Nonlinear output constraints handling for production optimization of oil reservoirs

Computational Geosciences

Volumn 16, Issue 2, 2012, Pages 499-517

  Suwartadi, Eka ^a   Krogstad, Stein ^b   Foss, Bjarne ^a  

^a NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Norway)

^b SINTEF ICT   (Norway)

Author keywords

Adjoint method; Oil reservoirs; Output constraints; Production optimization

Indexed keywords

ADJOINT METHOD; HYDROCARBON RESERVOIR; OIL PRODUCTION; OPTIMIZATION; VARIANCE ANALYSIS;

EID: 84857923445     PISSN: 14200597     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10596-011-9253-3     Document Type: Article

References (33)

1. Chen, Y., Oliver, D. S., Zhang, D.: Efficient ensemble-based closed-loop production optimization. SPE J. 14(4), 634-645 (2008).
2. Bryson, A., Ho, Y.: Applied Optimal Control. Hemisphere, Washington, D. C. (1975).
3. Mehra, R., Davis, R.: A Generalized gradient method for optimal control problems with inequality constraints and singular arch. IEEE Trans. Automat. Contr. 17, 69-79 (1972).
4. Hargraves, C., Paris, S.: Direct trajectory optimization using nonlinear programming and collocation. J. Guid. Control Dyn. 10(4), 338-342 (1987).
5. Bloss, K. F., Biegler, L. T., Schiesser, W. E.: Dynamics process optimization through adjoint formulations and constraint aggregation. Ind. Eng. Chem. Res. 38(2), 421-432 (1999).
6. Becerra, V. M.: Solving optimal control problems with state constraints using nonlinear programming and simulation tools. IEEE Trans. Ed. 43(3), 377-384 (2004).
7. Fiacco, A. V., McCormick, G. P.: Nonlinear Programming: Sequential Unconstrained Minimization Techniques. Wiley, New York (1968).
8. Forsgren, A., Gill, P. E., Wright, M. H.: Interior methods for nonlinear optimization. SIAM Rev. 44(4), 525-597 (2002).
9. Kreisselmeier, G., Steinhauser, R.: Systematic Control Design by Optimizing a Vector Performance Index. IFAC Symposium on CADS, Zurich (1979).
10. Griewank, A., Korzec, M.: Approximating Jacobians by the TR2 formula. Proc. Appl. Math. Mech. 5, 791-792 (2005).
11. Hinze, M., Pinnau, R., Ulbrich, M., Ulbrich, S.: Optimization with PDE Constraints. Springer, New York (2009).
12. Virnovsky, G. A.: Waterflooding strategy design using optimal control theory. In: Proceeding of 6th. European IOR-symp. Stavanger, Norway (1991).
13. Zakirov, I. S., Aanonsen, S. I., Zakirov, E. S., Palatnik, B. M.: Optimizing reservoir performance by automatic allocation of well rates. In: Proceeding of 5th. ECMOR Leoben, Austria (1996).
14. Jansen, J. D.: Adjoint-based optimization of multi-phase flow through porous media-a review. Comput. Fluids 46, 40-51 (2011). doi: 10. 1016/j. compfluid. 2010. 09. 039.
15. Wu, Z.: Conditioning geostatistical models to two-phase flow production Data. Ph. D. thesis, University of Tulsa (1999).
16. Rommelse, J. R.: Data assimilation in reservoir management. Ph. D. thesis, TU Delft (2009).
17. Zandvliet, M. J., Handels, M., van Essen, G. M., Brouwer, D. R., Jansen, J. D.: Adjoint-based well placement optimization under production constraints. SPE J. 13(4), 392-399 (2008).
18. Montleau, P. de., Cominelli, A., Neylon, K., Rowan, D., Pallister, I., Tesaker, O., Nygard, I.: Production optimization under constraints using adjoint gradient. In: Proceedings of ECMOR X-10th European Conference on the Mathematics of Oil Recovery Number A041. EAGE, Amsterdam, The Netherlands (2006).
19. Sarma, P., Chen, W. H., Durlofsky, L. J., Aziz, K.: Production optimization with adjoint models under nonlinear control-state path inequality constraints. SPEREE, 11(2), 326-339 (2008). Paper SPE 99959.
20. Kraaijevanger, J. F. B. M., Egberts, P. J. P., Valstar, J. R., Buurman, H. W.: Optimal waterflood design using the adjoint method. Paper SPE 105764 presented at 2007 SPE RSS, Houston, TX, USA, 26-28 Feb (2007).
21. Aziz, K., Settari, A.: Petroleum Reservoir Simulation. Applied Science, New York (1979).
22. van Essen, G. M., van den Hof, P. M. J., Jansen, J. D.: Hierarchical long-term and short-term production optimization. SPE J. 16(1), 191-199 (2011).
23. Chen, C., Li, G., Reynolds, A.: Robust constrained optimization of short and long-term NPV for closed-loop reservoir management. Paper SPE 141314 presented at 2011 SPE RSS, Houston, TX, USA, 21-23 Feb 2011.
24. Griewank, A., Walther, A.: Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation. SIAM, Philadelphia. ISBN 978-0-898716-59-7 (2008).
25. Suwartadi, E., Krogstad, S., Foss, B.: A Lagrangian-barrier function for adjoint state constraints optimization of oil reservoirs water flooding. In: IEEE Conference on Proceeding of 2010 49th, pp. 3884-3889 (2010). doi: 10. 1109/CDC. 2010. 5717749.
26. Jittorntrum, K., Osborne, M. R.: A modified barrier function method with improved rate of convergence for degenerate problems. J. Austral. Math. Soc, Series B 21, 305-329.
27. Byrd, R. H., Nocedal, J., Waltz, R. A.: KNITRO: an integrated package for nonlinear optimization. In: Di Pillo, G., Roma, M. (eds.) Large-Scale Nonlinear Optimization. Springer, USA (2006).
28. Conn, A. R., Gould, N. I. M., Toint, P. L.: Trust-Region Methods. SIAM, Philadelphia (2000).
29. Steihaug, T.: The conjugate gradient method and trust regions in large scale optimization. SIAM J. Numer. Anal. 20, 626-637 (1983).
30. Conn, A. R., Gould, N. I. M., Toint, P. L.: A globally convergent Lagrangian barrier algorithm for optimization with general inequality constraints and simple bounds. Math. Comput. 66(217), 216-288 (1997).
31. Lie, K.-A., Krogstad, S., Ligaarden, I. S., Natvig, L. R., Nilsen, H. M., Skafltestad, B.: Open-source MATLAB implementation of consistent discretisations on complex grids. Comput. Geosci. (2011). doi: 10. 1007/s10596-011-9244-4.
32. Christie, M. A., Blunt, M. J.: Tenth SPE comparative solution project: a comparative of upscaling technique. SPE Reserv. Evalu. Eng. 4, 308-317 (2001).
33. Rwechungura, R., Suwartadi, E., Dadashpour, M., Kleppe, J., Foss, B.: The Norne field case-a unique comparative case study. Paper SPE 127538 presented at 2010 SPE Intelligent Energy Conference and Exhibition, Utrecht, The Netherlands, 23-25 March 2010.