Dispersion in periodic porous media. Experience versus theory for two-dimensional systems

Didierjean, Sophie; Souto, Helio Pedro Amaral; Delannay, Renaud; Moyne, Christian

doi:10.1016/s0009-2509(96)00518-0

Cited by 26 publications

(20 citation statements)

References 17 publications

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“…3.13. Edwards et al (1991) and many other authors (Didierjean 1997;Eidsath et al 1983;Souto and Moyne 1997) use this equation for periodic media and present 2D computational results also for higher Peclet numbers. The comparison with experimental values uses a standard plot of the longitudinal dispersion coefficient divided by the molecular diffusion coefficient versus the Peclet number (Arya et al 1988).…”

Section: Introductionmentioning

confidence: 92%

Computation of the Longitudinal and Transverse Dispersion Coefficient in an Adsorbing Porous Medium Using Homogenization

2011

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This article compares for the first time, local longitudinal and transverse dispersion coefficients obtained by homogenization with experimental data of dispersion coefficients in porous media, using the correct porosity dependence. It is shown that the longitudinal dispersion coefficient can be reasonably represented by a simple periodic unit cell (PUC), which consists of a single sphere in a cube. We present a slightly modified and simplified approach to derive the homogenized equations, which emphasizes physical aspects of homogenization. Subsequently, we give full dimensional expressions for the dispersion tensor based on a comparison with the convective dispersion equation used for contaminant transport, inclusive the correct dependence on porosity. For the PUC of choice, the dispersion relations are identical to the relations obtained for periodic media. We show that commercial finite element software can be readily used to compute longitudinal and transverse dispersion coefficients in 2D and 3D. The 3D results are for the first time obtained at relevant Peclet numbers. There is good agreement for longitudinal dispersion. The computed transverse dispersion coefficients for a single sphere in a cube are much too low. The effect of adsorption on the dispersion coefficient is also studied. Adsorption does not affect the transverse dispersion coefficient. However, adsorption enhances the longitudinal dispersion coefficient in agreement with an analysis of homogenization applied to Taylor dispersion discussed in the literature.

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Section: Introductionmentioning

confidence: 92%

Computation of the Longitudinal and Transverse Dispersion Coefficient in an Adsorbing Porous Medium Using Homogenization

2011

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“…v is the Darcy's velocity caused by a macroscopic gradient of pressure. When D dis does not depend on the space variable X, an eventual asymmetry of the dispersion tensor D dis has no effect on the mass balance (1); the divergence operator kills the antisymmetric part of D dis (Carbonell and Whitaker 1983;Auriault and Adler 1995;Amaral Souto and Moyne 1997;Didierjean et al 1997). However, the antisymmetric part is of importance for porous media that are heterogeneous or in presence of flux boundary conditions like (2).…”

Section: Introductionmentioning

confidence: 99%

“…Symmetry is either directly adopted by invoking Onsager's relations, e.g., Bear et al (2010) or by upscaling the pore scale flow and assuming reversibility at this scale (Brenner 1980;Edwards et al 1991), or by introducing ad hoc statistical assumptions during the process (Bear 1972). On an other hand, asymmetry is stated without demonstration (Carbonell and Whitaker 1983;Auriault and Adler 1995;Amaral Souto and Moyne 1997;Didierjean et al 1997), or it is just ignored because dealing with the mass balance only (Mei 1992). However, the asymmetry is clearly shown to exist for flows through beds of propellers, although these porous media seem unrealistic (Koch and Brady 1987).…”

Section: Introductionmentioning

confidence: 99%

“…4. Note that the effective coefficients of random media are often investigated by periodization (Cherel et al 1988;Salles et al 1993;Amaral Souto 1993;Poutet et al 1996;Losic et al 1997;Amaral Souto and Moyne 1997;Owhadi 2003;Wood et al 2003;Sab and Nedjab 2005): the Representative Elementary Volume (REV) of a random medium can be chosen so as to contain a very large number of pores. Therefore, modifying the pores on the boundary of the REV to render periodic the REV only slightly change the effective coefficients.…”

Section: Introductionmentioning

confidence: 99%

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On the Asymmetry of the Dispersion Tensor in Porous Media

2010

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We investigate the properties of the dispersion tensor in porous media by making use of the method of homogenization by multiple scale expansions, which gives the dispersion model from the pore scale description. Results are valid for random or periodic structures as well. By investigating the domain of relatively small Péclet numbers, we show that the dispersion tensor is asymmetric in some cases. We also demonstrate that in the whole range of validity of the dispersion equation, the dispersion tensor verifies D dis i j (grad X p) = D dis ji (−grad X p). Links with Onsager's relations are given. Numerical investigations at finite Péclet numbers confirm the possible asymmetry of the dispersion tensor.

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“…Further discussions can be found in [10,36,60,5,24,25,9,26]. Experimentally, these phenomena have also been extensively studied (see summaries in [37,30,22]; see also [40,28]). …”

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confidence: 99%

Solute Transport in Porous Media. Media with Capillaries as Voids

Goldsztein¹

2008

SIAM J. Appl. Math.

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Abstract. We study solute transport in porous media with periodic microstructures consisting of interconnected thin channels. We discuss a local physical mechanism that occurs at the intersections of channels and promotes mixing of the solute with the solvent (i.e., the host liquid). We identify the parameter regime, where this mechanism is the dominant cause of dispersion, and obtain the effective or macroscopic transport equation that the concentration of solute satisfies when the medium is subjected to a time periodic applied pressure gradient. We conclude with illustrative examples. 1. Introduction. A porous medium is a material that contains relatively small spaces filled with fluid (such as a gas, a liquid, or a mixture of different fluids) embedded in a solid matrix. These fluid filled spaces are called pores or voids. With the exception of metals, some dense rocks, and some plastics, virtually all solid materials are porous to varying degrees.Solutes are materials that dissolve in liquids forming solutions. An example is salt (not at very large concentrations) in water. The host liquid, such as water in the mentioned example, is called the solvent. The transport of a solute in porous media depends on several factors, including the solvent and solute properties, the fluid velocity field within the porous medium, and the microgeometry, i.e., shape, size, and location of the solid part of the medium and the voids. The objective of this paper is to provide new tools for the study of the influence of these factors on solute transport.Solute transport in liquid filled porous media plays a significant role in several phenomena of scientific and technological importance including the transport of contaminants in soils [17,32], the transport of nutrients in bones [50,45,43,44,65,39], the intrusion of salt in fresh water in soils near ocean coasts, movement of minerals (e.g., fertilizers) in soils, secondary recovery techniques in oil reservoirs (where the injected fluid dissolves the reservoir's oil), the use of tracers in petroleum engineering and hydrology research projects, etc. (see more about these and other examples in [14,6,9,19,30,58]).Several theoretical methods are used to study solute transport in porous media [23]. These include the use of numerical experiments on networks of channels with varying widths forming regular grids [2,15,16,20,27,58,59], percolation methods [2,7,8,10,47,55,56,57,59,62], numerical experiments on media with fractal geometry [2,16,59,64], assuming periodic media and calculating the effective transport equation by means of the method of moments [2,11,12,13,14,31]

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Dispersion in periodic porous media. Experience versus theory for two-dimensional systems

Cited by 26 publications

References 17 publications

Computation of the Longitudinal and Transverse Dispersion Coefficient in an Adsorbing Porous Medium Using Homogenization

Computation of the Longitudinal and Transverse Dispersion Coefficient in an Adsorbing Porous Medium Using Homogenization

On the Asymmetry of the Dispersion Tensor in Porous Media

Solute Transport in Porous Media. Media with Capillaries as Voids

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