Fast Multiscale Reservoir Simulations using POD-DEIM Model Reduction

Handle URI:
http://hdl.handle.net/10754/593278
Title:
Fast Multiscale Reservoir Simulations using POD-DEIM Model Reduction
Authors:
Ghasemi, Mohammadreza; Yang, Yanfang; Gildin, Eduardo; Efendiev, Yalchin R. ( 0000-0001-9626-303X ) ; Calo, Victor M. ( 0000-0002-1805-4045 )
Abstract:
In this paper, we present a global-local model reduction for fast multiscale reservoir simulations in highly heterogeneous porous media with applications to optimization and history matching. Our proposed approach identifies a low dimensional structure of the solution space. We introduce an auxiliary variable (the velocity field) in our model reduction that allows achieving a high degree of model reduction. The latter is due to the fact that the velocity field is conservative for any low-order reduced model in our framework. Because a typical global model reduction based on POD is a Galerkin finite element method, and thus it can not guarantee local mass conservation. This can be observed in numerical simulations that use finite volume based approaches. Discrete Empirical Interpolation Method (DEIM) is used to approximate the nonlinear functions of fine-grid functions in Newton iterations. This approach allows achieving the computational cost that is independent of the fine grid dimension. POD snapshots are inexpensively computed using local model reduction techniques based on Generalized Multiscale Finite Element Method (GMsFEM) which provides (1) a hierarchical approximation of snapshot vectors (2) adaptive computations by using coarse grids (3) inexpensive global POD operations in a small dimensional spaces on a coarse grid. By balancing the errors of the global and local reduced-order models, our new methodology can provide an error bound in simulations. Our numerical results, utilizing a two-phase immiscible flow, show a substantial speed-up and we compare our results to the standard POD-DEIM in finite volume setup.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Physical Sciences and Engineering (PSE) Division
Publisher:
Society of Petroleum Engineers (SPE)
Journal:
SPE Reservoir Simulation Symposium
Conference/Event name:
SPE Reservoir Simulation Symposium
Issue Date:
23-Feb-2015
DOI:
10.2118/173271-MS
Type:
Conference Paper
Additional Links:
http://www.onepetro.org/doi/10.2118/173271-MS
Appears in Collections:
Conference Papers; Physical Sciences and Engineering (PSE) Division; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorGhasemi, Mohammadrezaen
dc.contributor.authorYang, Yanfangen
dc.contributor.authorGildin, Eduardoen
dc.contributor.authorEfendiev, Yalchin R.en
dc.contributor.authorCalo, Victor M.en
dc.date.accessioned2016-01-11T13:30:34Zen
dc.date.available2016-01-11T13:30:34Zen
dc.date.issued2015-02-23en
dc.identifier.doi10.2118/173271-MSen
dc.identifier.urihttp://hdl.handle.net/10754/593278en
dc.description.abstractIn this paper, we present a global-local model reduction for fast multiscale reservoir simulations in highly heterogeneous porous media with applications to optimization and history matching. Our proposed approach identifies a low dimensional structure of the solution space. We introduce an auxiliary variable (the velocity field) in our model reduction that allows achieving a high degree of model reduction. The latter is due to the fact that the velocity field is conservative for any low-order reduced model in our framework. Because a typical global model reduction based on POD is a Galerkin finite element method, and thus it can not guarantee local mass conservation. This can be observed in numerical simulations that use finite volume based approaches. Discrete Empirical Interpolation Method (DEIM) is used to approximate the nonlinear functions of fine-grid functions in Newton iterations. This approach allows achieving the computational cost that is independent of the fine grid dimension. POD snapshots are inexpensively computed using local model reduction techniques based on Generalized Multiscale Finite Element Method (GMsFEM) which provides (1) a hierarchical approximation of snapshot vectors (2) adaptive computations by using coarse grids (3) inexpensive global POD operations in a small dimensional spaces on a coarse grid. By balancing the errors of the global and local reduced-order models, our new methodology can provide an error bound in simulations. Our numerical results, utilizing a two-phase immiscible flow, show a substantial speed-up and we compare our results to the standard POD-DEIM in finite volume setup.en
dc.publisherSociety of Petroleum Engineers (SPE)en
dc.relation.urlhttp://www.onepetro.org/doi/10.2118/173271-MSen
dc.titleFast Multiscale Reservoir Simulations using POD-DEIM Model Reductionen
dc.typeConference Paperen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.identifier.journalSPE Reservoir Simulation Symposiumen
dc.conference.date23-25 Februaryen
dc.conference.nameSPE Reservoir Simulation Symposiumen
dc.conference.locationHouston, Texas, USAen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionTexas A & M Universityen
kaust.authorGhasemi, Mohammadrezaen
kaust.authorYang, Yanfangen
kaust.authorGildin, Eduardoen
kaust.authorEfendiev, Yalchin R.en
kaust.authorCalo, Victor M.en
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