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عدد المساهمات : 18984 التقييم : 35458 تاريخ التسجيل : 01/07/2009 الدولة : مصر العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
| موضوع: كتاب Numerical Simulation in Hydraulic Fracturing - Multiphysics Theory and Applications الأحد 12 مارس 2023, 11:50 pm | |
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أخواني في الله أحضرت لكم كتاب Numerical Simulation in Hydraulic Fracturing - Multiphysics Theory and Applications Xinpu Shen Guoyang Technology and Services, Houston, TX, USA William Standifird Halliburton, Consulting, Houston, TX, USA
و المحتوى كما يلي :
Table of Contents About the book series vii Editorial board ix Foreword by M.Y. Soliman xvii Authors’ preface xix About the authors xxi Acknowledgements xxiii 1 Introduction to continuum damage mechanics for rock-like materials 1 1.1 Introduction 1 1.2 The Barcelona model: scalar damage with different behaviors for tension and compression 2 1.2.1 Uniaxial behavior of the Barcelona model 3 1.2.2 Unloading behavior 4 1.2.3 Plastic flow 5 1.2.4 Yielding criterion 5 1.3 Mazars’s holonomic form of continuum damage model 5 1.3.1 Concepts 5 1.3.2 Criterion of damage initiation 7 1.3.3 Damage evolution law 7 1.4 Subroutine for UMAT and a plastic damage model with stress triaxiality-dependent hardening 8 1.4.1 Introduction 8 1.4.2 Formulation of the proposed model 8 1.4.3 Numerical validation of constitutive model at the local level 12 1.4.4 Concluding remarks 17 2 Optimizing multistage hydraulic-fracturing design based on 3D continuum damage mechanics analysis 19 2.1 Introduction 19 2.2 The workflow 20 2.3 Validation example 21 2.3.1 Background description of the tasks 22 2.3.2 3D geomechanical model at field scale 22 2.3.3 Numerical results of the geomechanical model at field scale 23 2.3.4 Submodel for stimulation process simulation 23 2.3.5 The plastic damage model 25 2.3.6 Determination of the optimized stage interval based on numerical solutions 28 2.3.7 Determination of the optimized well spacing based on numerical solutions 29 2.4 Conclusion 29 xiiixiv Table of Contents 3 Numerical analysis of the interaction between two zipper fracture wells using the continuum damage method 31 3.1 Introduction 31 3.2 Submodel for stimulation process simulation 32 3.3 Conclusions 40 4 Integrated workflow for feasibility study of cuttings reinjection based on 3D geomechanical analysis and case study 43 4.1 Introduction 43 4.2 The integrated workflow 45 4.3 Fault reactivation analysis 48 4.3.1 Fluid migration resulting from fault reactivation 49 4.3.2 Estimation of maximum intensity level of seismic behavior of the fault 49 4.4 Examples of validation 49 4.4.1 Location selection of the injection well 50 4.4.2 Geometry and mesh 50 4.4.3 Values of material parameters 50 4.4.4 Initial geostress 51 4.4.5 Pore pressure 52 4.4.6 Numerical results of principal stress ratio 52 4.4.7 Selection of the true vertical depth interval of the perforation section 53 4.4.8 Fracture simulation: calculation of injection pressure window 53 4.4.9 Fault reactivation and fluid migration 62 4.5 Fault reactivation and seismicity analysis 65 4.5.1 Analytical equation used to calculate the magnitude of seismic activity 65 4.5.2 Assumptions and simplifications adopted in the finite element method 67 4.5.3 Numerical results 68 4.5.4 Remarks 69 4.5.5 Prediction of the volume of fluid with cuttings that can be injected 70 4.6 Conclusion 70 5 Geomechanics-based wellbore trajectory optimization for tight formation with natural fractures 73 5.1 Introduction 73 5.2 Determining optimized trajectory in terms of the CSF concept 74 5.2.1 Workflow for the selection of an optimized trajectory 74 5.2.2 Numerical application 75 5.3 Trajectory optimization focusing on a fracturing