Chapter 1 Introduction ······································································· 1
1.1 Research background and significances ··········································· 1
1.2 Unstable dynamic propagation behaviours of the multistage hydrofracturing fracture network ······································································ 7
1.2.1 Deflection of fractures under the initiation sequence and perforation cluster spacing and well spacing ··········································· 9
1.2.2 Disturbance of the stress field in the propagation process of multiple fractures ·········· 15
1.3 Mechanisms of induced deflection of fluid-driven fractures ················· 16
1.3.1 Stress shadow effects between multiple fractures ······················ 17
1.3.2 Controlling factors of stress shadows ···································· 21
1.4 Numerical analysis of continuous stress field and discontinuous fracture ···· 25
1.4.1 Continuum-discontinuum numerical methods and models ··········· 26
1.4.2 Simulation of stress-dependent unstable dynamic propagation of fractures ····· 32
1.5 Challenges and perspectives ······················································· 37
1.6 Conclusions ·········································································· 38
References ·················································································· 39
Chapter 2 Dual bilinear cohesive zone model for fluid-driven propagation of multiscale tensile and shear fractures ······································ 48
2.1 Introduction ·········································································· 48
2.2 Governing partial differential equations for hydrofracturing ················· 52
2.2.1 Governing equations of solid deformation ······························ 53
2.2.2 Governing equations of fluid flow in fractured porous media ······· 55
2.3 Dual bilinear cohesive zone model ··············································· 56
2.4 Numerical discretization ··························································· 58
2.4.1 Finite element discretization for solid ··································· 58
2.4.2 Finite volume discretization for fluid ···································· 59
2.5 Detection and separation of discrete elements ·································· 60
2.6 Global algorithm and procedure ·················································· 62
2.7 Results and discussion ····························································· 63
2.7.1 Verification of fracture propagation through analytical solutions in KGD and PKN models ················ 63
2.7.2 Laboratory scales: dynamic propagation of small-size hydraulic fractures ······· 67
2.7.3 Engineering scales: dynamic propagation of large-size hydraulic fractures ······· 68
2.7.4 Distribution of tensile and shear fractures in hydrofracturing process ······· 73
2.8 Conclusions ·········································································· 75
References ·················································································· 76
Chapter 3 Multi-thread parallel computation method for dynamic propagation of hydraulic fracture networks ····························· 80
3.1 Introduction ·········································································· 80
3.2 Governing partial differential equations and fracture criteria for hydrofracturing ······· 83
3.3 Multi-thread parallel computation scheme for solid and fluid analysis ····· 83
3.4 Global algorithm and procedure ·················································· 84
3.5 Results and discussion ····························································· 86
3.5.1 Example 1: Verification for multi-thread parallel computation solutions of hydraulic fracture propagation ····························· 86
3.5.2 Example 2: Multi-thread parallel computation efficiency for fluid-driven fracture propagation ········································· 90
3.5.3 Example 3: Parallel computation using multi-type elements and meshes ······· 93
3.5.4 Example 4: Dynamic propagation behaviours of fractures under in-situ stresses and external fluid drive ··································· 96
3.6 Conclusions ·········································································· 99
References ················································································· 100
Chapter 4 Heterogeneous continuum-discontinuum computation method for dynamic diversion and penetration of hydraulic fractures contacting multi-layers and granules ······ 105
4.1 Introduction ········································································· 105
4.2 Governing partial differential equations and fracture criteria in fractured porous media ·········· 109
4.3 Combined finite element-discrete element-finite volume method and algorithm for multi-materials ···················································· 110
4.4 Numerical models of tight heterogeneous reservoirs with bedding and granules ······ 112
4.5 Results and discussions of dynamic propagation behaviours of hydraulic fractures in the multilayered reservoir ·········································· 118
4.5.1 A typical example implementation of fracture propagation and pore pressure in the heterogeneous tight reservoir with beddings ········ 118
4.5.2 Influence of bedding deviation angle and geomaterial properties on hydraulic fracture propagation ··········································· 120
4.5.3 Quantitative final length and propagation states of hydrofracturing networks in heterogeneous tight reservoirs with beddings ·········· 126
4.6 Results and discussions of dynamic propagation behaviours of hydraulic fractures in embedded multi-granule reservoir ································· 127
4.6.1 A typical example implementation of fracture propagation and pore pressure in the heterogeneous tight reservoir with granules ··· 127
4.6.2 Influence of granule distribution and geomaterial properties on hydraulic fracture ····· 129
4.6.3 Quantitative final length and propagation states of hydrofracturing networks in heterogeneous tight reservoirs with granules ··········· 132
4.7 Conclusions ········································································· 134
References ················································································· 135
Chapter 5 Dynamic propagation and intersection of hydraulic fractures and pre-existing natural fractures involving the sensitivity factors ······ 139
5.1 Introduction ········································································· 139
5.2 Combined finite element-discrete element method for hydrofracturing in fractured reservoirs ········· 142
5.2.1 Geomechanical equations in hydrofracturing and gas production ···· 142
5.2.2 Leak-off of fracturing fluid ··············································· 144
5.2.3 Discrete fracture network model ········································ 144
5.2.4 Numerical discretization ·················································· 145
