Seismic Reservoir Modeling

Dario Grana is an Associate Professor in the Department of Geology and Geophysics and in the School of Energy Resources at the University of Wyoming.Tapan Mukerji is a Research Professor in the Department of Energy Resources Engineering at Stanford University.Philippe Doyen is an independent consultant with worldwide responsibility for technology development in reservoir characterization.

• Preface xAcknowledgments xii1 Review of Probability and Statistics 11.1 Introduction to Probability and Statistics 11.2 Probability 31.3 Statistics 61.3.1 Univariate Distributions 61.3.2 Multivariate Distributions 121.4 Probability Distributions 161.4.1 Bernoulli Distribution 161.4.2 Uniform Distribution 171.4.3 Gaussian Distribution 171.4.4 Log-Gaussian Distribution 191.4.5 Gaussian Mixture Distribution 211.4.6 Beta Distribution 231.5 Functions of Random Variable 231.6 Inverse Theory 251.7 Bayesian Inversion 272 Rock Physics Models 292.1 Rock Physics Relations 292.1.1 Porosity – Velocity Relations 292.1.2 Porosity – Clay Volume – Velocity Relations 312.1.3 P-Wave and S-Wave Velocity Relations 322.1.4 Velocity and Density 332.2 Effective Media 342.2.1 Solid Phase 342.2.2 Fluid Phase 392.3 Critical Porosity Concept 432.4 Granular Media Models 442.5 Inclusion Models 462.6 Gassmann’s Equations and Fluid Substitution 512.7 Other Rock Physics Relations 562.8 Application 603 Geostatistics for Continuous Properties 663.1 Introduction to Spatial Correlation 663.2 Spatial Correlation Functions 703.3 Spatial Interpolation 773.4 Kriging 793.4.1 Simple Kriging 803.4.2 Data Configuration 853.4.3 Ordinary Kriging and Universal Kriging 883.4.4 Cokriging 903.5 Sequential Simulations 943.5.1 Sequential Gaussian Simulation 943.5.2 Sequential Gaussian Co-Simulation 1003.6 Other Simulation Methods 1023.7 Application 1054 Geostatistics for Discrete Properties 1094.1 Indicator Kriging 1094.2 Sequential Indicator Simulation 1144.3 Truncated Gaussian Simulation 1184.4 Markov Chain Models 1204.5 Multiple-Point Statistics 1234.6 Application 1275 Seismic and Petrophysical Inversion 1295.1 Seismic Modeling 1305.2 Bayesian Inversion 1335.3 Bayesian Linearized AVO Inversion 1355.3.1 Forward Model 1355.3.2 Inverse Problem 1375.4 Bayesian Rock Physics Inversion 1415.4.1 Linear – Gaussian Case 1425.4.2 Linear – Gaussian Mixture Case 1435.4.3 Non-linear – Gaussian Mixture Case 1465.4.4 Non-linear – Non-parametric Case 1495.5 Uncertainty Propagation 1525.6 Geostatistical Inversion 1545.6.1 Markov Chain Monte Carlo Methods 1565.6.2 Ensemble Smoother Method 1575.6.3 Gradual Deformation Method 1595.7 Other Stochastic Methods 1636 Seismic Facies Inversion 1656.1 Bayesian Classification 1656.2 Bayesian Markov Chain Gaussian Mixture Inversion 1726.3 Multimodal Markov Chain Monte Carlo Inversion 1766.4 Probability Perturbation Method 1796.5 Other Stochastic Methods 1817 Integrated Methods 1837.1 Sources of Uncertainty 1847.2 Time-Lapse Seismic Inversion 1867.3 Electromagnetic Inversion 1887.4 History Matching 1897.5 Value of Information 1928 Case Studies 1948.1 Hydrocarbon Reservoir Studies 1948.1.1 Bayesian Linearized Inversion 1948.1.2 Ensemble Smoother Inversion 1988.1.3 Multimodal Markov Chain Monte Carlo Inversion 2038.2 CO2 Sequestration Study 206Appendix: MATLAB Codes 211A.1 Rock Physics Modeling 211A.2 Geostatistical Modeling 213A.3 Inverse Modeling 217A.3.1 Seismic Inversion 218A.3.2 Petrophysical Inversion 220A.3.3 Ensemble Smoother Inversion 223A.4 Facies Modeling 226References 229Index 242

"This is a very timely book that combines traditional geoscience disciplines, rock physics and geostatistics with recent developments in inversion theory, all within an overall probabilistic framework. It will serve as both a reference and a source of inspiration for future development in this rapidly advancing field."—Patrick Alexander Connolly, Mathematical Geosciences