design for a disturbed field 76 5.3.1 The solution of the disturbed geostress field and F for non-zero αsf 78 5.3.2 The solution of the disturbed geostress field and F for zero αsf 80 5.4 Concluding remarks 82 6 Numerical solution of widened mud weight window for drilling through naturally fractured reservoirs 83 6.1 Introduction 83 6.2 Model description: theory 84 6.2.1 Constitutive model 84 6.2.2 Damage initiation criterion 85Table of Contents xv 6.2.3 Damage evolution law 85 6.2.4 Finite element type: the cohesive element 86 6.3 Fluid flow model of the cohesive element 87 6.3.1 Defining pore fluid flow properties 87 6.3.2 Tangential flow 87 6.3.3 Newtonian fluid 88 6.3.4 Power-law fluid 88 6.3.5 Normal flow across gap surfaces 88 6.4 Validation example: widened mud weight window for simple cases 88 6.4.1 Geometry 89 6.4.2 Initial conditions 89 6.4.3 Boundary condition 89 6.4.4 Loads 89 6.4.5 Values of material parameter 90 6.4.6 Procedure for numerical simulation of natural fracture opening under injection 91 6.4.7 Numerical results Case 1: injecting process, fracture opening, and propagation 91 6.4.8 Numerical results Case 2: static process after injection, fracture remains open 91 6.5 Remarks 93 6.6 Case Study 1: widened mud weight window (MWW) for subsalt well in deepwater Gulf of Mexico 94 6.6.1 Numerical results 94 6.7 Case Study 2: widened MWW for drilling in shale formation 96 6.7.1 Description of the well section in a shale gas formation 96 6.7.2 1D geomechanics analysis 97 6.7.3 Hydraulic plugging numerical analysis 99 6.8 Conclusions 102 7 Numerical estimation of upper bound of injection pressure window with casing integrity under hydraulic fracturing 103 7.1 Introduction 103 7.2 Workflow 106 7.3 Validation example 109 7.3.1 Initial pore pressure 109 7.3.2 Initial geostress field: sequence and direction of principal stress, and initial pore pressure 109 7.3.3 Casing: geometric parameters, material parameters 110 7.3.4 Cement ring: geometric parameters, material parameters 110 7.3.5 Mechanical properties of the rock formations 110 7.3.6 Stiffness degradation 111 7.3.7 Injection pressure 111 7.3.8 Boundary conditions to the global model 111 7.3.9 Finite element mesh of the global model 111 7.3.10 Finite element mesh of the submodel 111 7.3.11 Numerical results of casing deformation 113 7.4 Ending remarks 115xvi Table of Contents 8 Damage model for reservoir with multisets of natural fractures and its application in the simulation of hydraulic fracturing 117 8.1 Introduction 117 8.2 Expression of natural fractures with continuum-damage variable 118 8.3 Damage initiation condition 120 8.4 Damage evolution law 120 8.5 Damage-dependent permeability 120 8.6 Validation example: hydraulic fracturing of formation with natural fractures 121 8.6.1 Geometrical information of natural fractures 121 8.6.2 Damage tensor calculated using natural fracture information 122 8.6.3 Numerical simulation of hydraulic fracturing of a formation with natural fractures 123 8.7 Conclusions 129 9 Construction of complex initial stress field and stress re-orientation caused by depletion 131 9.1 Introduction 131 9.2 Construct initial stress field with a local model of complex stress pattern 132 9.2.1 Geology and one-dimensional (1D) geomechanics solution 132 9.2.2 Finite element model 135 9.2.3 Numerical results 138 9.3 Construction of initial geostress field and simulation of stress variation caused by pore pressure depletion 140 9.3.1 Geological structure in the region 140 9.3.2 Gas production plan 140 9.3.3 Finite element model 141 9.3.4 Numerical results 142 9.4 Conclusions 144 10 Information transfer software from finite difference grid to finite element mesh 145 10.1 Introduction 145 10.2 Description of principle 145 10.3 Numerical