Upscaling of 4D Seismic Data

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Upscaling of 4D Seismic Data

• Sigurd I. Aanonsen
• Centre for Integrated Petroleum Research,
  University of Bergen, Norway

Acknowledgments to
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OUTLINE

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

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Conditioning reservoir simulation models to 4D
data
INVERSE MODELLING
FORWARD MODELLING


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The HUTS project(History-Matching Using
Time-lapse Seismic)

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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 Poissons 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?

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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)

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Rescaling of Poissons ratio
AANONSEN ET AL. (2003) SPE 79665
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Moving average

• In one dimension
• Similarly in 2 and 3 dimensions

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Poissons ratio change
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Poissons ratio change
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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.

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Seismic data covariance
Covariance of AI (1992)
Covariance of normalized AI (1992)
EW
NS
100
50
50
100
Distance (no. of cells)
Distance (no. of cells)
Covariance of DPOIS (99-92)
Covariance of normalized DPOIS (99-92)
100
50
100
50
Distance (no. of cells)
Distance (no. of cells)
Correlation length 200 250 m
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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
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Upscaling of covariance
Arithmetic average
(1)
(2)
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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

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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
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Rescaling of Poissons ratio Summary

• 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

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Poissons ratio change (1999-1992) Bottom layer
INITIAL WOC
INITIAL GOC
DATA
SIMULATED USING BASE CASE MODEL
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Poissons ratio change (1999-1992) Bottom layer
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Poissons ratio change (1999-1992) Bottom layer
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Poissons ratio change
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Measured vs Simulated DPOIS (top simulation layer)
MEASURED
SIMULATED
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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.

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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