Skip to main content
Log in

Bayesian estimation of reservoir properties—effects of uncertainty quantification of 4D seismic data

  • Original Paper
  • Published:
Computational Geosciences Aims and scope Submit manuscript

Abstract

This paper shows a history matching workflow with both production and 4D seismic data where the uncertainty of seismic data for history matching comes from Bayesian seismic waveform inversion. We use a synthetic model and perform two seismic surveys, one before start of production and the second after 1 year of production. From the first seismic survey, we estimate the contrast in slowness squared (with uncertainty) and use this estimate to generate an initial estimate of porosity and permeability fields. This ensemble is then updated using the second seismic survey (after inversion to contrasts) and production data with an iterative ensemble smoother. The impact on history matching results from using different uncertainty estimates for the seismic data is investigated. From the Bayesian seismic inversion, we get a covariance matrix for the uncertainty and we compare using the full covariance matrix with using only the diagonal. We also compare with using a simplified uncertainty estimate that does not come from the seismic inversion. The results indicate that it is important not to underestimate the noise in seismic data and that having information about the correlation in the error in seismic data can in some cases improve the results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Aanonsen, S. I., Aavatsmark, I., Barkve, T., Cominelli, A., Gosselin, O., Kolasinski, M., Reme, H.: Effect of scale dependent data correlations in integrated history matching loop combining production data and 4D seismic data. In: SPE Reservoir Simulation Symposium, Houston, 3–5 February 2003. SPE paper 79665

  2. Aanonsen, S. I., Naevdal, G., Oliver, D. S., Reynolds, A. C., Vallès, B.: The ensemble Kalman filter in reservoir engineering—a review. SPE J. 14(3), 393–412 (2009)

    Article  Google Scholar 

  3. Bansal, R., Sen, M. K.: Ray-born inversion for fracture parameters. Geophys. J. Int. 180(3), 1274–1288 (2010)

    Article  Google Scholar 

  4. Buland, A., Omre, H.: Bayesian linearized AVO inversion. Geophysics 68(1), 185–198 (2003)

    Article  Google Scholar 

  5. Chen, J., Glinsky, M. E.: Stochastic inversion of seismic pp and ps data for reservoir parameter estimation. Geophysics 79(6), R233–R246 (2014)

    Article  Google Scholar 

  6. Chen, P., Jordan, T. H., Zhao, L.: Full three-dimensional tomography: a comparison between the scattering-integral and adjoint-wavefield methods. Geophys. J. Int. 170(1), 175–181 (2007)

    Article  Google Scholar 

  7. Chen, Y., Oliver, D. S.: Levenberg-Marquardt forms of the iterative ensemble smoother for efficient history matching and uncertainty quantification. Comput. Geosci. 17, 689–703 (2013)

    Article  Google Scholar 

  8. Chen, Y., Oliver, D. S.: History matching of the Norne full-field model with an iterative ensemble smoother. SPE Reserv. Eval. Eng. 17(02), 244–256 (2014)

    Article  Google Scholar 

  9. Dadashpour, M., Ciaurri, D. E., Mukerji, T., Kleppe, J., Landro, M.: A derivative-free approach for the estimation of porosity and permeability using time-lapse seismic and production data. J. Geophys. Eng. 7 (4), 351–368 (2010)

    Article  Google Scholar 

  10. Dong, Y., Oliver, D. S.: Quantitative use of 4D seismic data for reservoir description. SPE J. 10(1), 91–99 (2005)

    Article  Google Scholar 

  11. Dong, Y., Gu, Y., Oliver, D. S.: Sequential assimilation of 4D seismic data for reservoir description using the ensemble Kalman filter. J. Pet. Sci. Eng. 53, 83–99 (2006)

    Article  Google Scholar 

  12. Eclipse. Eclipse™. http://www.software.slb.com/products/foundation/Pages/eclipse.aspx

  13. Emerick, A., Reynolds, A.: Investigation of the sampling performance of ensemble-based methods with a simple reservoir model. Comput. Geosci. 17(2), 325–350 (2013a)

  14. Emerick, A. A.: Estimation of pressure and saturation fields from time-lapse impedance data using the ensemble smoother. J. Geophys. Eng. 11(3) (2014)

  15. Emerick, A. A., Reynolds, A. C.: History-matching production and seismic data in a real field case using the ensemble smoother with multiple data assimilation. In: 2013 SPE Reservoir Simulation Symposium, The Woodlands, February 18–20. Society of Petroleum Engineers. SPE 163675-MS (2013b)

  16. Emerick, A. A., Reynolds, A. C.: Ensemble smoother with multiple data assimilation. Comput. Geosci. 55, 3–15 (2013c)

  17. Emerick, A. A., de Moraes, P. J., Rodrigues, J. R. P.: History matching 4D seismic data with efficient gradient based methods (SPE-107179). In: SPE EUROPEC/EAGE Annual Conference and Exhibition, 11–14 June, London (2007)

