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Joint optimization of oil well placement and controls

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Abstract

Well placement and control optimization in oil field development are commonly performed in a sequential manner. In this work, we propose a joint approach that embeds well control optimization within the search for optimum well placement configurations. We solve for well placement using derivative-free methods based on pattern search. Control optimization is solved by sequential quadratic programming using gradients efficiently computed through adjoints. Joint optimization yields a significant increase, of up to 20% in net present value, when compared to reasonable sequential approaches. The joint approach does, however, require about an order of magnitude increase in the number of objective function evaluations compared to sequential procedures. This increase is somewhat mitigated by the parallel implementation of some of the pattern-search algorithms used in this work. Two pattern-search algorithms using eight and 20 computing cores yield speedup factors of 4.1 and 6.4, respectively. A third pattern-search procedure based on a serial evaluation of the objective function is less efficient in terms of clock time, but the optimized cost function value obtained with this scheme is marginally better.

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References

  1. Audet, C., Dennis, J.E. Jr.: Pattern search algorithms for mixed variable programming. SIAM J. Optim. 11(3), 573–594 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  2. Audet, C., Dennis, J.E. Jr.: Analysis of generalized pattern searches. SIAM J. Optim. 13(3), 889–903 (2002)

    Article  MathSciNet  Google Scholar 

  3. Audet, C., Dennis, J.E. Jr.: Mesh adaptive direct search algorithms for constrained optimization. SIAM J. Optim. 17(1), 188–217 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  4. Aziz, K., Settari, A.: Petroleum Reservoir Simulation. Applied Science, New York, NY (1979)

  5. Bangerth, W., Klie, H., Wheeler, M., Stoffa, P., Sen, M.: On optimization algorithms for the reservoir oil well placement problem. Comput. Geosci. 10(3), 303–319 (2006)

    Article  MATH  Google Scholar 

  6. Brouwer, D.R., Jansen, J.D.: Dynamic optimization of waterflooding with smart wells using optimal control theory. SPE J. 9(4), 391–402, SPE 78278 (2004)

    Google Scholar 

  7. Cao, H.: Development of techniques for general purpose simulators. PhD thesis, Dept. of Petroleum Engineering, Stanford University, Stanford, CA (2002)

  8. Christie, M.A., Blunt, M.J.: Tenth SPE comparative solution project: a comparison of upscaling techniques. SPE Reserv. Evalu. Eng. 4, 308–317, SPE 66599 (2001)

    Google Scholar 

  9. Clerc, M.: Particle Swarm Optimization. Wiley, London (2006)

    Book  MATH  Google Scholar 

  10. Conn, A.R., Scheinberg, K., Vicente, L.N.: Introduction to Derivative-Free Optimization. MPS-SIAM Series on Optimization, Society for Industrial and Applied Mathematics and the Mathematical Programming Society, Philadelphia, PA (2009)

  11. Dempe, S.: Foundations of Bilevel Programming. Kluwer Academic, New York (2002)

    MATH  Google Scholar 

  12. Eberhart, R.C., Kennedy, J., Shi, Y.: Swarm Intelligence. Morgan Kaufmann, Waltham (2001)

    Google Scholar 

  13. Echeverría Ciaurri, D., Isebor, O.J., Durlofsky, L.J.: Application of derivative-free methodologies for generally constrained oil production optimization problems. Int. J. Math. Model. Numer. Optim. 2(2), 134–161 (2011)

    Google Scholar 

  14. Echeverría Ciaurri, D., Mukerji, T., Durlofsky, L.J.: Derivative-free optimization for oil field operations. In: Yang, X.S., Koziel, S. (eds.) Computational Optimization and Applications in Engineering and Industry, no. 359 in Studies in Computational Intelligence. Springer, Berlin (2011)

    Google Scholar 

  15. Echeverría Ciaurri, D., Conn, A., Mello, U.T., Onwunalu, J.E.: Integrating mathematical optimization and decision making in intelligent fields. In: Proceedings of the SPE Intelligent Energy International, Utrecht, The Netherlands, SPE 149780 (2012)

  16. Ertekin, T., Abou-Kassem, J.H., King, G.R.: Basic Applied Reservoir Simulation. SPE Textbook Series, SPE, Richardson, TX (2001)

  17. Fletcher, R., Leyffer, S., Toint, P.L.: A brief history of filter methods. Tech. Rep. ANL/MCS/JA-58300, Argonne National Laboratory, Argonne, IL (2006)

  18. Forouzanfar, F., Li, G., Reynolds, A.C.: A two-stage well placement optimization method based on adjoint gradient. In: Proceedings of the SPE Annual Technical Conference and Exhibition, Florence, Italy, SPE 135304 (2010)

  19. Gill, P.E., Murray, W., Saunders, M.A.: SNOPT: an SQP algorithm for large-scale constrained optimization. SIAM Rev. 47(1), 99–131 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  20. Gill, P.E., Murray, W., Saunders, M.A.: User’s Guide for SNOPT Version 7: Software for Large Scale Nonlinear Programming. Stanford University, Stanford, CA, and University of California, San Diego, CA (2007)

  21. Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley Professional, Boston (1989)

