1887

Abstract

Summary

Optimizing the objectives of long-term reservoir management typically requires a high number of forward reservoir simulations. Two important remedies to reduce the runtime (and make the optimization problem manageable) are model reduction/upscaling and efficient computation of gradients. Adjoint methods are generally considered to be the most efficient means for obtaining gradients.

Furthermore, there has been much interest in reduced-order modelling (e.g., based on POD) for reservoir management optimization. Very promising results have been reported for models with somewhat limited complexity. Application to industry-standard cases is inhibited in part by the invasive nature of the approach with respect to simulator code, and the fact that the number of required basis functions is correlated with the degree of nonlinear dynamics.

In this work, we utilize ideas from POD to compute upscaled transmissibilities for a coarse model, rather than using the method directly to build a basis for the fine-scale state space. The proposed coarsening strategy takes as input any number of fine-scale states (pressure fields from e.g., a previous simulation), and produces a coarse-scale model calibrated to the specific flow scenario(s) dictated by the input. We argue that compared to traditional general-purpose upscaling approaches, much more aggressive coarsening can be applied in this type of scenario-specific upscaling. Utilizing a fully-implicit, three-phase, black-oil simulator with adjoint capabilities, we investigate the performance of our methodology by optimizing the net-present-value (NPV) for a real-field model. We consider multiple coarsening strategies and coarsening factors, and conclude that for the model considered, at least two orders of magnitude speed-up can be achieved whilst retaining sufficient accuracy.

Loading

Article metrics loading...

/content/papers/10.3997/2214-4609.20141864
2014-09-08
2024-04-26
Loading full text...

Full text loading...

References

  1. Cardoso, M.A., Durlofsky, L.J. and Sarma, P.
    [2008] Development and application of reduced-order modeling procedures for subsurface flow simulation. Int. J. Numer. Meth. Eng., to appear.
    [Google Scholar]
  2. Chen, Y., Durlofsky, L., Gerritsen, M. and Wen, X.
    [2003] A coupled local-global upscaling approach for simulating flow in highly heterogeneous formations. Advances in Water Resources, 26(10), 1041–1060, cited By (since 1996)170.
    [Google Scholar]
  3. Durlofsky, L.J.
    [2005] Upscaling and gridding of fine scale geological models for flow simulation. Presented at 8th International Forum on Reservoir Simulation Iles Borromees, Stresa, Italy, June 20–24, 2005.
    [Google Scholar]
  4. Gries, S., StÃijben, K., Brown, G., Chen, D. and Collins, D.
    [2013] Preconditioning for efficiently applying algebraic multigrid in fully implicit reservoir simulations. vol. 1,471–482, cited By (since 1996)0.
    [Google Scholar]
  5. Hasan, A., Gunnerud, V., Foss, B., Teixeira, A.F. and Krogstad, S.
    [2013] Decision analysis for long-term and short-term production optimization applied to the voador field. SPE Reservoir Characterization and Simulation Conference and Exhibition, SPE-166027-MS, doi:10.2118/166027‑MS.
    https://doi.org/10.2118/166027-MS [Google Scholar]
  6. Holden, L. and Nielsen, B.
    [2000] Global upscaling of permeability in heterogeneous reservoirs; the output least squares (ols) method. Transport in Porous Media, 40(2), 115–143, cited By (since 1996)66.
    [Google Scholar]
  7. Jansen, J.D.
    [2011] Adjoint-based optimization of multi-phase flow through porous media-areview. Computers & Fluids, 46(1, SI), 40–51, ISSN 0045-7930, doi:{10.1016/j.compfluid.2010.09.039}.
    https://doi.org/10.1016/j.compfluid.2010.09.039 [Google Scholar]
  8. Karimi-Fard, M. and Durlofsky, L.
    [2012] Accurate resolution of near-well effects in upscaled models using flow-based unstructured local grid refinement. SPE Journal, 17(4), 1084–1095, cited By (since 1996)1.
    [Google Scholar]
  9. Kourounis, D., Durlofsky, L., Jansen, J. and Aziz, K.
    [2014] Adjoint formulation and constraint handling for gradient-based optimization of compositional reservoir flow. Computational Geosciences, 18(2), 117–137, cited By (since 1996)0.
    [Google Scholar]
  10. Kraaijevanger, J.F.B.M., Egberts, P.J.P. and Buurman, J.R.V.H.W.
    [2007] Optimal waterflood design using the adjoint method. SPE Reservoir Simulation Symposium, 26-28 February, Houston, Texas, U.S.A, SPE-105764-MS, doi:10.2118/105764‑MS.
    https://doi.org/10.2118/105764-MS [Google Scholar]
  11. Lie, K.A., Krogstad, S., Ligaarden, I.S., Natvig, J.R., Nilsen, H. and Skaflestad, B.
    [2012] Open-source MATLAB implementation of consistent discretisations on complex grids. Comput. Geosci., 16, 297–322, doi:10.1007/s10596‑011‑9244‑4.
    https://doi.org/10.1007/s10596-011-9244-4 [Google Scholar]
  12. Møyner, O., Krogstad, S. and Lie, K.A.
    [2014] The application of flow diagnostics for reservoir management. SPE J., accepted.
    [Google Scholar]
  13. MRST
    [2014] The MATLAB Reservoir Simulation Toolbox, version 2014a. http://www.sintef.no/MRST/.
  14. Neidinger, R.
    [2010] Introduction to automatic differentiation and MATLAB object-oriented programming. SIAM Review, 52(3), 545–563, doi:10.1137/080743627.
    https://doi.org/10.1137/080743627 [Google Scholar]
  15. Peaceman, D.W.
    [1983] Interpretation of well-block pressures in numerical reservoir simulation with nonsquare grid blocks and anisotropic permeability. Soc. Petrol. Eng. J., 23(3), 531–543, doi:10.2118/10528‑PA, sPE 10528-PA.
    https://doi.org/10.2118/10528-PA [Google Scholar]
  16. van Doren, J.F.M., Markovinovic, R. and Jansen, J.D.
    [2006] Reduced-order optimal control of water flooding using proper orthogonal decomposition. Comput. Geosci., 10(1), 137–158, ISSN 1420-0597, doi:10.1007/s10596‑005‑9014‑2, workshop on Closed-Loop Reservoir Management, Delft, NETHERLANDS, JUN 28–30, 2004.
    https://doi.org/10.1007/s10596-005-9014-2 [Google Scholar]
http://instance.metastore.ingenta.com/content/papers/10.3997/2214-4609.20141864
Loading
/content/papers/10.3997/2214-4609.20141864
Loading

Data & Media loading...

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error