Reservoir history matching by ensemble smoother with principle component and sensitivity analysis for heterogeneous formations

Ensemble-based methods have been widely used in uncertainty quantification, particularly, in reservoir history matching. The search for a more robust method which holds high nonlinear problems is the focus for this area. The Ensemble Kalman Filter (EnKF) is a popular tool for these problems, but studies have noticed uncertainty in the results of the final ensemble, high dependent on the initial ensemble. The Ensemble Smoother (ES) is an alternative, with an easier impletation and low computational cost. However, it presents the same problem as the EnKF. The Ensemble Smoother with Multiple Data Assimilation (ES-MDA) seems to be a good alternative to these ensemble-based methods, once it assimilates tha same data multiple times. In this work, we analyze the efficiency of the Ensemble Smoother and the Ensemble Smoother with multiple data assimilation in a reservoir histoy matching of a turbidite model with 3 layers, considering permeability estimation and data mismatch.

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Efficient Dimensionality Reduction Methods in Reservoir History Matching

Energies ◽

10.3390/en14113137 ◽

2021 ◽

Vol 14 (11) ◽

pp. 3137

Author(s):

Amine Tadjer ◽

Reider B. Bratvold ◽

Remus G. Hanea

Keyword(s):

Data Assimilation ◽

Dimensionality Reduction ◽

Gaussian Process ◽

Latent Variable ◽

History Matching ◽

Production Performance ◽

Latent Variable Model ◽

Variable Model ◽

Multiple Data ◽

Ensemble Smoother

Production forecasting is the basis for decision making in the oil and gas industry, and can be quite challenging, especially in terms of complex geological modeling of the subsurface. To help solve this problem, assisted history matching built on ensemble-based analysis such as the ensemble smoother and ensemble Kalman filter is useful in estimating models that preserve geological realism and have predictive capabilities. These methods tend, however, to be computationally demanding, as they require a large ensemble size for stable convergence. In this paper, we propose a novel method of uncertainty quantification and reservoir model calibration with much-reduced computation time. This approach is based on a sequential combination of nonlinear dimensionality reduction techniques: t-distributed stochastic neighbor embedding or the Gaussian process latent variable model and clustering K-means, along with the data assimilation method ensemble smoother with multiple data assimilation. The cluster analysis with t-distributed stochastic neighbor embedding and Gaussian process latent variable model is used to reduce the number of initial geostatistical realizations and select a set of optimal reservoir models that have similar production performance to the reference model. We then apply ensemble smoother with multiple data assimilation for providing reliable assimilation results. Experimental results based on the Brugge field case data verify the efficiency of the proposed approach.

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Gaussian Processes Proxy Model with Latent Variable Models and Variogram-Based Sensitivity Analysis for Assisted History Matching

Energies ◽

10.3390/en13174290 ◽

2020 ◽

Vol 13 (17) ◽

pp. 4290

Author(s):

Dongmei Zhang ◽

Yuyang Zhang ◽

Bohou Jiang ◽

Xinwei Jiang ◽

Zhijiang Kang

Keyword(s):

Sensitivity Analysis ◽

Gaussian Processes ◽

Latent Variable ◽

History Matching ◽

Latent Variable Models ◽

High Dimensional ◽

Model Parameters ◽

Variable Model ◽

Assisted History Matching ◽

Proxy Models

Reservoir history matching is a well-known inverse problem for production prediction where enormous uncertain reservoir parameters of a reservoir numerical model are optimized by minimizing the misfit between the simulated and history production data. Gaussian Process (GP) has shown promising performance for assisted history matching due to the efficient nonparametric and nonlinear model with few model parameters to be tuned automatically. Recently introduced Gaussian Processes proxy models and Variogram Analysis of Response Surface-based sensitivity analysis (GP-VARS) uses forward and inverse Gaussian Processes (GP) based proxy models with the VARS-based sensitivity analysis to optimize the high-dimensional reservoir parameters. However, the inverse GP solution (GPIS) in GP-VARS are unsatisfactory especially for enormous reservoir parameters where the mapping from low-dimensional misfits to high-dimensional uncertain reservoir parameters could be poorly modeled by GP. To improve the performance of GP-VARS, in this paper we propose the Gaussian Processes proxy models with Latent Variable Models and VARS-based sensitivity analysis (GPLVM-VARS) where Gaussian Processes Latent Variable Model (GPLVM)-based inverse solution (GPLVMIS) instead of GP-based GPIS is provided with the inputs and outputs of GPIS reversed. The experimental results demonstrate the effectiveness of the proposed GPLVM-VARS in terms of accuracy and complexity. The source code of the proposed GPLVM-VARS is available at https://github.com/XinweiJiang/GPLVM-VARS.

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Integration of an Iterative Update of Sparse Geologic Dictionaries with ES-MDA for History Matching of Channelized Reservoirs

Geofluids ◽

10.1155/2018/1532868 ◽

2018 ◽

Vol 2018 ◽

pp. 1-21 ◽

Cited By ~ 9

Author(s):

Sungil Kim ◽

Baehyun Min ◽

Kyungbook Lee ◽

Hoonyoung Jeong

Keyword(s):

History Matching ◽

Gas Reservoirs ◽

Dynamic Data ◽

Multiple Data ◽

Ensemble Smoother ◽

Water Rate ◽

Non Gaussian ◽

Value Decomposition ◽

Channelized Reservoirs ◽

Channel Properties

This study couples an iterative sparse coding in a transformed space with an ensemble smoother with multiple data assimilation (ES-MDA) for providing a set of geologically plausible models that preserve the non-Gaussian distribution of lithofacies in a channelized reservoir. Discrete cosine transform (DCT) of sand-shale facies is followed by the repetition of K-singular value decomposition (K-SVD) in order to construct sparse geologic dictionaries that archive geologic features of the channelized reservoir such as pattern and continuity. Integration of ES-MDA, DCT, and K-SVD is conducted in a complementary way as the initially static dictionaries are updated with dynamic data in each assimilation of ES-MDA. This update of dictionaries allows the coupled algorithm to yield an ensemble well conditioned to static and dynamic data at affordable computational costs. Applications of the proposed algorithm to history matching of two channelized gas reservoirs show that the hybridization of DCT and iterative K-SVD enhances the matching performance of gas rate, water rate, bottomhole pressure, and channel properties with geological plausibility.

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