A Galerkin‐free/equation‐free model reduction method for single‐phase flow in fractured porous media
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 fr...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-06-01
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| Series: | Energy Science & Engineering |
| Subjects: | |
| Online Access: | https://doi.org/10.1002/ese3.643 |
| _version_ | 1828463588698750976 |
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| author | Dongxu Han Tingyu Li Qingfeng Tang Bo Yu Dongliang Sun |
| author_facet | Dongxu Han Tingyu Li Qingfeng Tang Bo Yu Dongliang Sun |
| author_sort | Dongxu Han |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-11T02:56:51Z |
| format | Article |
| id | doaj.art-68727f51af8045e298cb124dfbd4d7b7 |
| institution | Directory Open Access Journal |
| issn | 2050-0505 |
| language | English |
| last_indexed | 2024-12-11T02:56:51Z |
| publishDate | 2020-06-01 |
| publisher | Wiley |
| record_format | Article |
| series | Energy Science & Engineering |
| spelling | doaj.art-68727f51af8045e298cb124dfbd4d7b72022-12-22T01:23:08ZengWileyEnergy Science & Engineering2050-05052020-06-01861997201010.1002/ese3.643A Galerkin‐free/equation‐free model reduction method for single‐phase flow in fractured porous mediaDongxu Han0Tingyu Li1Qingfeng Tang2Bo Yu3Dongliang Sun4School of Mechanical Engineering Beijing Key Laboratory of Pipeline Critical Technology and Equipment for Deepwater Oil & Gas Development Beijing Institute of Petrochemical Technology Beijing ChinaSchool of Chemical Engineering and Technology Xi'an Jiaotong University Xi'an ChinaSchool of Mechanical Engineering Beijing Key Laboratory of Pipeline Critical Technology and Equipment for Deepwater Oil & Gas Development Beijing Institute of Petrochemical Technology Beijing ChinaSchool of Mechanical Engineering Beijing Key Laboratory of Pipeline Critical Technology and Equipment for Deepwater Oil & Gas Development Beijing Institute of Petrochemical Technology Beijing ChinaSchool of Mechanical Engineering Beijing Key Laboratory of Pipeline Critical Technology and Equipment for Deepwater Oil & Gas Development Beijing Institute of Petrochemical Technology Beijing ChinaAbstract 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.https://doi.org/10.1002/ese3.643fractured porous mediaGalerkin‐freePODreduced‐order model |
| spellingShingle | Dongxu Han Tingyu Li Qingfeng Tang Bo Yu Dongliang Sun A Galerkin‐free/equation‐free model reduction method for single‐phase flow in fractured porous media Energy Science & Engineering fractured porous media Galerkin‐free POD reduced‐order model |
| title | A Galerkin‐free/equation‐free model reduction method for single‐phase flow in fractured porous media |
| title_full | A Galerkin‐free/equation‐free model reduction method for single‐phase flow in fractured porous media |
| title_fullStr | A Galerkin‐free/equation‐free model reduction method for single‐phase flow in fractured porous media |
| title_full_unstemmed | A Galerkin‐free/equation‐free model reduction method for single‐phase flow in fractured porous media |
| title_short | A Galerkin‐free/equation‐free model reduction method for single‐phase flow in fractured porous media |
| title_sort | galerkin free equation free model reduction method for single phase flow in fractured porous media |
| topic | fractured porous media Galerkin‐free POD reduced‐order model |
| url | https://doi.org/10.1002/ese3.643 |
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