Generation of low-order reservoir models using Krylov-enhanced proper orthogonal decomposition method

Abstract

Reservoir simulation of realistic reservoir can be computationally demanding because of the large number of system unknowns. Model order reduction (MOR) technique represents a promising approach for accelerating the simulations. In this work, we focus on the application of a MOR technique called Krylov-enhanced proper orthogonal decomposition (KPOD), which combines the moment-matching property of Arnoldi with data generalization ability of proper orthogonal decomposition (POD) to alleviate POD’s dependence on the choice of snapshots and the particular input conditions. We apply KPOD and POD methods for a two-phase (oil–water) reservoir model which is solved by semi-implicit Euler discretization and consider two different scenarios to evaluate the predictive capability of POD and KPOD methods. The example demonstrates that even though the difference of inputs of testing and training process is larger, the results of KPOD are in close agreement with the full-order simulation, while the accuracy of POD becomes very poor. And because the number of base vector for KPOD is less, the KPOD is able to approximately reduce the simulation time by 3 times compared with the full-order reservoir model. The KPOD method outperforms POD method in computational efficiency and accuracy.

Keywords:

• Reservoir simulation
• model order reduction
• proper orthogonal decomposition
• Krylov-enhanced proper orthogonal decomposition
• semi-implicit Euler discretization