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.

scholarly journals Implementation of Region-Based Covariance Localization Ensemble Kalman Filter in History Matching Workflow

2017 ◽  
Vol 10 (1) ◽  
pp. 177-194
Author(s):  
Fajril Ambia ◽  
Tutuka Ariadji ◽  
Zuher Syihab ◽  
Agus Y. Gunawan
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
History Matching ◽  
Spatially Correlated ◽  
Reservoir Performance ◽  
Matching Process ◽  
True Model ◽  
Inherent Nature ◽  
The Many ◽  
Region Information

Background:History matching is an indispensable phase in the workflow of reservoir analysis. Nevertheless, there is a considerable challenge in performing the procedure in a proper scientific manner due to the inherent nature of non-unique solutions from the many-unknown variables with limited known equations.Objective:In this study, we introduce the Ensemble Kalman Filter (EnKF) method complemented by the Region-Based Covariance Localization (RCL) scheme to address the aforementioned issue.Method:The algorithms work initially by modifying the covariance localization generated by Gaussian correlation model using region information such as facies or flow unit, in which the area within a region is spatially correlated. Subsequently, the correlation between distant areas in the region is eliminated, hence promoting better modification of the distribution of the parameters while maintaining the characteristics of the predefined geological model of the reservoir.Result:Result shows that RCL scheme is capable of enhancing the performance of EnKF procedure and produce parameter distributions that is close to the true model of the reservoir.Conclusion:Implementation of the proposed methodology ameliorates the accuracy and reliability of the history matching process, thus establishing better consideration in predicting reservoir performance.

Quantifying Uncertainty for the PUNQ-S3 Problem in a Bayesian Setting With RML and EnKF

SPE Journal ◽  
2006 ◽  
Vol 11 (04) ◽  
pp. 506-515 ◽  
Author(s):  
Guohua Gao ◽  
Mohammad Zafari ◽  
Albert C. Reynolds
Keyword(s):  
Ensemble Kalman Filter ◽  
Oil Production ◽  
Production Data ◽  
A Posteriori ◽  
Reservoir Performance ◽  
Performance Predictions ◽  
Randomized Maximum Likelihood ◽  
The One ◽  
Probability Density Function Pdf

Summary The well known PUNQ-S3 reservoir model represents a synthetic problem which was formulated to test the ability of various methods and research groups to quantify the uncertainty in the prediction of cumulative oil production. Previous results reported on this project suggest that the randomized maximum likelihood (RML) method gives a biased characterization of the uncertainty. A major objective of this paper is to show that this is incorrect. With a correct implementation of the RML method within a Bayesian framework, we show that RML does an adequate job of sampling the a posteriori distribution for the PUNQ problem. In particular, the true predicted oil production lies within the band of predictions generated with the RML method and is not biased. We also apply the ensemble Kalman Filter (EnKF) method to the PUNQ data set, and show that this method also gives a reasonable quantification of the uncertainty in performance predictions with an uncertainty range similar to the one obtained with RML. Introduction We consider conditioning models to production data in a Bayesian framework and wish to generate a suite (ensemble) of models which represent a correct sampling of the conditional probability density function (pdf). By predicting future reservoir performance with each realization, we obtain a characterization of the uncertainty in predicted performance. Both the rejection algorithm and Markov chain Monte Carlo (MCMC) are theoretically sound sampling procedures, but they are too computationally inefficient for practical applications (Liu and Oliver 2003). Oliver et al. (1996) and Kitanidis (1986) independently proposed the randomized maximum likelihood (RML) method to generate an approximate sampling of the a posteriori pdf. Two different proofs (Oliver 1996; Reynolds et al. 1999) have been presented which show that the RML method samples the posterior probability density function (pdf) correctly if data are linearly related to the model; however, no rigorous theoretical foundation exists for the method when the relation between data and model is nonlinear, which is the case when the data represent production data. Computational results indicate that the RML method generates reasonable characterization of uncertainty for single-phase flow (Oliver et al. 1996; Reynolds et al. 1999; Liu and Oliver 2003). Our first objective is to show that, contrary to a previous claim (Floris 2001), RML gives a reasonable characterization of the uncertainty in predicted performance for the PUNQ-S3 problem; our second objective is to compare the quantification of uncertainty obtained with RML with the one obtained with the ensemble Kalman filter (EnKF). The PUNQ-S3 reservoir represents a synthetic model based on an actual reservoir (Floris et al. 2001; Barker et al. 2001). The problem was set up as a test case to allow various research groups to test their own methodology for the characterization of the uncertainty in reservoir performance predictions given some geologic information on the reservoir, hard data at well gridblocks and some scattered production data from the first 8 years of production. Then participants were asked to predict cumulative oil production for 16.5 years of total production and characterize the uncertainty in this prediction.

