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.

Simultaneous Estimation of Relative Permeability and Capillary Pressure for PUNQ-S3 Model With a Damped Iterative-Ensemble-Kalman-Filter Technique

SPE Journal ◽  
2017 ◽  
Vol 22 (03) ◽  
pp. 971-984 ◽  
Author(s):  
Yin Zhang ◽  
Zhaoqi Fan ◽  
Daoyong Yang ◽  
Heng Li ◽  
Shirish Patil
Keyword(s):  
Kalman Filter ◽  
Capillary Pressure ◽  
Relative Permeability ◽  
Ensemble Kalman Filter ◽  
History Matching ◽  
Simultaneous Estimation ◽  
Reservoir Models ◽  
Ensemble Smoother ◽  
Iterative Ensemble Smoother ◽  
Capillary Pressure Curves

Summary A damped iterative-ensemble-Kalman-filter (IEnKF) algorithm has been proposed to estimate relative permeability and capillary pressure curves simultaneously for the PUNQ-S3 model, while its performance has been compared with that of the CMOST module, iterative-ensemble-smoother (IES) algorithm, and traditional ensemble-Kalman-filter (EnKF) technique. The power-law model is used to represent the relative permeability and capillary pressure curves, while three-phase relative permeability for oil phase is determined by use of the modified Stone II model. By assimilating the observed production data, the relative permeability and capillary pressure curves are inversely, automatically, and successively updated, achieving an excellent agreement with the reference cases. Not only are the associated uncertainties reduced significantly during the updating process, but also each of the updated reservoir models predicts the production profile that is in good agreement with the reference cases. Although the damped IEnKF technique shows the highest accuracy on estimation results, history-matching results, and prediction performance for the PUNQ-S3 model, its computational expense is still high compared with the other three techniques. In addition, the variations in the ensemble of the updated reservoir models and production profiles of the damped IEnKF provide a robust and consistent framework for uncertainty analysis.

Assessing the Uncertainty in Reservoir Description and Performance Predictions With the Ensemble Kalman Filter

SPE Journal ◽  
2007 ◽  
Vol 12 (03) ◽  
pp. 382-391 ◽  
Author(s):  
Mohammad Zafari ◽  
Albert Coburn Reynolds
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
History Matching ◽  
Reservoir Characterization ◽  
Reservoir Performance ◽  
Reservoir Models ◽  
Performance Predictions ◽  
And Performance ◽  
Reservoir Description

Summary Recently, the ensemble Kalman Filter (EnKF) has gained popularity in atmospheric science for the assimilation of data and the assessment of uncertainty in forecasts for complex, large-scale problems. A handful of papers have discussed reservoir characterization applications of the EnKF, which can easily and quickly be coupled with any reservoir simulator. Neither adjoint code nor specific knowledge of simulator numerics is required for implementation of the EnKF. Moreover, data are assimilated (matched) as they become available; a suite of plausible reservoir models (the ensemble, set of ensemble members or suite or realizations) is continuously updated to honor data without rematching data assimilated previously. Because of these features, the method is far more efficient for history matching dynamic data than automatic history matching based on optimization algorithms. Moreover, the set of realizations provides a way to evaluate the uncertainty in reservoir description and performance predictions. Here we establish a firm theoretical relation between randomized maximum likelihood and the ensemble Kalman filter. Although we have previously generated reservoir characterization examples where the method worked well, here we also provide examples where the performance of EnKF does not provide a reliable characterization of uncertainty. Introduction Our main interest is in characterizing the uncertainty in reservoir description and reservoir performance predictions in order to optimize reservoir management. To do so, we wish to generate a suite of plausible reservoir models (realizations) that are consistent with all information and data. If the set of models is obtained by correctly sampling the pdf, then the set of models give a characterization of the uncertainty in the reservoir model. Thus, by predicting future reservoir performance with each of the realizations, and calculating statistics on the set of outcomes, one can evaluate the uncertainty in reservoir performance predictions.

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.

Uncertainty Quantification Using Streamline Based Inversion and Distance Based Clustering

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Jihoon Park ◽  
Jeongwoo Jin ◽  
Jonggeun Choe
Keyword(s):  
Uncertainty Quantification ◽  
Travel Time ◽  
History Matching ◽  
Reservoir Characterization ◽  
Uncertainty Assessment ◽  
Dynamic Responses ◽  
Time Inversion ◽  
Dynamic Data ◽  
Reservoir Models ◽  
Permeability Distribution

For decision making, it is crucial to have proper reservoir characterization and uncertainty assessment of reservoir performances. Since initial models constructed with limited data have high uncertainty, it is essential to integrate both static and dynamic data for reliable future predictions. Uncertainty quantification is computationally demanding because it requires a lot of iterative forward simulations and optimizations in a single history matching, and multiple realizations of reservoir models should be computed. In this paper, a methodology is proposed to rapidly quantify uncertainties by combining streamline-based inversion and distance-based clustering. A distance between each reservoir model is defined as the norm of differences of generalized travel time (GTT) vectors. Then, reservoir models are grouped according to the distances and representative models are selected from each group. Inversions are performed on the representative models instead of using all models. We use generalized travel time inversion (GTTI) for the integration of dynamic data to overcome high nonlinearity and take advantage of computational efficiency. It is verified that the proposed method gathers models with both similar dynamic responses and permeability distribution. It also assesses the uncertainty of reservoir performances reliably, while reducing the amount of calculations significantly by using the representative models.

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.

