Implementation and detailed assessment of a GNAT reduced-order model for subsurface flow simulation

Highlights: • Reduced-order model (ROM) for subsurface flow based on GNAT is presented. • ROM performance is assessed for a wide range of GNAT parameters. • Model accuracy is summarized using a dimensional stacking visualization. • ROM accuracy is shown to depend on nonlinearity in relative permeability functions. • GNAT is more accurate than POD-TPWL when perturbation from training run is large. -- Abstract: The large computational requirements associated with subsurface flow simulation limit the use of realistic models for demanding applications such as optimization and uncertainty quantification. This has motivated the development of reduced-order models, in particular those based on proper orthogonal decomposition (POD). In this study, we implement a POD-based Gauss–Newton with approximated tensors (GNAT) method for oil–water reservoir simulation. Our formulation, which is described in detail, incorporates promising features from previous implementations involving GNAT and discrete empirical interpolation method (DEIM) procedures. A theoretical analysis of the computational cost of GNAT for our problem, and the speedup it may provide relative to the full-order simulation, suggests a complex dependency of speedup on GNAT parameters and solver implementation. Systematic assessments, involving several comprehensive numerical experiments, are then presented. These include a detailed evaluation of GNAT performance on a 2D model, in which 576 different GNAT parameter combinations are considered, which allows us to elucidate the impact of parameter values on error. Detailed comparisons with an existing reduced-order modeling procedure based on trajectory piecewise linearization, POD-TPWL, are also presented. Around 1500 test cases, with varying levels of perturbation relative to training cases, are considered. We show that GNAT is only slightly more accurate than POD-TPWL for cases with small perturbation, but its accuracy advantage increases for larger perturbations. We also demonstrate the successful application of GNAT to a more realistic 3D model.