  18. Fahimuddin, A., Aanonsen, S., Skjervheim, J.-A.: Ensemble based 4d seismic history matching: integration of different levels and types of seismic data (SPE-131453). In: 72nd EAGE Conference & Exhibition (2010a)

  19. Fahimuddin, A., Aanonsen, S. I., Skjervheim, J.-A.: 4D seismic history matching of a real field case with EnKF: use of local analysis for model updating. In: SPE Annual Technical Conference and Exhibition, 19–22 September 2010, Florence (2010b)

  20. Feng, T., Skjervheim, J., Evensen, G.: Quantitative use of different seismic attributes in reservoir modeling. In: ECMOR XIII-13th European Conference on the Mathematics of Oil Recovery (2012)

  21. Grana, D.: Probabilistic approach to rock physics modeling. Geophysics 79(2), D123–D143 (2014)

    Article  Google Scholar 

  22. Grana, D., Mukerji, T.: Bayesian inversion of time-lapse seismic data for the estimation of static reservoir properties and dynamic property changes. Geophys. Prospect. 63(3), 637–655 (2015)

    Article  Google Scholar 

  23. Gu, Y., Oliver, D. S.: An iterative ensemble Kalman filter for multiphase fluid flow data assimilation. SPE J. 12(4), 438–446 (2007)

    Article  Google Scholar 

  24. Haverl, M., Aga, M., Reiso, E.: Integrated workflow for quantitative use of time-lapse seismic data in history matching: a North Sea field case (SPE-94453). In: SPE Europec/EAGE Annual Conference, 13–16 June 2005, Madrid (2005)

  25. Haverl, M. C., Skjervheim, J.-A., Landrø, M.: 4D seismic modeling integrated with the ensemble Kalman filter method for history matching of reservoir simulation model. In: 11th European Conference on the Mathematics of Oil Recovery (2008)

  26. Iglesias, M.: Iterative regularization for ensemble data assimilation in reservoir models. Comput. Geosci. 19 (1), 177–212 (2015)

    Article  Google Scholar 

  27. Jakobsen, M.: T-matrix approach to seismic forward modelling in the acoustic approximation. Stud. Geophys. Geod. 56, 1–20 (2012)

    Article  Google Scholar 

  28. Jakobsen, M., Ursin, B.: Nonlinear seismic waveform inversion using a born iterative T-matrix method. In: 82nd annual SEG meeting, Las Vegas (2012)

  29. Jakobsen, M., Ursin, B.: Full waveform inversion in the frequency domain using direct iterative T-matrix methods. J. Geophys. Eng. 12, 400–418 (2015)

    Article  Google Scholar 

  30. Jakobsen, M., Keers, H., Ruud, B., Psencik, I., Shahraini, A.: Waveform inversion of 4d seismic data using the ray-born approximation in the frequency domain. In: 72nd EAGE meeting, Barcelona (2010)

  31. Kirchner, A., Shapiro, S. A.: Fast repeat-modelling of time-lapse seismograms. Geophys. Prospect. 49(5), 557–569 (2001)

    Article  Google Scholar 

  32. Kretz, V., Le Ravalec-Dupin, M., Roggero, F.: An integrated reservoir characterization study matching production data and 4d seismic. SPE Reserv. Eval. Eng. 7(2), 116–122 (2004)

    Article  Google Scholar 

  33. Le Ravalec, M., Tillier, E., Veiga, S. D., Enchery, G., Gervais, V.: Advanced integrated workflows for incorporating both production and 4D seismic-related data into reservoir models. Oil Gas Sci. Technol.—Rev. IFP Energies Nouvelles 67(2), 207–220 (2012)

    Article  Google Scholar 

  34. Leeuwenburgh, O., Arts, R.: Distance parameterization for efficient seismic history matching with the ensemble Kalman filter. Comput. Geosci. 18(3–4), 535–548 (2014)

    Article  Google Scholar 

  35. Leeuwenburgh, O., Brouwer, J., Trani, M.: Ensemble-based conditioning of reservoir models to seismic data. Comput. Geosci. 15(2), 359–378 (2011)

    Article  Google Scholar 

  36. Li, G., Reynolds, A. C.: Iterative ensemble Kalman filters for data assimilation. SPE J. 14(3), 496–505 (2009)

    Article  Google Scholar 

  37. Lorentzen, R. J., Nævdal, G.: An iterative ensemble Kalman filter. IEEE Trans. Autom. Control 56(8), 1990–1995 (2011)

    Article  Google Scholar 

  38. Lorentzen, R. J., Nævdal, G., Shafieirad, A.: Estimating facies fields by use of the ensemble Kalman filter and distance functions-applied to shallow-marine environments. SPE J. 18, 146–158 (2013)

    Article  Google Scholar 

  39. Mavko, G., Mukerji, T., Dvorkin, J.: The rock physics handbook: tools for seismic analysis in porous media. Cambridge University Press, Cambridge (2003)