Quantitative 4D Seismic Assisted History Matching Using Ensemble-Based Methods on the Vilje Field

2020 ◽  
Author(s):  
Konrad Wojnar ◽  
Jon S?trom ◽  
Tore Felix Munck ◽  
Martha Stunell ◽  
Stig Sviland-Østre ◽  
...  
Keyword(s):  
Decision Making ◽  
Seismic Data ◽  
History Matching ◽  
Reservoir Characterization ◽  
Reservoir Management ◽  
History Match ◽  
Field Development ◽  
Qualitative And Quantitative ◽  
Reservoir Models ◽  
4D Seismic

Abstract The aim of the study was to create an ensemble of equiprobable models that could be used for improving the reservoir management of the Vilje field. Qualitative and quantitative workflows were developed to systematically and efficiently screen, analyze and history match an ensemble of reservoir simulation models to production and 4D seismic data. The goal of developing the workflows is to increase the utilization of data from 4D seismic surveys for reservoir characterization. The qualitative and quantitative workflows are presented, describing their benefits and challenges. The data conditioning produced a set of history matched reservoir models which could be used in the field development decision making process. The proposed workflows allowed for identification of outlying prior and posterior models based on key features where observed data was not covered by the synthetic 4D seismic realizations. As a result, suggestions for a more robust parameterization of the ensemble were made to improve data coverage. The existing history matching workflow efficiently integrated with the quantitative 4D seismic history matching workflow allowing for the conditioning of the reservoir models to production and 4D data. Thus, the predictability of the models was improved. This paper proposes a systematic and efficient workflow using ensemble-based methods to simultaneously screen, analyze and history match production and 4D seismic data. The proposed workflow improves the usability of 4D seismic data for reservoir characterization, and in turn, for the reservoir management and the decision-making processes.

scholarly journals History matching of petroleum reservoir models by the Ensemble Kalman Filter and parameterization methods

2013 ◽  
Vol 55 ◽  
pp. 84-95 ◽  
Author(s):  
Leila Heidari ◽  
Véronique Gervais ◽  
Mickaële Le Ravalec ◽  
Hans Wackernagel
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
History Matching ◽  
Petroleum Reservoir ◽  
Reservoir Models

Time-lapse seismic history matching with an iterative ensemble smoother and deep convolutional autoencoder

Geophysics ◽  
2019 ◽  
Vol 85 (1) ◽  
pp. M15-M31 ◽  
Author(s):  
Mingliang Liu ◽  
Dario Grana
Keyword(s):  
Data Assimilation ◽  
Seismic Data ◽  
History Matching ◽  
Time Lapse ◽  
Production Data ◽  
Data Set ◽  
Reservoir Models ◽  
Ensemble Smoother ◽  
Convolutional Autoencoder ◽  
Seismic Measurements

We have developed a time-lapse seismic history matching framework to assimilate production data and time-lapse seismic data for the prediction of static reservoir models. An iterative data assimilation method, the ensemble smoother with multiple data assimilation is adopted to iteratively update an ensemble of reservoir models until their predicted observations match the actual production and seismic measurements and to quantify the model uncertainty of the posterior reservoir models. To address computational and numerical challenges when applying ensemble-based optimization methods on large seismic data volumes, we develop a deep representation learning method, namely, the deep convolutional autoencoder. Such a method is used to reduce the data dimensionality by sparsely and approximately representing the seismic data with a set of hidden features to capture the nonlinear and spatial correlations in the data space. Instead of using the entire seismic data set, which would require an extremely large number of models, the ensemble of reservoir models is iteratively updated by conditioning the reservoir realizations on the production data and the low-dimensional hidden features extracted from the seismic measurements. We test our methodology on two synthetic data sets: a simplified 2D reservoir used for method validation and a 3D application with multiple channelized reservoirs. The results indicate that the deep convolutional autoencoder is extremely efficient in sparsely representing the seismic data and that the reservoir models can be accurately updated according to production data and the reparameterized time-lapse seismic data.

scholarly journals Assessment of multilevel ensemble-based data assimilation for reservoir history matching

2019 ◽  
Vol 24 (1) ◽  
pp. 217-239
Author(s):  
Kristian Fossum ◽  
Trond Mannseth ◽  
Andreas S. Stordal
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
History Matching ◽  
Computational Cost ◽  
Ensemble Size ◽  
Matching Problems ◽  
Reservoir Models ◽  
Reservoir History Matching ◽  
Computational Resources

AbstractMultilevel ensemble-based data assimilation (DA) as an alternative to standard (single-level) ensemble-based DA for reservoir history matching problems is considered. Restricted computational resources currently limit the ensemble size to about 100 for field-scale cases, resulting in large sampling errors if no measures are taken to prevent it. With multilevel methods, the computational resources are spread over models with different accuracy and computational cost, enabling a substantially increased total ensemble size. Hence, reduced numerical accuracy is partially traded for increased statistical accuracy. A novel multilevel DA method, the multilevel hybrid ensemble Kalman filter (MLHEnKF) is proposed. Both the expected and the true efficiency of a previously published multilevel method, the multilevel ensemble Kalman filter (MLEnKF), and the MLHEnKF are assessed for a toy model and two reservoir models. A multilevel sequence of approximations is introduced for all models. This is achieved via spatial grid coarsening and simple upscaling for the reservoir models, and via a designed synthetic sequence for the toy model. For all models, the finest discretization level is assumed to correspond to the exact model. The results obtained show that, despite its good theoretical properties, MLEnKF does not perform well for the reservoir history matching problems considered. We also show that this is probably caused by the assumptions underlying its theoretical properties not being fulfilled for the multilevel reservoir models considered. The performance of MLHEnKF, which is designed to handle restricted computational resources well, is quite good. Furthermore, the toy model is utilized to set up a case where the assumptions underlying the theoretical properties of MLEnKF are fulfilled. On that case, MLEnKF performs very well and clearly better than MLHEnKF.

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