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E-raamat: Wave Propagation in Drilling, Well Logging and Reservoir Applications

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Wave Propagation in Drilling, Well Logging and Reservoir ApplicationsSuurem pilt
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Wave propagation is central to all areas of petroleum engineering, e.g., drilling vibrations, MWD mud pulse telemetry, swab-surge, geophysical ray tracing, ocean and current interactions, electromagnetic wave and sonic applications in the borehole, but rarely treated rigorously or described in truly scientific terms, even for a single discipline. Wilson Chin, an MIT and Caltech educated scientist who has consulted internationally, provides an integrated, comprehensive, yet readable exposition covering all of the cited topics, offering insights, algorithms and validated methods never before published. A must on every petroleum engineering bookshelf! In particular, the book:





Delivers drillstring vibrations models coupling axial, torsional and lateral motions that predict rate-of-penetration, bit bounce and stick-slip as they depend on rock-bit interaction and bottomhole assembly properties, Explains why catastrophic lateral vibrations at the neutral point cannot be observed from the surface even in vertical wells, but providing a proven method to avoid them, Demonstrates why Fermat's "principle of least time" (used in geophysics) applies to non-dissipative media only, but using the "kinematic wave theory" developed at MIT, derives powerful methods applicable to general attenuative inhomogeneous media, Develops new approaches to mud acoustics and applying them to MWD telemetry modeling and strong transients in modern swab-surge applicagtions, Derives new algorithms for borehole geophysics interpretation, e.g., Rh and Rv in electromagnetic wave and permeability in Stoneley waveform analysis, and Outlines many more applications, e.g., wave loadings on offshore platforms, classical problems in wave propagation, and extensions to modern kinematic wave theory.

These disciplines, important to all field-oriented activities, are not treated as finite element applications that are simply gridded, "number-crunched" and displayed, but as scientific disciplines deserving of clear explanation. General results are carefully motivated, derived and applied to real-world problems, with results demonstrating the importance and predictive capabilities of the new methods.
Preface xxi
Acknowledgements xxiii
1 Overview and Fundamental Ideas
1(49)
1.1 The Classical Wave Equation
2(5)
1.1.1 Fundamental properties
2(3)
1.1.2 Reflection properties
5(1)
1.1.2.1 Example 1-1. Rigid end termination
5(1)
1.1.2.2 Example 1-2. Stress-free end
6(1)
1.1.2.3 Note on acoustics
6(1)
1.2 Fundamental Representation
7(1)
1.2.1 Taylor series
7(1)
1.2.2 Fourier series
7(1)
1.3 Separation of Variables and Eigenfunction Expansions
8(8)
1.3.1 Example 1-3. String with pinned ends and general initial conditions
9(1)
1.3.2 Example 1-4. String with distributed forces
10(1)
1.3.3 Example 1-5. Alternative boundary conditions
11(1)
1.3.4 Example 1-6. Mixed boundary conditions
11(2)
1.3.5 Example 1-7. Problems without initial conditions
13(1)
1.3.5.1 Example 1-7a. Naive approach
13(1)
1.3.5.2 Example 1-7b. Correct approach
14(1)
1.3.5.3 Example 1-7c. Faster approach
14(1)
1.3.6 Example 1-8. Dissipative wave solution
14(2)
1.4 Standing Versus Propagating Waves
16(4)
1.4.1 Standing waves
16(1)
1.4.2 Propagating waves
16(1)
1.4.3 Combined standing and propagating waves
17(1)
1.4.4 Characterizing propagating waves
17(3)
1.5 Laplace Transforms
20(6)
1.5.1 Wave equation derivation
20(1)
1.5.2 Example 1-9. String falling under its own weight
21(1)
1.5.3 Example 1-10. Semi-infinite string with a general end support
22(3)
1.5.3.1 Example 1-10a. Rectangular pulse
25(1)
1.5.3.2 Example 1-10b. Impulse response
25(1)
1.5.3.3 Example 1-10c. Incident sinusoidal wavetrain
26(1)
1.6 Fourier Transforms
26(4)
1.6.1 Example 1-11. Propagation of an initially static disturbance
27(1)
