Nonuniformity packed beds

Dimensional Flow of Fluids through Nonuniform Packed-Beds. AIChE Journal,... 

The axial dispersion coefficient [cf. Eq. (16-51)] lumps together all mechanisms leading to axial mixing in packed beds. Thus, the axial dispersion coefficient must account not only for moleciilar diffusion and convec tive mixing but also for nonuniformities in the fluid velocity across the packed bed. As such, the axial dispersion coefficient is best determined experimentally for each specific contac tor. 

On each of these, random and structured reactors behave quite differently. In terms of costs and catalyst loading, random packed-bed reactors usually are most favorable. So why would one use structured reactors As will become clear, in many of the concerns listed, structured reactors are to be preferred. Precision in catalytic processes is the basis for process improvement. It does not make sense to develop the best possible catalyst and to use it in an unsatisfactory reactor. Both the catalyst and the reactor should be close to perfect. Random packed beds do not fulfill this requirement. They are not homogeneous, because maldistributions always occur at the reactor wall these are unavoidable, originating form the looser packing there. These maldistributions lead to nonuniform flow and concentration profiles, and even hot spots can arise (1). A similar analysis holds for slurry reactors. For instance, in a mechanically stirred tank reactor the mixing intensity is highly non-uniform and conditions exist where only a relatively small annulus around the tip of the stirrer is an effective reaction space. 

Now the rate expression for the reaction A —> B together with (26) indicates that the deactivation depends on the composition of the reaction mixture and may vary along the length of the reactor. Under integral reactor conditions this leads to a nonuniform catalyst deactivation in a packed bed. So differential conditions are to be preferred to study this phenomenon. Various empirical activity functions have been proposed [15] whereby using Oc = f(t) instead of = /(cc) has the advantage of being independent of... 

An additional and important advantage of the recycle reactor, compared to the differential packed bed reactor, is that here flow uniformity through the bed is not required, so channeling is not a problem and one layer of catalyst or even separate particles can be used in the reactor. For packed bed reactors, flow nonuniformity would inhibit the application of the plug flow model. 

The distribution of gas over all parallel channels in the monolith is not necessarily uniform [2,5,6]. It may be caused by a nonuniform inlet velocity over the cross-sectional area of the monolith, due to bows in the inlet tube or due to gradual or sudden changes of the tube diameter. Such effects become important, because the pressure loss over the monolith itself is small. Also, a nonuniformity of channel diameters could be a cause at the operative low Reynolds numbers, as was reported for packed beds [7]. A number of devices were proposed to ensure a uniform inlet velocity [5,8], which indeed increases the total pressure drop. 

The averaging technique characteristic of the second approach may apply to the case of a tubular reactor where the ratio of the characteristic catalyst particle size to the diameter of a single tube is close to unity, but it is invalid, as will be shown, in the general case of fixed-bed reactors. This approach keeps out of a researcher s field of vision the problem of the reactor stability to local perturbations. At the same time, the technologist is often faced with hot spots in the catalyst bed of a fixed-bed reactor, which make its operation imperfect and even lead to an emergency situation in a number of cases, Until recently, nonuniformity of the fields of external parameters (e.g., nonuniform packing of the catalyst bed or nonuniformity of reactant stream velocity ) was considered the only cause of these phenomena. The question naturally arises whether the provision for uniformity of external conditions guarantees the uniformity of temperature and concentration profiles at the reactor cross-section. The present paper seeks to answer this question, which, as a matter of fact, has not yet been posed in such a form in the theory of chemical reactors. 

The drawbacks of randomly packed beds in microchannels are the high pressure drop and effects related to the nonuniform packing of the small catalyst particles, namely, channeling and maldistribution of the fluids. A large RTD results, which diminishes the reactor performance and, in the case of sequential reaction networks, the product selectivity. The reactor or the catalyst may be modified such that a structured bed is obtained. 

