Parent-Child, Multilateral Well

and Fracture Interactions

 

by

 

Wilson C. Chin

Xiaoying Zhuang

 

 

 

Table of Contents

 

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . x

 

  1. Parent-Child, Multilateral Well and Fracture Flow
  2. Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

    Additional questions raised . . . . . . . . . . . . . . . . . 1

    Problem identified . . . . . . . . . . . . . . . . . . . . . . . 2

    Why call them frac hits? . . . . . . . . . . . . . . . . . . . 5

    Is a frac hit model possible? . . . . . . . . . . . . . . . . 5

    1.1 Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

  3. Reservoir Flow Analysis Concise and Rigorous

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