基于水平集法的三维非均质岩石建模及水力压裂特性
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摘要
采用水平集法(LSM)描述非均质岩石的静态材料边界特性,探讨分层特性、含有随机分布包裹体特性和具有Weibull分布特性的三种非均质岩石材料有限元建模方法,并与基于完全流-固耦合弹塑性理论的弥散裂缝模型相结合进行水力压裂过程的模拟.在水力压裂模型中通过Corey关系和相对渗透率计算压裂液与原有液体混合的特性.最后进行符合Weibull分布的非均质岩石材料的水力压裂传播特性的计算,给出了等效开裂区域的发展过程、注水点处水压力与注水时间变化曲线和有效应力路径.模拟结果表明,采用水平集法能够有效地描述岩石材料的非均质特性,同时该法能够与弥散裂缝模型很好地结合,实现三维非均质岩石的建模与水力压裂过程的模拟.
The level set method( LSM) was introduced to describe the static material interface in a rock material. The finite element modeling procedures for the three-dimensional rock sample with the layered feature, randomly distributed inclusions and statistical Weibull distribution heterogeneity were given via the LSM. To study the propagation of hydraulic fracture,a smeared crack model based on the fully coupled,elasto-plastic,pore pressure-solid phase interaction theory was coupled to the LSM. The Corey relation and relative permeability were adopted to calculate the viscosity and permeability of mixture in the smeared cracked hydraulic fracture model.Finally,a case study that simulating hydraulic fracture propagation was carried out in a heterogeneous rock sample following Weibull distribution. The development of equivalent crack zone,pore pressure versus injection time and the effective stress path in the injected element were discussed. The simulation results indicate that the LSM coupling with smeared crack model can be w ell used for modeling the heterogeneity of three-dimensional rock material and simulating the hydraulic fracturing.
The level set method( LSM) was introduced to describe the static material interface in a rock material. The finite element modeling procedures for the three-dimensional rock sample with the layered feature, randomly distributed inclusions and statistical Weibull distribution heterogeneity were given via the LSM. To study the propagation of hydraulic fracture,a smeared crack model based on the fully coupled,elasto-plastic,pore pressure-solid phase interaction theory was coupled to the LSM. The Corey relation and relative permeability were adopted to calculate the viscosity and permeability of mixture in the smeared cracked hydraulic fracture model.Finally,a case study that simulating hydraulic fracture propagation was carried out in a heterogeneous rock sample following Weibull distribution. The development of equivalent crack zone,pore pressure versus injection time and the effective stress path in the injected element were discussed. The simulation results indicate that the LSM coupling with smeared crack model can be w ell used for modeling the heterogeneity of three-dimensional rock material and simulating the hydraulic fracturing.
引文
[1]朱君,叶鹏,王素玲,等.低渗透储层水力压裂三维裂缝动态扩展数值模拟[J].石油学报,2010,31(1):119-123.(Zhu Jun,Ye Peng,Wang Su-ling,et al. 3D numerical simulation of fracture dynamic propagation in hydraulic fracturing of low-permeability reservoir[J]. Acta Petrolei Sinica,2010,31(1):119-123.)
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[9] Li M,Guo P J,Stolle D,et al. Modeling method for a rock matrix with inclusions distributed and hydraulic fracturing characteristics[J]. Journal of Petroleum Science&Engineering,2017,157:409-421.
[10] Osher S,Sethian J A. Fronts propagating with curvaturedependent speed:algorithms based on Hamilton-Jacobi formulations[J]. Journal of Computational Physics,1988,79(1):12-49.
[11] Sukumar N,Chopp D L,Moes N,et al. Modeling holes and inclusions by level sets in the extended finite-element method[J]. Computer Methods in Applied Mechanics and Engineering,2001,190(46):6183-6200.
[12] Marrone S,Colagrossi A,TouzéD L,et al. Fast free-surface detection and level-set function definition in SPH solvers[J].Journal of Computational Physics, 2010, 229(10):3652-3663.
