Numerical simulation of wormhole propagation with the mixed hybridized discontinuous Galerkin finite element method
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910888215183360 |
|---|---|
| author | Zhang, Jiansong Zhu, Jiang Wang, Yiming Liu, Yanyu Guo, Hui |
| author_facet | Zhang, Jiansong Zhu, Jiang Wang, Yiming Liu, Yanyu Guo, Hui |
| contents | The acid treatment of carbonate reservoirs is a widely employed technique for enhancing the productivity of oil and gas reservoirs. In this paper, we present a novel combined hybridized mixed discontinuous Galerkin (HMDG) finite element method to simulate the dissolution process near the wellbore, commonly referred to as the wormhole phenomenon. The primary contribution of this work lies in the application of hybridization techniques to both the pressure and concentration equations. Additionally, an upwind scheme is utilized to address convection-dominant scenarios, and a ``cut-off" operator is introduced to maintain the boundedness of porosity. Compared to traditional discontinuous Galerkin methods, the proposed approach results in a global system with fewer unknowns and sparser stencils, thereby significantly reducing computational costs. We analyze the existence and uniqueness of the new combined method and derive optimal error estimates using the developed technique. Numerical examples are provided to validate the theoretical analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_16792 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Numerical simulation of wormhole propagation with the mixed hybridized discontinuous Galerkin finite element method Zhang, Jiansong Zhu, Jiang Wang, Yiming Liu, Yanyu Guo, Hui Numerical Analysis 65M12, 65M15, 65M25, 65M60 The acid treatment of carbonate reservoirs is a widely employed technique for enhancing the productivity of oil and gas reservoirs. In this paper, we present a novel combined hybridized mixed discontinuous Galerkin (HMDG) finite element method to simulate the dissolution process near the wellbore, commonly referred to as the wormhole phenomenon. The primary contribution of this work lies in the application of hybridization techniques to both the pressure and concentration equations. Additionally, an upwind scheme is utilized to address convection-dominant scenarios, and a ``cut-off" operator is introduced to maintain the boundedness of porosity. Compared to traditional discontinuous Galerkin methods, the proposed approach results in a global system with fewer unknowns and sparser stencils, thereby significantly reducing computational costs. We analyze the existence and uniqueness of the new combined method and derive optimal error estimates using the developed technique. Numerical examples are provided to validate the theoretical analysis. |
| title | Numerical simulation of wormhole propagation with the mixed hybridized discontinuous Galerkin finite element method |
| topic | Numerical Analysis 65M12, 65M15, 65M25, 65M60 |
| url | https://arxiv.org/abs/2503.16792 |