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Research Papers: Petroleum Engineering

Ensemble Kalman Filter With Principal Component Analysis Assisted Sampling for Channelized Reservoir Characterization

[+] Author and Article Information
Byeongcheol Kang

Department of Energy Systems Engineering,
Seoul National University,
Seoul 08826, South Korea
e-mail: qudcjf@snu.ac.kr

Hyungjun Yang

Department of Energy Systems Engineering,
Seoul National University,
Seoul 08826, South Korea
e-mail: yang4697@snu.ac.kr

Kyungbook Lee

Petroleum and Marine Research Division,
Korea Institute of Geoscience
and Mineral Resources,
Daejeon 34132, South Korea
e-mail: kblee@kigam.re.kr

Jonggeun Choe

Department of Energy Resources Engineering,
Seoul National University,
Seoul 08826, South Korea
e-mail: johnchoe@snu.ac.kr

1Corresponding author.

Contributed by the Petroleum Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received May 17, 2016; final manuscript received January 6, 2017; published online February 6, 2017. Editor: Hameed Metghalchi.

J. Energy Resour. Technol 139(3), 032907 (Feb 06, 2017) (12 pages) Paper No: JERT-16-1218; doi: 10.1115/1.4035747 History: Received May 17, 2016; Revised January 06, 2017

Ensemble Kalman filter (EnKF) is one of the widely used optimization methods in petroleum engineering. It uses multiple reservoir models, known as ensemble, for quantifying uncertainty ranges, and model parameters are updated using observation data repetitively. However, it requires a large number of ensemble members to get stable results, causing huge simulation time. In this study, we propose a sampling method using principal component analysis (PCA) and K-means clustering. It excludes poor ensemble with different geological trends to the reference so we can improve both speed and reliability of future predictions. A representative model, which is selected from candidate models of each cluster, has a role to choose proper ensemble for EnKF. For applying EnKF to channelized reservoirs, we compare cases with using 400, randomly picked 100, sampled 100 using Hausdorff distance, and sampled 100 by the proposed method. The proposed method shows improvements over the other cases compared. It gives stable uncertainty ranges and well-updated reservoir parameters after the assimilations. Randomly selected 100 ensemble members predict wrong reservoir performances, and 400 ensemble members exhibit too large uncertainty ranges with long simulation times. Even though more ensemble members are utilized, they provide worse results due to disturbance by improperly designed models. We confirm our sampling strategy in a real field case, PUNQ-S3, and it reduces simulation time as well as improves the future predictions for efficient and reliable history matching.

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Figures

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Fig. 1

Procedures of the sampling method proposed

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Fig. 2

Distribution of 625 eigenvalues of covariance matrix in the descending order

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Fig. 3

Proposed procedures for sampling good ensemble members (the points with "×" mean the centers of the clusters): (a) ten clusters using K-means clustering, (b) selection of candidate models, (c) determination of a representative model, and (d) 100 initial models selected

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Fig. 4

Input data for generating initial reservoir models: (a) training image and (b) facies data used

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Fig. 5

Comparison with sampled and nonsampled ensemble members: (a) reference model, (b) examples of models selected, and (c) examples of models executed

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Fig. 6

Initial and assimilated reservoir models by the proposed method

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Fig. 7

Comparison of WOPR results at wells P2 (a) and P5 (b) of the four cases (case 1 is for 400 initial models; case 2 is for 100 models randomly selected; case 3 is for 100 models using Hausdorff distance; and case 4 is for 100 models selected by the proposed method)

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Fig. 8

Comparison of WWCT results at wells P2 (a) and P5 (b) of the four cases

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Fig. 9

Uncertainty quantification and simulation efficiency of the four cases: (a) FOPT and (b) FWPT

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Fig. 10

Top structure map of PUNQ-S3 field (PRO: production well and X: future well site)

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Fig. 11

Mean of permeability distributions for each layer after EnKF updates

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Fig. 12

Comparison of prediction performances on WOPR and WWCT of the three cases (case 1 for 400 initial models; case 2 for 100 models randomly selected; and case 3 for 100 models by the proposed method): (a) and (c) well PRO-1 and (b) and (d) well PRO-11

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Fig. 13

Comparison of prediction performances at wells PRO-1 ((a) and (c)) and PRO-11 ((b) and (d)) on WBHP and WGOR of the three cases

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Fig. 14

Box plots of future predictions at the 6025th day: (a) FOPT, (b) FGPT, and (c) FWPT

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