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dc.contributor.authorYang, Yanfang
dc.contributor.authorGhasemi, Mohammadreza
dc.contributor.authorGildin, Eduardo
dc.contributor.authorEfendiev, Yalchin R.
dc.contributor.authorCalo, Victor
dc.date.accessioned2016-01-11T13:30:34Z
dc.date.available2016-01-11T13:30:34Z
dc.date.issued2016-12-14
dc.identifier.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
dc.identifier.issn1086-055X
dc.identifier.doi10.2118/173271-PA
dc.identifier.urihttp://hdl.handle.net/10754/593278
dc.description.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.
dc.description.sponsorshipEduardo 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.
dc.publisherSociety of Petroleum Engineers (SPE)
dc.relation.urlhttp://www.onepetro.org/doi/10.2118/173271-PA
dc.rightsArchived with thanks to Society of Petroleum Engineers (SPE)
dc.titleFast multiscale reservoir simulations with POD-DEIM model reduction
dc.typeConference Paper
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalSPE Reservoir Simulation Symposium
dc.conference.date23 March 2015 to 25 March 2015
dc.conference.nameSPE Reservoir Simulation Symposium
dc.conference.locationHouston, texas
dc.identifier.wosutWOS:000393304200017
dc.eprint.versionPre-print
dc.contributor.institutionTexas A and M University, Department of Mathematics at Texas, United States
dc.contributor.institutionCurtin University, CSRIO, Australia
dc.identifier.volume21
dc.identifier.issue6
dc.identifier.pages2141-2154
kaust.personEfendiev, Yalchin R.
dc.identifier.eid2-s2.0-85007164419
refterms.dateFOA2018-06-13T13:32:42Z
dc.date.published-online2015-02-23
dc.date.published-print2015


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