Analysis and extension of the theory of multicomponent fluid diffusion

Kerkhof, P.J.A.M.; Geboers, Marcel A. M.

doi:10.1016/j.ces.2004.12.042

Cited by 99 publications

(50 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…9͑d͒, showing the large deviation between simulation and theory when the density field is taken to be uniform at the mean pore density. The approximation of a uniform pore density is common to existing formulations, 9,10,23,24,[28][29][30][31][32][33][34]55 but is clearly in serious error, particularly for micropores where the inhomogeneity in the potential energy profile is stronger. Nevertheless, as indicated earlier, success in interpreting transport data from simulation or experiment is often found because of the presence of a few empirical phenomenological parameters.…”

Section: Transport In Binary H 2 /Ch 4 Mixturesmentioning

confidence: 99%

“…͑3͒ leads to the result i = w i , overcoming a major difficulty in the use of the Kerkhof and Geboers 23,24 approach. For the inhomogeneous nanopore fluid the partial viscosity of species i as well as the binary ͑i.e., mutual͒ diffusivities, D ij , are nonlocal properties, expressed as functions of locally averaged densities, k , following the LADM…”

Section: Theorymentioning

confidence: 99%

“…They argued that the most fundamental staring point was the Liouville equation and again used the BK equations ͑derived from the Liouville equations͒ as a point of departure. Their final result for mixtures included both a Stefan-Maxwell term and a viscous term, although the manner in which this was incorporated has been called into question; 23,24 furthermore, the underlying assumption of expansion about the mixture center of mass velocity remains despite the fact that these authors dismiss this as "not critical." Their equations were primarily aimed at membrane transport and this somewhat global view meant that adsorbate density gradients and inhomogeneities arising from the fluid-solid interaction were overlooked and, for the case of cylindrical capillaries, relies on the parabolic velocity profile arising from the classical Poiseuille flow model.…”

Section: Introductionmentioning

confidence: 99%

“…The theory is based on a constitutive model for the shear stress on a given component that is based on the strain rate of that component as suggested by Kerkhof and Geboers,23,24 while also representing wall effects in a novel manner through a species-specific friction coefficient in the momentum balance. The theory is validated with the help of molecular dynamics simulations for the H 2 / CH 4 binary system in a silica nanopore.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Friction based modeling of multicomponent transport at the nanoscale

Bhatia

Nicholson

2008

The Journal of Chemical Physics

View full text Add to dashboard Cite

We present here a novel theory of mixture transport in nanopores, which considers the fluid-wall momentum exchange in the repulsive region of the fluid-solid potential in terms of a species-specific friction coefficient related to the low density transport coefficient of that species. The theory also considers nonuniformity of the density profiles of the different species, while departing from a mixture center of mass frame of reference to one based on the individual species center of mass. The theory is validated against molecular dynamics simulations for single component as well as binary mixture flow of hydrogen and methane in cylindrical nanopores in silica, and it is shown that pure component corrected diffusivities, as well as binary Onsager coefficients are accurately predicted for pore sizes sufficiently large to accommodate more than a monolayer of any of the components. It is also found that the assumption of a uniform density profile can lead to serious errors, particularly at small pore diameter, as also the use of a mixture center of mass frame of reference. The theory demonstrates the existence of an optimum temperature for any fluid, at which the fractional momentum dissipation due to wall friction is a minimum.

show abstract

Section: Transport In Binary H 2 /Ch 4 Mixturesmentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Friction based modeling of multicomponent transport at the nanoscale

Bhatia

Nicholson

2008

The Journal of Chemical Physics

View full text Add to dashboard Cite

show abstract

“…Gas diffusion can be described by superposition of viscous and Knudsen flow (Markovic et al, 2009), and the phenomena of gas diffusion through porous materials has been discussed extensively by Kerkhof and Geboers (2005). Knudsen diffusion occurs when the scale length of a system is comparable to or smaller than the mean free path of the particles involved, e.g.…”

Section: Knudsen Diffusion Effectmentioning

confidence: 99%

Shale Gas Pseudo Two-Dimensional Unsteady Seepage Pressure Simulation Analysis in Capillary Model

