Packed beds illustration

The basic concepts of a gas-fluidized bed are illustrated in Figure 1. Gas velocity in fluidized beds is normally expressed as a superficial velocity, U, the gas velocity through the vessel assuming that the vessel is empty. At a low gas velocity, the soHds do not move. This constitutes a packed bed. As the gas velocity is increased, the pressure drop increases until the drag plus the buoyancy forces on the particle overcome its weight and any interparticle forces. At this point, the bed is said to be minimally fluidized, and this gas velocity is termed the minimum fluidization velocity, The bed expands slightly at this condition, and the particles are free to move about (Fig. lb). As the velocity is increased further, bubbles can form. The soHds movement is more turbulent, and the bed expands to accommodate the volume of the bubbles. 

Figure 3.2.1 illustrates the mixing in packed beds (Wilhelm 1962). As Reynolds number approaches the industrial range Rep > 100, the Peclet numbers approach a constant value. This means that dispersion is influenced by turbulence and the effect of molecular diffusion is negligible. 

Fluidised beds have been used previously for the industrial-scale recovery of the antibiotics streptomycin and novobiocin.30 However, more recently, considerable interest has been shown in the use of fluidised beds for the direct extraction of proteins from whole fermentation broths.31 In a packed bed, the adsorbent particles are packed within the contactor. The voidage, that is, the inter-particle space, is minimal and thus feedstock clarification is mandatory to avoid clogging of the bed. In a fluidised/expanded bed, the adsorbent bed is allowed to expand by irrigation with feedstock. Bed voidage is increased, allowing the passage of particulates in the feed. The diameters of the adsorbent beads are exaggerated for illustrative clarity. 

The model can also be applied to packed-beds. Figure 9.7 illustrates the range of existing data. 

If the enzyme charged to a batch reactor is pristine, some time will be required before equihbrium is reached. This time is usually short compared with the batch reaction time and can be ignored. Furthermore, 5o Eq is usually true so that the depletion of substrate to establish the equilibrium is negligible. This means that Michaelis-Menten kinetics can be applied throughout the reaction cycle, and that the kinetic behavior of a batch reactor will be similar to that of a packed-bed PFR, as illustrated in Example 12.4. Simply replace t with thatch to obtain the approximate result for a batch reactor. 

In this study, Pt/AliOj having high activity for CO oxidation and different affinities for fee adsorption of CO and Hi was selected as a catalyst/adsorbent In a conventional packed bed reactor (PBR), fee surface of fee catalyst is dominantly covered by COads with small amotmt of Oads fee CO conversion is therefore low. Several investigations on periodic operation have illustrated feat fee reaction front wife comparable amount of fee two adsorbed species leads to enhancement of fee CO conversion. Conceptually, this type of the reaction front should be generated by application of a CMBR, as well. Figure 1 illustrates an image of... 

Cylinders have the advantage that they are cheap to manufacture. In addition to varying the shape, the distribution of the active material within the pellets can be varied, as illustrated in Figure 6.7. For packed-bed reactors, the size and shape of the pellets and the distribution of active material within the pellets can be varied through the length of the reactor to control the rate of heat release (for exothermic reactions) or heat input (for endothermic reactions). This involves creating different zones in the reactor, each with its own catalyst designs. 

Illustration 12.7 indicates how to estimate an effective thermal conductivity for use with two-dimensional, pseudo homogeneous packed bed models. 

ILLUSTRATION 12.7 DETERMINATION OF THE EFFECTIVE THERMAL CONDUCTIVITY OF A PACKED BED OF CATALYST PELLETS... 

Conversion and Temperature Profiles for Packed Bed Reactor of Illustration 12.9... 

In this section a short description of a comparison between experimental and simulation results for heat transfer is illustrated (Nijemeisland and Dixon, 2001). The experimental set-up used was a single packed tube with a heated wall as shown in Fig. 8. The packed bed consisted of 44 one-inch diameter spheres. The column (single tube) in which they were packed had an inner diameter of two inches. The column consisted of two main parts. The bottom part was an unheated 6-inch packed nylon tube as a calming section, and the top part of the column was an 18-inch steam-heated section maintained at a constant wall temperature. The 44-sphere packed bed fills the entire calming section and part of the heated section leaving room above the packing for the thermocouple cross (Fig. 8) for measuring gas temperatures above the bed. 

If flow occurred in an open channel with no particles or fibers and if there were no other mixing mechanisms, all particles would transit the same distance from beginning to end. In a packed bed, each time a molecule or atom encounters a particle or fiber it must go around it to continue on. It is analogous to encounter a tree in a field—one either walks around it to the right or the left and that is equivalent to flipping a coin. Some molecules will encounter more particles than others as illustrated in the following scheme where each encounter causes a chance in direction and the path of a hypothetical molecule is traced by a line (Scheme 1). 

