Computational Geosciences

, Volume 17, Issue 2, pp 249–268 | Cite as

Hybrid differential evolution and particle swarm optimization for optimal well placement

  • E. Nwankwor
  • A. K. Nagar
  • D. C. Reid
Original Paper


There is no gainsaying that determining the optimal number, type, and location of hydrocarbon reservoir wells is a very important aspect of field development planning. The reason behind this fact is not farfetched—the objective of any field development exercise is to maximize the total hydrocarbon recovery, which for all intents and purposes, can be measured by an economic criterion such as the net present value of the reservoir during its estimated operational life-cycle. Since the cost of drilling and completion of wells can be significantly high (millions of dollars), there is need for some form of operational and economic justification of potential well configuration, so that the ultimate purpose of maximizing production and asset value is not defeated in the long run. The problem, however, is that well optimization problems are by no means trivial. Inherent drawbacks include the associated computational cost of evaluating the objective function, the high dimensionality of the search space, and the effects of a continuous range of geological uncertainty. In this paper, the differential evolution (DE) and the particle swarm optimization (PSO) algorithms are applied to well placement problems. The results emanating from both algorithms are compared with results obtained by applying a third algorithm called hybrid particle swarm differential evolution (HPSDE)—a product of the hybridization of DE and PSO algorithms. Three cases involving the placement of vertical wells in 2-D and 3-D reservoir models are considered. In two of the three cases, a max-mean objective robust optimization was performed to address geological uncertainty arising from the mismatch between real physical reservoir and the reservoir model. We demonstrate that the performance of DE and PSO algorithms is dependent on the total number of function evaluations performed; importantly, we show that in all cases, HPSDE algorithm outperforms both DE and PSO algorithms. Based on the evidence of these findings, we hold the view that hybridized metaheuristic optimization algorithms (such as HPSDE) are applicable in this problem domain and could be potentially useful in other reservoir engineering problems.


Differential evolution DE Particle swarm optimization PSO Hybridization HPSDE Reservoir simulation Well placement optimization 


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  1. 1.
    Aitokhuehi, I., Durlofsky, L.J., Artus, V., Yeten, B., Aziz, K.: Optimization of advanced well type and performance. In: 9th European Conference on the Mathematics of Oil Recovery, Cannes (2004)Google Scholar
  2. 2.
    Angeline, P.J.: Using selection to improve particle swarm optimization. In: Proceedings of the IEEE Congress on Evolutionary Computation (CEC), pp. 84–89. Anchorage, AL, USA (1998)Google Scholar
  3. 3.
    Bangerth, B.L., Klie, W.H., Wheeler, M.F., Stoffa, P.L., Sen, M.K.: On optimization algorithms for the reservoir oil well placement problem. Comput. Geosci. 10, 303–319 (2006)CrossRefGoogle Scholar
  4. 4.
    Banks, A., Vincent, J., Anyakoha, C.: A review of particle swarm optimization. Part II: hybridisation, combinatorial, multicriteria and constrained optimization, and indicative applications. Nat. Comput.: Int. J. 7(1), 109–124 (2008)CrossRefGoogle Scholar
  5. 5.
    Beckner, B.L., Song, X.: Field development planning using simulated annealing—optimal economic well scheduling and placement. In: SPE Annual Technical Conference and Exhibition (SPE 30650), Dallas (1995)Google Scholar
  6. 6.
    Bittencourt, A.C., Horne, R.N.: Reservoir development and design optimization. In: SPE Annual Tech. Conf. and Exhibtion (SPE 38895), San Antonio (1997)Google Scholar
  7. 7.
    Blackwell, T., Bentley, P.J.: Don’t push me! collision-avoiding swarms. In: IEEE Congress on Evolutionary Comput. pp. 1691–1696. Honolulu, Hawaii, USA (2002)Google Scholar
  8. 8.
    Bouzarkouna, Z., Ding, D.Y., Auger, A.: Well placement optimization with the covariance matrix adaptation evolution strategy and meta-models. Comput. Geosci. 16, 75–92 (2011)CrossRefGoogle Scholar
  9. 9.
