Abstract
In the past years, multi-point geostatistical simulation (MPS) geo-models have been used successfully to create realistic geological instances (facies fields). However, the conditioning of such geological deposits to production data is still a challenge, especially when an assisted history matching (AHM) model based on Bayesian inversion is used. This is hampered when we deal with complex geometry and topology and when the number of the facies types is greater than two. The estimation of the facies field is carried out combining two components: a parameterization of the facies field and a AHM method. In this study, we extend a parameterization of the facies fields, defined in a multidimensional normalized space by drawing from a marginal conditional Gaussian distribution. This is a generalization of a parameterization used in a previous study for channelized reservoirs and can be used for any type of geological layouts of the prior (in the MPS case, the training image). The parameterization ensures that the updates are always facies realization. However, traditional history matching methods tend to either destroy this topological structure or collapse into a single realization giving an unrealistic description of the uncertainty. To improve this issue, the iterative adaptive Gaussian mixture (IAGM) has been used as AHM method with a maximum of three iterations for the case studies. The method is tested for a 2D reservoir model, where four facies types are present, of which one exhibits channelized geometry. The topology is complex because two of the facies types cannot be in contact with each other. After assimilation of the production data, the IAGM was able to reduce the prior uncertainty toward an ensemble with realistic geological structure, with a good data match and predictive capacity.
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References
Aanonsen, S.I., Nævdal, G., Oliver, D.S., Reynolds, A.C., Vallès, B., et al.: The ensemble kalman filter in reservoir engineering—a review. Spe Journal 14(03), 393–412 (2009)
Caers, J., Zhang, T.: Multiple-point geostatistics: a quantitative vehicle for integrating geologic analogs into multiple reservoir models (2004)
Deutsch, C., Journel, A.: Geostatistical software library and user guide (gslib) (1998)
Deutsch, C.V., Wang, L.: Hierarchical object-based stochastic modeling of fluvial reservoirs. Math. Geol. 28(7), 857–880 (1996)
Evensen, G.: The ensemble kalman filter: theoretical formulation and practical implementation. Ocean Dyn. 53(4), 343–367 (2003)
Galli, A., Beucher, H., Le Loc, G., Doligez, B., et al.: The pros and cons of the truncated gaussian method. In: Geostatistical simulations, pp 217–233. Springer (1994)
Guardiano, F.B., Srivastava, R.M.: Multivariate geostatistics: beyond bivariate moments. In: Geostatistics Troia 92, pp 133–144. Springer (1993)
Jafarpour, B., Khodabakhshi, M.: A probability conditioning method (pcm) for nonlinear flow data integration into multipoint statistical facies simulation. Math. Geosci. 43(2), 133–164 (2011)
Journel, A.: Combining knowledge from diverse sources: an alternative to traditional data independence hypotheses. Math. Geol. 34(5), 573–596 (2002)
Krishnan, S., Boucher, A., Journel, A.G.: Evaluating information redundancy through the tau model. In: Geostatistics Banff 2004, pp. 1037–1046. Springer (2005)
Liu, N., Oliver, D.: Ensemble kalman filter for automatic history matching of geologic facies. J. Pet. Sci. Eng. 47(3–4), 147–161 (2005)
Lorentzen, R.J., Nævdal, G., et al.: Estimating facies fields using the ensemble kalman filter and distance functions, applied to shallow-marine environments. SPE Journal 3(1), 146–148 (2012)
Remy, N.: Sgems: the stanford geostatistical modeling software: a tool for new algorithms development. In: Geostatistics Banff 2004, pp 865–871. Springer (2005)
Sarma, P., Chen, W.H., et al.: Generalization of the ensemble kalman filter using kernels for nongaussian random fields. In: SPE Reservoir Simulation Symposium. Society of Petroleum Engineers (2009)
Sebacher, B., Hanea, R., Heemink, A.: A probabilistic parametrization for geological uncertainty estimation using the ensemble kalman filter (enkf). Comput. Geosci. 17(5), 813–832 (2013)
Sebacher, B., Stordal, A., Hanea, R.: Bridging multi point statistics and truncated gaussian fields for improved estimation of channelized reservoirs with ensemble methods. Comput. Geosci. 19(2), 341–369 (2015). doi:10.1007/s10596-014-9466-3
Stordal, A.: Iterative Bayesian inversion with gaussian mixtures: finite sample implementation and large sample asymptotics. Comput. Geosci. 19(1), 1–15 (2015). doi:10.1007/s10596-014-9444-9. ISSN 1420-0597
Stordal, A., Lorentzen, R.: An iterative version of the adaptive gaussian mixture filter. Comput. Geosci. (2014). doi:10.1007/s10596-014-9402-6
Stordal, A.S., Karlsen, H.A., Nævdal, G., Skaug, H.J., Vallès, B.: Bridging the ensemble kalman filter and particle filters: the adaptive gaussian mixture filter. Comput. Geosci. 15(2), 293–305 (2011)
Strebelle, S.: Conditional simulation of complex geological structures using multiple-point statistics. Math. Geol. 34(1), 1–21 (2002)
Zhao, Y., Reynolds, A.C., Li, G.: Generating facies maps by assimilating production data with enkf. SPE/DOE symposium on improvement oil recoveryTulsa 20-23 April (2008)
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Sebacher, B., Stordal, A. & Hanea, R. Complex geology estimation using the iterative adaptive Gaussian mixture filter. Comput Geosci 20, 133–148 (2016). https://doi.org/10.1007/s10596-015-9553-0
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DOI: https://doi.org/10.1007/s10596-015-9553-0