A Robust Plane Identification Algorithm for Hydraulic Fracture

doi:10.19596/j.cnki.1001-246x.8773

Abstract

Abstract:

The fracture morphology of hydraulic fracturing is a key parameter for evaluating the fracturing effect and predicting the yield. At present, the fracture information of fractured cracks is mainly extracted by microseismic monitoring at home and abroad, and it is difficult to obtain the fracture morphology through the planar identification algorithm by utilizing the microseismic data due to the existence of complex noise. For this reason, this paper proposes a robust planar identification algorithm for hydraulic fracturing cracks, the sampling projection algorithm (RANSAC-MP), which weakens the outlier noise caused by irrelevant rupture events through random sampling, and proposes a maximal projection planar fitting algorithm to minimize the influence of environmental noise, and at the same time, combines the noise resistance of the RANSAC algorithm and the advantages of the projection method with the noise resistance of the RANSAC algorithm. noise immunity and the dimension reduction effect of the projection method. The results show that the RANSAC-MP algorithm shows stronger robustness and higher computational accuracy under the influence of multiple noises, and the algorithm can directly process the original data when only a single fracture is formed by fracturing.

Key words: multiple noise effects, sampling-projection (RANSAC-MP), fracture identification, hydraulic fracturing, microseismic data points, robustness

CLC Number:

TE357

Ziyu LIN, Yuetian LIU, Xuehao PEI, Pingtian FAN, Liang XUE. A Robust Plane Identification Algorithm for Hydraulic Fracture[J]. Chinese Journal of Computational Physics, 2024, 41(5): 630-642.

Figures/Tables 14

Fig.1 Crack plane with normal vector n =[a, b, c]

Fig.2 Schematic diagram of RANSAC sampling points

Fig.3 3D scatter projection and control area (a) 3D scatter projection onto 2D plane; (b) intersecting circles appear; (c) an isolated circle

Fig.4 RANSAC-MP algorithm full process

Fig.5 Microseismic points with Gaussian noise at different scales and standard deviations (a)~(d) 100% data points with added Gaussian noise; (e)~(h) 50% data points with added Gaussian noise

Fig.6 Plane fitted by four algorithms with 100% data points with added Gaussian noise

Fig.7 Variations of plane normal vector pinch angle residuals with noise standard deviation fitted by different algorithms (100% data points with Gaussian noise added)

Fig.8 Variations of plane normal vector pinch angle residuals with noise standard deviation fitted by different algorithms (50% data points with Gaussian noise added)

Fig.9 Plane fitted by four algorithms at random noise

Table 1 Residuals of plane normal vector pinch angle fitted by different algorithms

添加Ⅱ类噪声比例/%	平面法向量夹角残差
添加Ⅱ类噪声比例/%	RANSAC-MP(K=3)	RANSAC-MP(K=5)	RANSAC-MP(K=7)	RANSAC	PCA	LS
0	0.00	0.00	0.00	0.00	0.00	0.00
2	0.00	0.00	0.00	0.00	1.15	1.43
10	0.00	0.00	0.00	0.00	3.91	6.48
20	0.00	0.00	0.00	0.00	2.78	8.82
30	0.00	0.00	0.00	0.00	5.70	8.27

Fig.10 Residuals of plane normal vector pinch angles fitted by different algorithms at multiple noises (a)100%, σ=0.1; (b) 100%, σ=0.2; (c) 100%, σ=0.3; (d) 50%, σ=0.1; (e) 50%, σ=0.2; (f) 50%, σ=0.3

Fig.11 Microseismic data from well N1 fitted by RANSAC-MP algorithm (a) original microseismic points; (b) microseismic points after noise reduction

Fig.12 Microseismic data from well N2 fitted by RANSAC-MP algorithm (a) original microseismic points; (b) microseismic points after noise reduction

Table 2 Planar fracture directions fitted by different algorithms

走向	RANSAC-MP(K=5)		RANSAC		PCA		LS
走向	降噪前/°	降噪后/°	降噪前/°	降噪后/°	降噪前/°	降噪后/°	降噪前/°	降噪后/°
N1	NE76.0	NE80.0	NE74.9	NE80.1	NE49.2	NE81.5	NE49.2	NE81.6
N2	NE61.3	NE64.6	NE60.8	NE65.7	NE44.9	NE60.7	NE44.8	NE60.5

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