Establishment and application of a new generalized mathematical model of water cut change law

doi:10.7623/syxb202207011

Acta Petrolei Sinica ›› 2022, Vol. 43 ›› Issue (7): 1007-1015,1034.DOI: 10.7623/syxb202207011

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Establishment and application of a new generalized mathematical model of water cut change law

Gao Wenjun¹, Cheng Long², Zhang Peng², Yuan Quan², Wang Wanli²

1. Research Institute of Exploration & Development, PetroChina Tuha Oilfield Company, Xinjiang Hami 839009, China;
2. Shanshan Oil Production Management District, PetroChina Tuha Oilfield Company, Xinjiang Hami 839009, China

Received:2021-04-13 Revised:2022-04-15 Online:2022-07-25 Published:2022-08-01

含水变化规律广义数学新模型的建立与应用

高文君¹, 程龙², 张棚², 袁泉², 王万里²

1. 中国石油吐哈油田公司勘探开发研究院新疆哈密 839009;
2. 中国石油吐哈油田公司鄯善采油管理区新疆哈密 839009

通讯作者: 高文君,男,1971年3月生,1994年获大庆石油学院油藏工程专业学士学位,现为中国石油吐哈油田公司勘探开发研究院高级工程师,主要从事油藏工程与提高采收率研究工作。
作者简介:高文君,男,1971年3月生,1994年获大庆石油学院油藏工程专业学士学位,现为中国石油吐哈油田公司勘探开发研究院高级工程师,主要从事油藏工程与提高采收率研究工作。Email:gaowj7132@petrochina.com.cn
基金资助:
中国石油吐哈油田公司科技专项（2022E-02-01）资助。

Abstract

Abstract: Based on the linear relationship of the existing water cut change law in the semi logarithmic coordinate system, a new generalized mathematical model of water cut change law is summarized, and the oil-water flow characteristic equation and the corresponding water drive characteristic curve of the mathematical model are derived. When the characteristic parameters n and m are taken as different values, the new mathematical model can not only be transformed into the classic water cut curves of Convex, S-Convex, S, S-Concave and Concave types, but also can describe the water cut curves of nearly S-shape or nearly linear type, which overcomes the previous empirical practice of selecting a specific water cut change law by relying on the viscosity of crude oil. By using the new generalized mathematical model of water cut change law, the data of 14 different reservoirs at home and abroad in stable water drive stage are fitted. The preliminary results show that there is a certain relationship between the characteristic parameters n and m and the mobility ratio of crude oil, which provides a new research direction for the comparative analysis of water cut rise factors between different reservoirs. Through the application of Paleogene-Neogene reservoir in Yanmuxi oilfield and the third reservoir in Kumkol North oilfield, whether the new generalized mathematical model is used for direct fitting or the corresponding water drive characteristic curve is used for indirect fitting, the fitting effect is good. This shows that the new generalized mathematical model has strong adaptability and stability, which is worth learning from other oilfields.

Key words: generalized mathematical model, water cut change law, flow characteristic equation, generalized water drive characteristic curve, flow mobility

摘要： 根据已有含水变化规律在半对数坐标系中呈直线关系的基础上，归纳出一种新的含水变化规律广义数学模型，并推导了该数学模型的油水渗流特征方程和对应的水驱特征曲线。新的数学模型在特征参数n、m取不同值时，不仅能转化为经典的凸形、S-凸形、S形、S-凹形、凹形含水变化曲线，而且也能描述近S形或近直线形含水变化曲线，克服了以往依靠原油黏度去选择某个特定含水变化规律的经验性方法的不足。利用新型含水变化规律广义数学模型，对国内外14个不同油藏稳定水驱阶段数据进行拟合的结果显示，特征参数n、m与原油的流度存在一定的关系，据此可以为不同油藏横向之间含水上升因素的对比分析提供新的研究方向。雁木西油田古近系—新近系油藏和Kumkol North油田Ⅲ油藏的应用结果表明，无论是采用新型广义数学模型进行直接拟合，还是采用其对应的水驱特征曲线进行间接拟合，其拟合效果均较好，表明新型广义数学模型具有较强的自适应性和稳定性。

关键词: 广义数学模型, 含水变化规律, 渗流特征方程, 广义水驱特征曲线, 流度

CLC Number:

TE34

Gao Wenjun, Cheng Long, Zhang Peng, Yuan Quan, Wang Wanli. Establishment and application of a new generalized mathematical model of water cut change law[J]. Acta Petrolei Sinica, 2022, 43(7): 1007-1015,1034.

