A generalized DEIM technique for model order reduction of porous media simulations in reservoir optimizations

High computational requirements limit the applications of subsurface flow simulation for practical problems, especially in the case of well-control optimization that requires lots of simulations. This has motivated the development of reduced-order models, particularly the methods based on Proper Orthogonal Decomposition (POD), to reduce the computational costs of the reservoir simulations. These methods construct several bases in order to transform the parameters of the simulation from a higher-dimensional space onto a lower-dimensional space. In this paper, a new method, GDEIM, based on the combination of POD, Galerkin projection and Discrete Empirical Interpolation Method (DEIM) with the generalized eigenvalue problem, is introduced and examined for a well-control optimization problem which leads to more accurate results in the reconstruction of the Full Order Model (FOM) compared with POD-DEIM despite much lower simulation costs.