Logistic和Generalized-Arc-Tangent产量递减方程理论推导
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摘要
为了揭示Logistic和Generalized-Arc-Tangent产量递减方程的渗流特征,选取特殊的油相相渗关系式,按照Arps产量递减方程理论,推导出了Logistic和Generalized-Arc-Tangent产量递减方程及其对应水相相渗关系式。研究结果表明,在注水保持地层压力的条件下,产量递减类型主要由油水两相渗流特征共同决定。推导出的油水两相相渗关系式均是以出口端含水饱和度为变量,符合行业相渗关系式标准,克服了以往产量递减方程理论推导时采用平均含水饱和度为变量的拟相渗关系式缺陷。通过吐哈丘陵油田、温五区块的应用,实际产量与经油水两相相渗关系式分别确定的产量基本一致。
To reveal the flow characteristics of Logistic and Generalized-Arc-Tangent production decline equations,the paper selects a special oil-phase relative permeability relation and deviates Logistic and Generalized-Arc-Tangent production decline equations and its corresponding water-phase relative permeability formula according to the derivation process of Arps production decline equation.The results show that the type of production decline is mainly determined by the characteristics of oil-water two-phase flows under the condition of maintaining formation pressure by water injection.The relative permeability relations of oil and water phases take the water saturations at the outlet as variables,which complies with the industrial standards of relative permeability relations and avoids the defects of the pseudorelative permeability relations using the average water saturation as a variable during previous decline equation derivation.The actual applications in Qiuling oilfield and Block Wen-5 in Tuha oilfield show that the actual production is consistent with the results obtained from the production decline equation determined by relative permeability relations of oil and water phases,respectively.
To reveal the flow characteristics of Logistic and Generalized-Arc-Tangent production decline equations,the paper selects a special oil-phase relative permeability relation and deviates Logistic and Generalized-Arc-Tangent production decline equations and its corresponding water-phase relative permeability formula according to the derivation process of Arps production decline equation.The results show that the type of production decline is mainly determined by the characteristics of oil-water two-phase flows under the condition of maintaining formation pressure by water injection.The relative permeability relations of oil and water phases take the water saturations at the outlet as variables,which complies with the industrial standards of relative permeability relations and avoids the defects of the pseudorelative permeability relations using the average water saturation as a variable during previous decline equation derivation.The actual applications in Qiuling oilfield and Block Wen-5 in Tuha oilfield show that the actual production is consistent with the results obtained from the production decline equation determined by relative permeability relations of oil and water phases,respectively.
引文
[1]高文君,张原平,阳兴华,等. Logistic产量递减方程渗流理论基础[J].新疆石油地质,2001,22(6):506-508.GAO Wenjun,ZHANG Yuanping,YANG Xinghua,et al. Percola-tion theory of Logistic production decline equation[J]. Xinjiang Pe-troleum Geology,2001,22(6):506-508.
[2]孙玉凯,高文君,刘瑛,等.广义反正切微分分布产量递减方程[J].新疆石油地质,2004,25(1):65-67.SUN Yukai,GAO Wenjun,LIU Ying,et al. Study on the generalizedArc-Tangent distribution production decline equation[J]. XinjiangPetroleum Geology,2004,25(1):65-67.
[3]高文君,王作进.产量递减方程判别理论基础及应用[J].新疆石油地质,1999,20(6):518-521.GAO Wenjun,WANG Zuojin. Fundamental theory on judgement ofproduction decline type and application[J]. Xinjiang Petroleum Ge-ology,1999,20(6):518-521.
[4]油气田开发专业标准化委员会.岩石中两相流体相对渗透率测定方法:SY/T 5345—2007[S].北京:石油工业出版社,2008.Standardization Committee for Oil-gas Field Development. Test meth-od for two phase relative permeability in rock:SY/T 5345—2007[S]. Beijing:Petroleum Industry Press,2008.
[5]高文君,郝魏,盛寒,等.水驱油田Arps产量递减方程渗流理论基础完善[J].新疆石油地质,2017,38(3):314-318.GAO Wenjun,HAO Wei,SHENG Han,et al. Improvement of perco-lation theory on Arps production decline equation in water-floodingoilfield[J]. Xinjiang Petroleum Geology,2017,38(3):314-318.
[6]姜汉桥,姚军,姜瑞忠.油藏工程原理与方法[M].山东东营:中国石油大学出版社,2006:245-262.JIANG Hanqiao,YAO Jun,JIANG Ruizhong. Reservoir engineeringtheory and method[M]. Dongying,Shandong:China University ofPetroleum Press,2006:245-262.