高文君, 程龙, 张棚, 袁泉, 王万里. 含水变化规律广义数学新模型的建立与应用[J]. 石油学报, 2022, 43(7): 1007-1015,1034.

References

[1] 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, 1998:137-142.
HUANG Bingguang, LIU Shuzhi.Practical petroleum reservoir engineering and dynamic analysis methods[M].Beijing:Petroleum Industry Press, 1998:137-142.
[2] 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, 1989:321-330.
QIN Tongluo, LI Dang, CHEN Yuanqian.Practical reservoir engineering method[M].Beijing:Petroleum Industry Press, 1989:321-330.
[3] МАКСИМОВ М И.Метод подсчета извлекаемых запасов нефти в конечной стадии эксплуатации нефтяных пластов в условиях вытеснения нефти водой[J].Геология нефти и газа, 1959, 3:42-47.
[4] 崔传智, 徐建鹏, 王端平, 等.特高含水阶段新型水驱特征曲线[J].石油学报, 2015, 36(10):1267-1271.
CUI Chuanzhi, XU Jianpeng, WANG Duanping, et al.A new water flooding characteristic curve at ultra-high water cut stage[J].Acta Petrolei Sinica, 2015, 36(10):1267-1271.
[5] 窦宏恩, 张虎俊, 沈思博.对水驱特征曲线的正确理解与使用[J].石油勘探与开发, 2019, 46(4):755-762.
DOU Hong'en, ZHANG Hujun, SHEN Sibo.Correct understanding and application of waterflooding characteristic curve[J].Petroleum Exploration and Development, 2019, 46(4):755-762.
[6] 刘瑛, 高文君.水驱特征曲线方法系统分类研究[J].新疆石油地质, 2007, 28(5):618-621.
LIU Ying, GAO Wenjun.A systematic classification of waterflood-characteristic-curve methods[J].Xinjiang Petroleum Geology, 2007, 28(5):618-621.
[7] 俞启泰.关于如何正确研究和应用水驱特征曲线——兼答《油气藏工程实用方法》一书[J].石油勘探与开发, 2000, 27(5):122-126.

