Description
Book SynopsisReal-world reservoirs are layered, heterogeneous and anisotropic, exposed to water and gas drives, faults, barriers and fractures. They are produced by systems of vertical, deviated, horizontal and multilateral wells whose locations, sizes, shapes and topologies are dictated on the fly, at randomby petroleum engineers and drillers at well sites. Wells may be pressure or rate-constrained, with these roles re-assigned during simulation with older laterals shut-in, newer wells drilled and brought on stream, and so on. And all are subject to steady and transient production, each satisfying different physical and mathematical laws, making reservoir simulation an art difficult to master and introducing numerous barriers to entry. All of these important processes can now be simulated in any order using rapid, stable and accurate computational models developed over two decades.
And what if it were further possible to sketch complicated geologies and lithologies, plus equally complex
Table of Contents
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™ 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
