新型油水相渗数学模型的建立及应用

doi:10.7657/XJPG20230110

摘要/Abstract

摘要：

针对Willhite油水相渗数学模型拟合油水两相渗流数据误差较大的问题，提出了一种新型油水相渗数学模型。新模型在进行油相和水相相渗曲线拟合时，均可利用含单变量的多元线性回归求得最优解，尤其在拟合弓背式水相相渗曲线时，待定参数最优估值与常见凹型水相相渗曲线待定参数最优估值差值小，使得算术平均法确定的多个岩样的标准水相相渗曲线基本位于所有岩样水相相渗曲线的中部。在得到标准油水两相相渗曲线后，结合油井见水后的Welge方程，利用水驱油解析法，确定了水驱前缘含水饱和度、水驱前缘后平均含水饱和度、含水率、驱油效率等参数的计算式，为水驱规律研究提供了一种新的方法。

关键词: 油相, 水相, 相对渗透率, Willhite数学模型, Welge方程, 水驱油解析法, 水驱规律

Abstract:

Large errors often occur in the fitting of oil-water two-phase flow data with the Willhite mathematical model. In this paper，a new mathematical model of oil/water relative permeability was proposed. When fitting the relative permeability curves of oil phase and water phase，the new model can use the multiple linear regression method with a single variable to obtain the optimal solution. Especially，when fitting the arched relative permeability curves of water phase，the difference between the optimal estimate of undetermined parameters in the arched curves and the optimal estimate of undetermined parameters in common concave relative permeability curves of water phase is small，so that the relative permeability curves of the standard water phase for multiple rock samples determined by using the arithmetic mean method are basically located in the middle of the relative permeability curves of water phase. After obtaining the relative permeability curves of the standard oil/water phase，combining with the Welge equation after water breakthrough in the oil production well，and by using the water displacing oil analytical method，the formulas for calculating parameters such as the water saturation at the water flooding front，the average water saturation after the water flooding front，water cut，and oil displacement efficiency were determined. This study provides a new method for investigating the water flooding laws.

Key words: oil phase, water phase, relative permeability, Willhite mathematical model, Welge equation, water displacing oil analytical method, water flooding law

中图分类号:

TE341

李婧, 范晖, 刘春茹, 杨芳. 新型油水相渗数学模型的建立及应用[J]. 新疆石油地质, 2023, 44(1): 70-75.

LI Jing, FAN Hui, LIU Chunru, YANG Fang. Establishment and Application of a New Mathematical Model of Oil/Water Relative Permeability[J]. Xinjiang Petroleum Geology, 2023, 44(1): 70-75.

