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Gradient-based production optimization with simulation-based economic constraints

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Abstract

In reservoir management, production optimization is performed using gradient-based algorithms that commonly rely on an adjoint formulation to efficiently compute control gradients. Often, however, economic constraints are implicitly embedded within the optimization procedure through well performance limits enforced at each reservoir simulation time-step. These limits effectively restrict the operational capabilities of the wells, e.g., they stop or shut down production depending on a predetermined profitability threshold for the well. Various studies indicate that the accuracy of the gradient and, by consequence, the performance of the optimization algorithm suffer from this type of heuristic constraint enforcement. In this paper, an analytical framework is developed to study the effects of enforcing simulator-based economic constraints when performing gradient-based production optimization that relies on derivatives obtained through an adjoint formulation. The framework attributes the loss in control gradient sensitivity to non-differentiable unscheduled changes in the well model equations. The discontinuous nature of these changes leads to inconsistencies within the adjoint gradient formulation. These inconsistencies, in turn, reduce gradient quality and subsequently decrease algorithmic performance. Based on the developed framework, we devise an efficient simulator-based mode of constraint enforcement that yields gradients with fewer consistency errors. In this implementation, the well model equations that violate constraints are removed from the governing system right after the violation occurs and are not reinserted until the next well status update. The constraint enforcement modes are further coupled with a strategy that improves the selection of initial controls for subsequent iterations of the optimization procedure. After a given simulation, the resulting combination of open and shut-in periods generates a status update schedule, or shut-in history. The shut-in history of the current optimal solution is saved and used in subsequent optimization iterations to make the status update a part of the optimal solution. The novel simulation-based constraint implementation, with and without shut-in history, is applied to two production optimization cases where, for a large set of initial guesses, and different model realizations, it retains and improves the performance of the search procedure compared to when using common modes of economic constraint enforcement during production optimization.

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References

  1. Bellout, M.C., Echeverría Ciaurri, D., Durlofsky, L.J., Foss, B., Kleppe, J.: Joint optimization of oil well placement and controls. Comput. Geosci. 16(4), 1061–1079 (2012)

    Article  Google Scholar 

  2. Bukshtynov, V., Volkov, O., Durlofsky, L.J., Aziz, K.: Comprehensive framework for gradient-based optimization in closed-loop reservoir management. Comput. Geosci. 19(4), 877–897 (2015)

    Article  Google Scholar 

  3. Cao, Y., Li, S., Petzold, L., Serban, R.: Adjoint sensitivity analysis for differential-algebraic equations: the adjoint DAE system and its numerical solution. SIAM J. Sci. Comput. 24(3), 1076–1089 (2003)

    Article  Google Scholar 

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

    Article  Google Scholar 

  5. Forouzanfar, F., Rossa, E., Russo, R., Reynolds, A.: Life-cycle production optimization of an oil field with an adjoint-based gradient approach. J. Pet. Sci. Eng. 112, 351–358 (2013)

    Article  Google Scholar 

  6. Geoquest: eclipse technical description Schlumberger (2005)

  7. Gill, P., Murray, W., Saunders, M.: User’s Guide for SNOPT Version 7: Software for Large-Scale Nonlinear Programming Stanford University (2008)

  8. Gill, P.E., Murray, W., Saunders, M.: SNOPT: An SQP algorithm for large-scale constrained optimization. SIAM J. Optim. 12(4), 979–1006 (2002)

    Article  Google Scholar 

  9. Haldorsen, H.: Choosing between rocks, hard places and a lot more: the economic interface. Norwegian Petroleum Society Special Publications 6(C), 291–312 (1996)

    Article  Google Scholar 

  10. Jansen, J.: Adjoint-based optimization of multi-phase flow through porous media—a review. Comput. Fluids 46(1), 40–51 (2011)

    Article  Google Scholar 

  11. Jansen, J.D., Fonseca, R.M., Kahrobaei, S., Siraj, M.M., Van Essen, G.M., Van den Hof, P.M.J.: The egg model—a geological ensemble for reservoir simulation. Geoscience Data Journal 1(2)

  12. Kourounis, D., Durlofsky, L.J., Jansen, J., Aziz, K.: Adjoint formulation and constraint handling for gradient-based optimization of compositional reservoir flow. Comput. Geosci. 18(2), 117–137 (2014)

    Article  Google Scholar 

  13. Liu, X., Reynolds, A.C.: Gradient-based multi-objective optimization with applications to waterflooding optimization. Comput. Geosci. 20(3), 677–693 (2016)

    Article  Google Scholar 

  14. de Montleau, P., Cominelli, A., Neylon, K., Rowan, D., Pallister, I., Tesaker, O., Nygard, I.: Production optimization under constraints using adjoint gradients. 10th European Conference on the Mathematics of Oil Recovery (A41) (2006)

  15. Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, New York (2006)

    Google Scholar 

  16. Peters, E., Chen, Y., Leeuwenburgh, O., Oliver, D.: Extended Brugge benchmark case for history matching and water flooding optimization. Comput. Geosci. 50, 16–24 (2013)

    Article  Google Scholar 

  17. Priestley, H.: Introduction to integration. Oxford University Press, Oxford (1997)

    Google Scholar 

  18. Riesz, F.: Sur les opérations fonctionnelles linéaires. C. R. Acad. Sci. Paris 149, 974–977 (1909)

    Google Scholar 

  19. Sarma, P., Durlofsky, L.J., Aziz, K., Chen, W.H.: Efficient real-time reservoir management using adjoint-based optimal control and model updating. Comput. Geosci. 10(1), 3–36 (2006)

    Article  Google Scholar 

  20. Svanberg, K.: The method of moving asymptotes - a new method for structural optimization. Int. J. Numer. Methods Eng. 24(2), 359–373 (1987)

    Article  Google Scholar 

  21. Talvila, E.: Necessary and sufficient conditions for differentiating under the integral sign. Am. Math. Mon. 108(6), 544–848 (2001)

    Article  Google Scholar 

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

    Article  Google Scholar 

  23. Volkov, O., Voskov, D.: Effect of time stepping strategy on adjoint-based production optimization. Comput. Geosci. 20(3), 707–722 (2016)

    Article  Google Scholar 

  24. Younis, R.: Modern advances in software and solution algorithms for reservoir simulation. PhD Thesis, Stanford University (2011)

  25. Zhou, Y.: Parallel general-purpose reservoir simulation with coupled reservoir models and multi-segment wells. PhD Thesis, Stanford University (2012)

Download references

Acknowledgments

The authors are grateful to the industrial affiliates of the Stanford University Reservoir Simulation Research (SUPRI–B) and Smart Fields Consortia, and the Center for Integrated Operations in the Petroleum Industry, NTNU, for their financial support. We also thank Timur Garipov for useful discussions and suggestions on different aspects of this work.

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Correspondence to Oleg Volkov.

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Volkov, O., Bellout, M.C. Gradient-based production optimization with simulation-based economic constraints. Comput Geosci 21, 1385–1402 (2017). https://doi.org/10.1007/s10596-017-9634-3

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