Fast Multiscale Reservoir Simulations using POD-DEIM Model Reduction

Mohammadreza Ghasemi, Yanfang Yang, Eduardo Gildin, Yalchin R. Efendiev, Victor M. Calo

Research output: Chapter in Book/Report/Conference proceedingConference contribution

34 Scopus citations

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.
Original languageEnglish (US)
Title of host publicationSPE Reservoir Simulation Symposium
PublisherSociety of Petroleum Engineers (SPE)
DOIs
StatePublished - Feb 23 2015

Fingerprint Dive into the research topics of 'Fast Multiscale Reservoir Simulations using POD-DEIM Model Reduction'. Together they form a unique fingerprint.

Cite this