﻿ 利用微地震事件重构三维缝网
 石油地球物理勘探  2019, Vol. 54 Issue (1): 102-111  DOI: 10.13810/j.cnki.issn.1000-7210.2019.01.012 0
 文章快速检索 高级检索

### 引用本文

LIU Xing, JIN Yan, LIN Botao, XIANG Jianhua, ZHONG Hua. A 3D fracture network reconstruction method based on microseismic events. Oil Geophysical Prospecting, 2019, 54(1): 102-111. DOI: 10.13810/j.cnki.issn.1000-7210.2019.01.012.

### 文章历史

① 中国石油大学(北京)石油工程学院, 北京 102200;
② 中国石油西南油气分公司, 四川成都 610065

A 3D fracture network reconstruction method based on microseismic events
LIU Xing , JIN Yan , LIN Botao , XIANG Jianhua , ZHONG Hua
① College of Petroleum Engineering, China University of Petroleum(Beijing), Beijing 102200, China;
② Southwest Oil & Gas Field Company, PetroChina, Chengdu, Sichuan 610065, China
Abstract: Previous research mainly focused on building 2D fracture models from the point view of qualitative and macroscopic.Microseismic events were often used to deprive some critic parameters to calibrate random discrete fracture model based on certain assumptions.As a result, there is a lack of robust methods to build 3D fracture network after fracturing.To solve this problem, we firstly apply the random sample consensus (RANSAC) method to detect fracture planes according to the geometric correlation between microseismic events and real fracture networks.After that, we develop a computing algorithm called robust 3D fracture reconstruction (RFM3D) to reconstruct 3D fracture network on the basis of building realistic single fracture geometric model.To verify the robustness and effectiveness of the algorithm, we put forward average distance index (ADI) to evaluate the similarity between two fracture networks.Also, analog events generated by Monte Carlo simulation added in noise points of different proportions are used to test the algorithm.The results show that:①Convex polygons can be used to describe real fracture geometric shape after fracturing experiments; ②RFM3D is easy to adapt different complex geometric models.It can eliminate effects of 10% noise and give a relatively accurate reconstruction of 3D fracture network under normal circumstances.Therefore, it has good robustness; ③The fracture network similarity index (ADI) increase with noise ratio in a logistic pattern and critical ADI value decreased with increase of noise ratio.Accordingly, it is necessary to eliminate noise in events under 10% to obtain an accurate and robust fracture network reconstruction.
Keywords: microseismic monitoring    3D fracture network    random sample consensus    fracture network reconstruction    hydraulic fracturing
0 引言

1 RFM3D原理 1.1 单裂缝几何模型及识别算法

 图 1 水力压裂物模实验及缝网描绘 (a)物模岩样1；(b)多边形双翼缝；(c)物模岩样2；(d)多边形复杂缝网σh为最小水平主应力，σH为最大水平主应力，σV为垂直主应力。

 $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1$ (1)
 图 2 随机多边形单裂缝几何模型

 {{\alpha }_{1}}=\left\{ \begin{align} &~\ \ \text{arctan}\left( -\frac{b}{a} \right)\ \ \ \text{arctan}\left( -\frac{b}{a} \right)\ge 0 \\ &\text{arctan}\left( -\frac{b}{a} \right)+\pi \ \ \ \ \ \text{arctan}\left( -\frac{b}{a} \right)<0 \\ \end{align} \right. (2)

 ${{\alpha }_{2}}=\text{arctan}\left( \text{ }\!\!~\!\!\text{ }\left| c \right|\sqrt{\frac{{{a}^{2}}+{{b}^{2}}}{\left| ab \right|}} \right)$ (3)

 {{\alpha }_{3}}~=\left\{ \begin{align} &{{\alpha }_{1}}+\frac{\pi }{2}\text{sgn}(a)\text{sgn}(c)=1, \text{sgn}(a)\text{sgn}(b)=1 \\ &{{\alpha }_{1}}+~\frac{3\pi }{2}\text{sgn}(a)\text{sgn}(c)=-1 \\ &{{\alpha }_{1}}-\frac{\pi }{2}\text{sgn}(a)\text{sgn}(c)=1, \text{sgn}(a)\text{sgn}(b)=-1 \\ \end{align} \right. (4)

