Seismic Reservoir Modeling

Оглавление

Dario Grana. Seismic Reservoir Modeling

Table of Contents

List of Tables

List of Illustrations

Guide

Pages

Seismic Reservoir Modeling. Theory, Examples, and Algorithms

Preface

Acknowledgments

1 Review of Probability and Statistics

1.1 Introduction to Probability and Statistics

1.2 Probability

Example 1.1

1.3 Statistics

1.3.1 Univariate Distributions

Example 1.2

1.3.2 Multivariate Distributions

1.4 Probability Distributions

1.4.1 Bernoulli Distribution

1.4.2 Uniform Distribution

1.4.3 Gaussian Distribution

1.4.4 Log‐Gaussian Distribution

1.4.5 Gaussian Mixture Distribution

1.4.6 Beta Distribution

1.5 Functions of Random Variable

1.6 Inverse Theory

1.7 Bayesian Inversion

Example 1.3

2 Rock Physics Models

2.1 Rock Physics Relations

2.1.1 Porosity – Velocity Relations

Example 2.1

2.1.2 Porosity – Clay Volume – Velocity Relations

2.1.3 P‐Wave and S‐Wave Velocity Relations

2.1.4 Velocity and Density

Example 2.2

2.2 Effective Media

2.2.1 Solid Phase

Example 2.3

Example 2.4

2.2.2 Fluid Phase

Example 2.5

2.3 Critical Porosity Concept

Example 2.6

2.4 Granular Media Models

Example 2.7

2.5 Inclusion Models

Example 2.8

2.6 Gassmann's Equations and Fluid Substitution

Example 2.9

2.7 Other Rock Physics Relations

2.8 Application

3 Geostatistics for Continuous Properties

3.1 Introduction to Spatial Correlation

3.2 Spatial Correlation Functions

Example 3.1

3.3 Spatial Interpolation

3.4 Kriging

3.4.1 Simple Kriging

Example 3.2

Example 3.3

3.4.2 Data Configuration

3.4.3 Ordinary Kriging and Universal Kriging

3.4.4 Cokriging

Example 3.4

3.5 Sequential Simulations

3.5.1 Sequential Gaussian Simulation

Example 3.5

3.5.2 Sequential Gaussian Co‐Simulation

Example 3.6

3.6 Other Simulation Methods

3.7 Application

4 Geostatistics for Discrete Properties

4.1 Indicator Kriging

Example 4.1

Example 4.2

4.2 Sequential Indicator Simulation

Example 4.3

Example 4.4

4.3 Truncated Gaussian Simulation

Example 4.5

4.4 Markov Chain Models

Example 4.6

4.5 Multiple‐Point Statistics

Example 4.7

4.6 Application

5 Seismic and Petrophysical Inversion

5.1 Seismic Modeling

Example 5.1

5.2 Bayesian Inversion

5.3 Bayesian Linearized AVO Inversion

5.3.1 Forward Model

5.3.2 Inverse Problem

Example 5.2

5.4 Bayesian Rock Physics Inversion

5.4.1 Linear – Gaussian Case

5.4.2 Linear – Gaussian Mixture Case

Example 5.3

5.4.3 Non‐linear – Gaussian Mixture Case

5.4.4 Non‐linear – Non‐parametric Case

Example 5.4

5.5 Uncertainty Propagation

Example 5.5

5.6 Geostatistical Inversion

5.6.1 Markov Chain Monte Carlo Methods

5.6.2 Ensemble Smoother Method

Example 5.6

5.6.3 Gradual Deformation Method

5.7 Other Stochastic Methods

6 Seismic Facies Inversion

6.1 Bayesian Classification

Example 6.1

Example 6.2

Example 6.3

Example 6.4

6.2 Bayesian Markov Chain Gaussian Mixture Inversion

Example 6.5

6.3 Multimodal Markov Chain Monte Carlo Inversion

Example 6.6

6.4 Probability Perturbation Method

6.5 Other Stochastic Methods

7 Integrated Methods

7.1 Sources of Uncertainty

7.2 Time‐Lapse Seismic Inversion

7.3 Electromagnetic Inversion

7.4 History Matching

7.5 Value of Information

8 Case Studies

8.1 Hydrocarbon Reservoir Studies

8.1.1 Bayesian Linearized Inversion

8.1.2 Ensemble Smoother Inversion

8.1.3 Multimodal Markov Chain Monte Carlo Inversion

8.2 CO2 Sequestration Study

Appendix: MATLAB Codes

A.1 Rock Physics Modeling

A.2 Geostatistical Modeling

A.3 Inverse Modeling

A.3.1 Seismic Inversion

A.3.2 Petrophysical Inversion

A.3.3 Ensemble Smoother Inversion

A.4 Facies Modeling

References

Index. a

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Отрывок из книги

Dario Grana

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Figure 1.6 Examples of different correlations of the joint distribution of two random variables X and Y. The correlation coefficient ρX,Y is 0.9 and −0.6 in the top plots and approximately 0 in the bottom plots.

Different probability mass and density functions can be used for discrete and continuous random variables, respectively. For parametric distributions, the function is completely defined by a limited number of parameters (e.g. mean and variance). In this section, we review the most common probability mass and density functions. Probability mass functions are commonly used in geoscience problems for discrete random variables such as facies or rock types, whereas PDFs are used for continuous properties such as porosity, fluid saturations, density, P‐wave and S‐wave velocity. Some applications in earth sciences include mixed discrete–continuous problems with both discrete and continuous random variables.

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