特高含水期相渗关系表征新理论与实践
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摘要
特高含水阶段油水相对渗透率比与含水饱和度半对数关系曲线发生转折,针对传统相渗线性理论难以适用于特高含水期水驱油田开发问题,开展了特高含水期相渗非线性理论研究。采用数学建模方法建立了相渗有理函数,基于局部加权回归理论对参数进行识别,通过构建F-统计量开展拟合优度检验,率先将有理拟合理论应用到特高含水期相渗关系表征。利用贝尔油田、榆树林油田、西峰油田及羊二庄油田实际数据,对比分析传统线性拟合方法、二次多项式拟合方法、指数拟合方法、基于数据变形的线性拟合法,新方法预测精度更高、相关性更强,且能准确反映特高含水期相渗曲线半对数坐标轴弯曲特性;基于新方法的水驱特征曲线预测精度更高、相关性更强。新方法对于改进特高含水期水驱评价方法及开发指标预测具有极强的实用性。
In the(extra) high water-cut stage, the semi-logarithmic curve showing the relationship between the oil/water relative permeability ratio and water saturation tends to reach a turning point. Thus, applying the traditional linear theory of the relative permeability curve to the development of oil/water displacement in the(extra) high water-cut stage is difficult. In this study,nonlinear theoretical study of relative permeability in the high water-cut stage was conducted using a rational function for relative permeability established through a mathematical modeling method. Its parameters were identified based on the local weighted regression theory, and the appropriateness of the fitting was tested by constructing F-statistics. This is the first study in which the rational fitting theory has been applied to the characterization of relative permeability relationships in the(extra) high watercut stage. Through the use of actual data from the Beier, Yushulin, Xifeng, and Yangerzhuang oilfields, the traditional linear fitting, quadratic polynomial fitting, exponential fitting, and linear fitting methods based on data deformation were compared and analyzed. The new method and the oil/water displacement characteristic curve on which the new method is based showed higher prediction precision and stronger correlation. The new method can be used to reflect accurately the semi-logarithmic axis bending characteristics of the relative permeability curve of the(extra) high water-cut stage.
In the(extra) high water-cut stage, the semi-logarithmic curve showing the relationship between the oil/water relative permeability ratio and water saturation tends to reach a turning point. Thus, applying the traditional linear theory of the relative permeability curve to the development of oil/water displacement in the(extra) high water-cut stage is difficult. In this study,nonlinear theoretical study of relative permeability in the high water-cut stage was conducted using a rational function for relative permeability established through a mathematical modeling method. Its parameters were identified based on the local weighted regression theory, and the appropriateness of the fitting was tested by constructing F-statistics. This is the first study in which the rational fitting theory has been applied to the characterization of relative permeability relationships in the(extra) high watercut stage. Through the use of actual data from the Beier, Yushulin, Xifeng, and Yangerzhuang oilfields, the traditional linear fitting, quadratic polynomial fitting, exponential fitting, and linear fitting methods based on data deformation were compared and analyzed. The new method and the oil/water displacement characteristic curve on which the new method is based showed higher prediction precision and stronger correlation. The new method can be used to reflect accurately the semi-logarithmic axis bending characteristics of the relative permeability curve of the(extra) high water-cut stage.
引文
[1]陈元千,陶自强.高含水期水驱曲线的推导及上翘问题的分析[J].断块油气田,1997, 4(3):19-24.CHEN Yuanqian, TAO Ziqiang. Derivation of water drive curve at high water-cut stage and its analysis of upwarding problem[J]. Fault-Block Oil&Gas Field, 1997, 4(3):19-24.
[2]高丽,宋考平,马春华,等.二段直线法预测高含水期油田开发指标[J].石油钻探技术,2008, 36(5):72-74.doi:10.3969/j.issn.1001-0890.2008.05.019GAO Li, SONG Kaoping, MA Chunhua, et al. Two straight lines to forecast development index of high water-cut oilfield[J]. Petroleum Drilling Techniques, 2008,36(5):72-74. doi:10.3969/j.issn.1001-0890.2008.05.019
[3]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 curves[J]. Acta Petrolei Sinica,1985, 6(2):69-78.
