Reservoir characterization using ensemble-based assimilation methods

Document Type : Research Paper


School of Mining Engineering, College of Engineering, University of Tehran, Tehran, Iran



Characterization of large reservoir models with a great number of uncertain parameters is frequently carried out by ensemble-based assimilation methods, due to their computational efficiency, ease of implementation, versatility, and non-necessity of adjoint code. In this study, multiple ensemble-based assimilation techniques are utilized to characterize the well-known PUNQ-S3 model. Accordingly, actual measurements are employed to determine porosity, horizontal and vertical permeabilities, and their associated uncertainties. In consequence, the uncertain parameters of the model will gradually be adapted toward the true values during the assimilation of actual measurements, including bottomhole pressure and production rates of the reservoir. Monotonic reduction of root-mean-squared error and capturing the key points of the maps (such as direction of anisotropy and porosity/permeability contrasts) verify successful estimation of the geostatistical properties of the PUNQ-S3 model during history matching. At the end of the assimilation process, the RMSE values for Deterministic Ensemble Kalman Filter, Ensemble Kalman Filter, Ensemble Kalman Filter with Bootstrap Regularization, Ensemble Transform Kalman Filter Symmetric Solution, Ensemble Transform Kalman Filter Random Rotation, and Singular Evolutive Interpolated Kalman filter are 1.120, 1.153, 1.132, 1.132, 1.129, and 1.113, respectively. In addition to RMSE, the quality of history match as well as prediction of future performance are looked into in order to assess the performance of the assimilation process. Obviously, the results of the ensemble-based assimilation methods closely match the true results both in the history match section and in the future prediction section. Besides, the uncertainty of future predictions is quantified using multiple history-matched realizations. This is due to the fact that Kalman-based filters use a Bayesian framework in the assimilation step. Accordingly, the updated ensemble members are samples of the posterior distribution through which the uncertainty of future performance is assessed.