[7]黄炳光,刘蜀知.实用油藏工程与动态分析方法[M].北京:石油工业出版社,1998:174-189.HUANG Bingguang,LIU Shuzhi. Practical petroleum reservoir engi-neering and dynamic analysis methods[M]. Beijing:Petroleum In-dustry Press,1998:174-189.
[8]陈元千.水驱曲线关系式的推导[J].石油学报,1985,6(2):69-78.CHEN Yuanqian. Derivation of relationships of water drive curve[J]. Acta Petrolei Sinica,1985,6(2):69-78.
[9]葛家理.现代油藏渗流力学原理(上册)[M].北京:石油工业出版社,2003:121-136.GE Jiali. The modern mechanics of fluids flow in oil reservoir(Ⅰ)[M]. Beijing:Petroleum Industry Press,2003:121-136.
[10]张继成,宋考平.相对渗透率特征曲线及其应用[J].石油学报,2007,28(4):104-107.ZHANG Jicheng,SONG Kaoping. Eigen curve of relative permea-bility and its application[J]. Acta Petrolei Sinica,2007,28(4):104-107.
[11]张原平,高文君,赵晓萍,等.广义反正切微分分布递减方程特征参数分析[J].新疆石油地质,2005,26(6):670-672.ZHANG Yuanping,GAO Wenjun,ZHAO Xiaoping,et al. Charac-teristic parameter analysis of generalized Arc-Tangent distributionproduction decline equation[J]. Xinjiang Petroleum Geology,2005,26(6):670-672.
[12]胡允栋.产量递减的指数分布和反正切微分分布规律[J].石油勘探与开发,1997,24(6):76-81.HU Yundong. Exponential and Arc-Tangent distributions of oil andgas production decline[J]. Petroleum Exploration and Development,1997,24(6):76-81.
[13]陈元千,郝明强. Arps递减微分方程的推导及应用[J].断块油气田,2014,21(1):57-58.CHEN Yuanqian,HAO Mingqiang. Derivation and application ofArps decline differential equation[J]. Fault-Block Oil&Gas Field,2014,21(1):57-58.
[14]陈元千.确定递减类型的新方法[J].石油学报,1990,11(1):74-79.CHEN Yuanqian. A new method of identify the type decline curve[J]. Acta Petrolei Sinica,1990,11(1):74-79.
[15]俞启泰.水驱油田产量递减规律[J].石油勘探与开发,1993,20(4):72-80.YU Qitai. Decline curve analysis for a water drive reservoir[J]. Pe-troleum Exploration and Development,1993,20(4):72-80.
[16]张虎俊.油气田产量双曲递减方程建立的新方法[J].新疆石油地质,1996,17(4):370-375.ZHANG Hujun. New method for establishing hyperbolic declineequation of field production[J]. Xinjiang Petroleum Geology,1996,17(4):370-375.
[17]计秉玉.产量递减方程的渗流理论基础[J].石油学报,1995,16(3):86-91.JI Bingyu. The fundamentals of seepage flow theory used on theproduction decline equations[J]. Acta Petrolei Sinica,1995,16(3):86-91.
[18]陈新彬,常毓文,王燕灵,等.低渗透储层产量递减模型的渗流机理及应用[J].石油学报,2011,32(1):113-116.CHEN Xinbin,CHANG Yuwen,WANG Yanling,et al. Percolationmechanism and application of a production-decline model in low-permeability reservoirs[J]. Acta Petrolei Sinica,2011,32(1):113-116.
[2]孙玉凯,高文君,刘瑛,等.广义反正切微分分布产量递减方程[J].新疆石油地质,2004,25(1):65-67.SUN Yukai,GAO Wenjun,LIU Ying,et al. Study on the generalizedArc-Tangent distribution production decline equation[J]. XinjiangPetroleum Geology,2004,25(1):65-67.
[3]高文君,王作进.产量递减方程判别理论基础及应用[J].新疆石油地质,1999,20(6):518-521.GAO Wenjun,WANG Zuojin. Fundamental theory on judgement ofproduction decline type and application[J]. Xinjiang Petroleum Ge-ology,1999,20(6):518-521.
