Reservoir Simulation and Well Interference Parent-Child, Multilateral Well and Fracture Interactions

Co-written by a world-renowned petroleum engineer, this breakthrough new volume teaches engineers how to configure, place and produce horizontal and multilateral wells in geologically complicated reservoirs, select optimal well spacings and fracture separations, and how to manage factors influencing well productivity using proven cost-effective and user-friendly simulation methods.

Charged in the 1990s with solving some of petroleum engineering's biggest problems that the industry deemed "unsolvable," the authors of this innovative new volume solved those problems, not just using a well-published math model, but one optimized to run rapidly, the first time, every time. This not only provides numerical output, but production curves and color pressure plots automatically. And each in a single hour of desk time.

Using their Multisim software that is featured in this volume, secondary school students at the Aldine Independent School District delivered professional quality simulations in a training program funded by some of the largest energy companies in the world. Think what you, as a professional engineer, could do in your daily work. Valuable with or without the software, this volume is the cutting-edge of reservoir engineering today, prefacing each chapter with a "trade journal summary" followed by hands-on details, allowing readers to replicate and extend results for their own applications.

This volume covers parent-child, multilateral well, and fracture flow interactions, reservoir flow analysis, many other issues involving fluid flow, fracturing, and many other common "unsolvable" problems that engineers encounter every day. It is a must-have for every engineer's bookshelf.

Wilson C. Chin, PhD, is an experienced petroleum engineer with over twenty books published by Wiley-Scrivener and other leading publishers and over a hundred articles published in scientific journals. He holds four dozen domestic and international patents and has received five major awards with the United States Department of Energy. Mr. Chin's interests include reservoir simulation, measurement while drilling, borehole electromagnetics, managed pressure drilling, formation testing, downhole vibrations, and drilling and cementing rheology.

Xiaoying Zhuang has almost a decade of experience in borehole rheology and reservoir fluid mechanics. From 2009 to 2011, she served as Co-Investigator for the United States Department of Energy in their sponsored research into well control, leading to a well-received book appearing in English and Chinese on the subject. "Jenny" has co-authored ten papers in her areas of technical interest.

Preface xi

Acknowledgements xv

1 Parent-Child, Multilateral Well and Fracture Flow 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

2 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

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