Upscaling a Navier-Stokes-Cahn-Hilliard model for two-phase porous-media flow with solute-dependent surface tension effects

Sharmin, Sohely; Bastidas, Manuela; Bringedal, Carina; Pop, Sorin

doi:10.1080/00036811.2022.2052858

Cited by 4 publications

(2 citation statements)

References 47 publications

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“…Commonly used two-phase porous-media flow models are relying on saturation-dependent quantities like relative permeability and capillary pressure. The situation here is similar, but capillary pressure is absent due to the assumed scaling of the capillary number [11]. Moreover, here K is not separated into absolute and relative permeability, and it reflects how the velocity of the mixture of the two fluids relate to the pressure gradient.…”

Section: The Effective Parametersmentioning

confidence: 96%

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A numerical scheme for two-scale phase-field models in porous media

Bastidas

Sharmin

Bringedal

et al. 2021

Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference

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A porous medium is a highly complex domain, in which various processes can take place at different scales. Examples in this sense are the multi-phase flow and reactive transport. Here, due to processes like dissolution or precipitation, or chemical deposition, which are encountered at the scale of pores (the micro-scale), the local structure and geometry of the pores may change, impacting the fluid flow. Since these micro-scale processes depend on the model unknowns (e.g., the solute concentration), free boundaries are encountered, separating the space available for flow from the solid, impermeable part in the medium. Here we consider a phase-field approach to model the evolution of the evolving interfaces at the micro-scale. For mineral precipitation and dissolution, we have evolving fluid-solid interfaces. If considering multi-phase flow, evolving fluid-fluid interfaces are also present. After applying a formal homogenization procedure, a two-scale phase-field model is derived, describing the averaged behavior of the system at the Darcy scale (the macro-scale). In this two-scale model, the micro and the macro scale are coupled through the calculation of the effective parameters. Although the resulting two-scale model is less complex than the original, the numerical strategies based on the homogenization theory remain computationally expensive as they require the computation of several problems over different scales, and in each mesh element. Here, we propose an adaptive two-scale scheme involving different techniques to reduce the computational effort without affecting the accuracy of the simulations. These strategies include iterations between scales, an adaptive selection of the elements wherein effective parameters are computed, adaptive mesh refinement, and efficient non-linear solvers.

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Section: The Effective Parametersmentioning

confidence: 96%

“…A macro-scale phase-field model for compressible fluids is derived in [8]. Here we consider a two-scale phasefield model derived by formal homogenization techniques [11]. The model includes variable surface-tension effects, depending on the concentration of a surfactant dissolved in one of the fluid phases.…”

Section: Introductionmentioning

confidence: 99%

A numerical scheme for two-scale phase-field models in porous media

Bastidas

Sharmin

Bringedal

et al. 2021

Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference

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On the Doubly Non-local Hele-Shaw–Cahn–Hilliard System: Derivation and 2D Well-Posedness

Peter,

Woukeng

2024

J Nonlinear Sci

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Starting from a classic non-local (in space) Cahn–Hilliard–Stokes model for two-phase flow in a thin heterogeneous fluid domain, we rigorously derive by mathematical homogenization a new effective mixture model consisting of a coupling of a non-local (in time) Hele-Shaw equation with a non-local (in space) Cahn–Hilliard equation. We then analyse the resulting model and prove its well-posedness. A key to the analysis is the new concept of sigma-convergence in thin heterogeneous domains allowing to pass to the homogenization limit with respect to the heterogeneities and the domain thickness simultaneously.

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Upscaling and Effective Behavior for Two-Phase Porous-Medium Flow Using a Diffuse Interface Model

Kelm,

Bringedal,

Flemisch

2024

Transp Porous Med

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We investigate two-phase flow in porous media and derive a two-scale model, which incorporates pore-scale phase distribution and surface tension into the effective behavior at the larger Darcy scale. The free-boundary problem at the pore scale is modeled using a diffuse interface approach in the form of a coupled Allen–Cahn Navier–Stokes system with an additional momentum flux due to surface tension forces. Using periodic homogenization and formal asymptotic expansions, a two-scale model with cell problems for phase evolution and velocity contributions is derived. We investigate the computed effective parameters and their relation to the saturation for different fluid distributions, in comparison to commonly used relative permeability saturation curves. The two-scale model yields non-monotone relations for relative permeability and saturation. The strong dependence on local fluid distribution and effects captured by the cell problems highlights the importance of incorporating pore-scale information into the macro-scale equations.

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Upscaling a Navier-Stokes-Cahn-Hilliard model for two-phase porous-media flow with solute-dependent surface tension effects

Cited by 4 publications

References 47 publications

A numerical scheme for two-scale phase-field models in porous media

A numerical scheme for two-scale phase-field models in porous media

On the Doubly Non-local Hele-Shaw–Cahn–Hilliard System: Derivation and 2D Well-Posedness

Upscaling and Effective Behavior for Two-Phase Porous-Medium Flow Using a Diffuse Interface Model

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