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Computational Geosciences

, Volume 18, Issue 3–4, pp 463–482 | Cite as

A derivative-free methodology with local and global search for the constrained joint optimization of well locations and controls

  • Obiajulu J. IseborEmail author
  • Louis J. Durlofsky
  • David Echeverría Ciaurri
ORIGINAL PAPER

Abstract

In oil field development, the optimal location for a new well depends on how it is to be operated. Thus, it is generally suboptimal to treat the well location and well control optimization problems separately. Rather, they should be considered simultaneously as a joint problem. In this work, we present noninvasive, derivative-free, easily parallelizable procedures to solve this joint optimization problem. Specifically, we consider Particle Swarm Optimization (PSO), a global stochastic search algorithm; Mesh Adaptive Direct Search (MADS), a local search procedure; and a hybrid PSO–MADS technique that combines the advantages of both methods. Nonlinear constraints are handled through use of filter-based treatments that seek to minimize both the objective function and constraint violation. We also introduce a formulation to determine the optimal number of wells, in addition to their locations and controls, by associating a binary variable (drill/do not drill) with each well. Example cases of varying complexity, which include bound constraints, nonlinear constraints, and the determination of the number of wells, are presented. The PSO–MADS hybrid procedure is shown to consistently outperform both stand-alone PSO and MADS when solving the joint problem. The joint approach is also observed to provide superior performance relative to a sequential procedure.

Keywords

Derivative-free optimization Field development optimization Well placement Production optimization Reservoir simulation-based optimization Nonlinear programming 

Mathematics Subject Classifications (2010)

90-08 90C11 90C26 90C30 90C56 90C90 

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References

  1. 1.
    Almeida, L.F., Tupac, Y.J., Lazo Lazo, J.G., Pacheco, M.A., Vellasco, M.M.B.R.: Evolutionary optimization of smart-wells control under technical uncertainties. Paper SPE 107872 presented at the Latin American & Caribbean petroleum engineering conference, Buenos Aires, Argentina (2007)Google Scholar
  2. 2.
    Audet, C., Dennis Jr., J.E.: Analysis of generalized pattern searches. SIAM J. Optim. 13(3), 889–903 (2002)CrossRefGoogle Scholar
  3. 3.
    Audet, C., Dennis Jr., J.E.: A pattern search filter method for nonlinear programming without derivatives. SIAM J. Optim. 14(4), 980–1010 (2004)CrossRefGoogle Scholar
  4. 4.
    Audet, C., Dennis Jr., J.E.: Mesh adaptive direct search algorithms for constrained optimization. SIAM J. Optim. 17(1), 188–217 (2006)CrossRefGoogle Scholar
  5. 5.
    Bangerth, W., Klie, H., Wheeler, M.F., Stoffa, P.L., Sen, M.K.: On optimization algorithms for the reservoir oil well placement problem. Comput. Geosci. 10(3), 303–319 (2006)CrossRefGoogle Scholar
  6. 6.
    Bellout, M.C., Echeverría Ciaurri, D., Durlofsky, L.J., Foss, B., Kleppe, J.: Joint optimization of oil well placement and controls. Comput. Geosci. 16(4), 1061–1079 (2012)CrossRefGoogle Scholar
  7. 7.
    Bonami, P., Biegler, L.T., Conn, A.R., Cornuéjols, G., Grossmann, I.E., Laird, C.D., Lee, J., Lodi, A., Margot, F., Sawaya, N., Wächter, A.: An algorithmic framework for convex mixed integer nonlinear programs. Discret. Optim. 5(2), 186–204 (2008)CrossRefGoogle Scholar
  8. 8.
    Brouwer, D.R., Jansen, J.D.: Dynamic optimization of waterflooding with smart wells using optimal control theory. SPE J. 9(4), 391–402 (2004)CrossRefGoogle Scholar
  9. 9.
    Cameron, D.A., Durlofsky, L.J.: Optimization of well placement, CO2 injection rates, and brine cycling for geological carbon sequestration. Int. J. Greenhouse Gas Control. 10, 100–112 (2012)CrossRefGoogle Scholar
  10. 10.
    Cao, H.: Development of techniques for general purpose simulators. Ph.D. thesis, Department of Petroleum Engineering, Stanford University (2002)Google Scholar
  11. 11.
    Cardoso, M.A., Durlofsky, L.J.: Linearized reduced-order models for subsurface flow simulation. J. Comput. Phys. 229, 681–700 (2010)CrossRefGoogle Scholar
  12. 12.
    Clerc, M.: The swarm and the queen: Towards a deterministic and adaptive particle swarm optimization. In: Proceedings of the 1999 Congress on Evolutionary Computation, pp. 1951–1957 (1999)Google Scholar
  13. 13.
    Clerc, M.: Particle Swarm Optimization. ISTE, London (2006)CrossRefGoogle Scholar
  14. 14.
    Deb, K.: An efficient constraint handling method for genetic algorithms. Comput. Methods Appl. Mech. Eng. 186(2–4), 311–338 (2000)CrossRefGoogle Scholar
  15. 15.
    Eberhart, R.C., Kennedy, J.: A new optimizer using particle swarm theory. In: Proceedings of the Sixth International Symposium on Micromachine and Human Science, pp. 39–43 (1995)Google Scholar
  16. 16.
    Echeverría Ciaurri, D., Conn, A.R., Mello, U.T., Onwunalu, J.E.: Integrating mathematical optimization and decision making in intelligent fields. Paper SPE 149780 presented at the SPE intelligent energy conference and exhibition, Utrecht, The Netherlands (2012)Google Scholar
  17. 17.
    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
  18. 18.
    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, Studies in Computational Intelligence, pp. 19–55. Springer, New York (2011)CrossRefGoogle Scholar
  19. 19.
    Fernández Martínez, J.L., García Gonzalo, E.: The generalized PSO: a new door to PSO evolution. J. Artif. Evol. Appl. 2008, 1–15 (2008)CrossRefGoogle Scholar
  20. 20.
    Fernández Martínez, J.L., García Gonzalo, E., Fernández Alvarez, J.P.: Theoretical analysis of particle swarm trajectories through a mechanical analogy. Int. J. Comput. Intell. Res. 4(2), 93–104 (2008)CrossRefGoogle Scholar
  21. 21.
    Fletcher, R., Leyffer, S., Toint, P.: A brief history of filter methods. Tech. rep. Mathematics and Computer Science Division, Argonne National Laboratory (2006)Google Scholar
  22. 22.
    Forouzanfar, F., Li, G., Reynolds, A.C.: A two-stage well placement optimization method based on adjoint gradient. Paper SPE 135304 presented at the SPE annual technical conference and exhibition, Florence, Italy (2010)Google Scholar
  23. 23.
    Forouzanfar, F., Reynolds, A.C., Li, G.: Optimization of the well locations and completions for vertical and horizontal wells using a derivative-free optimization algorithm. J. Pet. Sci. Eng. 86–87, 272–288 (2012)CrossRefGoogle Scholar
