三维各向异性油藏水平井产能新公式
|
摘要
目前常用的水平井产能预测公式未考虑实际油藏的三维各向异性特点及水平井渗流中典型的平面线性流特征,因此,产能预测结果往往过于乐观。针对此问题,通过坐标变换将三维各向异性油藏转换为等效的各向同性油藏,在此基础上,从水平井典型渗流特征出发,将油藏内流动区域划分为外部平面径向流、中间平面线性流以及内部垂向径向流3个区域,利用水电相似原理和等值渗流阻力方法,推导出三维各向异性油藏综合形式水平井产能新公式。与常规水平井产能公式对比发现:随着水平井长度的增加,平面线性流的渗流阻力及对产能的影响逐渐增大;平面各向异性对水平井产能影响显著,其变化规律受水平井与油藏主渗透率方向夹角的控制;水平井产能随着油藏垂直渗透率与平面渗透率比值的增大而增加,随着水平井与油藏主渗透率方向夹角的增加而增加。实例应用表明新公式预测精度大幅提高,误差仅为3%,可以用于指导水平井产能预测、水平井长度和方位优化。
The three-dimensional anisotropy of actual reservoirs and the typical linear flow characteristics in horizontalwell seepage are not considered in commonly used horizontal well productivity prediction formula,and thus the productivityprediction results tend to be optimistic. Aiming at solving this problem,the three-dimensional anisotropic reservoir is con-verted into an equivalent isotropic reservoir through coordinate transformation. Then the flow region in the reservoir can bedivided into external region with plane radial flow,middle region with plane linear flow and internal region with vertical ra-dial flow based on typical seepage characteristics of the horizontal wells. A new comprehensive formula for calculating theproductivity of horizontal wells in a three-dimensional anisotropic reservoir was derived by using the hydropower similarityprinciple and the equivalent flow resistance method. Comparison with the conventional horizontal well productivity formulashows that the flow resistance of the plane linear flow and its influence on the productivity gradually increase with the in-crease of the length of the horizontal well;the plane anisotropy has significant influence on the productivity of the horizontalwell,and its changing law is controlled by the angle between horizontal well and the main permeability direction of the res-ervoir;the productivity of the horizontal well increases with the increase of the vertical and horizontal permeability ratio,and increases with the increase of the angle between the horizontal well and the main permeability direction of the reservoir.The application shows that the new formula has higher prediction accuracy with an average deviation less than 3%,and itcan be used to guide horizontal well productivity prediction and optimization of horizontal section length and azimuth.
The three-dimensional anisotropy of actual reservoirs and the typical linear flow characteristics in horizontalwell seepage are not considered in commonly used horizontal well productivity prediction formula,and thus the productivityprediction results tend to be optimistic. Aiming at solving this problem,the three-dimensional anisotropic reservoir is con-verted into an equivalent isotropic reservoir through coordinate transformation. Then the flow region in the reservoir can bedivided into external region with plane radial flow,middle region with plane linear flow and internal region with vertical ra-dial flow based on typical seepage characteristics of the horizontal wells. A new comprehensive formula for calculating theproductivity of horizontal wells in a three-dimensional anisotropic reservoir was derived by using the hydropower similarityprinciple and the equivalent flow resistance method. Comparison with the conventional horizontal well productivity formulashows that the flow resistance of the plane linear flow and its influence on the productivity gradually increase with the in-crease of the length of the horizontal well;the plane anisotropy has significant influence on the productivity of the horizontalwell,and its changing law is controlled by the angle between horizontal well and the main permeability direction of the res-ervoir;the productivity of the horizontal well increases with the increase of the vertical and horizontal permeability ratio,and increases with the increase of the angle between the horizontal well and the main permeability direction of the reservoir.The application shows that the new formula has higher prediction accuracy with an average deviation less than 3%,and itcan be used to guide horizontal well productivity prediction and optimization of horizontal section length and azimuth.
引文
[1]吴月先,钟水清,徐永高,等.中国水平井技术实力现状及发展趋势[J].石油矿场机械,2008,37(3):33-36.WU Yuexian,ZHONG Shuiqing,XU Yonggao,et al.Present condition of horizontal well technique strength and its development trend in China[J].Oil Field Equipment,2008,37(3):33-36.
[2]孙玉平,陆家亮,巩玉政,等.我国气藏水平井技术应用综述[J].天然气技术与经济,2011,5(1):24-27.SUN Yuping,LU Jialiang,GONG Yuzheng,et al.Review and suggestion on application of horizontal well technology to gas reservoirs in China[J].Natural Gas Technology and Economy,2011,5(1):24-27.
