水驱曲线的进一步理论探讨及童氏图版的改进
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摘要
水驱曲线法、童氏图版法及Arps递减曲线法是目前最常用的油藏工程方法,但上述方法受到假设条件和统计数据不足的局限,在应用中存在适用范围不够宽、预测精度不够高等问题。根据Welge线性方程,推导出童氏图版系数的计算公式,改进了童氏图版;结合Welge线性方程和微分方程,进一步探讨了理论水驱曲线,引入了水驱前缘突破时基于单位液量的产量变化率即递减率的概念,并给出了相应的计算公式;基于相渗曲线幂函数表示法,将前缘含水饱和度微分方程转变为线性方程,得到了Welge系数的计算公式,同时还推导出近似理论水驱曲线,并给出了近似理论水驱曲线的参数解法。改进后的童氏图版及新型水驱曲线,理论基础更加扎实,适用范围更宽,预测精度更高。
The water flooding curve method,Tong's chart method and Arps decline curve method are the most commonly used reservoir engineering methods,whereas the above methods are limited by assumptions and statistical data,thus their application range is not wide enough and the prediction accuracy is not high enough during applications.According to the Welge linear equation,the calculation formula of the Tong's chart coefficient was derived,and the Tong's chart was improved.Combined with the Welge linear equation and the differential equation,the theoretical water flooding curve has been further discussed,and the concept of unit liquid production changing rate while the breakthrough of water flooding front occurs,namely the decline rate,was introduced,and the calculation formula was provided.Based on the power function expression of relative permeability curve,the differential equation of frontal water saturation was transformed into linear equation,and the calculation formula of Welge coefficient was obtained.The approximate theoretical water flooding curve was derived and the parameter solution of the approximate theoretical water flooding curve was obtained.The modified Tong's chart and the new water flooding curve exhibit a more solid theoretical foundation,wider application range and higher prediction accuracy.
The water flooding curve method,Tong's chart method and Arps decline curve method are the most commonly used reservoir engineering methods,whereas the above methods are limited by assumptions and statistical data,thus their application range is not wide enough and the prediction accuracy is not high enough during applications.According to the Welge linear equation,the calculation formula of the Tong's chart coefficient was derived,and the Tong's chart was improved.Combined with the Welge linear equation and the differential equation,the theoretical water flooding curve has been further discussed,and the concept of unit liquid production changing rate while the breakthrough of water flooding front occurs,namely the decline rate,was introduced,and the calculation formula was provided.Based on the power function expression of relative permeability curve,the differential equation of frontal water saturation was transformed into linear equation,and the calculation formula of Welge coefficient was obtained.The approximate theoretical water flooding curve was derived and the parameter solution of the approximate theoretical water flooding curve was obtained.The modified Tong's chart and the new water flooding curve exhibit a more solid theoretical foundation,wider application range and higher prediction accuracy.
引文
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[14]张金庆,安桂荣,许家峰,等.广适水驱曲线适应性分析及推广应用[J].中国海上油气,2013,25(6):56-60.ZHANG Jinqing,AN Guirong,XU Jiafeng,et al.Analyzing the applicability of an eurytopic water-drive curve and its extensible applications[J].China Offshore Oil and Gas,2013,25(6):56-60.
[15]凡哲元,任玉林,姜瑞忠.对童氏“7.5B”计算及乙型水驱法的改进[J].西南石油大学学报(自然科学版),2006,28(3):17-19.FAN Zheyuan,REN Yulin,JIANG Ruizhong.A new understanding to“7.5B”in Tong’s formula[J].Journal of Southwest Petroleum University(Science&Technology Edition),2006,28(3):17-19.
[16]范海军,朱学谦.高含水期油田新型水驱特征曲线的推导及应用[J].断块油气田,2016,23(1):105-108.FAN Haijun,ZHU Xueqian.Derivation and application of new water flooding characteristic curve in high water-cut oilfield[J].Fault-Block Oil&Gas Field,2016,23(1):105-108.
[17] ZHANG Jinqing,YANG Renfeng.A further study on Welge equation[J].Energy Exploration&Exploitation,2018.
[18]秦同洛,李璗,陈元千.实用油藏工程方法[M].北京:石油工业出版社,1989.
[19]塔雷克·艾哈迈德.油藏工程手册(第三版原书影印版)[M].北京:石油工业出版社,2009.AHMED T.Reservoir engineering handbook(Third Edition)[M].Beijing:Petroleum Industry press,2009.
[20]蒋庆坦,陈万珍.利用相对渗透率资料预测油藏动态的研究[J].石油勘探与开发,1985,12(1):38-45JIANG Qingtan,CHEN Wanzhen.Reservoir behavior prediction with the application of relative permeability[J].Petroleum Expoloration and Development,1985,12(1):38-45.
[21]陈元千.实用油气藏工程方法[M].北京:石油大学出版社,1998.
[2]童宪章.天然水驱和人工注水油藏的统计规律探讨[J].石油勘探与开发,1978,5(6):38-47.TONG Xianzhang.Study on statistical law of natural water and injecting water driving[J].Petroleum Expoloration and Development,1978,5(6):38-47.
[3]孙玉凯,高文君.常用油藏工程方法改进与应用[M].北京:石油工业出版社,2007.
