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Abstract

Summary

This work investigates the application in a Multifidelity Sequential Approximate Optmization (MSAO) framework of a proxy model that uses Trajectory Piecewise Linearization (TPWL) as a numerical complexity reduction technique and Proper Orthogonal Decomposition (POD) as the dimensional reduction technique. TPWL linearizes the reservoir simulation problem around previously converged states stored from a set of training simulations. Therefore, it is a semi-intrusive technique since it only needs simulation state maps and their derivatives to be exported. In this work TPWL stability is assured through the use of Petrov-Galerkin projection on the POD process.

The reservoir simulator used in this work is based on a fully implicit formulation in terms of mass fractions instead of saturations. The mass fraction formulation does not appear to affect the accuracy of TPWL when compared to the literature. Speedups in the order of five hundred and very good accuracy were obtained.

This work tests a new strategy for the number of required initial simulations. Instead of several simulations, it was used only one and considered the possibility of retraining if necessary. The need for retraining, the retraining process itself and how to assimilate new information into the TPWL model are studied in detail.

The problem in study is to determine optimum sequence of well controls to be used during the concession period in order to maximize NPV. The optimization algorithm proposed is based on a trust region framework. It uses TPWL with Kriging correction as a proxy model and decides when it must be retrained. A small number of simulations inside the trust region must be performed in order to build a Kriging correction model. Different schemes to perform these simulations were evaluated in order to increase the efficiency of the method. Different interpolation polynomials to be used in the Kriging correction also considered. The methodology was applied to synthetic reservoir models with good results.

© EAGE Publications BV
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/content/papers/10.3997/2214-4609.20141833
2014-09-08
2024-04-25

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References

  1. Afonso, S.M.B., Horowitz, B. and da Silva, M.F.
    [2011] Performance of a physical surrogate in the sequential approximate optimization of space trusses. International Journal for Computer-Aided Engineering and Software.
     [Google Scholar]
  2. Biggs, M.C.
    [1979] Constrained minimization using recursive quadratic programming. Towards Global Optimization (L.C.W.Dixon and G.P.Szergo, eds.).
     [Google Scholar]
  3. Cardoso, M.A.
    [2009] Development and application of reduced-order modeling procedures for reservoir simulation. Ph.D. thesis, Stanford University.
     [Google Scholar]
  4. Carlberg, K., Bou-Mosleh, C. and Farhat, C.
    [2009] Effcient nonlinear model reduction via a least-squares petrov-galerkin projection and compressive tensor approximations. International Journal for Numerical Methods in Engineering.
     [Google Scholar]
  5. Christie, M.A. and Blunt, M.J.
    [2001] Tenth spe comparative solution project: A comparison of upscaling techniques. SPE Reservoir Evaluation and Engineering.
     [Google Scholar]
  6. Ertekin, T., Abou-Kassem, J.H. and King, G.R.
    [2011] Basic Applied Reservoir Simulation. Society of Petroleum Engineering - SPE.
     [Google Scholar]
  7. Gildin, E., Ghasemi, M., Protasov, A. and Efendiev, Y.
    [2013] Nonlinear complexity reduction for fast simulation of flow in heterogeneous porous media. SPE Reservoir Simulation Symposium.
     [Google Scholar]
  8. Giunta, A.A.
    [2002] Use of data sampling, surrogate models, and numerical optimization in engineering design. 40th AIAA Aerospace Sciences Meeting and Exhibit, AIAA 2002–0538.
     [Google Scholar]
  9. Giunta, A.A. and Eldred, M.S.
    [2000] Implementation of a trust region model management strategy in the dakota optimization toolkit. 8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization.
     [Google Scholar]
  10. He, J.
    [2010] Enhanced linearized reduced-order models for subsurface flow simulation. Master’s thesis, Stanford University.
     [Google Scholar]
  11. Horowitz, B., Afonso, S.M.B. and de Mendonça, C.V.P.
    [2013] Surrogate based optimal water flooding management. Journal of Petroleum Science and Engineering.
     [Google Scholar]
  12. Jolliffe, I.T.
    [2002] Principal Component Analysis. Springer-Verlag, New York, 2nd edn.
     [Google Scholar]
  13. Krige, D.G.
    [1951] A statistical approach to some mine valuations and allied problems at the Witwatersrand. Master’s thesis, University of Witwatersrand.
     [Google Scholar]
  14. Maliska, C.R., da Silva, A.F.C., Czesnat, A.O., Lucianetti, R.M. and Junior., C.R.M.
    [1997] Three-dimensional multiphase flow simulation in petroleum reservoirs using the mass fractions as dependent variables. Fifth Latin American and Caribean Petroleum Engineering Conference and Exhibition, SPE39067, Society of Petroleum Engineering - SPE.
     [Google Scholar]
  15. Matheron, G.
    [1963] Principles of geostatistics. Economic Geology.
     [Google Scholar]
  16. Rewienski, M.J.
    [2003] A trajectory piecewise-linear approach to model order reduction of nonlinear dynamical systems. Ph.D. thesis, MIT.
     [Google Scholar]
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A Reduced Order Surrogate Model for Optimal Reservoir Management
Conference Proceedings 2014, 1 (2014); https://doi.org/10.3997/2214-4609.20141833
/content/papers/10.3997/2214-4609.20141833
/content/papers/10.3997/2214-4609.20141833
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