基于单元劈裂法的全耦合水力压裂数值模拟
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摘要
单元劈裂法(element partition method, EPM)是一种裂纹模拟方法,它利用三角单元的几何性质推导了劈裂单元的刚度矩阵.当有裂纹穿过时,三角单元转化为劈裂单元,可自动地将裂纹面之间的相互作用反映到计算模型中.通过这种方式,可以在背景网格中嵌入任意条裂纹而不需要引入额外自由度,避免了节理单元的设置及网格重构.这使得EPM在大规模节理计算方面具有较强的优势.为了更有效地模拟水力压裂,建立了劈裂单元的全耦合水-力方程,可同时考虑劈裂单元内水压对结点力的作用以及结点速度场对渗流场的作用. KGD模型验证结果表明该方法是有效的.该方法可以有效地模拟多裂纹水力扩展及汇合过程,为复杂地层压裂模拟提供了一套简单、有效的计算方法.
Element partition method(EPM) is a fracture simulation method. It takes advantage of geometry feature of triangular element to derive the stiffness matrix of a cracked element. Once a fracture runs across a triangular element, this element will be transformed into a cracked element. The contact and friction between crack faces are automatically incorporated into the numerical model. By this means, any number of fractures can be embedded into a prescribed background mesh without introduction of any extra degree of freedom. It avoids the setup of joint element and remeshing issues in fracture simulation. Hence, the EPM presents great advantage in dealing with the massive fractures. To simulate the hydraulic fracture more effectively, a fully hydro-mechanical coupled equation is established for the cracked element. It can account for the interactions between the mechanical field and the hydraulic field in a cracked element. The KGD verification suggests that this method is validated in hydraulic fracture simulation. It can effectively simulate the multiple hydraulic fracture propagation and coalescence. It provides a simple and efficient simulation method for hydraulic fracturing in the complex reservoir.
Element partition method(EPM) is a fracture simulation method. It takes advantage of geometry feature of triangular element to derive the stiffness matrix of a cracked element. Once a fracture runs across a triangular element, this element will be transformed into a cracked element. The contact and friction between crack faces are automatically incorporated into the numerical model. By this means, any number of fractures can be embedded into a prescribed background mesh without introduction of any extra degree of freedom. It avoids the setup of joint element and remeshing issues in fracture simulation. Hence, the EPM presents great advantage in dealing with the massive fractures. To simulate the hydraulic fracture more effectively, a fully hydro-mechanical coupled equation is established for the cracked element. It can account for the interactions between the mechanical field and the hydraulic field in a cracked element. The KGD verification suggests that this method is validated in hydraulic fracture simulation. It can effectively simulate the multiple hydraulic fracture propagation and coalescence. It provides a simple and efficient simulation method for hydraulic fracturing in the complex reservoir.
引文
1 Belytschko T,Black T.Elastic crack growth in finite elements with minimal remeshing.Int J Numer Meth Eng,1999,45:601-620
2 Mo?s N,Dolbow J,Belytschko T.A finite element method for crack growth without remeshing.Int J Numer Meth Eng,1999,46:131-150
3王涛,高岳,柳占立,等.基于扩展有限元法的水力压裂大物模实验的数值模拟.清华大学学报(自然科学版),2014,54:1304-1309
4曾庆磊,庄茁,柳占立,等.页岩水力压裂中多簇裂缝扩展的全耦合模拟.计算力学学报,2016,33:643-648
5盛茂,李根生.水力压裂过程的扩展有限元数值模拟方法.工程力学,2014,31:123-128
6 Lecampion B.An extended finite element method for hydraulic fracture problems.Commun Numer Meth Eng,2009,25:121-133
7 Zhang Z,Chen Y.Simulation of fracture propagation subjected to compressive and shear stress field using virtual multidimensional internal bonds.Int J Rock Mech Min Sci,2009,46:1010-1022
8张振南,陈永泉.一种模拟节理岩体破坏的新方法:单元劈裂法.岩土工程学报,2009,31:1858-1865
9黄恺,张振南.三维单元劈裂法与压剪裂纹数值模拟.工程力学,2010,27:51-58
