Effects on Time-lapse Seismic of a Hard Rock Layer beneath a Compacting Reservoir

1. Effects on Time-lapse Seismic of a Hard Rock Layer beneath a Compacting Reservoir Pamela Tempone Supervision: Martin Landrø & Erling Fjær

2. Vertical Displacement [m] Production Reservoir ΔP (ΔS, ΔV, Δφ, Δρ, etc.) Subsidence Compaction Reservoir + Surrounding Δσ, Δε Compacting reservoir Depth [Km] Changes in rock properties Reservoir + Surrounding ΔVp, Δ Vs, Δρ Time-shift in 4D seismic survey Distance [m] Problem Statement

3. Geomechanical modeling σ,ε Rock-physical modeling Vp, Vs, ρ Synthetic seismic modeling 4D Time-shift Prediction Method • Geomechanical modeling • Geertsma’s analytical model • Rock-physical modeling • Dilation parameter • Seismic modeling • Ray Tracing ΔP

4. 4D Seismic Data vs Synthetic Shearwater field (Staples et al, 2007)

5. Objective • Cause: hard rock layer beneath the compacting reservoir • Tool for capturing the strong time-shifts in the underburden • Extension to Geertsma’s analytical solution Shearwater field (Staples et al, 2007)

6. Method • Analytical solution: superposition of 3 linear systems; • Additivity property of the resultant system; • Model assumption: • Zero stress at free surface; • Zero displacement at z=K; • Linear elastic medium; • Homogeneous medium; • Uniform deformation properties;

7. Underburden = Nucleus of strain Displacement due to a Nucleus System 1+2 is equivalent to Geertsma’s solution

8. 2D modelCompacting reservoir Velocity model Additivity property of the analytical solution

9. Displacement Fields System 3 Effect of the rigid layer System 1+2 Geertsma’s model

10. Displacement – Rigid Layer Resultant systemGeertsma + Hard Rock Layer Vertical displacement

11. Strain Field Numerical solution for the strain: Reservoir Focus on the vertical strain

12. Vertical Strain System 1+2 Geertsma’s model Resultant system 1+2+3 Geertsma + Hard Rock Layer

13. Velocity Changes: Dilation Parameter • Change in relative seismic travel time for a single layer of thickness z (Landrø 2004): • Linear dependence of elastic wave velocities on strain (Hatchell 2005). • Lateral velocity changes

14. Changes in P-wave velocity System 1+2 Geertsma’s model Resultant system 1+2+3 Geertsma + Hard Rock Layer Horizontal position [m] Horizontal position [m]

15. Synthetic Seismic Modeling • Assuming reflector at each discretization point • Zero-offset TWT-shift is computed as follows: Hard Rock Layer Geertsma’s model

16. Time-shifts Synthetic System 1+2 – Geertsma’s model Resultant system 1+2+3 – Geertsma + Hard Rock Layer Horizontal position [m] Horizontal position [m]

17. Synthetics vs Real Data • Semi-analytical models: • Geertsma’s solution (Green) • Extension to Geertsma’s solution (Blu) Shearwater field (Staples et al, 2007) Time-shift

18. Discussions • Linear elastic medium • Homogeneous medium • Uniform deformation properties • Horizontal layer • Horizontal displacement • R factor has limitations • No layer in the overburden • Information from amplitude Geomechanics Rock physics Syntetic Seismic

19. Conclusions I Rigid layer causes: • An increase of the subsidence • An increase in the stretching between the bottom reservoir and the rigid layer • A decrease in time-shift under the reservoir Geertsma’s solution does not capture the strain field due to the stiff layer in the underburden. The increase of the time-shift along the overburden can be captured manipulating the R factor.

20. Conclusions II The extension to Geertsma’s model is: • A tool for improving seismic time-lapse time-shift interpretation • A key for interpreting the sudden time-shift reduction in the underburden • Narrowing the gap between real data and synthetic modeling

21. Future work • Geomechanics: • Extension to dipping reservoir and dipping rigid layer • Analytical methods vs Finite Element Method (FEM) • Synthetic seismic: FD modeling (TIGER) • Analysis of a real data set (Field in North Sea)

22. PETROMAX Acknowledgments