统一管道–界面单元法的构建及其在水力压裂模拟中的应用

doi:10.13722/j.cnki.jrme.2021.0207

Abstract
Figure/Table
References (0)
Related Citation (15)

Download: PDF (2915 KB) HTML (1 KB)
Export: BibTeX | EndNote (RIS)

Abstract This paper proposes a novel method，named as unified pipe-interface element method(UP-IEM)，for modelling the hydraulic fracture propagation in a permeable porous medium. There are two unified processes including the combination of the fluid flow and the fracture propagation into 1D pipe element and the unification of the matrix pipe and the fracture pipe as a same pipe with different hydraulic conductivities for solving the fluid flow using the same mathematical equations. UP-IEM overcomes the difficulties to consider the rock matrix permeability of traditional discrete fracture network model. The interface element is introduced to simulate the fracture propagation. For UP-IEM which has high efficiency，neither local crack propagation criteria nor tracking algorithms are required compared with traditional FEM and DEM. The deformation of the rock matrix is described by poroelasticity theory and effective stress concept. The cohesive zone model is used to simulate hydraulic fracture propagation and the contact-frictional model is utilized to model closure and slip of natural cracks. Besides，the fluid flow in porous medium and fractures is solved using Darcy law. A semi-explicit frame is built to solve the hydro-mechanical coupling problems. Three typical examples，including Terzaghi's consolidation test，unsymmetric four-points bending test and KGD model，are simulated. The simulation results are compared with analytical solutions and experimental results，verifying the accuracy and applicability of UP-IEM simulating fluid flow，fracture propagation and hydraulic fracturing. Furthermore，the hydraulic fracturing in models with single natural fracture and complex fracture network is simulated，analyzing the interaction between hydraulic fractures and pre-existing fractures and discussing the influence of in-suit stresses on the fracture propagation path. These examples show that UP-IEM could effectively simulate the hydraulic fracturing in discrete fractured rock.

Key words： rock mechanics hydraulic fracturing permeable porous medium unified pipe-interface element method numerical computation semi-explicit solution

	Service

	E-mail this article
	Add to my bookshelf
	Add to citation manager
	E-mail Alert
	RSS
	Articles by authors
	YAN Xiao1
	2
	JING Hongwen1
	SUN Zizheng3
	YU Liyuan1
	ZHANG Yiming4

Cite this article:

YAN Xiao1,2,JING Hongwen1, et al. Development of an unified pipe-interface element method and its application in hydraulic fracturing simulation[J]. , 2022, 41(2): 305-318.

URL:

https://rockmech.whrsm.ac.cn/EN/10.13722/j.cnki.jrme.2021.0207 OR https://rockmech.whrsm.ac.cn/EN/Y2022/V41/I2/305

