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

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

3. 4D Time-shift Prediction Method 1.Geomechanical modeling ∙Geertsma’s analytical model 2.Rock-physical modeling ∙Dilation parameter 3.Seismic modeling ∙Ray Tracing Geomechanical modeling Rock-physical modeling Synthetic seismic modeling σ,εσ,ε V p, V s, ρ ΔPΔP

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

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

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

10. Displacement – Rigid Layer Resultant system Geertsma + 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 Layer Dilation Factor Overburden4 Reservoir3.4 Underburden8.5 Hard rock layer10

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

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