    Braendler, D., Hendtlass, T.: The suitability of particle swarm optimisation for training neural hardware. In: International Conference on Industrial and Engineering Applications of Artificial Intelligence and Expert Systems, IEA/AIE, pp. 190–199. Springer, NY (2002)Google Scholar
  10. 10.
    Brandstatter, B., Baumgartner, U.: Particle swarm optimization–mass-spring system analogon. IEEE Trans. Magn. 38, 97–1000 (2002)Google Scholar
  11. 11.
    Centilmen, A., Ertekin, T., Grader, A.S.: Applications of neural networks in multiwell field development. In: SPE Annual Technical Conference and Exhibition (SPE 56433), Houston (1999)Google Scholar
  12. 12.
    Chakrabarti, R., Chattopadhyay, P.K., Basu, M., Panigrahi, C.K.: Particle swarm optimization technique for dynamic economic dispatch. J. Inst. Eng. India 87, 48–54 (2006)Google Scholar
  13. 13.
    Ciaurri, D.E., Mukerji, T., Durlofsky, L.J.: Derivative-free Optimization for Oil Field Operations Studies in Comput. Intell., vol. 359, pp. 19–55. Computational Optimization and Applications in Engr. and Ind. (2011)Google Scholar
  14. 14.
    Clerc, M.: Particle Swarm Optimization. iSTE, London (2006)CrossRefGoogle Scholar
  15. 15.
    Das, S., Konar, A.: A swarm intelligence approach to the synthesis of two-dimensional IIR filters. Eng. Appl. Artif. Intell. 20(8), 1086–1096 (2007). doi: 10.1016/j.engappai.2007.02.004. Accessed 18 Mar 2011CrossRefGoogle Scholar
  16. 16.
    Das, S., Abraham, A., Konar, A.: Particle Swarm Optimization and Differential Evolution Algorithms: Technical Analysis, Applications and Hybridization Perspectives. Accessed: 18 Mar 2011
  17. 17.
    Davendra, D., Zenlinka, I., Onwubolu, G.: Hybrid Differential Evolution—Scatter Search Algorithm for Permutative Optimization Evolutionary Computation, InTech, Vienna, Austria (2009)Google Scholar
  18. 18.
    Deep, K., Bansal, J.C.: Hybridization of particle swarm optimization with quadratic approximation. J. Oper. Res. 46, 3–24 (2009)Google Scholar
  19. 19.
    Deep, K., Das, K.N.: Quadratic approximation based hybrid genetic algorithm for function optimization. Appl. Math. Comput. 203(1), 86–98 (2008)CrossRefGoogle Scholar
  20. 20.
    Dong, X., Wu, Z., Dong, C., Chen, K., Wang, H.: Optimization of vertical well placement by using a hybrid particle swarm optimization. Wuhan Univ. J. Nat. Sci. 16(3), 237–240 (2011)CrossRefGoogle Scholar
  21. 21.
    Eberhart, R., Kennedy, J.: A new optimizer using particle swarm theory. In: Proceedings of the Sixth International Symposium on Micro Machine and Human Science, pp. 39–43. Nagoya, Japan (1995)Google Scholar
  22. 22.
    Engelbrecht, A.P.: Fundamentals of Computational Swarm Intel. Wiley, West Sussex (2005)Google Scholar
  23. 23.
    Farshi, M.M.: Improving genetic algorithms for optimum well placement. MSc. Thesis, Stanford University (2008)Google Scholar
  24. 24.
    Gong, T., Tuson, A.L.: Particle swarm optimization for quadratic assignment problems—a forma analysis approach. Int. J. Comput. Intell. Res. 4, 177–185 (2008)Google Scholar
  25. 25.
    Grimaccia, F., Mussetta, M., Zich, R.E.: Genetical swarm optimization: self-adaptive hybrid evolutionary algorithm for electromagnetics. IEEE Trans. Antennas Propag. 55(3), 781–785 (2007)CrossRefGoogle Scholar
  26. 26.