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

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.

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.

Structural Surface Uncertainty Modeling and Updating Using the Ensemble Kalman Filter

SPE Journal ◽  
2010 ◽  
Vol 15 (04) ◽  
pp. 1062-1076 ◽  
Author(s):  
A.. Seiler ◽  
S.I.. I. Aanonsen ◽  
G.. Evensen ◽  
J.C.. C. Rivenæs
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
History Matching ◽  
Reservoir Characterization ◽  
Production Data ◽  
Base Case ◽  
Future Production ◽  
Fixed Dimension ◽  
Structural Surface ◽  
Bottom Reservoir

Summary Although typically large uncertainties are associated with reservoir structure, the reservoir geometry is usually fixed to a single interpretation in history-matching workflows, and focus is on the estimation of geological properties such as facies location, porosity, and permeability fields. Structural uncertainties can have significant effects on the bulk reservoir volume, well planning, and predictions of future production. In this paper, we consider an integrated reservoir-characterization workflow for structural-uncertainty assessment and continuous updating of the structural reservoir model by assimilation of production data. We address some of the challenges linked to structural-surface updating with the ensemble Kalman filter (EnKF). An ensemble of reservoir models, expressing explicitly the uncertainty resulting from seismic interpretation and time-to-depth conversion, is created. The top and bottom reservoir-horizon uncertainties are considered as a parameter for assisted history matching and are updated by sequential assimilation of production data using the EnKF. To avoid modifications in the grid architecture and thus to ensure a fixed dimension of the state vector, an elastic-grid approach is proposed. The geometry of a base-case simulation grid is deformed to match the realizations of the top and bottom reservoir horizons. The method is applied to a synthetic example, and promising results are obtained. The result is an ensemble of history-matched structural models with reduced and quantified uncertainty. The updated ensemble of structures provides a more reliable characterization of the reservoir architecture and a better estimate of the field oil in place.

Importance of Distributed Temperature Sensor Data for Steam Assisted Gravity Drainage Reservoir Characterization and History Matching Within Ensemble Kalman Filter Framework

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Amit Panwar ◽  
Japan J. Trivedi ◽  
Siavash Nejadi
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
History Matching ◽  
Reservoir Characterization ◽  
Temperature Data ◽  
Gravity Drainage ◽  
Production Data ◽  
Facies Distribution ◽  
Steam Assisted Gravity Drainage ◽  
Temperature Observations

Distributed temperature sensing (DTS), an optical fiber down-hole monitoring technique, provides a continuous and permanent well temperature profile. In steam assisted gravity drainage (SAGD) reservoirs, the DTS plays an important role to provide depth-and-time continuous temperature measurement for steam management and production optimization. These temperature observations provide useful information for reservoir characterization and shale detection in SAGD reservoirs. However, use of these massive data for automated SAGD reservoir characterization has not been investigated. The ensemble Kalman filter (EnKF), a parameter estimation approach using these real-time temperature observations, provides a highly attractive algorithm for automatic history matching and quantitative reservoir characterization. Due to its complex geological nature, the shale barrier exhibits as a different facies in sandstone reservoirs. In such reservoirs, due to non-Gaussian distributions, the traditional EnKF underestimates the uncertainty and fails to obtain a good production data match. We implemented discrete cosine transform (DCT) to parameterize the facies labels with EnKF. Furthermore, to capture geologically meaningful and realistic facies distribution in conjunction with matching observed data, we included fiber-optic sensor temperature data. Several case studies with different facies distribution and well configurations were conducted. In order to investigate the effect of temperature observations on SAGD reservoir characterization, the number of DTS observations and their locations were varied for each study. The qualities of the history-matched models were assessed by comparing the facies maps, facies distribution, and the root mean square error (RMSE) of the predicted data mismatch. Use of temperature data in conjunction with production data demonstrated significant improvement in facies detection and reduced uncertainty for SAGD reservoirs. The RMSE of the predicted data is also improved. The results indicate that the assimilation of DTS data from nearby steam chamber location has a significant potential in significant reduction of uncertainty in steam chamber propagation and production forecast.

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