图/表 7

图1

表1

表2

图2

图3

图4

图5

参考文献 18

[1]	崔英怀, 高文君, 王洪关. 油藏工程基础与方法[M]. 北京: 石油工业出版社, 2018:15-24.
	CUI Yinghuai, GAO Wenjun, WANG Hongguan. Reservoir engineering fundamentals and method[M]. Beijing: Petroleum Industry Press, 2018:15-24.
[2]	陈元千, 李璗. 现代油藏工程[M]. 北京: 石油工业出版社, 2001:43-51.
	CHEN Yuanqian, LI Dang. Modern petroleum reservoir engineering[M]. Beijing: Petroleum Industry Press, 2001:43-51.
[3]	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. doi: 10.7623/syxb200704021
	ZHANG Jicheng, SONG Kaoping. Eigen curve of relative permeability and its application[J]. Acta Petrolei Sinica, 2007, 28(4):104-107. doi: 10.7623/syxb200704021
[4]	王国先, 谢建勇, 李建良, 等. 储集层相对渗透率曲线形态及开采特征[J]. 新疆石油地质, 2004, 25(3):301-304.
	WANG Guoxian, XIE Jianyong, LI Jianliang, et al. On relative permeability curves and production characteristics of reservoirs[J]. Xinjiang Petroleum Geology, 2004, 25(3):301-304.
[5]	高超, 杨满平, 王刚. 注水开发油藏油水相对渗透率曲线特征评价[J]. 复杂油气藏, 2013, 6(1):46-49.
	GAO Chao, YANG Manping, WANG Gang. Evaluation of oil/water relative permeability curve feature for water-flooding reservoirs[J]. Complex Hydrocarbon Reservoirs, 2013, 6(1):46-49.
[6]	杨宇, 周文, 邱坤泰, 等. 计算相对渗透率曲线的新方法[J]. 油气地质与采收, 2010, 17(2):105-107.
	YANG Yu, ZHOU Wen, QIU Kuntai, et al. A new method of calculating relative permeability curve[J]. Petroleum Geology and Recovery Efficiency, 2010, 17(2):105-107.
[7]	胡伟, 杨胜来, 翟羽佳, 等. 油水相对渗透率曲线优化校正新方法[J]. 石油学报, 2015, 36(7):871-875. doi: 10.7623/syxb201507011
	HU Wei, YANG Shenglai, ZHAI Yujia, et al. A new optimization and correction method of oil-water phase relative permeability curve[J]. Acta Petrolei Sinica, 2015, 36(7):871-875. doi: 10.7623/syxb201507011
[8]	高文君, 姚江荣, 公学成, 等. 水驱油田油水相对渗透率曲线研究[J]. 新疆石油地质, 2014, 35(5):552-557.
	GAO Wenjun, YAO Jiangrong, GONG Xuecheng, et al. Study on oil-water relative permeability curves in water flooding oilfields[J]. Xinjiang Petroleum Geology, 2014, 35(5):552-557.
[9]	付焱鑫, 蔡喜东, 赵嗣君, 等. 低饱和油藏渗流特征研究:以红台油田23块西山窑组油藏为例[J]. 新疆石油天然气, 2018, 14(1):68-74.
	FU Yanxin, CAI Xidong, ZHAO Sijun, et al. Research on the seepage characteristic of low saturation reservoirs in Hongtai oilfield[J]. Xinjiang Oil & Gas, 2018, 14(1):68-74.
[10]	王东琪, 殷代印. 水驱油藏相对渗透率曲线经验公式研究[J]. 岩性油气藏, 2017, 29(3):159-164.
	WANG Dongqi, YIN Daiyin. Empirical formulas of relative permeability curve of water drive reservoirs[J]. Lithologic Reservoirs, 2017, 29(3):159-164.
[11]	赵忠健, 何志祥, 李治平. 多油层分层参数测试新方法研究与实践[J]. 地质力学学报, 2006, 12(1):71-76.
	ZHAO Zhongjian, HE Zhixiang, LI Zhiping. New test methods for parameters of individual pay zones in a multi-zone reservoir research and practice[J]. Journal of Geomechanics, 2006, 12(1):71-76.
[12]	高文君, 付焱鑫, 潘有军, 等. 水驱油理论解析法[J]. 新疆石油地质, 2016, 37(1):51-55.
	GAO Wenjun, FU Yanxin, PAN Youjun, et al. Analytical method of water displacing oil theory[J]. Xinjiang Petroleum Geology, 2016, 37(1):51-55.
[13]	王陶, 朱卫红, 杨胜来, 等. 用相对渗透率曲线建立水平井采液、吸水指数经验公式[J]. 新疆石油地质, 2009, 30(2):235-237.
	WANG Tao, ZHU Weihong, YANG Shenglai, et al. Application of relative permeability curves to establishment of empirical formulas for fluid productivity index and injectivity index of horizontal well[J]. Xinjiang Petroleum Geology, 2009, 30(2):235-237.
[14]	葛家理. 现代油藏渗流力学原理[M]. 北京: 石油工业出版社, 2003:175-280.
	GE Jiali. The modern mechanics of fluids flow in oil reservoir[M]. Beijing: Petroleum Industry Press, 2003:175-280.
[15]	高文君, 殷瑞, 高能, 等. 新型分流量解析方程的建立与应用[J]. 新疆石油地质, 2021, 42(2):179-187.
	GAO Wenjun, YIN Rui, GAO Neng, et al. Establishment and application of a new analytical fractional flow equation[J]. Xinjiang Petroleum Geology, 2021, 42(2):179-187.
[16]	张金庆. 水驱曲线的进一步理论探讨及童氏图版的改进[J]. 中国海上油气, 2019, 31(1):86-93.
	ZHANG Jinqing. A further theoretical discussion on water flooding curve and improvement of Tong’s chart[J]. China Offshore Oil and Gas, 2019, 31(1):86-93.
[17]	杨明强, 高文君, 刘军辉. 采出程度与含水率和地层压力双因素数学模型及应用[J]. 长江大学学报(自然科学版), 2020, 17(6):28-36.
	YANG Mingqiang, GAO Wenjun, LIU Junhui. The two-factor mathematical model of recovery percent with both water cut and formation pressure and its application[J]. Journal of Yangtze University(Natural Science Edition), 2020, 17(6):28-36.
[18]	高文君, 铁麒, 郑巍, 等. 水驱油藏见水后Welge方程的确定及应用[J]. 新疆石油地质, 2022, 43(1):79-84.
	GAO Wenjun, TIE Qi, ZHENG Wei, et al. Determination and application of Welge equation for reservoirs after water breakthrough[J]. Xinjiang Petroleum Geology, 2022, 43(1):79-84.