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