PETROLEUM RELATED ROCK MECHANICS
CONTENTS CHAPTER ELASTICITY 11 STRESS 111 THE STRESS TENSOR 112 EQUATIONS OF EQUILIBRIUM 113 PRINCIPAL STRESSES IN TWO DIMENSIONS 114 MOHR’S STRESS CIRCLE 115 PRINCIPAL STRESSES IN THREE DIMENSIONS 116 MOHR’S STRESS CIRCLES IN THREE DIMENSIONS 117 STRESS INVARIANTS 118 DEVIATORIC STRESSES GEOMETRIC INTERPRETATION OF THE DEVIATORIC STRESS INVARIANTS 119 THE OCTAHEDRAL STRESSES 12 STRAIN 121 THE STRAIN TENSOR AND THE STRAIN INVARIANTS 122 COMPATIBILITY CONDITIONS 123 PRINCIPAL STRAINS 124 PLANE STRAIN AND PLANE STRESS 13 ELASTIC MODULI 14 STRAIN ENERGY 15 THERMOELASTICITY 151 THERMAL STRAIN 152 THERMAL STRESS 153 STRESS STRAIN RELATION FOR LINEAR THERMOELASTICITY 154 ISOTHERMAL AND ADIABATIC MODULI 155 EXAMPLE: THERMAL STRESSES IN A CONSTRAINED SQUARE PLATE 16 POROELASTICITY 161 SUSPENSION OF SOLID PARTICLES IN A ?UID 162 BIOT’S POROELASTIC THEORY FOR STATIC PROPERTIES 163 THE EFFECTIVE STRESS CONCEPT 164 PORE VOLUME COMPRESSIBILITY AND RELATED TOPICS 165 THE SKEMPTON COEF?CIENTS 166 THE CORRESPONDENCE TO THERMOELASTICITY 167 OTHER NOTATION CONVENTIONS 17 ANISOTROPY 171 ORTHORHOMBIC SYMMETRY 172 TRANSVERSE ISOTROPY 18 NONLINEAR ELASTICITY 181 STRESS–STRAIN RELATIONS 182 THE IMPACT OF CRACKS 19 TIME-DEPENDENT EFFECTS 191 CONSOLIDATION 192 CREEP REFERENCES FURTHER READING CHAPTER FAILURE MECHANICS 21 BASIC CONCEPTS 211 STRENGTH AND RELATED CONCEPTS 212 THE FAILURE SURFACE 22 TENSILE FAILURE 23 SHEAR FAILURE 231 THE MOHR–COULOMB CRITERION 232 THE GRIF?TH CRITERION 24 COMPACTION FAILURE 25 FAILURE CRITERIA IN THREE DIMENSIONS 251 CRITERIA INDEPENDENT OF THE INTERMEDIATE PRINCIPAL STRESS 252 CRITERIA DEPENDING ON THE INTERMEDIATE PRINCIPAL STRESS ?-PLANE REPRESENTATION PHYSICAL EXPLANATIONS 26 FLUID EFFECTS 261 PORE PRESSURE 262 PARTIAL SATURATION 263 CHEMICAL EFFECTS 27 PRESENTATION AND INTERPRETATION OF DATA FROM FAILURE TESTS 28 BEYOND THE YIELD POINT 281 PLASTICITY PLASTIC ?OW ASSOCIATED ?OW NON-ASSOCIATED ?OW HARDENING 282 SOIL MECHANICS NORMALLY CONSOLIDATED CLAYS OVERCONSOLIDATED CLAYS 283 LOCALIZATION 284 LIQUEFACTION 29 FAILURE OF ANISOTROPIC AND FRACTURED ROCKS 291 INTRINSIC ANISOTROPY AND THE FAILURE SURFACE 292 THE PLANE OF WEAKNESS MODEL 293 FRACTURED ROCK 210 STRESS HISTORY EFFECTS 2101 RATE EFFECTS AND DELAYED FAILURE 2102 FATIGUE GEOLOGICAL ASPECTS OF PETROLEUM RELATED ROCK MECHANICS 31 UNDERGROUND STRESSES 32 PORE PRESSURE 33 SEDIMENTOLOGICAL ASPECTS 331 GRAINS AND MINERALS 332 