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
Multisim
TM Features – Advanced Interactive Reservoir Modeling, 8Reservoir 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
MultisimTM Software Order, 326