History matching of multi-facies channelized reservoirs using ES-MDA with common basis DCT
Tóm tắt
History matching a channelized reservoir with multiple facies has always posed a great challenge to researchers. In this paper, we present a workflow combining the ensemble smoother with multiple data assimilation (ES-MDA) method with a parameterization algorithm referred to as the common basis discrete cosine transform (DCT) and a post-processing technique in order to integrate static and dynamic data into multi-facies channelized reservoir models. The parameterization algorithm is developed to capture the critical features and describe the geological similarity between different realizations in the prior ensemble by transforming the discrete facies indicators into continuous variables. And the ES-MDA method is employed to update the continuous variables by assimilating the static and dynamic data. Finally, a post-processing technique based on a regularization framework is used to improve the spatial continuity of facies and estimate the non-Gaussian distributed reservoir properties. We apply this automatic history matching workflow to two synthetic problems that represent complex three-facies (shale, levee, and sand) channelized reservoirs. One is a 2D three-facies reservoir with a relatively high number of channels and the other is a 3D three-facies five-layer reservoir containing two geological zones with different channel patterns. The computational results show that the proposed workflow can greatly reduce the uncertainty in the reservoir description through the integration of production data. And the posterior realizations can well preserve the key geological features of the prior models, with a good history data match and predictive capacity. In addition, we also illustrate the superiority of the common basis DCT over the traditional DCT algorithm.
Tài liệu tham khảo
Aanonsen, S.I., Nævdal, G., Oliver, D.S., Reynolds, A.C., Vallés, B.: The ensemble Kalman filter in reservoir engineering–a review. SPE J. 14(3), 393–412 (2009)
Agbalaka, C., Oliver, D.S.: Application of the EnKF and localization to automatic history matching of facies distribution and production data. Math. Geosci. 40(4), 353–374 (2008)
Bhark, E.W., Jafarpour, B., Datta-Gupta, A.: A new adaptively scaled production data integration approach using the discrete cosine parameterization. In: Proceedings of SPE Improved Oil Recovery Symposium, Tulsa, Oklahoma (2010)
Caers, J.: Geostatistical history matching under training-image based geological model constraints. In: Proceedings of the SPE Annual Technical Conference and Exhibition, San Antonio, Texas (2002)
Caers, J., Hoffman, T.: The probability perturbation method: A new look at Bayesian inverse modeling. Math. Geol. 38(1), 81–100 (2006)
Caers, J., Zhang, T.: Multiple-point geostatistics: a quantitative vehicle for integrating geologic analogs into multiple reservoir models, AAPG Special Volumes (2004)
Chang, H., Zhang, D., Lu, Z.: History matching of facies distributions with the EnKF and level set parameterization. J. Comput. Phys. 229, 8011–8030 (2010)
Deutsch, C.V., Wang, L.: Hierarchical object-based stochastic modeling of fluvial reservoirs. Math. Geol. 28(7), 857–880 (1996)
Elsheikh, A.H., Demyanov, V., Tavakoli, R., Christie, M.A., Wheeler, M.F.: Calibration of channelized subsurface flow models using nested sampling and soft probabilities. Adv. Water Resour. 75, 14–30 (2015)
Elsheikh, A.H., Wheeler, M.F., Hoteit, I.: Nested sampling algorithm for subsurface flow model selection, uncertainty quantification, and nonlinear calibration. Water Resour. Res. 49(12), 8383–8399 (2013)
Emerick, A.A., Reynolds, A.C.: History matching time-lapse seismic data using the ensemble Kalman filter with multiple data assimilations. Comput. Geosci. 16(3), 639–659 (2012)
Emerick, A.A., Reynolds, A.C.: Ensemble smoother with multiple data assimilations. Comput. Geosci. 55, 3–15 (2013a)
Emerick, A.A., Reynolds, A.C.: Investigation of the sampling performance of ensemble-based methods with a simple reservoir model. Comput. Geosci. 17(2), 325–350 (2013b)
Evensen, G.: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res. 99(C5), 10,143–10,162 (1994)
Gonzalez, R.C., Woods, R.E.: Digital image processing. Prentice hall Upper Saddle River (2002)
