TY  - BOOK
AU  - Chin,Wilson C.
TI  - Wave Propagation in Drilling, Well Logging and Reservoir Applications
T2  - Advances in Petroleum Engineering Series
SN  - 9781118925904
AV  - TN871.35 .C478 2014 
U1  - 622.1828 
PY  - 2014///
CY  - Newark
PB  - John Wiley & Sons, Incorporated
KW  - Geophysical well logging
KW  - Electronic books
N1  - Cover -- Title Page -- Copyright Page -- Contents -- Preface -- Acknowledgements -- 1 Overview and Fundamental Ideas -- 1.1 The Classical Wave Equation -- 1.1.1 Fundamental properties -- 1.1.2 Reflection properties -- 1.1.2.1 Example 1-1. Rigid end termination -- 1.1.2.2 Example 1-2. Stress-free end -- 1.1.2.3 Note on acoustics -- 1.2 Fundamental Representation -- 1.2.1 Taylor series -- 1.2.2 Fourier series -- 1.3 Separation of Variables and Eigenfunction Expansions -- 1.3.1 Example 1-3. String with pinned ends and general initial conditions -- 1.3.2 Example 1-4. String with distributed forces -- 1.3.3 Example 1-5. Alternative boundary conditions -- 1.3.4 Example 1-6. Mixed boundary conditions -- 1.3.5 Example 1-7. Problems without initial conditions -- 1.3.5.1 Example 1-7a. Naive approach -- 1.3.5.2 Example 1-7b. Correct approach -- 1.3.5.3 Example 1-7c. Faster approach -- 1.3.6 Example 1-8. Dissipative wave solution -- 1.4 Standing Versus Propagating Waves -- 1.4.1 Standing waves -- 1.4.2 Propagating waves -- 1.4.3 Combined standing and propagating waves -- 1.4.4 Characterizing propagating waves -- 1.5 Laplace Transforms -- 1.5.1 Wave equation derivation -- 1.5.2 Example 1-9. String falling under its own weight -- 1.5.3 Example 1-10. Semi-infinite string with a general end support -- 1.5.3.1 Example 1-10a. Rectangular pulse -- 1.5.3.2 Example 1-10b. Impulse response -- 1.5.3.3 Example 1-10c. Incident sinusoidal wavetrain -- 1.6 Fourier Transforms -- 1.6.1 Example 1-11. Propagation of an initially static disturbance -- 1.6.2 Example 1-12. Directional properties, special wave -- 1.7 External Forces Versus Boundary Conditions -- 1.7.1 Single point force -- 1.7.2 Properties of point loads -- 1.7.2.1 Example 1-13. Boundary conditions versus forces -- 1.7.2.2 Couples or dipoles -- 1.7.2.3 Multiple forces and higher order moments; 1.7.2.4 Symmetries and anti-symmetries -- 1.7.2.5 Impulse response -- 1.7.2.6 On the subtle meaning of impulse -- 1.7.2.7 Example 1-14. Incorrect use of impulse response -- 1.7.2.8 Additional models -- 1.7.2.9 Other delta function properties -- 1.8 Point Force and Dipole Wave Excitation -- 1.8.1 Example 1-15. Finite string excited by a time-varying concentrated point force -- 1.8.2 Example 1-16. Finite string excited by a time-varying point dipole (i.e., a force couple) -- 1.8.3 Example 1-17. Splitting of an applied initial disturbance -- 1.9 First-Order Partial Differential Equations -- 1.10 References -- 2 Kinematic Wave Theory -- 2.1 Whitham's Theory in Nondissipative Media -- 2.1.1 Uniform media -- 2.1.2 Example 2-1. Transverse beam vibrations -- 2.1.3 Example 2-2. Simple longitudinal oscillations -- 2.1.4 Example 2-3. Asymptotic stationary phase expansion -- 2.1.5 Simple consequences of KWT -- 2.1.6 Nonuniform media -- 2.1.7 Example 2-4. Numerical integration -- 2.1.8 