A New Parameterization Method for Large-Scale Reservoir History

Abstract:

A novel and simple parameterization method using an ensemble of unconditional model realizations is applied to decrease the dimension of the misfit objective function in large-scale history matching problems. The major advantage of this parameterization method is that the singular value decomposition (SVD) calculation is completely avoided, which saves time and cost for huge matrix decomposition and the eigenvectors computations in parameterization process. After objective function transforms from a higher dimension to a lower dimension by parameterization, a Monte Carlo approach is introduced to evaluate the gradient information in the lower domain. Unlike the adjoint-gradient algorithms, the gradient in our method is estimated by Monte Carlo stochastic method, which can be easily coupled with different numerical simulator and avoid complicated adjoint code. When the estimated gradient information is obtained, any gradient-based algorithm can be implemented for optimizing the objective function. The Monte Carlo algorithm combined with the parameterization method is applied to Brugge reservoir field. The result shows that our present method gives a good estimation of reservoir properties and decreases the geological uncertainty without SVD but with a lower final objective function value, which provides a more efficient and useful way for history matching in large scale field.

• Periodical: Applied Mechanics and Materials (Volume 733)
• Pages: 156-160
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.733.156
• Online since: February 2015
• Authors: Xia Yan*, Jun Li, Hui Zhao
• Keywords: Decomposition, Gradient Estimate, Large-Scale History Matching, Monte Carlo, Parameterization

References

[1] Hajizadeh Y., Christie M., Demyanov V. Comparative Study of Novel Population-Based Optimization Algorithms for History Matching and Uncertainty Quantification: PUNQ-S3 Revisited, 2010(SPE 136861).

DOI: 10.2118/136861-ms

[2] Spall J.C. Multivariate stochastic approximation using a simultaneous perturbation gradient approximation., IEEE Transactions on Automatic Control. 1992, 37(3): 332-341.

DOI: 10.1109/9.119632

[3] Gao G., G. Li, and A. C. Reynolds. A stochastic algorithm for automatic history matching,. SPE Journal, 2007, 12(2): 196-208.

DOI: 10.2118/90065-pa

[4] Gao G., M. Zafari, and A. C. Reynolds. Quantifying uncertainty for the PUNQ-S3 problem in a Bayesian setting with RML and EnKF,. SPE Reservoir Simulation Symposium, 2005 (SPE 93324).

DOI: 10.2118/93324-ms

[5] Zhang, F. and A. C. Reynolds, Optimization algorithms for automatic history matching of production data, Proceedings of 8th European Conference on the Mathematics of Oil Recovery, (2002).

DOI: 10.3997/2214-4609.201405958

[6] Gao G. and A. C. Reynolds. An improved implementation of the LBFGS algorithm for automatic history matching,. SPE Journal, 2006, 11(1): 5-17.

DOI: 10.2118/90058-pa

[7] Sarma, P, L. Durlofsky, and K. Aziz. Implementation of adjoint solution for optimal control of smart wells, , 2005(SPE 92864).

DOI: 10.2118/92864-ms

[8] Zhao Hui, Li Y., Yao J. Zhang K., et al, Theoretical research on Reservoir Closed-loop Production Management, Science China (Technological Sciences), 2011, 54(10): 2815-2824.

DOI: 10.1007/s11431-011-4465-2

[9] E. Patelli and H.J. Pradlwarter. Monte Carlo gradient estimation in high dimensions,. International Journal for Numerical Methods in Engineering, 2010, 81(2), 172–188.

DOI: 10.1002/nme.2687

[10] H.J. Pradlwarter. Relative importance of uncertain structural parameters. Part I: algorithm,. Computational Mechanics, 2006, 40(4), 627-635.

DOI: 10.1007/s00466-006-0127-9

[11] Xia Yan, A. C Reynolds. An Optimization Algorithm Based on Combining Finite-Difference Approximations and Stochastic Gradient, SPE Reservoir Simulation Symposium, 18-20 February 2013, the Woodlands, Texas, (SPE 163613).

[12] Peters, L. Arts, R.J., Brouwer, G.K., Geel, et al, Results of the Brugge Benchmark Study for Flooding Optimization and History Matching, SPE Reservoir Evaluation & Engineering, 2010, 13(3), 391-405.

DOI: 10.2118/119094-pa

[13] Chen C., Li G., Reynolds A.C., Closed-loop reservoir management on the Brugge test case, Computational Geosciences, 2010, 49(4), 327-335.

DOI: 10.1007/s10596-010-9181-7

[14] Chen Y., Oliver D.S., Zhang D. Efficient ensemble-based closed-loop production optimization,. SPE Journal, 2009, 14(4), 634-645.

DOI: 10.2118/112873-pa