The fastest HPLC separations are achieved using the maximum available pressure drop. Using reduced variables, Equation 9.6 illustrates a linear relationship between retention time and mobile phase viscosity for packed columns and fixed values of AP (pressure drop), Areq (required efficiency for a given separation) and (a constant that describes the permeability of the packed bed) [4]... 

When authors illustrate the subject of thermochemical conversion of solid fuels in the literature, the conversion zone in a packed bed is divided into different process zones (drying zone, pyrolysis zone, char combustion zone, and char gasification zone), one for each thermochemical conversion process. The spatial order of this process zones is herein referred to as the bed process structure or conversion process structure. The conversion process structure is a function of conversion concept. Even more important, the bed process structure can only exist in the diffusion controlled conversion regime when the conversion zone has a significant thickness. 

In order to illustrate this approach, we next consider the optimization of an ammonia synthesis reactor. Formulation of the reactor optimization problem includes the discretized modeling equations for a packed bed reactor, along with the set of knot placement constraints. The following case study illustrates how a differential-algebraic problem can be optimized efficiently using (27). In addition, suitable accuracy of the ODE model can be obtained at the optimum by directly enforcing error restrictions and adaptively adding elements. Finally, bounds on the continuous state profiles can be enforced directly in the optimization problem. 

Hollow cylindrical catalyst pellets are sometimes employed in commercial chemical reactors in order to avoid excessive pressure drops across a packed bed of catalyst. A more complex expression for the effectiveness factor is obtained for such geometry. This case was first discussed by Gunn [4]. Figure 2 illustrates the effectiveness factor curves obtained for the slab, sphere and cylinder. 

We shall first discuss the dispersion and backmixing models which adequately characterize flow in tubular and packed-bed systems then we shall consider combined models which are used for more complex situations. In connection with the various applications, the direct use of the age-distribution function for linear kinetics will also be illustrated. 

Equation (57) applies to material transport in tubes and yields an average deviation of 9.5% from the experimental data. An expression of similar form yielded an average deviation of 14.8% for the thermal transport. The ratio of thermal to material transport was found to be 1.09 with an average deviation of 13.7% (S3). Somewhat better agreement with predicted behavior was encountered for the studies on packed beds (S2). These data serve to illustrate the uncertainties which presently exist in the prediction of simultaneous material and thermal transfer under a variety of conditions. Satterfield s work has made a distinct contribution to understanding the macroscopic influences of combined thermal and material transport. Some of the discrepancy he noted may relate to assumptions concerning the nature of the chemical reaction associated with the decomposition of hydrogen peroxide. 

The most common method of whole broth adsorption with particulate matrices is by fluidizing the particles. Development of a stable fluidized bed with an increased interstitial volume is the key to the purification of biomass-containing feedstocks in this set-up. Two possible modes of protein adsorption can be realized The feed can be applied in a frontal mode as in packed bed chromatography or the column effluent can be recyled, leading to a situation comparable to a batch adsorption in a stirred tank. Frontal and single stage recirculating modes are illustrated in Fig. 2. 

For a gas-solid system, pg is negligibly small compared to (—dp/dH). Consequently, dpd/dH can be approximated by dp/dH. The relationship of pressure drop through the bed, Apb, and superficial gas velocity U for fluidization with uniform particles is illustrated in Fig. 9.5. In the figure, as U increases in the packed bed, Apb increases, reaches a peak, and then drops to a constant. As U decreases from the constant Apb, Apb follows a different path without passing through the peak. The peak under which the bed is operated is denoted the minimum fluidization condition, and its corresponding superficial gas velocity is defined as the minimum fluidization velocity, Umf. 

Baxendale et al. (2008) reported a bifurcated approach to the synthesis of thiazoles and imidazoles by coupling a glass microreactor and a packed-bed reactor to achieve a base-mediated condensation reaction. As Scheme 32 illustrates, reactions focused on the use of ethyl isocyanoacetate 123, as the cyanide source, with variations made via the isothiocyanate reagent, as illustrated in Table 13. 

The three principal reactor types employed in coal gasifier design are the moving packed bed, the entrained flow, and the fluidized bed reactor. In the discussion of gasification principles the moving packed bed (Fig. 3) was used to illustrate steam-oxygen or steam-air gasification of coal. 

H0 height of the packed bed. (B) Illustration of the adsorption step (left) in expanded bed mode, and elution (right) in packed bed mode. 

Equation 1.32 for the region close to the wall is illustrated in Fig. 1.6. The flow velocity is maximal at the plane of shear and then decays quickly as we move away from the wall. This should not be surprising as in a column packed with uncharged particles, EOF is generated at the tube wall and the interior of the tube contributes only the drag resistance. It should be noted that the flow velocity falls significantly as soon as we move a distance of one particle diameter away from the column wall. Previous experimental studies on packed beds that have been published in the literature support these findings [55]. 

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