5.3 Numerical models of fractured reservoir embedded discrete fracture networks ··· 146
5.3.1 Geometrical and finite element models ································ 146
5.3.2 Cases study for typical pre-existing natural fractures ················ 147
5.4 Results and discussion ···························································· 151
5.4.1 Sensitivity factors of pre-existing natural fractures ··················· 151
5.4.2 Quantitative length and volume of fracture networks ················ 155
5.4.3 Gas production in enhanced permeability fractured reservoirs ····· 160
5.5 Conclusions ········································································· 165
References ················································································· 166
Chapter 6 Unstable propagation of multiple hydraulic fractures and stress shadow effects in multilayered reservoirs ································ 171
6.1 Introduction ········································································· 171
6.2 Numerical methods for hydro-mechanical coupling and bedded interfaces ······· 173
6.2.1 Geomechanical equations ················································ 173
6.2.2 Characterization technology for bedded interfaces in multilayered reservoirs ····· 176
6.2.3 Local remeshing and microseismicity analysis ························ 177
6.3 Numerical models of multilayered reservoirs ·································· 177
6.4 Results and discussion ···························································· 181
6.4.1 Dynamic unstable propagation of multiple hydraulic fractures ····· 181
6.4.2 Evolution of stress field and injected fluid volume ··················· 184
6.4.3 Influences of in-situ stress and bedded interfaces in multilayered reservoirs ····· 190
6.4.4 Microseismic event distributions and magnitudes induced by unstable fractures ······ 192
6.5 Conclusions ········································································· 196
References ················································································· 197
Chapter 7 Unstable propagation of multiple hydraulic fractures and shear stress disturbance in multi-well hydrofracturing ······················· 202
7.1 Introduction ········································································· 202
7.2 Combined finite element-discrete element method considering thermal-hydro-mechanical coupling ············································ 205
7.3 Numerical models and cases of multiple horizontal wells ··················· 208
7.4 Results and analysis of unstable propagation of hydraulic fractures with variable well spacings ···························································· 211
7.4.1 Mesh refinement and thermal diffusion in fracture propagation process ····· 211
7.4.2 Fracture network propagation and shear stress shadows ············· 212
7.4.3 Quantitative analysis of propagation length and volume ············ 219
7.5 Results and analysis of unstable propagation of hydraulic fractures with variable initiation sequences ····················································· 222
7.5.1 Fracture network propagation and shear stress shadows ············· 222
7.5.2 Quantitative analysis of propagation length and volume ············ 231
7.6 Conclusions ········································································· 234
References ················································································· 235
Chapter 8 Unstable propagation of multiple three-dimensional hydraulic fractures and shear stress disturbance in heterogeneous reservoirs ·······239
8.1 Introduction ········································································· 239
8.2 Combined finite element-discrete element method for hydrofracturing ··· 244
8.2.1 Geomechanical equations in hydrofracturing considering hydro-mechanical coupling · 244
8.2.2 Leak-off of fracturing fluid ··············································· 246
8.2.3 Poroelastic effective medium model ···································· 247
8.2.4 Numerical discretization ·················································· 248
8.3 Three-dimensional numerical models of multistage hydrofracturing ······ 249
8.3.1 Three-dimensional geometrical and finite element models ·········· 249
8.3.2 Cases study for varying fracturing scenarios, perforation cluster spaces, and heterogeneous properties ··································· 250
8.4 Results and discussion ···························································· 255
8.4.1 Spatial propagation morphology of fracturing fracture network ···· 255
8.4.2 Disturbance of stress field during dynamic propagation of multiple hydraulic fractures ··········· 264
8.4.3 Quantitative area and volume of three-dimensional fracturing fracture networks ···· 275
8.5 Conclusions ········································································· 279
References ················································································· 280
Chapter 9 Unstable propagation of multiple three-dimensional hydraulic fractures and shear stress disturbance considering thermal diffusion ········· 285
9.1 Introduction ········································································· 285
9.2 Governing equation for hydrofracturing by considering thermal-hydromechanical coupling ····· 287
9.2.1 Solid deformation of rock matrix ········································ 287
9.2.2 Fluid flow in the rock matrix and fracture networks ················· 287
9.2.3 Thermal diffusion ·························································· 289
9.3 Heat transfer and mesh adaptive analysis of the fracture propagation process ··· 289
9.3.1 Heat transfer between the finite element nodes ······················· 289
9.3.2 Fracture criteria ···························································· 290
9.3.3 Local mesh refinement ···················································· 291
9.4 Three-dimensional numerical model with multiple perforations for parallel hydraulic fractures ······················································ 292
9.5 Results and analysis of unstable dynamic propagation of the threedimensional parallel hydraulic fractures ··················· 295
9.5.1 Perforation cluster spacing ··············································· 295
9.5.2 Sequential, simultaneous, and alternate fracturing ···················· 298
9.5.3 Thermal diffusion effects ················································· 304
9.6 Conclusions ········································································· 306
References ················································································· 307
Chapter 10 Summary and prospect ····················································· 311
10.1 Summary ·········································································· 311
10.2 Prospect ············································································ 315
