Post on 18-Apr-2018
Estimation of saturation and pressure changes from time-lapse seismic data and model re-
parameterization for seismic history matching.
Dario GranaDepartment of Geology and Geophysics University of Wyoming
IOR workshop, 28 April 2016
Seismic reservoir characterization
– 2
• Seismic data S depend on reservoir properties R through elastic properties m
• We can split the inverse problem into two sub-problems:
•
• ff
gg
)(
)(
mR
Sm
))(( SR gf
seismic linearized modeling
rock physics model
Forward model
– 3
Seismic forward model:Wavelet convolution
Linearized Aki-Richards approximation of Zoeppritz equations
Wavelet Reflection coefficients Seismogram
),()( mhrPP
– 4
Bayesian seismic inversion
• The seismic response of a sequence of layers can be then written as:
• At a given time t, the reflections coefficients can be approximated by the three term Shuey approximation
Forward model
– 8
Rock physics forward model:
Granular media models (Hertz-Mindlin contact theory)
P-wave velocity versus effective porosity
sw
cfV
V
RPMS
P
Bayesian petrophysical inversion
Elastic properties
Seismic data)( Sm|P
Gaussian mixture
likelihood
)|( mRP
Rock properties
)( SR|P
(Chapman-Kolmogorov)
Grana and Della Rossa, 2010
Buland and Omre, 2003
– 10
Time-lapse inversion
• In time-lapse reservoir modeling we aim to model reservoir property changes from repeated seismic surveys.
Inverse problem
Time-lapse seismic dataReservoir property changes
(saturation and pressure)
Grana and Mukerji, 2014
Challenges
• Elastic changes introduce time-shifts in the repeated seismic surveys (either we invert amplitudes and travel time or we correct for time-shifts and invert for amplitudes)
• The link between dynamic properties and elastic properties is not direct. Need a RPM to transform pressure and saturation into elastic properties.
• Mapping of data between different grid representations corresponding to the flow simulation, earth model and seismic grid frameworks.
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Example
• Time-lapse seismic changes
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Increase Pp by 100 MPa Before After Difference
Time-
aligned
difference
(Courtesy of G. Mavko)
Methods
• Method 1: to simultaneously invert base and repeated seismic surveys
– 13
(Courtesy of P. Doyen)
Methods
• Method 2: to invert seismic changes (difference in amplitudes)
* We cannot compute the difference directly because horizons of the repeated surveys are not aligned with the base survey. We must apply a warping method first.
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Methods
• 2-step approach
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1. We first estimate
2. We then estimate
3. We combine and using Chapman-Kolmogorov equation
( | ) ( | ) ( )P P P m S S m m
( | ) ( | ) ( )P P P R m m R R
Buland and El Ouair, 2006
( | )P m S ( | )P R m
( | ) ( | ) ( | )m
P P P d
R S R m m S mGrana and Mukerji, 2014
Seismic model
– 16
Seismic forward model:Wavelet convolution
Linearized Aki-Richards approximation of Zoeppritz equations
Wavelet Reflection coefficients Seismogram
),()( mhrPP
Methods for seismic history matching
• Option1: to match production data and time-lapse seismic data
• Option 2: to match production data and inverted seismic velocities (or impedances)
• Option 3: to match production data and inverted pressure and saturation (or a re-parameterization)
(plus several options for the parameterization and for the inverse method)
– 18
– 19
Re-parameterized seismic history matching
Bayesian time-lapse inversion Re-parameterization
Seismic history matching
(ES-MDA)
Synthetic example: waterflooding
– 20
Synthetic reservoir model (modified from Panzeri et al., 2014)
Synthetic example
– 22
• Porosity constant and known
• History matching of 6 years; forecast of 4 years
• Inverted seismic data every 6 months for 6 years (13 surveys)
• Ensemble Smoother MDA (4 assimilations)
– 29
Methodology
• Bayesian time-lapse inversion for pressure and saturation changes
• Re-parameterization of saturation snapshots through POD-DEIM
• History matching of production data and re-parameterized inverted seismic data through ES-MDA
– 30
Re-parameterization
• If we match the seismic data pointwise, we need a large ensemble to avoid ensemble collapse
• We want to avoid to compute CDD
• Issues with resolution, noise, quality of seismic data
– 33
Discrete Empirical Interpolation Method
Chaturantabut and Sorensen, 2010
• The projection basis is given by POD
• The interpolation indices are given by DEIM