Reservoir Simulation and Well Interference

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 xiAcknowledgements xv1 Parent-Child, Multilateral Well and Fracture Flow Interactions 1Additional questions raised 1Problem identified 2Why call them frac hits? 5Is a frac hit model possible? 51.1 Reference 72 Reservoir Flow Analysis – Concise and Rigorous Summary 92.1 Governing Equations and Numerical Formulation 9Steady flows of liquids 10Difference equation formulation 10The iterative scheme 12Modeling well constraints for liquids 13Steady and unsteady nonlinear gas flows 15Steady gas flows 16Well constraints for gas flows 18Transient, compressible flows 19Compaction, consolidation and subsidence 22Boundary conforming grids 23Stratigraphic meshes for layered media 24Modeling wellbore storage 252.2 References 273 Reservoir Simulation – Strengths, Limitations and Strategies 28Deficiencies affecting all simulators 283.1 Rectangular versus Curvilinear Coordinates 293.2 Fracture Simulations and Analytical Subtleties 33Aerodynamic analogies 333.3 A Digression – Advances in Geometric Modeling 353.3.1 Airfoil and three-dimensional wing flows 353.3.2 Two dimensional planar reservoir flows 363.4 Formulation Errors in Commercial Simulators 40Commingled reservoirs 40Unit mobility flow 40Well constraints, pressures and rates, kh products 40Upscaling methods and averaging 41Geometric gridding 42Input/output issues and 3D color graphics 42Matrix solvers and numerical inversion 42Meaning of farfield boundary conditions 43Grid density 43Simulator design philosophy 443.5 References 454 Parent-Child Well and Fracture Flow – A Simple Steady-State Example 464.1 A Simple Example – Steady Flow Parent-Child Well and Fracture Interactions 46Reference examples 47More interesting calculations 47Closing remarks 534.2 Two Reference Single-Well Analyses 54Reference Example A 54Reference Example B 574.3 Detailed Two-Well and Fracture Flow Analyses 59Run 1 – Two wells, different pressure constraints, homogeneous medium 59Run 2 – Two wells, identical pressure constraints in homogeneous isotropic medium 81Run 3 – Return to Run 1 well constraints, with Wells 1 and 2 joined using uniform fracture 84Run 4 – Incomplete fracture penetration at Well 1 91Closing remarks 964.4 References 965 Hydraulic Fracture Flow for Horizontal Wells in Anisotropic Media 975.1 Horizontal or Multilateral Wells Intersected by General Hydraulic Fractures in Fully Transient Flow 97Run 1 99Runs 2, 3 and 4 1015.2 Detailed Software Analysis 1055.2.1 Run 1. No fractures along vertical-to-horizontal well (for reference baseline comparisons) 1055.2.2 Run 2. Horizontal well intersected by a single hydraulic fracture 1425.2.3 Run 3. Horizontal well intersecting two fracture planes 1475.2.4 Run 4. Horizontal well intersecting three fractures 1495.2.5 Runs 5-6. Effects of anisotropy and fracture orientation 153Run 5 153Run 6 1555.3 References 1576 Cube Models in Reservoir Development 1586.1 Well Spacings, Parent-Child Effects and Reservoir Strategy in Modern Drilling 1586.1.1 Basic optimization problems 1586.1.2 Reservoir flow simulation versus statistical modeling approaches 1606.1.3 Cube model set-up and computed results 1616.1.4 Reservoir optimization and cost effectiveness 1666.1.5 Closing remarks 1686.1.6 References 1696.2 Detailed Software Analysis 1706.3 A More Optimal Production Method 1976.4 References 2007 Simulating While Drilling – Extending a Vertical Well Horizontally During Transient Production 2017.1 Declining Production with Horizontal Lateral Solution 2017.2 Detailed Software Analysis 2077.3 References 2368 Simulating While Drilling – Adding a Complicated Multilateral Well During Transient Production from a Vertical 2378.1 Vertical and Subsequent Multilateral Neighboring Well 2388.2 Detailed Software Analysis 2438.3 References 2649 Heterogeneous, Anisotropic, Layered Reservoir with Finite Tilted Fracture Plane Produced by Multilateral Wells 2659.1 Five Comparative Production Scenarios 266Run 1. Uniform isotropic reservoir (base reference) 267Run 2. Effect of high permeability fracture on Run 1 272Run 3. Highly heterogeneous three layer reservoir, isotropic flow within each sub-domain, no fracture planes 274Run 4. Effect of anisotropy on Run 1 (again, uniform kx, ky, with kz 50% smaller), no fractures 276Run 5. Nonlinear gas flows, results compared with Run 1 liquid baseline, assuming uniform kx, ky and kz, no fractures 278Closing remarks 2799.2 Detailed Software Analysis 280Run 1. Uniform isotropic reservoir (base reference) 281Layered geological description 281Software caution 283Layered drilling description 287Layer results and flow decline curves 300Run 2. Effect of high permeability fracture on Run 1 308Run 3. Highly heterogeneous three layer reservoir, isotropic flow within each sub-domain, no fracture planes 312Run 4. Effect of anisotropy on Run 1 (again, uniform kx, ky, with kz 50% smaller), no fractures 316Run 5. Nonlinear gas flows, results compared with Run 1 liquid baseline, assuming uniform kx, ky and kz, no fractures 3219.3 Closing Remarks 3289.4 References 32810 Advanced Reservoir Modeling with Multisim 32910.1 Features 330Reservoir Description 330Well System Modeling 330Additional Simulator Features 33010.2 Licensing Options 331Multisim 331Complementary Models 3314D TurboView 331Fluid Tracer 331Formation Testing Suite 33110.3 Disclaimer 332End-User License Agreement (EULA) 332Grant of license 332Descriptions of other rights and limitations 333Termination 334Copyright 334No warranties 334Limitation of liability 334Further disclaimers 335Additional restrictions 335End of EULA 335Cumulative References 336Index 351About the Authors 359Wilson C. Chin 359Xiaoying Zhuang 376