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 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

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.

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.

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