1. 4D Gravity Inversion Hyoungrea Bernard Rim
Korea Institute of Geoscience and Mineral Resources (KIGAM)
Gravity Workshop in KRISS
December 1, 2016

2. Outline Background Formulation 4D gravity inversion Numerical examples
Application to fluid fronts
Two different model objective functions
Numerical examples
compare single-time versus 4D inversion
compare single-component versus vector gravity
Summary

3. Time-Lapse Gravity Monitoring
Mimic Prudhoe Bay, GCWI
Δρ = 0.12 g/cm3
Year 2
Year 5
Year 10
Year 15
Year 20
Brady et al, 2002
(Krahenbuhl et al. 2013)

4. Research question:
How should the multiple sets of time-lapse data be interpreted coherently?

5. Separate single-time inversions
Layer-density distribution (e.g., Hare et al, 2008)
Binary inversion (e.g., Krahenbuhl & Li, 2012)
FCM inversion (Maag, 2014)
4D inversion for density change with time
4D inversion for reservoir properties
Capriotti (2013)
4D inversion for fluid front

6. Vector gravity: synthetic examples
Expanding plumes
Simulate vector gravity due to expanding plumes

7. Expanding plumes Injection vertical borehole 500 m expanding plumes
discrete representation with cubes

8. Expanding plumes
vertical borehole
Injection
500 m
expanding plumes

9. Statement of problem Data: borehole gravity at multiple times
Model: fluid fronts at corresponding times
Known top and bottom of the reservoir
Known density contrast due to fluid substitution

10. Model representation Distance from a reference point
Function of azimuth angle

11. Inversion Regularized approach Data misfit
Two different model objective functions

12. Model objective function-1
Generic regularization over azimuth and time

13. Model objective function-2
Regularization over arc length and time

14. synthetic example

15. Single-hole
Single-time inversions

16. Single-hole
4D inversion

17. Data comparison Time-1 Time-2 Time-3 Time-4 observed single-time inv
4D inv

18. Vertical- components
gravity
3-component
gravity

19. Data comparison (3-component data) Time-1 Time-2 Time-3 Time-4 gx gygz

20. Comparison of model objective functions
Time-3
Time-4
Model obj. function-1
Model obj. function-2:
Better accommodates rapid changes

21. Data comparison - 3 wells - vertical component Time-1 Time-2 Time-3
observed

22. Time-lapse vector gravity Prudhoe Bay

23. Time-lapse gravity inversion
vertical
gravity only
vector
gravity
3 monitoring
wells
4 monitoring
wells

24. Summary 4D gravity inversion for fluid front
Better performance than single-time inversions
Arc length-based model objective function better suited for detecting rapid change in the fluid front
Vector gravity

25. Work ahead
Efficient modeling for reservoir with variable thickness and depth
Consistent data misfit as a function of time
Choice of time-dependent weighting coefficients
Refine algorithm with field data

26. Thank You!