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.

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.

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.

Use of Channel Information Update and Discrete Cosine Transform in Ensemble Smoother for Channel Reservoir Characterization

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Hyungsik Jung ◽  
Honggeun Jo ◽  
Sungil Kim ◽  
Byeongcheol Kang ◽  
Hoonyoung Jeong ◽  
...  
Keyword(s):  
Discrete Cosine Transform ◽  
Computational Cost ◽  
Bimodal Distribution ◽  
Petroleum Engineering ◽  
Observation Data ◽  
Cosine Transform ◽  
Future Production ◽  
Ensemble Smoother ◽  
Information Update ◽  
Channel Information

Ensemble Kalman filter (EnKF) is one of the powerful optimization schemes for production data history matching in petroleum engineering. It provides promising characterization results and dependable future prediction of production performances. However, it needs high computational cost due to its recursive updating procedures. Ensemble smoother (ES), which updates all available observation data at once, has high calculation efficiency but tends to give unreliable results compared with EnKF. Particularly, it is challenging to channel reservoirs, because geological parameters of those follow a bimodal distribution. In this paper, we propose a new ES method using a channel information update scheme and discrete cosine transform (DCT). The former can assimilate channel information of ensemble models close to the reference, maintaining a bimodal distribution of parameters. DCT is also useful for figuring out main channel features by extracting out essential coefficients which represent overall channel characteristics. The proposed method is applied to two cases of 2D and 3D channel reservoirs and compared with EnKF and ES. The method not only provides reliable characterization results with clear channel connectivity but also preserves a bimodal distribution of parameters. In addition, it gives dependable estimations of future production performances by reducing uncertainties in the prior models.

FET SMALL-SIGNAL MODELING USING MEL-FREQUENCY CEPSTRAL COEFFICIENTS AND THE DISCRETE COSINE TRANSFORM

2010 ◽  
Vol 19 (08) ◽  
pp. 1835-1846 ◽  
Author(s):  
R. R. ELSHARKAWY ◽  
M. HINDY ◽  
S. EL-RABAIE ◽  
M. I. DESSOUKY
Keyword(s):  
Discrete Cosine Transform ◽  
Measurement Errors ◽  
Input Data ◽  
Small Signal ◽  
Scattering Parameters ◽  
Signal Modeling ◽  
Mel Frequency Cepstral Coefficients ◽  
Cosine Transform ◽  
Cepstral Coefficients ◽  
Small Signal Modeling

In this paper, a novel neural technique is proposed for FET small-signal modeling. This technique is based on the discrete cosine transform (DCT) and the Mel-frequency cepstral coefficients (MFCCs). The input data to traditional neural systems for FET small-signal modeling are the scattering parameters and the corresponding frequencies in a certain band, and the outputs are the circuit elements. In the proposed technique, the input data are considered random, and the MFCCs are calculated from these inputs and their DCT. The MFCCs are used to give a few features from the input random data sequence to be used for the training of the neural networks. The objective of using MFCCs is to characterize the random input sequence with features that are robust against measurement errors. The MFCCs extracted from the DCT of the inputs increase the robustness against measurement errors. There are two benefits that can be achieved using the proposed technique; a reduction in the number of neural inputs and hence a faster convergence of the neural training algorithm and a robustness against measurement errors in the testing phase. Experimental results show that the technique based on the DCT and MFCCs is less sensitive to measurement errors than using the actual measured scattering parameters.

Binary Level Set Methods for Dynamic Reservoir Characterization by Operator Splitting Scheme

2012 ◽  
Vol 4 (06) ◽  
pp. 780-798
Author(s):  
Changhui Yao
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Reservoir Characterization ◽  
Operator Splitting ◽  
Saddle Point Problem ◽  
Absolute Permeability ◽  
Point Problem ◽  
Splitting Scheme ◽  
Two Phase ◽  
The Absolute

AbstractIn this paper, operator splitting scheme for dynamic reservoir characterization by binary level set method is employed. For this problem, the absolute permeability of the two-phase porous medium flow can be simulated by the constrained augmented Lagrangian optimization method with well data and seismic time-lapse data. By transforming the constrained optimization problem in an unconstrained one, the saddle point problem can be solved by Uzawas algorithms with operator splitting scheme, which is based on the essence of binary level set method. Both the simple and complicated numerical examples demonstrate that the given algorithms are stable and efficient and the absolute permeability can be satisfactorily recovered.

History Matching of Channelized Reservoirs With Vector-Based Level-Set Parameterization

SPE Journal ◽  
2014 ◽  
Vol 19 (03) ◽  
pp. 514-529 ◽  
Author(s):  
Jing Ping ◽  
Dongxiao Zhang
Keyword(s):  
Level Set ◽  
History Matching ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Matching Problem ◽  
Level Set Function ◽  
Level Function ◽  
Set Up ◽  
Non Gaussian ◽  
Channelized Reservoirs

Summary For channelized reservoirs with unknown channel distributions, identifying the continuous and sinuous features of channel distributions is crucial for determining their production behaviors. However, traditional history-matching methods are not appropriate because the pixel-based rock-property fields are usually highly non-Gaussian. In this work, a vector-based level-set parameterization technique for channelized reservoirs is presented. We also propose a combination of this parameterization method and a frequently used history-matching approach, the ensemble Kalman filter (EnKF). To properly represent the continuity and sinuosity of its embedded features, the channelized reservoir is parameterized with a vector that consists of level-set function, real radius, and virtual radius on a representing node system. The level-function value indicates the existence of the particular facies; the real radius of a circle in two dimensions or a sphere in three dimensions signifies the size of the facies; and the virtual radius is used to ensure the continuity of the channelized facies. The 2D and 3D examples of channelized reservoirs are set up to demonstrate the capability of the proposed method. It is found that this method is effective to deal with the history-matching problem of channelized reservoirs.

Reservoir Characterization With the Discrete Cosine Transform

SPE Journal ◽  
2009 ◽  
Vol 14 (01) ◽  
pp. 182-201 ◽  
Author(s):  
Behnam Jafarpour ◽  
Dennis B. McLaughlin
Keyword(s):  
Discrete Cosine Transform ◽  
Reservoir Characterization ◽  
Cosine Transform

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 Reservoir characterization using stochastic initializations and the level set method

2008 ◽  
Vol 56 (3) ◽  
pp. 697-708 ◽  
Author(s):  
Rossmary Villegas ◽  
Oliver Dorn ◽  
Miguel Moscoso ◽  
Manuel Kindelan
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Reservoir Characterization
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