Fast multiscale reservoir simulations with POD-DEIM model reduction
Online Publication Date2015-02-23
Print Publication Date2015
Permanent link to this recordhttp://hdl.handle.net/10754/593278
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AbstractWe present a global/local model reduction for fast multiscale reservoir simulations in highly heterogeneous porous media. Our approach identifies a low-dimensional structure in the solution space. We introduce an auxiliary variable (the velocity field) in our model reduction that achieves a high compression of the model. This compression is achieved because the velocity field is conservative for any low-order reduced model in our framework, whereas a typical global model reduction that is based on proper-orthogonaldecomposition (POD) Galerkin projection cannot guarantee local mass conservation. The lack of mass conservation can be observed in numerical simulations that use finite-volume-based approaches. The discrete empirical interpolation method (DEIM) approximates fine-grid nonlinear functions in Newton iterations. This approach delivers an online computational cost that is independent of the fine-grid dimension. POD snapshots are inexpensively computed with local model-reduction techniques that are based on the generalized multiscale finite-element method (GMsFEM) that provides (1) a hierarchical approximation of the snapshot vectors, (2) adaptive computations with coarse grids, and (3) inexpensive global POD operations in small dimensional spaces on a coarse grid. By balancing the errors of the global and local reduced-order models, our new methodology provides an error bound in simulations. Our numerical results, by use of a two-phase immiscible flow, show a substantial speedup, and we compare our results with the standard POD-DEIM in a finite-volume setup.
CitationYang, Y., Ghasemi, M., Gildin, E., Efendiev, Y., & Calo, V. (2016). Fast Multiscale Reservoir Simulations With POD-DEIM Model Reduction. SPE Journal, 21(06), 2141–2154. doi:10.2118/173271-pa
SponsorsEduardo Gildin and Yalchin Efendiev acknowledge the partial support of the US Department of Defence Army ARO Project under grant number W911NF-12-1-0206. This publication also was made possible by National Priorities Research Program grant 7-1482-1278 from the Qatar National Research Fund (a member of The Qatar Foundation). Yalchin Efendiev would like to thank the partial support from the US Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under award number DE-FG02-13ER26165.
PublisherSociety of Petroleum Engineers (SPE)
Conference/Event nameSPE Reservoir Simulation Symposium