1.6.2 Example 1-12. Directional properties, special wave
28(2)
1.7 External Forces Versus Boundary Conditions
30(12)
1.7.1 Single point force
30(2)
1.7.2 Properties of point loads
32(1)
1.7.2.1 Example 1-13. Boundary conditions versus forces
32(1)
1.7.2.2 Couples or dipoles
33(3)
1.7.2.3 Multiple forces and higher order moments
36(1)
1.7.2.4 Symmetries and anti-symmetries
36(1)
1.7.2.5 Impulse response
36(3)
1.7.2.6 On the subtle meaning of impulse
39(1)
1.7.2.7 Example 1-14. Incorrect use of impulse response
39(1)
1.7.2.8 Additional models
39(1)
1.7.2.9 Other delta function properties
40(2)
1.8 Point Force and Dipole Wave Excitation
42(4)
1.8.1 Example 1-15. Finite string excited by a time-varying concentrated point force
42(2)
1.8.2 Example 1-16. Finite string excited by a time-varying point dipole (i.e., a force couple)
44(1)
1.8.3 Example 1-17. Splitting of an applied initial disturbance
45(1)
1.9 First-Order Partial Differential Equations
46(3)
1.10 References
49(1)
2 Kinematic Wave Theory
50(32)
2.1 Whitham's Theory in Nondissipative Media
51(6)
2.1.1 Uniform media
52(1)
2.1.2 Example 2-1. Transverse beam vibrations
52(1)
2.1.3 Example 2-2. Simple longitudinal oscillations
52(1)
2.1.4 Example 2-3. Asymptotic stationary phase expansion
53(1)
2.1.5 Simple consequences of KWT
54(2)
2.1.6 Nonuniform media
56(1)
2.1.7 Example 2-4. Numerical integration
56(1)
2.1.8 Ease of use is important to practical engineering
57(1)
2.2 Simple Attenuation Modeling
57(3)
2.2.1 The Q-model
57(1)
2.2.2 Relating Q to amplitude in space
58(1)
2.2.3 Relating Q to standing wave decay
59(1)
2.2.4 Kinematic wave generalization
59(1)
2.3 KWT in Homogeneous Dissipative Media
60(4)
2.3.1 Example 2-5. General initial value problem in uniform media
61(1)
2.3.2 Singularities of the kinematic field
62(1)
2.3.3 The energy singularity
62(1)
2.3.4 Example 2-6. Modeling dynamically steady motions
63(1)
2.4 High-Order Kinematic Wave Theory
64(6)
2.4.1 Basic assumptions
64(1)
2.4.2 The general amplitude equation
65(1)
2.4.3 Method of multiple scales
66(2)
2.4.4 Generalized wave results
68(2)
2.4.5 The low-order limit
70(1)
2.5 Effect of Low-Order Nonuniformities
70(6)
2.5.1 Detailed formal analysis
71(1)
2.5.2 Wave energy and momentum
71(2)
2.5.3 Example 2-7. String with variable properties
73(1)
2.5.4 Computational solution
73(1)
2.5.5 Dynamically steady problems
74(1)
2.5.6 Waves in nonuniform moving media
75(1)
2.5.7 Average Lagrangian formalism
75(1)
2.5.8 Example 2-8. Wave action conservation
75(1)
2.6 Three-Dimensional Kinematic Wave Theory
76(4)
2.6.1 Wave irrotationality
77(1)
2.6.2 The ray equation
78(1)
2.6.3 Frequency variation
78(1)
2.6.4 Energy variation
79(1)
2.6.5 Ray topology
79(1)
2.6.6 Example 2-9. Acoustics application
79(1)
2.7 References
80(2)
3 Examples from Classical Mechanics
82(27)
3.1 Example 3-1. Lateral Vibration of Simple Beams
82(3)
3.1.1 Example 3-1a. Hinged ends
84(1)
3.1.2 Example 3-1b. Clamped end, other end free
84(1)
3.2 Example 3-2. Acoustic Waves in Waveguides
85(11)
3.2.1 Simple waveguides
85(2)
3.2.2 Simple hydraulic flows
87(1)
3.2.3 Acoustic simplifications
87(1)
3.2.4 Three-dimensional wave equation
88(1)
3.2.5 Modal solution
88(2)
3.2.6 The dispersion relation
90(1)
3.2.7 Physical interpretation
90(1)
3.2.8 MWD notes
91(1)
3.2.9 Phase and group velocity
91(2)
3.2.10 The velocity potential
93(1)
3.2.11 Modeling MWD sources
94(2)
3.3 Example 3-3. Gravity-Capillary Waves in Deep Water
96(4)
3.3.1 Governing Laplace equation
96(1)
3.3.2 Boundary conditions, kinematic and dynamic
97(1)
3.3.3 Problem solution
98(1)
3.3.4 Energy considerations
99(1)
3.4 Example 3-4. Fluid-Solid Interaction -- Waves on Elastic Membranes
100(4)
3.4.1 Governing Rayleigh equation
101(1)
3.4.2 Boundary conditions for potential
102(1)
3.4.3 Eigenvalue bounds
103(1)
3.5 Example 3-5. Problems in Hydrodynamic Stability
104(2)
3.5.1 Neutral stability diagrams
104(1)
3.5.2 Borehole flow stability
105(1)
3.5.3 Stability of irrotational flows
106(1)
3.6 References
106(3)
4 Drillstring Vibrations: Classic Ideas and Modern Approaches
109(148)
4.1 Typical Downhole Vibration Environment
110(13)
