Abstract
Many authors have used higher-order spatial discretizations to reduce numerical diffusion, which can be particularly pronounced when simulating EOR processes involving active chemical substances that are transported by linear or weakly nonlinear waves. Most high-resolution methods reported in the literature are based on explicit temporal discretizations. This imposes severe time-step restrictions when applied to the type of grids seen in industry-standard simulation models of real assets, which usually have orders-of-magnitude variations in porosities and Darcy velocities that necessitate the use of implicit discretization. Herein, we propose a second-order WENO discretization suitable for complex grids with polyhedral cell geometries, unstructured topologies, large aspect ratios, and large variations in interface areas. The WENO scheme is developed as part of a standard, fully implicit formulation that solves for pressure and transported quantities simultaneously. We investigate the accuracy and utility of the WENO scheme for a series of test cases that involve corner-point and 2D/3D Voronoi grids and black-oil and compositional flow models.
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Acknowledgments
Lie was funded by the Research Council of Norway through grant no. 244361. Mykkeltvedt was funded by the Research Council of Norway and the industry partners of The National IOR Centre of Norway (ConocoPhillips Skandinavia AS, Aker BP ASA, Eni Norge AS, Total E&P Norge AS, Equinor ASA, Neptune Energy Norge AS, Lundin Norway AS, Halliburton AS, Schlumberger Norge AS, Wintershall Norge AS, and DEA Norge AS). Møyner was funded by VISTA, a basic research program funded by Statoil and conducted in close collaboration with The Norwegian Academy of Science and Letters.
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Lie, KA., Mykkeltvedt, T.S. & Møyner, O. A fully implicit WENO scheme on stratigraphic and unstructured polyhedral grids. Comput Geosci 24, 405–423 (2020). https://doi.org/10.1007/s10596-019-9829-x
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DOI: https://doi.org/10.1007/s10596-019-9829-x