Parent-Child, Multilateral Well
and Fracture Interactions
by
Wilson C. Chin
Xiaoying Zhuang
Table of Contents
Preface vii
Acknowledgements x
Interactions
1Additional questions raised 1
Problem identified 2
Why call them frac hits? 5
Is a frac hit model possible? 5
1.1 Reference 7
Summary 9
2.1 Governing Equations and Numerical Formulation 9
Steady flows of liquids 10
Difference equation formulation 10
The iterative scheme 12
Modeling well constraints for liquids 13
Steady and unsteady nonlinear gas flows 15
Steady gas flows 16
Well constraints for gas flows 18
Transient, compressible flows 19
Compaction, consolidation and subsidence 22
Boundary conforming grids 23
Stratigraphic meshes for layered media 24
Modeling wellbore storage 25
2.2 References 27
3. Reservoir Simulation Strengths, Limitations and
Strategies . 28
Deficiencies affecting all simulators 28
3.1 Rectangular versus Curvilinear Coordinates 29
3.2 Fracture Simulations and Analytical Subtleties 33
Aerodynamic analogies 33
3.3 A Digression Advances in Geometric Modeling 35
3.3.1 Airfoil and three-dimensional wing flows 35
3.3.2 Two dimensional planar reservoir flows 36
3.4 Formulation Errors in Commercial Simulators 40
Commingled reservoirs 40
Unit mobility flow 40
Well constraints, pressures and rates, kh products 40
Upscaling methods and averaging . 41
Geometric gridding 42
Input/output issues and 3D color graphics 42
Matrix solvers and numerical inversion 42
Meaning of farfield boundary conditions 43
Grid density 43
Simulator design philosophy 44
3.5 References 45
4. Parent-Child Well and Fracture Flow A Simple
Steady-State Example 46
4.1 A Simple Example Steady Flow Parent-Child Well and
Fracture Interactions . 46
Reference examples 47
More interesting calculations 47
Closing remarks 53
4.2 Two Reference Single-Well Analyses 54
Reference Example A 54
Reference Example B 57
4.3 Detailed Two-Well and Fracture Flow Analyses 59
Run 1 Two wells, different pressure constraints,
homogeneous medium 59
Run 2 Two wells, identical pressure constraints
in homogeneous isotropic medium 81
Run 3 Return to Run 1 well constraints, with
Wells 1 and 2 joined using uniform fracture 84
Run 4 Incomplete fracture penetration at Well 1 91
Closing remarks 96
4.4 References 96
5. Hydraulic Fracture Flow for Horizontal Wells in
Anisotropic Media. 97
5.1 Horizontal or Multilateral Wells Intersected by General
Hydraulic Fractures in Fully Transient Flow 97
Run 1 99
Runs 2, 3 and 4 101
5.2 Detailed Software Analysis 105
5.2.1 Run 1. No fractures along vertical-to-horizontal
well (for reference baseline comparisons) 105
5.2.2 Run 2. Horizontal well intersected by a single
hydraulic fracture 142
5.2.3 Run 3. Horizontal well intersecting two fracture
planes 147
5.2.4 Run 4. Horizontal well intersecting three
fractures 149
5.2.5 Runs 5-6. Effects of anisotropy and fracture
orientation 153
Run 5 153
Run 6 155
5.3 References 157
6. Cube Models in Reservoir Development 158
6.1 Well Spacings, Parent-Child Effects and Reservoir
Strategy in Modern Drilling 158
6.1.1 Basic optimization problems 158
6.1.2 Reservoir flow simulation versus statistical
modeling approaches 160
6.1.3 Cube model set-up and computed results 161
6.1.4 Reservoir optimization and cost effectiveness 166
6.1.5 Closing remarks 168
6.1.6 References 169
6.2 Detailed Software Analysis 170
6.3 A More Optimal Production Method 197
6.4 References 200
7. Simulating While Drilling Extending a Vertical Well
Horizontally During Transient Production 201
7.1 Declining Production with Horizontal Lateral
Solution 201
7.2 Detailed Software Analysis 207
7.3 References 236
8. Simulating While Drilling Adding a Complicated Multilateral
Well During Transient Production from a Vertical 237
8.1 Vertical and Subsequent Multilateral Neighboring
Well 238
8.2 Detailed Software Analysis 243
8.3 References 264
9. Heterogeneous, Anisotropic, Layered Reservoir with Finite
Tilted Fracture Plane Produced by Multilateral Wells 265
9.1 Five Comparative Production Scenarios 266
Run 1. Uniform isotropic reservoir (base reference) 267
Run 2. Effect of high permeability fracture on Run 1 272
Run 3. Highly heterogeneous three layer reservoir, isotropic
flow within each sub-domain, no fracture
planes 274
Run 4. Effect of anisotropy on Run 1 (again, uniform kx, ky,
with kz 50% smaller), no fractures 276
Run 5. Nonlinear gas flows, results compared with Run 1
liquid baseline, assuming uniform kx, ky and kz,
no fractures 278
Closing remarks 279
9.2 Detailed Software Analysis 280
Run 1. Uniform isotropic reservoir (base reference) 281
Layered geological description 281
Software caution 283
Layered drilling description 287
Layer results and flow decline curves 300
Run 2. Effect of high permeability fracture on Run 1 308
Run 3. Highly heterogeneous three layer reservoir, isotropic
flow within each sub-domain, no fracture planes 312
Run 4. Effect of anisotropy on Run 1 (again, uniform kx, ky,
with kz 50% smaller), no fractures 316
Run 5. Nonlinear gas flows, results compared with Run 1
liquid baseline, assuming uniform kx, ky and kz, no
fractures 321
9.3 Closing Remarks 328
9.4 References 328
10. Advanced Reservoir Modeling with Multisim 329
10.1 Features 330
Reservoir Description 330
Well System Modeling 330
Additional Simulator Features 330
10.2 Licensing Options 331
Multisim 331
Complementary Models 331
4D TurboView 331
Fluid Tracer 331
Formation Testing Suite 331
10.3 Disclaimer 332
End-User License Agreement (EULA) 332
Grant of license 332
Descriptions of other rights and limitations 333
Termination 334
Copyright 334
No warranties 334
Limitation of liability 334
Further disclaimers 335
Additional restrictions 335
End of EULA 335
Cumulative References 336
Index 351
About the Authors 359
Wilson C. Chin 359
Xiaoying Zhuang 376