The Rock Physics Handbook : Tools for Seismic Analysis of Porous Media

The Rock Physics Handbook addresses the relationships between geophysical observations and the underlying physical properties of rocks. It distills a vast quantity of background theory and laboratory results into a series of concise chapters that provide practical solutions to problems in geophysical data interpretation. This expanded second edition presents major new chapters on statistical rock physics and velocity-porosity-clay models for clastic sediments. Other new and expanded topics include anisotropic seismic signatures, borehole waves, models for fractured media, poroelastic models, and attenuation models. This new edition also provides an enhanced set of appendices with key empirical results, data tables, and an atlas of reservoir rock properties - extended to include carbonates, clays, gas hydrates, and heavy oils. Supported by a website hosting MATLAB® routines for implementing the various rock physics formulas, this book is a vital resource for advanced students and university faculty, as well as petroleum industry geophysicists and engineers. Half-title......Page 3 Title......Page 5 Copyright......Page 6 Contents......Page 7 Preface to the Second Edition......Page 13 Evenness and oddness......Page 15 Energy spectrum......Page 16 Sampling theorem......Page 17 Numerical details......Page 18 Fourier transform theorems......Page 19 Synopsis......Page 20 Causality......Page 22 Regression......Page 23 Distributions......Page 26 Monte Carlo simulations......Page 29 Bootstrap......Page 30 Statistical classification......Page 31 Synopsis......Page 32 Assumptions and limitations......Page 34 Synopsis......Page 35 Synopsis......Page 37 Voigt notation......Page 38 Isotropic: two independent constants......Page 40 Hexagonal or transversely isotropic: five independent constants......Page 41 Phase velocities for several elastic symmetry classes......Page 42 Kelvin notation......Page 44 Elastic eigentensors and eigenvalues......Page 46 Poissons ratio defined for anisotropic elastic materials......Page 47 Synopsis......Page 49 2.4 Tsvankin's extended Thomsen parameters for orthorhombic media......Page 53 Synopsis......Page 54 Synopsis......Page 57 Uses......Page 60 Synopsis......Page 61 Uses......Page 67 Synopsis......Page 68 Effective dry compressibility......Page 70 Stress-induced pore pressure: Skempton's coefficient......Page 71 Spherical cavity......Page 72 Penny-shaped crack: oblate spheroid......Page 73 Needle-shaped pore: prolate spheroid......Page 74 Two-dimensional tubes......Page 75 Plane strain......Page 76 Two-dimensional thin cracks......Page 77 Ellipsoidal cracks of finite thickness......Page 80 Deformation of spherical shells......Page 81 Synopsis......Page 82 Circular hole with principal stresses at infinity......Page 83 Stress concentration around an elliptical hole......Page 84 Stress around an inclined cylindrical hole......Page 85 Stress around a vertical cylindrical hole in a poroelastic medium......Page 86 Assumptions and limitations......Page 87 Synopsis......Page 88 Three-dimensional Mohr's circle......Page 89 2.12 Static and dynamic moduli......Page 90 Assumptions and limitations......Page 93 Synopsis......Page 95 Synopsis......Page 97 Synopsis......Page 100 NMO in an anisotropic Earth......Page 102 VTI symmetry with horizontal reflector......Page 103 Vertical symmetry axis with dipping reflector......Page 104 Tilted TI symmetry with dipping reflector......Page 105 Orthorhombic symmetry with horizontal reflector......Page 106 Synopsis......Page 107 Simple band-limited inverse of reflectivity time series......Page 109 Synopsis......Page 110 AVO: amplitude variations with offset......Page 111 Approximate forms......Page 114 Synopsis......Page 119 Transversely isotropic media: VTI......Page 122 Transversely isotropic media: HTI......Page 124 Orthorhombic media......Page 125 Arbitrary anisotropy......Page 