10 Zhang Z,Wang D,Ge X.A novel triangular finite element partition method for fracture simulation without enrichment of interpolation.Int JComput Methods,2013,10:1350015
11张振南,郑宏,葛修润.考虑裂尖点的三角单元劈裂法.中国科学:技术科学,2013,43:1136-1143
12陈亚雄,张振南.基于单元劈裂法的岩体粘结型结构面数值模拟.岩土力学,2013,34(Suppl 2):443-447
13 Zhang Z,Wang D,Ge X,et al.Three-dimensional element partition method for fracture simulation.Int J Geomech,2016,16:04015074
14 Zhang Z,Peng S,Ghassemi A,et al.Simulation of complex hydraulic fracture generation in reservoir stimulation.J Pet Sci Eng,2016,146:272-285
15 Zhang Z,Ghassemi A.Simulation of hydraulic fracture propagation near a natural fracture using virtual multidimensional internal bonds.Int JNumer Anal Meth Geomech,2011,35:480-495
16 Huang K,Zhang Z,Ghassemi A.Modeling three-dimensional hydraulic fracture propagation using virtual multidimensional internal bonds.Int JNumer Anal Meth Geomech,2013,37:2021-2038
17朱红光,易成,谢和平,等.基于立方定律的岩体裂隙非线性流动几何模型.煤炭学报,2016,41:822-828
18 Peng S,Zhang Z,Li C,et al.Simulation of water flow in fractured porous medium by using discretized virtual internal bond.J Hydrol,2017,555:851-868
19 Ching H Y.Mechanic of Hydraulic Fracturing.2nd ed.Houston:Gulf Professional Publishing,1997.1-8
20 Kipp M E,Sih G C.The strain energy density failure criterion applied to notched elastic solids.Int J Solids Struct,1975,11:153-173
21 Jeong D Y,Orringer O,Sih G C.Strain energy density approach to stable crack extension under net section yielding of aircraft fuselage.Theor Appl Fract Mech,1995,22:127-137
2 Mo?s N,Dolbow J,Belytschko T.A finite element method for crack growth without remeshing.Int J Numer Meth Eng,1999,46:131-150
3王涛,高岳,柳占立,等.基于扩展有限元法的水力压裂大物模实验的数值模拟.清华大学学报(自然科学版),2014,54:1304-1309
4曾庆磊,庄茁,柳占立,等.页岩水力压裂中多簇裂缝扩展的全耦合模拟.计算力学学报,2016,33:643-648
5盛茂,李根生.水力压裂过程的扩展有限元数值模拟方法.工程力学,2014,31:123-128
6 Lecampion B.An extended finite element method for hydraulic fracture problems.Commun Numer Meth Eng,2009,25:121-133
7 Zhang Z,Chen Y.Simulation of fracture propagation subjected to compressive and shear stress field using virtual multidimensional internal bonds.Int J Rock Mech Min Sci,2009,46:1010-1022
8张振南,陈永泉.一种模拟节理岩体破坏的新方法:单元劈裂法.岩土工程学报,2009,31:1858-1865
9黄恺,张振南.三维单元劈裂法与压剪裂纹数值模拟.工程力学,2010,27:51-58
10 Zhang Z,Wang D,Ge X.A novel triangular finite element partition method for fracture simulation without enrichment of interpolation.Int JComput Methods,2013,10:1350015
11张振南,郑宏,葛修润.考虑裂尖点的三角单元劈裂法.中国科学:技术科学,2013,43:1136-1143
12陈亚雄,张振南.基于单元劈裂法的岩体粘结型结构面数值模拟.岩土力学,2013,34(Suppl 2):443-447
13 Zhang Z,Wang D,Ge X,et al.Three-dimensional element partition method for fracture simulation.Int J Geomech,2016,16:04015074
14 Zhang Z,Peng S,Ghassemi A,et al.Simulation of complex hydraulic fracture generation in reservoir stimulation.J Pet Sci Eng,2016,146:272-285
15 Zhang Z,Ghassemi A.Simulation of hydraulic fracture propagation near a natural fracture using virtual multidimensional internal bonds.Int JNumer Anal Meth Geomech,2011,35:480-495
16 Huang K,Zhang Z,Ghassemi A.Modeling three-dimensional hydraulic fracture propagation using virtual multidimensional internal bonds.Int JNumer Anal Meth Geomech,2013,37:2021-2038
17朱红光,易成,谢和平,等.基于立方定律的岩体裂隙非线性流动几何模型.煤炭学报,2016,41:822-828
18 Peng S,Zhang Z,Li C,et al.Simulation of water flow in fractured porous medium by using discretized virtual internal bond.J Hydrol,2017,555:851-868
19 Ching H Y.Mechanic of Hydraulic Fracturing.2nd ed.Houston:Gulf Professional Publishing,1997.1-8
20 Kipp M E,Sih G C.The strain energy density failure criterion applied to notched elastic solids.Int J Solids Struct,1975,11:153-173
21 Jeong D Y,Orringer O,Sih G C.Strain energy density approach to stable crack extension under net section yielding of aircraft fuselage.Theor Appl Fract Mech,1995,22:127-137
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