[4]油气田开发专业标准化委员会.岩石中两相流体相对渗透率测定方法:SY/T 5345—2007[S].北京:石油工业出版社,2008.Standardization Committee for Oil-gas Field Development. Test meth-od for two phase relative permeability in rock:SY/T 5345—2007[S]. Beijing:Petroleum Industry Press,2008.
[5]高文君,郝魏,盛寒,等.水驱油田Arps产量递减方程渗流理论基础完善[J].新疆石油地质,2017,38(3):314-318.GAO Wenjun,HAO Wei,SHENG Han,et al. Improvement of perco-lation theory on Arps production decline equation in water-floodingoilfield[J]. Xinjiang Petroleum Geology,2017,38(3):314-318.
[6]姜汉桥,姚军,姜瑞忠.油藏工程原理与方法[M].山东东营:中国石油大学出版社,2006:245-262.JIANG Hanqiao,YAO Jun,JIANG Ruizhong. Reservoir engineeringtheory and method[M]. Dongying,Shandong:China University ofPetroleum Press,2006:245-262.
[7]黄炳光,刘蜀知.实用油藏工程与动态分析方法[M].北京:石油工业出版社,1998:174-189.HUANG Bingguang,LIU Shuzhi. Practical petroleum reservoir engi-neering and dynamic analysis methods[M]. Beijing:Petroleum In-dustry Press,1998:174-189.
[8]陈元千.水驱曲线关系式的推导[J].石油学报,1985,6(2):69-78.CHEN Yuanqian. Derivation of relationships of water drive curve[J]. Acta Petrolei Sinica,1985,6(2):69-78.
[9]葛家理.现代油藏渗流力学原理(上册)[M].北京:石油工业出版社,2003:121-136.GE Jiali. The modern mechanics of fluids flow in oil reservoir(Ⅰ)[M]. Beijing:Petroleum Industry Press,2003:121-136.
[10]张继成,宋考平.相对渗透率特征曲线及其应用[J].石油学报,2007,28(4):104-107.ZHANG Jicheng,SONG Kaoping. Eigen curve of relative permea-bility and its application[J]. Acta Petrolei Sinica,2007,28(4):104-107.
[11]张原平,高文君,赵晓萍,等.广义反正切微分分布递减方程特征参数分析[J].新疆石油地质,2005,26(6):670-672.ZHANG Yuanping,GAO Wenjun,ZHAO Xiaoping,et al. Charac-teristic parameter analysis of generalized Arc-Tangent distributionproduction decline equation[J]. Xinjiang Petroleum Geology,2005,26(6):670-672.
[12]胡允栋.产量递减的指数分布和反正切微分分布规律[J].石油勘探与开发,1997,24(6):76-81.HU Yundong. Exponential and Arc-Tangent distributions of oil andgas production decline[J]. Petroleum Exploration and Development,1997,24(6):76-81.
[13]陈元千,郝明强. Arps递减微分方程的推导及应用[J].断块油气田,2014,21(1):57-58.CHEN Yuanqian,HAO Mingqiang. Derivation and application ofArps decline differential equation[J]. Fault-Block Oil&Gas Field,2014,21(1):57-58.
[14]陈元千.确定递减类型的新方法[J].石油学报,1990,11(1):74-79.CHEN Yuanqian. A new method of identify the type decline curve[J]. Acta Petrolei Sinica,1990,11(1):74-79.
[15]俞启泰.水驱油田产量递减规律[J].石油勘探与开发,1993,20(4):72-80.YU Qitai. Decline curve analysis for a water drive reservoir[J]. Pe-troleum Exploration and Development,1993,20(4):72-80.
[16]张虎俊.油气田产量双曲递减方程建立的新方法[J].新疆石油地质,1996,17(4):370-375.ZHANG Hujun. New method for establishing hyperbolic declineequation of field production[J]. Xinjiang Petroleum Geology,1996,17(4):370-375.
[17]计秉玉.产量递减方程的渗流理论基础[J].石油学报,1995,16(3):86-91.JI Bingyu. The fundamentals of seepage flow theory used on theproduction decline equations[J]. Acta Petrolei Sinica,1995,16(3):86-91.
[18]陈新彬,常毓文,王燕灵,等.低渗透储层产量递减模型的渗流机理及应用[J].石油学报,2011,32(1):113-116.CHEN Xinbin,CHANG Yuwen,WANG Yanling,et al. Percolationmechanism and application of a production-decline model in low-permeability reservoirs[J]. Acta Petrolei Sinica,2011,32(1):113-116.
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