Generative well pattern design—principles, implementation, and test on OLYMPUS challenge field development problem

  • Pierre BergeyEmail author
Original Paper


A novel generative (well pattern) design approach is proposed for a reservoir well pattern design, building upon the observation that automated methods are slow to beat human-designed patterns. The approach relies upon the construction of 3D well patterns as a function of geology in a mindset in which functional requirements derive from reservoir engineering heuristics. The concept of well patterns as graphs is leveraged and expanded. Nodes are well parts and geological features. Edges represent functional requirements driven by economical and physical considerations; they are expressed as 3D functions of geology. Diffusive time of flight and a novel measure are proposed to quantify the relative suitability of model cells to the positioning of wells. A small, but deemed complete, set of requirements is proposed relative to the reservoir engineering domain. The search space for inserting wells is limited to cells non-dominated from the joint perspective of requirements applicable to the considered well type. Tentatively, optimal patterns are built by balancing weights given to each requirement. The process is applied to a single and to multiple realizations enabling consideration of uncertainties. Weights are few and display quasi-linear and independent relations to common objective functions. The approach was tested on the OLYMPUS field development benchmark problem. Results illustrate the potential for initializing optimization with performing candidates while maintaining geographic coverage. The search space dimension was reduced by a factor of ~ 10100. A solution was found within the first 92 investigated settings that reaches a net present value (8% discount) of 643M$. Such performances are of a nature to ensure systemic superiority over purely human-driven optimization processes and, upon integration in iterative search processes, over competing global parameterization schemes whenever few calls are made to the objective function.


Generative design Well pattern Optimization Uncertainties 

MSC classification

90C35 (operations research, mathematical programming/programming involving graphs or networks) 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



The author thanks Total for authorizing the publication of this article; B Mathis, D Gourlay, Ph Ricoux, JP Rolando, F Franco, D Marion, and M Cyrot for the managerial and moral support provided to the WISH venture; C Vouaux and C Begotto for their patience; B Corre, C Deutsch, O Babak, A Delafargue, P Thore, A Abadpour, and P Bauer for their insights on applied mathematics over the years; I Zine for his Java lessons; Th Harribey and the CIG team for their help on Java code matters; S Sangla for his fast marching method code development; and N Eberle and M Ronchi for their assistance in IX usage and IX-imbedded Python code.


  1. 1.
    Bouzarkouna, Z.: "Well placement optimization. PhD Thesis Université Paris Sud - Paris XI,," 2012. [Online]. Available:
  2. 2.
    Silva, V., C. M.A, Oliveira, D., Moraes, R.: Stochastic optimization strategies applied to OLYMPUS. In: EAGE/TNO Workshop on OLYMPUS Field Development Optimization, Barcelona (2018)Google Scholar
  3. 3.
    Fonseca, R., Geel, C., Leeuwenburgh, O.: "Description of OLYMPUS reservoir model for optimization challenge," 2017. [Online]. Available:
  4. 4.
    Chang, Y., Lorentzen, R., Naevdal, G., Feng, T.: OLYMPUS optimization under geological uncertainty. In: EAGE/TNO Workshop on OLYMPUS Field Development Optimization, Barcelona (2018)Google Scholar
  5. 5.
    Harb, A., Kassem, H., G. K.: "OLYMPUS field development optimization challenge," in EAGE/TNO Workshop on OLYMPUS Field Development Optimization, Barcelona (2018).Google Scholar
  6. 6.
    Emerick, A.A., Silva, E., Messer, B., Almeida, L.F., Szwarcman, D., Pacheco, M.A.C., V. M. M.B.R: Well placement optimization using a genetic algorithm with non-linear constraints. Soc. Petrol. Eng. (2009).
  7. 7.
    Onwunalu, J.E., Durlofsky, L.J.: Development and application of a new well pattern optimization algorithm for optimizing large scale field development. Soc. Petrol. Eng. (2009).
  8. 8.
    Schulze-Riegert, R., Anton, A., Baffoe, J., Geissenhoener, D., Jin Ng, K., Nwakile, M., Skripkin, S.: Standardized workflow design for field development plan optimization under uncertainty. In: EAGE/TNO Workshop on OLYMPUS Field Development Optimization, Barcelona (2018)Google Scholar
  9. 9.
    Bergey, P.: Patent application PCT/FR2019/051957 method for determining locations of wells in a field (2019)Google Scholar
  10. 10.
    Wikipedia, "Functional requirement," [Online]. Available:
  11. 11.
    Wikipedia, "Generative design," [Online]. Available:
  12. 12.
    Peaceman, D.W.: A new method for representing multiple wells with arbitrary rates in numerical reservoir simulation. Society of Petroleum Engineers. (1995). CrossRefGoogle Scholar
  13. 13.
    Sethian, J.: A fast marching level set method for monotonically advancing fronts. Proc. Natl. Acad. Sci. 1591–1595 (1996)CrossRefGoogle Scholar
  14. 14.
    Tsitsiklis, J.N.: Efficient algorithms for globally optimal trajectories. Automatic Control, IEEE Transactions. 1528–1538 (1995)CrossRefGoogle Scholar
  15. 15.
    Dijkstra, E.W.: A note on two problems in connexion with graphs. Numerische mathematik. 269–271 (1959)CrossRefGoogle Scholar
  16. 16.
    Lajevardi, S., Babak, O., Deutsch, C.: Estimating barrier shale extent and optimizing well placement in heavy oil reservoirs. Petroleum Geosciences. (2013). CrossRefGoogle Scholar
  17. 17.
    Bergey, P.: "Process for defining the locations of a plurality of wells in a field, related system and computer program product". Patent Application PCT/IB2017/001323, 26 September (2017)Google Scholar
  18. 18.
    Smutnick, C., Rudy, J., Żelaznyt, D.: "Very fast non-dominated sorting," Decision Making in Manufacturing and Services Vol. 8 • 2014 • No. 1–2, pp. 13-23 (2014)Google Scholar
  19. 19.
    Fredman, M.L., Tarjan, R.E.: "Fibonacci heaps and their uses in improved network optimization algorithms.," in 25th Annual Symposium on Foundations of Computer Science. IEEE. pp. 338&ndash, 346. doi:10.1109/SFCS.1984.715934. (1984)Google Scholar
  20. 20.
    Ng, P.-C.: "Route planning process". US Patent 20060161337A1, 19 01 (2005)Google Scholar
  21. 21.
    Bergey, P.: Defining 3D reservoir well patterns as functions of geology for robust design and faster optimization. In: EAGE/TNO Workshop on OLYMPUS Field Development Optimization, Barcelona (2018)Google Scholar
  22. 22.
    SCHLUMBERGER, 2018. [Online]. Available:
  23. 23.
    Hales, T.: "A formal proof of the Kepler conjecture," arXiv:1501.02155 [math.MG] (2015)Google Scholar
  24. 24.
    Sethian, J.A., Chorin, A.J., Concus, P.: Numerical solution of the Buckley-Leverett equations. Society of Petroleum Engineers. (1983).

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.EP/DSO/GIS/RRSTotal S.A.ParisFrance

Personalised recommendations