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Research Papers: Petroleum Engineering

Use of Clustered Covariance and Selective Measurement Data in Ensemble Smoother for Three-Dimensional Reservoir Characterization

[+] Author and Article Information
Kyungbook Lee, Taehun Lee

Petroleum and Marine Research Division,
Korea Institute of Geoscience
and Mineral Resources,
Daejeon 34132, South Korea

Seungpil Jung

E&P Business Division,
SK Innovation,
Seoul 03188, South Korea

Jonggeun Choe

Department of Energy Systems 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 January 22, 2016; final manuscript received August 2, 2016; published online August 23, 2016. Assoc. Editor: Daoyong (Tony) Yang.

J. Energy Resour. Technol 139(2), 022905 (Aug 23, 2016) (9 pages) Paper No: JERT-16-1036; doi: 10.1115/1.4034443 History: Received January 22, 2016; Revised August 02, 2016

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.

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Figures

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Fig. 1

Comparison of the assimilation scheme for observed data between EnKF and ES: (a) ES, (b) EnKF, and (c) observed data (Di represents observed data at the ith observation time ti)

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Fig. 2

Procedure of the clustered covariance using a distance-based method

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Fig. 3

Top structure map and the locations of production wells of PUNQ-S3 (modified from Ref. [34]) (WOC: water oil contact, GOC: gas oil contact, PRO: production well, and X: planned to be drilled in the future)

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Fig. 4

The average of the logarithm of horizontal permeability in the first layer of the benchmark model: (a) the reference field, (b) 100 initial ensemble models, (c) results of the standard ES, and (d) results of ES with clustered covariance

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Fig. 5

The result of the distance-based clustering with three models selected and displayed from the same cluster

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Fig. 6

Histogram of horizontal permeability in the first layer of PUNQ-S3: (a) the reference field, (b) initial ensemble model, (c) result of ES, and (d) result of ES with clustered covariance

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Fig. 7

Prediction of dynamic performances of the standard ES (the first row) and ES with clustered covariance (the second row) in the first layer of PUNQ-S3 until 16.5 y: (a) COP, (b) CGP, and (c) CWP. The thin lines represent the result of each updated model, and the thick line stands for the reference field's performance. The thick dot lines are P10, P50, and P90 of the 100 thin lines from the top to the bottom (COP: cumulative oil production, CGP: cumulative gas production, and CWP: cumulative water production)

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Fig. 8

The average of the logarithm of horizontal permeability in the benchmark model: (a) the reference field, (b) 100 initial ensemble models, (c) results of ES with selective data, and (d) results of the proposed method

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Fig. 9

Histogram of horizontal permeability on PUNQ-S3: (a) the reference field, (b) initial ensemble model, (c) result of ES with selective data, and (d) result of the proposed method

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Fig. 10

Prediction for cumulative water production until 16.5 y: (a) ES with selective data and (b) the proposed method. The thin lines represent the result of each updated model, and the thick line stands for the reference field's performance. The thick dot lines are P10, P50, and P90 of the 100 thin lines from the top to the bottom.

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