Uncertainty Quantification of Channelized Reservoirs using Ensemble Smoother
with a Distance-Based Method

doi:10.12972/ksmer.2015.52.2.139

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2015 Vol.52, Issue 2 Preview Page Next Page

Research Paper

Uncertainty Quantification of Channelized Reservoirs using Ensemble Smoother with a Distance-Based Method 거리기반 앙상블스무더를 이용한 채널저류층 불확실성평가: 이경북 · 정승필 · 최종근
Kyungbook Lee, Seungpil Jung and Jonggeun Choe

30 April 2015. pp. 139-147

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Abstract

This paper suggests a new method of ensemble smoother(ES) for reliable uncertainty quantification.The method uses several Kalman gains rather than one representative Kalman gain. When the proposed methodis applied to channelized reservoirs, the results manage typical overshooting and filter divergence problems. Also,they conserve channel connectivity and bimodal distribution of the model parameter. The proposed method cankeep history matching time short since there are no modifications in the standard ES. Therefore, the time ofthe proposed method reduces more than 97% of that of ensemble Kalman filter(EnKF) with 45 assimilation stepsand 200 total ensembles. The ES with a distance-based method provides reliable productions with reasonableuncertainty ranges. Also, prediction time of future performances can be reduced since the representative ensemblesfrom each group estimate similar uncertainty ranges over all ensembles. Therefore, the proposed method can beapplied for decision making because it gives fast and reliable uncertainty quantification for channelized reservoirs.

Keywords

Channelized reservoir characterization

Uncertainty quantification

Ensemble smoother

Distance-based method

Ensemble Kalman filter

본 연구에서는 앙상블스무더의 불확실성평가 신뢰도를 향상하기 위해 초기앙상블을 잘 대표하는 다수의 칼만게인을 이용하는 기법을 제안하였다. 제안된 거리기반 앙상블스무더를 채널저류층에 적용한 결과, 기존의 오버슈팅과 필터발산 문제를 해결하였고 채널연결성과 이봉분포의 특징을 잘 보존하였다. 제안된 기법은앙상블스무더의 수식과 교정방식을 수정없이 사용하므로 계산속도가 빠르다. 따라서 200개의 앙상블로 45번의교정을 수행한 경우, 앙상블칼만필터의 소요시간보다 97% 이상 감소시켰다. 거리기반 앙상블스무더의 경우 유정별 생산량뿐만 아니라 누적 오일 및 물 생산량을 성공적으로 예측하였고 편향없는 불확실성을 제공하였다.또한 군집별 대표앙상블만으로 전체앙상블과 비슷한 수준의 불확실성평가가 가능하므로 군집수에 반비례하여소요시간이 줄어든다. 따라서 제안된 기법은 빠르고 신뢰할 수 있는 불확실성평가가 가능하므로 채널저류층개발 시 의사결정을 위한 도구로 활용될 수 있다.

