Skip to main content
Log in

Drainage area maximization in unconventional hydrocarbon fields with integer linear programming techniques

Annals of Operations Research Aims and scope Submit manuscript

Abstract

The drainage area maximization problem for an unconventional hydrocarbon field is addressed with the objective of designing a development plan that optimizes total production while satisfying environmental and operating constraints. The various characteristics of the problem are presented and a solution approach is developed around an integer linear programming model applied to a discretisation of the field’s geographical area. Computational experiments show that the approach provides a practical response to the problem, generating solutions that comply with all of the constraints. The algorithm implemented under this approach has been incorporated into a software tool for planning and managing unconventional hydrocarbon operations and has been used since 2018 by two leading petroleum companies in Argentina to improve unconventional development plans for the country’s “Vaca Muerta” geological formation.

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

Access this article

Price includes VAT (Finland)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Notes

  1. Many companies use the term “pad” as an equivalent of “surface facility”.

  2. https://www.improntait.com/en/ufo.

References

  • Achterberg, T. (2009). Scip: Solving constraint integer programs. Mathematical Programming Computation, 1(1), 1–41.

    Article  Google Scholar 

  • Bomze, I. M., Budinich, M., Pardalos, P. M., & Pelillo, M. (1999). The maximum clique problem. In Handbook of combinatorial optimization (pp. 1–74). Kluwer Academic Publishers.

  • Corrêa, R. C., Delle Donne, D., Koch, I., & Marenco, J. (2018). General cut-generating procedures for the stable set polytope. Discrete Applied Mathematics, 245, 28–41.

    Article  Google Scholar 

  • Fekete, S. P., & Schepers, J. (1997). On more-dimensional packing iii: Exact algorithms. Technical paper ZPR97-290, Mathematisches Institut, Universität zu Köln.

  • Gamrath, G., Anderson, D., Bestuzheva, K., Chen, W. K., Eifler, L., Gasse, M., Gemander, P., Gleixner, A., Gottwald, L., Halbig, K., Hendel, G., Hojny, C., Koch, T., Le Bodic, P., Maher, S., Matter, F., Miltenberger, M., Mühmer, E., Müller, B., Pfetsch, M., Schlösser, F., Serrano, F., Shinano, Y., Tawfik, C., Vigerske, S., Wegscheider, F., Weninger, D., & Witzig, J. (2020). The SCIP Optimization Suite 7.0. ZIB-Report. Zuse Institut Berlin.

  • Gedruckt, A., & Scheithauer, G. (1997). Equivalence and dominance for problems of optimal packing of rectangles. Ricerca Operativa, 83, 3–34.

    Google Scholar 

  • Giandomenico, M., Rossi, F., & Smriglio, S. (2013). Strong lift-and-project cutting planes for the stable set problem. Mathematical Programming, 141(1), 165–192.

    Article  Google Scholar 

  • Grötschel, M., Lovász, L., & Schrijver, A. (1993). Geometric algorithms and combinatorial optimization. Springer.

  • Hadjiconstantinou, E., & Christofides, N. (1995). An exact algorithm for general, orthogonal, two-dimensional knapsack problems. European Journal of Operational Research, 83, 39–56.

    Article  Google Scholar 

  • Koch, T. (2004). Rapid mathematical programming. Ph.D. Thesis, Technische Universität Berlin.

  • Kumlander, D. (2004). A new exact algorithm for the maximum-weight clique problem based on a heuristic vertex-coloring and a backtrack search. In Proceedings of the fourth international conference on engineering computational technology.

  • Lodi, A., Martello, S., & Monaci, M. (2002). Two-dimensional packing problems: A survey. European Journal of Operational Research, 141, 241–252.

    Article  Google Scholar 

  • Martello, S., Monaci, M., & Vigo, D. (2003). An exact approach to the strip-packing problem. INFORMS Journal on Computing, 15, 310–319.

    Article  Google Scholar 

  • Martello, S., Pisinger, D., & Vigo, D. (1998). The three-dimensional bin packing problem. Operations Research, 48, 256–267.

    Article  Google Scholar 

  • Martello, S., & Vigo, D. (1998). Exact solution of the two-dimensional finite bin packing problem. Management Science, 44(3), 388–399.

    Article  Google Scholar 

  • Östergård, P. (1999). A new algorithm for the maximum-weight clique problem. Electronic Notes in Discrete Mathematics, 3, 153–156.

    Article  Google Scholar 

  • Rebennack, S., Oswald, M., Theis, D. O., Seitz, H., Reinelt, G., & Pardalos, P. M. (2011). A branch and cut solver for the maximum stable set problem. Journal of Combinatorial Optimization, 21(4), 434–457.

    Article  Google Scholar 

  • Rossi, F., & Smriglio, S. (2001). A branch-and-cut algorithm for the maximum cardinality stable set problem. Operations Research Letters, 28, 63–74.

    Article  Google Scholar 

  • San Segundo, P., Rodríguez-Losada, D., & Jiménez, A. (2011). An exact bit-parallel algorithm for the maximum clique problem. Computers & Operations Research, 38(2), 571–581.

    Article  Google Scholar 

  • Shimizu, S., Yamaguchi, K., Saitoh, T., & Masuda, S. (2017). Fast maximum weight clique extraction algorithm: Optimal tables for branch-and-bound. Discrete Applied Mathematics, 223, 120–134.

    Article  Google Scholar 

Download references

Acknowledgements

The authors wish to thank Pablo Pazos for his helpful comments on the geological aspects of this paper, and Kenneth Rivkin for his useful suggestions on the final version. The authors would also like to express their gratitude towards the anonymous reviewers for their detailed comments and suggestions, which greatly improved this manuscript. The third author was partially financed by ISCI, Chile (ICM-FIC: P05-004-F, CONICYT: FB0816), UBACyT Grant 20020170100495BA (Argentina), and PIP-CONICET Grant 11220200100084CO (Argentina).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Javier Marenco.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aliaga, F., Delle Donne, D., Durán, G. et al. Drainage area maximization in unconventional hydrocarbon fields with integer linear programming techniques. Ann Oper Res 316, 891–904 (2022). https://doi.org/10.1007/s10479-022-04620-8

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-022-04620-8

Keywords

Navigation