Prof. David Lumley from the Centre of Energy Geoscience at the Uni. Of Western Australia presents his work on “Nonlinear Uncertainty Analysis: 4D Seismic reservoir monitoring”.
STERILITY TESTING OF PHARMACEUTICALS ppt by DR.C.P.PRINCE
David Lumley - 4D uncertainty - Nov 11, 2015
1. 11/11/2015
1
david.lumley@uwa.edu.auLumley et al., 2014
Nonlinear Uncertainty Analysis:
4D Seismic reservoir monitoring
Prof David Lumley
+ various colleagues and students over the years...
UWA School of Physics; School of Earth & Environment
david.lumley@uwa.edu.auLumley et al., 2014
Outline
• Define “4D”
• Examples of 4D seismic
• Define “uncertainty”
• Nonlinear uncertainty analysis + examples
2. 11/11/2015
2
david.lumley@uwa.edu.auLumley et al., 2014
Outline
• Define “4D”
• Examples of 4D seismic
• Define “uncertainty”
• Nonlinear uncertainty analysis + examples
david.lumley@uwa.edu.auLumley et al., 2014
Geophysics definition of “4D”
1D = f(x1): eg. well logs f(z)
f =
porosity, clay content, age
facies, velocity, density…
3. 11/11/2015
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david.lumley@uwa.edu.auLumley et al., 2014
Geophysics definition of “4D”
2D = f(x1,x2): eg. maps, cross-sections (x,z)
f =
porosity, clay content, age
structural depth, facies,
reflectivity…
Lumley et al.
david.lumley@uwa.edu.auLumley et al., 2014
Geophysics definition of “4D”
3D = f(x,y,z): volumes (x,y,z)
f =
porosity, clay content, age
velocity, reflectivity…
Niri & Lumley, 2013
4. 11/11/2015
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david.lumley@uwa.edu.auLumley et al., 2014
Geophysics definition of “4D”
4D = f(x,y,z,t): hyper-cubes (x,y,z,t)
f =
porosity, clay content, age
velocity, reflectivity…
Lumley, 1995
david.lumley@uwa.edu.auLumley et al., 2014
Outline
• Define “4D”
• Examples of 4D seismic
• Define “uncertainty”
• Nonlinear uncertainty analysis + examples
5. 11/11/2015
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david.lumley@uwa.edu.auLumley et al., 2014
Rock properties can change over time
with fluids, stress, temperature etc…
Duffaut et al.2011
david.lumley@uwa.edu.auLumley et al., 2014
Seismic Image – 2D cross-section
Lumley
6. 11/11/2015
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david.lumley@uwa.edu.auLumley et al., 2014
Seismic Image – zoom on reservoirs
OWC
Lumley
david.lumley@uwa.edu.auLumley et al., 2014
TIME 1 amplitude map
extracted along top of reservoir structure
Lumley et al., 2003
7. 11/11/2015
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david.lumley@uwa.edu.auLumley et al., 2014
TIME 2 amplitude map
extracted along top of reservoir structure
Lumley et al., 2003
david.lumley@uwa.edu.auLumley et al., 2014
4D amplitude difference map
extracted along top of reservoir structure
Lumley et al., 2003
8. 11/11/2015
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david.lumley@uwa.edu.auLumley et al., 2014
4D Monitoring of Steam Injectors
Sigit et al., 1999
steam costs > $2 MM / day
david.lumley@uwa.edu.auLumley et al., 2014
Before… After!
courtesy of Statoil
Monitoring Injection
9. 11/11/2015
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david.lumley@uwa.edu.auLumley et al., 2014
Injection Pressure Anomaly
Before After
Lumley et al., 2003Lumley et al.
