考虑裂尖塑性区影响的水力压裂缝高计算模型

李玉伟; 龙敏; 汤继周; 陈勉; 付晓飞

doi:10.11698/PED.2020.01.17

石油勘探与开发 >

2020 , Vol. 47 >Issue 1: 175 - 185

DOI: https://doi.org/10.11698/PED.2020.01.17

石油工程

考虑裂尖塑性区影响的水力压裂缝高计算模型

李玉伟 ,
龙敏 ,
汤继周 ,
陈勉 ,
付晓飞

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1. 东北石油大学石油工程学院,黑龙江大庆 163318;
2. School of Engineering and Applied Sciences, Harvard University,Cambridge 02138,USA;
3. 中国石油大学（北京）石油工程学院,北京 102249

李玉伟（1983-）,男,黑龙江友谊人,博士,东北石油大学石油工程学院副教授,主要从事非常规油气储集层压裂开发理论与技术方面的研究。地址：黑龙江省大庆市高新技术开发区学府街99号,东北石油大学石油工程学院,邮政编码：163318。E-mail: liyuweibox@126.com

收稿日期: 2019-07-15

网络出版日期: 2020-01-17

基金资助

黑龙江省优秀青年科学基金项目“煤层二氧化碳泡沫压裂模型与模拟研究”（YQ2019E007）

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A hydraulic fracture height mathematical model considering the influence of plastic region at fracture tip

LI Yuwei ,
LONG Min ,
TANG Jizhou ,
CHEN Mian ,
FU Xiaofei

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1. School of Petroleum Engineering, Northeast Petroleum University, Daqing 163318, China;
2. School of Engineering and Applied Sciences, Harvard University, Cambridge 02138, USA;
3. School of Petroleum Engineering, China University of Petroleum, Beijing 102249, China

Received date: 2019-07-15

Online published: 2020-01-17

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摘要

为了对水力压裂裂缝高度进行准确预测,针对高应力多分层的复杂地层,基于断裂力学理论分析裂缝扩展过程中裂缝尖端应力集中产生的塑性区分布对缝高扩展的影响,建立水力压裂缝高计算模型并进行求解,通过与其他2种缝高模型（MFEH、FracPro）计算结果进行对比以验证该模型的准确性。模型实例计算的敏感性分析表明：水力压裂的缝高会呈现阶梯生长的扩展形态,且裂缝缝高越大,阶梯生长的现象越明显;地应力对裂缝缝高的生长起主要的控制作用,地层岩石断裂韧性只在一定程度上对缝高生长有抑制作用;压裂液密度的增大有利于裂缝下尖端的扩展。图11表2参35

关键词： 水力压裂; 裂缝高度; 裂尖塑性区; 断裂韧性; 高应力多分层地层

本文引用格式

李玉伟 , 龙敏 , 汤继周 , 陈勉 , 付晓飞 . 考虑裂尖塑性区影响的水力压裂缝高计算模型[J]. 石油勘探与开发, 2020 , 47(1) : 175 -185 . DOI: 10.11698/PED.2020.01.17

Abstract

To predict fracture height in hydraulic fracturing, we developed and solved a hydraulic fracture height mathematical model aiming at high stress and multi-layered complex formations based on studying the effect of plastic region generated by stress concentration at fracture tip on the growth of fracture height. Moreover, we compared the results from this model with results from two other fracture height prediction models (MFEH, FracPro) to verify the accuracy of the model. Sensitivity analysis by case computation of the model shows that the hydraulic fracture growth in ladder pattern, and the larger the fracture height, the more obvious the ladder growth pattern is. Fracture height growth is mainly influenced by the in-situ stresses. Fracture toughness of rock can prohibit the growth of fracture height to some extent. Moreover, the increase of fracturing fluid density can facilitate the propagation of the lower fracture tip.