PRE-DEPOSITION AND DEPOSITION 333 POST-DEPOSITION 34 MECHANICAL PROPERTIES OF SEDIMENTARY ROCKS 341 SANDSTONE 342 CHALK 343 SHALE 344 ROCK SALT STRESSES AROUND BOREHOLES BOREHOLE FAILURE CRI- TERIA 41 STRESSES AND STRAINS IN CYLINDRICAL COORDINATES 42 STRESSES IN A HOLLOW CYLINDER 421 THE EQUILIBRIUM EQUATIONS 422 STRESS DISTRIBUTIONS WITH CONSTANT PORE PRESSURE 423 STRESS DISTRIBUTIONS WITH VARYING PORE PRESSURE THE SUPERPOSITION PRINCIPLE RADIAL ?OW 424 STRESS DISTRIBUTIONS WITH HEAT ?OW 425 STRESS DISTRIBUTIONS IN NONLINEAR FORMATIONS 43 ELASTIC STRESSES AROUND WELLS—THE GENERAL SOLUTION 431 TRANSFORMATION FORMULAS 432 THE GENERAL ELASTIC SOLUTION 433 BOREHOLE ALONG A PRINCIPAL STRESS DIRECTION 44 POROELASTIC TIME DEPENDENT EFFECTS 441 WELLBORE PRESSURE INVASION 442 DRILLOUT INDUCED PORE PRESSURE CHANGES 45 BOREHOLE FAILURE CRITERIA 451 VERTICAL HOLE, ISOTROPIC HORIZONTAL STRESSES AND IMPERMEABLE BOREHOLE WALL 452 VERTICAL HOLE, ISOTROPIC HORIZONTAL STRESSES AND PERMEABLE BOREHOLE WALL 453 BOREHOLE ALONG A PRINCIPAL STRESS DIRECTION 454 BOREHOLE IN A GENERAL DIRECTION 46 BEYOND FAILURE INITIATION 461 A SIMPLE PLASTICITY MODEL THE TRESCA CRITERION THE MOHR–COULOMB CRITERION DEFORMATION AND PLASTIC STRAIN 47 SPHERICAL COORDINATES 471 BASIC EQUATIONS 472 STRESS DISTRIBUTION AROUND A SPHERICAL CAVITY WITH NO ?UID ?OW 473 STRESS DISTRIBUTION WITH ?UID ?OW ELASTIC WAVE PROPAGATION IN ROCKS 51 THE WAVE EQUATION 52 P- AND S-WAVES 53 ELASTIC WAVES IN POROUS MATERIALS 531 BIOT’S THEORY OF ELASTIC WAVE PROPAGATION 532 DISPERSION DUE TO LOCAL ?OW 54 ATTENUATION 55 ANISOTROPY 551 THE CHRISTOFFEL EQUATION 552 WEAK ANISOTROPY 56 ROCK MECHANICS AND ROCK ACOUSTICS 561 STATIC AND DYNAMIC MODULI 562 STRESS STATE AND STRESS HISTORY 563 ADDITIONAL EFFECTS TEMPERATURE PARTIAL SATURATION CHEMICAL EFFECTS 57 RE?ECTIONS AND REFRACTIONS 571 INTERFACE WAVES 58 BOREHOLE ACOUSTICS 581 BOREHOLE MODES 582 BOREHOLE ALTERATION 59 SEISMICS ROCK MODELS 61 LAYERED MEDIA 62 MODELS INVOLVING POROSITY ONLY 63 GRAIN PACK MODELS 64 MODELS FOR CRACKS AND OTHER INCLUSIONS 641 LINEAR, ISOTROPIC MODELS 642 ANISOTROPIC MODELS 643 MODELS ACCOUNTING FOR INTERACTIONS 644 CRACK DEVELOPMENT IN STRESSED ROCKS 65 FRACTURED ROCKS 651 SINGLE FRACTURES 652 ROCKS WITH MANY FRACTURES MECHANICAL PROPERTIES AND STRESS DATA FROM LABO- RATORY ANALYSIS 71 CORE SAMPLES FOR ROCK MECHANICAL LABORATORY ANALYSIS 711 CORE REPRESENTATIVENESS AND SIZE EFFECTS 712 CORE ALTERATION 713 CORE