Competing Effect of Pore Fluid and Texture -- Case Study Depth (m) Sw Sxo. m Poisson's Ratio.. GOC.1 5 7 8 9 P-Impedance OWC 15 GR.. RHOB.5 1 Saturation...5. 1. 1.5 Vs (km/s).. Poisson's Ratio 5 7 P-Impedance Negative velocity contrast at gas-oil contact 1
Elastic Moduli and Crossplot Elastic Moduli vs. Depth Cross-Plot Cross-Plot by Zones and Common Fluid Substitution Depth (m) 5 5 Depth > OWC GOC < Depth < OWC Depth < GOC m M (GPa) M (GPa) GOC 15 15 OWC WATER SUBSTITUTION 15 GR.. M-Modulus (GPa) G-Modulus (GPa)
Rock Texture Diagnostic by Effective-Medium Models 8 5 Constant Contact Cement Contact Cement M (GPa) G (GPa) 15 GOC Uncemented (Friable) WATER SUBSTITUTION OWC 75 15 GR
GRANULAR ROCK EFFECTIVE-MEDIUM MODELS 5 Velocity- Dry Sandstones - MPa Oseberg Diversity in Sandstones P-Wave Velocity (km/s).1 Troll Ottawa+ Clay Well.. Log. Vs (km/s) 1 QUARTZ Consolidated Suspension Reuss Bound Critical Concept 8 SANDSTONES 5 SANDSTONES M-Modulus (GPa) Shear Modulus (GPa)....8 1 Diagenesis....8 1....8 1 Quartz Sandstone Sand Suspension Frame-Supported Fluid-Supported φ c POROSITY %
Critical -- Two Extreme Examples Solid Fractured Structure Bulk Modulus (GPa) 5 SOLID GLASS Frame-Supported Foam Disintegrated Foam Honeycomb Structure Calcite CHALKS POROUS GRAINS CRACKED IGNEOUS ROCKS....8....8 1....8 1 Compressional Modulus (GPa) 8 Cracked Igneous Rocks with Percolating Cracks Pumice with Honeycomb Structure....8 1 Various Materials Material Critical Sandstones % Limestones % Dolomites % Pumice 8% Chalks 5% Rock Salt % Cracked Igneous Rocks 5% Oceanic Basalts % Sintered Glass Beads % Glass Foam 9% 5
Critical Models and Diagenesis OSEBERG M-Modulus (GPa) Depth m TROLL Marl 5 5 75 GR 5 1 Vs (km/s)..5 RHOB.1. Velocity 5 P-Impedance 8 7 5 Contact Cement Equation Unconsolidated Shale Equation.1
Contact Cement and Diagenesis Well 1 Back-scatter Well 1 Cathodoluminescent Quartz Cement Contact Cement.1 mm P-WAVAE VELOCITY (km/s) Clay Cement CORE DATA SATURATED Non-Contact Cement.. POROSITY 7
Contact Cement Theory Uncemented Grains Cemented Grains CONTACT STRESS NO GRAINS: GLASS : EPOXY Contact Stress X.5.1 x/r EXPERIMENT THEORY Normal Stress SOFT MEDIUM STIFF Soft Cement.1. x/r.1. x/r.1. x/r Stiff Cement 8
Importance of Contact Cement Cemented GLASS BEADS ED GLASS BEADS 8 Uncemented (Percent) 8 Confining Pressure (MPa) LOOSE GLASS BEADS AFTER Why Cement Preserved Grains Normal Stress No....8 1 Coordinate along Cement Layer 9
ARTIFICIAL MATERIALS 5 Upper HS GLASS-EPOXY Contact Cement Examples JC Self-Consistent Compressional Modulus (GPa) 5 Lower DEM Lower HS Contact Cement Model.1 (Void Concentration) Upper HS QUARTZ-ICE QUARTZ CLAY RESERVOIR-RELATED Dry-Rock Vp at MPa (km/s) CONTACT FRIABLE Sleipner Well 1 Log Oseberg Compressional Modulus (GPa) Self-Consistent JC Lower DEM Lower HS..5..5 Troll..5..5 Contact Cement Model.1 (Void Concentration)
Grains without Cement -- Hertz-Mindlin Contact Theory dt df F a F df dt Hertz-Mindlin Contact Solution Contact Stiffness a R = (1 ν) π G C(1 φ) P S n S τ = ag 1 ν = 8aG ν MODIFIED LOWER HASHIN-SHTRIKMAN WITH HERTZ-MINDLIN M-Modulus (GPa) 8 SOLID Increasing Pressure HERTZ- MINDLIN.1 Dry Rock MPa Differential Pressure Dry Rock MPa Differential Pressure Troll Ottawa+Clay Ottawa Near-Wellbore Damage?.5 Vs (km/s) 1.5 11
Modified Lower Hashin-Shtrikman -- Applications Wilmington Field -- Oil Behind Casing.1 Density- (Open Hole) Dipole Sonic (Cased)..5 Depth (ft) 5 Dipole....1.1.5. Density 7 Shallow Sea- Bottom Sediment Depth (mbsf) 8 1 Data This Model Suspension a.5.55..5 Neutron b 1.5 1. 1.7 1.8 P-Wave Velocity (km/s) 1
Appendix -- Elastic Bounds Voigt and Reuss Composite Voigt Reuss M V = f i M i M R = ( N i=1 N i =1 f i M i 1 ) 1 Hashin-Shtrikman 5 5 Hashin-Shtrikman Bounds: Realization Effective Bulk Modulus (GPa) Voigt Reuss 5 Hashin-Shtrikman Effective Shear Modulus (GPa) 5 Voigt 5 Reuss 15 Hashin-Shtrikman....8 1....8 1 Clay Content Clay Content 5 Voigt Reuss Hashin-Shtrikman....8 1 Clay Content N f i [ K i + G ] 1 i =1 min G K min eff [ [ [ N i =1 N i=1 G i + G min G i + G max f i 9K min + 8G min K min + G min f i G eff 9K max + 8G max K max + G max ] 1 N i =1 G min ] 1 G max f i K i + G max ] 1 G max 9K min + 8G min K min + G min 9K max + 8G max K max + G max 1
GP17/1 # Cementation in Well Log Data 5 5 5 WELL LOG DATA WELL LOG DATA WELL LOG DATA COMPRESSSIONAL MODULUS (GPa) COMPRESSSIONAL MODULUS (GPa) COMPRESSSIONAL MODULUS (GPa) LOUISIANA.1 POROSITY NORTH SEA.1 POROSITY NORTH SEA (Heimdal) LOUISIANA.1 POROSITY 1