Lai

et al. 2014

Oil Gas Sci. Technol. – Rev. IFP Energies nouvelles

View full text Add to dashboard Cite

-Shale gas is rapidly growing as a source of natural gas in China. Compared with the conventional gas reservoir, the shale gas reservoir is characterized by low porosity, low permeability, and adsorbed gas, making the flow mechanism of shale gas reservoir more complex. In this study, we investigated six factors influencing the gas flow: the Darcy flow, the slippage effect, the Knudsen diffusion effect, the desorption of gas on pore walls, the diffusion effect of gas in organic matter, and the matrix deformation effect. We simplified gas flow in the development process to only include gas flow in the capillaries and then considered the six influence factors. This study establishes a shale gas pseudo two-dimensional unsteady capillary seepage mathematical model based on the continuity equation, using the implicit difference method to solve the mathematical model. Certain capillary parameters were added to the calculation, and the study analyzed the effect of the different factors on both the pressure distribution and the cumulative gas production. Results show that the Knudsen diffusion effect and the desorption of gas from pore walls have lower impact on the pressure than the others factors. The diffusion effect of gas in organic matter, the slippage effect, and the matrix deformation effect have a stronger impact on the pressure. The gas in organic matter continuously diffuses into the capillary with the increasing of the production time, and the pressure drop becomes slow because of the gas diffusion.Re´sume´-Analyse des instabilite´s d'une simulation pseudo-bidimensionnelle de la pression de filtration de gaz de schiste dans un mode`le capillaire -Le gaz de schiste connaıˆt une croissance rapide en tant que source de gaz naturel en Chine. En comparaison du re´servoir de gaz conventionnel, le re´servoir de gaz de schiste se caracte´rise par une faible porosite´, une faible perme´abilite´, et par le gaz adsorbe´qui rend le me´canisme d'e´coulement du re´servoir de gaz de schiste plus complexe. Dans cette e´tude, nous avons e´tudie´six facteurs qui influencent le de´bit de gaz : l'e´coulement selon le mode`le de Darcy, l'effet de glissement, l'effet de diffusion Knudsen, la de´sorption du gaz sur les parois poreuses, l'effet de diffusion du gaz dans la matie`re organique et l'effet de de´formation de la matrice. Nous avons simplifie´le de´bit de gaz dans un mode`le pour inclure uniquement le de´bit de gaz dans les capillaires et ensuite e´tudier les six facteurs d'influence. Cette e´tude de´veloppe un mode`le mathe´matique de pe´ne´tration capillaire instable et pseudo-bidimensionnelle du gaz de schiste en se fondant sur l'e´quation de continuiteé t en utilisant la me´thode de diffe´rence implicite pour re´soudre le mode`le mathe´matique.

show abstract

Mass Transport in Multilayer Porous Metallic Membranes – Diagnosis, Identification and Validation

et al. 2009

View full text Add to dashboard Cite

For a reliable description of mass transfer in membrane reactors the multilayer structure of the membrane is essential. This paper discusses methods which are sufficient to distinguish between homogeneous and composite membranes, and some others which are not. Different mass transport experiments (single gas permeation, isobaric diffusion, transient diffusion) with a porous metallic membrane consisting of two layers and the dusty gas model were used for this purpose. Simultaneous identification of mass transport parameters of both layers was achieved by modern optimization techniques on single gas permeation data. These parameters were validated by isobaric or transient diffusion measurements. Copyright © 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim [accessed April 22, 2009

show abstract

Analysis and extension of the theory of multicomponent fluid diffusion

Cited by 99 publications

References 30 publications

Friction based modeling of multicomponent transport at the nanoscale

Friction based modeling of multicomponent transport at the nanoscale

Shale Gas Pseudo Two-Dimensional Unsteady Seepage Pressure Simulation Analysis in Capillary Model

Mass Transport in Multilayer Porous Metallic Membranes – Diagnosis, Identification and Validation

Contact Info

Product

Resources

About