邻井分布式光纤监测水力裂缝扩展半解析正演模型

doi:10.3969/j.issn.2096-1693.2025.02.018

石油科学通报 ›› 2025, Vol. 10 ›› Issue (4): 778-790. doi: 10.3969/j.issn.2096-1693.2025.02.018

邻井分布式光纤监测水力裂缝扩展半解析正演模型

毛渝¹^,²(), 陈勉¹^,²^,^*(), 隋微波¹^,², 何乐³, 朱炬辉³

1 中国石油大学(北京)石油工程学院，北京 102249
2 中国石油大学(北京)油气资源与探测国家重点实验室，北京 102249
3 中国石油集团川庆钻探工程有限公司井下作业公司，成都 610051

收稿日期:2024-10-27 修回日期:2025-03-07 出版日期:2025-08-15 发布日期:2025-08-05
通讯作者: *陈勉(1962年—)，博士、教授、博士生导师，主要从事石油工程岩石力学研究，chenm@cup.edu.cn。
作者简介:毛渝(1999年—)，在读博士研究生，主要从事石油工程水力压裂光纤监测研究，myleyu@126.com。
基金资助:
国家自然科学基金重点项目“提高超深大斜度井压裂效率的关键力学问题研究”(52334001);中国石油集团油田技术服务有限公司科学研究与技术开发项目“页岩油气勘探开发关键技术研究与应用”课题4“页岩储层光纤智能监测与裂缝评价技术研究与应用”(2023T-002-001)

Semi-analytical forward model for hydraulic fracture propagation monitoring using distributed fiber optics in adjacent wells

MAO Yu¹^,²(), CHEN Mian¹^,²^,^*(), SUI Weibo¹^,², HE Le³, ZHU Juhui³

1 College of Petroleum Engineering, China University of Petroleum, Beijing 102249, China
2 State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing 102249, China
3 CNPC Chuanqing Drilling Engineering Company Limited Downhole Operation Company, Chengdu 610051, China

Received:2024-10-27 Revised:2025-03-07 Online:2025-08-15 Published:2025-08-05

摘要/Abstract

摘要：

邻井分布式光纤监测技术逐渐成为非常规油气藏压裂过程中裂缝监测的重要手段之一，建立邻井分布式光纤应变正演模型对于探究邻井光纤应变响应机理和裂缝几何特征反演等具有重要意义，但现有的光纤应变响应正演解释模型存在裂缝扩展模型选择灵活性不足和网格精度导致的计算效率降低等问题。本文建立了任意开度与几何形态裂缝扩展过程中应力—位移场的半解析计算模型，构建了邻井光纤应变正演模型。通过硬币型裂缝计算案例对裂缝周围应力场进行求解并与Sneddon解析解进行了对比分析，采用水平邻井光纤监测垂直椭圆裂缝计算案例正演了邻井光纤应变响应，并与位移不连续法邻井光纤应变正演结果进行对比分析，分析表明本文模型在经典常规算例下的计算结果与解析方法和位移不连续方法具有一致性。本文进一步将不同裂缝扩展模型与半解析应变计算模型耦合应用于现场光纤数据解释，针对美国HFTS-2矿场实验中B1H井19段和B2H井20段邻井光纤监测结果，本模型模拟结果契合了现场光纤数据响应特征模式，对于呈现复杂特征的B2H井20段，本文模型模拟结果在细节特征和时间尺度上相较于位移不连续法计算模型有更好的对应效果。本模型建立了任意开度与几何形态裂缝扩展邻井光纤应变正演模型，减少了邻井光纤正演计算量，同时可以耦合多种裂缝扩展模型，在现场数据正演解释中可以实现细节特征和时间尺度的更优匹配。

关键词: 水力压裂, 光纤监测, 半解析, 裂缝监测, 正演模型

Abstract:

Distributed fiber optic monitoring in adjacent wells has increasingly become an essential technique for fracture surveillance during hydraulic fracturing of unconventional oil and gas reservoirs. Developing forward models for distributed fiber optic strain response in adjacent wells is of significant importance for understanding the mechanism of fiber response and for the inversion of fracture geometries. However, existing forward interpretation models face limitations from insufficient flexibility in the selection of fracture propagation models, and by computational inefficiency caused by grid-based discretization, especially when high precision is required. To address these limitations, this study presents a semi-analytical stress-displacement field model for simulating fracture propagation with arbitrary aperture and geometric shape. Based on this, a forward modeling framework for adjacent well distributed fiber optic strain response is established. Using a penny-shaped fracture as a representative example, the stress field around the fracture is calculated and benchmarked against the classical Sneddon analytical solution. A forward simulation of fiber optic strain response for a scenario where a horizontal adjacent well monitors a vertically oriented elliptical fracture is conducted. The results are compared with the forward-modeled strain response from the Displacement Discontinuity Method(DDM). The results reveal strong consistency between the semi-analytical model and both the analytical and DDM solutions in classical benchmark cases, confirming the model’s validity and applicability. The model is further coupled with various fracture propagation models and applied to the interpretation of real field data. In particular, distributed fiber optic monitoring results from Stage 19 of Well B1H and Stage 20 of Well B2H in the Hydraulic Fracturing Test Site 2 (HFTS-2) project in the United States are analyzed. The modeling results show that the proposed approach accurately reproduces the characteristic patterns observed in field fiber data. For Stage 20 of Well B2H, which exhibits higher-complexity response characteristics, the model provides a closer match to observed details and temporal evolution compared with the DDM-based approach. In conclusion, this study establishes a semi-analytical forward modeling approach for fiber optic strain in adjacent wells under arbitrary fracture aperture and geometry, significantly reducing computational cost and improving efficiency. The model’s flexibility enables seamless integration with a variety of fracture propagation models, enhancing its capacity to accurately capture complex fracture behaviors observed in field monitoring. This provides a powerful tool for detailed interpretation and analysis of distributed fiber optic data in adjacent well applications.

Key words: hydraulic fracturing, fiber optic monitoring, semi-analytical, fracture monitoring, forward model

中图分类号:

TE33
TE357

毛渝, 陈勉, 隋微波, 何乐, 朱炬辉. 邻井分布式光纤监测水力裂缝扩展半解析正演模型[J]. 石油科学通报, 2025, 10(4): 778-790.

MAO Yu, CHEN Mian, SUI Weibo, HE Le, ZHU Juhui. Semi-analytical forward model for hydraulic fracture propagation monitoring using distributed fiber optics in adjacent wells[J]. Petroleum Science Bulletin, 2025, 10(4): 778-790.

https://sykxtb.cup.edu.cn/CN/Y2025/V10/I4/778

图/表 19

图1 裂缝扩展邻井LF-DAS响应示意图^[21]

Fig. 1 Schematic diagram of adjacent well LF-DAS response to fracture propagation^[21]

图2 邻井光纤监测水力压裂过程示意图

Fig. 2 Schematic diagram of hydraulic fracturing monitoring process using fiber optics in adjacent wells

图3 裂缝扩展时地层应力状态示意图(红色区域为裂缝面)

Fig. 3 Schematic diagram of the stress state in the formation during fracture propagation (the red area represents the fracture surface)

图4 通过点力等效替代裂缝内压力示意图

Fig. 4 Schematic diagram of pressure inside the fracture equivalent to point force substitution

图5 z=0平面σ_z随r/c变化图

Fig. 5 The σ_z with r/c changes in the z=0 plane

图6 光纤测点i与标距l示意图

Fig. 6 Schematic diagram of fiber optic measurement point i and gauge length l

图7 邻井光纤应变率求解流程图

Fig. 7 Flowchart for solving fiber optic strain rate in adjacent wells

图8 硬币型裂缝应力计算示意图

Fig. 8 Schematic diagram of stress calculation for a Sneddon penny-shaped crack

图9 硬币型裂缝模式下本文模型与Sneddon计算方法应力分布对比图

Fig. 9 Comparison of stress distribution for a pennyshaped crack calculated by the paper's model and Sneddon’s method

图10 光纤监测井(红色)与压裂井分布示意图

Fig. 10 Schematic diagram of the fiber optic monitoring well (red) and fractured well

表1 模型对比模拟参数表

Table 1 Comparative simulation parameters of the models

弹性模量/GPa	泊松比	泵注排量/(m³/min)	泵注时间/min	压粘度/cp	滤失系数/(m/s^0.5)	固定缝高/m
21.4	0.26	3.18	60	5	0.000 09	21

图11 本文半解析方法与Liu等方法应变率计算结果对比

Fig. 11 The strain rates calculated by the semi-analytical method in this paper and Liu et al’s

图12 裂缝半缝长与压裂时间关系图

Fig. 12 Relationship between half-fracture length and fracturing time

图13 美国HFTS-2矿场试验井位分布图^[18,35]

Fig. 13 Well location distribution map of the HFTS-2 field test in the United States^[18,35]

表2 现场水平邻井监测模拟参数表

Table 2 Simulation parameters for field horizontal adjacent well monitoring

弹性模量/GPa	泊松比	泵注排量/(m³/min)	泵注时间/min	压裂液粘度/cp	滤失系数/(m/s^0.5)	固定缝高/m
21.4	0.26	4	300	5	0.0011	21

图14 B1H井第19段水平邻井监测现场数据(左)与半解析模型正演结果(右)对比图

Fig. 14 Comparison between field data from the 19th stage of well B1H horizontal adjacent well monitoring (left) and forward modeling results of the semi-analytical model (right)

表3 现场垂直邻井监测模拟参数表

Table 3 Simulation parameters for field vertical adjacent well monitoring

弹性模量/GPa	泊松比	泵注排量/(m³/min)	泵注时间/min	压裂液粘度/cp	滤失系数/(m/s^0.5)
21.4	0.26	4	300	5	0.00005

图15 现场垂直邻井监测模拟裂缝缝高与缝长随时间变化示意图

Fig. 15 Schematic diagram of the variation of fracture height and length with time in field vertical adjacent well monitoring simulation

图16 B2H井第20段垂直邻井监测现场数据^[26](a)与Srinivasan^[26](b)和半解析模型(c)结果对比图

Fig. 16 Comparison of field data from the vertical adjacent well monitoring in stage 20 of well B2H^[26](a), Srinivasan’s model^[26](b), and the semi-analytical model (c)

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邻井分布式光纤监测水力裂缝扩展半解析正演模型

Semi-analytical forward model for hydraulic fracture propagation monitoring using distributed fiber optics in adjacent wells

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