Computational Geosciences

, Volume 18, Issue 3–4, pp 483–504 | Cite as

Waterflood management using two-stage optimization with streamline simulation

  • Tailai Wen
  • Marco R. Thiele
  • David Echeverría Ciaurri
  • Khalid Aziz
  • Yinyu Ye


Waterflooding is a common secondary oil recovery process. Performance of waterfloods in mature fields with a significant number of wells can be improved with minimal infrastructure investment by optimizing injection/production rates of individual wells. However, a major bottleneck in the optimization framework is the large number of reservoir flow simulations often required. In this work, we propose a new method based on streamline-derived information that significantly reduces these computational costs in addition to making use of the computational efficiency of streamline simulation itself. We seek to maximize the long-term net present value of a waterflood by determining optimal individual well rates, given an expected albeit uncertain oil price and a total fluid injection volume. We approach the optimization problem by decomposing it into two stages which can be implemented in a computationally efficient manner. We show that the two-stage streamline-based optimization approach can be an effective technique when applied to reservoirs with a large number of wells in need of an efficient waterflooding strategy over a 5 to 15-year period.


Reservoir management Waterflooding Optimization Streamline simulation Decline model 

JEL Classifications (2010)

49M37 65K10 90C26 90C90 


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  1. 1.
    Alhuthali, A., Oyerinde, D., Datta-Gupta, A.: Optimal waterflood management using rate control. SPE Reserv. Eval. Eng. 10(5), 539–551 (2007)CrossRefGoogle Scholar
  2. 2.
    Aronofsky, J.S., Masse, L., Natanson, S.G.: A model for the mechanism of oil recovery from the porous matrix due to water invasion in fractured reservoirs. Pet. Trans. AIME 213, 17–19 (1958)Google Scholar
  3. 3.
    Audet, C., Dennis, J.E.: Analysis of generalized pattern searches. SIAM J. Optim. 13(3), 889–903 (2002)CrossRefGoogle Scholar
  4. 4.
    Audet, C., Dennis, J.E.: Mesh adaptive direct search algorithms for constrained optimization. SIAM J. Optim. 17(1), 188–217 (2006)CrossRefGoogle Scholar
  5. 5.
    Aziz, K., Settari, A.: Petroleum reservoir simulation. Applied Science Publishers, vol. 476. London (1979)Google Scholar
  6. 6.
    Batycky, R., Seto, A.C., Fenwick, D.: Assisted history matching of a 1.4 million-cell simulation model for judy creek ‘a’ pool waterflood/hcmf using a streamline-based workflow. In: Proceedings of the SPE108701 2007 SPE ATCE, Anaheim, CA, 11–14 Nov (2007)Google Scholar
  7. 7.
    Batycky, R.P., Blunt, M.J., Thiele, M.R.: A 3D field-scale streamline-based reservoir simulator. SPE Reserv. Eng. 12(4), 246–254 (1997)CrossRefGoogle Scholar
  8. 8.
    Batycky, R.P., Thiele, M.R., Baker, R.O., Chugh, S.H.: Revisiting reservoir flood-surveillance methods using streamlines. SPE Reserv. Eval. Eng. 11(2), 387–394 (2006)CrossRefGoogle Scholar
  9. 9.
    Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 3(1), 1–122 (2011)CrossRefGoogle Scholar
  10. 10.
    Brouwer, D.R., Jansen, J.D.: Dynamic optimization of water flooding with smart wells using optimal control theory. SPE J. 9(4), 391–402 (2004)CrossRefGoogle Scholar
  11. 11.
    Caers, J., Krishnan, S., Wang, Y., Kovscek, A.: A geostatistical approach to streamline-based history matching. SPE J. 7(3), 250–266 (2002)CrossRefGoogle Scholar
  12. 12.
    Chen, Y., Oliver, D.S., Zhang, D.: Efficient ensemble-based closed-loop production optimization. SPE J. 14(4), 634–645 (2009)CrossRefGoogle Scholar
  13. 13.
    Conn, A.R., Gould, N., Toint, P.L.: Trust-region methods, vol. 1. Society for Industrial Mathematics (2000)Google Scholar
  14. 14.
    Conn, A.R., Scheinberg, K., Vicente, L.: Introduction to derivative-free optimization, vol. 8. Society for Industrial Mathematics (2009)Google Scholar
  15. 15.
    Datta-Gupta, A., King, M.J.: Streamline simulation: theory and practice. Textbook Series SPE, Richardson (2007)Google Scholar
  16. 16.
    Echeverría Ciaurri, D., Isebor, O.J., Durlofsky, L.J.: Application of derivative-free methodologies to generally constrained oil production optimisation problems. Int. J. Math. Model. Numer. Optim. 2(2), 134–161 (2011)Google Scholar
