Skip to main content
SpringerLink
Log in

Hybrid differential evolution and particle swarm optimization for optimal well placement

  • Original Paper
  • Published:
Computational Geosciences Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  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)

  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)

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

  6. Bittencourt, A.C., Horne, R.N.: Reservoir development and design optimization. In: SPE Annual Tech. Conf. and Exhibtion (SPE 38895), San Antonio (1997)

  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)

  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)

    Article  Google Scholar 

  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. Brandstatter, B., Baumgartner, U.: Particle swarm optimization–mass-spring system analogon. IEEE Trans. Magn. 38, 97–1000 (2002)

    Google Scholar 

  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)

  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. 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)

  14. Clerc, M.: Particle Swarm Optimization. iSTE, London (2006)

    Book  Google Scholar 

  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 2011

    Article  Google Scholar 

  16. Das, S., Abraham, A., Konar, A.: Particle Swarm Optimization and Differential Evolution Algorithms: Technical Analysis, Applications and Hybridization Perspectives. www.softcomputing.net/aciis.pdf. Accessed: 18 Mar 2011

  17. Davendra, D., Zenlinka, I., Onwubolu, G.: Hybrid Differential Evolution—Scatter Search Algorithm for Permutative Optimization Evolutionary Computation, InTech, Vienna, Austria (2009)

  18. Deep, K., Bansal, J.C.: Hybridization of particle swarm optimization with quadratic approximation. J. Oper. Res. 46, 3–24 (2009)

    Google Scholar 

  19. Deep, K., Das, K.N.: Quadratic approximation based hybrid genetic algorithm for function optimization. Appl. Math. Comput. 203(1), 86–98 (2008)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

  22. Engelbrecht, A.P.: Fundamentals of Computational Swarm Intel. Wiley, West Sussex (2005)

    Google Scholar 

  23. Farshi, M.M.: Improving genetic algorithms for optimum well placement. MSc. Thesis, Stanford University (2008)

  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. 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)

    Article  Google Scholar 

  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)

  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. Haykin, S.: Neural Networks. Macmillan, New York (1999)

    Google Scholar 

  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)

  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. Higashi, N., Iba, H.: Particle swarm optimization with Gaussian mutation. In: Proceedings of the IEEE Swarm Intell. Symposium, pp. 72–79. Indianapolis, IN (2003)

  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)

  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)

    Article  Google Scholar 

  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. 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)

  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)

    Article  Google Scholar 

  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)

  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. Lampinen, J.: A constraint handling approach for the differential evolution algorithm. In: Proc. the Congress on Evolutionary Computation, vol. 2, pp. 1468–1473 (2002)

  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)

  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)

  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)

  43. Madavan, N.: Aerodynamic shape optimisation using hybrid differential evolution. In: AIAA-2003–3792, 21st AIAA Applied Aerodynamic Conference, Orlando, Florida, USA (2003)

  44. Michalewicz, Z., Schoenauer, M.: Evolutionary algorithms for constrained parameter optimization problems. Evol. Comput. 4(1), 1–32 (1996)

    Article  Google Scholar 

  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)

  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)

  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)

    Article  Google Scholar 

  48. Onwunalu, J.: Optimization of nonconventional well placement using genetic algorithms and statistical proxy. Master’s Thesis, Stanford University (2006)

  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)

  50. Plagianakos, V.P., Vrahatis, M.N.: Parallel evolutionary training algorithms for ‘hardware-friendly’ neural networks. Nat. Comput. 1, 307–322 (2002)

    Article  Google Scholar 

  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)

  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)

  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. 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)

    Article  Google Scholar 

  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)

  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. 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)

  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. Spall, J.C.: Multivariate stochastic approximation using a simultaneous perturbation gradient approximation. IEEE Trans. Automat. Contr. 37(3), 332–341 (1992)

    Article  Google Scholar 

  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)

  61. Storn, R., Price, K.: Differential evolution—simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 11, 341–359 (1997)

    Article  Google Scholar 

  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)

  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)

  64. Thangaraj, R., Pant, M., Abraham, A., Bouvry, P.: Particle swarm optimization: hybridization perspectives and experimental illustrations. Appl. Math. Comput. 217, 5208–5226 (2011)

    Article  Google Scholar 

  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. 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)

  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)

  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)

  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)

    Article  Google Scholar 

  70. Wolpert, D.H., Macready, W.G.: No free lunch theorems for optimization. IEEE Trans. Evol. Comput. 1, 67–82 (1997)

    Article  Google Scholar 

  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)

  72. Yeten, B.: Optimum deployment of nonconventional wells. Ph.D. thesis, Stanford University (2003)

  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. 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)

Download references

Author information

Authors and Affiliations

  1. Centre for Applicable Mathematics and Systems Science, Department of Mathematics and Computer Science, Liverpool Hope University, Liverpool, UK

    E. Nwankwor, A. K. Nagar & D. C. Reid

  2. Department of Geosciences, University of Liverpool, Liverpool, UK

    E. Nwankwor

Authors
  1. E. Nwankwor
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. K. Nagar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. D. C. Reid
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. Nwankwor.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nwankwor, E., Nagar, A.K. & Reid, D.C. Hybrid differential evolution and particle swarm optimization for optimal well placement. Comput Geosci 17, 249–268 (2013). https://doi.org/10.1007/s10596-012-9328-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10596-012-9328-9

Keywords

Search

Navigation