Upscaling the Navier-Stokes-Cahn-Hilliard model for incompressible multiphase flow in inhomogeneous porous media
Fuente:
arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914356921368576 |
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| author | Zhang, Chunhua Liu, Peiyao Peng, Cheng Wang, Lian-Ping Guo, Zhaoli |
| author_facet | Zhang, Chunhua Liu, Peiyao Peng, Cheng Wang, Lian-Ping Guo, Zhaoli |
| contents | This work presents a macroscopic model for the flow of two immiscible and incompressible fluids within inhomogeneous porous media. At the pore scale, the flow is governed by the full Navier-Stokes equations
while the phase interface evolution is described by the Cahn-Hilliard equation. Applying the volume averaging method, we rigorously derive upscaled equations that characterize the Darcy-scale behavior of
the two-phase system. The derivation yields unclosed terms originating from spatial derivations, which are subsequently closed by modeling them as functions of averaged quantities and specific transport coefficients. These coefficients are evaluated by solving localized closure problems defined on representative elementary volumes (REVs). A key contribution of this study is the formal incorporation of wetting behavior
into the averaged chemical potential. We further discuss the theoretical distinctions between the proposed framework and standard empirical two-phase Darcy models. Finally,
numerical simulations of the upscaled equations are performed, demonstrating the model's capability to capture essential two-phase flow characteristics in porous media. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16009 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Upscaling the Navier-Stokes-Cahn-Hilliard model for incompressible multiphase flow in inhomogeneous porous media Zhang, Chunhua Liu, Peiyao Peng, Cheng Wang, Lian-Ping Guo, Zhaoli Fluid Dynamics Mathematical Physics Computational Physics Geophysics This work presents a macroscopic model for the flow of two immiscible and incompressible fluids within inhomogeneous porous media. At the pore scale, the flow is governed by the full Navier-Stokes equations while the phase interface evolution is described by the Cahn-Hilliard equation. Applying the volume averaging method, we rigorously derive upscaled equations that characterize the Darcy-scale behavior of the two-phase system. The derivation yields unclosed terms originating from spatial derivations, which are subsequently closed by modeling them as functions of averaged quantities and specific transport coefficients. These coefficients are evaluated by solving localized closure problems defined on representative elementary volumes (REVs). A key contribution of this study is the formal incorporation of wetting behavior into the averaged chemical potential. We further discuss the theoretical distinctions between the proposed framework and standard empirical two-phase Darcy models. Finally, numerical simulations of the upscaled equations are performed, demonstrating the model's capability to capture essential two-phase flow characteristics in porous media. |
| title | Upscaling the Navier-Stokes-Cahn-Hilliard model for incompressible multiphase flow in inhomogeneous porous media |
| topic | Fluid Dynamics Mathematical Physics Computational Physics Geophysics |
| url | https://arxiv.org/abs/2504.16009 |