[3]张芨强,王雯娟,马帅,等.薄层与厚层油藏水平井产能计算方法[J].油气地质与采收率,2018,25(1):77-81.ZHANG Jiqiang,WANG Wenjuan,MA Shuai,et al.Derivation of productivity formula for horizontal wells in thin and thick reservoirs[J].Petroleum Geology and Recovery Efficiency,2018,25(1):77-81.
[4]吴月先.中国陆上油气水平井技术成效及新思考[J].石油钻探技术,2007,35(2):83-86.WU Yuexian.Discussions about China onshore horizontal drilling technology[J].Petroleum Drilling Techniques,2007,35(2):83-86.
[5]陈元千.双水平井注蒸汽开采重质油藏GASD产能计算公式的推导与对比[J].油气地质与采收率,2018,25(3):77-81.CHEN Yuanqian.Derivation and comparison of the GASD productivity calculation formula of steam flooding in dual-horizontal well for recovery of heavy oil reservoirs[J].Petroleum Geology and Recovery Efficiency,2018,25(3):77-81.
[6]袁淋,李晓平,张璐,等.水平井稳态产能公式对比与分析[J].岩性油气藏,2013,25(6):127-132.YUAN Lin,LI Xiaoping,ZHANG Lu,et al.Analysis and correlation of steady-state productivity formulas for horizontal wells[J].Lithologic Reservoirs,2013,25(6):127-132.
[7]JOSHI S D.Augmentation of well production using slant and horizontal wells[R].SPE 15375,1986.
[8]GIGER F M,REISS L H,JOURDAN A P.The reservoir engineering aspects of horizontal drilling[R].SPE 13024,1984.
[9]BORISOV J P.Oil production using horizontal and multiple deviationwells[M].Oklahoma:The R&D Library Translation,1984.
[10]陈元千.水平井产量公式的推导与对比[J].新疆石油地质,2008,29(1):68-71.CHEN Yuanqian.Derivation and correlation of production rate formula for horizontal well[J].Xinjiang Petroleum Geology,2008,29(1):68-71.
[11]窦宏恩.预测水平井产能的一种新方法[J].石油钻采工艺,1996,18(1):76-81.DOU Hong’en.A new method of predicting the productivity of horizontal well[J].Oil Drilling&Production Technology,1996,18(1):76-81.
[12]李璗,王卫红,王爱华.水平井产量公式分析[J].石油勘探与开发,1997,24(5):76-79.LI Dang,WANG Weihong,WANG Aihua.Analysis of productivity formulae of horizontal well[J].Petroleum Exploration and Development,1997,24(5):76-79.
[13]郭肖,陈路原,杜志敏.关于Joshi水平井产能公式的讨论[J].西南石油大学学报:自然科学版,2003,25(2):41-43.GUO Xiao,CHEN Luyuan,DU Zhimin.Discussion about Joshi’s horizontal well productivity formula[J].Journal of Southwest Petroleum Institute:Editon of Natural Sciences,2003,25(2):41-43.
[14]KUCHUK F J,GOODE P A,BRICE B W,et al.Pressure-transient analysis for horizontal wells[J].Journal of Petroleum Technology,1990,42(8):974-1 031.
[15]OZKAN E,RAGHAVAN R,JOSHI S D.Horizontal well pressure analysis[J].SPE Formation Evaluation,1989,4(4):567-575.
[16]陈元千,郭二鹏,彭子璇,等.各向异性断块油藏水平井产能公式的推导[J].石油学报,2017,38(12):1 420-1 424.CHEN Yuanqian,GUO Erpeng,PENG Zixuan,et al.Derivation of productivity formulas for horizontal wells in anisotropic faultblock reservoirs[J].Acta Petrolei Sinica,2017,38(12):1 420-1 424.
[17]李传亮,林兴,朱苏阳.长水平井的产能公式[J].新疆石油地质,2014,35(3):361-364.LI Chuanliang,LIN Xing,ZHU Suyang.A production rate equation for long horizontal wells[J].Xinjiang Petroleum Geology,2014,35(3):361-364.
[18]汪益宁,李洪,曹淑慧,等.各向异性底水油藏长水平井产能公式[J].油气地质与采收率,2016,23(4):108-111,116.WANG Yining,LI Hong,CAO Shuhui,et al.Productivity formula of long horizontal well in anisotropic bottom-water reservoir[J].Petroleum Geology and Recovery Efficiency,2016,23(4):108-111,116.