128 3.7 Elastic impedance......Page 129 Elastic impedance expressions: isotropic......Page 132 Elastic impedance expressions: VTI anisotropic......Page 133 Elastic impedance expressions: orthorhombic x2-x3 symmetry plane......Page 134 Synopsis......Page 135 Synopsis......Page 141 Synopsis......Page 143 Assumptions and limitations......Page 147 Synopsis......Page 148 Assumptions and limitations......Page 151 Synopsis......Page 152 One-dimensional layered poroelastic medium......Page 157 Assumptions and limitations......Page 159 Layered (one-dimensional) media......Page 160 Synopsis......Page 164 Torsional waves......Page 169 Bar resonance......Page 170 Porous, fluid-saturated rods......Page 171 Assumptions and limitations......Page 173 Isotropic elastic formation......Page 174 Transversely isotropic (TI) elastic formation......Page 176 Isotropic, poroelastic, permeable formation......Page 178 Extensions......Page 182 Synopsis......Page 183 Uses......Page 187 Synopsis......Page 188 Synopsis......Page 189 Synopsis......Page 191 Synopsis......Page 192 Synopsis......Page 193 More on dry-rock compressibility......Page 195 Synopsis......Page 197 Synopsis......Page 199 Synopsis......Page 204 Modified DEM with critical porosity constraints......Page 206 Uses......Page 207 Synopsis......Page 208 Special cases of crack distributions......Page 212 Heavily faulted structures......Page 214 Assumptions and limitations......Page 216 Synopsis......Page 217 Assumptions and limitations......Page 218 Synopsis......Page 219 Synopsis......Page 224 Uses......Page 228 4.14 Elastic constants in finely layered media: general layer anisotropy......Page 229 Synopsis......Page 230 Assumptions and limitations......Page 232 Quasi-static fracture compliance......Page 233 Assumptions and limitations......Page 237 Synopsis......Page 238 Assumptions and limitations......Page 242 Porosity......Page 243 Coordination number......Page 246 Binary mixtures of spheres......Page 248 Other practical parameters affecting packing......Page 250 Synopsis......Page 251 Sorting......Page 256 Contact stiffnesses and effective moduli......Page 259 The Hertz-Mindlin Model......Page 260 The Walton model......Page 262 The Digby model......Page 263 The Jenkins et al. model......Page 265 The Brandt model......Page 266 The Johnson et al. model......Page 267 The cemented-sand model......Page 269 The uncemented (soft) sand model......Page 272 The stiff-sand and intermediate stiff-sand models......Page 274 Caveat on the use of effective medium models for granular media......Page 276 Assumptions and limitations......Page 277 Hexagonal close packing......Page 278 Assumptions and limitations......Page 279 Synopsis......Page 280 Slow S-wave......Page 283 Extensions......Page 285 Assumptions and limitations......Page 286 Synopsis......Page 287 Compressibility form......Page 289 Linear form......Page 290 Velocity form......Page 291 Pore stiffness interpretation......Page 292 Biot coefficient......Page 294 Assumptions and limitations......Page 295 Synopsis......Page 296 Synopsis......Page 298 Assumptions and limitations......Page 300 Synopsis......Page 301 Uses......Page 303 Synopsis......Page 304 Uses......Page 305 Synopsis......Page 306 Assumptions and limitations......Page 308 Synopsis......Page 309 Assumptions and limitations......Page 310 Synopsis......Page 311 Synopsis......Page 312 Extensions......Page 315 Synopsis......Page 316 Uses......Page 317 Synopsis......Page 318 Extensions......Page 319 Synopsis......Page 320 Extensions......Page 323 High- and low-frequency limits......Page 324 Attenuation......Page 328 Partial water saturation......Page 329 Full water saturation (wet rock)......Page 331 Assumptions and limitations......Page 333 Caveat on very dry rocks......Page 334 Caveat on frequency......Page 335 Effective fluid model......Page 336 Critical relaxation scale......Page 337 Patchy saturation......Page 338 Brie's fluid mixing equation......Page 