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We apply dynamic mode decomposition (DMD) and proper orthogonal decomposition(POD) methods to flows in highly-heterogeneous porous media to extract thedominant coherent structures and derive reduced-order models via Galerkinprojection. Permeability fields with high contrast are considered toinvestigate the capability of these techniques to capture the main flowfeatures and forecast the flow evolution within a certain accuracy. A DMD-basedapproach shows a better predictive capability due to its ability to accuratelyextract the information relevant to long-time dynamics, in particular, theslowly-decaying eigenmodes corresponding to largest eigenvalues. Our studyenables a better understanding of the strengths and weaknesses of theapplicability of these techniques for flows in high-contrast porous media.Furthermore, we discuss the robustness of DMD- and POD-based reduced-ordermodels with respect to variations in initial conditions, permeability fields,and forcing terms.

Mode Decomposition Methods for Flows in High-Contrast Porous Media. Part I. Global Approach