Characterization of Various Channel Fields Using an Initial Ensemble Selection Schemeand Covariance Localization

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Hyungsik Jung ◽  
Honggeun Jo ◽  
Kyungbook Lee ◽  
Jonggeun Choe
Keyword(s):  
History Matching ◽  
Selection Scheme ◽  
Localization Function ◽  
Ensemble Selection ◽  
Ensemble Smoother ◽  
Initial Ensemble ◽  
Relative Errors ◽  
Non Gaussian ◽  
Time Required ◽  
Filter Divergence

Ensemble Kalman filter (EnKF) uses recursive updates for data assimilation and provides dependable uncertainty quantification. However, it requires high computing cost. On the contrary, ensemble smoother (ES) assimilates all available data simultaneously. It is simple and fast, but prone to showing two key limitations: overshooting and filter divergence. Since channel fields have non-Gaussian distributions, it is challenging to characterize them with conventional ensemble based history matching methods. In many cases, a large number of models should be employed to characterize channel fields, even if it is quite inefficient. This paper presents two novel schemes for characterizing various channel reservoirs. One is a new ensemble ranking method named initial ensemble selection scheme (IESS), which selects ensemble members based on relative errors of well oil production rates (WOPR). The other is covariance localization in ES, which uses drainage area as a localization function. The proposed method integrates these two schemes. IESS sorts initial models for ES and these selected are also utilized to calculate a localization function of ES for fast and reliable channel characterization. For comparison, four different channel fields are analyzed. A standard EnKF even using 400 models shows too large uncertainties and updated permeability fields lose channel continuity. However, the proposed method, ES with covariance localization assisted by IESS, characterizes channel fields reliably by utilizing good 50 models selected. It provides suitable uncertainty ranges with correct channel trends. In addition, the simulation time of the proposed method is only about 19% of the time required for the standard EnKF.

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

Geofluids ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-21 ◽  
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.

Enhanced History Matching of Gas Reservoirs With an Aquifer Using the Combination of Discrete Cosine Transform and Level Set Method in ES-MDA

2019 ◽  
Vol 141 (7) ◽  
Author(s):  
Sungil Kim ◽  
Hyungsik Jung ◽  
Jonggeun Choe
Keyword(s):  
Discrete Cosine Transform ◽  
Level Set Method ◽  
Level Set ◽  
Measurement Errors ◽  
History Matching ◽  
Reservoir Characterization ◽  
Gas Reservoirs ◽  
Cosine Transform ◽  
Ensemble Smoother ◽  
Non Gaussian

Reservoir characterization is a process to make dependable reservoir models using available reservoir information. There are promising ensemble-based methods such as ensemble Kalman filter (EnKF), ensemble smoother (ES), and ensemble smoother with multiple data assimilation (ES-MDA). ES-MDA is an iterative version of ES with inflated covariance matrix of measurement errors. It provides efficient and consistent global updates compared to EnKF and ES. Ensemble-based method might not work properly for channel reservoirs because its parameters are highly non-Gaussian. Thus, various parameterization methods are suggested in previous studies to handle nonlinear and non-Gaussian parameters. Discrete cosine transform (DCT) can figure out essential channel information, whereas level set method (LSM) has advantages on detailed channel border analysis in grid scale transforming parameters into Gaussianity. However, DCT and LSM have weaknesses when they are applied separately on channel reservoirs. Therefore, we propose a properly designed combination algorithm using DCT and LSM in ES-MDA. When DCT and LSM agree with each other on facies update results, a grid has relevant facies naturally. If not, facies is assigned depending on the average facies probability map from DCT and LSM. By doing so, they work in supplementary way preventing from wrong or biased decision on facies. Consequently, the proposed method presents not only stable channel properties such as connectivity and continuity but also similar pattern with the true. It also gives trustworthy future predictions of gas and water productions due to well-matched facies distribution according to the reference.

Use of Clustered Covariance and Selective Measurement Data in Ensemble Smoother for Three-Dimensional Reservoir Characterization

2016 ◽  
Vol 139 (2) ◽  
Author(s):  
Kyungbook Lee ◽  
Seungpil Jung ◽  
Taehun Lee ◽  
Jonggeun Choe
Keyword(s):  
Ensemble Kalman Filter ◽  
History Matching ◽  
Reservoir Characterization ◽  
Three Dimensional ◽  
Measurement Data ◽  
Minkowski Distance ◽  
Reliable Prediction ◽  
Reservoir Models ◽  
Ensemble Smoother ◽  
Filter Divergence

