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Bayesian inversion of time-lapse seismic data for porosity, pressure and saturation changes

Annual Meeting 2013. Stanford Center for Reservoir Forecasting. Bayesian inversion of time-lapse seismic data for porosity, pressure and saturation changes. Dario Grana, Tapan Mukerji. Introduction. In time-lapse studies we aim to estimate pressure and saturation changes.

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Bayesian inversion of time-lapse seismic data for porosity, pressure and saturation changes

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  1. Annual Meeting 2013 Stanford Center for Reservoir Forecasting Bayesian inversion of time-lapseseismic data for porosity, pressure and saturation changes Dario Grana, Tapan Mukerji

  2. Introduction • In time-lapse studies we aim to estimate pressure and saturation changes • Changes in dynamic properties can be measured from well/lab data. The main source of information are time-lapse seismic data. Time-lapse seismic data Dynamic property changes Inverse problem SCRF 2013

  3. Motivation • Inverted data can be used in seismic history matching to improve the reservoir description • The probabilistic approach allows to quantify the uncertainty in predicted data SCRF 2013

  4. Introduction • In pressure-saturation estimation the physical model is not linear and the dynamic property changes are not normally distributed. • Changes in dynamic properties are not independent of initial rock properties (static reservoir model) SCRF 2013

  5. Bayesian inversion • We propose a Bayesian approach for the simultaneous estimation of porosity jointly with pressure and saturation changes from time-lapse seismic data. SCRF 2013

  6. Bayesian inversion • We propose a Bayesian approach for the simultaneous estimation of porosity jointly with pressure and saturation changes from time-lapse seismic data. SCRF 2013

  7. Bayesian inversion • We propose a Bayesian approach for the simultaneous estimation of porosity jointly with pressure and saturation changes from time-lapse seismic data. Seismic data, Changes in seismic data Elastic properties, Changes in elastic properties (velocities or impedances) Reservoir properties (porosity) Changes in dynamic properties (saturation and pressure) SCRF 2013

  8. Bayesian inversion • Seismic data Sdepend on reservoir properties R through elastic properties m • We can split the inverse problem into two sub-problems: seismic linearized modeling rock physics model SCRF 2013

  9. Physical model Seismic forward model: • Wavelet convolution • Linearized Aki-Richards approximation of Zoeppritz equations Wavelet Reflection coefficients Seismogram SCRF 2013

  10. Physical model Rock physics forward model: • Granular media models (Hertz-Mindlin contact theory) • Gassmann’s equations • Velocity-pressure relations P-wave velocity versus effective porosity SCRF 2013

  11. Outline • Introduction • Theory and Inversion workflow • Application • Conclusions SCRF 2013

  12. Inversion workflow • We first estimate Buland and Omre, 2003 Buland and El Ouair, 2006 SCRF 2013

  13. Inversion workflow • We first estimate • We then estimate Buland and Omre, 2003 Buland and El Ouair, 2006 SCRF 2013

  14. Inversion workflow • We first estimate • We then estimate • We combine and using Chapman-Kolmogorov equation Buland and Omre, 2003 Buland and El Ouair, 2006 2 1 Grana and Della Rossa , 2010 SCRF 2013

  15. Seismic data Elastic properties Inversion workflow SCRF 2013

  16. Seismic data Rock physics likelihood function Elastic properties Inversion workflow SCRF 2013

  17. Seismic data Rock physics likelihood function Elastic properties Reservoir properties Inversion workflow (Chapman-Kolmogorov) SCRF 2013

  18. Simultaneous Bayesian 4D inversion Combined Inverse problem We estimate the posterior distribution SCRF 2013

  19. Reservoir property estimation Using statistical rock physics we estimate the likelihood We use non-parametric pdfs and we estimate them using Kernel Density Estimation (KDE) SCRF 2013

  20. Outline • Introduction • Theory and Inversion workflow • Application • Conclusions SCRF 2013

  21. 2D application: synthetic model Porosity injector Net-to-gross producer Pressure Saturation SCRF 2013

  22. 2012 2017 2D application: synthetic model Saturation Pressure SCRF 2013

  23. Assumptions • Porosity does not change in time (no compaction effect). • Initial pressure and saturation (pre-production) are known. SCRF 2013

  24. 2D application: seismic model SCRF 2013

  25. Synthetic seismic surveys SCRF 2013

  26. Time-lapse seismic differences SCRF 2013

  27. Rock physics likelihood • Different scenarios: • Pressure decreases – Saturation insitu • Pressure increases – Saturation insitu • Pressure insitu – Water replaced oil • Pressure insitu – Gas replaced oil • Pressure decreases – Water replaced oil • Pressure decreases – Gas replaced oil • Pressure increases – Water replaced oil • Pressure increases – Gas replaced oil SCRF 2013

  28. Rock physics likelihood SCRF 2013

  29. Elastic property changes % SCRF 2013

  30. Reservoir property changes SCRF 2013

  31. Point-wise posterior probabilities SCRF 2013

  32. Application: Norne SCRF 2013

  33. Application: Norne • Seismic differences (2003-2001) SCRF 2013

  34. Application: Norne SCRF 2013

  35. Application: Norne SCRF 2013

  36. Outline • Introduction • Theory and Inversion workflow • Application • Conclusions SCRF 2013

  37. Conclusions • We presented a full Bayesian methodology to estimate reservoir properties and their changes from seismic data • The method allows to assess the uncertainty in the estimation of reservoir properties • Inverted data can be used in seismic history matching to improve the reservoir description SCRF 2013

  38. Acknowledgments • Prof. Tapan Mukerji and Prof. Jef Caers • Stanford University, SRB and SCRF for supporting my research • Thank you for the attention SCRF 2013

  39. Backup SCRF 2013

  40. Rock physics model Log of porosity, saturation, mineralogical fractions, Fluid properties Mineral parameters Mixing laws Voigt-Reuss-Hill Mineral fractions Matrix Moduli Estimated Vp, Vs and Density RP Model Nur, Hertz-Mindlin, Kuster-Toksoz,… Saturation, Fluid properties Batzle Wang MacBeth’s relation Gassmann Dry Rock Moduli SCRF 2013

  41. MacBeth modified We assume that SCRF 2013

  42. Bayesian 3D inversion Seismic Inverse problem SCRF 2013

  43. Bayesian 3D inversion Seismic Inverse problem If the prior distribution of m is Gaussian If the model G is linear Then the posterior distribution is Gaussian Buland and Omre (2003) SCRF 2013

  44. Bayesian 4D inversion Time-lapse Inverse problem SCRF 2013

  45. Bayesian 4D inversion Time-lapse Inverse problem If the prior distribution of Δm is Gaussian If the model G is linear Then the posterior distribution is Gaussian Buland and El Ouair (2006) SCRF 2013

  46. Base seismic and time-lapse inversion We then compute the relative impedance change asΔIP = 1 - IPrep/IPbase SCRF 2013

  47. Base seismic and time-lapse inversion SCRF 2013

  48. Non-parametric pdfs: KDE Clay Vs (m/s) Sand Shale Vp (m/s) SCRF 2013

  49. Application: Norne • Calibration well: well E2 • Three angle stacks: near, mid, far • Base survey + seismic differences (2003-2001; 2004-2001; 2006-2001) • Goal: estimate dynamic property changes in 2003, 2004, and 2006 SCRF 2013

  50. Application: Norne Well E2 SCRF 2013

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