Upscaling of Navier–Stokes equations in porous media: Theoretical, numerical and experimental approach

Narsilio, Guillermo A.; Buzzi, Olivier; Fityus, Stephen; Yun, Tae Sup; Smith, David W.

doi:10.1016/j.compgeo.2009.05.006

Cited by 117 publications

(75 citation statements)

References 14 publications

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“…Our IMPES model will be adjusted by using closure expressions [78] for saturation curves that incorporate surface tension as it influences capillary pressure. We also aim to control the pore structure of our system through photolithography techniques [16,26] and perform microparticle image velocimetry measurements [29] to map streamline profiles that can be compared to expected flow distributions as calculated by finite element analysis [79]. The approach we have used here can be used to evaluate other enhanced oil recovery systems, including other types of polymers or surfactants [80], nanoparticles [81,82], and foams [83,84].…”

Section: Discussionmentioning

confidence: 99%

Waterflooding of Surfactant and Polymer Solutions in a Porous Media Micromodel

Yeh

Juárez

2018

Colloids and Interfaces

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Abstract:In this study, we examine microscale waterflooding in a randomly close-packed porous medium. Three different porosities were prepared in a microfluidic platform and saturated with silicone oil. Optical video fluorescence microscopy was used to track the water front as it flowed through the porous packed bed. The degree of water saturation was compared to water containing two different types of chemical modifiers, sodium dodecyl sulfate (SDS) and polyvinylpyrrolidone (PVP), with water in the absence of a surfactant used as a control. Image analysis of our video data yielded saturation curves and calculated fractal dimension, which we used to identify how morphology changed the way in which an invading water phase moved through the porous media. An inverse analysis based on the implicit pressure explicit saturation (IMPES) simulation technique used mobility ratio as an adjustable parameter to fit our experimental saturation curves. The results from our inverse analysis combined with our image analysis show that this platform can be used to evaluate the effectiveness of surfactants or polymers as additives for enhancing the transport of water through an oil-saturated porous medium.

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Section: Discussionmentioning

confidence: 99%

Waterflooding of Surfactant and Polymer Solutions in a Porous Media Micromodel

Yeh

Juárez

2018

Colloids and Interfaces

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“…becomes very large because the details of the geometry have to be accounted for very precisely (Narsilio et al, 2009).…”

Section: Modeling Of the Fluid Flowmentioning

confidence: 99%

Numerical modeling of erosion using an improvement of the extended finite element method

Cottereau¹,

Dı́ez²

2011

European Journal of Environmental and Civil Engineering

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ABSTRACT. We present in this paper a numerical model of the erosion of a soil that accounts for both the flow in the open fluid and the flow of fluid through the porous soil. The interface between the open fluid and the soil is represented using a level-set function, and the erosion is controlled by the shear stress vector. The evaluation of the approximate value of this gradient is particularly focused on, and an improved method, called XFE+ method, is presented. Numerical results in 2D and 3D illustrate the accuracy and the potentiality of this method.RÉSUMÉ. Cet article décrit un modèle numérique d'érosion du sol, qui prend en compte à la fois le fluide dans le sol, considéré comme un milieu poreux, et le fluide extérieur. L'interface entre les deux milieux est représentée à l'aide d'une fonction level-set, et l'érosion est contrôlée par le gradient de la vitesse du fluide. Nous nous concentrons particulièrement sur l'évaluation numérique de ce gradient, et introduisons une méthode, appelée méthode XFE+, pour l'améliorer. Des résultats numériques en 2D et 3D montrent la précision et les potentialités de cette mé-thode.

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“…Stokes micro problems are then solved on these local pore geometries. We mention explicit analytic results for simple geometries [46], applications to textile modeling [55], and validation of predicted permeability using micro-tomography [36]. …”

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confidence: 99%

An Adaptive Finite Element Heterogeneous Multiscale Method for Stokes Flow in Porous Media

Abdulle¹,

Budáč²

2015

Multiscale Model. Simul.

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A finite element heterogeneous multiscale method is proposed for solving the Stokes problem in porous media. The method is based on the coupling of an effective Darcy equation on a macroscopic mesh, with unknown permeabilities recovered from micro finite element calculations for Stokes problems on sampling domains centered at quadrature points in each macro element. The numerical method accounts for non-periodic microscopic geometry that can be obtained from a smooth deformation of a reference pore sampling domain. The computational work is nevertheless independent of the smallness of the pore structure. A priori error estimates reveal that the overall accuracy of the numerical scheme is limited by the regularity of the solutions of the Stokes micro problems. This regularity is low for a typical situation of non-convex microscopic pore geometries. We therefore propose an adaptive scheme with micro-macro mesh refinement driven by residual-based indicators that quantify both the macro and micro errors. A posteriori error analysis is derived for the new method. Two and three dimensional numerical experiments confirm the robustness and the accuracy of the adaptive method.Keywords. Stokes flow, Darcy equation, numerical homogenization, a posteriori error estimates, adaptive finite element method AMS subject classifications. 65N30, 76D07, 74Qxx, 35Q861. Introduction. Fluid flow through porous media is an important process appearing in a wide range of engineering and technical applications. It is present in the modeling of subsurface contamination and filtration, textile properties, biomedical materials, or natural reservoirs [30,50,55,56]. The length-scale of a porous structure is usually much smaller than the computational domain of interest. Standard numerical methods relying on discretization of the porous domain, such as the finite element method (FEM), need to resolve the finest scale of the geometry, which is denoted by ε in what follows. Such techniques often lead to numerical problems of prohibitive size and computational cost.In practical applications one is often interested in macroscopic quantities such as bulk properties of the fluid flow. Mathematical models describing such macroscopic quantities are based on averaging techniques such as homogenization. The derivation of effective equations of flow in porous media can be traced back to Darcy [28]. Rigorous homogenization theory of Stokes flow in periodic porous media appeared first in [44] with a proof of convergence by Tartar [47]. This proof was generalized by Allaire [10] to allow for connected solid porous structures in three dimensions. The effective pressure is given by an elliptic (Darcy) equation which contains the effective permeability tensor that depends on the pore geometry and can be computed using the so-called Stokes micro problems. The homogenization theory was further expanded by introducing correctors and ε-dependent error estimates [34] (see also [21]) and to random stochastically homogeneous media [15].Numerical multiscale algo...

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Upscaling of Navier–Stokes equations in porous media: Theoretical, numerical and experimental approach

Cited by 117 publications

References 14 publications

Waterflooding of Surfactant and Polymer Solutions in a Porous Media Micromodel

Waterflooding of Surfactant and Polymer Solutions in a Porous Media Micromodel

Numerical modeling of erosion using an improvement of the extended finite element method

An Adaptive Finite Element Heterogeneous Multiscale Method for Stokes Flow in Porous Media

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