validation 147 10.4 Conclusion 148 Nomenclature 149 References 153 Subject index 159 Book series page 16 Subject index activated plastic status index (AC) 64–66 analytical modeling 70 angle azimuth 75, 118, 119, 122, 123 breakout 133–135 directional 137 anisotropic damage model 2 vector form 2 anisotropy 1, 2, 59 anticline (structure) 133, 135 approximate model (simplified) 141 asymmetric distribution fractures 106 natural 106 Barcelona model 2–5 plastic flow 5 yielding criterion 5 uniaxial behavior 3, 4 unloading behavior 4, 5 Benzeggagh-Kenane (BK) 85 BI (see brittleness index) BK (see Benzeggagh-Kenane) borehole 59, 89, 128, 139, 140 surface 59 bottom formation 75 boundary conditions 20, 22–24, 31, 32, 48, 64, 75, 89, 100, 108, 109, 111, 123, 135 boundary effect 76, 125, 128, 129, 140 bridge plug 103, 104 brittleness index (BI) 47, 48, 53 caging, effectiveness of 101 calculation elastoplastic damage 12 fluid leakoff 86, 87 cap formation 59–61, 70 bottom 60 integrity 43, 45, 59, 60, 70 estimation 44, 59, 60 Capasso-Mantica method 145, 146 case study construction of initial geostress field 140–144 cuttings reinjection (3D) 49–65 drilling through naturally fractured reservoirs 83–102 geomechanical analysis (3D) 49–65 hydraulic fracturing of formation with natural fractures 121–129 stress variation through pore pressure depletion 140–144 casing 103, 105–111, 113–115, 132 axis of 106–108 deformation 103–106, 108, 109, 113–115 by poor cementing quality 113 calculation 107 numerical solution of 109, 115 potential 103 significant 103–105, 109, 115 value 113 geometric parameters 110 material 109, 110 parameters 110 CDM (see continuum damage, mechanics) cement sheath 109, 110 cementing 108, 109, 111–114 material 109 quality good 109, 113 poor 109, 113, 114 work quality 112 coefficient, transversal deformation 108 cohesive element 86–91 Coh3D8P 86, 87 surfaces 87, 88 cohesive strength (CS) 62, 63, 74, 85, 108 complex faulting field 132 initial stress field 131, 133, 135, 137, 139, 141, 143 stress pattern 132 components directional 119 principal 131 compression 2, 3, 7, 13, 16–17 uniaxial 5, 13, 14, 16 compressive hoop stress 93, 94, 96 conditions initial 23, 89, 100, 123 pore pressure boundary 64, 89 constitutive model 2, 8, 10, 12, 13, 84 elastic 76 construction of complex initial stress field 131, 133, 135, 137, 139, 141, 143 continuum damage 3, 31, 35–37, 39, 121, 125, 128 CDM-based fracture property 60 mechanics (CDM) 1–19, 79, 108 model 5, 16, 29, 31 159160 Subject index contour of activated plastic status index AC 65, 66 damage intensity 79, 80, 126–129 pore pressure 49, 64, 77, 79, 80, 125–127, 129 distribution 68 shear strain intensity 125–128 stress component 35, 38, 40, 41 conversion software finite difference grid to finite element mesh 145–148 cracking strain 25, 26 cracks 1, 3, 85, 89, 117 injection-induced 64 volumetric density of 19, 20, 31 CRI (see cuttings reinjection) critically stressed fractures (CSF) 73, 74, 76, 77, 80, 82 concept 74 CS (see cohesive strength) CSF (see critically stressed fractures) curves, stress-strain 9, 16 cuttings 45, 50, 70 disposal 50 cuttings reinjection (CRI) 43, 44, 47, 50, 59, 69–71 design 43 feasibility study 43–46, 49, 70 hydraulic fracturing analysis 44 modeling 43–71 target formation 59, 71 damage conjugate 8–10, 120, 123 contour 124, 125, 127–129 dependent permeability 120, 121 evolution 1, 3, 8, 15, 55, 60, 85, 90 law 1, 7, 8, 10, 85, 86, 120 initiation 3, 7, 55, 60, 90, 108, 120 condition 120 criterion 85 intensity 80, 81, 124–129 localized band of 128, 129 mechanics analysis 20, 21 model 1, 2, 17, 18, 25, 41, 117–129 complex 2 damage initiation condition 120 equivalent-strain-based 1 holonomic 5, 7, 120 isotropic 2 nonlinear 18 orthotropic 120 plasticity-based 2, 8, 31 scalar continuum 