Skip to main content
SpringerLink
Log in

A least squares approach for efficient and reliable short-term versus long-term optimization

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

Abstract

The uncertainties related to long-term forecasts of oil prices impose significant financial risk on ventures of oil production. To minimize risk, oil companies are inclined to maximize profit over short-term horizons ranging from months to a few years. In contrast, conventional production optimization maximizes long-term profits over horizons that span more than a decade. To address this challenge, the oil literature has introduced short-term versus long-term optimization. Ideally, this problem is solved by a posteriori multi-objective optimization methods that generate an approximation to the Pareto front of optimal short-term and long-term trade-offs. However, such methods rely on a large number of reservoir simulations and scale poorly with the number of objectives subject to optimization. Consequently, the large-scale nature of production optimization severely limits applications to real-life scenarios. More practical alternatives include ad hoc hierarchical switching schemes. As a drawback, such methods lack robustness due to unclear convergence properties and do not naturally generalize to cases of more than two objectives. Also, as this paper shows, the hierarchical formulation may skew the balance between the objectives, leaving an unfulfilled potential to increase profits. To promote efficient and reliable short-term versus long-term optimization, this paper introduces a natural way to characterize desirable Pareto points and proposes a novel least squares (LS) method. Unlike hierarchical approaches, the method is guaranteed to converge to a Pareto optimal point. Also, the LS method is designed to properly balance multiple objectives, independently of Pareto front’s shape. As such, the method poses a practical alternative to a posteriori methods in situations where the frontier is intractable to generate.

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. Aziz, K., Settari, A.: Petroleum reservoir simulation. Applied Science Publishers London, 476 (1979)

  2. Bailey, W.J., Couet, B., Wilkinson, D.: Framework for field optimization to maximize asset value. SPE Reserv. Eval. Eng. 8, 7–25 (2005)

    Article  Google Scholar 

  3. Biegler, L.T.: Solution of dynamic optimization problems by successive quadratic programming and orthogonal collocation. Comput. Chem. Eng. 8, 243–248 (1984)

    Article  Google Scholar 

  4. Biegler, L.T.: A survey on sensitivity-based nonlinear model predictive control. In: 10th IFAC International Symposium on Dynamics and Control of Process Systems. Mumbaim, India, pp. 499–510 (2013)

  5. Bock, H.G., Plitt, K.J.: A multiple shooting algorithm for direct solution of optimal control problems In: Proceedings 9th IFAC World Congress Budapest. Pergamon Press, pp. 243–274 (1984)

  6. Brouwer, D.R., Jansen, J.D.: Dynamic optimization of waterflooding with smart wells using optimal control theory. SPE J. 9(4), 391–402 (2004)

    Article  Google Scholar 

  7. Capolei, A., Jørgensen, J. B.: Solution of constrained optimal control problems using multiple shooting and esdirk methods. In: 2012 American Control Conference, pp. 295–300 (2012)

  8. Capolei, A., Suwartadi, E., Foss, B., Jørgensen, J. B.: A meanvariance objective for robust production optimization in uncertain geological scenarios. J. Pet. Sci. Eng. 125, 23–37 (2015)

    Article  Google Scholar 

  9. Chen, C., Li, G., Reynolds, A.: Robust constrained optimization of short-and long-term net present value for closed-loop reservoir management. SPE J. 17(3), 849–864 (2012)

    Article  Google Scholar 

  10. Chen, Z.: Reservoir simulation: Mathematical techniques in oil recovery. SIAM, Philadelphia, USA (2007)

    Book  Google Scholar 

  11. Christiansen, L.H., Capolei, A., Jørgensen, J.B.: Time-explicit methods for joint economical and geological risk mitigation in production optimization. Journal of Petroleum Science and Engineering, 2016. doi:10.1016/j.petrol.2016.04.018

  12. Codas, A., Foss, B., Camponogara, E.: Output-constraint handling and parallelization for oil-reservoir control optimization by means of multiple shooting. SPE J. 20(4), 856–871 (2015)

    Article  Google Scholar 

  13. Fonseca, R.M., Leeuwenburgh, O., Van den Hof, P.M.J., Jansen, J.D.: Ensemble-based hierarchical multi-objective production optimization of smart wells. Comput. Geosci. 18(3), 449–461 (2014). ISSN 1573-1499

  14. Fonseca, R.M., Reynolds, A.C., Jansen, J.D.: Generation of a pareto front for a bi-objective water flooding optimization problem using approximate ensemble gradients. J. Pet. Sci. Eng. 147, 249–260 (2016)

    Article  Google Scholar 

  15. Fonseca, R.M., Stordal, A.S., Leeuwenburgh, O., Van den Hof, P.M.J., Jansen, J.D.: Robust ensemble-based multi-objective optimization. In: ECMOR XIV-14th European conference on the mathematics of oil recovery, 2014

  16. Isebor, O.J., Durlofsky, L.J.: Biobjective optimization for general oil field development. J. Pet. Sci. Eng. 119, 123 – 138 (2014). ISSN 0920-4105

    Article  Google Scholar 

  17. Jansen, J.D., Bosgra, O.H., Van den Hof, P.M.J.: Model-based control of multiphase flow in subsurface oil reservoirs. J. Process Control 18(9), 846–855 (2008)

