Abstract
Optimizing objectives of long-term reservoir management typically requires a high number of 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. In this work, we employ a global approach to compute upscaled transmissibilities for a coarse model. 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, 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. For the optimization approach, we develop a control switching approach for efficient handling of output constraints. We consider moderately upscaled models, and conclude that for the case we consider, at least two orders of magnitude speed-up can be achieved whilst retaining sufficient accuracy.
Similar content being viewed by others
References
Aliyev, E., Durlofsky, L.J.: Multilevel Field-Development Optimization Using a Sequence of Upscaled Models. SPE Reservoir Simulation Symposium held in Houston, Texas, USA, 23–25 February 2015, SPE 173198-MS (2015)
Cardoso, M.A., Durlofsky, L.J., Sarma, P.: Development and application of reduced-order modeling procedures for subsurface flow simulation. Int. J. Numer. Methods Eng. 77(9), 1322–1350 (2009)
Chen, Y., Durlofsky, L., Gerritsen, M., Wen, X.: A coupled local-global upscaling approach for simulating flow in highly heterogeneous formations. Adv. Water Resour. 26(10), 1041–1060 (2003)
Chen, Y., Ollver, D.: Ensemble-based closed-loop optimization applied to brugge field. SPE Reserv. Eval. Eng. 13(1), 56–71 (2010)
Durlofsky, L.J.: 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 (2005)
Gries, S., Stüben, K., Brown, G.L., Chen, D., Collins, D.A.: Preconditioning for efficiently applying algebraic multigrid in fully implicit reservoir simulations. SPE J. 19(4), 726–736 (2014)
Hasan, A., Foss, B., Krogstad, S., Gunnerud, V., Teixeira, A.F.: Decision analysis for long-term and short-term production optimization applied to the voador field. SPE Reservoir Characterization and Simulation Conference and Exhibition, 16-18 September, Abu Dhabi, UAE, SPE 166027-MS (2013)
Holden, L., Nielsen, B.: Global upscaling of permeability in heterogeneous reservoirs; the output least squares (ols) method. Transp. Porous Media 40(2), 115–143 (2000)
Jansen, J.D.: Adjoint-based optimization of multi-phase flow through porous media—a review. Comput. Fluids 46(1, SI), 40–51 (2011)
Karimi-Fard, M., Durlofsky, L.: Accurate resolution of near-well effects in upscaled models using flow-based unstructured local grid refinement. SPE J. 17(4), 1084–1095 (2012)
Kourounis, D., Durlofsky, L., Jansen, J., Aziz, K.: Adjoint formulation and constraint handling for gradient-based optimization of compositional reservoir flow. Comput. Geosci. 18(2), 117–137 (2014)
Kraaijevanger, J.F.B.M., Egberts, P.J.P., Buurman, J.R.V.H.W.: Optimal waterflood design using the adjoint method. SPE Reservoir Simulation Symposium, 26-28 February, Houston, Texas, U.S.A, SPE-105764-MS (2007)
Krogstad, S., Lie, K.A., Møyner, O., Nilsen, H.M., Raynaud, X., Skaflestad, B.: MRST-AD - an open-source framework for rapid prototyping and evaluation of reservoir simulation problems. SPE Reservoir Simulation Symposium held in Houston, Texas, USA, 23–25 February 2015, SPE 173317-MS (2015)
Lie, K.A., Krogstad, S., Ligaarden, I.S., Natvig, J.R., Nilsen, H., Skaflestad, B.: Open-source MATLAB implementation of consistent discretisations on complex grids. Comput. Geosci. 16, 297–322 (2012)
Møyner, O., Krogstad, S., Lie, K.A.: The application of flow diagnostics for reservoir management. SPE J. (2014) accepted
MRST: The MATLAB Reservoir Simulation Toolbox, version 2014a. http://www.sintef.no/MRST/ (2014)
Neidinger, R.: Introduction to automatic differentiation and MATLAB object-oriented programming. SIAM Rev. 52(3), 545–563 (2010)
Peaceman, D.W.: Interpretation of well-block pressures in numerical reservoir simulation with nonsquare grid blocks and anisotropic permeability. Soc. Petrol. Eng. J. 23(3), 531–543 (1983). SPE 10528-PA
van Doren, J.F.M., Markovinovic, R., Jansen, J.D.: Reduced-order optimal control of water flooding using proper orthogonal decomposition. Comput. Geosci. 10(1), 137–158 (2006)
Younis, R.: Advances in Modern Computational Methods for Nonlinear Problems; A Generic Efficient Automatic Differentiation Framework, and Nonlinear Solvers That Converge All The Time. Ph.D. thesis, Stanford University, Palo Alto, California (2009)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Krogstad, S., Raynaud, X. & Nilsen, H.M. Reservoir management optimization using well-specific upscaling and control switching. Comput Geosci 20, 695–706 (2016). https://doi.org/10.1007/s10596-015-9497-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10596-015-9497-4