2, 25 poro-elastoplastic 50, 54 reservoir with multisets of natural fractures 117–129 uses 7 tensor 119–123, 126, 129 natural fracturesrelated 117 value continuum 27 maximum continuum 27 variable (DV ) 2, 3, 5, 7, 9, 16, 20, 28, 29, 85, 118, 121 continuum 20, 25, 28, 30 synthetic 4, 20 values 20, 29 summation of 28, 29 zone 84, 85 damaged material 4, 7, 12 data-transfer 145, 147, 148 platform 145, 147, 148 procedure 145, 146 deformation 68, 113 behavior 62, 108 targets fault 67 deformed mesh 113, 114 direction azimuth 97, 136 normal 55, 85, 89, 90, 100, 111, 117 tangential 85 discretization 22, 24, 32, 48, 62 displacement 24, 87, 89, 132, 135 component, vertical 68, 69 magnitude 64, 66 relative 67, 69 values, vertical 113 distribution of HD-induced fractures 104, 105 synthetic damage 27 domain local calculation 146 radius, optimized 146 drilling 70, 83, 91, 96, 98, 102, 103, 128 numerical solution 83–102 through naturally fractured reservoirs 83–102 Drucker-Prager type plastic damage model 2, 18 dual-porosity 118 DV (see damage, variable) effect of natural fractures permeability 84 effective fracture 20, 28–30 concept 30 stress 3, 33–41, 46, 85, 94, 99, 123, 137 principal 46 ratio 23, 43, 46, 47, 51, 98, 134 space 3, 5, 8, 9, 11, 89, 100 elastic behavior, linear 3 parameters 55, 90 elasticity modulus of 110 values of 110 parameters of 50, 51, 62, 63 elastoplastic model 109 ideal 110 porous 108 fault 43–45, 49, 50, 52, 56, 62–65, 67–71, 106, 117, 131–133, 135 bottom location 64 intensity level of seismic behavior 49Subject index 161 major 52 material 49, 62, 67 reaction 45, 62 reactivation 43–45, 49, 52, 60, 62, 64, 65, 67, 69, 70 analysis 43, 45, 48, 50, 54, 60, 62, 69, 70 beginning stage of 64, 65 injection-related 44 risk 44, 52 surface 67 system 131, 132 thrust fault 131, 132 faulting factors 52 FD (see finite difference) FE (see finite element (FE)/method (FEM)) feasibility study of cuttings reinjection 3D geomechanical analysis 43–71 fault reactivation analysis 48, 49 fluid migration resulting from fault reactivation 49 fluid volume injected 70 prediction 70 intensity level of seismic behavior 49 seismic activity analytical equation 65–67 integrated workflow 45–48 FEM (see finite element (FE)/method (FEM)) FG (see fracture, gradient) finite difference (FD) 135, 145, 147 analyses 145 conversion to finite element mesh 145–148 grid 145, 147 node locations 146, 147 source 145, 146 mesh 146 finite element (FE)/method (FEM) 8, 20, 22, 30, 31, 45, 47, 49, 50, 60, 62, 63, 67, 70, 74, 75, 111, 123, 125, 135, 142, 145, 146 analysis (FEA) 74, 75, 83, 145 mesh 25, 50, 62, 75, 111, 112, 135, 141, 145–148 location 147 nodal information of mechanical variables 146 nodes 145, 146 location 147 values 147 model 22, 45, 47, 49, 54, 59, 60, 62, 67, 70, 74, 123, 135, 141, 146 submodeling techniques 70 flow, normal 87, 88 flow rates, constant injection 91, 93, 96 fluid flow model 87 injection 24, 31, 32, 55, 91 leakoff coefficients 88 migration 43–45, 48–50, 60, 62, 64, 67, 69, 70 power-law 87, 88 formation 49–51, 59, 60, 62, 63, 73–76, 84, 89, 91, 104–109, 111, 115, 121, 123, 131, 132, 134, 135, 143–145 layer 75, 106, 134 direction 142 material 28, 110 matrix 62, 90, 94, 118 overburden 50, 106 permeability (see also main entry permeability) 83 pore pressure 115 integrity tests 83 properties 59, 104 salt 50 shale 96, 98, 106 shale oil/gas 117, 118 stimulation result 128 stress cage 84 tight-sand oil 22, 121 tops 78, 131, 132, 134, 135, 140 unconsolidated sand 83, 84 fracture analysis 19, 30 vertical 59 aperture 83 area 29, 119, 128 effective 29 asymmetric distribution 115 clouds of 19, 108 density 117–119 natural 106, 119 development 25, 30, 54, 118, 128 distribution 41 energy 1, 2, 55, 60, 85, 86, 90 far-field 128 generation 24, 29, 32, 121 