水平井油水两相流阵列电磁波持水率计算方法及应用

doi:10.13809/j.cnki.cn32-1825/te.2023.04.012

摘要/Abstract

摘要：

准确求取水平井多相流持水率和反演井筒流体分布是揭示水平井开发动态的关键基础，以国产阵列电磁波持水率计为切入点开展研究，在对比分析现有阵列持水率定量计算方法基础上，提出了一种基于阵列探头径向投影中点切分面积计算持水率方法，同时对比建立了水平井筒油水两相流高、中、低含水率条件流体介质分布反演方法。研究表明，新方法计算水平井持水率平均绝对误差为4.43 %，相对误差为16.34 %，明显优于目前采用的权系数法和径向等高面积法；同时，高、中、低含水条件水平井筒流体分布反演以高斯径向基函数法和多元线性法最为匹配，研究成果为矿场水平井多相流生产动态评价奠定基础。

关键词: 水平井, 油水两相, 阵列电磁波持水率, 阵列持水率计算, 流动成像

Abstract:

The accurate calculation of the water holdup and the inversion of fluid distribution for multi-phase flow play a crucial role in understanding the development performance in horizontal wells. This study builds upon the array electromagnetic wave holdup instrument and proposes a novel method for calculating water holdup. The method is based on the weight of the mid-point tangential area of the probe's radial projection. Additionally, inversion methods for oil-water phase distribution in horizontal wells, considering high, middle, and low water content, were developed by comparing them with existing quantitative calculation methods of the array holdup instrument. The results demonstrated that the new method exhibited an average absolute error of 4.43 % and relative errors of 16.34 %. These values were significantly better than those obtained using the weight coefficient method and the radial contour area method. For the inversion of fluid distribution in horizontal wells with high, middle, and low water cut conditions, the Gaussian Radial Basis method and multivariate linear method provided the best matches. This research lays a solid foundation for evaluating the production performance of multi-phase flow in horizontal wells.

Key words: horizontal well, water and oil phase, array electromagnetic wave water holdup, array water holdup calculation methods, flowing image

中图分类号:

TE33

陈猛,谢韦峰,张煜,杨国锋,刘向君. 水平井油水两相流阵列电磁波持水率计算方法及应用[J]. 油气藏评价与开发, 2023, 13(4): 505-512.

CHEN Meng,XIE Weifeng,ZHANG Yu,YANG Guofeng,LIU Xiangjun. Methods and application for water holdup calculation and flowing image based on array electromagnetic wave instrument in horizontal water-oil wells[J]. Petroleum Reservoir Evaluation and Development, 2023, 13(4): 505-512.

图/表 14

表1

持水率计算方法比较"

计算方法	表达式	优点	适用范围
平均插值法	$Y w = ∑ i = 1 12 Y w i / 12$	简洁，高效，只考虑持水率探头测量值	层流，适用于低流量
分层界面法	$Y w = a r c c o s 1 - n / 6 - 1 - n / 6 n / 3 - n 2 / 36 π$	考虑油水分界面影响，适用于大斜井、水平井	层流，适用于低流量
成像法	式（5）—式（8）	直观反映流体分布状态	精确度与成像算法有关
权系数法	$Y w = ∑ W i Y w i$	考虑权重与探头距离、顶部距离有关	层流
径向等高面积法	A1∶A2∶A3∶A4∶A5= 0.142∶0.231∶0.253∶0.231∶0.142	准确度与面积细分程度和划分方式有关	层流

表1

图1

图2

表2

图3

图4

表3

图5

表4

表5

表6

表7

表8

图6

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理论持水率	径向等高面积法	相对误差	径向投影中点切分面积法	相对误差	平均插值法	相对误差	分层界面法	相对误差	权系数法	相对误差
100	100	0	100	0	100	0	100	0	100	0
90	86	4.4	92	2.2	75	16.7	20	77.8	91	1.1
70	63	10.0	67	4.2	59	15.7	39	44.3	64	8.6
50	39	22.0	36	28.0	43	14.0	61	22.0	39	22.0
30	18	40.0	24	20.0	35	16.7	29	3.3	28	6.7
10	21	110.0	16	60.0	30	200.0	20	100.0	21	110.0
0	0	0	0	0	0	0	0	0	0	0
平均		26.6		16.3		37.6		35.3		21.2

反演算法	原理	优点
多元线性法	持水率是x、y方向的线性函数	高含水、中含水有较好层界面识别效果
距离反比加权法	与距离呈反比例关系	高含水成像均匀，低含水时效果较差
高斯径向基函数法	与距离呈指数关系	低含水时成像效果优于其他3种方法
克里金法	与距离呈变差函数关系	低含水时成像效果略低于高斯径向基函数法

探头	高含水	中含水	低含水	探头	高含水	中含水	低含水
1	1.00	0.13	0		7	0.48	0.58	0
2	1.00	0.25	0	8	1.00	0.20	0
3	1.00	0.60	0	9	0.97	0.28	0
4	1.00	0.30	0	10	1.00	0.02	0
5	1.00	0.53	0.25	11	1.00	0.02	0
6	0.22	0.60	0.04	12	1.00	0	0

反演方法	高含水（C_w≥70 %）	中含水（30 %≤C_w<70 %）	低含水（C_w<30 %）
多元线性法
距离反比加权法
高斯径向基函数法
克里金法

成像算法	高含水	中含水	低含水
多元线性法	分层界面较清晰	分层界面较清晰	识别效果不明显
距离反比加权法	出现“牛眼”现象	分布相对均匀	出现“牛眼”现象
高斯径向基函数法	削弱油相分布	层界面波动	油水分层界面明显
克里金法	分层界面弯曲，能反映油相流体	成像结构相对均匀	界面弯曲程度大于高斯径向基法，整体均匀