Key words： hydraulic fracturing; fracture height; plastic region at fracture tip; fracture toughness; multi-layered formation with high in-situ stresses

参考文献

[1] 仝少凯, 高德利. 水力压裂基础研究进展及发展建议[J]. 石油钻采工艺, 2019, 41(1): 106-120.
TONG Shaokai, GAO Deli.Basic research progress and development suggestions on hydraulic fracturing[J]. Oil Drilling & Production Technology, 2019, 41(1): 106-120.
[2] 谭鹏, 金衍, 侯冰, 等. 煤岩定向井水力裂缝起裂及非平面扩展实验[J]. 石油勘探与开发, 2017, 44(3): 439-445.
TAN Peng, JIN Yan, HOU Bing, et al.Experimental investigation on fracture initiation and non-planar propagation of hydraulic fractures in coal seams[J]. Petroleum Exploration and Development, 2017, 44(3): 439-445.
[3] XIA H Q, YANG S D, GONG H H, et al.Research on rock brittleness experiment and logging prediction of hydraulic fracture height and width[J]. Journal of Southwest Petroleum University, 2013, 35(4): 81-89.
[4] TANG J, WU K.A 3-D model for simulation of weak interface slippage for fracture height containment in shale reservoirs[J]. International Journal of Solids and Structures, 2018, 144: 248-264.
[5] 包劲青, 刘合, 张广明, 等. 分段压裂裂缝扩展规律及其对导流能力的影响[J]. 石油勘探与开发, 2017, 44(2): 281-288.
BAO Jingqing, LIU He, ZHANG Guangming, et al.Fracture propagation laws in staged hydraulic fracturing and their effects on fracture conductivities[J]. Petroleum Exploration and Development, 2017, 44(2): 281-288.
[6] LI Y, YANG S, ZHAO W, et al.Experimental of hydraulic fracture propagation using fixed-point multistage fracturing in a vertical well in tight sandstone reservoir[J]. Journal of Petroleum Science and Engineering, 2018, 171(12): 704-713.
[7] LI Y, RUI Z, ZHAO W, et al.Study on the mechanism of rupture and propagation of T-type fractures in coal fracturing[J]. Journal of Natural Gas Science and Engineering, 2018, 52: 379-389.
[8] FLEWELLING S A, TYMCHAK M P, WARPINSKI N.Hydraulic fracture height limits and fault interactions in tight oil and gas formations[J]. Geophysical Research Letters, 2013, 40(14): 3602-3606.
[9] 张林, 赵喜民, 刘池洋, 等. 沉积作用对水力压裂裂缝缝长的限制作用[J]. 石油勘探与开发, 2008, 35(2): 201-204.
ZHANG Lin, ZHAO Ximin, LIU Chiyang, et al.Deposition confines hydraulic fracture length[J]. Petroleum Exploration and Development, 2008, 35(2): 201-204.
[10] FIGUEIREDO B, TSANG C F, RUTQVIST J, et al.Study of hydraulic fracturing processes in shale formations with complex geological settings[J]. Journal of Petroleum Science and Engineering, 2017, 152: 361-374.
[11] 刘乃震, 张兆鹏, 邹雨时, 等. 致密砂岩水平井多段压裂裂缝扩展规律[J]. 石油勘探与开发, 2018, 45(6): 1059-1068.
LIU Naizhen, ZHANG Zhaopeng, ZOU Yushi, et al.Propagation law of hydraulic fractures during multi-staged horizontal well fracturing in a tight reservoir[J]. Petroleum Exploration and Development, 2018, 45(6): 1059-1068.
[12] LI Y, LONG M, ZUO L, et al.Brittleness evaluation of coal based on statistical damage and energy evolution theory[J]. Journal of Petroleum Science and Engineering, 2019, 172: 753-763.
[13] LABUDOVIC V.The effect of Poisson's ratio on fracture height[J]. Journal of Petroleum Technology, 1984, 36(2): 287-290.
[14] WENG X, KRESSE O, COHEN C E, et al.Modeling of hydraulic fracture network propagation in a naturally fractured formation[R]. SPE 140253, 2011.