[4]俞启泰.几种重要水驱特征曲线的油水渗流特征[J].石油学报,1999, 20(1):56-60. doi:10.3321/j.issn:0253-2697.1999.01.011YU Qitai. Characteristics of oil-water seepage flow for several important water drive curves[J]. Acta Petrolei Sinica, 1999, 20(1):56-60. doi:10.3321/j.issn:0253-2697.1999.01.011
[5]陈元千.油田可采储量计算方法[J].新疆石油地质,2000, 21(2):130-137. doi:10.3969/j.issn.1001-3873.-2000.02.011CHEN Yuanqian. Calculation methods of recoverable reserves of oilfields[J]. Xinjiang Petroleum Geology,2000, 21(2):130-137. doi:10.3969/j.issn.1001-3873.-2000.02.011
[6]王怒涛,罗志锋,黄炳光,等.新型水驱特征曲线系列(II)[J].西南石油大学学报(自然科学版),2008, 30(1):106-108. doi:10.3863/j.issn.1000-2634.-2008.01.029WANG Nutao, LUO Zhifeng, HUANG Bingguang, et al.New type water drive characteristic curve series(Ⅱ)[J].Journal of Southwest Petroleum University(Science&Technology Edition), 2008, 30(1):106-108. doi:10.3863/j.-issn. 1000-2634.2008.01.029
[7]魏洪涛,王怒涛,黄炳光.两种新型水驱特征曲线系列[J].西南石油大学学报(自然科学版),2009, 31(6):117-122. doi:10.3863/j.issn.1674-5086.2009.06.026WEI Hongtao, WANG Nutao, HUANG Bingguang. Twonew types of water flooding characteristic curve series[J].Journal of Southwest Petroleum University(Science&Technology Edition), 2009, 31(6):117-122. doi:10.3863/j.-issn. 1674-5086.2009.06.026
[8] WANG Jiqiang,SHI Chengfang,JI Shuhong,et al. New water drive characteristic curves at ultra-high water cut stage[J]. Petroleum Exploration and Development, 2017,44(6):1010-1015. doi:10.1016/S1876-3804(17)30113-1
[9] SONG Zhaojie, LI Zhiping, LAI Fengpeng, et al. Derivation of water flooding characteristic curve for high water-cut oilfields[J]. Petroleum Exploration and Development, 2013, 40(2):216-223. doi:10.1016/S1876-3804(13)60025-7
[10]肖阳,蔡振忠,江同文,等.缝洞型碳酸盐岩油藏水驱特征曲线研究[J].西南石油大学学报(自然科学版),2012, 34(6):87-93. doi:10.3863/j.issn.-1674-5086.2012.06.012XIAO Yang,CAI Zhenzhong,JIANG Tongwen, et al.The study on water drive characteristic curve of fracturedvuggy carbonate reservoir[J]. Journal of Southwest Petroleum University(Science&Technology Edition), 2012,34(6):87-93. doi:10.3863/j.issn.1674-5086.2012.06.012
[11] YUE Ping, XIE Zhiwei, LIU Haohan, et al. Application of water injection curves for the dynamic analysis of fractured-vuggy carbonate reservoirs[J]. Journal of Petroleum Science and Engineering, 2018, 169:220-229. doi:10.1016/j.petrol.2018.05.062
[12]孙雷,冯乔,陈国利,等.CO2混相驱拟含气率与采出程度图版的建立[J].西南石油大学学报(自然科学版),2014, 36(1):83-88. doi:10.11885/j.issn.1674-5086.2013.10.14.06SUN Lei,FENG Qiao, CHEN Guoli,et al. Establishment of the chart of equivalent gas ratio-recovery degree for CO2 miscible flooding[J]. Journal of Southwest Petroleum University(Science&Technology Edition), 2014, 36(1):83-88. doi:10.11885/j.issn.1674-5086.2013.10.14.06
[13]苑志旺,杨宝泉,杨莉,等.注气驱油藏新型气驱特征曲线推导及应用[J].西南石油大学学报(自然科学版),2018,40(2):135-141. doi:10.11885/j.issn.1674-5086.-2017.04.23.01YUAN Zhiwang, YANG Baoquan, YANG Li, et al.Derivation and practice of the new gas flooding characteristic curve of reservoir with gas injection flooding[J]. Journal of Southwest Petroleum University(Science&Technology Edition), 2018, 40(2):135-141. doi:10.11885/j.-issn.1674-5086.2017.04.23.01
[14] LIU Zhibin, LIU Haohan. An effective method to predict oil recovery in high water cut stage[J]. Journal ofHydrodynamics, Ser. B, 2015, 27(6):988-995. doi:10.-1016/S1001-6058(15)60561-3
[15]郑威,杜志敏,汪周华,等.相渗曲线对凝析气井动态影响研究[J].西南石油大学学报,2007, 29(2):10-13.doi:10.3863/j.issn. 1674-5086.2007.02.003ZHENG Wei,DU Zhimin,WANG Zhouhua,et al. The influence of relative permeability curves on gas condensate well performance[J]. Journal of Southwest Petroleum University, 2007, 29(2):10-13. doi:10.3863/j.issn.1674-5086.2007.02.003
[16] YUAN Zhiwang, YANG Baoquan, YANG Li, et al. Watercut rising mechanism and optimized water injection technology for deepwater turbidite sandstone oilfield:A case study of AKPO Oilfield in Niger Delta Basin, West Africa[J]. Petroleum Exploration and Development, 2018,45(2):302-311. doi:10.1016/S1876-3804(18)30033-8
[17]张金庆,孙福街.相渗曲线和水驱曲线与水驱储量的关系[J].新疆石油地质,2010, 31(6):629-631.ZHANG Jinqing, SUN Fujie. Quantitative relationship between relative permeability curve, water drive curve and waterflood reserve[J]. Xinjiang Petroleum Geology, 2010,31(6):629-631.