Ease of use is important to practical engineering -- 2.2 Simple Attenuation Modeling -- 2.2.1 The Q-model -- 2.2.2 Relating Q to amplitude in space -- 2.2.3 Relating Q to standing wave decay -- 2.2.4 Kinematic wave generalization -- 2.3 KWT in Homogeneous Dissipative Media -- 2.3.1 Example 2-5. General initial value problem in uniform media -- 2.3.2 Singularities of the kinematic field -- 2.3.3 The energy singularity -- 2.3.4 Example 2-6. Modeling dynamically steady motions -- 2.4 High-Order Kinematic Wave Theory -- 2.4.1 Basic assumptions -- 2.4.2 The general amplitude equation -- 2.4.3 Method of multiple scales -- 2.4.4 Generalized wave results -- 2.4.5 The low-order limit -- 2.5 Effect of Low-Order Nonuniformities -- 2.5.1 Detailed formal analysis -- 2.5.2 Wave energy and momentum -- 2.5.3 Example 2-7. String with variable properties -- 2.5.4 Computational solution; 2.5.5 Dynamically steady problems -- 2.5.6 Waves in nonuniform moving media -- 2.5.7 Average Lagrangian formalism -- 2.5.8 Example 2-8. Wave action conservation -- 2.6 Three-Dimensional Kinematic Wave Theory -- 2.6.1 Wave irrotationality -- 2.6.2 The ray equation -- 2.6.3 Frequency variation -- 2.6.4 Energy variation -- 2.6.5 Ray topology -- 2.6.6 Example 2-9. Acoustics application -- 2.7 References -- 3 Examples from Classical Mechanics -- 3.1 Example 3-1. Lateral Vibration of Simple Beams -- 3.1.1 Example 3-1a. Hinged ends -- 3.1.2 Example 3-1b. Clamped end, other end free -- 3.2 Example 3-2. Acoustic Waves in Waveguides -- 3.2.1 Simple waveguides -- 3.2.2 Simple hydraulic flows -- 3.2.3 Acoustic simplifications -- 3.2.4 Three-dimensional wave equation -- 3.2.5 Modal solution -- 3.2.6 The dispersion relation -- 3.2.7 Physical interpretation -- 3.2.8 MWD notes -- 3.2.9 Phase and group velocity -- 3.2.10 The velocity potential -- 3.2.11 Modeling MWD sources -- 3.3 Example 3-3. Gravity-Capillary Waves in Deep Water -- 3.3.1 Governing Laplace equation -- 3.3.2 Boundary conditions, kinematic and dynamic -- 3.3.3 Problem solution -- 3.3.4 Energy considerations -- 3.4 Example 3-4. Fluid-Solid Interaction - Waves on Elastic Membranes -- 3.4.1 Governing Rayleigh equation -- 3.4.2 Boundary conditions for potential -- 3.4.3 Eigenvalue bounds -- 3.5 Example 3-5. Problems in Hydrodynamic Stability -- 3.5.1 Neutral stability diagrams -- 3.5.2 Borehole flow stability -- 3.5.3 Stability of irrotational flows -- 3.6 References -- 4 Drillstring Vibrations: Classic Ideas and Modern Approaches -- 4.1 Typical Downhole Vibration Environment -- 4.1.1 What is wave motion? -- 4.1.2 Drillstring vibration modes, axial, torsional and lateral -- 4.1.2.1 Axial vibrations -- 4.1.2.2 Transverse vibrations -- 4.1.2.3 Torsional vibrations -- 4.1.2.4 Whirling vibrations; 4.1.2.5 Coupled axial, torsional and lateral vibrations -- 4.1.2.6 Transient and dynamically steady oscillations -- 4.1.2.7 Understanding the environment -- 4.1.3 Long-standing vibrations issues -- 4.1.3.1 Example 4-1. Case of the missing waves -- 4.1.3.2 Example 4-2. Looking for resonance in all the wrong places -- 4.1.3.3 Example 4-3. Drillstrings that don't drill -- 4.1.3.4 Example 4-4. Modeling coupled vibrations -- 4.1.3.5 Example 4-5. Energy transfer mechanisms -- 4.1.4 Practical applications -- 4.1.4.1 Anecdotal stories -- 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) -- 4.1.5 Elastic line model of the drillstring -- 4.1.5.1 Early efforts -- 4.1.5.2 Elastic line simplifications -- 4.1.5.3 Historical precedents -- 4.1.5.4 Our focus -- 4.1.6 Objectives and discussion plan -- 4.2 Axial Vibrations -- 4.2.1 Pioneering axial vibration studies -- 4.2.2 Governing differential equations -- 4.2.2.1 Damped wave equation -- 4.2.2.2 External forces and displacement sources -- 4.2.2.3 Dynamic and static solutions -- 4.2.2.4 Free-fall as a special solution -- 4.2.2.5 More on AC/DC interactions -- 4.2.3 Conventional separation of AC/DC solutions -- 4.2.3.1 Sign conventions -- 4.2.3.2 Static weight on bit -- 4.2.4 Boundary conditions - old and new ideas -- 4.2.4.1 Surface boundary conditions -- 4.2.4.2 Conventional bit boundary conditions -- 4.2.4.3 Modeling rock-bit interactions -- 4.2.4.4 Empirical notes on rock-bit interaction (Laboratory drillbit data -- Single-tooth impact results) -- 4.2.4.5 Modeling drillbit kinematics using "displacement sources" (Analogies from earthquake seismology) -- 4.2.5 Global energy balance -- 4.2.5.1 Formulation summary; 4.2.5.2 Energy considerations (The drillstring -- The surface -- Combined drillstring/ surface system) -- 4.2.5.3 Detailed bit motions -- 4.2.6 Simple solution for rate-of-penetration -- 4.2.6.1 Field motivation -- 4.2.6.2 Simple analytical solution -- 4.2.6.3 Classic fixed end -- 4.2.6.4 Classic free end -- 4.2.6.5 Other possibilities -- 4.2.6.6 Simple derivative model -- 4.2.6.7 The general impedance mode -- 4.2.6.8 Modeling the constants alpha, beta and gamma -- 4.2.7 Finite difference modeling -- 4.2.7.1 Elementary considerations -- 4.2.7.2 Transient finite difference modeling (The solution methodology -- Stability of the scheme -- Grid sizes, time steps, and convergence) -- 4.2.8 Complete formulation and numerical solution -- 4.2.8.1 The boundary value problem -- 4.2.8.2 Computational objective -- 4.2.8.3 Difference approximations -- 4.2.9 Modeling pipe-to-collar area changes -- 4.2.9.1 Matching conditions -- 4.2.9.2 Finite difference model -- 4.2.9.3 Generalized formulation -- 4.2.9.4 Alternative boundary conditions -- 4.2.10 Example Fortran implementation -- 4.2.10.1 Code fragment -- 4.2.10.2 Modeling dynamically steady problems -- 4.2.10.3 Jarring issues and stuck pipe problems -- 4.2.11 Drillstring and formation imaging -- 4.2.11.1 Drillstring imaging -- 4.2.11.2 Seeing ahead of the bit: MWD-VSP and vibration logging (MWD-VSP -- Vibration logging of the formation) -- 4.2.11.3 Notes on rock-bit interaction -- 4.2.11.4 Basic mathematical approach -- 4.2.11.5 More rock-bit interaction models (An inelastic impact model -- Elastic impacts, with stress effects) -- 4.2.11.6 Separating incident from reflected waves (Delay line method -- Differential technique -- Three-wave formulation -- Digital analysis methods) -- 4.3 Lateral Bending Vibrations -- 4.3.1 Why explain this drilling paradox? -- 4.3.2 Lateral vibrations in deepwater operations; 4.3.2.1 Marine risers
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