Advanced Petroleum Reservoir Simulation (Wiley-Scrivener)

Advanced Petroleum Reservoir Simulation......Page 5
Contents......Page 7
Foreword......Page 15
Introduction......Page 17
1.1 Essence of Reservoir Simulation......Page 23
1.3 Material Balance Equation......Page 27
1.3.2 Statistical Method......Page 28
1.3.3 Analytical Methods......Page 29
1.3.4 Finite Difference Methods......Page 30
1.3.5 Darcy's Law......Page 33
1.4.1 Speed and Accuracy......Page 34
1.4.2 New Fluid Flow Equations......Page 35
1.4.3 Coupled Fluid Flow and Geo-mechanical Stress Model......Page 38
1.4.4 Fluid Flow Modeling Under Thermal Stress......Page 39
1.5.1 Experimental Challenges......Page 40
1.5.2.3 Viscous Fingering During Miscible Displacement......Page 42
1.5.2.5 Improvement in Data Processing Techniques......Page 43
1.5.3 Remote Sensing and Real-time Monitoring......Page 44
1.5.3.1 Monitoring Offshore Structures......Page 45
1.5.3.3 Use of 3-D Sonogram......Page 46
1.5.3.4 Virtual Reality (VR) Applications......Page 47
1.5.3.5 Intelligent Reservoir Management......Page 48
1.6 Economic Models Based on Futuristic Energy Pricing Policies......Page 49
1.7 Integrated System of Monitoring, Environmental Impact and Economics......Page 51
2. Reservoir Simulator-input/output......Page 53
2.1 Input and Output Data......Page 54
2.2 Geological and Geophysical Modeling......Page 56
2.3 Reservoir Characterization......Page 59
2.3.1 Representative Elementary Volume, REV......Page 60
2.3.2 Fluid and Rock Properties......Page 63
2.3.2.1 Fluid Properties......Page 64
2.3.2.1.1 Crude Oil Properties......Page 65
2.3.2.1.2 Natural Gas Properties......Page 67
2.3.2.1.3 Water Content Properties......Page 68
2.3.3 Rock Properties......Page 69
2.4 Upscaling......Page 74
2.4.1 Power Law Averaging Method......Page 75
2.4.2 Pressure-solver Method......Page 76
2.4.3 Renormalization Technique......Page 78
2.4.4 Multiphase Flow Upscaling......Page 79
2.5 Pressure/Production data......Page 82
2.5.1 Phase Saturations Distribution......Page 83
2.6 Reservoir Simulator Output......Page 84
2.7 History-matching......Page 87
2.7.1 History-matching Formulation......Page 90
2.7.2.1 Measurement Uncertainty......Page 93
2.7.2.2 Upscaling Uncertainty......Page 96
2.7.2.3 Model Error......Page 97
2.7.2.4 The Prediction Uncertainty......Page 98
2.8 Real-time Monitoring......Page 99
3. Reservoir Simulators: Problems, Shortcomings, and Some Solution Techniques......Page 105
3.1 Multiple Solutions in Natural Phenomena......Page 107
3.1.1 Knowledge Dimension......Page 110
3.2 Adomian Decomposition......Page 125
3.2.1 Governing Equations......Page 127
3.2.2 Adomian Decomposition of Buckley–Leverett Equation......Page 130
3.2.3 Results and Discussions......Page 132
3.3 Some Remarks on Multiple Solutions......Page 135
4. Mathematical Formulation of Reservoir Simulation Problems......Page 137
4.1 Black Oil Model and Compositional Model......Page 138
4.2.1 Basic Definitions......Page 140
4.2.2 Primary and Secondary Parameters and Model Variables......Page 142
4.2.3 Mass Conservation Equation......Page 145
4.2.4 Energy Balance Equation......Page 148
4.2.5 Volume Balance Equation......Page 154
4.2.6 The Motion Equation in Porous Medium......Page 155
4.2.7 The Compositional System of Equations and Model Variables......Page 160
4.3.1 The Black Oil Model......Page 163
4.3.2 The Water Oil Model......Page 165
4.4.1 Isothermal Volatile Oil Reservoir......Page 168
4.4.2 Steam Injection Inside a Dead Oil Reservoir......Page 171
4.4.3 Steam Injection in Presence of Distillation and Solution Gas......Page 172
5. The Compositional Simulator Using the Engineering Approach......Page 177
5.1 Finite Control Volume Method......Page 178
5.1.1 Reservoir Discretization in Rectangular Coordinates......Page 179
5.1.2 Discretization of Governing Equations......Page 180
5.1.2.1 Components Mass Conservation Equation......Page 181
5.1.2.2 Energy Balance Equation......Page 189
5.1.3 Discretization of Motion Equation......Page 192
5.2 Uniform Temperature Reservoir Compositional Flow Equations in a 1-D Domain......Page 194
5.3 Compositional Mass Balance Equation in a Multidimensional Domain......Page 200
5.3.1 Implicit Formulation of Compositional Model in Multi-Dimensional Domain......Page 202
5.3.2 Reduced Equations of Implicit Compositional Model in Multidimensional Domain......Page 205
5.3.3.1 Production Wells......Page 208
5.3.3.2 Injection Wells......Page 210
5.3.4 Fictitious Well Rate Terms (Treatment of Boundary Conditions)......Page 211
5.4.1 Energy Balance Equation......Page 215
