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# David Lumley - 4D uncertainty - Nov 11, 2015

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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”.

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### David Lumley - 4D uncertainty - Nov 11, 2015

1. 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. 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. 3. 11/11/2015 3 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. 4. 11/11/2015 4 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. 5. 11/11/2015 5 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. 6. 11/11/2015 6 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. 7. 11/11/2015 7 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. 8. 11/11/2015 8 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. 9. 11/11/2015 9 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. 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. 11/11/2015 11 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. 12. 11/11/2015 12 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. 13. 11/11/2015 13 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. 14. 11/11/2015 14 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. 15. 11/11/2015 15 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. 16. 11/11/2015 16 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. 17. 11/11/2015 17 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
18. 18. 11/11/2015 18 david.lumley@uwa.edu.auLumley et al., 2014 Example: low resolution data Gravity data david.lumley@uwa.edu.auLumley et al., 2014 “Mickey Mouse model” Gravity data
19. 19. 11/11/2015 19 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. 20. 11/11/2015 20 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. 21. 11/11/2015 21 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. 22. 11/11/2015 22 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. 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. 24. 11/11/2015 24 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
25. 25. 11/11/2015 25 david.lumley@uwa.edu.auLumley et al., 2014 4D NR Noise T1 T2 T2-T1 david.lumley@uwa.edu.auLumley et al., 2014 4D Repeatability Saul & Lumley, 2013
26. 26. 11/11/2015 26 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. 27. 11/11/2015 27 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. 28. 11/11/2015 28 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. 29. 11/11/2015 29 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…
30. 30. 11/11/2015 30 david.lumley@uwa.edu.auLumley et al., 2014 Reservoir container david.lumley@uwa.edu.auLumley et al., 2014 Reservoir properties
31. 31. 11/11/2015 31 david.lumley@uwa.edu.auLumley et al., 2014 Up/down scaling david.lumley@uwa.edu.auLumley et al., 2014 porosity clay fraction
32. 32. 11/11/2015 32 david.lumley@uwa.edu.auLumley et al., 2014 Rock physics param pdfs david.lumley@uwa.edu.auLumley et al., 2014 Sources of 4D error and uncertainty • Physics (modeling/inversion operators/code) • Linear versus nonlinear • Acoustic, Elastic, Anisotropy, Attenuation… • Convolution, Raytracing, Finite Difference… • Algorithm implementations • Etcetera…
33. 33. 11/11/2015 33 david.lumley@uwa.edu.auLumley et al., 2014 4D FD elastic modeling david.lumley@uwa.edu.auLumley et al., 2014 1 layer CO2 Lumley et al., 2008 synth PSDM
34. 34. 11/11/2015 34 david.lumley@uwa.edu.auLumley et al., 2014 real PSTM 1 layer CO2 StatoilLumley et al., 2008 synth PSDM david.lumley@uwa.edu.auLumley et al., 2014 Sources of 4D error and uncertainty • Optimization criteria (inversion/estimation) • Least squares (L2), Least absolute (L1), hybrid… • Optimal fit to data, amplitude, phase… • Multiple objectives, weighting schemes… • Inversion constraints (soft, hard, weighted…) • Optimization method (gradients, stochastic, MC, PSO, genetic…) • Resolution, Null space, Non-uniqueness… • Etcetera…
35. 35. 11/11/2015 35 david.lumley@uwa.edu.auLumley et al., 2014 Multi-objective optimisation find a reservoir model m such that: min E = (seismic)p + (logs)q + (geology)r + … david.lumley@uwa.edu.auLumley et al., 2014 13.22 13.27 13.32 13.37 13.42 13.47 13.52 13.57 36 41 46 ObjectiveFunction2 Objective Function 1 Generation 1 13.22 13.24 13.26 13.28 13.3 13.32 13.34 13.36 35 36 37 38 39 40 ObjectiveFunction2 Objective Function 1 Generation 10 13.12 13.14 13.16 13.18 13.2 13.22 13.24 13.26 30 32 34 36 38 ObjectiveFunction2 Objective Function 1 Generation 20 13 13.02 13.04 13.06 13.08 13.1 13.12 26 27 28 29 30 ObjectiveFunction2 Objective Function 1 Generation 50 12.96 12.97 12.98 12.99 13 13.01 13.02 13.03 13.04 13.05 13.06 24 25 26 27 28 29 ObjectiveFunction2 Objective Function 1 Generation 70 12.95 12.96 12.97 12.98 12.99 13 13.01 13.02 13.03 13.04 13.05 24 25 26 27 28 ObjectiveFunction2 Objective Function 1 Generation 100 Multi-objective optimization – “Pareto front” 70 Niri & Lumley 2013
36. 36. 11/11/2015 36 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. 37. 11/11/2015 37 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
38. 38. 11/11/2015 38 david.lumley@uwa.edu.auLumley et al., 2014 4D seismic image of water saturation (Sw) a b david.lumley@uwa.edu.auLumley et al., 2014 4D seismic inversion for water saturation (Sw) Sw a b
39. 39. 11/11/2015 39 david.lumley@uwa.edu.auLumley et al., 2014 {Sw} for 1000 realizations a b david.lumley@uwa.edu.auLumley et al., 2014 signal to noise ratio “S/N” of Sw a b
40. 40. 11/11/2015 40 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
41. 41. 11/11/2015 41 david.lumley@uwa.edu.auLumley et al., 2014