4.1.1 What is wave motion?
110(1)
4.1.2 Drillstring vibration modes, axial, torsional and lateral
111(1)
4.1.2.1 Axial vibrations
111(1)
4.1.2.2 Transverse vibrations
112(1)
4.1.2.3 Torsional vibrations
113(1)
4.1.2.4 Whirling vibrations
113(1)
4.1.2.5 Coupled axial, torsional and lateral vibrations
113(1)
4.1.2.6 Transient and dynamically steady oscillations
114(1)
4.1.2.7 Understanding the environment
114(1)
4.1.3 Long-standing vibrations issues
115(1)
4.1.3.1 Example 4-1. Case of the missing waves
115(1)
4.1.3.2 Example 4-2. Looking for resonance in all the wrong places
116(1)
4.1.3.3 Example 4-3. Drillstrings that don't drill
116(1)
4.1.3.4 Example 4-4. Modeling coupled vibrations
116(1)
4.1.3.5 Example 4-5. Energy transfer mechanisms
116(1)
4.1.4 Practical applications
117(1)
4.1.4.1 Anecdotal stories
117(1)
4.1.4.2 Applications to the field (Structural damage; Formation damage; Directional drilling; Increasing rate of penetration; Improved MWD tools and mud motors; Formation imaging; Psychological discomfort)
117(2)
4.1.5 Elastic line model of the drillstring
119(1)
4.1.5.1 Early efforts
119(1)
4.1.5.2 Elastic line simplifications
120(1)
4.1.5.3 Historical precedents
120(1)
4.1.5.4 Our focus
121(1)
4.1.6 Objectives and discussion plan
122(1)
4.2 Axial Vibrations
123(61)
4.2.1 Pioneering axial vibration studies
124(2)
4.2.2 Governing differential equations
126(1)
4.2.2.1 Damped wave equation
126(1)
4.2.2.2 External forces and displacement sources
127(1)
4.2.2.3 Dynamic and static solutions
128(1)
4.2.2.4 Free-fall as a special solution
128(1)
4.2.2.5 More on AC/DC interactions
129(1)
4.2.3 Conventional separation of AC/DC solutions
129(1)
4.2.3.1 Sign conventions
130(1)
4.2.3.2 Static weight on bit
131(1)
4.2.4 Boundary conditions - old and new ideas
132(1)
4.2.4.1 Surface boundary conditions
132(1)
4.2.4.2 Conventional bit boundary conditions
133(1)
4.2.4.3 Modeling rock-bit interactions
134(2)
4.2.4.4 Empirical notes on rock-bit interaction (Laboratory drillbit data; Single-tooth impact results)
136(3)
4.2.4.5 Modeling drillbit kinematics using "displacement sources" (Analogies from earthquake seismology)
139(3)
4.2.5 Global energy balance
142(1)
4.2.5.1 Formulation summary
142(1)
4.2.5.2 Energy considerations (The drillstring; The surface; Combined drillstring/surface system)
142(2)
4.2.5.3 Detailed bit motions
144(1)
4.2.6 Simple solution for rate-of-penetration
145(1)
4.2.6.1 Field motivation
145(1)
4.2.6.2 Simple analytical solution
146(1)
4.2.6.3 Classic fixed end
146(1)
4.2.6.4 Classic free end
146(1)
4.2.6.5 Other possibilities
147(1)
4.2.6.6 Simple derivative model
147(1)
4.2.6.7 The general impedance mode
147(2)
4.2.6.8 Modeling the constants alpha, beta and gamma
149(1)
4.2.7 Finite difference modeling
149(1)
4.2.7.1 Elementary considerations
149(2)
4.2.7.2 Transient finite difference modeling (The solution methodology; Stability of the scheme; Grid sizes, time steps, and convergence)
151(5)
4.2.8 Complete formulation and numerical solution
156(1)
4.2.8.1 The boundary value problem
156(1)
4.2.8.2 Computational objective
157(1)
4.2.8.3 Difference approximations
157(2)
4.2.9 Modeling pipe-to-collar area changes
159(1)
4.2.9.1 Matching conditions
160(1)
4.2.9.2 Finite difference model
160(1)
4.2.9.3 Generalized formulation
161(1)
4.2.9.4 Alternative boundary conditions
161(1)
4.2.10 Example Fortran implementation
162(1)
4.2.10.1 Code fragment
162(3)
4.2.10.2 Modeling dynamically steady problems
