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Research Papers: Petroleum Engineering

Enhanced History Matching of Gas Reservoirs With an Aquifer Using the Combination of Discrete Cosine Transform and Level Set Method in ES-MDA

[+] Author and Article Information
Sungil Kim

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

Hyungsik Jung

Department of Energy Systems Engineering,
Seoul National University,
Seoul, 08826, South Korea
e-mail: hs6735@snu.ac.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 July 7, 2017; final manuscript received December 26, 2018; published online January 18, 2019. Editor: Hameed Metghalchi.

J. Energy Resour. Technol 141(7), 072906 (Jan 18, 2019) (15 pages) Paper No: JERT-17-1343; doi: 10.1115/1.4042413 History: Received July 07, 2017; Revised December 26, 2018

Reservoir characterization is a process to make dependable reservoir models using available reservoir information. There are promising ensemble-based methods such as ensemble Kalman filter (EnKF), ensemble smoother (ES), and ensemble smoother with multiple data assimilation (ES-MDA). ES-MDA is an iterative version of ES with inflated covariance matrix of measurement errors. It provides efficient and consistent global updates compared to EnKF and ES. Ensemble-based method might not work properly for channel reservoirs because its parameters are highly non-Gaussian. Thus, various parameterization methods are suggested in previous studies to handle nonlinear and non-Gaussian parameters. Discrete cosine transform (DCT) can figure out essential channel information, whereas level set method (LSM) has advantages on detailed channel border analysis in grid scale transforming parameters into Gaussianity. However, DCT and LSM have weaknesses when they are applied separately on channel reservoirs. Therefore, we propose a properly designed combination algorithm using DCT and LSM in ES-MDA. When DCT and LSM agree with each other on facies update results, a grid has relevant facies naturally. If not, facies is assigned depending on the average facies probability map from DCT and LSM. By doing so, they work in supplementary way preventing from wrong or biased decision on facies. Consequently, the proposed method presents not only stable channel properties such as connectivity and continuity but also similar pattern with the true. It also gives trustworthy future predictions of gas and water productions due to well-matched facies distribution according to the reference.

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Figures

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Fig. 1

Three options for dynamic data use in a model and comparison of simulation time in EnKF

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Fig. 2

One example of overall update procedures of a channel reservoir using DCT

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Fig. 3

Whole procedure of DCT, LSM, and the combination of DCT and LSM in ES-MDA

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Fig. 4

Details of LSM application in a two facies reservoir model of sand and shale: (a) Calculation of the distance for sand criterion and (b) Final distance of sand and shale criterion

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Fig. 5

Characteristics of the ways DCT and LSM work in a reservoir model

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Fig. 6

Training image for generation of initial reservoir models, the reference field, and aquifer modeling: (a) Training image for right channel thickness, (b) Training image for thicker channel width, (c) Reference field, and (d) Aquifer modeling of a reservoir

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Fig. 7

Total simulation time and assimilation time steps for ES-MDA

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Fig. 8

Final updated permeability distribution of each method: averages of ensemble members: (a) Reference field, (b) Initial ensemble, (c) Initial ensemble of thicker channel, (d) DCT, (e) LSM, (f) DCT and LSM, (g) DCT in thicker channel, (h) LSM in thicker channel, and (i) DCT and LSM in thicker channel

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Fig. 9

Facies field examples of ensemble members by each method: (a) Ensemble number 1, (b) Ensemble number 8, (c) Ensemble number 1 of thicker channel, and (d) Ensemble number 8 of thicker channel

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Fig. 10

Updated facies fields of ensemble number one in five iterations by each method in the thicker channel

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Fig. 11

Aquifer strengths of initial and final assimilated ensembles by each method: (a) Initial ensemble, (b) DCT, (c) LSM, (d) The proposed (the combination of DCT and LSM), (e) DCT (thicker channel), (f) LSM (thicker channel), and (g) The proposed (thicker channel)

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Fig. 12

Well gas and water productions of initial and updated ensembles by each method (P: production well): (a) Initial ensemble (gas), (b) DCT(gas), (c) LSM (gas), (d) The proposed (gas), (e) Initial ensemble (water), (f) DCT (water), (g) LSM (water), and (h) The proposed (water)

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Fig. 13

Well gas and water productions of initial and updated ensembles by each method (thicker channel): (a) Initial ensemble (gas), (b) DCT(gas), (c) LSM (gas), (d) The proposed (gas), (e) Initial ensemble (water), (f) DCT (water), (g) LSM (water), and (h) The proposed (water)

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Fig. 14

Total water production of initial and updated ensembles by each method: (a) Initial, (b) DCT, (c) LSM, (d) The combination, (e) Initial (f) DCT (g) LSM, and (h) The combination

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