Tensor-based reduced order modeling in reservoir engineering: An application to production optimization∗

In this paper, a novel framework for reduced order modeling in reservoir engineering is introduced, where tensor decompositions and representations of flow profiles are used to characterize empirical features of flow simulations. The concept of classical Galerkin projection is extended to perform projections of flow equations onto empirical tensor subspaces, generating in this way, reduced order approximations of the original mass and momentum conservation equations. The methodology is applied to compute gradient-based optimal production strategies for water flooding using tensor-based reduced order adjoints.