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

Abstract

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

CLC Number:

TE33

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.

Figures/Tables 14

Table 1

Comparison of different water holdup calculation methods"

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

Table 1

Fig. 1

Fig. 2

Table 2

Fig. 3

Fig. 4

Table 3

Fig. 5

Table 4

Table 5

Table 6

Table 7

Table 8

Fig. 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

Methods and application for water holdup calculation and flowing image based on array electromagnetic wave instrument in horizontal water-oil wells

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面积法	权重
径向等高面积法	A1∶A2∶A3∶A4∶A5=0.142∶0.231∶0.253∶0.231∶0.142
径向投影中点切分面积法	A1∶A2∶A3∶A4∶A5∶A6∶A7=0.011∶0.075∶0.250∶0.327∶0.250∶0.075∶0.011

介质	1号	2号	3号	4号	5号	6号	7号	8号	9号	10号	11号	12号
气	7 793	8 217	7 877	7 952	8 290	8 166	8 094	7 924	7 840	7 956	8 039	7 924
油	9 693	10 117	9 777	9 852	10 190	10 066	9 994	9 824	9 740	9 856	9 939	9 824
水	20 382	19 227	21 247	21 267	19 042	18 270	19 433	21 446	22 593	21 983	19 987	21 227

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