[19]李传亮,朱苏阳,董凤玲.综合形式的水平井产量公式[J].新疆石油地质,2016,37(3):311-313.LI Chuanliang,ZHU Suyang,DONG Fengling.A comprehensive production formula for horizontal wells[J].Xinjiang Petroleum Geology,2016,37(3):311-313.
[20]陈元千,邹存友.考虑各向异性和偏心距影响的水平井产量公式推导、对比与应用(为庆祝《新疆石油地质》创刊30周年而作)[J].新疆石油地质,2009,30(4):486-489.CHEN Yuanqian,ZOU Cunyou.Derivation,comparison and application of horizontal well production formula considering anisotropy and eccentricity effects[J].Xinjiang Petroleum Geology,2009,30(4):486-489.
[21]陈元千,郭二鹏.对Joshi各向异性水平井产量公式的质疑、推导与对比[J].新疆石油地质,2008,29(3):331-334.CHEN Yuanqian,GUO Erpeng.Query,derivation and comparison about Joshi’s production rate formula for horizontal well in anisotropic reservoir[J].Xinjiang Petroleum Geology,2008,29(3):331-334.
[22]吕成远,王锐,赵淑霞,等.低渗透油藏CO2非混相驱替特征曲线研究[J].油气地质与采收率,2017,24(5):111-114.LüChengyuan,WANG Rui,ZHAO Shuxia,et al.Study on displacement characteristic curve in CO2immiscible flooding for low permeability reservoirs[J].Petroleum Geology and Recovery Efficiency,2017,24(5):111-114.
[23]祝浪涛,廖新维,陈志明,等.应力敏感性低渗透油藏CO2混相驱试井模型[J].油气地质与采收率,2017,24(4):88-93.ZHU Langtao,LIAO Xinwei,CHEN Zhiming,et al.Well test model of CO2miscible flooding in the low-permeability reservoirs with stress sensitivity[J].Petroleum Geology and Recovery Efficiency,2017,24(4):88-93.
[24]刘月田.各向异性油藏水平井渗流和产能分析[J].石油大学学报:自然科学版,2002,26(4):40-44,47.LIU Yuetian.Analysis on seepage flow and productivity of a horizontal well in an anisotropic reservoir[J].Journal of the University of Petroleum,China:Edition of Natural Science,2002,26(4):40-44,47.
[25]席岩,李军,柳贡慧,等.页岩储层各向异性对套管应力影响敏感性研究[J].特种油气藏,2016,23(6):128-132.XI Yan,LI Jun,LIU Gonghui,et al.Sensitivity study of shale reservoir anisotropy on casing stress[J].Special Oil&Gas Reservoirs,2016,23(6):128-132.
[26]任岚,何易东,赵金洲,等.基于各向异性扩散方程的页岩气井改造体积计算模型[J].大庆石油地质与开发,2017,36(4):153-159.REN Lan,HE Yidong,ZHAO Jinzhou,et al.Calculating model of the shale gas well SRV based on anisotropic diffusion equation[J].Petroleum Geology&Oilfield Development in Daqing,2017,36(4):153-159.
[27]罗晓容,张立宽,雷裕红,等.储层结构非均质性及其在深层油气成藏中的意义[J].中国石油勘探,2016,21(1):28-36.LUO Xiaorong,ZHANG Likuan,LEI Yuhong,et al.Structural heterogeneity of reservoirs and its implication on hydrocarbon accumulation in deep zones[J].China Petroleum Exploration,2016,21(1):28-36.
[28]卢晨刚,张遂安,毛潇潇,等.致密砂岩微观孔隙非均质性定量表征及储层意义:以鄂尔多斯盆地X地区山西组为例[J].石油实验地质,2017,39(4):556-561.LU Chengang,ZHANG Suian,MAO Xiaoxiao,et al.Quantitative characterization of microscopic pore heterogeneity in tight sandstones and its reservoir significance:A case study of the Shanxi Formation in X area,Ordos Basin[J].Petroleum Geology&Experiment,2017,39(4):556-561.
[29]陈元千,郝明强,孙兵,等.水平井产量公式的对比研究[J].新疆石油地质,2012,33(5):566-569.CHEN Yuanqian,HAO Mingqiang,SUN Bing,et al.Comparative study of the production rate formulas for horizontal wells[J].Xinjiang Petroleum Geology,2012,33(5):566-569.
