董卓等：基于最小应变能密度因子断裂准则的岩石裂纹水力压裂研究 ·445· ◆=1.00 0u=20 MPa =15 MPa sk=1.25 14 o,=15 MPa 24 P=28 MPa ◆k=1.50 P=28 MPa p=6 MPa +=1.75 12 p=6 MPa 20c,=0.6 =0.25 =0.25 10 16 2 6 $g,=0.4 番g=0.6 ★任，=0.8 1020304050607080 16 0.-20MPa 0.=15 MPa 14 P=28 MPa 12 p=6 MPa m=0.25 0 -◆-0=0.15 =0.25 t=0.35 810203040506070800 ) 图13不同因素对起裂角8的影响.(a)侧压系数：(b)比奥系数：()泊松比 Fig.13 Effect of different factors on the fracture initiation angle:(a)lateral pressure coefficient:(b)Biot's coefficient:(c)Poisson's ratio 各项同性的不足，为后续研究提供依据 horizontal wells.Nat Gas Geasci,2016,27(11):2043 (李旺，李连崇，唐春安.水平井平行裂缝间诱导应力干扰机 制的数值模拟研究.天然气地球科学，2016,27(11)：2043) 参考文献 [6]Liu C.Shi F,Lu D T,et al.Numerical simulation of simultane- [Chen M,Jin Y,Zhang G Q.Petroleum Engineering Rock Mechan- ous multiple fractures initiation in unconventional reservoirs ics.Beijing:Science Press,2008 through injection control of horizontal well.J Petrol Sci Eng, (陈勉，金衍，张广清.石油工程岩石力学.北京：科学出版 2017,159:603 社，2008) [7]Shi F,Wang X L,Liu C,et al.An XFEM-based method with re- 2]Liu JZ,Liu X G,Zhang X,et al.The great scale rock experi- duction technique for modeling hydraulic fracture propagation in ment simulating hydraulic fracturing.Acta Geophys Sin,1994,37 formations containing frictional natural fractures.Eng Fract Mech, (Suppl 1):161 2017,173:64 (刘建中，刘翔男，张雪，等.大尺度水压致裂模拟实验.地 [8]Nadimi S,Miscovic 1,McLennan J.A 3D peridynamic simulation 球物理学报，1994,37（增刊1）：161) of hydraulic fracture process in a heterogeneous medium.Petrol B]Jiang H,Chen M,Zhang G Q,et al.Impart of oriented perfora- Sei Eng,2016,145:444 tionon hydraulic fracture initiation and propagation.ChinRock 9]Lian Z L,Zhang J,Wang X X,et al.Simulation study of charac- Mech Eng,2009,28(7):1321 teristics of hydraulic fracturing propagation.Rock Soil Mech, (姜浒，陈勉，张广清，等.定向射孔对水力裂缝起裂与延伸 2009,30(1):169 的影响.岩石力学与工程学报，2009,28(7)：1321) (连志龙，张劲，王秀喜，等.水力压裂扩展特性的数值模拟 4]Wang D,Chen M,Jon Y,et al.Experimental study of fracture 研究.岩土力学，2009,30(1)：169) initiation and propagation from a wellbore /49th US Rock Me- [10]Wang X L,Shi F,Liu H,et al.Numerical simulation of hydrau- chanics/Geomechanics Symposium.San Francisco,2015:ARMA- lic fracturing in orthotropic formation based on the extended finite 2015-068 element method.J Nat Gas Sci Eng,2016,33:56 [5]Li W,Li L C,Tang C A.Numerical simulation research on mech- [11]Hosseini S M.On the linear elastic fracture mechanics applica- anism of induced stress perturbation between parallel fractures in tion in Barnett shale hydraulic fracturing //47th US Rock Me-董 卓等: 基于最小应变能密度因子断裂准则的岩石裂纹水力压裂研究 图 13 不同因素对起裂角 θ0的影响． ( a) 侧压系数; ( b) 比奥系数; ( c) 泊松比 Fig． 13 Effect of different factors on the fracture initiation angle: ( a) lateral pressure coefficient; ( b) Biot’s coefficient; ( c) Poisson’s ratio 各项同性的不足，为后续研究提供依据． 参 考 文 献 ［1］ Chen M，Jin Y，Zhang G Q． Petroleum Engineering Ｒock Mechan￾ics． Beijing: Science Press，2008 ( 陈勉，金衍，张广清． 石油工程岩石力学． 北京: 科学出版 社，2008) ［2］ Liu J Z，Liu X G，Zhang X，et al． The great scale rock experi￾ment simulating hydraulic fracturing． Acta Geophys Sin，1994，37 ( Suppl 1) : 161 ( 刘建中，刘翔鹗，张雪，等． 大尺度水压致裂模拟实验． 地 球物理学报，1994，37( 增刊 1) : 161) ［3］ Jiang H，Chen M，Zhang G Q，et al． Impart of oriented perfora￾tion on hydraulic fracture initiation and propagation． Chin J Ｒock Mech Eng，2009，28( 7) : 1321 ( 姜浒，陈勉，张广清，等． 定向射孔对水力裂缝起裂与延伸 的影响． 岩石力学与工程学报，2009，28( 7) : 1321) ［4］ Wang D，Chen M，Jon Y，et al． Experimental study of fracture initiation and propagation from a wellbore / / 49th US Ｒock Me￾chanics /Geomechanics Symposium． San Francisco，2015: AＲMA- 2015-068 ［5］ Li W，Li L C，Tang C A． Numerical simulation research on mech￾anism of induced stress perturbation between parallel fractures in horizontal wells． Nat Gas Geosci，2016，27( 11) : 2043 ( 李旺，李连崇，唐春安． 水平井平行裂缝间诱导应力干扰机 制的数值模拟研究． 天然气地球科学，2016，27( 11) : 2043) ［6］ Liu C，Shi F，Lu D T，et al． Numerical simulation of simultane￾ous multiple fractures initiation in unconventional reservoirs through injection control of horizontal well． J Petrol Sci Eng， 2017，159: 603 ［7］ Shi F，Wang X L，Liu C，et al． An XFEM-based method with re￾duction technique for modeling hydraulic fracture propagation in formations containing frictional natural fractures． Eng Fract Mech， 2017，173: 64 ［8］ Nadimi S，Miscovic I，McLennan J． A 3D peridynamic simulation of hydraulic fracture process in a heterogeneous medium． J Petrol Sci Eng，2016，145: 444 ［9］ Lian Z L，Zhang J，Wang X X，et al． Simulation study of charac￾teristics of hydraulic fracturing propagation． Ｒock Soil Mech， 2009，30( 1) : 169 ( 连志龙，张劲，王秀喜，等． 水力压裂扩展特性的数值模拟 研究． 岩土力学，2009，30( 1) : 169) ［10］ Wang X L，Shi F，Liu H，et al． Numerical simulation of hydrau￾lic fracturing in orthotropic formation based on the extended finite element method． J Nat Gas Sci Eng，2016，33: 56 ［11］ Hosseini S M． On the linear elastic fracture mechanics applica￾tion in Barnett shale hydraulic fracturing / / 47th US Ｒock Me- · 544 ·