Main Subjects

[1] Tokhmechi B, J Nasiri, H Azizi, M Rabiei, V Rasouli. Wavelet Neural Network: A Hybrid Method in Modeling Heterogeneous Reservoirs. Int J Min Geo-Eng. 53 (2019) 203-11, doi:
[2] Jo H, W Pan, JE Santos, H Jung, MJ Pyrcz. Machine learning assisted history matching for a deepwater lobe system. J Petrol Sci Eng. 207 (2021) 109086, doi:
[3] Li Y, M Onur. INSIM-BHP: A physics-based data-driven reservoir model for history matching and forecasting with bottomhole pressure and production rate data under waterflooding. J Comput Phys. 473 (2022) 111714, doi:
[4] Ma X, K Zhang, J Wang, C Yao, Y Yang, H Sun, et al. An Efficient Spatial-Temporal Convolution Recurrent Neural Network Surrogate Model for History Matching. SPE J. 27 (2022) 1160-75, doi:
[5] Lewis JM, S Lakshmivarahan, S Dhall. Dynamic data assimilation: a least squares approach. 1st ed. Cambridge University Press, New York, 2006.
[6] Evensen G. Sequential data assimilation with a nonlinear quasi‐geostrophic model using Monte Carlo methods to forecast error statistics. J Geophys Res-Oceans. 99 (1994) 10143-62, doi:
[7] Lorentzen R, K Fjelde, F Jonny, A Lage, N Geir, E Vefring. Underbalanced and low-head drilling operations: Real time interpretation of measured data and operational support. In: SPE Annual Technical Conference and Exhibition. New Orleans, Louisiana (2001), doi:
[8] Chang H, D Zhang, Z Lu. History matching of facies distribution with the EnKF and level set parameterization. J Comput Phys. 229 (2010) 8011-30, doi:
[9] Akter F, S Imtiaz, S Zendehboudi, K Hossain. Modified Ensemble Kalman filter for reservoir parameter and state estimation in the presence of model uncertainty. J Petrol Sci Eng. 199 (2021) 108323, doi:
[10] Jahanbakhshi S, MR Pishvaie, RB Boozarjomehry. Impact of initial ensembles on posterior distribution of ensemble-based assimilation methods. J Petrol Sci Eng. 171 (2018) 82-98, doi:
[11] Abdolhosseini H, E Khamehchi. History matching using traditional and finite size ensemble Kalman filter. J Nat Gas Sci Eng. 27 (2015) 1748-57, doi:
[12] Zhang Y, Z Fan, D Yang, H Li, S Patil. Simultaneous estimation of relative permeability and capillary pressure for PUNQ-S3 model with a damped iterative-ensemble-Kalman-filter technique. SPE J. 22 (2017) 971 - 84, doi:
[13] Xue L, S Gu, L Mi, L Zhao, Y Liu, Q Liao. An automated data-driven pressure transient analysis of water-drive gas reservoir through the coupled machine learning and ensemble Kalman filter method. J Petrol Sci Eng. 208 (2022) 109492, doi:
[14] Nævdal G, T Mannseth, EH Vefring. Near-well reservoir monitoring through ensemble Kalman filter. In: SPE/DOE Improved Oil Recovery Symposium. Tulsa, Oklahoma (2002), doi:
[15] Wen X-H, W Chen. Real-time reservoir model updating using ensemble Kalman filter. SPE J. 11 (2006) 431-42, doi:
[16] Skjervheim JA, G Evensen, SI Aanonsen, BO Ruud, TA Johansen. Incorporating 4D seismic data in reservoir simulation models using ensemble Kalman filter. SPE J. 12 (2007) 282-92, doi:
[17] Sakov P, PR Oke. A deterministic formulation of the ensemble Kalman filter: an alternative to ensemble square root filters. Tellus. 60 (2008) 361-71, doi:
[18] Gao G, M Zafari, AC Reynolds. Quantifying uncertainty for the PUNQ-S3 problem in a Bayesian setting with RML and EnKF. SPE J. 11 (2006) 506-15, doi:
[19] Gu Y, DS Oliver. History matching of the PUNQ-S3 reservoir model using the ensemble Kalman filter. SPE J. 10 (2005) 217 - 24, doi:
[20] Lee K, S Jung, T Lee, J Choe. Use of clustered covariance and selective measurement data in ensemble smoother for three-dimensional reservoir characterization. J Energy Resour Technol. 139 (2017), doi:
[21] Watanabe S, A Datta-Gupta. Use of phase streamlines for covariance localization in ensemble Kalman filter for three-phase history matching. SPE Reserv Eval Eng. 15 (2012) 273-89, doi:
[22] Arouri Y, M Sayyafzadeh. An adaptive moment estimation framework for well placement optimization. Computat Geosci. 26 (2022) 957–73, doi:
[23] Raji S, A Dehnamaki, B Somee, MR Mahdiani. A new approach in well placement optimization using metaheuristic algorithms. J Petrol Sci Eng. 215 (2022) 110640, doi:
[24] Lorentzen RJ, G Nævdal, A Shafieirad. Estimating facies fields by use of the ensemble Kalman filter and distance functions--applied to shallow-marine environments. SPE J. 3 (2013) 146-58, doi:
[25] Delijani EB, MR Pishvaie, RB Boozarjomehry. Subsurface characterization with localized ensemble Kalman filter employing adaptive thresholding. Adv Water Resour. 69 (2014) 181-96, doi:
[26] Evensen G. Data assimilation: the ensemble Kalman filter. 2nd ed. Springer Science & Business Media, New York, 2009.
[27] Bishop CH, BJ Etherton, SJ Majumdar. Adaptive sampling with the ensemble transform Kalman filter. Part I: Theoretical aspects. Mon Weather Rev. 129 (2001) 420-36, doi:<0420:ASWTET>
[28] Sakov P, PR Oke. Implications of the form of the ensemble transformation in the ensemble square root filters. Mon Weather Rev. 136 (2008) 1042-53, doi:
[29] Zhang Y, DS Oliver. Improving the ensemble estimate of the Kalman gain by bootstrap sampling. Math Geosci. 42 (2010) 327-45, doi:
[30] Nerger L, T Janji, J Schröter, W Hiller. A unification of ensemble square root Kalman filters. Mon Weather Rev. 140 (2012) 2335-45, doi:
[31] Sun AY, A Morris, S Mohanty. Comparison of deterministic ensemble Kalman filters for assimilating hydrogeological data. Adv Water Resour. 32 (2009) 280-92, doi:
[32] Floris FJT, MD Bush, M Cuypers, F Roggero, AR Syversveen. Methods for quantifying the uncertainty of production forecasts: a comparative study. Pet Geosci. 7 (2001) 87-96, doi:
[33] Verga F, M Cancelliere, D Viberti. Improved application of assisted history matching techniques. J Petrol Sci Eng. 109 (2013) 327-47, doi:
[34] Remy N, A Boucher, J Wu. Applied geostatistics with SGeMS: A user's guide. 1st ed. Cambridge University Press, New York, 2009.
[35] Tahernejad MM, R Khalo Kakaei, M Ataei. Analyzing the effect of ore grade uncertainty in open pit mine planning; A case study of Rezvan iron mine, Iran. Int J Min Geo-Eng. 52 (2018) 53-60, doi:
[36] Hajizadeh Y, M Christie, V Demyanov. Ant colony optimization for history matching and uncertainty quantification of reservoir models. J Petrol Sci Eng. 77 (2011) 78-92, doi:
[37] Kotsuki S, CH Bishop. Implementing Hybrid Background Error Covariance into the LETKF with Attenuation-Based Localization: Experiments with a Simplified AGCM. Mon Weather Rev. 150 (2022) 283-302, doi:
[38] Wernitz S, E Chatzi, B Hofmeister, M Wolniak, W Shen, R Rolfes. On noise covariance estimation for Kalman filter-based damage localization. Mech Syst Sig Process. 170 (2022) 108808, doi:
[39] Xing X, B Liu, W Zhang, J Wu, X Cao, Q Huang. An Investigation of Adaptive Radius for the Covariance Localization in Ensemble Data Assimilation. J Mar Sci Eng. 9 (2021) 1156, doi:
[40] Moradi M, O Asghari, G Norouzi, M Riahi, R Sokooti. Joint Bayesian Stochastic Inversion of Well Logs and Seismic Data for Volumetric Uncertainty Analysis. Int J Min Geo-Eng. 49 (2015) 131-42, doi: