Towards enhanced mixing of a high viscous miscible blob in porous media
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910121576103936 |
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| author | Rahaman, Mijanur Kalita, Jiten C. Pramanik, Satyajit |
| author_facet | Rahaman, Mijanur Kalita, Jiten C. Pramanik, Satyajit |
| contents | In this study, we investigate the rectilinear displacement and deformation of a highly viscous, miscible circular blob influenced by a less viscous fluid within a homogeneous porous medium featuring physically realistic no-flux boundaries. We utilize a fourth-order accurate compact finite difference scheme for the spatial discretization of the nonlinear partial differential equations that govern this phenomenon. The resulting semi-discrete equations are then integrated using the second-order Crank-Nicolson (CN) method. We conduct numerical simulations for a Péclet number ($Pe \leq 3000$) and a log-mobility ratio $0 \leq R \leq 7$, which reveal three distinct pattern formations: comet-shape, lump-shape, and viscous fingering instability. Our results demonstrate that the deformation, spreading, and mixing of the blob vary non-ideally with both $Pe$ and $R$, a behavior attributed to the blob's initial curvature. Consequently, enhanced mixing can be achieved at intermediate values of $Pe$ and $R$, suggesting the existence of an optimal mixing condition. These findings have significant implications for fields such as oil recovery, CO$_2$ sequestration, pollution remediation, and chromatography separation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_08034 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Towards enhanced mixing of a high viscous miscible blob in porous media Rahaman, Mijanur Kalita, Jiten C. Pramanik, Satyajit Fluid Dynamics In this study, we investigate the rectilinear displacement and deformation of a highly viscous, miscible circular blob influenced by a less viscous fluid within a homogeneous porous medium featuring physically realistic no-flux boundaries. We utilize a fourth-order accurate compact finite difference scheme for the spatial discretization of the nonlinear partial differential equations that govern this phenomenon. The resulting semi-discrete equations are then integrated using the second-order Crank-Nicolson (CN) method. We conduct numerical simulations for a Péclet number ($Pe \leq 3000$) and a log-mobility ratio $0 \leq R \leq 7$, which reveal three distinct pattern formations: comet-shape, lump-shape, and viscous fingering instability. Our results demonstrate that the deformation, spreading, and mixing of the blob vary non-ideally with both $Pe$ and $R$, a behavior attributed to the blob's initial curvature. Consequently, enhanced mixing can be achieved at intermediate values of $Pe$ and $R$, suggesting the existence of an optimal mixing condition. These findings have significant implications for fields such as oil recovery, CO$_2$ sequestration, pollution remediation, and chromatography separation. |
| title | Towards enhanced mixing of a high viscous miscible blob in porous media |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2509.08034 |