geometry 44, 92 gradient (FG) 83, 84, 98 near-wellbore 83 induced 49, 62, 73, 64, 68, 69, 77, 84, 104, 111, 115, 128, 131 initial 92 initiation 45, 53, 54, 70 pressure 60 length 56, 70 effective 20, 21 generated 45, 69 induced 106 mechanics 1 analysis 59 model 29 planar 19, 44 vertical 57 modeling 19, 20 mouth 91 natural 19, 41, 73–78, 82–84, 89, 91, 93, 94, 97, 98, 102, 106, 115, 117–123, 125, 126, 128, 129 concepts 117 continuum-damage variable 118, 119 damage tensor 122, 123 direction of 73, 78, 126, 129 distribution of 75, 104, 110 geometry 121, 122 initial width 84162 Subject index fracture (continued) major 100 multisets of 117–119, 121, 123, 125, 127, 129 partial 117 permeability 84, 102 single 120, 129 system, equivalent 118 vertical 100 near-wellbore 128 network 127–129 complex 126, 129 networking 127, 128 opening 54, 56–59, 84, 85, 88, 90–94, 100–102 maximum 92, 94, 120 natural 91, 117 values 91, 94, 101 variation of 91, 93, 95, 100 pair of 96 permeability (see also main entry permeability) 84 planar 19 problems 2 propagation 19, 20, 48, 56–60, 70, 78, 83, 85, 89, 91 analysis 19 calculations of 54 damage-based 54, 55 development 106 horizontal 55 induced 117 process 57 resistance 84 situation 54 solution 20 stable 45, 56, 60, 61 status 56 vertical 57 properties 60, 118 representative equivalent 96 reservoir volume 33–35, 37–39 sealing 83 shape 59 simulation 52–54 hydraulic 54 single 55, 90, 96 stressed 73 surface 55, 74, 85, 86, 90, 102 vertical 57–59 volume 24, 32, 33, 35–37, 39, 40 generated 70 width 54, 56, 57, 59, 70, 71 increment 102 maximum 56 resultant 59 value 59, 71 zipper fracture 19, 31–33, 35, 37, 39, 41, 121 zone 28–30, 33, 132 increased effective 29 fractured (see fracture) fracturing (see hydraulic fracturing (HF)) function of submodel 135 gap fluid volume rate (GFVR) 88 gas, natural 103 production, 19, 20, 30 resources 19, 20 geomechanical model (see model (numerical), geomechanical) geomechanical modeling (see modeling/solution (numerical), geomechanical) geometry of fracture opening 92 natural fractures 117, 121, 122 submodel 32, 55, 136 geostress 81, 89, 97, 100, 125, 126, 140 distribution 22, 43, 110 field, disturbed 78, 80–82 initial directions of 131 field 23, 46, 54, 63, 74, 75, 91, 109, 110, 131, 135, 140, 144 construction 132–140 simulation of stress variation by pore pressure depletion 140–144 given 39, 41 geostructures 132, 135, 143, 144 GFVR (see gap fluid volume rate) 88 GOM (see Gulf of Mexico) Gulf of Mexico (GOM) 83 deepwater 83, 84, 94 HF (see hydraulic fracturing (HF)) Hooke’s law 3, 4 hoop stress 84, 91–94, 101 distribution 93, 96 horizontal stress (see stress, horizontal) horizontal wells (see well, horizontal) 19–22, 29, 32, 104, 121 hydraulic fracturing (HF) (see also entries below main entry modeling/solutions (numerical)) 18–20, 28–30, 43–46, 48, 50, 52–54, 62, 73, 74, 77–84, 91, 102–104, 106–108, 110–112, 117, 118, 120–124, 129, 144–146 activities 147 analysis 48, 70, 77 behavior 89 casing deformation (induced) 104 maximum value 114 modeling 103 design/process 31, 73, 76, 82, 84, 104, 111 hydraulic 19, 30, 103, 128, 129 multistage 103 optimized 103, 126 primary 73 formation with natural fractures 121–129Subject index 163 injection (stimulation) 19, 20, 26, 27, 30–35, 37–39, 41, 43–45, 47–50, 52–54, 56, 57, 70, 73, 78, 79, 91, 92, 95, 103–108, 111, 115, 117, 118, 124, 125, 127, 129 design 54 effects 24, 32 flow 32, 40, 55, 89, 91, 100, 124 fluid 19, 20, 31, 64, 69, 70 formation 59 load/loading 23, 32, 33, 84, 91, 103, 105, 106, 108, 123–125 maximum injection 107 microcracking/damage 3 operation 109, 110, 114 point/location 20, 27–29, 32, 44, 52, 53, 60, 62–64, 69, 70, 126, 129 pressure 39, 44, 45, 47, 56, 57, 59–61, 64, 70, 89–94, 96, 100, 102, 103, 105, 107–111, 113–115 bottomhole 