Chapter
1.1. General Introduction
1.2. Understanding Isotropy
1.3. Elasticity and Displacement
1.3.3. Constitutive Equations of Linear Elasticity
1.3.4. Isotropic Linear Elasticity
1.4. Elastic Constants and Interrelation
1.5. Equation of Motion in Isotropic Media
1.5.1. Plane Wave in 3-D Space
1.5.2. Simplified 1-D Wave Equation
1.6. Equation of Motion in Anisotropic Media
1.6.1. Generalized Plane Wave in Anisotropic Media
1.6.2. Plane Wave in Transversely Isotropic Media
Chapter 2: Introduction to Wave Propagation
2.1. Wave Propagation in Poroelastic Media
2.1.1. Biot's High-Frequency Limit
2.1.2. Biot's Low-Frequency Limit: Purely Elastic Wave
2.1.3. Biot's Low-Frequency Limit: Viscoelastic Dissipation
Assumptions & Limitations: Biot's Theory
2.2. Acoustic Dispersion and Critical Frequency
2.2.1. Qualitative Discussion
2.2.2. General Quantitative Solution
2.2.2.1. Compressional wave
2.3. Geerstma-Smit Approximation
Assumptions Geerstma-Smit Approximation
2.4. Gassmann's Theory of Fluid-Saturated Media
Assumptions & Limitations: Gassmann's Theory
2.5. Biot's Theory and Gassmann's Prediction
2.6. Wavetrain Propagation in a Borehole
2.6.2. Acoustic Modes in a Borehole
2.6.4. Pseudo-Rayleigh Waves
Chapter 3: Borehole Acoustic Logging
3.1. Acoustic Tool Principle (Monopole)
3.1.1. Single Transmitter Monopole Tool
Limitations of the Single Transmitter Monopole Tool
3.1.2. Borehole Compensated Sonic
Limitations & Advantages of Monopole BHC Measurement
3.1.3. Long-Spaced Sonic and BHC
Limitations & Advantages of LSS & BHC Measurements
Limitations & Advantages of Array Sonic Measurement
3.2. Waveforms in Monopole Tool
3.2.1. Waveforms in a Fast Formation
3.2.2. Waveforms in a Slow Formation
3.3. The Tool Principle (Dipole Acoustic Tool)
Limitations & Advantages of Dipole Sonic Measurement
3.4. Further Tool Advancements
Limitations & Advantages of Sonic Scanner Measurement
3.4.2. Quadrupole Sonic LWD Tool
Limitations & Advantages of Sonic Quadrupole Measurement
3.4.3. Seismic While Drilling
3.5. Borehole Waveform Processing
3.5.1. First-motion Detection
3.5.2. Semblance Correlation
3.5.3. Slowness-Time-Coherence
3.5.3.2. Dispersion (bias) correction
3.5.3.3. Dispersion correction: weighted spectral average concept
3.5.4. Dispersive Processing
3.5.4.1. Flexural dispersion characteristics
3.5.4.2. Dispersive analog of STC
3.5.4.3. Dispersive STC (DSTC)
3.5.5.1. Slowness-frequency projection
3.5.5.2. Error bars (Cramer-Rao bounds)
3.6. Enhanced Vertical Resolution (Multi-Shot Semblance)
3.7. Depth of Investigation
3.7.1. Source-Receiver Spacing and Alteration
3.7.2. Measurement Frequency
3.8. Altered Zone: Concluding Comment
Chapter 4: Rock Physics Models
4.1. General Assumptions and Implications
4.2. Dry Compressibility: Micromechanical Consideration
4.3. Saturated Rock: Biot-Gassmann and Brown-Korringa Models
4.4. Composite Media: Generalized Gassmann's Model
4.5. Composite Porous Rock: Elastic Bounds
4.5.1. Voigt-Reuss Bounds
4.5.2. Voigt-Reuss-Hill (VRH) Approximation
4.5.3. Hashin-Shtrikman (HS) Bounds
4.5.4. Beran-Molyneux-McCoy and McCoy-Silnutzer Bounds
4.6. Kuster-Toksoz Effective Medium Model
Advantages Kuster-Toksoz Model
4.7. Self-Consistent Theory of Effective Composites
4.7.1. OConnell and Budiansky Approximation
4.7.2. Wu's Two-Phase Approximation
Advantages & Limitations: Self-Consistent Models
4.8. Differential Effective Medium Theory
Advantages & Limitations: Differential Effective Medium Theory
4.9. DEM Analytical Approximation
4.9.1. Analytical DEM (Li and Zhang)
4.9.2. Analytical Approximation (Berryman-Pride-Wang)
Advantages Modified-DEM Theory
4.11. Elasticity of Granular Media: Contact Consideration
4.11.1. Hertz-Mindlin Model
4.11.4. Coordination Number
4.12. Modified HS Bound: Contact Consideration