YU Qitai.How to study and apply the water displacement curves correctly -a reply to the book "Practical Methods of Petroleum Reservoir Engineering"[J].Petroleum Exploration and Development, 2000, 27(5):122-126.
[8] 陈元千.地层原油粘度与水驱曲线法关系的研究[J].新疆石油地质, 1998, 19(1):61-67.
CHEN Yuanqian.Study on the relation between formation oil viscosity and water drive curve method[J].Xinjiang Petroleum Geology, 1998, 19(1):61-67.
[9] 徐君, 高文君, 彭玮, 等.两种驱替特征曲线特性对比[J].新疆石油地质,, 2007, 28(2):194-196.
XU Jun, GAO Wenjun, PENG Wei, et al.Characteristic correlation of two water displacement curves[J].Xinjiang Petroleum Geology, 2007, 28(2):194-196.
[10] 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, 4(6):38-67.
TONG Xianzhang.On exploration of statistical regularity in naturally flooded and artificially water flooded reservoirs[J].Petroleum Exploration and Development, 1978, 4(6):38-67.
[11] 陈元千.一个新型水驱曲线关系式的推导及应用[J].石油学报, 1993, 14(2):65-73.
CHEN Yuanqian.Derivation of a new type of water displacement curve and it's application[J].Acta Petrolei Sinica, 1993, 14(2):65-73.
[12] 高文君, 徐冰涛, 王谦, 等.利用水驱特征曲线确定活塞式驱程度指数的方法[J].新疆石油地质, 2000, 21(4):311-314.
GAO Wenjun, XU Bingtao, WANG Qian, et al.Using water drive curves for determination of piston displacement degree index[J].Xinjiang Petroleum Geology, 2000, 21(4):311-314.
[13] 赫恩杰, 蒋明, 熊铁, 等.童氏图版的改进及应用[J].新疆石油地质, 2003, 24(3):232-233.
HE Enjie, JIANG Ming, XIONG Tie, et al.Modification and its application of Tong's chart method[J].Xinjiang Petroleum Geology, 2003, 24(3):232-233.
[14] 李瑞升, 李冬艳, 高文君.低黏低渗油田新型水驱规律的建立及应用[J].新疆石油天然气, 2019, 15(4):52-55.
LI Ruisheng, LI Dongyan, GAO Wenjun.Establishment and application of new water-flooding characteristic law in low viscosity and low permeability oilfields[J].Xinjiang Oil & Gas, 2019, 15(4):52-55.
[15] 邹存友, 于立君.中国水驱砂岩油田含水与采出程度的量化关系[J].石油学报, 2012, 33(2):288-292.
ZOU Cunyou, YU Lijun.A quantization relationship between water cut and degree of reserve recovery for waterflooding sandstone reservoirs in China[J].Acta Petrolei Sinica, 2012, 33(2):288-292.
[16] 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, 2018:212-278.
CUI Yinghuai, GAO Wenjun, WANG Hongguan.Reservoir engineering fundamentals and method[M].Beijing:Petroleum Industry Press, 2018:212-278.
[17] 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.
YU Qitai.Characteristics of oil water seepage flow for several important water drive curves[J]. Acta Petrolei Sinica, 1999, 20(1):56-60.
[18] WELGE H J.A simplified method for computing oil recovery by gas or water drive[J].Journal of Petroleum Technology, 1952, 4(4):91-98.
[19] 沈永欢, 梁在中, 许履瑚, 等.实用数学手册[M].北京:科学出版社, 1992:298-306.
SHEN Yonghuan, LIANG Zaizhong, XU Lühu, et al.Handbook of practical mathematics[M].Beijing:Science Press, 1992:298-306.
[20] 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.
[21] 钟德康.相对渗透率相关方程式的研究与应用[J].大庆石油地质与开发, 1985, 4(4):37-46.
ZHONG Dekang.Study on correlation equation for relative permeability and its application[J].Petroleum Geology & Oilfield Development in Daqing, 1985, 4(4):37-46.
[22] 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.
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.
[23] 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.
[24] 狄勤丰, 张景楠, 叶峰, 等.驱替过程中重力舌进特征的核磁共振可视化实验[J].石油学报, 2017, 38(10):1183-1188.
DI Qinfeng, ZHANG Jingnan, YE Feng, et al.Nuclear magnetic resonance visualization experiment of gravity tongue characteristics in the displacement process[J].Acta Petrolei Sinica, 2017, 38(10):1183-1188.
[25] 胡绍彬, 徐庆龙, 郭玲玲, 等.采出液含水对生产气油比的影响规律[J].石油学报, 2018, 39(1):116-121.
HU Shaobin, XU Qinglong, GUO Lingling, et al.Influence of water cut of produced liquid on produced gas-oil ratio[J].Acta Petrolei Sinica, 2018, 39(1):116-121.
[26] 毕海滨, 段晓文, 郑婧, 等.致密油生产动态特征及可采储量评估方法[J].石油学报, 2018, 39(2):172-179.
BI Haibin, DUAN Xiaowen, ZHENG Jing, et al.Production dynamic characteristics and recoverable reserve estimation method of tight oil[J].Acta Petrolei Sinica, 2018, 39(2):172-179.
[27] 崔传智, 李松, 杨勇, 等.特高含水期油藏平面分区调控方法[J].石油学报, 2018, 39(10):1155-1161.
CUI Chuanzhi, LI Song, YANG Yong, et al.Planar zoning regulation and control method of reservoir at ultra-high water cut stage[J].Acta Petrolei Sinica, 2018, 39(10):1155-1161.
[28] 高文君, 殷瑞, 杨静.新型水驱特征曲线的建立及理论基础[J].石油学报, 2020, 41(3):342-347.
GAO Wenjun, YIN Rui, YANG Jing.Establishment and theoretical basis of the new water-flooding characteristic curve[J].Acta Petrolei Sinica, 2020, 41(3):342-347.
[29] 计秉玉.对油气藏工程研究方法发展趋势的几点认识[J].石油学报, 2020, 41(12):1774-1778.
JI Bingyu.Some understandings on the development trend in research of oil and gas reservoir engineering methods[J].Acta Petrolei Sinica, 2020, 41(12):1774-1778.
[30] 郭建林, 郭智, 崔永平, 等.大型致密砂岩气田采收率计算方法[J].石油学报, 2018, 39(12):1389-1396.
GUO Jianlin, GUO Zhi, CUI Yongping, et al.Recovery factor calculation method of giant tight sandstone gas field[J].Acta Petrolei Sinica, 2018, 39(12):1389-1396.

Establishment and application of a new generalized mathematical model of water cut change law

含水变化规律广义数学新模型的建立与应用

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