Jafapour, B., Khodabakhsi, M.: A probability conditioning method (PCM) for nonlinear flow data integration into multipoint statistical facies simulation. Math. Geol. 43(2), 133–164 (2011)
Jafarpour, B., McLaughlin, D.B.: Estimating channelized reservoir permeabilities with the ensemble Kalman filter: The importance of ensemble design. SPE J. 14(2), 374–388 (2009a)
Jafarpour, B., McLaughlin, D.B.: Reservoir characterization with the discrete cosine transform. SPE J. 14 (1), 182–201 (2009b)
Khaninezhad, M.M., Jafarpour, B., Li, L.: Sparse geologic dictionaries for subsurface flow model calibration: Part I. Inversion formulation. Adv. Water Resour. 39, 106–121 (2012a)
Khaninezhad, M.M., Jafarpour, B., Li, L.: Sparse geologic dictionaries for subsurface flow model calibration: Part II. Robustness to uncertainty. Adv. Water Resour. 39, 122–136 (2012b)
Le, D.H., Emerick, A.A., Reynolds, A.C.: An adaptive ensemble smoother with multiple data assimilation for assisted history matching. In: Proceedings of the SPE Reservoir Simulation Symposium. Houston, Texas (2015a)
Le, D.H., Younis, R., Reynolds, A.C.: A history matching procedure for non-Gaussian facies based on ES-MDA. In: Proceedings of the SPE Reservoir Simulation Symposium. Houston, Texas (2015b)
Liu, N., Oliver, D.S.: Ensemble Kalman filter for automatic history matching of geologic facies. J. Pet. Sci. Eng. 47(3–4), 147–161 (2005)
Oliver, D.S., Chen, Y.: Recent progress on reservoir history matching: a review. Comput. Geosci. 15, 185–221 (2011)
Ping, J., Zhang, D.: History matching of fracture distributions by ensemble Kalman filter combined with vector based level set parameterization. J. Pet. Sci. Eng. 108, 288–303 (2013)
Ping, J., Zhang, D.: History matching of channelized reservoirs with vector-based level-set parameterization. SPE J. 19(3), 514–529 (2014)
Rao, K.R., Yip, P.: Discrete cosine transform: algorithms, advantages, applications. Academic press (1990)
Reynolds, A.C., Zafari, M., Li, G.: Iterative forms of the ensemble Kalman filter. In: Proceedings of 10th European Conference on the Mathematics of Oil Recovery, Amsterdam (2006)
Sarma, P., Durlofsky, L.J., Aziz, K.: Kernel principal component analysis for efficient differentiable parameterization of multipoint geostatistics. Math. Geosci. 40, 3–32 (2008)
Seiler, A., Aanonsen, S.I., Evensen, G., Reivenæs, J.C.: Structural uncertainty modeling and updating using the ensemble Kalman filter. SPE J. 15(4), 1062–1076 (2010)
Strebelle, S.: Conditional simulation of complex geological structures using multiple-point statistics. Math. Geol. 34(1), 1–22 (2002)
Tavakoli, R., Srinivasan, S., ElSheikh, A.H., Wheeler, M.F.: Efficient integration of production and seismic data into reservoir models exhibiting complex connectivity using an iterative ensemble smoother. In: Proceedings of the SPE Reservoir Simulation Symposium, Houston, Texas (2015)
Tavakoli, R., Srinivasan, S., Wheeler, M.F.: Rapid updating of stochastic models by use of an ensemble-filter approach. SPE J. 19(3), 500–513 (2014)
Thulin, K., Li, G., Aanonsen, S.I., Reynolds, A.C.: Experiments on adjusting initial fluid contacts with EnKF, TUPREP Research Report 24 The University of Tulsa (2007)
van Leeuwen, P.J., Evensen, G.: Data assimilation and inverse methods in terms of a probabilistic formulation. Mon. Weather. Rev. 124, 2898–2913 (1996)
Vo, H.X., Durlofsky, L.J.: A new differentiable parameterization based on principal component analysis for the low-dimensional representation of complex geological models. Math. Geosci. 46(7), 775–813 (2014)
Vo, H.X., Durlofsky, L.J.: Data assimilation and uncertainty assessment for complex geological models using a new PCA-based parameterization. Comput. Geosci. 19(4), 747–767 (2015)
Vo, H.X., Durlofsky, L.J.: Regularized kernel PCA for the efficient parameterization of complex geological models. J. Comput. Phys. 322, 859–881 (2016)
Wang, Y., Li, G., Reynolds, A.C.: Estimation of depths of fluid contacts by history matching using iterative ensemble-Kalman smoothers. SPE J. 15(2), 509–525 (2010)
Zafari, M., Reynolds, A.C.: Assessing the uncertainty in reservoir description and performance predictions with the ensemble Kalman filter. SPE J. 12(3), 382–391 (2007)