Real-Time Reservoir Characterization using Ensemble Kalman Filter During Waterflooding

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2006 Vol.43, Issue 2 Preview Page Next Page

Real-Time Reservoir Characterization using Ensemble Kalman Filter During Waterflooding 앙상블 칼만필터를 이용한 실시간 수공법 저류층 특성화: 박광원, 신용덕, 최종근
Kwangwon Park, Yongduk Shin and Jonggeun Choe

30 April 2006. pp. 143-150

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Abstract

In order to estimate reserves and maximize oil productions, it is critical to characterize an unknown reservoir. However, it is challenging because of severe non-linearity, non-uniqueness, and large number of variables with different levels of uncertainties. Ensemble Kalman filter (EnKF), known as a recursive data process algorithm, can make it possible to update many unknown variables simultaneously and assess the uncertainties within a model, measurements, and estimations. In this paper, we investigated applicabilities of EnKF for real-time reservoir update. For our objectives, we developed a reservoir characterization model using EnKF combined with a multiphase reservoir simulator. The developed model gave reliable results with measurement noises up to 10%, when the size of ensemble is larger than 100 ensemble members and when we normalize the static properties. With further researches and field applications, EnKF can be a powerful automatic history matching technique.

Keywords

Reservoir characterization

Ensemble Kalman filter

Real-time update

Automatic history matching

Uncertainty assessment

저류층 특성화는 매장량을 예측하고 생산량을 증가시키기 위해 필수적인 과정이다. 하지만 이는 시스템의 강한 비선형성, 비유일성, 서로 다른 수준의 불확실성을 포함한 다양한 변수들로 인해 매우 어렵다. 앙상블 칼만필터는 비선형시스템에서 오차를 포함한 반응을 실시간으로 처리하여 불확실성이 정량적으로 감소된 결과를 제시하는 반복적 자료 처리 기법이다. 이 연구에서는 앙상블 칼만필터를 적용하여 저류층을 특성화하는 모델을 개발하였다. 개발한 모델을 가상의 수공법 저류층에 적용한 결과, 신뢰할 만한 결과를 얻었다. 측정값에 포함된 오차의 수준, 앙상블크기, 정적 특성의 통계적 분포특성 등의 조건을 달리하여 앙상블 칼만필터를 적용한 결과, 측정오차가 10% 정도 되어도, 앙상블 개수가 100 이상이고 정규화를 적용하면 신뢰할만한 결과를 얻을 수 있었다. 이 연구를 통하여 자동 히스토리 매칭을 위한 앙상블 칼만필터의 적용성에 대한 가능성을 확인하였다.

키워드

저류층 특성화

앙상블 칼만필터

실시간 갱신

자동 히스토리 매칭

불확실성 평가

References

박광원, 최종근, 2004, “저류층 특성화를 위한 관측정 분포 최적화,” 한국자원공학회지, 제41권 5호, pp. 373-380.
Choe, J., Ki, S., Park, K., and Park, C., 2004, “Stochastic Optimization Using Streamline Simulation for Aquifer Characterization,” Proceedings of 32nd International Geological Congress, International Association for Mathematical Geology, Florence, Italy, Aug. 20-28.
Evensen, G., 2003, “The Ensemble Kalman Filter: Theoretical Formulation and Practical Implementation,” Ocean Dynamics, Vol. 53, No. 4, pp. 343-367.
Evensen, G., 1994, “Sequential Data Assimilation with a Nonlinear Quasi-Geostrophic Model Using Monte Carlo Methods to Forecast Error Statistics,” J. of Geophysical Research, Vol. 99, pp. 10,143-10,162.
Gu, Y. and Oliver, D.S., 2004, “History Matching of the PUNQ-S3 Reservoir Model Using the Ensemble Kalman Filter,” paper 89942 presented at the SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers, Houston, Texas, Sep. 26-29.
Jang, M., and Choe, J., 2004, “An Inverse System for Incorporation of Conditioning to Pressure and Streamline-Based Calibration,” J. of Contaminant Hydrology, Vol. 69, pp. 139-156.
Jang, M. and Choe, J., 2002, “Stochastic Optimization for Global Minimization and Geostatistical Calibration,” J. of Hydrology, Vol. 266, pp. 40-52.
Kalman, 1960, “A New Approach to Linear Filtering and Prediction Problems,” J. of Basic Engineering, Vol. 82, pp. 35-45.
Nævdal, G., Johnsen, L.M., Aanonsen, S.I., and Vefring, E.H., 2003, “Reservoir Monitoring and Continuous Model Updating Using Ensemble Kalman Filter,” paper SPE 84372 presented at the SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers, Denver, Colorado, Oct. 5-8.
Nævdal, G. and Vefring, E.H., 2002, “Near-Well Reservoir Monitoring Through Ensemble Kalman Filter,” paper SPE 75235 presented at the SPE/DOE Improved Oil Recovery Symposium, Society of Petroleum Engineers, Tulsa, Oklahoma, Apr. 13-17.
Park, K., Choe, J., and Ki, S., 2005, “Real-Time Aquifer Characterization Using Ensemble Kalman Filter,” Proceedings of GIS and Spatial Analysis 2005 Annual Conference of the International Association for Mathematical Geology Conference, International Association for Mathematical Geology, Toronto, Canada, Aug. 21-26, pp. 756-761.
Wen, X.-H and Chen, W.H., 2005, “Real-Time Reservoir Model Updating Using Ensemble Kalman Filter,” paper 93324 presented at the SPE 2005 Reservoir Simulation and Symposium, Society of Petroleum Engineers, Houston, Texas, Jan. 31 - Feb. 2.