    Guyaguler, B., Horne, R.N.: Uncertainty assessment of well placement optimization. In: SPE Annual Tech. Conf. and Exhibition (SPE 71625), New Orleans, LA (2001)Google Scholar
  27. 27.
    Hajizadeh, Y., Christie, M., Demyanov, V.: History Matching with Differential Evolution Approach; A Look at New Search Strategies SPE EUROPEC/EAGE Annual Conference and Exhibition, Barcelona, Spain ISBN 978–90–73781–86–3 (2010). doi: 10.2118/130253-MS
  28. 28.
    Haykin, S.: Neural Networks. Macmillan, New York (1999)Google Scholar
  29. 29.
    Hendtlass, T., Randall, M.: A survey of ant colony and particle swarm metaheuristics and their application to discrete optimization problems. In: Proc. of the Inaugural Workshop on Artificial Life (AL’01), pp. 15–25 (2001)Google Scholar
  30. 30.
    Hendtlass, T.: A combined swarm differential evolution algorithm for optimization problems. In: Proceedings of the 14th Int. Conf. on Ind. and Eng. App. of Artificial Intell. and Expert Systems. Lecture Notes in Computer Science, vol. 2070, pp. 11–18 Springer, Berlin (2001)Google Scholar
  31. 31.
    Higashi, N., Iba, H.: Particle swarm optimization with Gaussian mutation. In: Proceedings of the IEEE Swarm Intell. Symposium, pp. 72–79. Indianapolis, IN (2003)Google Scholar
  32. 32.
    Jian, M., Chen, Y.: Introducing recombination with dynamic linkage discovery to particle swarm optimization. In: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 85–86 (2006)Google Scholar
  33. 33.
    Juang, C.F.: A hybrid of genetic algorithm and particle swarm optimization for recurrent network design. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 34(2), 997–1006 (2004)CrossRefGoogle Scholar
  34. 34.
    Kennedy, J.: Small worlds and mega-minds: effects of neighborhood topology on particle swarm performance. In: Proceedings of Cong. of Evolutionary Computation, vol. 3, pp. 1931–1938. IEEE, New York (1999)Google Scholar
  35. 35.
    Kennedy, J., Eberhart, R.: Particle swarm optimization. In: IEEE, Neural Networks Council Staff, IEEE Neural Networks Council (eds.) Proc. IEEE International Conference on Neural Networks, pp. 1942–1948. IEEE, Los Alamitos (1995)Google Scholar
  36. 36.
    Kosmidis, V.D., Perkins, J.D., Pistikopoulos, E.N.: A mixed integer optimization formulation for the well scheduling problem on petroleum fields. Comput. Chem. Eng. 29(7), 1523–1541 (2005)CrossRefGoogle Scholar
  37. 37.
    Krink, T., Vesterstrøm, J.S., Riget, J.: Particle swarm optimization with spatial particle extension. In: Proceedings of the 4th Congress on Evolutionary Computation, pp. 1474–1479 (2002)Google Scholar
  38. 38.
    Lampinen, J., Zelinka, I.: Mechanical engineering design by differential evolution. In: Corne, D., Dorigo, M., Glover, F. (eds.) New Ideas in Optimisation, pp. 127–146. McGraw-Hill, London (1999)Google Scholar
  39. 39.
    Lampinen, J.: A constraint handling approach for the differential evolution algorithm. In: Proc. the Congress on Evolutionary Computation, vol. 2, pp. 1468–1473 (2002)Google Scholar
  40. 40.
    Litvak, M., Gane, B., Williams, G., Mansfield, M., Angert, P., Macdonald, C., McMurray, L., Skinner, R., Walker, G.J.: Field development optimization technology. Paper SPE 106426 presented at the SPE Reservoir Simulation Symposium, Houston (2007)Google Scholar
  41. 41.
    Løvbjerg, M., Krink, T.: Extending particle swarms with self-organized criticality. In: Proc. of the 4th Congress on Evolutionary Computation, pp. 1588–1593 (2002)Google Scholar
  42. 42.