[18]王金勋,刘庆杰,杨普华,等.应用逾渗理论计算非稳态法油水相渗曲线[J].石油勘探与开发,2001,28(2):79-82. doi:10.3321/j.issn:1000-0747.2001.02.024WANG Jinxun, LIU Qingjie, YANG Puhua, et al. Calculating the relative permeability from displacement experiments based on percolation theory[J]. Petroleum Exploration and Development, 2001, 28(2):79-82. doi:10.-3321/j.issn:1000-0747.2001.02.024
[19]戴胜群,付波,洪秀娥,等.油藏综合相渗曲线拟合方法[J].油气藏评价与开发,2011,1(3):1-4. doi:10.-3969/j.issn.2095-1426.2011.03.001DAI Shengqun,FU Bo, HONG Xiu'e,et al. The methods to fit the curve of integrated relative permeability in reservoir[J]. Reservoir Evaluation and Development, 2011,1(3):1-4. doi:10.3969/j.issn.2095-1426.2011.03.001
[20]叶仲斌,彭克宗,吴小玲,等.克拉玛依油田三元复合驱相渗曲线研究[J].石油学报,2000, 21(1):49-54.doi:10.3321/j.issn:0253-2697.2000.01.009YE Zhongbin, PENG Kezong, WU Xiaoling, et al. Oil field development[J]. Acta Petrolei Sinica,2000, 21(1):49-54. doi:10.3321/j.issn:0253-2697.2000.01.009
[21]陈元千.水驱曲线法的分类、对比与评价[J].新疆石油地质,1994, 15(4):348-356.CHEN Yuanqian. Classification, correlation and evaluation of water-drive performance curve analysis method[J].Xinjiang Petroleum Geology, 1994, 15(4):348-356.
[22]邴绍献.特高含水期相渗关系表征研究[J].石油天然气学报,2012, 34(10):118-120. doi:10.3969/j.issn.1000-9752.2012.10.028BING Shaoxian. Study on relative permeability equation adapted at ultra-high water-cut stage[J]. Journal of Oil and Gas Technology,2012,34(10):118-120. doi:10.-3969/j.issn.1000-9752.2012.10.028
[23]于卓熙.带有误差变量的自回归模型的回归函数的局部多项式估计[D].长春:吉林大学,2006:4-8.YU Zhuoxi. Local polynomial estimator of the regression function in autoregressive models with errors in variables[D]. Changchun:Jilin University, 2006:4-8.
[24]刘浩瀚.概率论与数理统计[M].北京:高等教育出版社,2015:113-115.
[25]陈元千.相对渗透率曲线和毛管压力曲线的标准化方法[J].石油实验地质,1990, 12(1):64-70.CHEN Yuanqian. Standardization on the curves of permeability and capillary pressure[J]. Experimental Petroleum Geology, 1990, 12(1):64-70.
[26]董大鹏.低渗透油田油水两相渗流机理研究[D].成都:成都理工大学,2007:71-78.DONG Dapeng. A study of percolation rules of oil-water two-phase flow in low-permeability reservoirs[D]. Chengdu:Chengdu University of Technology, 2007:71-78.
[2]高丽,宋考平,马春华,等.二段直线法预测高含水期油田开发指标[J].石油钻探技术,2008, 36(5):72-74.doi:10.3969/j.issn.1001-0890.2008.05.019GAO Li, SONG Kaoping, MA Chunhua, et al. Two straight lines to forecast development index of high water-cut oilfield[J]. Petroleum Drilling Techniques, 2008,36(5):72-74. doi:10.3969/j.issn.1001-0890.2008.05.019
[3]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 curves[J]. Acta Petrolei Sinica,1985, 6(2):69-78.