History matching is essential for estimating reservoir performances and decision makings. Ensemble Kalman filter (EnKF) has been researched for inverse modeling due to lots of advantages such as uncertainty quantification, real-time updating, and easy coupling with any forward simulator. However, it requires lots of forward simulations due to recursive update. Although ensemble smoother (ES) is much faster than EnKF, it is more vulnerable to overshooting and filter divergence problems. In this research, ES is coupled with both clustered covariance and selective measurement data to manage the two typical problems mentioned. As preprocessing work of clustered covariance, reservoir models are grouped by the distance-based method, which consists of Minkowski distance, multidimensional scaling, and K-means clustering. Also, meaningless measurement data are excluded from assimilation such as shut-in bottomhole pressures, which are too similar on every well. For a benchmark model, PUNQ-S3, a standard ES with 100 ensembles, shows severe over- and undershooting problem with log-permeability values from 36.5 to −17.3. The concept of the selective use of observed data partially mitigates the problem, but it cannot match the true production. However, the proposed method, ES with clustered covariance and selective measurement data together, manages the overshooting problem and follows histogram of the permeability in the reference field. Uncertainty quantifications on future field productions give reliable prediction, containing the true performances. Therefore, this research extends the applicatory of ES to 3D reservoirs by improving reliability issues.

scholarly journals Efficient Dimensionality Reduction Methods in Reservoir History Matching

Energies ◽  
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.

scholarly journals Joint Estimation of Hydraulic and Biochemical Parameters for Reactive Transport Modelling with a Modified ILUES Algorithm

Water ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 2161
Author(s):  
Ruicheng Zhang ◽  
Nianqing Zhou ◽  
Xuemin Xia ◽  
Guoxian Zhao ◽  
Simin Jiang
Keyword(s):  
Reactive Transport ◽  
Biochemical Parameters ◽  
Transport Model ◽  
Joint Estimation ◽  
Model Parameters ◽  
Transport Modelling ◽  
Selection Scheme ◽  
Related Model ◽  
Ensemble Smoother ◽  
Iterative Ensemble Smoother

Multicomponent reactive transport modeling is a powerful tool for the comprehensive analysis of coupled hydraulic and biochemical processes. The performance of the simulation model depends on the accuracy of related model parameters whose values are usually difficult to determine from direct measurements. In this situation, estimates of these uncertain parameters can be obtained by solving inverse problems. In this study, an efficient data assimilation method, the iterative local updating ensemble smoother (ILUES), is employed for the joint estimation of hydraulic parameters, biochemical parameters and contaminant source characteristics in the sequential biodegradation process of tetrachloroethene (PCE). In the framework of the ILUES algorithm, parameter estimation is realized by updating local ensemble with the iterative ensemble smoother (IES). To better explore the parameter space, the original ILUES algorithm is modified by determining the local ensemble partly with a linear ranking selection scheme. Numerical case studies based on the sequential biodegradation of PCE are then used to evaluate the performance of the ILUES algorithm. The results show that the ILUES algorithm is able to achieve an accurate joint estimation of related model parameters in the reactive transport model.

Improved Estimation and Forecasting Through Residual-Based Model Error Quantification

SPE Journal ◽  
2020 ◽  
Vol 25 (02) ◽  
pp. 951-968 ◽  
Author(s):  
Minjie Lu ◽  
Yan Chen
Keyword(s):  
History Matching ◽  
Historical Data ◽  
Total Error ◽  
Model Error ◽  
Complex Nature ◽  
Model Parameters ◽  
Observation Error ◽  
Model Errors ◽  
Ensemble Smoother ◽  
Iterative Ensemble Smoother

Summary Owing to the complex nature of hydrocarbon reservoirs, the numerical model constructed by geoscientists is always a simplified version of reality: for example, it might lack resolution from discretization and lack accuracy in modeling some physical processes. This flaw in the model that causes mismatch between actual observations and simulated data when “perfect” model parameters are used as model inputs is known as “model error”. Even in a situation when the model is a perfect representation of reality, the inputs to the model are never completely known. During a typical model calibration procedure, only a subset of model inputs is adjusted to improve the agreement between model responses and historical data. The remaining model inputs that are not calibrated and are likely fixed at incorrect values result in model error in a similar manner as the imperfect model scenario. Assimilation of data without accounting for model error can result in the incorrect adjustment to model parameters, the underestimation of prediction uncertainties, and bias in forecasts. In this paper, we investigate the benefit of recognizing and accounting for model error when an iterative ensemble smoother is used to assimilate production data. The correlated “total error” (a combination of model error and observation error) is estimated from the data residual after a standard history-matching using the Levenberg-Marquardt form of iterative ensemble smoother (LM-EnRML). This total error is then used in further data assimilations to improve the estimation of model parameters and quantification of prediction uncertainty. We first illustrate the method using a synthetic 2D five-spot example, where some model errors are deliberately introduced, and the results are closely examined against the known “true” model. Then, the Norne field case is used to further evaluate the method. The Norne model has previously been history-matched using the LM-EnRML (Chen and Oliver 2014), where cell-by-cell properties (permeability, porosity, net-to-gross, vertical transmissibility) and parameters related to fault transmissibility, depths of water/oil contacts, and relative permeability function are adjusted to honor historical data. In this previous study, the authors highlighted the importance of including large amounts of model parameters, the proper use of localization, and heuristic adjustment of data noise to account for modeling error. In this paper, we improve the last aspect by quantitatively estimating model error using residual analysis.

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