A phase-field method for the direct simulation of two-phase flows in pore-scale media using a non-equilibrium wetting boundary condition

Alpak, Faruk O.; Rivière, Béatrice; Frank, Florian

doi:10.1007/s10596-015-9551-2

Cited by 78 publications

(63 citation statements)

References 71 publications

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“…Besides, its kinetic nature provides many of the advantages of molecular dynamics, making the LBM particularly suitable for pore-scale simulation of multiphase flows in porous media. A number of multiphase, multicomponent LBM models have been proposed in literature, which can be classified into four main categories: colorgradient model [Gunstensen et al, 1991;Reis and Phillips, 2007;Liu et al, 2012;Huang et al, 2014], pseudopotential model [Shan and Chen, 1993, 1994, Kang et al, 2002Pan et al, 2004;Landry et al, 2014], free-energy model [Swift et al, 1996;Hao and Cheng, 2010;Alpak et al, 2016], and mean-field model [He et al, 1999;Yiotis et al, 2007]. For a comprehensive review of these models, interested readers are referred to Chen and Doolen [1998], Huang et al [2015], and Liu et al [2016].…”

Section: Introductionmentioning

confidence: 99%

Lattice Boltzmann simulation of immiscible two‐phase flow with capillary valve effect in porous media

Liu

Valocchi

2017

Water Resources Research

121

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A new algorithm for imposing the contact angle on solid surfaces is proposed in the Lattice Boltzmann color‐gradient model. The capability and accuracy of this algorithm are validated by simulation of contact angles for a droplet resting on a flat surface and on a cylindrical surface. The color‐gradient model with the proposed contact angle algorithm is then used to study the capillary valve effect in porous media. As a preliminary study, the capillary valve effect is explained by simulating immiscible two‐phase displacement within a single‐pore geometry. It is shown that the capillary valve effect is accurately captured by the present simulations. Further simulations of drainage and imbibition are also conducted to understand the capillary valve effect in an experiment‐matched pore‐network micromodel. The simulated results are found to agree quantitatively with the experimental results reported in literature, except for a few differences which result from the exclusion of contact angle hysteresis in the proposed algorithm.

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Section: Introductionmentioning

confidence: 99%

Lattice Boltzmann simulation of immiscible two‐phase flow with capillary valve effect in porous media

Liu

Valocchi

2017

Water Resources Research

121

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“…The development of diffuse-interface models in hydrodynamics and their application to a wide variety of interfacial phenomena is presented in a comprehensive review paper by [1]. A more recent survey of phase-field models [2] addresses improvements as modeling ternary fluids [3,4,5,6,7], drop coalescence and retraction in viscoelastic fluids [8], and contact angle boundary conditions [9,10,11,12,13,14,15].…”

Section: Introductionmentioning

confidence: 99%

A finite volume / discontinuous Galerkin method for the advective Cahn–Hilliard equation with degenerate mobility on porous domains stemming from micro-CT imaging

et al. 2018

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A numerical method is formulated for the solution of the advective Cahn-Hilliard (CH) equation with constant and degenerate mobility in three-dimensional porous media with non-vanishing velocity on the exterior boundary. The CH equation describes phase separation of an immiscible binary mixture at constant temperature in the presence of a mass constraint and dissipation of free energy. Porous media / pore-scale problems specifically entail high-resolution images of rocks in which the solid matrix and pore spaces are fully resolved. The interior penalty discontinuous Galerkin method is used for the spatial discretization of the CH equation in mixed form, while a semi-implicit convexconcave splitting is utilized for temporal discretization. The spatial approximation order is arbitrary, while it reduces to a finite volume scheme for the choice of elementwise constants. The resulting nonlinear systems of equations are reduced using the Schur complement and solved via Newton's method. The numerical scheme is first validated using numerical convergence tests and then applied to a number of fundamental problems for validation and numerical experimentation purposes including the case of degenerate mobility. First-order physical applicability and robustness of the numerical method are shown in a breakthrough scenario on a voxel set obtained from a micro-CT scan of a real sandstone rock sample.

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“…The common goal in these approaches is to formulate thermodynamically consistent stress tensors and mesoscale balance laws, including the impact of surface tension on the momentum balance, as well as properly tracking interfacial dynamics [25]. Pore-scale modeling of immiscible two-phase flow using phase-field models has been done in [37][38][39]. We have successfully used the phase-field modeling framework to describe wetting and capillary phenomena in porous media, from unsaturated flow [40], thin films, and partial wetting [41,42] to pattern formation during immiscible displacement in Hele-Shaw flow [43].…”

Section: Introductionmentioning

confidence: 99%

Pore-scale modeling of phase change in porous media

Cueto‐Felgueroso

Juanes

2018

Phys. Rev. Fluids

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The combination of high-resolution visualization techniques and pore-scale flow modeling is a powerful tool used to understand multiphase flow mechanisms in porous media and their impact on reservoir-scale processes. One of the main open challenges in pore-scale modeling is the direct simulation of flows involving multicomponent mixtures with complex phase behavior. Reservoir fluid mixtures are often described through cubic equations of state, which makes diffuse-interface, or phase-field, theories particularly appealing as a modeling framework. What is still unclear is whether equation-of-state-driven diffuse-interface models can adequately describe processes where surface tension and wetting phenomena play important roles. Here we present a diffuse-interface model of single-component two-phase flow (a van der Waals fluid) in a porous medium under different wetting conditions. We propose a simplified Darcy-Korteweg model that is appropriate to describe flow in a Hele-Shaw cell or a micromodel, with a gap-averaged velocity. We study the ability of the diffuse-interface model to capture capillary pressure and the dynamics of vaporization-condensation fronts and show that the model reproduces pressure fluctuations that emerge from abrupt interface displacements (Haines jumps) and from the breakup of wetting films.

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A phase-field method for the direct simulation of two-phase flows in pore-scale media using a non-equilibrium wetting boundary condition

Cited by 78 publications

References 71 publications

Lattice Boltzmann simulation of immiscible two‐phase flow with capillary valve effect in porous media

Lattice Boltzmann simulation of immiscible two‐phase flow with capillary valve effect in porous media

A finite volume / discontinuous Galerkin method for the advective Cahn–Hilliard equation with degenerate mobility on porous domains stemming from micro-CT imaging

Pore-scale modeling of phase change in porous media

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