  24. 24.
    Guyaguler, B., Horne, R.N.: Uncertainty assessment of well-placement optimization. SPE J. 7(1), 24–32 (2004)Google Scholar
  25. 25.
    Harding, T.J., Radcliffe, N.J., King, P.R.: Optimization of production strategies using stochastic search methods. Paper SPE 35518 presented at the European 3-D reservoir modelling conference, Stavanger, Norway (1996)Google Scholar
  26. 26.
    Hu, X., Eberhart, R.: Solving constrained nonlinear optimization problems with particle swarm optimization. In: Proceedings of the 6th World Multiconference on Systemics, Cybernetics and Informatics (2002)Google Scholar
  27. 27.
    Humphries, T.D., Haynes, R.D., James, L.A.: Simultaneous optimization of well placement and control using a hybrid global-local strategy. In: Proceedings of the 13th European Conference on the Mathematics of Oil Recovery, Biarritz, France (2012)Google Scholar
  28. 28.
    Isebor, O.J.: Derivative-free optimization for generalized oil field development. Ph.D. thesis, Department of Energy Resources Engineering, Stanford University (2013)Google Scholar
  29. 29.
    Isebor, O.J., Echeverría Ciaurri, D., Durlofsky, L.J.: Generalized field development optimization using derivative-free procedures. Paper SPE 163631 presented at the SPE reservoir simulation symposium, The Woodlands, Texas (2013)Google Scholar
  30. 30.
    Jones, D.R., Schonlau, M., Welch, W.J.: Efficient global optimization of expensive black-box functions. J. Glob. Optim. 13(4), 455–492 (1998)CrossRefGoogle Scholar
  31. 31.
    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)CrossRefGoogle Scholar
  32. 32.
    Le Digabel, S.: Algorithm 909: NOMAD: Nonlinear optimization with the MADS algorithm. ACM Trans. Math. Softw. 37(4), 44:1–44:15 (2011)CrossRefGoogle Scholar
  33. 33.
    Li, L., Jafarpour, B.: A variable-control well placement optimization for improved reservoir development. Comput. Geosci. 16(4), 871–889 (2012)CrossRefGoogle Scholar
  34. 34.
    Nocedal, J., Wright, S.J.: Numerical Optimization, 2nd edn. Springer, New York (2006)Google Scholar
  35. 35.
    Onwunalu, J.E.: Optimization of field development using particle swarm optimization and new well pattern descriptions. Ph.D. thesis, Department of Energy Resources Engineering, Stanford University (2010)Google Scholar
  36. 36.
    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)CrossRefGoogle Scholar
  37. 37.
    Parsopoulos, K.E., Vrahatis, M.N.: Particle swarm optimization method for constrained optimization problems. In: Proceedings of the Euro-International Symposium on Computational Intelligence (2002)Google Scholar
  38. 38.
    Powell, M.J.D.: The BOBYQA algorithm for bound constrained optimization without derivatives. Tech. rep., Department of Applied Mathematics and Theoretical Physics, University of Cambridge (2009)Google Scholar
  39. 39.
    Sarma, P., Chen, W.H.: Efficient well placement optimization with gradient-based algorithm and adjoint models. Paper SPE 112257 presented at the SPE intelligent energy conference and exhibition, Amsterdam, The Netherlands (2008)Google Scholar
  40. 40.
    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(1), 3–36 (2006)CrossRefGoogle Scholar
  41. 41.
    Vaz, A.I., Vicente, L.N.: A particle swarm pattern search method for bound constrained global optimization. J. Glob. Optim. 39(2), 197–219 (2007)CrossRefGoogle Scholar
  42. 42.
    Wang, C., Li, G., Reynolds, A.C.: Optimal well placement for production optimization. Paper SPE 111154 presented at the SPE Eastern regional meeting, Lexington, Kentucky (2007)Google Scholar
  43. 43.
    Wang, H., Echeverría Ciaurri, D., Durlofsky, L.J., Cominelli, A.SPE J. 17(1), 112–121 (2012)CrossRefGoogle Scholar
  44. 44.
    Yeten, B., Durlofsky, L.J., Aziz, K.: Optimization of nonconventional well type, location and trajectory. SPE J. 8(3), 200–210 (2003)CrossRefGoogle Scholar
  45. 45.
    Zandvliet, M., Handels, M.: Adjoint-based well-placement optimization under production constraints. SPE J. 13(4), 392–399 (2008)CrossRefGoogle Scholar
  46. 46.
    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)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Obiajulu J. Isebor
    • 1
    Email author
  • Louis J. Durlofsky
    • 1
  • David Echeverría Ciaurri
    • 2
  1. 1.Department of Energy Resources EngineeringStanford UniversityStanfordUSA
  2. 2.T. J. Watson Research Center, IBMYorktown HeightsUSA

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