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.