كتاب Numerical Simulation in Hydraulic Fracturing - Multiphysics Theory and Applications
منتدى هندسة الإنتاج والتصميم الميكانيكى
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منتدى هندسة الإنتاج والتصميم الميكانيكى
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 كتاب Numerical Simulation in Hydraulic Fracturing - Multiphysics Theory and Applications

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كتاب Numerical Simulation in Hydraulic Fracturing - Multiphysics Theory and Applications  Empty
مُساهمةموضوع: كتاب Numerical Simulation in Hydraulic Fracturing - Multiphysics Theory and Applications    كتاب Numerical Simulation in Hydraulic Fracturing - Multiphysics Theory and Applications  Emptyالأحد 12 مارس 2023, 11:50 pm

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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

كتاب Numerical Simulation in Hydraulic Fracturing - Multiphysics Theory and Applications  N_s_i_10
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

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