Development and application of reduced-order modeling procedures for subsurface flow simulation

• Published in: International journal for numerical methods in engineering Vol. 77; no. 9; pp. 1322 - 1350
• Main Authors: Cardoso, M. A., Durlofsky, L. J., Sarma, P.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 26.02.2009; Wiley
• Subjects: Applied sciences; Characteristics of producing layers. Reservoir geology. In situ fluids; Computational techniques; Crude oil, natural gas and petroleum products; Crude oil, natural gas, oil shales producing equipements and methods; Energy; Exact sciences and technology; Fluid dynamics; Fuels; Fundamental areas of phenomenology (including applications); General theory; Mathematical methods in physics; missing point estimation; Physics; production optimization; proper orthogonal decomposition; Prospecting and production of crude oil, natural gas, oil shales and tar sands; reduced-order model; reservoir simulation; Large dimension; Scale models; Underground storage; Water flow; Greenhouse gases; missing point estimation; Optimization; Grids; Reservoir engineering; reservoir simulation; reduced-order model; Scaling laws; Modelling; Reduced order systems; Karhunen-Loeve transforms; proper orthogonal decomposition; production optimization
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.2453

The optimization of subsurface flow processes is important for many applications, including oil field operations and the geological storage of carbon dioxide. These optimizations are very demanding computationally due to the large number of flow simulations that must be performed and the typically large dimension of the simulation models. In this work, reduced‐order modeling (ROM) techniques are applied to reduce the simulation time of complex large‐scale subsurface flow models. The procedures all entail proper orthogonal decomposition (POD), in which a high‐fidelity training simulation is run, solution snapshots are stored, and an eigen‐decomposition (SVD) is performed on the resulting data matrix. Additional recently developed ROM techniques are also implemented, including a snapshot clustering procedure and a missing point estimation technique to eliminate rows from the POD basis matrix. The implementation of the ROM procedures into a general‐purpose research simulator is described. Extensive flow simulations involving water injection into a geologically complex 3D oil reservoir model containing 60 000 grid blocks are presented. The various ROM techniques are assessed in terms of their ability to reproduce high‐fidelity simulation results for different well schedules and also in terms of the computational speedups they provide. The numerical solutions demonstrate that the ROM procedures can accurately reproduce the reference simulations and can provide speedups of up to an order of magnitude when compared with a high‐fidelity model simulated using an optimized solver. Copyright © 2008 John Wiley & Sons, Ltd.