Estimation of Porosity and Permeability from 4D-Seismic and Production Data

1. Estimation of Porosity and Permeability from 4D-Seismic and Production Data Using Principal Component Analysis Smart Fields Seminar Stanford University July 31, 2008

2. Outline • The Norne Field • The history matching problem • Integrating production and seismic data • The optimization problem • Principal Component Analysis • Results • Conclusions

3. Norne field • Discovered at 1991 • Size: 9 * 3 Km with 110 m oil and 75 m gas column • Seismic Survey: • Base: 1991 (Conventional) • 1th: July 2001 Q-Marine survey • 2th: August 2003 Q-Marine survey • 3th: August 2004 Q-Marine survey • 4th: August 2006 Q-Marine survey • 5th: July 2008 Q-Marine survey

4. Norne Simulation Model E • Model is redesigned based on 2004 geo model • 46 x 122 x 22, DX & DY~ 80-100 m • 46 development wells which only 22 are available • 15 producer • 8 injector D G C

5. Survey Difference 2003 - 2001 well CHT2

6. Semi Synthetic Model injector producer Permeability Porosity

7. Outline • The Norne Field • The history matching problem • Integrating production and seismic data • The optimization problem • Principal Component Analysis • Results • Conclusions

8. Inversion process Initial Guess (d) Response of the system M(θ*) Forward Modeling OPTIMIZATION min || M(θ)- M(θ*)|| Predicted parameters (K,Φ)

9. Outline • The Norne Field • The history matching problem • Integrating production and seismic data • The optimization problem • Principal Component Analysis • Results • Conclusions

10. Time-Lapse Seismic Data BASE MONITOR MONITOR-BASE

11. Am= f(X,∆V,∆ρ) (∆V,∆ρ)= f(T,Sf,P,C) X = Acquisition effects T = Temperature Sf = Fluid Saturation P = Pressure/Stress C = Compaction Assumptions: • No temperature variation • No Compaction Adding 4D seismic data Am Time(sec) • Variations in S and P affect 4D Am • Variations in K and  affect S and P • Variations in K and  affect 4D Am

12. Adding 4D seismic data Real 4D Seismic Processed 4D Seismic Real Production Data Sim. Production Data Sim Seismic Data Processing Match Petro Elastic model Reservoir Properties Flow Simulation ΔS, ΔP

13. Forward Models Used Production • Fluid Flow Simulation (Eclipse 100) Seismic • Petro Elastic Model • Gassmann’s equation (Saturation) • Hertz Mindlin Model (Pressure) • Forward seismic Modeling (Matrix propagation techniques)

14. Outline • The Norne Field • The history matching problem • Integrating production and seismic data • The optimization problem • Principal Component Analysis • Results • Conclusions

15. Objective Function Observed Data Production Seismic

16. Bound Constraints Geological bound Constraints

17. Bound Constraints

18. Four Optimization Strategies √ √ √ √ √ √ √ √ √ √ * production data is added after 15 iterations

19. All Strategies Reduce Cost Function P SZG ALT SZG+P

20. Production Matching WOPR WBHPI WBHPP WWPR

21. 4D Seismic Matching Zero Offset Amplitude Mismatch AVO Gradients Mismatch 121% 140% 20% 20%

22. Estimated Porosity/Permeability

23. Estimated Porosity/Permeability Φ K Real Real Estimated Estimated

24. Estimated Porosity/Permeability porosity error permeability error

25. Outline • The Norne Field • The history matching problem • Integrating production and seismic data • The optimization problem • Principal Component Analysis • Results • Conclusions

26. Motivation for PCA • reduce CPU time • have a geologically acceptable estimate CPU-TIME=Number of forward Simulation x Number of Iterations expected

27. Principal Component Analysis • Orthogonal linear transformation • Other names: • Karhunen-Loeve Transform (KLT) • Proper Orthogonal Decomposition (POD) • Hotelling Transform • Involves eigenvalue decomposition / singular value decomposition of a covariance matrix • Application: • reduces dimension in multidimensional data sets • Introduces naturally geologic constraints

28. Principal Component Analysis • Interpretation as data compression orthonormal with and so that is maximized from D. Echeverria Ciaurri et al. 2008

29. Porosity Realizations • Matrix Approach: when size of the problem is huge • Turning Ban: has artifacts andconditioning to local data is difficult • Fractals: conditioning to local data is difficult • Annealing: recommended for permeability • Sequential Gaussian Simulation

30. Available Statistical Data • Log porosity of the wells • Permeability-porosity relation • Porosity distribution variogram

31. Sequential Gaussian Simulation • All conditional distribution is Gaussian and the mean and variance is given by kriging. Procedure • Transform data to normal scores • Establish grid network and coordinate system • Compute the variogram corresponding to available well data • Simulate realization by ordinary kriging which is conditioned to • variogram • local well data • … • Back transform all values

32. Realizations Porosity #1 Porosity #2 Porosity #3 Permeability #1 Permeability #2 Permeability #3

33. Effect of PCA (Porosity) Original 200 components Normalized variance 100 components 50 components Number of components

34. Effect of PCA (Permeability) Original 200 components Normalized variance 100 components 50 components Number of components

35. Optimization strategies using PCA PCA-STG1 PCA-STG2 i Optimization loop Optimization loop Iteration loop Iteration loop

36. Outline • The Norne Field • The history matching problem • Integrating production and seismic data • The optimization problem • Principal Component Analysis • Results • Conclusions

37. Cost Function

38. Estimated Porosity/Permeability

39. Estimated Porosity real porosity estimated porosity NOT-PCA estimated porosity PCA-STG1 estimated porosity PCA-STG2

40. Estimated Permeability estimated permeability NOT-PCA real permeability estimated permeability PCA-STG1 estimated permeability PCA-STG2

41. Outline • The Norne Field • The history matching problem • Integrating production and seismic data • The optimization problem • Principal Component Analysis • Results • Conclusions

42. Conclusions • Adding 4D seismic to production data yields a better history match • If geologic constraints are not considered, the matched solutions might not be geologically realistic • If numerical gradients are used in the history matching, the computational load can be prohibitive for practical applications

43. Conclusions • By Principal Component Analysis (PCA) we can speed up the gradient-based optimization considerably and at the same time take into account geologicconstraints • The good results obtained with this PCA-based technique in a semi synthetic case from the Norne field encourage to apply to the history matching of the complete field

44. Future Work • Apply PCA-based optimization to the complete field • Use distributed computing in gradient approximation • Test alternative optimization algorithms • Study efficient methods (adjoints) for gradient computation • Extension of PCA to Kernel PCA

45. Acknowledgements Stanford NTNU NFR • STATOIL for permission to use the reservoir model • Schlumberger-GeoQuest for the use of the Eclipse simulator. • Alexey Stovas (NTNU) for the seismic forward modeling • Jan Ivar Jensen (NTNU) For assistance

46. Thank You!

47. Estimation of Porosity and Permeability from 4D-Seismic and Production Data Using Principal Component Analysis Smart Fields Seminar Stanford University July 31, 2008