Abstract
We discuss a nonlinear domain-decomposition preconditioning method for fully implicit simulations of multicomponent porous media flow based on the additive Schwarz preconditioned exact Newton method (ASPEN). The method efficiently accelerates nonlinear convergence by resolving unbalanced nonlinearities in a local stage and long-range interactions in a global stage. ASPEN can improve robustness and significantly reduce the number of global iterations compared with standard Newton, but extra work introduced in the local steps makes each global iteration more expensive. We discuss implementation aspects for the local and global stages. We show how the global-stage Jacobian can be transformed to the same form as the fully implicit system, so that one can use standard linear preconditioners and solvers. We compare the computational performance of ASPEN to standard Newton on a series of test cases, ranging from conceptual cases with simplified geometry or flow physics to cases representative of real assets. Our overall conclusion is that ASPEN is outperformed by Newton when this method works well and converges in a few iterations. On the other hand, ASPEN avoids time-step cuts and has significantly lower runtimes in time steps where Newton struggles. A good approach to computational speedup is therefore to adaptively switch between Newton and ASPEN throughout a simulation. A few examples of switching strategies are outlined.
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Cai, X.-C., Keyes, D.E.: Nonlinearly preconditioned inexact Newton algorithms. SIAM J. Sci. Comput. 24(1), 183–200 (2002). https://doi.org/10.1137/S106482750037620X
Liu, L., Keyes, D.E.: Field-split preconditioned inexact Newton algorithms. SIAM J. Sci. Comput. 37(3), 1388–1409 (2015). https://doi.org/10.1137/140970379
Skogestad, J.O., Keilegavlen, E., Nordbotten, J.M.: Domain decomposition strategies for nonlinear flow problems in porous media. J. Comput. Phys. 234, 439–451 (2013). https://doi.org/10.1016/j.jcp.2012.10.001
Liu, L., Keyes, D.E., Sun, S.: Fully implicit two-phase reservoir simulation with the additive Schwarz preconditioned inexact Newton method. In: SPE Reservoir Characterization and Simulation Conference and Exhibition, 16-18 September, Abu Dhabi, UAE (2013)https://doi.org/10.2118/166062-MS
Luo, L., Cai, X.-C., Keyes, D.E.: Nonlinear preconditioning strategies for two-phase flows in porous media discretized by a fully implicit discontinuous Galerkin method. SIAM J. Sci. Comput. , 317–344 (2021). https://doi.org/10.1137/20M1344652
Dolean, V., Gander, M.J., Kheriji, W., Kwok, F., Masson, R.: Nonlinear preconditioning: How to use a nonlinear Schwarz method to precondition Newton’s method. SIAM J. Sci. Comput. 38(6), 3357–3380 (2016). https://doi.org/10.1137/15M102887X
Li, J., Wong, Z.Y., Tomin, P., Tchelepi, H.: Sequential implicit Newton method for coupled multi-segment wells. In: SPE Reservoir Simulation Conference, Galveston, Texas, USA, April 2019 (2019). https://doi.org/10.2118/193833-MS
Li, J., Tomin, P., Tchelepi, H.: Sequential fully implicit Newton method for compositional flow and transport. J. Comput. Phys. 444, 110541 (2021). https://doi.org/10.1016/j.jcp.2021.110541
Jiang, J., Tchelepi, H.A.: Nonlinear acceleration of sequential fully implicit (SFI) method for coupled flow and transport in porous media. Comput. Methods App. Mech. Eng. 352, 246–275 (2019). https://doi.org/10.1016/j.cma.2019.04.030
Zhou, Y., Jiang, J., Tomin, P.: Inexact methods for black-oil sequential fully implicit SFI scheme. In: SPE Reservoir Simulation Conference, On-Demand, October 2021 (2021). https://doi.org/10.2118/203900-MS
Jiang, J., Tomin, P., Zhou, Y.: Inexact methods for sequential fully implicit (SFI) reservoir simulation. Comput. Geosci. 25(5), 1709–1730 (2021). https://doi.org/10.1007/s10596-021-10072-z
Klemetsdal, Ø., Moncorgé, A., Møyner, O., Lie, K.-A.: A numerical study of the additive Schwarz preconditioned exact Newton method (ASPEN) as a nonlinear preconditioner for immiscible and compositional porous media flow. Comput. Geosci. 26, 1045–1063 (2022). https://doi.org/10.1007/s10596-021-10090-x
Klemetsdal, Ø.S., Moncorgé, A., Nilsen, H.M., Møyner, O., Lie, K.-.A.: An adaptive sequential fully implicit domain-decomposition solver. SPE J. 27(01), 566–578 (2021). https://doi.org/10.2118/203991-PA
Lie, K.-A.: An Introduction to Reservoir Simulation Using MATLAB/GNU Octave: User Guide for the MATLAB Reservoir Simulation Toolbox (MRST). Cambridge University Press (2019). https://doi.org/10.1017/9781108591416
Luo, L., Cai, X.-C., Yan, Z., Xu, L., Keyes, D.E.: A multilayer nonlinear elimination preconditioned inexact Newton method for steady-state incompressible flow problems in three dimensions. SIAM Journal of Scientific Computing 42(6), 1404–1428 (2020). https://doi.org/10.1137/19M1307184
Lie, K.-A., Møyner, O. (eds.): Advanced Modeling with the MATLAB Reservoir Simulation Toolbox. Cambridge University Press, (2021). https://doi.org/10.1017/9781009019781
Rasmussen, A.F., Sandve, T.H., Bao, K., Lauser, A., Hove, J., Skaflestad, B., Klöfkorn, R., Blatt, M., Rustad, A.B., Sævareid, O., Lie, K.-A., Thune, A.: The Open Porous Media Flow reservoir simulator. Comput. Math. Appl. 81, 159–185 (2021). https://doi.org/10.1016/j.camwa.2020.05.014
Younis, R.M.: Modern advances in software and solution algorithms for reservoir simulation. PhD thesis, Stanford University (2011)
Zhou, Y.: Parallel general-purpose reservoir simulation with coupled reservoir models and multisegment wells. PhD thesis, Stanford University (2012)
Wallis, J.R., Kendall, R.P., Little, T.E.: Constrained residual acceleration of conjugate residual methods. In: SPE Reservoir Simulation Symposium, Dallas, Texas, February 1985 (1985). https://doi.org/10.2118/13536-MS
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(04), 726–736 (2014). https://doi.org/10.2118/163608-PA
Fonseca, R.M., Rossa, E.D., Emerick, A.A., Hanea, R.G., Jansen, J.D.: Introduction to the special issue: Overview of OLYMPUS optimization benchmark challenge. Comput. Geosci. 24(6), 1933–1941 (2020). https://doi.org/10.1007/s10596-020-10003-4
Acknowledgements
The authors thank TotalEnergies EP Norge AS for funding and TotalEnergies for the permission to publish this research. The Sleipner model is published by Equinor ASA on behalf of the Sleipner Group. The specific version used herein is based on the dataset available from the Open Porous Media initiative.
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The research leading to the results reported in this manuscript received partial funding from TotalEnergies EP Norge AS. Arthur Moncorgé is employed by TotalEnergies SE. Apart from this, the authors have no financial or competing interests to declare that are relevant to the content of this article.
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Møyner, O., Rasmussen, A.F., Klemetsdal, Ø. et al. Nonlinear domain-decomposition preconditioning for robust and efficient field-scale simulation of subsurface flow. Comput Geosci 28, 241–251 (2024). https://doi.org/10.1007/s10596-023-10215-4
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DOI: https://doi.org/10.1007/s10596-023-10215-4