165(2)
4.2.10.3 Jarring issues and stuck pipe problems
167(1)
4.2.11 Drillstring and formation imaging
168(1)
4.2.11.1 Drillstring imaging
169(1)
4.2.11.2 Seeing ahead of the bit: MWD-VSP and vibration logging (MWD-VSP; Vibration logging of the formation)
169(2)
4.2.11.3 Notes on rock-bit interaction
171(2)
4.2.11.4 Basic mathematical approach
173(1)
4.2.11.5 More rock-bit interaction models (An inelastic impact model; Elastic impacts, with stress effects)
174(5)
4.2.11.6 Separating incident from reflected waves (Delay line method; Differential technique; Three-wave formulation; Digital analysis methods)
179(5)
4.3 Lateral Bending Vibrations
184(32)
4.3.1 Why explain this drilling paradox?
184(1)
4.3.2 Lateral vibrations in deepwater operations
185(1)
4.3.2.1 Marine risers
185(1)
4.3.2.2 Bending vibrations in directional control
186(1)
4.3.2.3 Plan for remainder of chapter
186(1)
4.3.3 A downhole paradox -- "Case of the vanishing waves"
186(1)
4.3.3.1 Physical features observed at failure
187(1)
4.3.3.2 Field evidence widely available
187(2)
4.3.3.3 Wave trapping, a simple analogy
189(1)
4.3.3.4 Extension to general systems
190(1)
4.3.4 Why drillstrings fail at the neutral point
191(1)
4.3.4.1 Beam equation analysis
192(1)
4.3.4.2 Kinematic wave modeling
193(6)
4.3.4.3 Bending amplitude distribution in space
199(3)
4.3.4.4 Designing safe drill collars
202(1)
4.3.4.5 Viscous dissipation
203(1)
4.3.5 Surface detection of downhole bending disturbances
203(1)
4.3.5.1 Detecting lateral vibrations
203(1)
4.3.5.2 Nonlinear axial equation
204(1)
4.3.5.3 Detecting lateral vibrations from the surface
205(1)
4.3.6 Linear boundary value problem formulation
206(1)
4.3.6.1 General linear equation
206(1)
4.3.6.2 Auxiliary conditions
207(1)
4.3.7 Finite difference modeling
208(1)
4.3.7.1 Pentadiagonal difference equations
209(1)
4.3.7.2 Finite difference beam recipe
210(1)
4.3.7.3 Additional modeling considerations (Borehole wall contacts; Modeling steady state oscillations; Simulating area changes)
211(1)
4.3.8 Example Fortran implementation
212(3)
4.3.9 Nonlinear interaction between axial and lateral bending vibrations
215(1)
4.4 Torsional and Whirling Vibrations
216(11)
4.4.1 Torsional wave equation
216(3)
4.4.2 Stick-slip oscillations
219(1)
4.4.2.1 Energy considerations
220(1)
4.4.2.2 Static torque effects on bending
221(1)
4.4.2.3 Finite difference modeling
222(1)
4.4.2.4 WOB/TOB (Weight-on-bit/Torque-on-bit)
222(1)
4.4.2.5 Applications to MWD telemetry
223(1)
4.4.2.6 Example Fortran implementation
223(2)
4.4.2.7 Whirling motions (Example 4-6. Machine shaft example; Example 4-7. Generalized whirl)
225(1)
4.4.2.8 Causes of whirling motions
226(1)
4.5 Coupled Axial, Torsional and Lateral Vibrations
227(21)
4.5.1 Importance to PDC bit dynamic
227(1)
4.5.2 Coupled axial, torsional and bending vibrations
228(1)
4.5.2.1 Example 4-8. Simple desktop experiment
228(1)
4.5.3 Notes on the coupled model
229(1)
4.5.4 Coupled axial, torsional and bending vibrations
229(1)
4.5.4.1 Partial differential equations
230(1)
4.5.4.2 Finite differencing the coupled bending equations
231(2)
4.5.4.3 Computational recipe
233(1)
4.5.4.4 Modes of coupling
233(1)
4.5.4.5 Numerical considerations
234(1)
4.5.4.6 General Fortran implementation
235(4)
4.5.4.7 Example calculations: bit-bounce, stick-slip, rate-of-penetration and drillstring precession (Test A. Smooth drilling and making hole; Test B. Rough drilling with bit bounce; Model limitations and extensions)