 图 3 alpha-shape形状识别算法示意图
1.2 基于RANSAC的裂缝产状识别方法

RANSAC由Fisvhler等[21]首次提出，主要为了解决被部分噪点污染的数据集的最小二乘估计失真问题。该算法基于随机抽样改进传统的最小二乘法，大大增强了对有效点集的识别，在噪点比例超过10%时仍然能识别有效点集，是一种非常稳健的拟合算法，因此在图像处理领域得到广泛应用。对于单裂缝产状的识别，RANSAC首先将所处理的点集分为噪点和有效点，通过随机抽样挑选一个随机样本；然后使用人为设定的阈值将样本的噪点率控制在合理范围内；最后将选择的样本代入给定的裂缝产状几何方程(式(1))，通过回归得到几何模型的对应产状参数(图 4)。

 图 4 RANSAC算法识别单裂缝产状示意图
1.3 RFM3D

 图 5 基于微地震数据的RFM3D流程

(1) 从微地震事件集合S中随机抽取一个大小为n的样本，并将样本进行裂缝产状模型最小二乘回归得到模型产状参数αtest

(2) 设定距离阈值t，计算剩余所有微地震事件点到该裂缝面的距离，由统计得到在阈值范围内的点集StestS，当Stest的大小满足要求时，认为选定的点集符合裂缝的拟合条件。

(3) 重复步骤(1)，再次随机选择一个大小为n的样本，得到阈值范围内的标识点集Sin和产状参数标识向量αc，如果|Sin|＜|Stest|，令Sin=Stest，则αc= αtest

(4) 设定点集阈值为T，重复步骤(1)~(3)，直到|Sin|≥T为止，经统计得到总迭代次数N，进而得到首个单裂缝产状参数向量α11= αc，并将Sin代入alpha-shape形状识别算法，得到裂缝的形状参数向量α12，通过组合得到首个裂缝几何模型的全部产状和形状参数向量α1

(5) 从原始事件点集S中去除Sin得到剩余微地震事件点集Sres，对Sres重复步骤(1)~(4)得到第二个裂缝模型的全部参数向量α2

(6) 重复步骤(1)~步骤(5) m次，直止得到所有裂缝的几何参数向量α1, …, αm，算法运行结束。

 $N=~\frac{\text{lg}\left( 1-p \right)~}{\text{lg}(1-{{\omega }^{n}})}$ (5)

2 模型稳健性定量分析 2.1 模型稳健性模拟分析

 图 6 不同裂缝数目m的缝网模拟结果(噪点比例均为10%) (a)m=5；(b)m=10；(c)m=15；(d)m=20

 图 7 裂缝数目为10的不同噪点比例的RFM3D结果 (a)原始缝网；(b)5%；(c)10%；(d)15%；(e)20%；(f)25%
2.2 模型鲁棒性分析方法

 图 8 多边形裂缝相似性度量示意图

(1) 假设模拟缝网和重构缝网的个数均为m，首先确定两种缝网的单裂缝对应关系，形成m个裂缝对。

(2) 分别计算第i个裂缝对的顶点平均距离Lfi和裂缝中心点的距离Dfi

(3) 重复步骤(1)~(2)遍历所有裂缝对，得到重构缝网和模拟缝网的平均单裂缝ADI

 $\text{ADI}=\frac{\sum\limits_{i=1}^{m}{(\text{L}{{\text{f}}_{i}}+\text{D}{{\text{f}}_{i}})}}{2m}$ (6)

2.3 缝网相似性模拟分析

 图 9 RFM3D算法噪点比例—ADI曲线 设定噪点比例范围为0~200%(步长为2%)，缝网中裂缝数目分别为3、5、7、9、10(步长为2)，编写MATLAB程序对每种缝网进行100次RFM3D，分别计算重构缝网和模拟缝网的ADI

 图 10 m—噪点比例曲线
2.4 模型稳健性定量分析

3 工程应用分析 3.1 工程地质背景

YY1井位于川中隆起区的川西南低陡褶带，钻遇志留系龙马溪组页岩储层，平均孔隙度为5.28%，基质渗透率均值分布范围为(4~5)×10-5mD，含气孔隙度平均值为2%，含气饱和度平均值约为50%，总体上储层物性较好。井下成像测井和岩心资料表明，YY1井中的天然裂缝主要为构造裂缝以及超压填充裂缝，其中构造裂缝形成的张开缝多为高角度垂直缝，超压裂缝多为微细裂缝，空间呈网状分布，延伸距离较小，大多数被矿物充填(图 11a)；该区最大水平主应力方位约为135°(图 11b)，YY1井所在地区天然裂缝总体发育方向(图 11c)与该区最大主应力方向夹角较大，在水力压裂过程中地应力使高角度天然裂缝闭合，因此不利于天然裂缝的张开[23]。由YY1井三个压裂段微地震监测结果(图 12)可见：①由于地应力的屏蔽作用，未出现远井天然裂缝的激发响应产生的微地震事件点，均匀分布的事件点有利于RFM3D，在一定程度上降低了由孤立事件点引起的误差；②YY1井微地震监测为3级接收，现场实时处理并定位的有效微地震事件点共1800个；③从微地震事件震级及分布特征看，事件在压裂施工全程均有发生，受地应力屏蔽作用的影响，事件点沿井分布较为集中，未出现高导流的长段水力裂缝，并且在3个施工段分布相对均匀；④对于每一级压裂来说，平均缝长和平均缝宽约为200m。为了评估YY1井压裂效果，对YY1井的微地震事件点进行RFM3D，并结合地应力和天然裂缝分析结果对RFM3D结果进行对比、验证。

