Accelerating oil reservoir simulations using POD on the fly

A reduced order model (ROM) is presented for the long-term calculation of subsurface oil/water flows. As in several previous ROMs in the field, the Newton iterations in the full model (FM) equations, which are implicit in time, are projected onto a set of modes obtained by applying proper orthogonal decomposition (POD) to a set of snapshots computed by the FM itself. The novelty of the present ROM is that the POD modes are (i) first calculated from snapshots computed by the FM in a short initial stage, and then (ii) updated on the fly along the simulation itself, using new sets of snapshots computed by the FM in even shorter additional runs. Thus, the POD modes adapt themselves to the local dynamics along the simulation, instead of being completely calculated at the outset, which requires a computationally expensive preprocess. This strategy is robust and computationally efficient, which is tested in 10- and 30-year simulations for a realistic reservoir model taken from the SAIGUP project.