1. Upscaling of 4D Seismic Data
Sigurd I. Aanonsen
Centre for Integrated Petroleum Research, University of Bergen, Norway
Acknowledgments to

2. Mapping 4D data to Simulation grid
OUTLINE
Introduction
History-matching with 4D seismic data
Mapping 4D data to Simulation grid
Upscaling
Downscaling
Uncertainty / data covariance
Some conclusions and challenges

3. Conditioning reservoir simulation models to 4D data
INVERSE MODELLING
FORWARD MODELLING
Real seismograms
SEISMIC MODELLING
Simulated Seismic data
MISMATCH ?
SEISMIC PROCESSING
Processed seismic data
ROCK PHYSICS
Elastic properties (Vp, Vs, Impedance, ...)
SEISMIC INVERSION
MISMATCH
Elastic properties (Vp, Vs, Impedance, ...)
ROCK PHYSICS
RESERVOIR SIMULATOR
Pressures, saturations
MISMATCH
Dynamic reservoir properties (pressures, saturations, fluid contacts)
Petrophysical properties (porosity, permeability)
Petrophysical properties (porosity, permeability)
To be determined:

4. The HUTS project (History-Matching Using Time-lapse Seismic)
Petrophysical properties (porosity, permeability)
Dynamic reservoir properties (pressures, saturations, fluid contacts)
ROCK PHYSICS
Elastic properties (Vp, Vs, Impedance, ...)
SEISMIC INVERSION
SEISMIC PROCESSING
INVERSE MODELLING
MISMATCH
Real seismograms
Processed seismic data
RESERVOIR SIMULATOR
Pressures, saturations
FORWARD MODELLING
SEISMIC MODELLING
Simulated Seismic data ?
Petrophysical properties (porosity, permeability)
To be determined:

5. Objective function in 4D history matching
q – model parameters to be determined
p(q) – simulated production data
s(q) – simulated seismic data: Simulator + rock mechanics model
dp – production data
ds – seismic data: Poisson’s ratio, r, and Acoustic Impedance, Zp
CP and CS – covariance matrices (weight matrices)
How should we map the seismic data from seismic grid to simulation grid?
How should we determine the coefficients of this objective function, i.e., uncertainty in the seismic data?
The dimension of Cs may be large
Is it sufficient to use diagonal matrices?

6. Seismic grid vs simulation model grid
Horizontal cell size:
Seismic grid: 25 x 37.5 m
Simulation grid: 100 x 200 m in oil zone
up to 1600 x 200 m in aquifer and
gas cap
Vertical cell size (layer thickness)
Seismic grid: ~ 10 m (4 layers)
Simulation grid: 0.20 m – 26 m (7 layers)

7. Rescaling of Poisson’s ratio
ORIGINAL DATA AVERAGED. FINE GRID
INITIAL GOC
INITIAL WOC
MOVING AVERAGE, 20x20x1
GOC-I
WOC-I
ORIGINAL DATA. FINE GRID
INITIAL WOC
INITIAL GOC
Red:
Increased water
Blue:
Increased
gas
GOC-I
WOC-I
UPSCALED FROM ORIGINAL DATA
UPSCALED FROM AVERAGED DATA
AANONSEN ET AL. (2003) SPE 79665

8. Moving average
In one dimension:
Similarly in 2 and 3 dimensions

9. Poisson’s ratio change
LAYER 10

10. Poisson’s ratio change
LAYER 9

11. Role of the covariances
Difficult to determine covariances from measurement errors.
Is it possible to estimate these from the data itself?
We restrict the estimation to approximately rectangular uniform grids.

12. Seismic data covariance
Covariance of AI (1992)
Covariance of normalized AI (1992) EW NS 50
100 50
100
Distance (no. of cells)
Distance (no. of cells)
Covariance of DPOIS (99-92)
Covariance of normalized DPOIS (99-92) 50
100 50
100
Distance (no. of cells)
Distance (no. of cells)
Correlation length: 200 – 250 m

13. Effect of data correlations PUNQ-S3 case
Generated synthetic seismic data with correlated noise. Two regressions:
Case 1: Correct (non-diagonal) covariance matrix
Case 2: Diagonal matrix (correlations neglected)
Convergences to the wrong solution if correlations are neglected

14. Upscaling of covariance
Arithmetic average:
(1)
(2)

15. Upscaling of covariance
Horizontal upscaling:
Upscale standard deviation in RMS (arithmetic average)
Use Eq. (2) to calculate a modification factor for each value of dx
I-index 1 2
3-4 ; 37-38
5-6 ; 35-36
7-34 39 dx
1600
800
400
200
100
1000 Nx 64 32 16 8 4 40
SD/<SD>
0.24
0.33
0.44
0.55
0.64
0.29
1/SQRT(NxNy)
0.06
0.08
0.11
0.16
0.22
0.07

16. Upscaling of covariance
Vertical upscaling:
Downscale to min thickness using the equation for variance of averaged quantity (Eq(2)).
Upscale again to wanted thickness using the same equation.
The result is a mapping of covariance for any thickness combination.
Seismic grid
Simulation grid
4 layers
Approximately constant thickness,
dz ~ 10 m
7 layers
Highly varying thickness both laterally and vertically
dz min = 0.20 m; dzmax = 26 m

17. Rescaling of Poisson’s ratio Summary
ORIGINAL DATA AVERAGED. FINE GRID
INITIAL GOC
INITIAL WOC
MOVING AVERAGE, 20x20x1
GOC-I
WOC-I
ORIGINAL DATA. FINE GRID
INITIAL WOC
INITIAL GOC
Red:
Increased water
Blue:
Increased
gas
GOC-I
WOC-I
Remove noice in seismic data using moving average
Map the averaged data from seismic grid to simulation grid using RMS (arithmetic average and sampling)
Estimate data covariance matrix (uncertainty and correlations) on the fine grid from the noise, i.e., the difference between original data and averaged data. Need to account for non-stationarity.
Upscale covariance matrix from seismic grid grid to simulation grid

18. Poisson’s ratio change (1999-1992) Bottom layer
INITIAL GOC
INITIAL WOC
DATA
SIMULATED USING BASE CASE MODEL

19. Poisson’s ratio change (1999-1992) Bottom layer
ORIGINAL DATA. FINE GRID
DATA UPSCALED TO SIMULATION GRID
SIMULATED DATA BEFORE HISTORY MATCHING
INITIAL WOC
INITIAL GOC

20. Poisson’s ratio change (1999-1992) Bottom layer
SIMULATED DATA BEFORE HISTORY MATCHING
INITIAL WOC
BEST MODEL
OBTAINED BY MANUALLY CHANGING PERMEABILITIES
MEASURED DATA

21. Poisson’s ratio change

22. Measured vs Simulated DPOIS (top simulation layer)

23. Some conclusions from history-matching runs
Managed to get significant reduction in objective function, but not enough to be fully satified.
Adding seismic data did not improve production data match, which was already very good, but hopefully a more correct solution is obtained.
History-matching using only seismic data destroyed production data match.

24. History Matching with 4D Data Main Challenges
Scaling issues:
Low vertical resolution in seismic data combined with very variable resolution in simulated data
High areal resolution of seismic data
Current geomodelling techniques not flexible enough to capture variations seen in the seismic.
Handling of uncertainties in seismic data:
How to handle large uncertainty in absolute values of inverted data?
Rock mechanics modelling:
Large differences between absolute values of simulated and inverted elastic parameters