339 Synopsis......Page 340 Synopsis......Page 345 Results for specific correlation functions......Page 347 Low- and high-frequency limits......Page 349 Permeability fluctuations......Page 350 Uses......Page 351 Synopsis......Page 352 Synopsis......Page 353 Brine......Page 354 Gas......Page 355 Oil......Page 356 Live oil......Page 357 Assumptions and limitations......Page 360 Synopsis......Page 361 Synopsis......Page 364 Uses......Page 365 Assumptions and limitations......Page 366 Synopsis......Page 367 Uses......Page 368 Synopsis......Page 369 Uses......Page 370 Uses......Page 371 Uses......Page 372 VP-density......Page 373 VP-VS......Page 375 Uses......Page 376 Limestones......Page 377 Dolomite......Page 378 Sandstones and shales......Page 379 Sandstones: effects of porosity......Page 381 Sandstones: effects of fluids and frequency......Page 382 Critical porosity model......Page 383 Krief's relations......Page 386 Greenberg and Castagna's relations......Page 388 Vernik's relations......Page 390 Xu and White's relation......Page 391 Assumptions and limitations......Page 393 Synopsis......Page 394 Assumption and limitations......Page 396 Synopsis......Page 397 7.13 Attenuation and quality factor relations......Page 398 Uses......Page 399 Synopsis......Page 400 Assumptions and limitations......Page 402 Synopsis......Page 403 Diffusivity......Page 405 Sinusoidal pressure disturbance......Page 406 Assumptions and limitations......Page 407 Synopsis......Page 408 Useful examples of viscous flow......Page 409 Synopsis......Page 410 Assumptions and limitations......Page 414 Synopsis......Page 415 Mixed particle sizes......Page 419 Assumptions and limitations......Page 420 Synopsis......Page 421 Synopsis......Page 424 Nonlinear diffusion......Page 425 Hyperbolic equation of filtration (diffusion)......Page 426 Assumptions and limitations......Page 427 Synopsis......Page 428 Assumptions and limitations......Page 431 Synopsis......Page 432 Synopsis......Page 435 Synopsis......Page 438 9.5 Cross-property bounds and relations between elastic and electrical parameters......Page 443 Dry rocks......Page 445 Wet rocks......Page 446 Gassmann-based relations......Page 448 Uses......Page 449 Assumptions and limitations......Page 450 Chalks......Page 451 Dolomite......Page 454 Sandstones......Page 456 Tight-gas sandstones......Page 458 Limestone......Page 460 High-porosity sandstones......Page 462 Poorly consolidated sandstones......Page 464 Length......Page 466 Area......Page 467 Pressure......Page 468 Other conversions......Page 469 Fundamental constants......Page 470 A.5 Velocities and moduli of ice and methane hydrate......Page 471 Air......Page 482 Ethane (C2H6)......Page 483 Methane (CH4)......Page 484 Hydrogen (H2)......Page 485 Oxygen (O2)......Page 486 A.8 Standard temperature and pressure......Page 488 References......Page 493 Index ......Page 517 This fully updated text addresses the relationships between geophysical observations and the underlying physical properties of rocks. It distills a vast quantity of background theory and laboratory results into a series of concise chapters that provide practical solutions to problems in geophysical data interpretation. Now in its second edition, major new chapters are presented on statistical rock physics and velocity-porosity-clay models for clastic sediments. Other new and expanded topics include anisotropic seismic signatures, borehole waves, models for fractured media, poroelastic models, and attenuation models. Also new to this edition is an enhanced set of appendices with key empirical results, data tables, and an atlas of reservoir rock properties - extended to include carbonates, clays, gas hydrates, and heavy oils. Supported by a website hosting MATLAB routines for implementing the various rock physics formulas, this book is a vital resource for advanced students and university faculty, as well as petroleum industry geophysicists and engineers.