[4]张金庆,杨仁锋.理论水驱曲线的提出及其与产量递减曲线的关系探讨[J].中国海上油气,2018,30(4):86-92.DOI:10.11935/j.issn.1673-1506.2018.04.010.ZHANG Jinqing,YANG Renfeng.Proposing of theoretical waterflooding curve and discussion on the relationship between theoretical waterflooding curve and production decline curve[J].China Offshore Oil and Gas,2018,30(4):86-92.DOI:10.11935/j.issn.1673-1506.2018.04.010.
[5]李宁,孙雷,潘毅,等.童氏“7.5”的新计算方法及应用[J].科学技术与工程,2014,14(34):155-158.LI Ning,SUN Lei,PAN Yi,et al.Tong’s“7.5”new calculation method and application[J].Science Technology and Engineering,2014,14(34):155-158.
[6]王柏力.童氏含水与采出程度关系图版的改进及应用[J].大庆石油地质与开发,2006,25(4):62-64.WANG Boli.Adaptation and application of Tong’s chart for relation between water cut and recovery degree[J].Petroleum Geology&Oilfield Development in Daqing,2006,25(4):62-64.
[7]叶锋.改进的童氏图版在低渗透油藏中的应用[J].油气地质与采收率,2009,16(4):109-110.YE Feng.The application of the improved Tong’s chart in the low permeability oil reservoir[J].PGRE,2009,16(4):109-110.
[8]薛颍,石立华,席天德.童氏水驱曲线的改进及应用[J].西南石油大学学报(自然科学版),2015,37(1):141-145.XUE Ying,SHI Lihua,XI Tiande.Tong’s water drive curve improvement and its application[J].Journal of Southwest Petroleum University(Science&Technology Edition),2015,37(1):141-145.
[9]尹大庆,林东维,朱文波,等.水驱砂岩油藏修正童氏图版含水率预测方法[J].大庆石油地质与开发,2014,33(2):54-57.YIN Daqing,LIN Dongwei,ZHU Wenbo,et al.Predicting method for the water cut of water flooded sandstone oil reservoirs by corrected Tong’s chart board[J].Petroleum Geology and Oilfield Development in Daqing,2014,33(2):54-57.
[10]马奎前,孙召勃,贾晓飞,等.对水驱曲线中童氏“7.5B”公式再认识和改进[J].特种油气藏,2018,25(2):107-110.MA Kuiqian,SUN Zhaobo,JIA Xiaofei,et al.Recognition and improvement of Tong’s 7.5Bin waterflooding curve[J].Special Oil and Gas Reservoirs,2018,25(2):107-110.
[11]王继强,石成方,纪淑红,等.特高含水期新型水驱特征曲线[J].石油勘探与开发,2017,44(6):955-960.WANG Jiqiang,SHI Chengfang,JI Shuhong,et al.New water drive characteristic curves at ultra-high water cut stage[J].Pe-troleum Exploration and Development,2017,44(6):955-960.
[12]宋兆杰,李治平,赖枫鹏,等.高含水期油田水驱特征曲线关系式的理论推导[J].石油勘探与开发,2013,40(2):201-208.SONG Zhaojie,LI Zhiping,LAI Fengpeng,et al.Derivation of water flooding characteristic curve for high water-cut oilfields[J].Petroleum Expoloration and Development,2013,40(2):201-208.
[13]张金庆.水驱油田产量预测模型[M].北京:石油工业出版社,2013.
[14]张金庆,安桂荣,许家峰,等.广适水驱曲线适应性分析及推广应用[J].中国海上油气,2013,25(6):56-60.ZHANG Jinqing,AN Guirong,XU Jiafeng,et al.Analyzing the applicability of an eurytopic water-drive curve and its extensible applications[J].China Offshore Oil and Gas,2013,25(6):56-60.
[15]凡哲元,任玉林,姜瑞忠.对童氏“7.5B”计算及乙型水驱法的改进[J].西南石油大学学报(自然科学版),2006,28(3):17-19.FAN Zheyuan,REN Yulin,JIANG Ruizhong.A new understanding to“7.5B”in Tong’s formula[J].Journal of Southwest Petroleum University(Science&Technology Edition),2006,28(3):17-19.
[16]范海军,朱学谦.高含水期油田新型水驱特征曲线的推导及应用[J].断块油气田,2016,23(1):105-108.FAN Haijun,ZHU Xueqian.Derivation and application of new water flooding characteristic curve in high water-cut oilfield[J].Fault-Block Oil&Gas Field,2016,23(1):105-108.
[17] ZHANG Jinqing,YANG Renfeng.A further study on Welge equation[J].Energy Exploration&Exploitation,2018.
[18]秦同洛,李璗,陈元千.实用油藏工程方法[M].北京:石油工业出版社,1989.
[19]塔雷克·艾哈迈德.油藏工程手册(第三版原书影印版)[M].北京:石油工业出版社,2009.AHMED T.Reservoir engineering handbook(Third Edition)[M].Beijing:Petroleum Industry press,2009.
[20]蒋庆坦,陈万珍.利用相对渗透率资料预测油藏动态的研究[J].石油勘探与开发,1985,12(1):38-45JIANG Qingtan,CHEN Wanzhen.Reservoir behavior prediction with the application of relative permeability[J].Petroleum Expoloration and Development,1985,12(1):38-45.
[21]陈元千.实用油气藏工程方法[M].北京:石油大学出版社,1998.