  17. 17.
    Echeverría Ciaurri, D., Mukerji, T., Durlofsky, L.J.: Derivative-free optimization for oil field operations. In: Computational Optimization and Applications in Engineering and Industry, pp. 19–55. Springer (2011)Google Scholar
  18. 18.
    van Essen, G.M., Van den Hof, P.M.J., Jansen, J.D.: Hierarchical long-term and short-term production optimization. SPE J. 16(1), 191–199 (2011)CrossRefGoogle Scholar
  19. 19.
    Fletcher, R., Leyffer, S.: Nonlinear programming without a penalty function. Math. Program. 91(2), 239–269 (2002)CrossRefGoogle Scholar
  20. 20.
    Goldberg, D.E.: Genetic algorithms in search, optimization, and machine learning. Addison-Wesley (1989)Google Scholar
  21. 21.
    Grant, M., Boyd, S.: CVX: MATLAB software for disciplined convex programming, version 1.21 (2011)Google Scholar
  22. 22.
    Hooke, R., Jeeves, T.A.: Direct search solution of numerical and statistical problems. J. ACM 8(2), 212–229 (1961)CrossRefGoogle Scholar
  23. 23.
    Kennedy, J., Eberhart, R.: Particle swarm optimization. In: IEEE International Conference on Neural Networks. Perth (1995)Google Scholar
  24. 24.
    Kolda, T., Lewis, R., Torczon, V.: Optimization by direct search: new perspectives on some classical and modern methods. SIAM Rev. 45, 385–482 (2003)CrossRefGoogle Scholar
  25. 25.
    Kramer, O., Echeverría Ciaurri, D., Koziel, S.: Derivative-free optimization. In: Computational optimization, methods and algorithms, pp. 61–83. Springer (2011)Google Scholar
  26. 26.
    Li, K., Horne, R.: An analytical model for production decline-curve analysis in naturally fractured reservoirs. SPE Reserv. Eval. Eng. 8(3), 197–204 (2005)CrossRefGoogle Scholar
  27. 27.
    Lolomari, T., Bratvedt, K., Crane, M., Milliken, W.J., Tyrie, J.J.: The use of streamline simulation in reservoir management: methodology and case studies. In: SPE Annual Technical Conference and Exhibition. Dallas (2000)Google Scholar
  28. 28.
    Luenberger, D., Ye, Y.: Linear and Nonlinear Programming, vol. 116. Springer, New York (2008)Google Scholar
  29. 29.
    Milliken, W., Emanuel, A., Chakravarty, A.: Applications of 3D streamline simulation to assist history matching. SPE Reserv. Eval. Eng. 4(6), 502–508 (2001)CrossRefGoogle Scholar
  30. 30.
    Muskat, M., Wyckoff, R.D.: The flow of homogeneous fluids through porous media. McGraw-Hill, New York (1937)Google Scholar
  31. 31.
    Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, New York (2006)Google Scholar
  32. 32.
    Sarma, P., Durlofsky, L.J., Aziz, K., Chen, W.H.: Efficient real-time reservoir management using adjoint-based optimalcontrol and model updating. Comput. Geosci. 10(1), 3–36 (2006)CrossRefGoogle Scholar
  33. 33.
    Storn, R., Price, K.: Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 11(4), 341–359 (1997)CrossRefGoogle Scholar
  34. 34.
    Streamsim Technologies: 3DSL User Manual v4.10. Streamsim Technologies (2012)Google Scholar
  35. 35.
    Thiele, M.R.: Streamline simulation. In: The 8th International Forum on Reservoir Simulation, Stresa. Lago Maggiore (2005)Google Scholar
  36. 36.
    Thiele, M.R., Batycky, R.P.: Using streamline-derived injection efficiencies for improved waterflood management. SPE Reserv. Eval. Eng. 9(2), 187–196 (2006)CrossRefGoogle Scholar
  37. 37.
    Thiele, M.R., Batycky, R.P., Fenwick, D.: Streamline simulation for modern reservoir-engineering workflows. J. Pet. Technol. 62(1), 64–70 (2010)CrossRefGoogle Scholar
  38. 38.
    Wang, Y., Kovscek, A.R.: Streamline approach for history matching production data. SPE J. 5(4), 353–362 (2000)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Tailai Wen
    • 1
  • Marco R. Thiele
    • 2
  • David Echeverría Ciaurri
    • 3
  • Khalid Aziz
    • 4
  • Yinyu Ye
    • 5
  1. 1.Institute for Computational and Mathematical EngineeringStanford UniversityStanfordUSA
  2. 2.Department of Energy Resources EngineeringStreamsim Technologies, Inc./Stanford UniversityStanfordUSA
  3. 3.IBM Thomas J. Watson Research CenterYorktown HeightsUSA
  4. 4.Department of Energy Resources EngineeringStanford UniversityStanfordUSA
  5. 5.Department of Management Science and EngineeringStanford UniversityStanfordUSA

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