Packed beds tortuosity

Tortuosity. Although it was implied in the derivation of equation 4.9 that a single value of the Kozeny constant K" applied to all packed beds, in practice this assumption does not hold. 

For packed beds, the use of these equations for predictions is limited by inaccuracy in the velocity-profile data. Therefore, Bischoff and Levenspiel (B14) used the equations in a semiempirical way for interpolating between the existing data. The results are shown in Figs. 15 and 16, for both empty tubes and packed beds. The heavy lines show the regions of experimental data, and the dashed lines, the interpolations. For sufficiently low flow rates, the curves lead into the reciprocal Schmidt number (modified by a tortuosity factor in packed beds). The data of Blackwell (B16, B17) at very low flow rates seems to verify this. At high flow rates, liquids and gases show no differences because of the... 

One example of this type of reactor is in the synthesis of catalyst powders and pellets by growing porous soHd oxides from supersaturated solution. Here the growth conditions control the porosity and pore diameter and tortuosity, factors that we have seen are crucial in designing optimal catalysts for packed bed, fluidized bed, or slurry reactors. 

In addition to the packed bed acting as an ultrafilter, the porous frits used at both ends of the column may act as very effective filtering devices. Thus a 2-vim porosity frit would have an average pore radius of 1 lun. Because of the tortuosity and relatively wide pore-size distribution present in frits, it would be safe to assume that it contains much smaller crevices which can entrap macromolecules. 

The extraction of toluene and 1,2 dichlorobenzene from shallow packed beds of porous particles was studied both experimentally and theoretically at various operating conditions. Mathematical extraction models, based on the shrinking core concept, were developed for three different particle geometries. These models contain three adjustable parameters an effective diffusivity, a volumetric fluid-to-particle mass transfer coefficient, and an equilibrium solubility or partition coefficient. K as well as Kq were first determined from initial extraction rates. Then, by fitting experimental extraction data, values of the effective diffusivity were obtained. Model predictions compare well with experimental data and the respective value of the tortuosity factor around 2.5 is in excellent agreement with related literature data. 

In this work extraction models are developed for three different particle geometries using the shrinking core concept. Model calculations will be compared and fitted to extraction data of toluene and 1,2 dichlorobenzene (DCB) from shallow packed beds in order to obtain values of the efective diffusivity (De) and the tortuosity factor. 

Figure 7 presents the parameters of the reactor model and the operating conditions simulated. A packed bed of catalyst with a loading of catalyst equivalent to 0.11 gr of Shell 105 catalyst/void cc of reactor is assumed. A membrane 5 microns thick with 20 A pore radii is placed on inner side of a 3/8" I.D. porous support. The pore size of this support is considered to be large enough that it does not exhibit any resistance to mass transfer. A tortuosity... 

A relationship is expected between Hr and Ha. However, if the packing density depends on the radial position, the bed tortuosity and eddy diffusion may be different in the axial and radial directions. Furthermore, the mass transfer resistances do not affect Hf. Although, in the general case. Da and Dr could both be functions of the coordinates z and r and of the concentration, we assumed in writing Eq. 2.18 that they are constant. This would constitute the second order approximation of a model of physical columns, the other models discussed here being first order approximations since they all assume a homogeneous column. 

At low Reynolds numbers, the friction factor for flow in tubes is / = 16/Re. For packed beds, both / and V are adjusted by a tortuosity factor to account for the fact that a fluid element travels a longer distance (winding through the pore space) than bed length L. Empiricism has led to adjustments in either the tortuosity or the final equation or both (depending on the derivation) to yield a well-accepted result for... 

To enhance the rate of penetration, y y has to be made as high as possible, 0 as low as possible, and p as low as possible. For the dispersion of powders into Hquids, surfactants should be used that lower 0 but do not reduce too much the viscosity of the liquid should also be kept at a minimum. Thickening agents (such as polymers) should not be added during the dispersion process. It is also necessary to avoid foam formation during the dispersion process. For a packed bed of particles, r may be replaced by K, which contains the effective radius of the bed and a tortuosity factor, which takes into account the complex path formed by the channels between the particles, that is ... 

It should also be noted that the B-term in the original van Deemter equation included a tortuosity factor, y, that also accounts for the nature of the packed bed. There is no such factor in the 5-term for open tubular columns, of course. 

A. dispersion caused by mokcular diffusion Dispersion due to molecular diffusion in the interparticle void spaces is described by the void fraction of the bed, e, and the tortuosity of the diffusion path in the void space. Unlike the diffusion in porous particles reviewed in Chapter 4, the latter is considered close to unity for diffusion in packed beds. Then,... 

For a packed bed of particles, r may be replaced by K, which contains the effective radius of the bed and a tortuosity factor, which takes into account the complex path formed by the channels between the particles, i.e. 

Consider the following application of fixed-bed, activated carbon adsorption for the control of VOC emissions. An industrial waste gas consists of 0.5 vol% acetone in air at 300 K and 1 atm. It flows at the rate of 2.3 kg/s through a fixed bed packed with activated carbon. The bed has a cross-sectional area of 5.0 m2 and is packed to a depth of 0.3 m. The external porosity of the bed is 40%, its bulk density is 630 kg/m3, and the average particle size is 6 mm. The average pore size of the activated carbon particles is 20 A, the internal porosity is 60%, and the tortuosity factor is 4.0. A Langmuir-type adsorption isotherm applies with qm = 0.378 kg VOC/kg of carbon, K = 0.867 kPa-1. At the break point, the effluent concentration will be 5% of the feed concentration. Calculate ... 

Porosity of deposit layer 0.8 Influent concentration 0-1 g/l Tortuosity of solid deposit 3.7 Catalyst packing spherical catalyst particles Diameter 0.003 m Porosity of catalyst 0.65 Bed porosity 0.37... 

Two types of techniques are commonly used for the determination of the internal void fraction and the tortuosity. The first uses a column packed with the catalyst and having a djdp ratio such that the flow approximates the ideal plug flow pattern, it is conveniently inserted in the furnace of a gas chromatograph that has all the parts for detecting the feed and response signals, besides temperature- and flow controls and six way valves. A narrow tracer pulse is injected in the carrier gas flow and the response is measured at the exit of the column. The pulse widens as a consequence of the dispersion in the bed, adsorption on the catalyst surface and effective diffusion inside the catalyst particle. The tracer does not have to be the component A itself The injected pulse should have an adequate residence time in the column and sufficient widening. Preference is given to transient measurements because steady state operation would not measure the effect of the dead end pores. 

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