    Løvbjerg, M., Rasmussen, T., Krink, T.: Hybrid particle swarm optimizer with breeding and subpopulations. In: Proc. of the 3rd Genetic and Evolutionary Computation Conference (GECCO-2001), vol. 1, pp. 469–476 (2001)Google Scholar
  43. 43.
    Madavan, N.: Aerodynamic shape optimisation using hybrid differential evolution. In: AIAA-2003–3792, 21st AIAA Applied Aerodynamic Conference, Orlando, Florida, USA (2003)Google Scholar
  44. 44.
    Michalewicz, Z., Schoenauer, M.: Evolutionary algorithms for constrained parameter optimization problems. Evol. Comput. 4(1), 1–32 (1996)CrossRefGoogle Scholar
  45. 45.
    Miranda, V., Fonseca, N.: New evolutionary particle swarm algorithm (EPSO) applied to voltage/VAR control. In: The 14th Power Systems Computation Conference (PSCC’02), Seville, Spain (2002)Google Scholar
  46. 46.
    Montes, G., Bartolome, P., Udias, A.L.: The use of genetic algorithms in well placement optimization. In: SPE Latin American and Caribbean Petroleum Engineering Conference, SPE 69439 (2001)Google Scholar
  47. 47.
    Onwunalu, J., 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
  48. 48.
    Onwunalu, J.: Optimization of nonconventional well placement using genetic algorithms and statistical proxy. Master’s Thesis, Stanford University (2006)Google Scholar
  49. 49.
    Perez-Guerrero, R.E., Cedeno-Maldonado, J.R.: Economic power dispatch with non-smooth cost functions using differential evolution. In: Proc. the 37th Annual North American Power Symposium 2005, pp. 183–190 (2005)Google Scholar
  50. 50.
    Plagianakos, V.P., Vrahatis, M.N.: Parallel evolutionary training algorithms for ‘hardware-friendly’ neural networks. Nat. Comput. 1, 307–322 (2002)CrossRefGoogle Scholar
  51. 51.
    Plagianakos, V.P., Vrahatis, M.N.: Training neural networks with threshold activation functions and constrained integer weights. In: IEEE Int. Joint Conf. on Neural Networks (IJCNN 2000), Como, Italy (2000)Google Scholar
  52. 52.
    Poli, R., Di Chio, C., Langdon, W.B.: Exploring extended particle swarms: a genetic programming approach. In: Beyer, H.-G., et al. (eds.) GECCO 2005: Proceedings of the 2005 Conf. on Genetic and Evolutionary Computation, pp. 169–176. Washington, DC (2005)Google Scholar
  53. 53.
    Poli, R., Langdon, W.B., Holland, O.: Extending particle swarm optimization via genetic programming. In: Keijzer, M., et al. (eds.) Lecture Notes in Computer Science. Proceedings of the 8th European Conference on Genetic Programming, vol. 3447, pp. 291–300. Springer, Berlin, Lausanne, Switzerland (2005)Google Scholar
  54. 54.
    Ratnaweera, A., Halgamuge, S.K., Watson, H.C.: Self-organizing hierarchical particle swarm optimizer with time varying accelerating coefficients. IEEE Trans. Evol. Comput. 8(3), 240–255 (2004)CrossRefGoogle Scholar
  55. 55.
    Robinson, J., Sinton, S., Rahmat-Samii, Y.: Particle swarm, genetic algorithm, and their hybrids: optimization of a profiled corrugated horn antenna. In: IEEE International Symposium on Antennas & Propagation, pp. 314–317. San Antonio, Texas (2002)Google Scholar
  56. 56.
    Rogalsky, T., Derksen, R.W., Kocabiyik, S.: Differential evolution in aerodynamic optimization. Can. Aeronaut. Space Inst. J. 46, 183–190 (2000)Google Scholar
  57. 57.
    Sarma, P., Chen, W.H.: Efficient well placement optimization with gradient-based algorithms and adjoint models. In: Paper SPE 112257 Presented at the 2008 SPE Intelligent Energy Conf. and Exhib Amsterdam (2008)Google Scholar
  58. 58.