 图 11 YY1井地应力方位和裂缝方位[24] (a)YY1井裂缝特征；(b)最大水平主应力方位；(c)天然裂缝方位

 图 12 YY1井三个压裂段微地震监测结果
3.2 RFM3D结果分析

 图 13 YY1井RFM3D结果(a)及裂缝与微地震事件对比图(b)

 图 14 YY1井三维缝网产状分布
4 结束语

(1) 通过室内压裂实验发现，可用随机多边形模型描述实际裂缝形状。

(2) RFM3D算法易于匹配复杂的裂缝几何模型，在一般条件下该算法至少能克服10%的噪点干扰，可较准确地重构压裂缝网的几何形态，算法具有较好的稳健性。

(3) 随着噪点比例增大，重构相似性指标(ADI)随噪点比例满足logistic增长模式；随着缝网中裂缝数目的增多，ADI临界点也随之降低。因此，在重构大规模体积缝网时噪点比例应严格控制在10%以下才能得到稳定、可靠的结果。

 [1] 闫鑫, 胡天跃, 何怡原. 地表测斜仪在监测复杂水力裂缝中的应用[J]. 石油地球物理勘探, 2016, 51(3): 480-486. YAN Xin, HU Tianyue, HE Yiyuan. Application of surface tiltmeter in monitoring complicated hydraulic fractures[J]. Oil Geophysical Prospecting, 2016, 51(3): 480-486. [2] 严永新, 张永华, 陈祥, 等. 微地震技术在裂缝监测中的应用研究[J]. 地学前缘, 2013, 20(3): 270-274. YAN Yongxin, ZHANG Yonghua, CHEN Xiang, et al. The application of microseismic technology in fracture monitoring[J]. Earth Science Frontiers, 2013, 20(3): 270-274. [3] 刘博, 梁雪莉, 容娇君, 等. 非常规油气层压裂微地震监测技术及应用[J]. 石油地质与工程, 2016, 30(1): 142-145. LIU Bo, LIANG Xueli, RONG Jiaojun, et al. Microseismic monitoring technology and its application in unconventional reservoir fracturing[J]. Petroleum Geology and Engineering, 2016, 30(1): 142-145. DOI:10.3969/j.issn.1673-8217.2016.01.038 [4] 容娇君, 李彦鹏, 徐刚, 等. 微地震裂缝检测技术应用实例[J]. 石油地球物理勘探, 2015, 50(5): 919-924. RONG Jiaojun, LI Yanpeng, XU Gang, et al. Fracture detection with microseismic[J]. Oil Geophysical Prospecting, 2015, 50(5): 919-924. [5] 张山, 刘清林, 赵群, 等. 微地震监测技术在油田开发中的应用[J]. 石油物探, 2002, 41(2): 226-231. ZHANG Shan, LIU Qinglin, ZHAO Qun, et al. Application of microseismic monitoring technology in development of oil field[J]. Geophysical Prospecting for Petroleum, 2002, 41(2): 226-231. DOI:10.3969/j.issn.1000-1441.2002.02.021 [6] 唐杰, 方兵, 蓝阳, 等. 压裂诱发的微地震震源机制及信号传播特性[J]. 石油地球物理探, 2015, 50(4): 643-649. TANG Jie, FANG Bing, LAN Yang, et al. Focal mechanism of micro-seismic induced by hydro-fracture and its signal propagation[J]. Oil Geophysical Prospecting, 2015, 50(4): 643-649. [7] Cai M, Kaiser P K, Martin C D. Quantification of rock mass damage in underground excavations from microseismic event monitoring[J]. International Journal of Rock Mechanics and Mining Sciences, 2001, 38(8): 1135-1145. DOI:10.1016/S1365-1609(01)00068-5 [8] Sherilyn W, Ozgen C, Billingsley R L. Methods to cali-brate low-amplitude surface monitoring microseismic results via integration of geology, production data and reservoir simulation[J]. CSEG Recorder, 2012, 37(8): 32-38. [9] Maxwell S C, Weng X, Kresse O, et al.Modeling microseismic hydraulic fracture deformation[C]. SPE Annual Technical Conference and Exhibition, 2013, 1-10. [10] 赵争光, 秦月霜, 杨瑞召. 地面微地震监测致密砂岩储层水力裂缝[J]. 地球物理学进展, 2014, 29(5): 2136-2139. ZHAO Zhengguang, QIN Yueshuang, YANG Ruizhao. Hydraulic fracture mapping for a tight sands reservoir by surface based microseismic monitoring[J]. Progress in Geophysics, 2014, 29(5): 2136-2139. [11] Yu X, Rutledge J, Leaney S, et al. Discrete fracture network generation from microseismic data by use of moment tensor and event location constrained hough transforms[J]. SPE Journal, 2016, 21(1): 221-232. DOI:10.2118/168582-PA [12] 杨瑞召, 李德伟, 庞海玲, 等. 