Local forward-mode automatic differentiation for high performance parallel pilot-level reservoir simulation. Robust reservoir simulation requires accurate linearization and involve complex property evaluations and dynamics. Handcoded Jacobian derivative calculations require significant resources to maintain and change, when taking into account all needed features for industrially relevant simulations. Automatic differentiation (AD) is a technique which gives machine precision accuracy of derivatives while requiring minimal extra effort, essentially only requiring the implementation of the residual equations. This makes extending the model simpler and less error-prone.

The optimal use of AD techniques depend on the particular grid structures and discretizations used. Here we present how local forward-mode AD can be used with a discretization based on the Distributed Uniform Numerics Enviroment (DUNE) grid interface to achieve a high performance reservoir simulator.

This paper discusses how one can exploit the structure of the full reservoir equations to obtain a dense data representation with only local evaluations in the AD framework, thereby avoiding excessive treatment of sparse sets or matrices. We highlight aspects of the C++ implementation which contribute to giving clean code, parallel performance and efficient use of modern microprocessors. Finally, the OPM Flow simulator is used to demonstrate the approach on field case examples.


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  1. Chen, Z.
    [2000] Formulations and Numerical Methods of the Black Oil Model in Porous Media.SIAM Journal on Numerical Analysis, 38(2), 489514.
    [Google Scholar]
  2. CLOC
    [2018] CLOC web site. https://github.com/AlDanial/cloc.
  3. Equinor
    [2018] Norne benchmark case web site. http://www.ipt.ntnu.no/norne/wiki/doku.php?id=start.
  4. Forsythe, G. and Wasow, W.R.
    [1960] Finite-difference Methods for Partial Differential Equations.Wiley.
    [Google Scholar]
  5. Griewank, A. and Walther, A.
    [2008] Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, Second Edition.Society for Industrial and Applied Mathematics, Philadelphia, PA.
    [Google Scholar]
  6. Iri, M.
    [1991] History of Automatic Differentiation and Rounding Error Estimation. In: Griewank, A. and Corliss, G.F. (Eds.) Automatic Differentiation of Algorithms: Theory, Implementation, and Application, SIAM, Philadelphia, PA, 116.
    [Google Scholar]
  7. ISAPP
    [2018] The Olympus field development optimization study. http://www.isapp2.com/optimization-challenge.html.
  8. Krogstad, S., Lie, K.A., Myner, O., Nilsen, H.M., Raynaud, X. and Skaflestad, B.
    [2015] MRST-AD - an open-source framework for rapid prototyping and evaluation of reservoir simulation problems.SPE Reservoir Simulation Symposium. Paper 173317-MS presented at the 2015 Reservoir simulation Symposium, Houston, Texas, USA, 2325 February 2015.
    [Google Scholar]
  9. Li, X. and Zhang, D.
    [2014] A backward automatic differentiation framework for reservoir simulation.Computational Geosciences, 18(6), 10091022.
    [Google Scholar]
  10. Lie, K.A., Krogstad, S., Ligaarden, I.S., Natvig, J.R., Nilsen, H.M. and Skaflestad, B.
    [2011] Open-source MATLAB implementation of consistent discretisations on complex grids.Computational Geosciences, 16(2), 297322.
    [Google Scholar]
  11. OPM
    [2018] OPM GitHub page. https://github.com/OPM.
  12. Saad, Y.
    [1996] Iterative Methods for Sparse Linear Systems.PWS Publishing, first edn.
    [Google Scholar]
  13. Schlumberger
    [2016] Eclipse 100 Technical Description 2016.01.
    [Google Scholar]
  14. Todd, M., Longstaff, W. et al.
    [1972] The development, testing, and application of a numerical simulator for predicting miscible flood performance.Journal of Petroleum Technology, 24(07), 874882.
    [Google Scholar]
  15. Voskov, D.V. and Tchelepi, H.A.
    [2012] Comparison of nonlinear formulations for two-phase multi-component eos based simulation.J. Petrol. Sci. Engrg., 8283, 101111.
    [Google Scholar]
  16. Younis, R.M.
    [2011] Modern advances in software and solution algorithms for reservoir simulation.Stanford University.
    [Google Scholar]
  17. Zhou, Y., Tchelepi, H.A. and Mallison, B.T.
    [2011] Automatic differentiation framework for compositional simulation on unstructured grids with multi-point discretization schemes.SPE Reservoir Simulation Symposium 2011. SPE 141592-MS.
    [Google Scholar]

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