Dispersion in fixed beds

A correlation developed by Chung and Wen (23) for dispersion in fixed beds was used to estimate the dispersion coefficient Dm ... 

Figure 3.14 Axial dispersion in fixed-bed reactors (a) iiquid flow and (b) gas flow [6]. Gray area represents experimental results. (Adapted from [6], Figure 27.24 Copyright 2012, Wiley-VCH GmbH Co. KGaA.)...

Gunn DJ, Pryce C. Dispersion in fixed beds. Transactions of the Institution of Chemical Engineers 1969 47 t341-t350. 

Gunn DJ. Axial and radial dispersion in fixed beds. Chemical Engineering Science 1987 42 363-373. 

Criteria used to Exclude a Significant Influence of Dispersion in Fixed Bed Reactors... 

Examination of the criteria for significant dispersion in fixed bed reactors shows that in practical cases of fixed bed reactor modeling, axial dispersion of mass and heat as well as radial dispersion of mass are negligible, which should be proven by the criteria summarized in Table 4.10.8. Then the mass and heat balance equations (4.10.125) and (4.10.126) simplify to ... 

Equations (4.10.195) and (4.10.194) can now be compared with the estimations given in Section 4.10.6.4 for the dispersion in fixed beds. According to Eigure 4.10.60 in combination with the assumption of the analogy of dispersion of mass and heat, the radial Peclet number is approximately 10 for high RCp numbers. Thus we get ... 

Unlike the diffusion in catalyst pellets, molecular as well as eddy (turbulent) diffusion causes the mass dispersion in fixed-beds. The effective molecular diffusivity may be obtained by simply multiplying the gas molecular diffusivity by the factor s/k, where the tortuosity factor k is often taken as 1.5. The theory on eddy diffusivity is not well established. Therefore, the effective diffusivities are often correlated in the following form ... 

Most methods of separating molecules in solution use direct contact of immiscible fluids or a sohd and a fluid. These methods are helped by dispersion of one phase in the other, fluid phase, but they are hindered by the necessity for separating the dispersed phase. Fixed-bed adsorption processes overcome the hindrance by immobilizing the solid adsorbent, but at the cost of cyclic batch operation. Membrane processes trade direct contact for permanent separation of the two phases and offer possibilities for high selectivity. 

Kjaer (K9) gives a very comprehensive study of concentration and temperature profiles in fixed-bed catalytic reactors. Both theoretical and experimental work is reported for a phthallic anhydride reactor and various types of ammonia converters. Fair agreement was obtained, but due to the lack of sufficiently accurate thermodynamic and kinetic data, definite conclusions as to the suitability of the dispersed plug flow model could not be reached. However, the results seemed to indicate that the... 

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. 

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. 

Although the hydrogenation activity of metal sulfides is lower by several orders of magnitude than that of metal catalysts, sulfides allow operations under conditions that are impractical for metals. They are generally used as highly dispersed materials on a high surface area support, such as y-alumina, in fixed bed operation. Most important is catalyst design to minimize deactivation due to the deposition of metals (V, Ni) in the feed and of coke at the mouths of the pores. Metal sulfides can also be used as finely dispersed phases in continuous slurry reactors to reduce the mass transport limitations of heavy oils. 

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. ... 

In fixed-bed operation, in addition to the two-step mass transport mechanism, advection and dispersion play key roles in ion exchange. These factors must be considered. As influent concentration is assumed low, solution velocity can be considered constant. If pore diffusion is an important factor in the ion uptake, the following equations can be used. Similar expressions for surface diffusion can be obtained ... 

The bulk diffusion coefficient of lipase was estimated [55]. The dispersion coefficient is used to characterize the axial dispersion in a packed bed. This parameter accounts for the dispersion due to molecular diffusion as well as eddy diffusion due to velocity differences around the particles. A correlation used to estimate the dispersion coefficient Dm in fixed beds was developed by Chung and Wen [56]. 

The principal aspect that reflects flow distribution in fixed beds is dispersion. Flow through a packed bed is commonly represented by dispersed plug flow in which all mechanisms contributing to mixing are lumped together in effective dispersion coefficients, and A model analogous to Pick s law, as given by Equation (14.15), is applicable ... 

Radial dispersion of mass and heat in fixed bed gas-solid catalytic reactors is usually expressed by radial Peclet number for mass and heat transport. In many cases radial dispersion is negligible if the reactor is adiabatic because there is then no driving force for long range gradients to exist in the radial direction. For non-adiabatic reactors, the heat transfer coeflScient at the wall between the reaction mixture and the cooling medium needs also to be specified. 

Non-linear two point boundary value differential equations arise in fixed bed catalytic reactors mainly in connection with the diffusion and reaction in porous catalyst pellets. It may also arise in the modelling of axial and radial dispersion in the catalyst bed. In addition they also arise in cases of counter-current cooling or heating of the reactor. For this last case, the use of a shooting technique with an iterative procedure similar to the Newton method (Fox s method) seems to be the easiest and most straightforward technique (Kubicek and Hlavacek, 1983). 

The anponent in (10.10-4) is also equal to (-ybW/lff). When beckoiixing and axial dispersion occur (I -S ) will be less than (l — S ). In the usual Re, mages encountered in fixed-bed extractions t can be estimated by using the following equations 7... 

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