  18. Jørgensen, J. B.: Adjoint sensitivity results for predictive control, state- and parameter-estimation with nonlinear models. In: Proceedings of the European Control Conference 2007. Kos, Greece, pp. 3649?3656 (2007)

  19. Lie, K.A., Krogstad, S., Ligaarden, I.S., Natvig, J.R., Nilsen, H.M., Skaflestad, B.: Open-source matlab implementation of consistent discretisations on complex grids. Comput. Geosci. 16(2), 297–322 (2012)

    Article  Google Scholar 

  20. Liu, X., Reynolds, A.C.: Gradient-based multi-objective optimization with applications to waterflooding optimization. Computational Geosciences, pp. 1–17, 2015. doi:10.1007/s10596-015-9523-6

  21. Liu, X., Reynolds, A.C.: Pareto optimal solutions for minimizing risk and maximizing expected value of life-cycle npv of production under nonlinear constraints. In: SPE Reservoir Simulation Symposium, pp. 23–25, Texas, USA, 2015. doi:10.2118/173274-MS

  22. Liu, X., Reynolds, A.C.: A multiobjective steepest descent method with applications to optimal well control. Comput. Geosci. 20(2), 355–374 (2016). ISSN 1573-1499

    Article  Google Scholar 

  23. Miettinen, K.: Nonlinear multi-objective optimization. Kluwer Academic Publishers, Massachusetts, USA (1999)

    Google Scholar 

  24. Nocedal, J., Wright, J.S.: Numerical optimization. Springer (2006)

  25. Oliver, D.S., Chen, Y.: Recent progress on reservoir history matching: A review. Comput. Geosci. 15(1), 185–221 (2011). doi:10.1007/s10596-010-9194-2

    Article  Google Scholar 

  26. Oliver, D.S., Reynolds, A.C., Liu, N.: Inverse theory for petroleum reservoir characterization and history matching. Cambridge University Press, Cambridge (2008). doi:10.1017/CBO9780511535642

    Book  Google Scholar 

  27. Pareto, V.: Manual of political economy. The MacMillian Press Ltd (1971)

  28. Pavlikov, K., Uryasev, S.: Cvar norm and applications in optimization. Optim. Lett. 8(7), 1999–2020 (2014)

    Article  Google Scholar 

  29. Sarma, P., Aziz, K., Durlofsky, L.J.: Implementation of adjoint solution for optimal control of smart wells. In: Proceedings of SPE Reservoir Simulation Symposium, pp. 295–300 (2005)

  30. Siraj, M.M., Van den Hof, P.M.J., Jansen, J.D.: Handling risk of uncertainty in model-based production optimization: a robust hierarchical approach. 2nd IFAC Workshop Autom. Control Offshore Oil Gas Prod. Florianpolis, Brazil 48(6), 248–253 (2015)

  31. Siraj, M.M., Van den Hof, P.M.J., Jansen, J.D.: Model and economic uncertainties in balancing short-term and long-term objectives in water-flooding optimization. In: 2015 SPE Reservoir Simulation Symposium, 2015

  32. Suwartadi, E., Krogstad, S., Foss, B.: Nonlinear output constraints handling for production optimization of oil reservoirs. Comput. Geosci. 16, 499–517 (2012)

    Article  Google Scholar 

  33. Valladao, D.M., Torrado, R.R., Flach, B., Embid, S.: On the stochastic response surface methodology for the determination of the development plan of an oil & gas field. In: SPE Middle East Intelligent Energy Conference and Exhibition, pp. 28–30, Manama, Bahrain, 2013. doi:10.2118/173274-MS

  34. Van Essen, G., Van den Hof, P.M.J., Jansen, J.D.: Hierarchical long-term and short-term production optimization. SPE J. 16(1), 191–199 (2011)

  35. Van Essen, G., Zandvliet, M., Van den Hof, P.M.J., Bosgra, O., Jansen, J.D.: Robust waterflooding optimization of multiple geological scenarios. SPE J. 14(1), 202–210 (2009)

  36. Völcker, C.J., Jørgensen, B., Thomsen, P.G., Stenby, E.H.: Simulation of subsurface two-phase flow in an oil reservoir. In: European Control Conference 2009, pp. 1221–1226 (2009)

  37. Völcker, C., Jørgensen, J.B., Stenby, E.H.: Oil reservoir production optimization using optimal control. In: 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), pp. 7937–7943. IEEE (2011)

  38. Waltz, F.: An engineering approach: hierarchical optimization criteria. IEEE Trans. Autom. Control 12, 179–180 (1967)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics and Computer Science & Center for Energy Resources Engineering, Technical University of Denmark (DTU), DK-2800, Kongens Lyngby, Denmark

    Lasse Hjuler Christiansen, Andrea Capolei & John Bagterp Jørgensen

Authors
  1. Lasse Hjuler Christiansen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrea Capolei
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. John Bagterp Jørgensen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to John Bagterp Jørgensen.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Christiansen, L.H., Capolei, A. & Jørgensen, J.B. A least squares approach for efficient and reliable short-term versus long-term optimization. Comput Geosci 21, 411–426 (2017). https://doi.org/10.1007/s10596-017-9620-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10596-017-9620-9

Keywords

Mathematics Subject Classifications (2010)

Search

Navigation