Next Generation Multiscale Methods for Reservoir Simulation
Abstract
In this thesis, we discuss multiscale simulation techniques for flow and transport in porous media, discretized on unstructured grids. The model equations considered are taken from the field of reservoir simulation, where several orders of magnitude variation in parameters and complex fluid physics result in highly challenging simulation problems.
We consider several novel multiscale solvers and the subsequent extension to compressible multiphase black-oil and compositional flow. The examples include both conceptual models and full field-scale models with industrial complexity in properties, fluid physics, geology and grid types. The thesis also describes the application of numerical experiments termed flow diagnostics for optimization and ranking problems, with and without multiscale solvers.
In order to facilitate the research on linear and nonlinear solvers, an open source general purpose simulator framework based on object orientation is developed. This framework aims to enable researchers to rapidly extend or improve existing models and solvers, which is exemplified in this thesis by the development of a simulator for polymer flooding with non-Newtonian fluid physics.
Finally, we also consider transport solvers based on a novel parametrization of Newton updates for the three-phase saturation equations with nonconvex, non-monotone flux functions that can converge for much larger timesteps than the current state of the art solvers.
Has parts
Paper 1: Møyner, Olav; Lie, Knut Andreas. The Multiscale Finite-Volume Method on Stratigraphic Grids. SPE Journal 2014 ;Volum 19.(5) s. 816-831 - Is not included due to copyright available at http://dx.doi.org/10.2118/163649-PAPaper 2: Møyner, Olav; Krogstad, Stein; Lie, Knut-Andreas. The application of flow diagnostics for reservoir management. SPE Journal 2014 ;Volum 20.(2) s. 306-323 - Is not included due to copyright available at http://dx.doi.org/10.2118/171557-PA
Paper 3: Møyner, Olav; Lie, Knut Andreas. A multiscale two-point flux-approximation method. Journal of Computational Physics 2014 ;Volum 275. s. 273-293 http://dx.doi.org/10.1016/j.jcp.2014.07.003 The article in is reprinted with kind permission from Elsevier, sciencedirect.com
Paper 4: Møyner, Olav. Construction of Multiscale Preconditioners on Stratigraphic Grids. ECMOR XIV - 14th European conference on the mathematics of oil recovery - Is not included due to copyright available at http://dx.doi.org/10.3997/2214-4609.20141775
Paper 5: Møyner, Olav; Lie, Knut-Andreas. A multiscale restriction-smoothed basis method for high contrast porous media represented on unstructured grids. Journal of Computational Physics 2016 ;Volum 304. s. 46-71 http://dx.doi.org/10.1016/j.jcp.2015.10.010 The article in is reprinted with kind permission from Elsevier, sciencedirect.com
Paper 6: Lie, Knut-Andreas; Møyner, Olav; Krogstad, Stein. Application of Flow Diagnostics and Multiscale Methods for Reservoir Management. I: SPE Reservoir Simulation Symposium - Is not included due to copyright available at http://dx.doi.org/10.2118/173306-MS
Paper 7: Krogstad, Stein; Lie, Knut-Andreas; Møyner, Olav; Nilsen, Halvor Møll; Raynaud, Xavier; Skaflestad, Bård. MRST-AD: an open-source framework for rapid prototyping and evaluation of reservoir simulation problems. I: SPE Reservoir Simulation Symposium - Is not included due to copyright available at http://dx.doi.org/10.2118/173317-MS
Paper 8: Møyner, Olav; Lie, Knut-Andreas. A multiscale restriction-smoothed basis method for compressible black-oil models. SPE Journal 2016 ;Volum 21.(6) s. 2079-2096 - Is not included due to copyright available at http://dx.doi.org/10.2118/173265-PA
Paper 9: Hilden, Sindre Tonning; Møyner, Olav; Lie, Knut-Andreas; Bao, Kai. Multiscale simulation of polymer flooding with shear effects. Transport in Porous Media 2016 ;Volum 113.(1) s. 111-135 - Is not included due to copyright available at http://dx.doi.org/10.1007/s11242-016-0682-2
Paper 10: Shah, Swej; Møyner, Olav; Tene, Matei; Lie, Knut-Andreas; Hajibeygi, Hadi. The multiscale restriction smoothed basis method for fractured porous media (F-MsRSB). Journal of Computational Physics 2016 ;Volum 318. s. 36-57 http://dx.doi.org/10.1016/j.jcp.2016.05.001 The article in is reprinted with kind permission from Elsevier, sciencedirect.com
Paper 11: Bao, Kai; Lie, Knut-Andreas; Møyner, Olav; Liu, Ming. Fully Implicit Simulation of Polymer Flooding with MRST. I: ECMOR XV - Proceedings of 15th European Conference on the Mathematics of Oil Recovery - Is not included due to copyright available at http://dx.doi.org/10.3997/2214-4609.201601880
Paper 12: Lie, Knut-Andreas; Møyner, Olav; Natvig, Jostein Roald; Antonina, Kozlova; Bratvedt, Kyrre; Watanabe, S; Li, Z. Successful Application of Multiscale Methods in a Real Reservoir Simulator Environment. I: ECMOR XV - Proceedings of 15th European Conference on the Mathematics of Oil Recovery - Is not included due to copyright available at http://dx.doi/org/10.3997/2214-4609.201601893
Paper 13: Møyner, Olav. Nonlinear Solver for Three-phase Transport Problems Based on Approximate Trust Regions. I: ECMOR XV - Proceedings of 15th European Conference on the Mathematics of Oil Recovery - Is not included due to copyright available at http://dx.doi.org/10.3997/2214-4609.201601899
Paper 14: Møyner, Olav; Tchelepi,Hamdi. A Multiscale Restriction-Smoothed Basis Method for Compositional Models. proceedings of the SPE Reservoir Simulation Conference - Is not included due to copyright available at http://dx.doi.org/10.2118/182679-MS