    Google Scholar 

  40. Moser, T. J.: Review of ray-Born forward modeling for migration and diffraction analysis. Stud. Geophys. Geod. 56(2), 411–432 (2012)

    Article  Google Scholar 

  41. Muhumuza, K.: Modelling and inversion of time-lapse seismic waveform data using scattering theory. Master’s thesis. Rijksuniversiteit Groningen (2015)

  42. Mukerji, T., Jørstad, A., Avseth, P., Mavko, G., Granli, J. R.: Mapping lithofacies and pore-fluid probabilities in a North Sea reservoir: Seismic inversions and statistical rock physics. Geophysics 66(4), 988–1001 (2001)

    Article  Google Scholar 

  43. Nævdal, G., Johnsen, L. M., Aanonsen, S. I., Vefring, E. H.: Reservoir monitoring and continuous model updating using ensemble Kalman filter. SPE J. 10(1), 66–74 (2005)

    Article  Google Scholar 

  44. Oliver, D. S., Chen, Y.: Recent progress on reservoir history matching: a review. Comput. Geosci. 15, 185–221 (2010)

    Article  Google Scholar 

  45. Peters, L., Arts, R. J., Brouwer, G. K., Geel, C. R., Cullick, S., Lorentzen, R. J., Chen, Y., Dunlop, K. N. B., Vossepoel, F. C., Xu, R., Sarma, P., Alhutali, A. H., Reynolds, A. C.: Results of the Brugge benchmark study for flooding optimization and history matching. SPE Reserv. Eval. Eng. 13(3), 391–405 (2010)

    Article  Google Scholar 

  46. Remy, N., Boucher, A., Wu, J.: Applied Geostatistics with SGeMS. Cambridge University Press, Cambridge (2009)

    Book  Google Scholar 

  47. Roggero, F., Lerat, O., Ding, D. Y., Berthet, P., Bordenave, C., Lefeuvre, F., Perfetti, P.: History matching of production and 4D seismic data: application to the Girassol Field, Offshore Angola. Oil Gas Sci. Technol.—Rev. IFP Energies Nouvelles 67(2), 237–262 (2012)

    Article  Google Scholar 

  48. Shaw, R. K., Sen, M. K.: Born integral, stationary phase and linearized reflection coefficients in weak anisotropic media. Geophys. J. Int. 158(1), 225–238 (2004)

    Article  Google Scholar 

  49. Skjervheim, J., Ruud, B., Aanonsen, S., Evensen, G., Johansen, T.: Using the ensemble Kalman filter with 4D data to estimate properties and lithology of reservoir rocks. In: ECMOR X-10th European Conference on the Mathematics of Oil Recovery (2006)

  50. Skjervheim, J.-A., Evensen, G.: An ensemble smoother for assisted history matching. In: SPE Reservoir simulations symposium, The Woodlands, February 21–23. SPE141929-MS (2011)

  51. Skjervheim, J.-A., Evensen, G., Aanonsen, S. I., Ruud, B. O., Johansen, T. A.: Incorporating 4D seismic data in reservoir simulation using ensemble Kalman filter. SPE J. 12(3), 282–292 (2007)

    Article  Google Scholar 

  52. Stephen, K. D., Soldo, J., MacBeth, C., Christie, M.: Multiple-model seismic and production history matching: a case study. SPE J. 11(4), 418–430 (2006)

    Article  Google Scholar 

  53. Tarantola, A.: Inverse problem theory and methods for model parameter estimation. SIAM (2005)

  54. The MathWorks. http://www.mathworks.com

  55. Trani, M., Arts, R., Leeuwenburgh, O.: Seismic history matching of fluid fronts using the ensemble Kalman filter. SPE J. 18(1), 159–171 (2013)

    Article  Google Scholar 

  56. Vasco, D. W., Keers, H., Khazanehdari, J., Cooke, A.: Seismic imaging of reservoir flow properties: resolving water influx and reservoir permeability. Geophysics 73(1), O1–O13 (2008)

    Article  Google Scholar 

  57. Wang, Y., Li, G., Reynolds, A. C.: Estimation of depths of fluid contacts and relative permeability curves by history matching using iterative ensemble-Kalman smoothers. SPE J. 15(2), 509–525 (2010)

    Article  Google Scholar 

  58. Zhao, Y., Reynolds, A. C., Li, G.: Generating facies maps by assimilating production data and seismic data with the ensemble Kalman filter, SPE-113990. In: Proceedings of SPE IOR Symposium, Tulsa, April 21–23. (2008)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Geir Nævdal.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Eikrem, K.S., Nævdal, G., Jakobsen, M. et al. Bayesian estimation of reservoir properties—effects of uncertainty quantification of 4D seismic data. Comput Geosci 20, 1211–1229 (2016). https://doi.org/10.1007/s10596-016-9585-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10596-016-9585-0

Keywords

Navigation