Adaptive POD-Galerkin Technique for Reservoir Simulation and Optimization

This paper introduces a novel method using an adaptive functional basis for reduced order models based on proper orthogonal decomposition (POD). The method is intended to be applied, in particular, to hydrocarbon reservoir simulations, where a range of varying boundary conditions must be explored. The proposed method allows updating the POD functional basis constructed for a specific problem setting to match varying boundary conditions, such as modified well locations and geometry, without the necessity to recalculate each time the entire set of basis functions. This adaptive technique leads to a significant reduction in the number of snapshots required to calculate the new basis, and hence reduces the computational cost of the simulations. The proposed method was applied to a two-dimensional immiscible displacement model; the simulations were performed using a high-resolution model, a classical POD reduced model, and a reduced model whose POD basis was adapted to varying well locations and geometry. Numerical simulations show that the proposed approach leads to a reduction of the required number of model snapshots by a few orders of magnitude compared to the classical POD scheme, without noticeable loss of accuracy of calculated fluid production rates. The adaptive POD scheme can therefore provide a significant gain in computational efficiency for problems where multiple or iterative simulations with varying boundary conditions are required, such as optimization of well design or production optimization.