david.lumley@uwa.edu.auLumley et al., 2014
Permanent Array 4D example
Map of amplitude
changes
Map of compaction
2003 2004 2005 200820072006
LoFS Survey
Timeline
1 2 3 4 5 6 7 8 9 1
0
Map of amplitude
changes
Map of compaction
2003 2004 2005 200820072006
LoFS Survey
Timeline
1 2 3 4 5 6 7 8 9 1
0
Map of amplitude
changes
Map of compaction
2003 2004 2005 200820072006
LoFS Survey
Timeline
1 2 3 4 5 6 7 8 9 1
0
Map of amplitude
changes
Map of compaction
2003 2004 2005 200820072006
LoFS Survey
Timeline
1 2 3 4 5 6 7 8 9 1
0
Map of amplitude
changes
Map of compaction
2003 2004 2005 200820072006
LoFS Survey
Timeline
1 2 3 4 5 6 7 8 9 1
0
Map of amplitude
changes
Map of compaction
2003 2004 2005 200820072006
LoFS Survey
Timeline
1 2 3 4 5 6 7 8 9 1
0
Map of amplitude
changes
Map of compaction
2003 2004 2005 200820072006
LoFS Survey
Timeline
1 2 3 4 5 6 7 8 9 1
0
Map of amplitude
changes
Map of compaction
2003 2004 2005 200820072006
LoFS Survey
Timeline
1 2 3 4 5 6 7 8 9 1
0
Map of amplitude changes Map of compaction
2003 2004 2005 200820072006
LoFS Survey
Timeline
1 2 3 4 5 6 7 8 9 10
10. 11/11/2015
10
david.lumley@uwa.edu.auLumley et al., 2014
Outline
• Define “4D”
• Examples of 4D seismic
• Define “uncertainty”
• Nonlinear uncertainty analysis + examples
david.lumley@uwa.edu.auLumley et al., 2014
errors vs. uncertainty
input output
A B
transform
11. 11/11/2015
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david.lumley@uwa.edu.auLumley et al., 2014
errors vs. uncertainty
various data results
A B
workflow
david.lumley@uwa.edu.auLumley et al., 2014
errors vs. uncertainty
earth model simulated data
A B
Forward modeling… F
12. 11/11/2015
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david.lumley@uwa.edu.auLumley et al., 2014
errors vs. uncertainty
geophysics data image of the earth
A B
Imaging… F*
david.lumley@uwa.edu.auLumley et al., 2014
errors vs. uncertainty
geophysics data earth model
A B
Inversion… F-1
13. 11/11/2015
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david.lumley@uwa.edu.auLumley et al., 2014
errors vs. uncertainty
geophysics data earth model
Inversion… F-1
A + errors B + ???
david.lumley@uwa.edu.auLumley et al., 2014
errors vs. uncertainty
geophysics data earth model
Inversion… F-1
A + errors B + uncertainty!
14. 11/11/2015
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david.lumley@uwa.edu.auLumley et al., 2014
errors vs. uncertainty
model simulated data
A + errors B + ???
Forward modeling… F
david.lumley@uwa.edu.auLumley et al., 2014
errors vs. uncertainty
model simulated data
A + errors B + uncertainty!
Forward modeling… F
15. 11/11/2015
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david.lumley@uwa.edu.auLumley et al., 2014
Errors Uncertainty
Domain 1 Domain 2
A Definition of “uncertainty”
david.lumley@uwa.edu.auLumley et al., 2014
Forward Modeling
Model space Data space
m d
F
16. 11/11/2015
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david.lumley@uwa.edu.auLumley et al., 2014
Model space
+ errors
Data space
+ uncertainty
m + d +
F +
Forward Modeling
david.lumley@uwa.edu.auLumley et al., 2014
Model space
+ errors
Data space
+ uncertainty
m +
dmod +
F +
dobs +
Forward Modeling
17. 11/11/2015
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david.lumley@uwa.edu.auLumley et al., 2014
* You may have the right model, but it may not fit the data!
* You may have the wrong model, but it may fit the data!
Model space
+ errors
Data space
+ uncertainty
m +
dmod +
F +
dobs +
david.lumley@uwa.edu.auLumley et al., 2014
Non-uniqueness, null space…
Model “null” space Data space
m + m’ d +
F(m’)≈ 0
19. 11/11/2015
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david.lumley@uwa.edu.auLumley et al., 2014
Model “null” space Data space
m + imi’ d +
F(m’)≈ 0
* There are infinitely many models that fit the data!
