Model order reduction of a reservoir simulation by SOD-DEIM

Abstract

The large computational costs associated with reservoir simulations restrict using fine and realistic reservoir models for challenging applications such as history matching and well control optimization. This has led to the progress of reduced-order models in order to decrease computational requirements of subsurface flow simulations, especially, those that are based on proper orthogonal decomposition (POD). In this paper, an alternative method named smooth orthogonal decomposition (SOD) is used instead of POD and combined with the discrete empirical interpolation method (DEIM) for flow simulations in two-phase reservoirs. Two assessments included a two-dimensional case and a three-dimensional case are presented. These assessments comprised the accuracy and total simulation times for POD-DEIM and SOD-DEIM models show more precise results for SOD-DEIM compared with POD-DEIM in the regeneration of the full order models despite much lower simulation costs. In the end, the SOD-DEIM is tested for optimizing the well-control parameters of the three-dimensional case.