[1]	张东晓，杨婷云. 页岩气开发综述[J]. 石油学报，2013，34(4)：792-801.(ZHANG Dongxiao，YANG Tingyun. An overview of shale gas production[J]. Acta Petrolei Sinica，2013，34(4)：792-801.(in Chinese)))
[2]	侯冰，武安安，常智，等. 页岩油储层多甜点压裂裂缝垂向扩展实验研究[J]. 岩土工程学报，2021，43(7)：1-9.(HOU Bing，WU Anan，CHANG Zhi，et al. Experimental study on fracture vertical propagation mechanism of multi-sweet spots shale oil reservoir[J]. Chinese Journal of Geotechnical Engineering，2021，43(7)：1-9.(in Chinese))
[3]	WU Y H，CHENG L S，MA L Q，et al. A transient two-phase flow model for production prediction of tight gas wells with fracturing fluid-induced formation damage[J]. Journal of Petroleum Science and Engineering，2021，199：108351.
[4]	SPENCE D A，SHARP P. Self-similar solutions for elastohydrodynamic cavity flow[J]. Proceedings of the Royal Society of a Mathematical and Physical Sciences. London：[s.n.]，1985：289-313.
[5]	DETOURANY E. Propagation regimes of fluid-driven fractures in impermeable rocks[J]. International Journal of Geomechanics，2004，4(1)：35-45.
[6]	BUNGER A P，DETOURANY E，GARAGASH D I. Toughness- dominated hydraulic fracture with leak-off[J]. International Journal of Fracture，2005，134(2)：175-190.
[7]	FU P，JHNSON S M，CARRIGAN C R. An explicitly coupled hydro-geomechanical model for simulating hydraulic fracturing in arbitrary discrete fracture networks[J]. International Journal for Numerical and Analytical Methods in Geomechanics，2013，37(14)：2 278-2 300.
[8]	SCHREFLER B A，SECCHI S，SIMONI L. On adaptive refinement techniques in multi-field problems including cohesive fracture[J]. Computer Methods in Applied Mechanics and Engineering，2006，195(4-6)：444-461.
[9]	张瑛堃，陈尚斌，李学元，等，页岩气储层水力压裂扩展有限元模拟方法及应用[J]. 天然气地球科学，2021，32(1)：109-118. (ZHANG Yingkun，CHEN Shangbin，LI Xueyuan，et al. Hydraulic fracturing simulation technology of shale gas reservoir and application of extended finite element method[J]. Natural Gas Geoscience，2021，32(1)：109-118.(in Chinese))
[10]	LECAMPION B. An extended finite element method for hydraulic fracture problems[J]. Communications in Numerical Methods in Engineering，2009，25(2)：121-133.
[11]	孙可明，张树翠，辛利伟. 页岩气储层层理方向对水力压裂裂纹扩展的影响[J]. 天然气工业，2016，36(2)：45-51.(SUN Keming，ZHANG Shucui，XIN Liwei. Impact of bedding directions of shale gas reservoirs on hydraulically induced crack propagation[J]. Natural Gas Industry，2016，36(2)：45-51.(in Chinese))
[12]	周治东，程万，魏子俊，等，基于BEM的水力裂缝起裂与扩展数值模拟[J]. 地球物理学进展，2020，35(2)：807-814.(ZHOU Zhidong，CHENG Wan，WEI Zijun，et al. Numerical simulation of hydraulic fracture initiation and propagation based on BEM[J]. Progress in Geophysics，2020，35(2)：807-814.(in Chinese))
[13]	陈铭，张士诚，胥云，等. 基于互补算法的水力裂缝与天然裂缝相互作用边界元模型[J]. 岩石力学与工程学报，2018，37(增2)：3 947-3 957.(CHEN Ming，ZHANG Shicheng，XU Yun，et al. Boundary element model for mechanical interaction between hydraulic fracture and natural fracture based on complementary algorithm[J]. Chinese Journal of Rock Mechanics and Engineering. 2018，37(Supp.2)：3 947-3 957.(in Chinese))
[14]	易良平，胡滨，李小刚，等. 基于相场法的煤砂互层水力裂缝纵向延伸计算模型[J]. 煤炭学报，2020，45(增2)：1-10.(YING Liangping，HU Bin，LI Xiaogang，et al. Calculation model of hydraulic crack vertical propagation in coal-sand interbedded formation based on the phase field method[J]. Journal of China Coal Society，2020，45(Supp.2)：1-10.(in Chinese))
[15]	ZHUANG X Y，ZHOU S W，SHENG M，et al.，On the hydraulic fracturing in naturally-layered porous media using the phase field method[J]. Engineering Geology，2020，266：105306.
[16]	CHEN W，KONIETZKY H，LIU C，et al. Hydraulic fracturing simulation for heterogeneous granite by discrete element method[J]. Computers and Geotechnics，2018，95：1-15.
[17]	ZEEB C，KONIETZKY H. Simulating the Hydraulic Stimulation of Multiple Fractures in an Anisotropic Stress Field Applying the Discrete Element Method[J]. Energy Procedia，2015，76：264-272.
[18]	YAN C Z，JIAO Y Y. A 2D fully coupled hydro-mechanical finite-discrete element model with real pore seepage for simulating the deformation and fracture of porous medium driven by fluid[J]. Computers and Structures，2018，196：311-326.
[19]	YAN C Z，JIAO Y Y，ZHENG H. A fully coupled three-dimensional hydro-mechanical finite discrete element approach with real porous seepage for simulating 3D hydraulic fracturing[J]. Computers and Geotechnics，2018，96：73-89.
[20]	XU Z H，MA G W，LI S C. A graph-theoretic pipe network method for water flow simulation in a porous medium：GPNM[J]. International Journal of Heat and Fluid Flow，2014，45：81-97.
[21]	REN F，MA G W，WANG Y，et al. Unified pipe network method for simulation of water flow in fractured porous rock[J]. Journal of Hydrology，2017，547：80-96.
[22]	BARENBLATT G I. The mathematical theory of equilibrium cracks in brittle fracture[J]. Advances in Applied Mechanics，1962，7： 55-129.
[23]	SEGURA J M，CAROL I. Coupled hm analysis using zero-thickness interface elements with double nodes. part i：Theoretical model[J]. International Journal for Numerical and Analytical Methods in Geomechanics，2008，32(18)：2 083-2 101
[24]	CARRIER B，GRANET S. Numerical modeling of hydraulic fracture problem in permeable medium using cohesive zone model[J]. Engineering Fracture Mechanics，2012，79：312-328.
[25]	NGUYEN V P，LIAN H，RABCZUK T，et al. Modelling hydraulic fractures in porous media using flow cohesive interface elements[J]. Engineering Geology，2017，225：68-82.
[26]	TERZAGHI K. Theoretical soil mechanics[M]. New York：John Wiley and Sons，1965：265-296.
[27]	OLIVER J，HUESPE A E，CANTE J C. An implicit/explicit integration scheme to increase computability of non-linear material and contact/friction problems[J]. Computer Methods in Applied Mechanics and Engineering，2008，197(21-24)：1 865-1 889.
[28]	SUN Z Z，YAN X，LIU R T，et al.，Transient analysis of grout penetration with time-dependent viscosity inside 3D fractured rock mass by unified pipe-network method[J]. Water，2018，10(9)：1 122.
[29]	SUN Z Z，YAN X，HAN W Q，et al. Simulating the filtration effects of cement-grout in fractured porous media with the 3D unified pipe-network method[J]. Processes，2019，7(1)：46.
[30]	YAN X，SUN Z Z，LI S C，et al. Evaluation of effectiveness of CO2 sequestration using portland cement in geological reservoir based on unified pipe-network method[J]. Energies，2020，13(2)：387.
[31]	VERRUIJT A. Theory and problems of poroelasticity[Ph. D. Thesis][D]. Delft，The Netherlands：Delft University of Technology，2013.
[32]	WANG C，ZHU Z M，LIU H J. On the I-II mixed mode fracture of granite using four-point bend specimen[J]. Fatigue and Fracture of Engineering Materials and Structures，2016，39(10)：1 193-1 203.