Reservoir Engineering in Modern Oilfields

Preface ix

Acknowledgements xiii

1 Reservoir Modeling - Background and Overview 1

Overview 1

Reservoir modeling landscape 1

Reflections on simulation and modeling 2

Reservoir Flow Algorithms for Petroleum Engineers 3

Multisim(TM) Features - Advanced Interactive

Reservoir Modeling 8

Reservoir description 9

Well system modeling 9

Additional simulator features 9

Simple Wells to Multilateral Systems for Laymen 10

Advanced Graphics for Color Display 17

Tracer Movement in Three-Dimensional Reservoirs 21

2 Mathematical Modeling Ideas, Numerical Methods and Software 25

Overview and Background 25

Formulation errors 25

I/O problems 26

Fundamental Issues and Problems 26

Numerical stability 27

Inadequacies of the von Neumann test 28

Convergence 28

Physical resolution 29

Direct solvers 29

Modern simulation requirements 30

Pressure constraints 32

Flow rate constraints 32

Object-oriented geobodies 33

Plan for remaining sections 33

Governing Equations and Numerical Formulation 33

Steady flows of liquids 33

Difference equation formulation 34

The iterative scheme 35

Modeling well constraints for liquids 36

Steady and unsteady nonlinear gas flows 38

Steady gas flows 39

Well constraints for gas flows 40

Transient, compressible flows 42

Compaction, consolidation and subsidence 44

Boundary conforming grids 45

Stratigraphic meshes for layered media 46

Modeling wellbore storage 47

Early 1990s Validation Calculations 48

Simulation capabilities 48

Data structures and programming 49

Example 2-1. Convergence acceleration, two deviated horizontal gas wells in a channel sand 49

Example 2-2. Dual-lateral horizontal completion in a fractured, dipping, heterogeneous, layered formation 53

Example 2-3. Stratigraphic grids, drilling dome-shaped structures 56

Example 2-4. Simulating-while-drilling horizontal gas wells through a dome-shaped reservoir 58

Example 2-5. Modeling wellbore storage effects and compressible borehole flow transients 64

3 Simulation Capabilities - User Interface with Basic Well 71

Example 3-1. Single vertical well, user interface and menu structure for steady flow 71

Example 3-2. Volume flow rate constraint at a well 91

Example 3-3. Pressure constraint and transient shut-in 94

Example 3-4. Heterogeneities, anisotropy and multiple wells 110

Example 3-5. Reversing well constraints - consistency check 128

Example 3-6. Changing farfield boundary conditions 131

Example 3-7. Fluid depletion in a sealed reservoir 135

Example 3-8. Depletion in rate constrained well in sealed reservoir 147

Example 3-9. Steady flow from five spot pattern 148

Example 3-10. Drilling additional wells while simulating 153

4 Vertical, Deviated, Horizontal and Multilateral Well Systems 175

Overview, 175

Example 4-1. Multilateral and vertical wells in multilayer media 176

Example 4-2. Dual lateral with transient operations 204

Example 4-3. Producer and injector conversions 239

Example 4-4. Production with top and bottom drives 265

Example 4-5. Transient gas production from dual horizontal with wellbore storage effects 275

5 Well Models and Productivity Indexes 290

Radial vs 3D modeling - loss of wellbore resolution 290

Analogies in computational aerodynamics 291

Curvilinear grids in reservoir simulation 293

Productivity index modeling 295

References 296

Index 308

About the Author 312

Professional interests 312

Scientific book publications 313

United States patents 314

Recent patent applications 315

International and domestic patents 315

Journal articles and conference publications 318

Multisim' Software Order 326

Features 326

Licensing options 327

Disclaimer 328