4.12.1. Modified Lower HS Bound (Soft-Sand Model)
4.12.2. Modified Upper HS Bound (Stiff-Sand Model)
4.13. Elasticity of Granular Media: Cemented Contact Model
4.13.1. Contact-Cement Model
4.13.2. Constant-Cement Model
Advantages & Limitations: Contact Models
4.14. Elasticity of Porous Media: Empirical Considerations
4.14.1. Murphy-Schwartz-Hornby Correlation
4.14.3. Extended Biot-Gassmann-Krief (BGK) Model
4.14.4. Critical and Consolidation Porosity Model
Chapter 5: Sonic Porosity-Lithology
5.1. Velocity: Semi-Empirical Relations
5.1.1. Wyllie Time-Average Concept
5.1.2. Tixier Compaction Correction
5.1.3. Raymer-Hunt-Gardner (RHG) Relation
5.1.4. Tosaya Velocity-Porosity-Clay Equation
5.1.5. Castagna Velocity-Porosity-Clay Relationship
5.1.6. Castagna Polynomial Regression for Clean Lithology
5.1.7. Han Velocity-Porosity-Clay Equation
5.1.8. Vernik Velocity-Porosity Classification Model
5.1.9. Krief Velocity-Porosity Model
5.1.10. Velocity Semi-Empiricism: Concluding Comments
5.2. Vp/Vs: Semi-Empirical Relation
5.4. Velocity-Porosity in Carbonates
5.5. Velocity-Stress Interrelation
5.5.1. Siliciclastic Rock
5.5.1.1. Velocity-stress empirical law
5.5.1.2. Vp/Vs-stress in an under-compacted reservoir
5.6. Velocity-Density Interrelation
5.7. Velocity-Porosity: Effective Medium Implication
5.7.1. Single Porosity Model
5.7.2. Double Porosity Model
Chapter 6: Stoneley Permeability
6.1. Borehole Stoneley Wave
6.1.1. Propagation Concept
6.1.2. Stoneley Permeability Correlation
6.2. Biot's Low-Frequency Domain
6.3. Theoretical Modeling
Key Assumptions: White's Model
6.4. Lab and Field Results
6.5. Quantitative Permeability Index
6.6. Other Effects on Stoneley Propagation
6.6.2.1. Dual frequency approach
6.6.2.2. Detailed mathematical model
6.7. Sensitivity of Stoneley Permeability
6.8. Petrophysical Limitation
6.9. Practical Problems and Solutions
6.9.1. Mud Slowness and Attenuation
6.9.2. Elastic Properties Input
6.9.3. Stoneley Attenuation
6.9.4. Borehole Irregularity
6.9.5. Resolution and Depth of Investigation
Chapter 7: Acoustic Saturation
7.1. Fluid Effect on Acoustic Response
7.1.1. Biot's Formulation (Viscoelastic Media)
7.1.4. Squirt Model—Intermediate Frequency
7.2. Fluid Substitution Modeling
7.2.1. Homogeneous Isotropic Media
7.2.2. Impact of Pore Geometry on Fluid Substitution
7.2.3. Substitution in Laminated Shaly Sand
7.2.4. Fluid Substitution Without Shear
7.2.5. Key Pointers in Fluid Substitution
7.3. Fluid Substitution in Anisotropic Rock
7.3.1. Anisotropic Gassmann's Equation
7.3.2. Anisotropic Brown-Korringa Equation
7.3.3. Anisotropic VTI Rock Mavko-Bandyopadhyay Equation
7.3.4. Anisotropic HTI Rock, Gurevich Equation
7.4. Acoustics of Partial/Patchy Saturation
7.5. Modulus Decomposition
7.5.1. Concept for Clean Formation
7.5.2. Concept for Composite Rock
7.5.3. Application to Shaly Sand
7.5.4. Application to Carbonate Composite
Chapter 8: Anisotropy Evaluation
8.2. Thomsen Parameters for Weak Elastic Anisotropy
8.3. Extended Thomsen Model: Strong Anisotropy
8.4. Thomsen Parameters for Finely Layered VTI Media
8.5. Fluid Effect on Thomsen Parameter and Anisotropic Gassmann's Equation
8.6. Stress-Induced Anisotropy
8.6.1. Uniaxial Small Stress on an Isotropic Elastic Medium
8.6.2. Triaxial and Larger Stress on Isotropic Media
8.7.1. Clay Anisotropy VTI Model
8.7.2. Anisotropy in Dry Clay
8.7.3. Effect of Fluids in Shales
8.7.4. Effect of Kerogen on Velocity Anisotropy
8.8. Anisotropic Consideration of Borehole Acoustic Mode
8.8.1. Crossed-Dipole Anisotropy Analysis
8.9. Intrinsic and Stress-Induced Anisotropy Differentiation
8.10. Anisotropy Analysis Through Stoneley Waves
8.10.1. Anisotropy Estimation
8.10.2. Deviated Borehole: Comparison With Cross-Dipole
8.11. Anisotropic Consideration in an Inclined Borehole
Chapter 9: Rock Strength And Stress Analysis