[2]孙玉平,陆家亮,巩玉政,等.我国气藏水平井技术应用综述[J].天然气技术与经济,2011,5(1):24-27.SUN Yuping,LU Jialiang,GONG Yuzheng,et al.Review and suggestion on application of horizontal well technology to gas reservoirs in China[J].Natural Gas Technology and Economy,2011,5(1):24-27.
[3]张芨强,王雯娟,马帅,等.薄层与厚层油藏水平井产能计算方法[J].油气地质与采收率,2018,25(1):77-81.ZHANG Jiqiang,WANG Wenjuan,MA Shuai,et al.Derivation of productivity formula for horizontal wells in thin and thick reservoirs[J].Petroleum Geology and Recovery Efficiency,2018,25(1):77-81.
[4]吴月先.中国陆上油气水平井技术成效及新思考[J].石油钻探技术,2007,35(2):83-86.WU Yuexian.Discussions about China onshore horizontal drilling technology[J].Petroleum Drilling Techniques,2007,35(2):83-86.
[5]陈元千.双水平井注蒸汽开采重质油藏GASD产能计算公式的推导与对比[J].油气地质与采收率,2018,25(3):77-81.CHEN Yuanqian.Derivation and comparison of the GASD productivity calculation formula of steam flooding in dual-horizontal well for recovery of heavy oil reservoirs[J].Petroleum Geology and Recovery Efficiency,2018,25(3):77-81.
[6]袁淋,李晓平,张璐,等.水平井稳态产能公式对比与分析[J].岩性油气藏,2013,25(6):127-132.YUAN Lin,LI Xiaoping,ZHANG Lu,et al.Analysis and correlation of steady-state productivity formulas for horizontal wells[J].Lithologic Reservoirs,2013,25(6):127-132.
[7]JOSHI S D.Augmentation of well production using slant and horizontal wells[R].SPE 15375,1986.
[8]GIGER F M,REISS L H,JOURDAN A P.The reservoir engineering aspects of horizontal drilling[R].SPE 13024,1984.
[9]BORISOV J P.Oil production using horizontal and multiple deviationwells[M].Oklahoma:The R&D Library Translation,1984.
[10]陈元千.水平井产量公式的推导与对比[J].新疆石油地质,2008,29(1):68-71.CHEN Yuanqian.Derivation and correlation of production rate formula for horizontal well[J].Xinjiang Petroleum Geology,2008,29(1):68-71.
[11]窦宏恩.预测水平井产能的一种新方法[J].石油钻采工艺,1996,18(1):76-81.DOU Hong’en.A new method of predicting the productivity of horizontal well[J].Oil Drilling&Production Technology,1996,18(1):76-81.
[12]李璗,王卫红,王爱华.水平井产量公式分析[J].石油勘探与开发,1997,24(5):76-79.LI Dang,WANG Weihong,WANG Aihua.Analysis of productivity formulae of horizontal well[J].Petroleum Exploration and Development,1997,24(5):76-79.
[13]郭肖,陈路原,杜志敏.关于Joshi水平井产能公式的讨论[J].西南石油大学学报:自然科学版,2003,25(2):41-43.GUO Xiao,CHEN Luyuan,DU Zhimin.Discussion about Joshi’s horizontal well productivity formula[J].Journal of Southwest Petroleum Institute:Editon of Natural Sciences,2003,25(2):41-43.
[14]KUCHUK F J,GOODE P A,BRICE B W,et al.Pressure-transient analysis for horizontal wells[J].Journal of Petroleum Technology,1990,42(8):974-1 031.
[15]OZKAN E,RAGHAVAN R,JOSHI S D.Horizontal well pressure analysis[J].SPE Formation Evaluation,1989,4(4):567-575.
[16]陈元千,郭二鹏,彭子璇,等.各向异性断块油藏水平井产能公式的推导[J].石油学报,2017,38(12):1 420-1 424.CHEN Yuanqian,GUO Erpeng,PENG Zixuan,et al.Derivation of productivity formulas for horizontal wells in anisotropic faultblock reservoirs[J].Acta Petrolei Sinica,2017,38(12):1 420-1 424.
[17]李传亮,林兴,朱苏阳.长水平井的产能公式[J].新疆石油地质,2014,35(3):361-364.LI Chuanliang,LIN Xing,ZHU Suyang.A production rate equation for long horizontal wells[J].Xinjiang Petroleum Geology,2014,35(3):361-364.
[18]汪益宁,李洪,曹淑慧,等.各向异性底水油藏长水平井产能公式[J].油气地质与采收率,2016,23(4):108-111,116.WANG Yining,LI Hong,CAO Shuhui,et al.Productivity formula of long horizontal well in anisotropic bottom-water reservoir[J].Petroleum Geology and Recovery Efficiency,2016,23(4):108-111,116.
