Fixed beds axial dispersion

Determination of Controlling Rate Factor The most important physical variables determining the controlhng dispersion factor are particle size and structure, flow rate, fluid- and solid-phase diffu-sivities, partition ratio, and fluid viscosity. When multiple resistances and axial dispersion can potentially affect the rate, the spreading of a concentration wave in a fixed bed can be represented approximately... 

Thrust, 4 Trickle-flow, 79 fixed-bed, 90-104 holdup and axial dispersion gas phase, 92-94 liquid phase, 94-102... 

When a number of competing reactions are involved in a process, and/or when the desired product is obtained at an intermediate stage of a reaction, it is important to keep the residence-time distribution in a reactor as narrow as possible. Usually, a broadening of the residence-time distribution results in a decrease in selectivity for the desired product. Hence, in addition to the pressure drop, the width of the residence-time distribution is an important figure characterizing the performance of a reactor. In order to estimate the axial dispersion in the fixed-bed reactor, the model of Doraiswamy and Sharma was used [117]. This model proposes a relationship between the dispersive Peclet number ... 

D. Tang, A. Jess, X. Ren, B. Blumich, S. Stapf 2004, (Axial dispersion and wall effects in narrow fixed bed reactors — a comparative study based on RTD- and NMR-measurements), Chem. Eng. Tech-nol. 27, 866. 

Figure 3.35 Axial dispersion in liquid-solid fixed beds (for e = 0.45 and Sc = 1000). Average value is estimated by data given by Levenspiel (1972).

Gas-solid fixed beds For axial dispersion in gas-solid fixed beds, the Edwards-Richardson correlation can be used (Wen and Fan, 1975 Andrigo et al., 1999). 

If the radial diffusion or radial eddy transport mechanisms considered above are insufficient to smear out any radial concentration differences, then the simple dispersed plug-flow model becomes inadequate to describe the system. It is then necessary to develop a mathematical model for simultaneous radial and axial dispersion incorporating both radial and axial dispersion coefficients. This is especially important for fixed bed catalytic reactors and packed beds generally (see Volume 2, Chapter 4). 

Having pointed out the modifications to be made to a design based upon the plug flow approach, it is salutary to note that axial dispersion is seldom of importance in fixed bed tubular reactors. This point is illustrated in Example 3.8. 

Other factors limiting the overall rate can be external or internal mass transfer, or axial dispersion in a fixed-bed reactor. Pertinent dimensionless numbers are the Biot number Bi, the Damkohler number of the second kind Dan, or the Bodenstein number Bo (Eqs. (5.46)—(5.48)]. 

Potential pitfalls exist in ranking catalysts based solely on correlations of laboratory tests (MAT or FFB) to riser performance when catalysts decay at significantly different rates. Weekman first pointed out the erroneous conversion ranking of decaying catalysts in fixed bed and moving bed isothermal reactors (1-3). Phenomena such as axial dispersion in the FFB reactor, the nonisothermal nature of the MAT test, and feedstock differences further complicate the catalyst characterization. In addition, differences between REY, USY and RE-USY catalyst types exist due to differences in coke deactivation rates, heats of reaction, activation energies and intrinsic activities. 

Fixed-bed reactors may exhibit axial dispersion. If axial dispersion is important for reactor simulation, analysis, or design, a variant of the one-dimensional homogeneous model that contains an axial dispersion term may be used. Approximate criteria to determine if mass and heat axial dispersion have to be considered are available (see, e.g., Froment and Bischoff, Chemical Reactor Analysis and Design, Wiley, 1990). 

In the vast majority of experimental studies, the backmixing characteristics of a flowing phase are examined using a -pulse tracer input. For the fixed-bed systems shown in Fig. 3-2, if a perfect pulse input is used, then, as shown by Levenspiel,5 6 the axial dispersion coefficient or the Peclet number can be obtained from the variance of the RTD curve. For example, for a closed system and large extent of dispersion, the variance, it, is related to the Peclet number by the equation... 

The third and fourth condition are fulfilled by Tarhan [25]. Axial dispersion is fundamentally local backmixing of reactants and products in the axial, or longitudinal direction in the small interstices of the packed bed, which is due to molecular diffusion, convection, and turbulence. Axial dispersion has been shown to be negligible in fixed-bed gas reactors. The fourth condition (no radial dispersion) can be met if the flow pattern through the bed already meets the second condition. If the flow velocity in the axial direction is constant through the entire cross section and if the reactor is well insulated (first condition), there can be no radial dispersion to speak of in gas reactors. Thus, the one-dimensional adiabatic reactor model may be actualized without great difficulties. ... 

An analysis is made of the factors which pose a limit to representative downscaling of catalyst testing in continuous fixed-bed reactors operated with either gas or gas-liquid flow. Main limiting factors are the axial dispersion and, in the case of gas-liquid operation, also the contacting of the catalyst. The effects of catalyst and reactor geometries are quantified, and boundaries for safe operation are indicated. 

Consider a tubular fixed-bed reactor accomplishing a highly exothermic gas-phase reaction. Assuming that axial dispersion can be neglected, the mass and energy balances can be written as follows and allow for radial gradients ... 

Insufficient bed compression, which leads to void volumes at the column inlet, is another source of axial dispersion. Preparative columns should therefore always exhibit a possibility for adjusting the compression of the packed bed. Fixed bed-length columns are not very stable at inner diameters >20 mm. 

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