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Estimation of Porosity and Permeability from 4D-Seismic and Production Data Using Principal Component Analysis

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Estimation of Porosity and Permeability from 4D-Seismic and Production Data Using Principal Component Analysis

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Presentation Transcript

    1. 1

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

    3. 3 Norne field

    4. 4 Norne Simulation Model 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

    5. 5 Survey Difference 2003 - 2001

    6. 6 Semi Synthetic Model

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

    8. 8 Inversion process

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

    10. 10 Time-Lapse Seismic Data

    11. 11 Adding 4D seismic data

    12. 12 Adding 4D seismic data

    13. 13 Forward Models Used

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

    15. 15 Objective Function

    16. 16 Bound Constraints

    17. 17 Bound Constraints

    18. 18 Four Optimization Strategies

    19. 19

    20. 20 Production Matching

    21. 21 4D Seismic Matching

    22. 22 Estimated Porosity/Permeability

    23. 23 Estimated Porosity/Permeability

    24. 24 Estimated Porosity/Permeability

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

    26. 26 Motivation for PCA reduce CPU time have a geologically acceptable estimate

    27. 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. 28 Principal Component Analysis

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

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

    31. 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. 32 Realizations

    33. 33 Effect of PCA (Porosity)

    34. 34 Effect of PCA (Permeability)

    35. 35 Optimization strategies using PCA PCA-STG1

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

    37. 37 Cost Function

    38. 38 Estimated Porosity/Permeability

    39. 39 Estimated Porosity

    40. 40 Estimated Permeability

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

    42. 42 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 Conclusions

    43. 43 By Principal Component Analysis (PCA) we can speed up the gradient-based optimization considerably and at the same time take into account geologic constraints 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 Conclusions

    44. 44 Future Work

    45. 45 Acknowledgements

    46. 46 Thank You!

    47. 47

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