A Galerkin‐free/equation‐free model reduction method for single‐phase flow in fractured porous media. Issue 6 (8th February 2020)

• Record Type: Journal Article
• Authors: Han, Dongxu; Li, Tingyu; Tang, Qingfeng; Yu, Bo; Sun, Dongliang
• Is Part Of: Energy science & engineering. Volume 8:Issue 6(2020)
• Page Start: 1997
• Page End: 2010
• Publication Date: 2020-02-08
• Subjects: fractured porous media -- Galerkin‐free -- POD -- reduced‐order model; Energy industries -- Periodicals; Energy development -- Periodicals; Power resources -- Periodicals; 621.042
• DOI: 10.1002/ese3.643
• Languages: English
• ISSNs: 2050-0505

Abstract

Abstract: Using traditional high‐fidelity numerical simulation to simulate fluid flow in fractured porous media in a real field remains challenging. It involves a large number of degrees of freedom when matrix and fracture equations are solved. To address this challenge, we propose a Galerkin‐free framework to construct a reduced‐order model (ROM) based on the proper orthogonal decomposition (POD). Compared with the typical POD‐based modeling process commonly used in previous studies, the POD‐ROM can be built without performing the Galerkin projection of flow equations onto the low‐dimensional space spanned by the POD basis functions. The numerical integration method was incorporated to obtain the POD time coefficients based on the flow equations solved by the conventional finite volume method. Two complex fracture cases reflecting high‐contrast porous media in a two‐dimensional domain were designed to verify the accuracy and efficiency of the established Galerkin‐free POD‐ROM. Sensitivity analysis of parameters was conducted to examine the adaptability of the ROM. The results illustrate that, compared with the fine‐scale model, the ROM can significantly reduce the CPU time without compromising the quality of the numerical solutions. Abstract : We construct a reduced‐order model for flow in fractured porous media based on the POD and Galerkin‐free method. Compared with the fine‐scale model, the ROM can significantly reduce the CPU time without compromising the quality of the numerical solutions.