Reservoir Engineering in Modern Oilfields:

Vertical, Deviated, Horizontal and Multilateral Well Systems

by

Wilson C. Chin, Ph.D., M.I.T.

Stratamagnetic Software, LLC

Houston, Texas and Beijing, China

Table of Contents

Preface, v

Acknowledgements, viii

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

MultisimTM 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

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

Multisim^{TM} Software Order, 326