HANDLING 714 PREPARATION OF TEST SAMPLES 72 LABORATORY EQUIPMENT 721 THE LOAD FRAME 722 THE TRIAXIAL CELL 723 MEASUREMENTS OF STRESSES AND STRAINS 724 ACOUSTIC MEASUREMENTS 73 LABORATORY TESTS FOR ROCK MECHANICAL PROPERTY DETERMINATION 731 STRESSES ON CYLINDRICAL SAMPLES 732 DRAINED AND UNDRAINED TEST CONDITIONS 733 STANDARD TRIAXIAL COMPRESSION TESTS 734 INTERPRETATION OF ELASTIC MODULI FROM TRIAXIAL TESTS 735 UNCON?NED (UNIAXIAL) COMPRESSION TESTS 736 HYDROSTATIC TESTS 737 TRIAXIAL TESTING OF SHALES 738 OEDOMETER (KO) TEST 739 STRESS PATH TESTS CONSTANT STRESS RATIO TESTS CONSTANT MEAN STRESS (CMS) TESTS 7310 OTHER TRIAXIAL FAILURE TESTS EXTENSION TESTS MULTIPLE AND CONTINUOUS FAILURE STATE TRIAXIAL TESTS TRUE TRIAXIAL TESTS 7311 HOLLOW CYLINDER TESTS 7312 MEASUREMENTS ON SMALL SAMPLES 74 LABORATORY TESTS FOR STRESS DETERMINATION 741 DIFFERENTIAL STRAIN CURVE ANALYSIS 742 ANELASTIC STRAIN RECOVERY 743 ACOUSTIC TECHNIQUES DIFFERENTIAL WAVE VELOCITY ANALYSIS ACOUSTIC EMISSION 75 INDEX TESTS 751 TENSILE STRENGTH INDICATORS 752 HARDNESS MEASUREMENTS 753 INDENTATION AND SCRATCH TESTS 754 SPECI?C SHALE CHARACTERIZATION TESTS MECHANICAL PROPERTIES AND IN SITU STRESSES FROM FIELD DATA 81 ESTIMATION OF ELASTIC PARAMETERS 811 ACOUSTIC WIRELINE LOGS FULL WAVEFORM SONIC TOOLS MULTIPOLE SONIC TOOLS 812 ACOUSTIC LOGGING WHILE DRILLING 813 ACOUSTIC MEASUREMENTS ON DRILL CUTTINGS 82 ESTIMATION OF STRENGTH PARAMETERS 821 LOG DATA (WIRELINE AND MWD) 822 DRILL CUTTINGS MEASUREMENTS 823 EMPIRICAL CORRELATIONS 824 DRILLING DATA 83 ESTIMATION OF IN SITU STRESSES 831 THE DENSITY LOG (OVERBURDEN STRESS) 832 BOREHOLE LOGS (HORIZONTAL STRESS DIRECTIONS) CALIPER LOGS IMAGE LOGS 833 FRACTURE TESTS (HORIZONTAL STRESS MAGNITUDES) LEAK-OFF TESTS AND EXTENDED LEAK-OFF TESTS MINI-FRAC TESTS WIRELINE TOOLS EMPIRICAL RELATIONS 834 OTHER METHODS STABILITY DURING DRILLING 91 UNSTABLE BOREHOLES: SYMPTOMS, REASONS AND CONSEQUENCES 911 TIGHT HOLE/STUCK PIPE 912 LOST CIRCULATION 92 ROCK MECHANICS ANALYSIS OF BOREHOLE STABILITY DURING DRILLING 93 TIME-DELAYED BOREHOLE FAILURE 931 ESTABLISHMENT OF PORE PRESSURE EQUILIBRIUM 932 TEMPERATURE EFFECTS 933 CREEP 94 INTERACTION BETWEEN SHALE AND DRILLING ?UID 95 BOREHOLE STABILITY ANALYSIS FOR WELL DESIGN 96 USE OF PRESSURE GRADIENTS 961 INTRODUCTION 962 DEPTH REFERENCE AND DEPTH CORRECTIONS 97 BEYOND SIMPLE STABILITY ANALYSIS 971 FIELD CASES: THE BOREHOLE STABILITY PROBLEM IN COMPLEX GEOLOGY CASE 1: DRILLING-INDUCED LATERAL