239(5)
4.5.4.8 Precessional instabilities
244(1)
4.5.4.9 Comments on Dunayevsky model
244(2)
4.5.4.10 Direct simulation of bit precession
246(1)
4.5.4.11 Drillstring vibrations in horizontal wells
247(1)
4.6 References
248(9)
5 Mud Acoustics in Modern Drilling
257(49)
5.1 Governing Lagrangian Equations
258(9)
5.1.1 Hydraulic versus acoustic motion
258(1)
5.1.2 Differential equation
259(1)
5.1.3 Area and material discontinuities
259(2)
5.1.4 Mud acoustic formulation
261(1)
5.1.5 Example 5-1. Idealized reflections and transmissions
261(2)
5.1.6 Example 5-2. Classical water hammer
263(1)
5.1.7 Example 5-3. Acoustic pipe resonances
263(1)
5.1.7.1 Closed-closed ends
264(1)
5.1.7.2 Open-open ends
264(1)
5.1.7.3 Closed-open ends
264(1)
5.1.8 Example 5-4. Passage through area obstructions
265(1)
5.1.9 Example 5-5. Transmission through contrasting media
266(1)
5.2 Governing Eulerian Equations
267(5)
5.2.1 Steady and unsteady hydraulic limits
268(1)
5.2.2 Separating hydraulic and acoustic effects
269(3)
5.3 Transient Finite Differencing Modeling
272(3)
5.3.1 Basic difference model
272(1)
5.3.2 Modeling area discontinuities
273(1)
5.3.2.1 Axial vibrations
273(1)
5.3.2.2 Mud acoustics
274(1)
5.4 Swab-Surge Modeling
275(3)
5.4.1 Wave physics of swab-surge
275(2)
5.4.2 Designing a swab-surge simulator
277(1)
5.5 MWD Mud Pulse Telemetry
278(16)
5.5.1 Basic MWD system components
278(1)
5.5.2 Candidate transmission technologies -- with brief survey of early work
279(2)
5.5.3 Mud pulse telemetry -- the acoustic source
281(1)
5.5.3.1 Positive pressure poppet valves
281(2)
5.5.3.2 Negative pressure valves
283(2)
5.5.3.3 Mud siren sources
285(1)
5.5.3.4 Signal generation at the source
286(1)
5.5.3.5 Mechanical design considerations (Packaging constraints; Shock and vibration; Mud erosion; Power requirements; High pressure and temperature; Fluid mechanics problems)
287(2)
5.5.3.6 Mud pulse telemetry -- the transmission channel
289(1)
5.5.3.7 The transmission channel uphole
290(1)
5.5.3.8 Telemetry design objectives
291(1)
5.5.3.9 Additional practical considerations
292(1)
5.5.3.10 The theoretical maximum
293(1)
5.5.3.11 Acoustic signals in the annulus
293(1)
5.6 Recent MWD Developments
294(9)
5.7 References
303(3)
6 Geophysical Ray Tracing
306(25)
6.1 Classical Wave Modeling -- Eikonal Methods and Ray Tracing
307(3)
6.1.1 The plane wave
307(1)
6.1.2 High frequency limit
307(1)
6.1.3 Eikonal equation in nonuniform media
308(1)
6.1.4 Continuing the series
308(1)
6.1.5 Integrating the eikonal equation
308(2)
6.1.6 Summary of ray tracing results
310(1)
6.2 Fermat's Principal of Least Time (via Calculus of Variations)
310(2)
6.2.1 Travel time along a ray
310(1)
6.2.2 Calculus of variations
311(1)
6.2.3 Eikonal solution satisfies least time condition
312(1)
6.3 Fermat's Principle Revisited Via Kinematic Wave Theory
312(1)
6.4 Modeling Wave Dissipation
313(4)
6.4.1 Example 6-1. A simple model
314(1)
6.4.2 Example 6-2. Another case history
314(1)
6.4.3 Example 6-3. Motivating damped wave study
314(1)
6.4.4 The quality factor Q
315(1)
6.4.5 A simple example
315(2)
6.5 Ray Tracing Over Large Space-Time Scales
317(3)
6.5.1 High-order modulation equations
317(1)
6.5.1.1 The low-order limit
318(1)
6.5.1.2 Extended eikonal equations
318(1)
6.5.1.3 Extended eikonal equations in homogeneous medium
318(1)
6.5.1.4 The seismic limit
319(1)
6.5.1.5 Example 6-4. Simple rock formations
319(1)
6.6 Subtle High-Order Effects
320(4)
