Blucher Mechanical Engineering Proceedings

Maio 2014, vol.1, num.1 - 10th World Congress on Computational Mechanics
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WATERFLOODING OPTIMIZATION UNDER UNCERTAINTY

WATERFLOODING OPTIMIZATION UNDER UNCERTAINTY

Jr, J. D. Lira; Willmersdorf, R. B.; Horowitz, B.; Afonso, S. M. B.

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This paper presents a computational methodology for dynamic allocation of the rates in the production and injection wells, considering uncertainties related to the petrophysical properties such as permeability. The permeability field is considered as a stochastic field, featuring uncertainty as an input variable of the model. The stochastic input fields are described with the Karhunen-Loève expansion, and the stochastic responses of interest are expressed with polynomial chaos expansion. In this work surrogate models are used, to reduce the computational cost of the whole process. The surrogate models are used together with the strategy named sequential approximation optimization (SAO). The layered and nested methodology is used to perform optimization under uncertainties. Waterflooding case studies on a model reservoir are shown. The optimization cases of dynamic allocation of production rates shows that the methodologies presented here have achieved robust results.

This paper presents a computational methodology for dynamic allocation of the rates in the production and injection wells, considering uncertainties related to the petrophysical properties such as permeability. The permeability field is considered as a stochastic field, featuring uncertainty as an input variable of the model. The stochastic input fields are described with the Karhunen-Loève expansion, and the stochastic responses of interest are expressed with polynomial chaos expansion. In this work surrogate models are used, to reduce the computational cost of the whole process. The surrogate models are used together with the strategy named sequential approximation optimization (SAO). The layered and nested methodology is used to perform optimization under uncertainties. Waterflooding case studies on a model reservoir are shown. The optimization cases of dynamic allocation of production rates shows that the methodologies presented here have achieved robust results.

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DOI: 10.5151/meceng-wccm2012-18732

Referências bibliográficas
  • [1] Alexandrov, N., Dennis Jr., J.E., Lewisand, R.M. and Torezon, V. “A Trust Region Framework for Managing the Use of Approximation Models in Optimization”, NASA/CR-201745; ICASE Report No. 97-50, 1997.
  • [2] Afonso, S. M., Horowitz, B., Lira Junior, J. D., Carmo,, A., Cunha, J., Willmerdorf, R. Comparison of Surrogate Building Techniques for Engineering Problems. XXIX Cilamce, 2008.
  • [3] Cmg - Computer ModelLing Group Ltd, “Imex - User´s Guide”, 2006.
  • [4] Du, Q., Vance, F., Gunzburguer; M. Centroidal Voronoi Tessellations: Applications and Algorithms, Society for Industrial and Applied Mathematics, 1999.
  • [5] Eldred, M.S, Giunta, A. A., Wojtkiewicz, J., Trucano, T. G. Formulations for Surrogate- Based Optimization under Uncertainty. AIAA Paper 2002-5585, 2002.
  • [6] Eldred, M.S., Giunta, A.A. and Collis, S.S. “Second-Order Corrections for SurrogateBased Optimization with Model Hierarchies”, Paper AIAA-2004-4457 in Proceedings of the 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Albany, NY, 2004.
  • [7] Eldred, M. S., et al., “Dakota - User´s Manual”, 2008.
  • [8] Eldred, M. S., Webster, C. G. Evaluation of non-Intrusive Approaches for Winer- Askey Generalized Polynomial Chaos. AIAA Paper 2008-1892, 2008.
  • [9] Forrester, I. J., Sobester, A., Keane, A. J. Engineering Design via Surrogate Modeling, John Wiley and Sons, 2008.
  • [10] Ghanem, R., “Probabilistic Characterization of Transport in Heterogeneous Media”. Computer Methods in Applied Mechanics and Engineering, Elservier, 158 199-220, 1998.
  • [11] Giunta, A.A., Watson, L.T. A Comparison of Approximation Modeling Techniques: Polynomial versus Interpolating Models. Paper AIAA-98-4758 in proceedings of 7th AIAA/ USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis Andamp; Optimization, St. Louis, MI, 1998.
  • [12] Giunta, A. A., Eldred, M. S. Implementation of a Trust Region Model Management Strategy in The Dakota Optimization Toolkit, AIAA-2000-4935, 2000.
  • [13] Giunta,, A. A., Use of Data Sampling, Surrogate Models, and Numerical Optimization in Engineering Design, Proceedings of the 40th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 2002.
  • [14] Huang, S. P., Quek, S. T., Phoon, K. K. Convergence study of the truncated Karhunen– Loeve expansion for simulation of stochastic processes. International Journal for Numerical Methods in Engineering. 52:1029–1043, 2001.
  • [15] Jones, D. R., Schonlau, M., Welch, W. J. Efficient Global Optimization of Expensive Black-Box Functions. Kluwer Acadmeic Publishers, 1998.
  • [16] Keane, A.J., Nair, P.B., Computational Approaches for Aerospace Design: The Pursuit of Excellence, John-Wiley and Sons, 2005.
  • [17] Lira Jr, J. D. Otimização com Modelos Substitutos Considerando Incertezas em Reservatório de Petróleo. Phd Thesis, Civil Engineering, UFPE, Brazil, 2012.
  • [18] Oliveira, D.F.B., Técnicas de Otimização da Produção para Reservatórios de Petróleo: Abordagens Sem Uso de Derivadas para Alocação Dinâmica das Vazões de Produção e Injeção. Master Thesis, Civil Engineering, UFPE, Brasil, 2006.
  • [19] Sarma, P., Durlosfky, L. J., Aziz, K., “Kernel Principal Component Analysis for Efficient Differentiable Parameterization of Multipoint Geostatistics”. Math Geosci 40:3-32, 2008.
  • [20] Scholkopf, B., Smola, A, Muller K., “Nonlinear Component Analysis as a Kernel Eigenvalue Problem”, Technical Report No. 44, Max-Planck Institut für biologische Kybernetik, Arbeitsgruppe Bülthoff, 1996.
  • [21] Simpson, T. W, Maurey, T.M , Korte, J.K , Mistree, F. “Kriging Models for Global Approximations in simulation-Based Multidisciplinary Design Optimization” , AIAA Journal, 39(12), 2233-2241, 2001.
  • [22] Tatang, M. Direct Incorporation of Uncertainty in Chemical and Environmental Enginering Systems. Phd Thesis, MIT, 1995.
  • [23] Van Essen, G.M., Zandvliet, M. J., Van Den Hof, P. M. J., Bosgra, O. H. Robust Waterflooding Optimization of Multiple Geological Scenarios, SPE 102913, SPE Journal, 2006.
  • [24] Xiu, D., Karniads, G. Modeling Uncertainty in Flow Simulation via Generalized Polynomial Chaos. Journal of Computational Physics 187 137-167, 2003.
Como citar:

Jr, J. D. Lira; Willmersdorf, R. B.; Horowitz, B.; Afonso, S. M. B.; "WATERFLOODING OPTIMIZATION UNDER UNCERTAINTY", p-2138-2151. In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1]. São Paulo: Blucher, 2014.
ISSN 23580828, DOI 10.5151/meceng-wccm2012-18732

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