키워드

채널저류층 특성화

불확실성평가

앙상블스무더

거리기반기법

앙상블칼만필터

References

Aanonsen, S.I., Nævdal, G., Oliver, D.S., Reynolds, A.C. and Vallès, B., 2009, “The ensemble Kalman filter in reservoir engineering--a review,” SPE Journal, Vol. 14, No. 3, pp. 393-412.
Chen, Y. and Oliver, D.S., 2012, “Ensemble randomized maximum likelihood method as an iterative ensemble smoother,” Mathematical Geosciences, Vol. 44, No. 1, pp. 1-26.
Emerick, A.A. and Reynolds, A.C., 2013, “Ensemble smoother with multiple data assimilation,” Computers & Geosciences, Vol. 55, pp. 3-15.
Evensen, G., 1994, “Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics,” Journal of Geophysical Research, Vol. 99, No. C5, pp. 10,143-10,162.
Honarkhah, H. and Caers, J., 2010, “Stochastic Simulation of Patterns Using Distance-Based Pattern Modeling,” Mathematical Geosciences, Vol. 42, No. 5, pp. 487-517.
Jafarpour, B. and McLaughlin, D.B., 2009, “Reservoir characterization with the discrete cosine transform,” SPE Journal, Vol. 14, No. 1, pp. 182-201.
Jeong, H., Ki, S. and Choe, J., 2010, “Reservoir characterization from insufficient static data using gradual deformation method with ensemble Kalman filter,” Energy Sources, Part A, Vol. 32, No. 10, pp. 942-951.
Jung, A., Fenwick, D.H. and Caers, J., 2013, “Training image-based scenario modeling of fractured reservoirs for flow uncertainty quantification.,” Computational Geosciences, Vol. 17, No. 6, pp. 1,015-1,031.
Jung, S. and Choe, J., 2009, “Improvement of Numerical Stability in History-matching Using Streamline Assisted Ensemble Kalman Filter,” J. of The Korean Society for Geosystem Engineering, Vol. 46, No. 4, pp. 453-465.
Lee, K., Jeong, H., Jung, S. and Choe, J., 2013a, “Characterization of Channelized Reservoir using Ensemble Kalman Filter with Clustered Covariance,” Energy Exploration and Exploitation, Vol. 31, No. 1, pp. 17-29.
Lee, K., Jeong, H., Jung, S. and Choe, J., 2013b, “Improvement of ensemble smoother with clustered covariance for channelized reservoirs,” Energy Exploration and Exploitation, Vol. 31, No. 5, pp. 713-726.
Lee, K., Jo, G. and Choe, J., 2011, “Improvement of ensemble Kalman filter for improper initial ensembles,” Geosystem Engineering, Vol. 14, No. 2, pp. 79-84.
Lorentzen, R.J., Flornes, K.M. and Nævdal, G., 2009, “History matching channelized reservoir using the ensemble Kalman filter,” Proc. of the International Petroleum Technology Conference, Doha, Qatar, December 7-9.
Nævdal, G. and Vefring, E.H., 2002, “Near-well reservoir monitoring through ensemble Kalman filter,” Proc. of the SPE/DOE Improved Oil Recovery Symposium, Tulsa, Oklahoma, USA, April 13-17.
Oliver, D.S. and Chen, Y., 2011, “Recent progress on reservoir history matching: A review,” Computational Geosciences, Vol. 15, No. 1, pp. 185-221.
Park, K., Shin, Y. and Choe, J., 2006, “Real-Time Reservoir Characterization using Ensemble Kalman Filter During Waterflooding,” J. of The Korean Society for Geosystem Engineering, Vol. 43, No. 2, pp. 143-150.
Sarma, P. and Chen, W.H., 2009, “Generalization of the ensemble Kalman filter using kernels for non-Gaussian random fields,” Proc. of the SPE Reservoir Simulation Symposium, The Woodlands, Texas, USA, February 2-4.
Shin, Y., Jeong, H. and Choe, J., 2010, “Reservoir characterization using an EnKF and a non-parametric approach for highly non-Gaussian permeability fields,” Energy Sources, Part A, Vol. 32, No. 16, pp. 1,569-1,578.
Skjervheim, J.-A., Evensen, G., Hove J. and Vab, J.G., 2011, “An ensemble smoother for assisted history matching,” Proc. of the SPE Reservoir Simulation Symposium, The Woodlands, Texas, USA, February 21-23.
Suzuki, S. and Caers, J., 2008, “A distance-based prior model parameterization for constraining solutions of spatial inverse problems,” Mathematical Geosciences, Vol. 40, No. 4, pp. 445-469.
Van Leeuwen, P.J. and Evensen, G., 1996, “Data assimilation and inverse methods in terms of a probabilistic formulation,” Monthly Weather Review, Vol. 124, pp. 2,898-2,913.
Watanabe, S., Datta-Gupta, A., Efendiev, Y. and Devegowda, D., 2009, “A hybrid ensemble Kalman filter with coarse scale constraint for nonlinear dynamics,” Proc. of the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, USA, October 4-7.

Information

Publisher :The Korean Society of Mineral and Energy Resources Engineers
Publisher(Ko) :한국자원공학회
Journal Title :Journal of the Korean Society of Mineral and Energy Resources Engineers
Journal Title(Ko) :한국자원공학회지
Volume : 52
No :2
Pages :139-147
DOI :https://doi.org/10.12972/ksmer.2015.52.2.139

[1] Aanonsen, S.I., Nævdal, G., Oliver, D.S., Reynolds, A.C. and Vallès, B., 2009, “The ensemble Kalman filter in reservoir engineering--a review,” SPE Journal, Vol. 14, No. 3, pp. 393-412.

[2] Chen, Y. and Oliver, D.S., 2012, “Ensemble randomized maximum likelihood method as an iterative ensemble smoother,” Mathematical Geosciences, Vol. 44, No. 1, pp. 1-26.

[3] Emerick, A.A. and Reynolds, A.C., 2013, “Ensemble smoother with multiple data assimilation,” Computers & Geosciences, Vol. 55, pp. 3-15.