[19]李传亮,朱苏阳,董凤玲.综合形式的水平井产量公式[J].新疆石油地质,2016,37(3):311-313.LI Chuanliang,ZHU Suyang,DONG Fengling.A comprehensive production formula for horizontal wells[J].Xinjiang Petroleum Geology,2016,37(3):311-313.
[20]陈元千,邹存友.考虑各向异性和偏心距影响的水平井产量公式推导、对比与应用(为庆祝《新疆石油地质》创刊30周年而作)[J].新疆石油地质,2009,30(4):486-489.CHEN Yuanqian,ZOU Cunyou.Derivation,comparison and application of horizontal well production formula considering anisotropy and eccentricity effects[J].Xinjiang Petroleum Geology,2009,30(4):486-489.
[21]陈元千,郭二鹏.对Joshi各向异性水平井产量公式的质疑、推导与对比[J].新疆石油地质,2008,29(3):331-334.CHEN Yuanqian,GUO Erpeng.Query,derivation and comparison about Joshi’s production rate formula for horizontal well in anisotropic reservoir[J].Xinjiang Petroleum Geology,2008,29(3):331-334.
[22]吕成远,王锐,赵淑霞,等.低渗透油藏CO2非混相驱替特征曲线研究[J].油气地质与采收率,2017,24(5):111-114.LüChengyuan,WANG Rui,ZHAO Shuxia,et al.Study on displacement characteristic curve in CO2immiscible flooding for low permeability reservoirs[J].Petroleum Geology and Recovery Efficiency,2017,24(5):111-114.
[23]祝浪涛,廖新维,陈志明,等.应力敏感性低渗透油藏CO2混相驱试井模型[J].油气地质与采收率,2017,24(4):88-93.ZHU Langtao,LIAO Xinwei,CHEN Zhiming,et al.Well test model of CO2miscible flooding in the low-permeability reservoirs with stress sensitivity[J].Petroleum Geology and Recovery Efficiency,2017,24(4):88-93.
[24]刘月田.各向异性油藏水平井渗流和产能分析[J].石油大学学报:自然科学版,2002,26(4):40-44,47.LIU Yuetian.Analysis on seepage flow and productivity of a horizontal well in an anisotropic reservoir[J].Journal of the University of Petroleum,China:Edition of Natural Science,2002,26(4):40-44,47.
[25]席岩,李军,柳贡慧,等.页岩储层各向异性对套管应力影响敏感性研究[J].特种油气藏,2016,23(6):128-132.XI Yan,LI Jun,LIU Gonghui,et al.Sensitivity study of shale reservoir anisotropy on casing stress[J].Special Oil&Gas Reservoirs,2016,23(6):128-132.
[26]任岚,何易东,赵金洲,等.基于各向异性扩散方程的页岩气井改造体积计算模型[J].大庆石油地质与开发,2017,36(4):153-159.REN Lan,HE Yidong,ZHAO Jinzhou,et al.Calculating model of the shale gas well SRV based on anisotropic diffusion equation[J].Petroleum Geology&Oilfield Development in Daqing,2017,36(4):153-159.
[27]罗晓容,张立宽,雷裕红,等.储层结构非均质性及其在深层油气成藏中的意义[J].中国石油勘探,2016,21(1):28-36.LUO Xiaorong,ZHANG Likuan,LEI Yuhong,et al.Structural heterogeneity of reservoirs and its implication on hydrocarbon accumulation in deep zones[J].China Petroleum Exploration,2016,21(1):28-36.
[28]卢晨刚,张遂安,毛潇潇,等.致密砂岩微观孔隙非均质性定量表征及储层意义:以鄂尔多斯盆地X地区山西组为例[J].石油实验地质,2017,39(4):556-561.LU Chengang,ZHANG Suian,MAO Xiaoxiao,et al.Quantitative characterization of microscopic pore heterogeneity in tight sandstones and its reservoir significance:A case study of the Shanxi Formation in X area,Ordos Basin[J].Petroleum Geology&Experiment,2017,39(4):556-561.
[29]陈元千,郝明强,孙兵,等.水平井产量公式的对比研究[J].新疆石油地质,2012,33(5):566-569.CHEN Yuanqian,HAO Mingqiang,SUN Bing,et al.Comparative study of the production rate formulas for horizontal wells[J].Xinjiang Petroleum Geology,2012,33(5):566-569.