A critical review of dispersion in packed beds

doi:10.1007/S00231-005-0019-0

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A critical review of dispersion in packed beds

Journal Article•DOI•

A critical review of dispersion in packed beds

João M.P.Q. Delgado¹•Institutions (1)

Faculdade de Engenharia da Universidade do Porto¹

01 Feb 2006-Heat and Mass Transfer (Springer-Verlag)-Vol. 42, Iss: 4, pp 279-310

TL;DR: In this paper, the authors summarized and reviewed a great deal of information from the literature on dispersion in packed beds, and provided empirical correlations for the prediction of the dispersion coefficients (D T and D L) over the entire range of practical values of Sc and Pem.

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Abstract: The phenomenon of dispersion (transverse and longitudinal) in packed beds is summarized and reviewed for a great deal of information from the literature. Dispersion plays an important part, for example, in contaminant transport in ground water flows, in miscible displacement of oil and gas and in reactant and product transport in packed bed reactors. There are several variables that must be considered, in the analysis of dispersion in packed beds, like the length of the packed column, viscosity and density of the fluid, ratio of column diameter to particle diameter, ratio of column length to particle diameter, particle size distribution, particle shape, effect of fluid velocity and effect of temperature (or Schmidt number). Empirical correlations are presented for the prediction of the dispersion coefficients (D T and D L) over the entire range of practical values of Sc and Pem, and works on transverse and longitudinal dispersion of non-Newtonian fluids in packed beds are also considered.

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Journal Article•DOI•

Review on heat conduction, heat convection, thermal radiation and phase change heat transfer of nanofluids in porous media: Fundamentals and applications

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Huijin Xu¹, Z.B. Xing, Fuqiang Wang², Ziming Cheng²•Institutions (2)

Shanghai Jiao Tong University¹, Harbin Institute of Technology²

23 Feb 2019-Chemical Engineering Science

TL;DR: In this article, the authors focused on various flow and heat transfer modes of nanofluid, metal foam and the combination of the two, with the physical properties of nanophluid and metal foam summarized.

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252 citations

Journal Article•DOI•

Numerical simulations of transfer and transport properties inside packed beds of spherical particles

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Frederic Augier, F. Idoux, Jean-Yves Delenne¹•Institutions (1)

University of Montpellier¹

01 Feb 2010-Chemical Engineering Science

TL;DR: In this article, the authors investigate the transport and transfer properties inside packed beds of spherical particles by means of CFD simulations and show that this treatment has very little influence on the results when analyzed with dimensionless numbers as Nu=f(Re, Pr) or Sh=f (Re, Sc).

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121 citations

Journal Article•DOI•

Transition from creeping via viscous-inertial to turbulent flow in fixed beds.

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Dzmitry Hlushkou¹, Ulrich Tallarek¹•Institutions (1)

Otto-von-Guericke University Magdeburg¹

08 Sep 2006-Journal of Chromatography A

TL;DR: Microscopic analysis shows that this steady, nonlinear flow regime is characterized by the development of an inertial core in the pore-level profile, i.e., at increasing Reynolds number velocity profiles in individual pores become flatter towards the center of the pores, while the velocity gradient increases close to the solid-liquid interface.

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114 citations

Journal Article•DOI•

Evidence of compound-dependent hydrodynamic and mechanical transverse dispersion by multitracer laboratory experiments.

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Gabriele Chiogna¹, C. Eberhardt¹, Peter Grathwohl¹, Olaf A. Cirpka¹, Massimo Rolle¹ - Show less +1 more•Institutions (1)

University of Tübingen¹

15 Jan 2010-Environmental Science & Technology

TL;DR: It is shown that transverse mechanical dispersion depends on the diffusion coefficient of the compound, at least at the experimental bench-scale, which has to be considered in reactive-transport models.

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Abstract: Mass transfer, mixing, and therefore reaction rates during transport of solutes in porous media strongly depend on dispersion and diffusion. In particular, transverse mixing is a significant mechanism controlling natural attenuation of contaminant plumes in groundwater. The aim of the present study is to gain a deeper understanding of vertical transverse dispersive mixing of reaction partners in saturated porous media. Multitracer laboratory experiments in a quasi two-dimensional tank filled with glass beads were conducted and transverse dispersion coefficients were determined from high-resolution vertical concentration profiles. We investigated the behavior of conservative tracers (i.e., fluorescein, dissolved oxygen, and bromide), with different aqueous diffusion coefficients, in a range of grain-related Peclet numbers between 1 and 562. The experimental results do not agree with the classical linear parametric model of hydrodynamic dispersion, in which the transverse component is approximated as the su...

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109 citations

Journal Article•DOI•

Statistical analysis of packed beds, the origin of short-range disorder, and its impact on eddy dispersion.

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Siarhei Khirevich¹, Anton Daneyko¹, Alexandra Höltzel¹, Andreas Seidel-Morgenstern², Andreas Seidel-Morgenstern³, Ulrich Tallarek¹ - Show less +2 more•Institutions (3)

University of Marburg¹, Max Planck Society², Otto-von-Guericke University Magdeburg³

09 Jul 2010-Journal of Chromatography A

TL;DR: The presented approach defines a strictly scientific route to the key morphology-transport relationships of current and future chromatographic supports, including their morphological reconstruction, statistical analysis, and the correlation with relevant transport phenomena.