[4] Evensen, G., 1994, “Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics,” Journal of Geophysical Research, Vol. 99, No. C5, pp. 10,143-10,162.

[5] Honarkhah, H. and Caers, J., 2010, “Stochastic Simulation of Patterns Using Distance-Based Pattern Modeling,” Mathematical Geosciences, Vol. 42, No. 5, pp. 487-517.

[6] Jafarpour, B. and McLaughlin, D.B., 2009, “Reservoir characterization with the discrete cosine transform,” SPE Journal, Vol. 14, No. 1, pp. 182-201.

[7] Jeong, H., Ki, S. and Choe, J., 2010, “Reservoir characterization from insufficient static data using gradual deformation method with ensemble Kalman filter,” Energy Sources, Part A, Vol. 32, No. 10, pp. 942-951.

[8] Jung, A., Fenwick, D.H. and Caers, J., 2013, “Training image-based scenario modeling of fractured reservoirs for flow uncertainty quantification.,” Computational Geosciences, Vol. 17, No. 6, pp. 1,015-1,031.

[9] Jung, S. and Choe, J., 2009, “Improvement of Numerical Stability in History-matching Using Streamline Assisted Ensemble Kalman Filter,” J. of The Korean Society for Geosystem Engineering, Vol. 46, No. 4, pp. 453-465.

[10] Lee, K., Jeong, H., Jung, S. and Choe, J., 2013a, “Characterization of Channelized Reservoir using Ensemble Kalman Filter with Clustered Covariance,” Energy Exploration and Exploitation, Vol. 31, No. 1, pp. 17-29.

[11] Lee, K., Jeong, H., Jung, S. and Choe, J., 2013b, “Improvement of ensemble smoother with clustered covariance for channelized reservoirs,” Energy Exploration and Exploitation, Vol. 31, No. 5, pp. 713-726.

[12] Lee, K., Jo, G. and Choe, J., 2011, “Improvement of ensemble Kalman filter for improper initial ensembles,” Geosystem Engineering, Vol. 14, No. 2, pp. 79-84.

[13] Lorentzen, R.J., Flornes, K.M. and Nævdal, G., 2009, “History matching channelized reservoir using the ensemble Kalman filter,” Proc. of the International Petroleum Technology Conference, Doha, Qatar, December 7-9.

[14] Nævdal, G. and Vefring, E.H., 2002, “Near-well reservoir monitoring through ensemble Kalman filter,” Proc. of the SPE/DOE Improved Oil Recovery Symposium, Tulsa, Oklahoma, USA, April 13-17.

[15] Oliver, D.S. and Chen, Y., 2011, “Recent progress on reservoir history matching: A review,” Computational Geosciences, Vol. 15, No. 1, pp. 185-221.

[16] Park, K., Shin, Y. and Choe, J., 2006, “Real-Time Reservoir Characterization using Ensemble Kalman Filter During Waterflooding,” J. of The Korean Society for Geosystem Engineering, Vol. 43, No. 2, pp. 143-150.

[17] Sarma, P. and Chen, W.H., 2009, “Generalization of the ensemble Kalman filter using kernels for non-Gaussian random fields,” Proc. of the SPE Reservoir Simulation Symposium, The Woodlands, Texas, USA, February 2-4.

[18] Shin, Y., Jeong, H. and Choe, J., 2010, “Reservoir characterization using an EnKF and a non-parametric approach for highly non-Gaussian permeability fields,” Energy Sources, Part A, Vol. 32, No. 16, pp. 1,569-1,578.

[19] Skjervheim, J.-A., Evensen, G., Hove J. and Vab, J.G., 2011, “An ensemble smoother for assisted history matching,” Proc. of the SPE Reservoir Simulation Symposium, The Woodlands, Texas, USA, February 21-23.

[20] Suzuki, S. and Caers, J., 2008, “A distance-based prior model parameterization for constraining solutions of spatial inverse problems,” Mathematical Geosciences, Vol. 40, No. 4, pp. 445-469.

[21] Van Leeuwen, P.J. and Evensen, G., 1996, “Data assimilation and inverse methods in terms of a probabilistic formulation,” Monthly Weather Review, Vol. 124, pp. 2,898-2,913.

[22] Watanabe, S., Datta-Gupta, A., Efendiev, Y. and Devegowda, D., 2009, “A hybrid ensemble Kalman filter with coarse scale constraint for nonlinear dynamics,” Proc. of the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, USA, October 4-7.

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