[13] Myslinski A. Level set method for optimization of contact problems[J]. Engineering Analysis with Boundary Elements,2008,32(11):986-994.
[14] Stolarska M,Chopp D L. Modeling thermal fatigue cracking in integrated circuits by level sets and the extended finite element method[J]. International Journal of Engineering Science,2003,41(20):2381-2410.
[15] Li M,Guo P J,Stolle D,et al. Development of hydraulic fracture zone in heterogeneous material based on smeared crack method[J]. Journal of Natural Gas Science&Engineering,2016,35:761-774.
[16] Corey A T. The interrelation between gas and oil relative permeabilities[J]. Producers Monthly,1954,19:38-41.
[2]刘建军,冯夏庭,裴桂红.水力压裂三维数学模型研究[J].岩石力学与工程学报,2003,22(12):2042-2046.(Liu Jian-jun,Feng Xia-ting,Pei Gui-hong. Study on mathematical model of three dimensional hydraulic fracturing[J]. Chinese Journal of Rock Mechanics and Engineering,2003,22(12):2042-2046.)
[3] Priester C,Morton L C,Kinsey S T,et al. Numerical modeling of hydraulic fracture problem in permeable medium using cohesive zone model[J]. Engineering Fracture Mechanics,2012,79(1):312-328.
[4] Ren Q,Dong Y,Yu T. Numerical modeling of concrete hydraulic fracturing with extended finite element method[J].Science in China Series E:Technological Sciences,2009,52(3):559-565.
[5] Pak A. Numerical modeling of hydraulic fracturing[D].Edmonton:University of Alberta,1997.
[6] Bazant Z P,Lin F B. Nonlocal smeared cracking model for concrete fracture[J]. Journal of Structure Engineer,1988,114(11):2493-2510.
[7] Hu Y,Chen G,Cheng W,et al. Simulation of hydraulic fracturing in rock mass using a smeared crack model[J].Computers and Structures,2014,137(6):72-77.
[8]李明,梁力,Guo Pei-jun,等.弥散裂缝模型水力压裂数值方法的网格敏感性分析[J].东北大学学报(自然科学版),2015,36(9):1337-1341.(Li Ming,Liang Li,Guo Pei-jun,et al. Mesh sensitivity analysis of solution to hydraulic fracture problems based on a smeared crack model[J]. Journal of Northeastern University(Nature Science),2015,36(9):1337-1341.)
[9] Li M,Guo P J,Stolle D,et al. Modeling method for a rock matrix with inclusions distributed and hydraulic fracturing characteristics[J]. Journal of Petroleum Science&Engineering,2017,157:409-421.
[10] Osher S,Sethian J A. Fronts propagating with curvaturedependent speed:algorithms based on Hamilton-Jacobi formulations[J]. Journal of Computational Physics,1988,79(1):12-49.
[11] Sukumar N,Chopp D L,Moes N,et al. Modeling holes and inclusions by level sets in the extended finite-element method[J]. Computer Methods in Applied Mechanics and Engineering,2001,190(46):6183-6200.
[12] Marrone S,Colagrossi A,TouzéD L,et al. Fast free-surface detection and level-set function definition in SPH solvers[J].Journal of Computational Physics, 2010, 229(10):3652-3663.
[13] Myslinski A. Level set method for optimization of contact problems[J]. Engineering Analysis with Boundary Elements,2008,32(11):986-994.
[14] Stolarska M,Chopp D L. Modeling thermal fatigue cracking in integrated circuits by level sets and the extended finite element method[J]. International Journal of Engineering Science,2003,41(20):2381-2410.
[15] Li M,Guo P J,Stolle D,et al. Development of hydraulic fracture zone in heterogeneous material based on smeared crack method[J]. Journal of Natural Gas Science&Engineering,2016,35:761-774.
[16] Corey A T. The interrelation between gas and oil relative permeabilities[J]. Producers Monthly,1954,19:38-41.
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