SHIFTS ALONG PRE-EXISTING FRACTURES (MEILLON ST FAUST FIELD, FRANCE) CASE 2: DRILLING IN A COMPLEX GEOLOGICAL SETTING WITH HIGH TECTONIC STRESSES (CUSIANA FIELD, COLOMBIA) CASE 3: THE HEIDRUN FIELD, NORWEGIAN SEA 972 DRILLING IN DEPLETED RESERVOIRS 973 DRILLING BELOW DEEP WATER 974 SURGE AND SWAB EFFECTS 975 HOLE CLEANING 976 AMOUNT AND QUALITY OF INPUT DATA SOLIDS PRODUCTION 101 OPERATIONAL ASPECTS OF SOLIDS PRODUCTION 1011 CONSEQUENCES OF SOLIDS PRODUCTION 1012 WELL COMPLETION AND SOLIDS CONTROL 102 SAND 1021 NECESSARY AND SUF?CIENT CONDITIONS FOR SAND PRODUCTION 1022 FORCES ON A SAND GRAIN 1023 CRITICAL DRAWDOWN FOR CYLINDRICAL CAVITIES SHEAR FAILURE TENSILE FAILURE 1024 STABILITY AND COLLAPSE OF SAND ARCHES THE IMPACT OF WATER 1025 RATE OF PRODUCED SAND 1026 SAND TRANSPORT 1027 SAND PREDICTION 103 CHALK MECHANICS OF HYDRAULIC FRACTURING 111 CONDITIONS FOR TENSILE FAILURE 112 FRACTURE INITIATION AND FORMATION BREAKDOWN 113 FRACTURE ORIENTATION, GROWTH AND CON?NEMENT 114 FRACTURE SIZE AND SHAPE 115 FRACTURE CLOSURE 1151 ESTIMATION OF ?3 FROM SHUT-IN/DECLINE TESTS 1152 ESTIMATION OF ?3 FROM ?OWBACK TESTS 116 THERMAL EFFECTS ON HYDRAULIC FRACTURING RESERVOIR GEOMECHANICS 121 COMPACTION AND SUBSIDENCE 122 MODELLING OF RESERVOIR COMPACTION 1221 UNIAXIAL RESERVOIR COMPACTION 1222 THE DEPLETING SPHERE 1223 RESERVOIR STRESS PATH THE ELLIPSOIDAL RESERVOIR ELASTIC CONTRAST NON-ELLIPSOIDAL RESERVOIRS 1224 BEYOND SIMPLE ELASTIC THEORY 1225 TIME DELAYED RESERVOIR COMPACTION 123 FROM COMPACTION TO SUBSIDENCE 1231 GEERTSMA’S NUCLEUS OF STRAIN MODEL THE EFFECT OF THE FREE SURFACE THE SIZE OF THE SUBSIDENCE BOWL SUBSIDENCE ABOVE A DISK SHAPED RESERVOIR SOME EXAMPLE RESULTS 1232 STRESS ALTERATION IN THE OVERBURDEN 124 GEOMECHANICAL EFFECTS ON RESERVOIR PERFORMANCE 1241 COMPACTION DRIVE 1242 STRESS EFFECTS ON POROSITY POROSITY CHANGE DURING DEPLETION OVERBURDEN CORRECTION OF LABORATORY MEASURED POROSITY 1243 STRESS EFFECTS ON PERMEABILITY FLOOD DIRECTIONALITY IN THE ?ELD PERMEABILITY CHANGES UNDER ISOTROPIC STRESS CONDITIONS PERMEABILITY CHANGES UNDER ANISOTROPIC STRESS CONDITIONS 1244 GEOMECHANICS IN RESERVOIR SIMULATION WEAKLY COUPLED TECHNIQUE FULLY COUPLED SIMULATION 1245 SEISMIC RESERVOIR MONITORING FLUID SUBSTITUTION CHANGES IN TEMPERATURE CHANGES IN PORE PRESSURE AND RESERVOIR STRESSES 125 WELL PROBLEMS AND RESERVOIR GEOMECHANICS 1251 CASING DAMAGE 1252 RESERVOIR GEOMECHANICS AS A TOOL TO OPTIMIZE DRILLING AND PRODUCTION STRATEGIES