页岩气压裂微地震监测中的裂缝成像方法[J]. 天然气工业, 2017, 37(5): 31-37. YANG Ruizhao, LI Dewei, PANG Hailing, et al. Fracture imaging of the surface based microseismic monitoring in shale gas fracking:methods and application[J]. Natural Gas Industry, 2017, 37(5): 31-37. [13] 张云银, 刘海宁, 李红梅, 等. 应用微地震监测数据估算储层压裂改造体积[J]. 石油地球物理勘探, 2017, 52(2): 309-314. ZHANG Yunyin, LIU Haining, LI Hongmei, et al. Reservoir fracturing volume estimation with micro-seismic monitoring data[J]. Oil Geophysical Prospecting, 2017, 52(2): 309-314. [14] 宋维琪, 冯超. 微地震有效事件自动识别与定位方法[J]. 石油地球物理勘探, 2013, 48(2): 283-288. SONG Weiqi, FENG Chao. Automatic identification and localization of microseismic effective events[J]. Oil Geophysical Prospecting, 2013, 48(2): 283-288. [15] Baecher G B. Statistical analysis of rock mass fracturing[J]. Journal of the International Association for Mathematical Geology, 1983, 15(2): 329-348. DOI:10.1007/BF01036074 [16] Geier J E, Lee K, Dershowitz W S. Field validation of conceptual models for fracture geometry[J]. Transactions of American Geophysical Union, 1988, 69(44): 1177. [17] Dershowitz W S.Rock Joint Systems[D]. Massachu-setts Institute of Technology, Massachusetts, USA, 1984, 520-534. [18] Stsub I, Fredriksson A, Outters N.Strategy for a rock mechanics site descriptive model[R]. SKB Report R-02-02, Swedish Nuclear Fuel and Waste Management Co, 2002, 25-26. [19] Alghalandis Y F. ADFNE:Open source software for discrete fracture network engineering, two and three-dimensional applications[J]. Computers & Geosciences, 2017, 102(5): 1-11. [20] Liang J, Edelsbrunner H, Fu P, et al. Analytical shape computation of macromolecules:Ⅰ.Molecular area andvolume through alpha shape[J]. Proteins, 1998, 33(1): 1-17. DOI:10.1002/(ISSN)1097-0134 [21] Fisvhler M A, Bolles R C. Random sample consensus:a paradigm for model fitting with applications to ima-ge analysis and automated cartography[J]. Communications of the ACM, 1981, 24(6): 381-395. DOI:10.1145/358669.358692 [22] 刘宏申, 秦锋. 确定轮廓形状匹配中形状描述函数的方法[J]. 华中科技大学学报(自然科学版), 2005, 33(4): 13-16. LIU Hongshen, QIN Feng. Method of determining the function of description of shape in shape matching[J]. Journal of Huazhong University of Science & Technology (Nature Science Edition), 2005, 33(4): 13-16. DOI:10.3321/j.issn:1671-4512.2005.04.005 [23] 黄继新, 彭仕宓, 王小军, 等. 成像测井资料在裂缝和地应力研究中的应用[J]. 石油学报, 2006, 27(6): 65-69. HUANG Jixin, PENG Shimi, WANG Xiaojun, et al. Applications of imaging logging data in the research of fracture and ground stress[J]. Acta Petrolei Sinica, 2006, 27(6): 65-69. DOI:10.3321/j.issn:0253-2697.2006.06.014 [24] 李亚男.页岩气储层测井评价及其应用——以川南地区为例[D].北京: 中国矿业大学(北京), 2014. [25] Peng Tan, Yan Jin, Ke Han, et al. Analysis of hydraulic fracture initiation and vertical propagation behavior in laminated shale formation[J]. Fuel, 2017, 206(10): 482-493.