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Research Papers: Petroleum Engineering

Use of Channel Information Update and Discrete Cosine Transform in Ensemble Smoother for Channel Reservoir Characterization

[+] Author and Article Information
Hyungsik Jung

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

Honggeun Jo

Department of Energy Systems Engineering,
Seoul National University,
Seoul 08826, Korea
e-mail: jhg1331@snu.ac.kr

Sungil Kim

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

Byeongcheol Kang

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

Hoonyoung Jeong

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

Jonggeun Choe

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

Contributed by the Petroleum Division of ASME for publication in the Journal of Energy Resources Technology. Manuscript received September 14, 2018; final manuscript received May 21, 2019; published online July 12, 2019. Assoc. Editor: Hameed Metghalchi.

J. Energy Resour. Technol 142(1), 012901 (Jul 12, 2019) (12 pages) Paper No: JERT-17-1368; doi: 10.1115/1.4043856 History: Received September 14, 2018; Accepted May 21, 2019

Ensemble Kalman filter (EnKF) is one of the powerful optimization schemes for production data history matching in petroleum engineering. It provides promising characterization results and dependable future prediction of production performances. However, it needs high computational cost due to its recursive updating procedures. Ensemble smoother (ES), which updates all available observation data at once, has high calculation efficiency but tends to give unreliable results compared with EnKF. Particularly, it is challenging to channel reservoirs, because geological parameters of those follow a bimodal distribution. In this paper, we propose a new ES method using a channel information update scheme and discrete cosine transform (DCT). The former can assimilate channel information of ensemble models close to the reference, maintaining a bimodal distribution of parameters. DCT is also useful for figuring out main channel features by extracting out essential coefficients which represent overall channel characteristics. The proposed method is applied to two cases of 2D and 3D channel reservoirs and compared with EnKF and ES. The method not only provides reliable characterization results with clear channel connectivity but also preserves a bimodal distribution of parameters. In addition, it gives dependable estimations of future production performances by reducing uncertainties in the prior models.

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Figures

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Fig. 1

Comparison between EnKF and ES: (a) EnKF and (b) ES

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Fig. 2

An example of CDF mapping: histogram and CDF of (a) prior parameter and (b) posterior parameter (note that μsand, μshale, and φ are updated)

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Fig. 3

An example of DCT application

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Fig. 4

Procedure of the proposed method (the numeric values are calculation results for the demonstration of each step)

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Fig. 5

The reference of 2D channel reservoir: (a) log permeability field and (b) histogram

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Fig. 6

Mean of log permeability fields: (a) initial, assimilated by (b) EnKF, (c) ES, and (d) the proposed method

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Fig. 7

Log permeability fields and their histograms of two ensemble members: (a) initial, assimilated by (b) EnKF, (c) ES, and (d) the proposed method

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Fig. 8

WOPR predictions of ensembles: (a) initial, assimilated by (b) EnKF, (c) ES, and (d) the proposed method (P represents a production well)

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Fig. 9

WWCT predictions of ensembles: (a) initial, assimilated by (b) EnKF, (c) ES, and (d) the proposed method

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Fig. 10

Histograms of channel information: initial (a) sand ratio, (b) mean permeability of sand, (c) mean permeability of shale, assimilated (d) sand ratio, (e) mean permeability of sand, and (f) mean permeability of shale

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Fig. 11

The reference field and its histogram of 3D Egg model

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Fig. 12

Average log permeability fields and their histograms (Egg model): (a) initial, assimilated by (b) EnKF, (c) ES, and (d) the proposed method

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Fig. 13

WOPR predictions of ensembles (Egg model): (a) initial, assimilated by (b) EnKF, (c) ES, and (d) the proposed method

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Fig. 14

WWCT predictions of ensembles (Egg model): (a) initial, assimilated by (b) EnKF, (c) ES, and (d) the proposed method

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Fig. 15

Histograms of channel information (Egg model): initial (a) sand ratio, (b) mean permeability of sand, (c) mean permeability of shale, assimilated (d) sand ratio, (e) mean permeability of sand, and (f) mean permeability of shale

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