The solid phase could be a reactant, product, or catalyst. In general the decision on the choice of the particle size rests on an analysis of the extra-and intra-particle transport processes and chemical reaction. For solid-catalyzed reactions, an important consideration in the choice of the particle size is the desire to utilize the catalyst particle most effectively. This would require choosing a particle size such that the generalized Thiele modulus < gen, representing the ratio of characteristic intraparticle diffusion and reaction times, has a value smaller than 0.4 see Fig. 13. Such an effectiveness factor-Thiele modulus analysis may suggest particle sizes too small for use in packed bed operation. The choice is then either to consider fluidized bed operation, or to used shaped catalysts (e.g., spoked wheels, grooved cylinders, star-shaped extrudates, four-leafed clover, etc.). Another commonly used procedure for overcoming the problem of diffu-sional limitations is to have nonuniform distribution of active components (e.g., precious metals) within the catalyst particle. 

To the extent that dispersion in an inertia free porous medium flow arises from a nonuniform velocity distribution, its physical basis is the same as that of Taylor dispersion within a capillary. Data on solute dispersions in such flows show the long-time behavior to be Gaussian, as in capillaries. The Taylor dispersion equation for circular capillaries (Eq. 4.6.30) has therefore been applied empirically as a model equation to characterize the dispersion process in chromatographic separations in packed beds and porous media, with the mean velocity identified with the interstitial velocity. In so doing it is implicitly assumed that the mean interstitial velocity and flow pattern is independent of the flow rate, a condition that would, for example, not prevail when inertial effects become important. 

The over-all heat-transfer coefficients for the fixed-bed and hot-gas-recycle systems were calculated from a correlation of heat transfi through packed beds. A relatively high transfer coefficient of 50 Btu/(hr) (sq ft) ( F) is obtained for the hot-gas-recycle system because of the high linear velocity of the gas. A uniform amount of reaction has been assumed through the catalyst bed. When the reaction occurs nonuniformly and a large amount of conversion takes place in a limited area, as is often the case near the point of entry of the fresh gas, the gradients are higher. 

In addition to the effect of nonuniform flow distribution, packed beds have variations in local velocity that also cause departures from plug flow. The average interstitial velocity is n /e, or 2.5 mq for typical bed of spheres... 

A major proUem of large-diameter steel columns is their tendency to develop voids at the colunm top due to a collapse of the bed. The void space is detrimental to the separatiorL Also, the collapse of the bed nuty create large nonuniformities in the packed bed itself, whkh also is detrimental to the... 

The van Deemter equation provides a simple and useful description of the basic phenomena in a packed bed. However, it has two shortcomings. The first is the fact that the A term, describing the nonuniformity of the packed bed, has been introduced in a rather ad hoc manner and does not withstand careful theoretical examination. The second problem arises from the fact that in many practical cases, especially in gas chromatography, a downward curvature is observed on the right-hand branch of the HETP-linear velocity plot, which cannot be accounted for by the van Deemter theory. Something is wrong. 

We are able to show that in a well-packed (i.e., a uniform column), this concept gives rise to a term that is practically constant over the range of interest, that is, in accordance with the van Deemter equation. In a nonuniform bed, on the other hand, it gives rise to the curvature of the increasing branch of the HETP-velocity plot that has been observed experimentally. Consequently, a uniform, well-packed bed can be described by the van E>eemter equation, while a poorly packed bed needs to be described by an equation that contains a term incorporating the curvature. 

Hartwick (17) aligned uniformly sized fibers into a densely packed hexagonal array. The interstices between the fibers represented the flow channels. There was no transport between the channels. The performance of the device was low relative to its permeability. This is not unexpected A key property of a packed bed is the radial mass transfer, which evens out flow nonuniformities. Tto is not possible in a device consisting of parallel independent flow paths. In an array of circular parallel channels, the breakthrough time for an unretained sample is inversely proportional to the square of the diameter of the channel. To obtain a plate count of 10,000 plates, it would be necessary that the relative standard deviation of the channel diameter is under 0.5% (see also the footnote in Section 2.1.4). This is clearly a tall order. For retained peaks, similar demands would need to be placed on the uniformity of the stationary phase from channel to channel. 

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