    MATH  Google Scholar 

  22. Griffin, J.D., Kolda, T.G.: Nonlinearly-constrained optimization using asynchronous parallel generating set search. Tech. Rep. SAND2007-3257, Sandia National Laboratories, Livermore, CA (2007)

  23. Griffin, J.D., Kolda, T.G., Lewis, R.M.: Asynchronous parallel generating set search for linearly-constrained optimization. SIAM J. Sci. Comput. 30(4), 1892–1924 (2008)

    Article  MathSciNet  Google Scholar 

  24. Güyagüler, B., Horne, R.N., Rogers, L., Rosenzweig, J.J.: Optimization of well placement in a Gulf of Mexico waterflooding project. In: Proceedings of the SPE Annual Technical Conference and Exhibition, Dallas, TX, SPE 63221 (2000)

  25. Hooke, R., Jeeves, T.A.: Direct search solution of numerical and statistical problems. J. ACM 8(2), 212–229 (1961)

    Article  MATH  Google Scholar 

  26. Jansen, J.D., Brouwer, D.R., Naevdal, G., van Kruijsdiik, C.P.J.W.: Closed-loop reservoir management. First Break 23, 43–48 (2005)

    Google Scholar 

  27. Kolda, T.G., Lewis, R.M., Torczon, V.: Optimization by direct search: new perspectives on some classical and modern methods. SIAM Rev. 45(3), 385–482 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  28. Nocedal, J., Wright, S.J.: Numerical Optimization, 2nd edn. Springer, New York (2006)

    MATH  Google Scholar 

  29. Onwunalu, J.E., Durlofsky, L.J.: Application of a particle swarm optimization algorithm for determining optimum well location and type. Comput. Geosci. 14(1), 183–198 (2010)

    Article  MATH  Google Scholar 

  30. Peaceman, D.W.: Interpretation of well-block pressures in numerical reservoir simulation. SPE J. 18(3), 183–194, SPE 6893 (1978)

    Google Scholar 

  31. Pironneau, O.: On optimum design in fluid mechanics. J. Fluid Mech. 64, 97–110 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  32. Plantenga, T.D.: HOPSPACK 2.0 user manual. Tech. Rep. SAND2009-6265, Sandia National Laboratories, Livermore, CA (2009)

  33. Powell, M.J.D.: The BOBYQA algorithm for bound constrained optimization without derivatives. Tech. Rep. NA2009/06, Department of Applied Mathematics and Theoretical Physics, Cambridge, UK (2009)

  34. Sarma, P., Chen, W.H.: Efficient well placement optimization with gradient-based algorithm and adjoint models. In: Proceedings of the SPE Intelligent Energy Conference and Exhibition, Amsterdam, The Netherlands, SPE 112257 (2008)

  35. Sarma, P., Durlofsky, L.J., Aziz, K., Chen, W.H.: Efficient real-time reservoir management using adjoint-based optimal control and model updating. Comput. Geosci. 10, 3–36 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  36. Torczon, V.: On the convergence of pattern search algorithms. SIAM J. Optim. 7(1), 1–25 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  37. Wang, C., Li, G., Reynolds, A.C.: Optimal well placement for production optimization. In: Proceedings of the SPE Eastern Regional Meeting, Lexington, KY, SPE 111154 (2007)

  38. Wang, H., Echeverría Ciaurri, D., Durlofsky, L.J., Cominelli, A.: Optimal well placement under uncertainty using a retrospective optimization framework. SPE J. 17(1), 112–121, SPE 141950 (2012)

    Google Scholar 

  39. Yeten, B., Durlofsky, L.J., Aziz, K.: Optimization of nonconventional well type, location, and trajectory. SPE J. 8(9), 200–210, SPE 86880 (2003)

    Google Scholar 

  40. Zandvliet, M., Handels, M., van Essen, G., Brouwer, R., Jansen, J.D.: Adjoint-based well-placement optimization under production constraints. SPE J. 13(4), 392–399, SPE 105797 (2008)

    Google Scholar 

  41. Zhang, K., Li, G., Reynolds, A.C., Yao, J., Zhang, L.: Optimal well placement using an adjoint gradient. J. Pet. Sci. Eng. 73(3–4), 220–226 (2010)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Petroleum Engineering and Applied Geophysics, Center for Integrated Operations in the Petroleum Industry, NTNU, Trondheim, Norway

    Mathias C. Bellout & Jon Kleppe

  2. Department of Petroleum and Energy Analytics, T.J. Watson Research Center, IBM, Yorktown Heights, NY, USA

    David Echeverría Ciaurri

  3. Department of Energy Resources Engineering, Stanford University, Stanford, CA, USA

    Louis J. Durlofsky

  4. Department of Engineering Cybernetics, Center for Integrated Operations in the Petroleum Industry, NTNU, Trondheim, Norway

    Bjarne Foss

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  1. Mathias C. Bellout
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  2. David Echeverría Ciaurri
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  3. Louis J. Durlofsky
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  4. Bjarne Foss
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  5. Jon Kleppe
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Correspondence to Mathias C. Bellout.

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Bellout, M.C., Echeverría Ciaurri, D., Durlofsky, L.J. et al. Joint optimization of oil well placement and controls. Comput Geosci 16, 1061–1079 (2012). https://doi.org/10.1007/s10596-012-9303-5

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  • DOI: https://doi.org/10.1007/s10596-012-9303-5

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