[4]俞启泰.几种重要水驱特征曲线的油水渗流特征[J].石油学报,1999, 20(1):56-60. doi:10.3321/j.issn:0253-2697.1999.01.011YU Qitai. Characteristics of oil-water seepage flow for several important water drive curves[J]. Acta Petrolei Sinica, 1999, 20(1):56-60. doi:10.3321/j.issn:0253-2697.1999.01.011
[5]陈元千.油田可采储量计算方法[J].新疆石油地质,2000, 21(2):130-137. doi:10.3969/j.issn.1001-3873.-2000.02.011CHEN Yuanqian. Calculation methods of recoverable reserves of oilfields[J]. Xinjiang Petroleum Geology,2000, 21(2):130-137. doi:10.3969/j.issn.1001-3873.-2000.02.011
[6]王怒涛,罗志锋,黄炳光,等.新型水驱特征曲线系列(II)[J].西南石油大学学报(自然科学版),2008, 30(1):106-108. doi:10.3863/j.issn.1000-2634.-2008.01.029WANG Nutao, LUO Zhifeng, HUANG Bingguang, et al.New type water drive characteristic curve series(Ⅱ)[J].Journal of Southwest Petroleum University(Science&Technology Edition), 2008, 30(1):106-108. doi:10.3863/j.-issn. 1000-2634.2008.01.029
[7]魏洪涛,王怒涛,黄炳光.两种新型水驱特征曲线系列[J].西南石油大学学报(自然科学版),2009, 31(6):117-122. doi:10.3863/j.issn.1674-5086.2009.06.026WEI Hongtao, WANG Nutao, HUANG Bingguang. Twonew types of water flooding characteristic curve series[J].Journal of Southwest Petroleum University(Science&Technology Edition), 2009, 31(6):117-122. doi:10.3863/j.-issn. 1674-5086.2009.06.026
[8] WANG Jiqiang,SHI Chengfang,JI Shuhong,et al. New water drive characteristic curves at ultra-high water cut stage[J]. Petroleum Exploration and Development, 2017,44(6):1010-1015. doi:10.1016/S1876-3804(17)30113-1
[9] SONG Zhaojie, LI Zhiping, LAI Fengpeng, et al. Derivation of water flooding characteristic curve for high water-cut oilfields[J]. Petroleum Exploration and Development, 2013, 40(2):216-223. doi:10.1016/S1876-3804(13)60025-7
[10]肖阳,蔡振忠,江同文,等.缝洞型碳酸盐岩油藏水驱特征曲线研究[J].西南石油大学学报(自然科学版),2012, 34(6):87-93. doi:10.3863/j.issn.-1674-5086.2012.06.012XIAO Yang,CAI Zhenzhong,JIANG Tongwen, et al.The study on water drive characteristic curve of fracturedvuggy carbonate reservoir[J]. Journal of Southwest Petroleum University(Science&Technology Edition), 2012,34(6):87-93. doi:10.3863/j.issn.1674-5086.2012.06.012
[11] YUE Ping, XIE Zhiwei, LIU Haohan, et al. Application of water injection curves for the dynamic analysis of fractured-vuggy carbonate reservoirs[J]. Journal of Petroleum Science and Engineering, 2018, 169:220-229. doi:10.1016/j.petrol.2018.05.062
[12]孙雷,冯乔,陈国利,等.CO2混相驱拟含气率与采出程度图版的建立[J].西南石油大学学报(自然科学版),2014, 36(1):83-88. doi:10.11885/j.issn.1674-5086.2013.10.14.06SUN Lei,FENG Qiao, CHEN Guoli,et al. Establishment of the chart of equivalent gas ratio-recovery degree for CO2 miscible flooding[J]. Journal of Southwest Petroleum University(Science&Technology Edition), 2014, 36(1):83-88. doi:10.11885/j.issn.1674-5086.2013.10.14.06
[13]苑志旺,杨宝泉,杨莉,等.注气驱油藏新型气驱特征曲线推导及应用[J].西南石油大学学报(自然科学版),2018,40(2):135-141. doi:10.11885/j.issn.1674-5086.-2017.04.23.01YUAN Zhiwang, YANG Baoquan, YANG Li, et al.Derivation and practice of the new gas flooding characteristic curve of reservoir with gas injection flooding[J]. Journal of Southwest Petroleum University(Science&Technology Edition), 2018, 40(2):135-141. doi:10.11885/j.-issn.1674-5086.2017.04.23.01