[15] FISHER M K, WARPINSKI N R.Hydraulic-fracture-height growth: Real data[J]. SPE Production & Operations, 2012, 27(1): 8-19.
[16] GU H, SIEBRITS E.Effect of formation modulus contrast on hydraulic fracture height containment[R]. SPE 103822, 2008.
[17] VALKO P, ECONOMIDES M J.Hydraulic fracture mechanics[M]. Chichester: Wiley, 1995.
[18] SIMONSON E R, ABOU-SAYED A S, CLIFTON R J. Containment of massive hydraulic fractures[J]. Society of Petroleum Engineers Journal, 1978, 18(1): 27-32.
[19] AHMED U.Fracture height prediction[J]. Journal of Petroleum Technology, 1988, 40(7): 813-815.
[20] NEWBERRY B M, NELSON R F, AHMED U.Prediction of vertical hydraulic fracture migration using compressional and shear wave slowness[R]. SPE 13895, 1985.
[21] ECONOMIDES M J, HILL A D, EHLIG-ECONOMIDES C, et al.Petroleum production systems[M]. 2nd ed. Upper Saddle River: Prentice Hall, 2012.
[22] FUNG R L, VILAYAKUMAR S, CORMACK D E.Calculation of vertical fracture containment in layered formations[J]. SPE Formation Evaluation, 1987, 2(4): 518-522.
[23] ECONOMIDES M J, NOLTE K G.Reservoir stimulation[M]. 3rd ed. West Sussex, UK: John Wiley & Sons, 2000.
[24] LIU S, VALKÓ P P.A rigorous hydraulic-fracture equilibrium-height model for multilayer formations[J]. SPE Production & Operations, 2017, 33(2): 214-234.
[25] LIU S, VALKÓ P P.An improved equilibrium-height model for predicting hydraulic fracture height migration in multi-layered formations[R]. SPE 173335, 2015.
[26] HOWARD I C, OTTER N R.On the elastic-plastic deformation of a sheet containing an edge crack[J]. Journal of the Mechanics and Physics of Solids, 1975, 23(2): 139-149.
[27] 程远方, 曲连忠, 赵益忠, 等. 考虑尖端塑性的垂直裂缝延伸计算[J]. 大庆石油地质与开发, 2008, 27(1): 102-105.
CHENG Yuanfang, QU Lianzhong, ZHAO Yizhong, et al.Extension calculation of vertical fracture considering fracture tip plasticity[J]. Petroleum Geology & Oilfield Development in Daqing, 2008, 27(1): 102-105.
[28] ERDOGAN F, SIH G C.On the crack extension in plates under plane loading and transverse shear[J]. Journal of Basic Engineering, 1963, 85(4): 519-527.
[29] DUGDALE D S.Yielding of steel sheet containing slits[J]. Journal of the Mechanics & Physics of Solids, 1960, 8(2): 100-104.
[30] ERDOGAN F.On the stress distribution in plates with collinear cuts under arbitrary loads[C]//Proceedings of the 4th U.S. National Congress of Applied Mechanics. Oxford: Pergamon Press, 1962: 547-553.
[31] BOWIE O L, TRACY P G.On the solution of the Dugdale model[J]. Engineering Fracture Mechanics, 1978, 10(2): 249-256.
[32] THEOCARIS P S.Dugdale model for two collinear unequal cracks[J]. Engineering Fracture Mechanics, 1983, 8(3): 545-559.
[33] HAYES D J, WILLIAMS J G.A practical method for determining Dugdale model solution for cracked bodies of arbitrary shape[J]. International Journal of Fracture Mechanics, 1972, 8(3): 239-256.
[34] BIRD W W, MARTIN J B.A secant approximation for holonomic elastic-plastic incremental analysis with a von Mises yield condition[J]. Engineering Computations, 1986, 3(3): 192-201.
[35] WARPINSKI N R, MOSCHOVIDIS Z A, PARKER C D, et al.Comparison study of hydraulic fracturing models-test case: GRI staged field experiment No.3[J]. SPE Production & Facilities, 1994, 9(1): 7-16.

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