Mathematical Geoenergy

A rigorous mathematical problem-solving framework for analyzing the Earths energy resources

GeoEnergy encompasses the range of energy technologies and sources that interact with the geological subsurface. Fossil fuel availability studies have historically lacked concise modeling, tending instead toward heuristics and overly-complex processes.Mathematical GeoEnergy:Oil Discovery, Depletion and Renewal details leading-edge research based on a mathematically-oriented approach to geoenergy analysis.

Volume highlights include:

• Applies a formal mathematical framework to oil discovery, depletion, and analysis
• Employs first-order applied physics modeling, decreasing computational resource requirements
• Illustrates model interpolation and extrapolation to fill out missing or indeterminate data
• Covers both stochastic and deterministic mathematical processes for historical analysis and prediction
• Emphasizes the importance of up-to-date data, accessed through the companion website
• Demonstrates the advantages of mathematical modeling over conventional heuristic and empirical approaches
• Accurately analyzes the past and predicts the future of geoenergy depletion and renewal using models derived from observed production data

Intuitive mathematical models and readily available algorithms makeMathematical GeoEnergy:Oil Discovery, Depletion and Renewalan insightful and invaluable resource for scientists and engineers using robust statistical and analytical tools applicable to oil discovery, reservoir sizing, dispersion, production models, reserve growth, and more.

Paul Pukite,BAE Systems, USA

Dennis Coyne,PeakOilBarrel.com, USA

Daniel Challou,University of Minnesota, USA

Preface vii

1. Introduction to Mathematical Geoenergy 1

2. Stochastic Modeling 5

Part I: Depletion

3. Fossil Fuel Depletion Modeling 13

4. Discovering Oil Reserves 17

5. Analysis of Production and the Shock Model .41

6. Characterizing Discovery, Production, and Reserve Growth 61

7. Comparing the Oil Production Model to Data 85

8. Alternative Characterization and Models 109

9. Models for Future Production 131

Part II: Renewal

10. Energy Transition: Applying Probabilities and Physics 157

11. Wind Energy 167

12. Wave Energy 179

13. Geophysical Energy 205

14. Thermal Energy: Diffusion and Heat Content 213

15. Latent Energy: Hydrological Cycle 225

16. Gravitational Potential Energy: Terrain and Topography 233

17. Solar Energy: Thermodynamic Balance 267

18. Geoenergy Conversion .273

19. Dissipative Energy: Resilience, Durability, and Reliability 291

20. Dispersed Energy: Particulates and Transport in the Environment 305

21. Electromagnetic Energy: Noise and Uncertainty .319

Epilogue 327

Appendix A: The Effect and Role of Feedback 329

Appendix B: Using Pipes and Flow to Compute Convolution 331

Appendix C: Dispersion Analogies 333

Appendix D: Regional Oil Discovery and Production Profiles 341

Appendix E: Compartment Models 343

Appendix F: US Reserve Growth 345

Appendix G: Table of Acronyms 349

Index 351a