[14] LIU Zhibin, LIU Haohan. An effective method to predict oil recovery in high water cut stage[J]. Journal ofHydrodynamics, Ser. B, 2015, 27(6):988-995. doi:10.-1016/S1001-6058(15)60561-3
[15]郑威,杜志敏,汪周华,等.相渗曲线对凝析气井动态影响研究[J].西南石油大学学报,2007, 29(2):10-13.doi:10.3863/j.issn. 1674-5086.2007.02.003ZHENG Wei,DU Zhimin,WANG Zhouhua,et al. The influence of relative permeability curves on gas condensate well performance[J]. Journal of Southwest Petroleum University, 2007, 29(2):10-13. doi:10.3863/j.issn.1674-5086.2007.02.003
[16] YUAN Zhiwang, YANG Baoquan, YANG Li, et al. Watercut rising mechanism and optimized water injection technology for deepwater turbidite sandstone oilfield:A case study of AKPO Oilfield in Niger Delta Basin, West Africa[J]. Petroleum Exploration and Development, 2018,45(2):302-311. doi:10.1016/S1876-3804(18)30033-8
[17]张金庆,孙福街.相渗曲线和水驱曲线与水驱储量的关系[J].新疆石油地质,2010, 31(6):629-631.ZHANG Jinqing, SUN Fujie. Quantitative relationship between relative permeability curve, water drive curve and waterflood reserve[J]. Xinjiang Petroleum Geology, 2010,31(6):629-631.
[18]王金勋,刘庆杰,杨普华,等.应用逾渗理论计算非稳态法油水相渗曲线[J].石油勘探与开发,2001,28(2):79-82. doi:10.3321/j.issn:1000-0747.2001.02.024WANG Jinxun, LIU Qingjie, YANG Puhua, et al. Calculating the relative permeability from displacement experiments based on percolation theory[J]. Petroleum Exploration and Development, 2001, 28(2):79-82. doi:10.-3321/j.issn:1000-0747.2001.02.024
[19]戴胜群,付波,洪秀娥,等.油藏综合相渗曲线拟合方法[J].油气藏评价与开发,2011,1(3):1-4. doi:10.-3969/j.issn.2095-1426.2011.03.001DAI Shengqun,FU Bo, HONG Xiu'e,et al. The methods to fit the curve of integrated relative permeability in reservoir[J]. Reservoir Evaluation and Development, 2011,1(3):1-4. doi:10.3969/j.issn.2095-1426.2011.03.001
[20]叶仲斌,彭克宗,吴小玲,等.克拉玛依油田三元复合驱相渗曲线研究[J].石油学报,2000, 21(1):49-54.doi:10.3321/j.issn:0253-2697.2000.01.009YE Zhongbin, PENG Kezong, WU Xiaoling, et al. Oil field development[J]. Acta Petrolei Sinica,2000, 21(1):49-54. doi:10.3321/j.issn:0253-2697.2000.01.009
[21]陈元千.水驱曲线法的分类、对比与评价[J].新疆石油地质,1994, 15(4):348-356.CHEN Yuanqian. Classification, correlation and evaluation of water-drive performance curve analysis method[J].Xinjiang Petroleum Geology, 1994, 15(4):348-356.
[22]邴绍献.特高含水期相渗关系表征研究[J].石油天然气学报,2012, 34(10):118-120. doi:10.3969/j.issn.1000-9752.2012.10.028BING Shaoxian. Study on relative permeability equation adapted at ultra-high water-cut stage[J]. Journal of Oil and Gas Technology,2012,34(10):118-120. doi:10.-3969/j.issn.1000-9752.2012.10.028
[23]于卓熙.带有误差变量的自回归模型的回归函数的局部多项式估计[D].长春:吉林大学,2006:4-8.YU Zhuoxi. Local polynomial estimator of the regression function in autoregressive models with errors in variables[D]. Changchun:Jilin University, 2006:4-8.
[24]刘浩瀚.概率论与数理统计[M].北京:高等教育出版社,2015:113-115.
[25]陈元千.相对渗透率曲线和毛管压力曲线的标准化方法[J].石油实验地质,1990, 12(1):64-70.CHEN Yuanqian. Standardization on the curves of permeability and capillary pressure[J]. Experimental Petroleum Geology, 1990, 12(1):64-70.
[26]董大鹏.低渗透油田油水两相渗流机理研究[D].成都:成都理工大学,2007:71-78.DONG Dapeng. A study of percolation rules of oil-water two-phase flow in low-permeability reservoirs[D]. Chengdu:Chengdu University of Technology, 2007:71-78.
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