david.lumley@uwa.edu.auLumley et al., 2014
Uncertainty ≠ Non-uniqueness
20. 11/11/2015
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david.lumley@uwa.edu.auLumley et al., 2014
Inversion …imaging, estimation
Model space Data space
F-1
m d
david.lumley@uwa.edu.auLumley et al., 2014
Inversion …imaging, estimation
Model space
+ uncertainty
Data space
+ errors
F-1 +
m + d +
21. 11/11/2015
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david.lumley@uwa.edu.auLumley et al., 2014
Inversion …imaging, estimation
Model space
+ uncertainty
+ non-uniqueness
Data space
+ errors
F-1 +
m + + m’ d +
david.lumley@uwa.edu.auLumley et al., 2014
Inversion …imaging, estimation
Model space
+ uncertainty
+ non-uniqueness
* Regularization *
* Model-shaping *
Data space
+ errors
F-1 +
m + + imi’ d +
22. 11/11/2015
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david.lumley@uwa.edu.auLumley et al., 2014
“Mickey Mouse model”
Gravity data
david.lumley@uwa.edu.auLumley et al., 2014
Outline
• Define “4D”
• Examples of 4D seismic
• Define “uncertainty”
• Nonlinear uncertainty analysis + examples
23. 11/11/2015
23
david.lumley@uwa.edu.auLumley et al., 2014
“Closing the loop… history matching”
Observed
Data; t++
Inversion
Estimated
model; t++
Simulation
Predicted
data
david.lumley@uwa.edu.auLumley et al., 2014
4D amplitude difference map
extracted along top of reservoir structure
Lumley et al., 2003
24. 11/11/2015
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david.lumley@uwa.edu.auLumley et al., 2014
Sources of 4D error and uncertainty
• 4D Seismic data errors
• Non-repeatable noise
• Source-receiver positioning errors
• Changes in the water column / near-surface / overburden
• Changes in acquisition geometry
• Changes in source-receiver characteristics
• Non 4D-compliant processing flow
• Etcetera…
david.lumley@uwa.edu.auLumley et al., 2014
3D Noise
data = “signal” + noise
26. 11/11/2015
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david.lumley@uwa.edu.auLumley et al., 2014
after Landro
4D NRMS vs. position error
david.lumley@uwa.edu.auLumley et al., 2014
image image difference
Image difference
after 40-60 cm tidal
corrections
Eiken et al., EAGE 1999
4D tidal corrections
27. 11/11/2015
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david.lumley@uwa.edu.auLumley et al., 2014
Line A: before the platform Line B: after the platform
with Petrobras
david.lumley@uwa.edu.auLumley et al., 2014
“Statistical” image processing
Baseline Monitor Difference
Lumley et al., SEG, 1998
28. 11/11/2015
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david.lumley@uwa.edu.auLumley et al., 2014
Lumley et al., SEG, 1998
Baseline Monitor Difference
“Physics-based” image processing
david.lumley@uwa.edu.auLumley et al., 2014
1999 Local Diff Global Diff
?
4D Local vs. Global optimization
Lumley et al. 2003
29. 11/11/2015
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david.lumley@uwa.edu.auLumley et al., 2014
Local image difference Global image difference
CO2 injectors?
Lumley et al. 2003
4D Local vs. Global Optimization
david.lumley@uwa.edu.auLumley et al., 2014
Sources of 4D error and uncertainty
• Model definition
• Model parameterization (acoustic, elastic, aniso, attenuation…)
• Physical property relationships (velocity-pressure…)
• Model discretization/sampling (fine, coarse, up/down-scale…)
• Model relationships (geology, seismic, fluid flow…)
• Etcetera…
36. 11/11/2015
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david.lumley@uwa.edu.auLumley et al., 2014
a) Reference Litho-facies model
b) Before MO model updating c) After MO model updating
Average Mismatch error reduced from 36.5% to 14.6%
Multi-objective optimization – “Pareto front”
Niri & Lumley 2013
david.lumley@uwa.edu.auLumley et al., 2014
How to quantify 4D errors + uncertainty?
37. 11/11/2015
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david.lumley@uwa.edu.auLumley et al., 2014
How to quantify 4D errors + uncertainty?
>> Nonlinear stochastic error propagation
david.lumley@uwa.edu.auLumley et al., 2014
d1 d2 p
N=1000 realizations
Sw Pp
4D inversion
statistics
N=1000
40. 11/11/2015
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david.lumley@uwa.edu.auLumley et al., 2014
Probability that Sw > 0.5
a
b
david.lumley@uwa.edu.auLumley et al., 2014
“Closing the loop… history matching”
Observed
Data; t++
Inversion
Estimated
model; t++
Simulation
Predicted
data