1. Uncertainties in quantitative time-lapse seismic analysis by M
Uncertainties in quantitative time-lapse seismic analysis   by   M. Landrø1   1Department of Petroleum Technology and Applied Geophysics, NTNU, 7491 Trondheim, Norway  
FORCE SEMINAR, Stavanger 5th June 2001

2. Outline Introduction Uncertainty estimation
Only fluid saturation changes
Saturation and pressure changes
Conclusions

4. Consider a multidi-variate function S
Then the uncertainty in S is given by
if a,b,c ... are indepent variables

5. ka represents the link between saturation and velocity changes
The curve for velocity versus saturation changes is based upon a calibrated Gassman model. The current curve was calibrated to several wells at the Gullfaks field.
This curve is more linear than the previous curve for pressure changes.
ka represents the link between saturation and velocity changes

6. z The simplest case: Saturation changes within the reservoir layer
a = P-wave velocity
in reservoir layer
Two-way
traveltime:
Pre production
Post production
Relative change in traveltime:
Rock physics input:

7. The simplest case: Saturation changes within the reservoir layer
Uncertainty in saturation estimate based on traveltime information only:

8. Fluid changes only: Uncertainty in estimated saturation
changes from time shift analysis only
DT=4ms ka=0.1
dka=0.05
dDT = 2ms
dDT = 1ms

9. Fluid changes only: Uncertainty in estimated saturation
changes from time shift analysis only
DT=4ms ka=0.1
dDT = 1 ms
dka=0.05
dka=0.01

10. Amplitude and traveltime information independendent parameters?
changes at
top reservoir
(red)
and traveltime
changes at base
reservoir (blue)
- To some extent yes, if top reservoir and base reservoir
events are well separated in depth

11. Estimated pulldown by simple picking of shift in peak amplitude of the
near base Cook reflector
Top Cook
Base Cook
Peak Time Shift: 6.4 ms

12. Traveltime shift estimated by picking max amplitude of base Cook on 85 and 96 datasets - pressure zone shown in black
Outline of overpressured zone based on time-lapse AVO

13. D R0 = Intercept change 0 < j < 1
The simplest case: Saturation changes within the reservoir layer
D R0 = Intercept change
The next step: Using both traveltime and amplitude information (i.e. changes in traveltime and amplitude due to saturation changes)
0 < j < 1
j=1 means only amplitude info used
j=0 means only traveltime info used

14. Fluid changes only: Uncertainty in estimated saturation
changes from time shift and amplitude change analysis
DT = 4ms ka = kq = 0.05
dDT = 1ms DR = dDR = 0.04
traveltime only
dka = dkq = 0.05
dka = dkq = 0.01

15. The simplest case: Saturation changes within the reservoir layer
Uncertainty in saturation change estimate is now given by:
An optimal scaling factor can now be determined by minimizing the uncertainty in DS:

16. DT = 4ms ka = 0.1 kq = 0.05 dDT = 1ms DR = 0.05 dDR = 0.04
Fluid changes only: Optimal scaling factor (j)
j=1 means only amplitude info used
j=0 means only traveltime info used
DT = 4ms ka = kq = 0.05
dDT = 1ms DR = dDR = 0.04
dka = dkq = 0.05
dka = dkq = 0.01

17. Estimated saturation and pressure changes at top Cook interface
OWC
Saturation changes
Pressure changes
- 27% of remaining reserves in this segment has been produced in 1996
- Notice that pressure anomaly crosses the OWC and terminates close to faults
Reference: “Discrimination between pressure and fluid saturation changes from time-lapse seismic data” , M. Landrø, Geophysics May-June 2001
Extension of this work: “Discrimination between pressure and fluid saturation changes from time-lapse multicomponent seismic data” , M. Landrø, H. Veire, K. Duffaut and N. Al-Najjar, submitted for presentation at the SEG 2001 meeting

18. The relation between pore pressure changes and velocity changes
- usually obtained from ultrasonic dry core measurements
This slide shows a typical velocity versus pressure curve based upon ultrasonic core measurements. Notice that a pore pressure increase leads to a reduction in effective stress or pressure, and that the P-wave velocity is more sensitive to pore pressure increases than pore pressure decreases.
The validity of such core measurements are of course questinable, especially for low effective stresses. On the other hand, it is a way to establish a link between seismic parameters and reservoir pressure.
Also notice the non-linear behaviour of this curve.
la represents the link between pressure and velocity changes

19. Comparison with the Hertz-Mindlin model:
- dense pack of identical spheres
- Vp proportional to P**1/6 (EXP=1/6)

20. Pressure and saturation changes
Simplyfied versions of saturation and pressure estimates

21. Fluid and pressure changes: Uncertainties in pressure and
saturation changes versus uncertainty in reflectivity changes
DP = 0.8 MPa
DS = 0.48
Saturation
Pressure
ka = kq = la = 0.035
DR = DG = 0.01
dka = dkq = dla = 0.01
Assumption: Uncertainty in DG ~ DR0

22. Fluid and pressure changes: Uncertainties in pressure and
saturation changes versus uncertainty in reflectivity changes
Pressure
Saturation
DP = -5 MPa
DS = 0.5
ka = kq = la = 0.035
DR = DG = 0.11
dka = dkq = dla = 0.01
Assumption: Uncertainty in DG ~ DR0

23. Uncertainty in DS : 80% Uncertainty in DP : 40%
Combining uncertainty estimates with the estimated maps:
OWC
Saturation changes
Pressure changes
DP = -5 MPa
DS = 0.5
Uncertainty in DS : 80%
Uncertainty in DP : 40%
Saturation
Pressure
Reference: “Discrimination between pressure and fluid saturation changes from time-lapse seismic data” , M. Landrø, Geophysics May-June 2001

24. Conclusions
Simple uncertainty analysis give a quick overview on critical factors in a time-lapse seismic study
Confirms that rock physics input and seismic repeatability are crucial factors
Uncertainty analysis can be used to design optimal mixing of for instance traveltime and amplitude information in a 4D project
Uncertainties (especially when estimating both pressure and saturation changes) are high - but helps to compare uncertainty level between pressure and saturation changes

25. BUT:
- Map views are always important
- Hard to assign uncertainties
- if the next step in 4-D is quantitative mapping of
saturation, pressure, temperature, compaction ....
we need to study uncertainties

26. Acknowledgments The participants in the ATLASS project:
CGG, ENI-AGIP, Norsk Hydro, Shell, Statoil, Delft University and NTNU
EC for financial support
The organizing committe for FORCEing me to give this paper
Abstracts: