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Research Papers: Petroleum Engineering

Characterization of Various Channel Fields Using an Initial Ensemble Selection Scheme
and Covariance Localization

[+] Author and Article Information
Hyungsik Jung

Department of Energy Systems Engineering,
Seoul National University,
Seoul 08826, South Korea
e-mail: hs6735@snu.ac.kr

Honggeun Jo

Department of Energy Systems Engineering,
Seoul National University,
Seoul 08826, South Korea
e-mail: jhg1331@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 January 3, 2017; final manuscript received August 18, 2017; published online September 18, 2017. Assoc. Editor: Daoyong (Tony) Yang.

J. Energy Resour. Technol 139(6), 062906 (Sep 18, 2017) (12 pages) Paper No: JERT-17-1002; doi: 10.1115/1.4037811 History: Received January 03, 2017; Revised August 18, 2017

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.

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References

Figures

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Fig. 1

Determination of drainage area boundary using the direction of interfacial oil velocity: (a) one-dimensional and (b) two-dimensional

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Fig. 2

Log permeability field: (a) reference, (b) mean of 400 ensemble, and (c) mean of 50 models selected by IESS

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Fig. 3

WOPR results of initial ensembles: (a) 400 ensemble and (b) 50 models selected by IESS

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Fig. 4

WWCT results of initial ensembles: (a) 400 ensemble and (b) 50 models selected by IESS

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Fig. 5

The average of assimilated log permeability field by the standard EnKF (a), EnKF assisted by IESS (b), and ES assisted by IESS (c)

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Fig. 6

WOPR results of assimilated ensembles by the three methods: (a) the standard EnKF, (b) EnKF assisted by IESS, and (c) ES assisted by IESS

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Fig. 7

WWCT results of assimilated ensembles by the three methods: (a) the standard EnKF, (b) EnKF assisted by IESS, and (c) ES assisted by IESS

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Fig. 8

Updated results by the proposed method: (a) the average permeability field, (b) WOPR, and (c) WWCT

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Fig. 9

Permeability histogram of the reference and results by the four methods (the reference field: sand 500 md and shale 5 md): (a) reference, (b) the standard EnKF, (c) EnKF assisted by IESS, (d) ES assisted by IESS, and (e) the proposed method

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Fig. 10

Total simulation time for the four methods compared

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Fig. 11

Log permeability fields of cases 1 and 2: (a) reference, (b) 50 selected models, (c) the standard EnKF, and (d) the proposed method

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Fig. 12

Permeability histograms of cases 1 and 2: (a) reference, (b) 50 selected models, (c) the standard EnKF, and (d) the proposed method

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Fig. 13

Log permeability field of a complicated channel (case 3): (a) reference, (b) 400 initial ensemble, (c) 50 selected models, (d) the standard EnKF, and (e) the proposed method

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Fig. 14

Permeability histograms of the complicated channel (case 3): (a) reference, (b) the standard EnKF, and (c) the proposed method

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