9.1. In-Situ Stress: A Fundamentals
9.2. Stress Evaluation: Process Consideration
9.2.4. Pore Pressure Change
9.3. Stress Evaluation: Other Numerical Estimation
9.4. Static Stress-Strain and Deformation
9.5. Static And Dynamic Moduli
9.6. Rock Strength and Failure
9.6.1. Coulomb Failure Model
9.6.2. Mohr-Coulomb Failure Criterion
9.6.3. Griffith Failure Criterion
9.6.4. Mogi's Empirical Criterion
9.6.5. Hoek-Brown Failure Criterion
9.6.6. Modified Lade Failure Criterion
9.6.7. Modified Wiebols-Cook Failure Criterion
9.6.8. Drucker-Prager Failure Criterion
9.7. Empirical Rock Strength
9.8. Pore Pressure Evaluation
9.8.1. Geo-Pressure Concept
9.8.1.1. Hydrostatic pressure
9.8.1.2. Lithostatic pressure
9.8.1.3. Effective stress
9.8.2. Hottmann And Johnson's Method
9.8.3. Eaton's Method of Pressure Prediction
9.8.3.1. Resistivity approach
9.8.3.2. Sonic velocity approach
9.8.3.3. Modified Eaton's method
9.8.4. Bower's Sonic Method
9.8.5. Miller's Sonic Method
9.8.7. Porosity Dependent Pressure Prediction
9.9. Pore Compressibility
9.9.2. Core Measurement: Uniaxial Loading
Chapter 10: Core Elasticity Measurements
10.1. Scaling of Elastic Properties
10.2. Experimental Rock Elastic Properties
10.2.1. Porosity, Pore Geometry, and Clays
10.2.2. Confining and Fluid Pressures
Fluid type and saturation
10.2.4. Frequency Dependence of Elastic Waves
10.2.5. Temperature Dependence of Elastic Waves
10.2.6. Elastic Wave Anisotropy
10.2.7. Rock-Fluid Interactions
10.3. Experimental Systems for Rock Elasticity Measurement
10.3.1. Ultrasonic Transducers
10.3.2. Resonance Techniques
10.3.3. Stress-Strain Measurements at Seismic Frequencies
10.4. Other Experimental Elastic Developments
10.4.1. Multipath Transducer Systems
10.4.2. Noncontacting Laser Ultrasonic System
10.4.3. Scanning Acoustic Microscopy
10.4.3.1. Atomic-force acoustic microscopy
10.4.5. High-Pressure Experimental System Considerations
10.5. Limitations and Advantages of Elastic Core Measurements
Chapter 11: Casedhole Acoustics
11.1. Cement Evaluation: Sonic Logging
11.1.1. CBL-VDL Sonic Tool
11.1.2. Compensated Cement Bond Sonic Tool (CBT)
11.2. Cement and Casing Evaluation: Ultrasonic Logging
11.2.1. Ultrasonic Cement Evaluation Tool
11.2.1.1. Micro-annulus effect
11.2.1.2. Additional interface effect
11.2.2. Acoustic Televiewer/Scanner
11.3. New Cement Evaluation Concept: Flexural Mode
11.3.1. Flexural and TIE Mode
11.3.2. Interpreting Attenuation, Impedance
11.3.3. Interpreting Third-Interface Echo (TIE)
11.4. Casedhole Acoustics for Formation Evaluation
11.4.1. Wave Propagation in Casedhole
11.4.2. Dipole in Casedhole
11.4.2.1. Frequency effect
11.4.2.2. Tool eccentricity effect
11.4.3. Casedhole Hydrocarbon Interpretation
Chapter 12: Rock Physics Workflow and Example
12.1. Composite Matrix Elastic Properties
12.2. Mixed Fluid Bulk Modulus
12.3. Velocity/Elastic Moduli Prediction (Empirical)
12.3.1. Siliciclastics: Water-Saturated Vp and Vs From Porosity, Clay, and Effective Pressure
12.3.2. Siliciclastics: Water-Saturated Vs from Vp
12.3.3. Siliciclastics: Dry Frame Modulus from Porosity
12.3.4. Siliciclastics: Dry Frame Vs From Vp or Vice Versa
12.3.5. Carbonate: Vs From Vp and Vice Versa
12.4. Velocity/Elastic Moduli Prediction (Model)
12.4.1. Kuster-Toksoz Effective Medium
12.4.2. Wu's Self-Consistent Model
12.4.3. Differential Effective Medium Model
12.5. Fluid Substitution Modeling
12.5.1. General Gassmann's Substitution
12.5.2. Shale-Sand Mixture Model (Xu-White)
Chapter Appendix A: Elastic Properties of Rock Minerals
Chapter Appendix B: Elastic/Physical Properties of Fluids
Chapter Appendix C: Conversion Table
Pressure Gradient/Density
Handbook of Borehole Acoustics and Rock Physics for Reservoir Characterization
Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.