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108 citations

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References

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Book•

Conduction of Heat in Solids

[...]

H. S. Carslaw, John Conrad Jaeger

31 Dec 1959

TL;DR: In this paper, a classic account describes the known exact solutions of problems of heat flow, with detailed discussion of all the most important boundary value problems, including boundary value maximization.

...read moreread less

Abstract: This classic account describes the known exact solutions of problems of heat flow, with detailed discussion of all the most important boundary value problems.

...read moreread less

21,807 citations

"A critical review of dispersion in ..." refers methods in this paper

...The partial differential equation describing tracer transport in the bed reduces to DL @2C @z2 u @C @z ¼ @C @t ; ð2Þ where z measures length along the bed, and if L is sufficiently large (semi-infinite bed), the appropriate boundary conditions are C ¼ C0 0 z L t ¼ 0; ð3aÞ uCS ¼ uC DL @C @z z ¼ 0 t > 0; ð3bÞ @C @z ¼ 0 z ¼ L t > 0: ð3cÞ For a step input, the concentration at the outlet of the bed (z=L) can be obtained by Carslaw and Jaeger [28], who give the exact solution of the equivalent heattransfer problem....
[...]
...The result with axial dispersion neglected was given by Carslaw and Jaeger [28]...
[...]
...The result with axial dispersion neglected was given by Carslaw and Jaeger [28] C C0 ¼ R 2u 4DTz exp r 2u 4DTz : ð26Þ This solution includes a simplification possible when z/r > 5 (axial dispersion neglected)....
[...]
...For a step input, the concentration at the outlet of the bed (z=L) can be obtained by Carslaw and Jaeger [28], who give the exact solution of the equivalent heattransfer problem....
[...]

Book•

The mathematics of diffusion

[...]

John Crank

01 Jan 1956

TL;DR: Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained.

...read moreread less

Abstract: Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained

...read moreread less

20,495 citations

"A critical review of dispersion in ..." refers methods in this paper

...The analytical model for an instantaneous finite source in one dimension is first presented by Crank [36]....
[...]

Book•

Dynamics of fluids in porous media

[...]

Jacob Bear

01 Jan 1972

TL;DR: In this paper, the Milieux poreux Reference Record was created on 2004-09-07, modified on 2016-08-08 and the reference record was updated in 2016.

...read moreread less

Abstract: Keywords: Ecoulement souterrain ; Milieux poreux Reference Record created on 2004-09-07, modified on 2016-08-08

...read moreread less

12,446 citations

Journal Article•DOI•

Dispersion of soluble matter in solvent flowing slowly through a tube

[...]

Geoffrey Ingram Taylor

25 Aug 1953-Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences

TL;DR: In this paper, it was shown analytically that the distribution of concentration produced in this way is centred on a point which moves with the mean speed of flow and is symmetrical about it in spite of the asymmetry of the flow.

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Abstract: When a soluble substance is introduced into a fluid flowing slowly through a small-bore tube it spreads out under the combined action of molecular diffusion and the variation of velocity over the cross-section. It is shown analytically that the distribution of concentration produced in this way is centred on a point which moves with the mean speed of flow and is symmetrical about it in spite of the asymmetry of the flow. The dispersion along the tube is governed by a virtual coefficient of diffusivity which can be calculated from observed distributions of concentration. Since the analysis relates the longitudinal diffusivity to the coefficient of molecular diffusion, observations of concentration along a tube provide a new method for measuring diffusion coefficients. The coefficient so obtained was found, with potassium permanganate, to agree with that measured in other ways. The results may be useful to physiologists who may wish to know how a soluble salt is dispersed in blood streams.

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4,530 citations

"A critical review of dispersion in ..." refers background or methods in this paper

...The dependence of the axial dispersion coefficient on the position in packed beds was first examined by Taylor [139]....
[...]
...Since the early experiments of Slichter [131] and particularly since the analysis of dispersion during solute transport in capillary tubes, developed by Taylor [139] and Aris [3, 4], a lot of work has been done on the description of the principles of solute transport in porous media of inert particles (e....
[...]
...2.1 Experimental techniques Since the development of the dispersion approximation for the study of solute transport in capillary tubes by Taylor [139], the flow of the tracer is described by dispersion due to molecular diffusion and radial velocity variations....
[...]
...Since the early experiments of Slichter [131] and particularly since the analysis of dispersion during solute transport in capillary tubes, developed by Taylor [139] and Aris [3, 4], a lot of work has been done on the description of the principles of solute transport in porous media of inert particles (e.g. soils) and in packed bed reactors [11, 45]....
[...]
...Since the development of the dispersion approximation for the study of solute transport in capillary tubes by Taylor [139], the flow of the tracer is described by dispersion due to molecular diffusion and radial velocity variations....
[...]

Book•

Porous Media: Fluid Transport and Pore Structure

[...]

F. A. L. Dullien

01 Jan 1979

TL;DR: In this paper, the authors examined the relationship between transport properties and pore structure of porous material and presented models of pore structures with a discussion of how such models can be used to predict the transport properties of porous media.

...read moreread less

Abstract: This book examines the relationship between transport properties and pore structure of porous material. Models of pore structure are presented with a discussion of how such models can be used to predict the transport properties of porous media.

...read moreread less

3,638 citations