Information

Publisher :The Korean Society of Mineral and Energy Resources Engineers
Publisher(Ko) :한국자원공학회
Journal Title :Journal of the Korean Society for Geosystem Engineering
Journal Title(Ko) :한국지구시스템공학회지
Volume : 43
No :2
Pages :143-150

[1] 박광원, 최종근, 2004, “저류층 특성화를 위한 관측정 분포 최적화,” 한국자원공학회지, 제41권 5호, pp. 373-380.

[2] Choe, J., Ki, S., Park, K., and Park, C., 2004, “Stochastic Optimization Using Streamline Simulation for Aquifer Characterization,” Proceedings of 32nd International Geological Congress, International Association for Mathematical Geology, Florence, Italy, Aug. 20-28.

[3] Evensen, G., 2003, “The Ensemble Kalman Filter: Theoretical Formulation and Practical Implementation,” Ocean Dynamics, Vol. 53, No. 4, pp. 343-367.

[4] Evensen, G., 1994, “Sequential Data Assimilation with a Nonlinear Quasi-Geostrophic Model Using Monte Carlo Methods to Forecast Error Statistics,” J. of Geophysical Research, Vol. 99, pp. 10,143-10,162.

[5] Gu, Y. and Oliver, D.S., 2004, “History Matching of the PUNQ-S3 Reservoir Model Using the Ensemble Kalman Filter,” paper 89942 presented at the SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers, Houston, Texas, Sep. 26-29.

[6] Jang, M., and Choe, J., 2004, “An Inverse System for Incorporation of Conditioning to Pressure and Streamline-Based Calibration,” J. of Contaminant Hydrology, Vol. 69, pp. 139-156.

[7] Jang, M. and Choe, J., 2002, “Stochastic Optimization for Global Minimization and Geostatistical Calibration,” J. of Hydrology, Vol. 266, pp. 40-52.

[8] Kalman, 1960, “A New Approach to Linear Filtering and Prediction Problems,” J. of Basic Engineering, Vol. 82, pp. 35-45.

[9] Nævdal, G., Johnsen, L.M., Aanonsen, S.I., and Vefring, E.H., 2003, “Reservoir Monitoring and Continuous Model Updating Using Ensemble Kalman Filter,” paper SPE 84372 presented at the SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers, Denver, Colorado, Oct. 5-8.

[10] Nævdal, G. and Vefring, E.H., 2002, “Near-Well Reservoir Monitoring Through Ensemble Kalman Filter,” paper SPE 75235 presented at the SPE/DOE Improved Oil Recovery Symposium, Society of Petroleum Engineers, Tulsa, Oklahoma, Apr. 13-17.

[11] Park, K., Choe, J., and Ki, S., 2005, “Real-Time Aquifer Characterization Using Ensemble Kalman Filter,” Proceedings of GIS and Spatial Analysis 2005 Annual Conference of the International Association for Mathematical Geology Conference, International Association for Mathematical Geology, Toronto, Canada, Aug. 21-26, pp. 756-761.

[12] Wen, X.-H and Chen, W.H., 2005, “Real-Time Reservoir Model Updating Using Ensemble Kalman Filter,” paper 93324 presented at the SPE 2005 Reservoir Simulation and Symposium, Society of Petroleum Engineers, Houston, Texas, Jan. 31 - Feb. 2.

Journal of the Korean Society of Mineral and Energy Resources Engineers ISSN:2288-0291(Print) 2288-2790(Online) 한국자원공학회지

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