6.6.1 A low-order nonlinear wave equation
320(1)
6.6.2 Singularities in the low-order model
321(1)
6.6.3 Existence of the singularity
321(1)
6.6.4 Entropy conditions
322(2)
6.7 Travel-Time Modeling
324(5)
6.7.1 Applications to crosswell tomography
324(1)
6.7.2 Applications to surface seismics
325(1)
6.7.3 Finite difference calculation of travel times
325(1)
6.7.4 Difficulties with simple difference formulation
326(1)
6.7.4.1 Two space dimensions
326(1)
6.7.4.2 Three space dimensions
326(1)
6.7.4.3 Analysis of the problem
327(2)
6.8 References
329(2)
7 Wave and Current Interaction in the Ocean
331(7)
7.1 Wave Kinematics and Energy Summary
331(3)
7.1.1 Damped waves in deep water
332(1)
7.1.1.1 Effect of low-order dissipation
332(1)
7.1.1.2 Effect of variable background flow
332(1)
7.1.2 Waves in finite depth water
333(1)
7.2 Sources of Hydrodynamic Loading
334(1)
7.3 Instabilities Due to Heterogeneity
334(3)
7.4 References
337(1)
8 Borehole Electromagnetics - Diffusive and Propagation Transients
338(20)
8.1 Induction and Propagation Resistivity
339(5)
8.2 Conductive Mud Effects in Wireline and MWD Logging
344(2)
8.3 Longitudinal Magnetic Fields
346(3)
8.4 Apparent Anisotropic Resistivities for Electromagnetic Logging Tools in Horizontal Wells
349(7)
8.5 Borehole Effects -- Invasion and Eccentricity
356(1)
8.6 References
357(1)
9 Reservoir Engineering -- Steady, Diffusive and Propagation Models
358(9)
9.1 Buckley-Leverett Multiphase Flow
358(8)
9.1.1 Example boundary value problems
361(1)
9.1.2 General initial value problem
361(1)
9.1.3 General boundary value problem for infinite core
362(1)
9.1.4 Variable q(t) rate
362(1)
9.1.5 Mudcake dominated invasion
363(1)
9.1.6 Shock velocity
363(1)
9.1.7 Pressure solution
364(2)
9.2 References
366(1)
10 Borehole Acoustics - New Approaches to Old Problems
367(27)
10.1 Stoneley Waves in Permeable Wells - Background
368(4)
10.1.1 Analytical simplifications and new "lumped" parameters
369(1)
10.1.2 Properties of Stoneley waves from KWT analysis
370(1)
10.1.2.1 Dissipation due to permeability
370(1)
10.2.2.2 Phase velocity and attenuation decrement
370(1)
10.1.2.3 Relative magnitudes, phase and group velocities
371(1)
10.1.2.4 Amplitude and group velocity dependence
372(1)
10.2 Stoneley Wave Kinematics and Dynamics
372(12)
10.2.1 Energy redistribution within wave packets
372(3)
10.2.2 Dynamically steady Stoneley waves in heterogeneous media
375(1)
10.2.3 Permeability prediction from energy considerations
376(2)
10.2.4 Permeability prediction from phase considerations
378(1)
10.2.5 Example permeability predictions
378(6)
10.3 Effects of Borehole Eccentricity
384(7)
10.3.1 Industry formulations, solutions and approaches
384(1)
10.3.2 Successes in eccentricity modeling
385(3)
10.3.3 Applications to borehole geophysics
388(1)
10.3.3.1 General displacement approach
389(1)
10.3.3.2 Numerical solution strategy (Defining the grid; Creating the governing equations; Specifying the problem domain)
390(1)
10.4 References
391(3)
Cumulative Refrences 394(16)
Index 410(9)
About the Author 419
Wilson C. Chin, who earned his Ph.D. at M.I.T., has published ten books on original oilfield research, and over one hundred papers and forty patents in well logging and petroleum engineering.  He has collaborated with leading companies and universities worldwide and worked extensively in high-data-rate MWD design and advanced electromagnetic algorithm development.
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