111 curves of 48, 60 hydraulic 89, 103 maximum 94, 109 maximum value of safe 103, 115 time-dependent 91 value 45, 48, 54, 60, 91, 108, 111, 113 window (IPW) 43, 45, 48, 50, 53, 54, 57, 70, 103, 105, 107, 109, 111, 113, 115 safe 103, 115 process 31–33, 92, 93, 108, 111 simulation 22, 23, 32 stable 25 rate 39, 44, 47, 48, 54, 56, 57, 59, 105, 124, 125 given 56, 58 proper 44, 45 values 48, 59 resultant 103 safe 104 maximum 109, 114 sections 43, 45, 47, 70 sequential 39, 41 simultaneous 39, 41 stable 59 step 32, 89, 100 stimulation 28, 33, 34, 36–38 simultaneous 40 stages 29, 30 measures 73 model example 117 operation/procedure 44, 87, 103, 106, 109, 117, 122, 124–126, 131 design 131 modeling 129 multistage 103 optimization for tight formation wellbore trajectory 73–82 CSF concept 74–76 workflow 74, 75 numerical application 75, 76 results, optimal 22 simulation 19, 31, 43, 44, 48, 77, 86, 117, 121, 123 fracture analysis 44 stages 104 intervals 19–22, 28, 30, 106 design of 19, 30 of multistage hydraulic fracturing 19–21 multistage 19–21, 30, 103 optimizing design 19, 21, 23, 25, 27, 29 zipper fracturing 31 hydraulic plugging 83, 84, 93, 98–102 inclination angle of natural fractures 78 initial geostress (see geostress, initial) initial width of natural fracture (see fracture, natural, initial width) initial pore pressure (see pore pressure, initial) initial stress field (see geostress, initial) injection (see hydraulic fracturing (HF), injection (stimulation)) inverse analysis 17, 117, 118 IPW (see injection, pressure, window (IWP)) iteration procedure 12 LCM (see lost circulation materials (LCM)) local model of complex stress pattern (see model (numerical), local, complex stress pattern) logging data 45, 74, 83, 96–99, 118, 121, 135 while drilling (LWD) 83 lost circulation materials (LCM) 83, 84, 93, 94, 102 Lower Pinda formation 62, 63 LWD (see logging, while drilling) material density 110 model 54 elastic 62 nonlinear 8 nonpermeable 106 porous elastoplastic 62 user-developed 8 parameters 7, 9, 13, 23, 25, 50, 79, 90, 94, 107, 109, 110, 120 of plastic damage model 25 values 100 properties 4, 109 maximum fracture opening (see fracture, opening, maximum) maximum fracture width (see fracture, width, maximum) maximum injection pressure (see hydraulic fracturing (HF), injection (stimulation), pressure, maximum) maximum intensity level of seismic behavior (see seismic, activity, behavior, maximum intensity level)164 Subject index maximum value of casing deformation (see hydraulic fracturing (HF), casing deformation (induced), maximum) Mazar’s holonomic form of continuum damage model 5–7 concepts 5–7 criterion of damage initiation 7 damage evolution law 7 Mazars-Pijaudier-Cabot damage model 1 mechanical properties 60, 84, 107, 109, 110, 146 parameters of 107, 109 variables 23, 31, 33–39, 45, 49, 64, 87, 146 microcracks 3, 4, 29, 84 microseismic data (see seismic, activity, microseismic data) Mises stress 57, 64, 76, 77 contour 79–81 model (numerical) 56, 67, 83, 102, 103, 112, 115, 123, 132, 135–137, 141, 144 accuracy 54 block 132 calibration 108 formation structures 142 formulation 9 geomechanical 21–23, 62, 69, 71, 132, 145 geometry 22, 23, 62, 63, 89, 91, 111 large 106 local 132, 135 of complex stress pattern 132 micromechanical models 1 parameters 5, 16, 79 plastic damage 25 poro-elastoplastic 50 power-law 87 scale/size 22, 135 simplified 49, 54, 106, 118, 141 single-permeability 118 solid-mechanics 84 strain-based 2 uses 32 modeling/solution (numerical) 19, 22, 28, 29, 31–33, 35, 37, 39, 41, 45, 50, 54, 64, 83–105, 107–109, 111, 113, 115, 125, 129, 132, 135, 139–141, 144 casing deformation 103 construction of initial geostress field 140–144 cuttings reinjection (3D) 43–71 damage evolution law 85–86 damage initiation criterion 85 