    Shi, Y., Eberhart, R.C.: A modified particle swarm optimizer. In: Proc. IEEE International Conf. on Evol. Comput., pp. 69–73. IEEE, Piscataway, NJ (1998)Google Scholar
  59. 59.
    Spall, J.C.: Multivariate stochastic approximation using a simultaneous perturbation gradient approximation. IEEE Trans. Automat. Contr. 37(3), 332–341 (1992)CrossRefGoogle Scholar
  60. 60.
    Storn, R., Price, K.: Differential evolution—a simple and efficient adaptive scheme for global optimization over continuous spaces. Tech. Rep. TR-95–012, Inter. Computer Science Institute (ICSI) (1995)Google Scholar
  61. 61.
    Storn, R., Price, K.: Differential evolution—simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 11, 341–359 (1997)CrossRefGoogle Scholar
  62. 62.
    Sum-Im, T., Taylor, G.A., Irving, M.R., Song, Y.H.: A differential evolution algorithm for multistage transmission expansion planning. In: Proc. the 42nd International Universities Power Engineering Conference (UPEC 2007), pp. 357–364. Brighton, UK (2007) Google Scholar
  63. 63.
    Tasoulis, D.K., Plagianakos, V.P., Vrahatis, M.N.: Differential evolution algorithms for finding predictive gene subsets in microarray data. In: Artificial Intelligence Applications and Innovations. IFIP Int’l Federation for Information Processing, vol. 204, pp. 484–491 (2006)Google Scholar
  64. 64.
    Thangaraj, R., Pant, M., Abraham, A., Bouvry, P.: Particle swarm optimization: hybridization perspectives and experimental illustrations. Appl. Math. Comput. 217, 5208–5226 (2011)CrossRefGoogle Scholar
  65. 65.
    Van Essen, G.M., Zandvliet, M.J., Van den Hof, P.M.J., Bosgra, O.H., Jansen, J.D.: Robust waterflooding optimization of multiple geological scenarios. SPE Journal 14(1), 202–210 (2009)Google Scholar
  66. 66.
    Vasiljevic, D., Golobic, J.: Comparison of the classical dumped least squares and genetic algorithm in the optimization of doublets. In: Proceedings of the First Workshop on Soft Computing, pp. 200–204. Nagoya, Japan (1996)Google Scholar
  67. 67.
    Wang, C., Li, G., Reynolds, A.C.: Optimal well placement for production optimization. In: Paper SPE 111154 Presented at SPE Eastern Regional Meeting, Lexington (2007)Google Scholar
  68. 68.
    Wang, J., Buckley, J.S.: Automatic history matching using differential evolution algorithm. In: Int’l Symposium of the Soc. of Core Analysts Trondheim, Norway (2006)Google Scholar
  69. 69.
    Wang, S.K., Chiou, J.P., Liu, C.W.: Non-smooth/non-convex economic dispatch by a novel hybrid differential evolution algorithm. IEE Proc. Gener. Transm. Distrib. 1(5), 793–803 (2007)CrossRefGoogle Scholar
  70. 70.
    Wolpert, D.H., Macready, W.G.: No free lunch theorems for optimization. IEEE Trans. Evol. Comput. 1, 67–82 (1997)CrossRefGoogle Scholar
  71. 71.
    Xie, X., Zhang, W., Yang, Z.: A dissipative particle swarm optimization. In: IEEE Congress on Evolutionary Computation, pp. 1456–1461. Honolulu, Hawaii, USA (2002)Google Scholar
  72. 72.
    Yeten, B.: Optimum deployment of nonconventional wells. Ph.D. thesis, Stanford University (2003)Google Scholar
  73. 73.
    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)Google Scholar
  74. 74.
    Zhang, W.J., Xie, X.F.: DEPSO: hybrid particle swarm with differential evolution operator. In: IEEE International Conference on Systems, Man and Cybernetics (SMCC), pp. 3816–3821. Washington DC, USA (2003)Google Scholar

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© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.Centre for Applicable Mathematics and Systems Science, Department of Mathematics and Computer ScienceLiverpool Hope UniversityLiverpoolUK
  2. 2.Department of GeosciencesUniversity of LiverpoolLiverpoolUK

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