5.4.2 Implicit Formulation of Variable Temperature Reservoir Compositional Flow Equations......Page 219
5.5 Solution Method......Page 223
5.5.1 Solution of Model Equations Using Newton's Iteration......Page 224
5.6 The Effects of Linearization......Page 229
5.6.1 Case I: Single Phase Flow of a Natural Gas......Page 230
5.6.2 Effect of Interpolation Functions and Formulation......Page 236
5.6.3 Effect of Time Interval......Page 237
5.6.5 Effect of Number of Gridblocks......Page 239
5.6.6 Spatial and Transient Pressure Distribution Using Different Iinterpolation Functions......Page 241
5.6.7 CPU Time......Page 244
5.6.8 Case II: An Oil/Water Reservoir......Page 246
6.1 Background......Page 267
6.2 Permeability Alteration......Page 270
6.3 Porosity Alteration......Page 271
6.4 Pore Volume Change......Page 273
6.5 A Comprehensive MBE with Memory for Cumulative Oil Recovery......Page 274
6.6 Numerical Simulation......Page 277
6.6.1 Effects of Compressibilities on Dimensionless Parameters......Page 279
6.6.2 Comparison of Dimensionless Parameters Based on Compressibility Factor......Page 280
6.6.4 Effects of Compressibility Factor with M Values......Page 281
6.6.5 Comparison of Models Based on RF......Page 282
6.6.6 Effects of M on MBE......Page 284
6.7 Appendix 6A: Development of an MBE for a Compressible Undersaturated Oil Reservoir......Page 286
6.7.1 Development of a New MBE......Page 287
6.7.2 Conventional MBE......Page 294
6.7.3 Significance of Cepm......Page 296
6.7.4 Water Drive Mechanism with Water Production......Page 297
6.7.5 Depletion Drive Mechanism with No Water Production......Page 298
7.1 Improvement of the Numerical Scheme......Page 299
7.1.1 The Governing Equation......Page 301
7.1.2.1 Barakat–Clark FTD Scheme......Page 303
7.1.2.2 DuFort–Frankel Scheme......Page 305
7.1.3 Proposed Barakat–Clark CTD Scheme......Page 306
7.1.4 Accuracy and Truncation Errors......Page 307
7.1.5 Some Results and Discussion......Page 308
7.1.6 Influence of Boundary Conditions......Page 315
7.2.1 Stability Criterion and Onset of Fingering......Page 317
7.2.2 Base Stable Case......Page 318
7.2.3 Base Unstable Case......Page 324
7.2.4.1 Effect of Injection Pressure......Page 331
7.2.4.2 Effect of Overall Porosity......Page 336
7.2.4.3 Effect of Mobility Ratio......Page 339
7.2.4.4 Effect of Longitudinal Dispersion......Page 342
7.2.4.5 Effect of Transverse Dispersion......Page 346
7.2.4.6 Effect of Aspect Ratio......Page 349
7.2.5.1 Selected Experimental Model......Page 352
7.2.5.2 Physical Model Parameters......Page 353
7.2.5.3 Comparative Study......Page 354
7.2.5.4 Concluding Remarks......Page 358
8.1 Essence of Knowledge, Science, and Emulation......Page 361
8.1.1 Simulation vs. Emulation......Page 362
8.1.2 Importance of the First Premise and Scientific Pathway......Page 364
8.1.3 Mathematical Requirements of Nature Science......Page 366
8.1.4 The Meaningful Addition......Page 370
8.1.5 "Natural" Numbers and the Mathematical Content of Nature......Page 372
8.2.1 The Importance of Time as the Fourth Dimension......Page 376
8.2.2 Towards Modeling Truth and Knowledge......Page 384
8.3 Examples of Linearization and Linear Thinking......Page 385
8.4 The Single-Parameter Criterion......Page 387
8.4.2.1 The Currently Used Model......Page 388
8.4.2.2 Towards Achieving Multiple Solutions......Page 394
8.5 The Conservation of Mass and Energy......Page 396
8.5.1 The Avalanche Theory......Page 397
8.5.2 Aims of Modeling Natural Phenomena......Page 402
8.5.2 Challenges of Modeling Sustainable Petroleum Operations......Page 404
8.6 The Criterion: The Switch that Determines the Direction at a Bifurcation Point......Page 408
8.6.1 Some Applications of the Criterion......Page 410
8.7 The Need for Multidimensional Study......Page 418
8.8 Assessing the Overall Performance of a Process......Page 421
8.9 Implications of Knowledge-Based Analysis......Page 428
8.9.1 A General Case......Page 429
8.9.2 Impact of Global Warming Analysis......Page 432
8.10 Examples of Knowledge-Based Simulation......Page 435
9. Final Conclusions......Page 443
A.2 The Simulator......Page 445
A.3 Data File Preparation......Page 447
A.3.1 Format Procedure A......Page 448
A.3.4 Format Procedure D......Page 449
A.4 Description of Variables Used in Preparing a Data File......Page 450
A.5 Instructions to Run Simulator and Graphic Post Processor on PC......Page 461
A.6 Limitations Imposed on the Compiled Versions......Page 463
A.7 Example of a Prepared Data File......Page 464
References......Page 469
Index......Page 485