damage model 117–129 reservoir with multisets of natural fractures 117–129 drilling through naturally fractured reservoirs 83–102 geomechanical 49, 62, 73–75, 132, 147 analysis 43–46, 74, 97, 134, 135, 145, 147, 148 3D 43–71 solutions 43, 45, 49, 53 fault reactivation analysis 48, 49 case study 49–65 fluid migration resulting from fault reactivation 49 fluid volume injected 70 prediction 70 intensity level of seismic behavior 49 seismic activity analytical equation 65–67 integrated workflow 45–48 modeling 49–65 hydraulic fracturing 117–129 interaction between two zipper fracture wells 31–41 inverse 17, 117, 118 normal flow across gap surfaces 88 of fracture propagation 70 of hydraulic fracturing 123 of interaction between two zipper fracture wells continuum damage method 31–41 of plastic deformation 110 of widened mud weight window 83–101 stress variation through pore pressure depletion 140–144 formation with natural fractures 121–129 upper bound of injection pressure window 103–115 wellbore trajectory optimization 73–82 widened mud weight window for drilling 83–102 mud weight 102 pressure 89, 91, 101 mud weight window (MWW) 83–101 drilling through naturally fractured reservoirs 83–102 numerical solution 83–102 case study 88–101 theory 84–87 damage evolution law 85, 86 damage initiation criterion 85 Newtonian fluid 88 normal flow across gap surfaces 88 pore fluid flow properties 87 power-law fluid 88 tangential flow 87 multistage hydraulic fracturing (see hydraulic fracturing (HF), stages, multistage) MWW (see mud weight window (MWW)) natural fracture (see fracture, natural) near-wellbore fracture gradient (see fracture, gradient, near-wellbore) Newtonian fluid 87–88 nonpermeable material models (see material, model, nonpermeable) normal flow across gap surfaces 88 numerical analysis (see modeling/solution (numerical)) numerical model (see model (numerical)) numerical modeling (see modeling/solution (numerical))Subject index 165 offset wells 20, 28, 51, 63, 73, 76, 123, 135 offshore field 44 oil 19, 20, 30, 43, 103 tight-sand 19, 30, 31 unconventional 19, 20 orthotropic permeability 78, 119, 121, 123 tensor 78, 123, 129 parallel wells 29, 30 PBP (see plug breaking pressure) peak strength envelope 18 perforation section 20, 32, 43, 47, 50, 53, 56, 59, 71, 104, 106 permeability 23, 41, 49, 78, 84, 88, 91, 118, 120, 121, 123, 124, 128 damage dependent 79, 120, 121 dual 118 permeability model 121 plugging apparatus (PPA) 83 single 118 tensor 123, 124 petroleum industry 103, 145, 148 plastic damage 2, 8, 9 model 1, 2, 8, 22, 25, 31 multiplier 12, 13 deformation 139, 140 flow 5, 9, 76 region 8, 9, 49, 64, 139, 140 plug breaking pressure (PBP) 84 Poisson’s ratio 5, 23, 25, 47, 75, 90, 94, 97–99, 106, 108, 110, 131 pore pressure 22–24, 31, 33, 49, 52, 63–65, 68, 69, 76, 77, 79–81, 108–111, 123, 125, 127, 145–147 depletion 132, 140–144 field/distribution 25, 26, 33–41, 64, 65, 68, 125, 145, 147 initial 23, 24, 79, 109, 110 reservoir 32 original formation 108 unloading 81, 82 porosity 106, 118, 145 dual 118 porous flow 44, 49, 62, 78, 115, 118, 119, 141, 145 power-law fluid 88 PPA (see permeability, plugging apparatus (PPA)) pressure values (see hydraulic fracturing (HF), injection (stimulation)) principal stress (see stress, principal) PSR (see stress, principal, principal stress ratio) representative volume element (RVE) 1 reservoir 22, 24, 75–82, 117–119, 121, 123, 125, 127, 129, 132, 135, 145 analyses 145, 146 formation 23, 75, 76, 89, 117, 141, 143 anti-cline 76 fractured tight-sand 121 tight-gas 132 fractured 83, 118 model 144 dual-permeability 118 equivalent 118 single-permeability 118 stimulation (see hydraulic fracturing (HF), injection (stimulation)) safe injection pressure (see hydraulic fracturing (HF), injection (stimulation), pressure, safe) salt 50, 132 body 131, 132, 140 seismic activity 45, 49, 62 analytical equation 65–67 behavior 45, 48, 49, 60, 67, 69 maximum intensity level 48, 49 microseismic data 20, 21, 28, 41, 104, 123, 124 analysis 44, 45, 49, 67, 70 magnitude of 43, 45, 49, 62, 65 seismicity 69, 70 analysis 65 shale gas formation 96, 102 ductile failure of 46, 47 natural fractured 83 shear strain 125–128 shear stress 46, 47, 74, 88, 132 factor 47 transverse 87 stage intervals (see hydraulic fracturing (HF), stages, interval) stiffness 84, 85 degradation 111 recovery 4 stimulation (see hydraulic fracturing (HF), injection (stimulation)) strain inelastic 1, 25, 26 lateral 12, 14, 15, 108 loading 1, 12, 14, 15 localization 3 volumetric 14, 15 stress 3, 12, 25, 54, 74, 85, 94, 131, 132, 137, 141 cage 84, 90, 93, 94, 102 caging 83, 102 calculation process 137 compressive 23, 46, 63, 98 confinement, hydrostatic 15, 16 distribution 20, 45, 47, 57, 58, 70, 81 field 50, 54, 73, 76, 77, 79, 80, 82, 132 disturbed 79, 82 initial 51, 74, 75, 78, 131, 132 horizontal 33, 35, 36, 38–40, 51, 59, 62, 73, 94, 111, 123, 129, 131 normal 46, 74 orientation 141, 142, 144 pattern 97, 98 normal fault 51 reverse fault 110166 Subject index stress (continued) principal 22, 73, 98, 109, 110, 123, 128, 131, 132, 136, 138, 144 components 5, 46, 97, 135, 138, 139, 144 directions 23, 109, 117, 123, 126, 129, 131, 136, 144 principal stress ratio (PSR) 45, 46, 51, 52 re-orientation 131, 133, 135, 137, 139, 141, 143 caused by depletion 131, 140 rotation 132, 137, 138, 140, 142 shadow 20, 30 solution, disturbed fracturing 77 state 4, 13 effective 11 triaxial 4 status, critical 73, 74 stress-strain behavior 15–17 triaxiality 8–10 variation 106, 140, 141 submodel 20, 22–26, 31–41, 48, 50, 54–57, 59, 70, 108, 109, 111, 112, 135–137, 139, 140 analysis 135 reservoir level 20 size 135 small scale 23, 31, 48 submodeling concept 48 techniques 23, 31, 48, 54, 135 use 54 subsidence 132, 142 tangential flow 87 tensile strength 25, 84, 86 tension 2, 3, 7, 13, 16, 120 uniaxial 13–15 thrust faults (see fault, thrust fault) tight formation 73, 74, 78, 82, 118 optimization for wellbore trajectory 73–82 case study 49–65 CSF concept 74–76 numerical application 75, 76 workflow 74, 75 unconventional hydrocarbon resources 19, 30, 31, 103 Underground Research Laboratory (URL) 131 uniaxial behavior 3 upper bound of injection pressure window 103–115 case study (validation) 109–115 workflow (modeling) 106–109 Upper Pinda formation 62, 63, 68 URL (see Underground Research Laboratory) well 22, 29, 132, 134 horizontal 19–22, 29, 32, 104, 121 offset 20, 28, 51, 63, 73, 76, 123, 135 parallel 29, 30 wellbore 22, 59, 73, 74, 83, 84, 89, 91–94, 96, 100–103, 106, 111, 135, 147 hoop stress 83 surface 84, 89–91, 93, 96, 100, 102 trajectory 73 optimized 73, 78 for tight formation 73–82 CSF concept 74–76 numerical application 75, 76 workflow 74, 75 widened mud weight window (widened MWW) 83–85, 87–89, 91, 93–97, 99, 101 workflow 20, 21, 44, 45, 47, 49, 73–75, 82, 83, 94, 96, 102–104, 106, 107, 109, 115, 117, 141, 144 CSF concept 74, 75 damage mechanics analysis 20, 21 feasibility study of cuttings reinjection 3D geomechanical analysis 43–71 fault reactivation analysis 48, 49 analytical equation 65–67 fluid migration resulting from fault reactivation 49 fluid volume injected 70 integrated workflow 45–48 intensity level of seismic behavior 49 prediction 70 case study 49–65 Young’s modulus 4, 5, 23, 25, 47, 62, 94, 106–108, 110, 111 value 3, 49, 63, 67, 75, 107, 108 zero-discharge policies 43–45 zipper fracture 19, 31–33, 35, 37, 39, 41, 121 wells 31 numerical analysis of the interaction continuum damage method 31–41 zipper fracturing 31 #ماتلاب,#متلاب,#Matlab,
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