模拟[J].西南石油大学学报(自然科学版),2021,43(3):93-100.YANG Zhaozhong,LIAO Zijia,LI Xiaogang,et al. Production simulation of fractured horizontal well with non-uniform space distribution of fracture conductivity in shale gas reservoir[J]. Journal of Southwest Petroleum University(Science&Technology Edition),2021,43(3):93-100.
- [12] BENNETT C O,ROSATO N D,REYNOLDS A C,et al. Influence of fracture heterogeneity and wing length on the response of vertically fractured wells[J]. Society of Petroleum Engineers Journal,1983,23(2):219-230.
- [13]任勇,郭建春,赵金洲,等.压裂井裂缝导流能力研究[J].河南石油,2005,19(1):46-48.REN Yong, GUO Jianchun, ZHAO Jinzhou, et al. Study on fracture conductivity of fractured wells[J]. Henan Petroleum,2005,19(1):46-48.
- [14]牟珍宝,樊太亮.圆形封闭油藏变导流垂直裂缝井非稳态渗流数学模型[J].油气地质与采收率,2006,13(6):66-69.MU Zhenbao,FAN Tailiang. Mathematical model with un-steadystate filtering flow of vertically fractured well with varying conductivity for closed circle oil reservoir[J]. Petroleum Geology and Recovery Efficiency,2006,13(6):66-69.
- [15]张晓亮,李娣,孙君书,等.低渗透油藏压裂井产能分析[J].科技导报,2011,29(19):58-61.ZHANG Xiaoliang, LI Di, SUN Junshu, et al. Fractured well productivity of low permeability reservoir[J]. Science&Technology Review,2011,29(19):58-61.
- [16]李准,吴晓东,韩国庆,等.考虑裂缝导流能力时效性的多级压裂水平井产能半解析模型[J].石油钻采工艺,2019,41(3):354-362.LI Zhun,WU Xiaodong,HAN Guoqing,et al. Semi-analytical model of multi-stage fractured horizontal well productivity considering time-dependent fracture conductivity[J]. Oil Drilling&Production Technology,2019,41(3):354-362.
- [17]韩珊,车明光,苏旺,等.四川盆地威远区块页岩气单井产量预测方法及应用[J].特种油气藏,2022, 29(6):141-149.HAN Shan,CHE Mingguang,SU Wang,et al. Prediction method and application of single shale gas well production in Weiyuan Block, Sichuan Basin[J]. Special Oil&Gas Reservoirs,2022,29(6):141-149.
- [18]姜瑞忠,徐建春,傅建斌.致密油藏多级压裂水平井数值模拟及应用[J].西南石油大学学报(自然科学版),2015,37(3):45-52.JIANG Ruizhong, XU Jianchun, FU Jianbin. Multistage fractured horizontal well numerical simulation and application for tight oil reservoir[J]. Journal of Southwest Petroleum University(Science&Technology Edition),2015,37(3):45-52.
- [19] MIRZA T B,SAMI A,MUZAMMIL H R. Productivity increase estimation for multi stage fracturing in horizontal wells for tight oil reservoirs[R]. SPE 178030,2015.
- [20]董鹏,陈志明,于伟.压裂后页岩油藏多裂缝直井产能模型:以鄂尔多斯盆地页岩油井为例[J].大庆石油地质与开发,2022,41(1):155-165.DONG Peng, CHEN Zhiming, YU Wei. Study on productivity model for multiple-fracture vertical well in shale oil reservoirs after fractured:A case of shale oil wells in Ordos Basin[J].Petroleum Geology&Oilfield Development in Daqing,2022,41(1):155-165.
- [21]孙召勃,贾晓飞,杨馥榕.考虑摩阻损失的稠油油藏水平井产能计算新方法[J].非常规油气,2022,9(6):94-99.SUN Zhaobo, JIA Xiaofei, YANG Furong. A new calculation method of horizontal well productivity in heavy oil reservoir considering friction loss[J]. Unconventional Oil&Gas, 2022, 9(6):94-99.
- [22]赵红兵.致密油藏体积压裂水平井产能主控因素评判技术研究[D].西安:西安石油大学,2021.ZHAO Hongbing. Study on the evaluation technology of main controlling factors for productivity of volume fracturing horizontal wells in tight reservoirs[D]. Xi’an:Xi’an Shiyou University,2021.
- [23]马亮亮.非均质致密油藏压裂水平井产能预测模型[J].大庆石油地质与开发,2022,41(4):168-174.MA Liangliang. Productivity prediction model for fractured horizontal well in heterogeneous tight oil reservoirs[J]. Petroleum Geology&Oilfield Development in Daqing, 2022, 41(4):168-174.
- [24] ECONOMIDES M, OLIGNEY R, VALKóP. Unified fracture design:Bridging the gap between theory and practice[D].Alvin:Orsa Press,2002.
- [25] WEI Y, ECONOMIDES M J. Transverse hydraulic fractures from a horizontal well[R]. SPE 94671,2005.
- [26] MUKHERJEE H,ECONOMIDES M J. A parametric comparison of horizontal and vertical well performance[J]. SPE Formation Evaluation,1991,6(2):209-216.
- [27] GAO H,HU Y,DUAN L C,et al. An analytical solution of the pseudosteady state productivity index for the fracture geometry optimization of fractured wells[J].Energies,2019,12(1):176.
- [28] MAO D,MILLER D S,KARANIKAS J M,et al. Influence of finite hydraulic-fracture conductivity on unconventional hydrocarbon recovery with horizontal wells[J]. SPE Journal,2017,22(6):1790-1807.
- [29]胥元刚,张琪.变裂缝导流能力下水力压裂整体优化设计方法[J].大庆石油地质与开发,2000,19(2):40-42,54.XU Yuangang,ZHANG Qi. Overall optimizing designation method for hydraulic fracturing under variable fracture diverting capacity[J]. Petroleum Geology&Oilfield Development in Daqing,2000,19(2):40-42,54.
- [30] HUANG J,SAFARI R,PEREZ O,et al. Reservoir depletioninduced proppant embedment and dynamic fracture closure[R].SPE 195135,2019.
- [31]苏映宏,吴忠维,崔传智,等.水力压裂支撑裂缝导流能力计算与分析[J].大庆石油地质与开发,2021,40(6):62-71.SU Yinghong,WU Zhongwei,CUI Chuanzhi,et al. Calculation and analysis of the propped fracture conductivity created by hydraulic fracturing[J].Petroleum Geology&Oilfield Development in Daqing,2021,40(6):62-71.
- [32] MONTGOMERY C T,STEANSON R E. Proppant selection:The key to successful fracture stimulation[J]. Journal of Petroleum Technology,1985,37(12):2163-2172.
- [33] SUN H D,OUYANG W P,ZHANG M,et al. Advanced production decline analysis of tight gas wells with variable fracture conductivity[J]. Petroleum Exploration and Development, 2018,45(3):472-480.
- [34] ZHANG L,ZHOU F,MOU J,et al. A new method to improve long-term fracture conductivity in acid fracturing under high closure stress[J]. Journal of Petroleum Science and Engineering,2018,171:760-770.
- [35] PEARSON C M, GREEN C A, MCGILL M, et al. Extendedtime conductivity testing of proppants used for multi-stage horizontal completions[R]. SPE 205272,2022.
- [36]曹磊.潜油电泵运行工况监控技术研究[D].大庆:东北石油大学,2018.CAO Lei. Research on monitoring technology of operating condition of electrical submersible pump[D]. Daqing:Northeast Petroleum University,2018.
- 水平井
- 分段压裂
- 裂缝导流能力
- 统一压裂设计
- 生产指数
horizontal well - multi-stage fracturing
- fracture conductivity
- unified fracture design
- productivity index