In packed bed reactors

They convert the initial value problem into a two-point boundary value problem in the axial direction. Applying the method of lines gives a set of ODEs that can be solved using the reverse shooting method developed in Section 9.5. See also Appendix 8.3. However, axial dispersion is usually negligible compared with radial dispersion in packed-bed reactors. Perhaps more to the point, uncertainties in the value for will usually overwhelm any possible contribution of D. ... 

The modeling of mass transport in packed bed reactors applies the theory of dispersion [32]. The conservation of mass for the average concentration [Pg.515]

In Chapter 11, we indicated that deviations from plug flow behavior could be quantified in terms of a dispersion parameter that lumped together the effects of molecular diffusion and eddy dif-fusivity. A similar dispersion parameter is usefl to characterize transport in the radial direction, and these two parameters can be used to describe radial and axial transport of matter in packed bed reactors. In packed beds, the dispersion results not only from ordinary molecular diffusion and the turbulence that exists in the absence of packing, but also from lateral deflections and mixing arising from the presence of the catalyst pellets. These effects are the dominant contributors to radial transport at the Reynolds numbers normally employed in commercial reactors. 

The general question of whether or not plug flow can be attained is discussed in Volume 3, Section 1.7. (Tubular Reactors) and the special case of Plug-Flow (Fermenters) is considered in Chapter 5, Section 5.11.3. A more detailed consideration of dispersion in packed bed reactors and those effects which enhance and invalidate plug flow is given in Chapter 3, Section 3.6.1. 

Numerical Solution Techniques for Partial Differential Equations Arising in Packed Bed Reactor Modeling... 

In packed-bed reactors, the catalyst is fully wetted, whereas the heat and mass transfer efficiency is higher than that observed in trickle-bed reactors. However, low operation efficiency may appear due to backmixing of the liquid phase. Moreover, high liquid-phase residence times can result in the occurrence of homogeneous side reactions. 

E.U. Schlunder, Transport phenomena in packed bed reactors, in Chemical Reactor Engineering Reviews—Houston, ACS Symposium 72, American Chemical Society, Washington, DC, 1978. 

McGreavy and THORNTON(23) have developed an alternative approach to the problem of identifying such regions of unique and multiple solutions in packed bed reactors. Recognising that the resistance to heat transfer is probably due to a thin gas film surrounding the particle, but that the resistance to mass transfer is within the porous solid, they solved the mass and heat balance equations for a pellet with modified boundary conditions. Thus the heat balance for the pellet represented by equation 3.24 was replaced by ... 

The importance of dispersion and its influence on flow pattern and conversion in homogeneous reactors has already been studied in Chapter 2. The role of dispersion, both axial and radial, in packed bed reactors will now be considered. A general account of the nature of dispersion in packed beds, together with details of experimental results and their correlation, has already been given in Volume 2, Chapter 4. Those features which have a significant effect on the behaviour of packed bed reactors will now be summarised. The equation for the material balance in a reactor will then be obtained for the case where plug flow conditions are modified by the effects of axial dispersion. Following this, the effect of simultaneous axial and radial dispersion on the non-isothermal operation of a packed bed reactor will be discussed. 

The axial dispersion model also gives a good representation of fluid mixing in packed-bed reactors. Figure 8-34 depicts the correlation for flow of fluids in packed beds. 

The fluidized bed reactor has been used for phenol removal instead of fixed bed as most of the products formed are insoluble. The operation in packed bed reactors would lead to clogging phenomena and undesirable pressure drop [47, 88]. When deactivation of biocatalysts occurs and regeneration is needed, the liquid-solid circulating fluidized bed is a worthy alternative, as demonstrated for phenol polymerization [89]. The continuous enzymatic polymerization was carried out in a riser section and a downcomer was used for the regeneration of the coated immobilized particles. 

In packed bed reactors the solid catalyst is held stationary by plates at the top and bottom of the bed. In contrast, in fluidized bed reactors, the catalyst bed is relatively loosely packed, and there is no plate at the top. Rapid fluid flow from the bottom raises the bed and ensures good mixing, leading to insignificant temperature or concentration gradients. However, due to high fluid velocity some catalyst carryover is common. 

The first three types (pellets, extrudates and granules) are primarily used in packed bed operations. Usually two factors (the diffusion resistance within the porous structure and the pressure drop over the bed) determine the size and shape of the particles. In packed bed reactors, cooled or heated through the tube wall, radial heat transfer and heat transfer from the wall to the bed becomes important too. For rapid, highly exothermic and endothermic reactions (oxidation and hydrogenation reactions, such as the ox-... 

Hie most commonly found shape of catalyst particle today is the hollow cylinder. One reason is the convenience of manufacture. In addition there are often a number of distinct process advantages in the use of ring-shaped particles, the most important being enhancement of the chemical reaction under conditions of diffusion control, the larger transverse mixing in packed bed reactors, and the possible significant reduction in pressure drop. It is remarkable (as discussed later) that the last advantage may even take the form of reduced pressure losses and an increased chemical reaction rate per unit reactor volume [11]. 

With this definition, for spheres, the use of Equation 8.39 gives just the diameter of sphere. Expressions of equivalent diameters for different particle shapes as used in packed bed reactors are presented in Table 8.1. ... 

In the third type of gas-liquid-solid reaction, only two of the three phases take part into the reaction, the third phase being an inert phase. This type of reaction can be further subdivided into three catagories. Some reactions are strictly gas liquid reactions, but they are often carried out in packed-bed reactors operating under countercurrent-flow conditions. Here, the solid imparts momentum transfer and allows better gas-liquid contact and gas-liquid interfacial mass... 

The packed bed reactors section of this volume presents topics of catalyst deactivation and radial flow reactors, along with numerical techniques for solving the differential mass and energy balances in packed bed reactors. The advantages and limitations of various models (e.g., pseudo-homogeneous vs. heterogeneous) used to describe packed bed reactors are also presented in this section. 

Reactants and products must diffuse through high-molecular-weight liquid hydrocarbons during FT synthesis. The liquid phase may be confined to the mesoporous structure within catalyst pellets or extend to the outer surface and the interstitial spaces between pellets, depending on the reactor design and hydrodynamic properties. In packed-bed reactors, the characteristic diffusion distance equals the radius of the pellets plus the thickness of any liquid boundary layer surrounding them. Intrapellet diffusion usually becomes... 

The effects of diffusional restrictions on the activity and selectivity of FT synthesis processes have been widely studied (32,52,56-60). Intrapellet diffusion limitations are common in packed-bed reactors because heat transfer and pressure-drop considerations require the use of relatively large particles. Bubble columns typically use much smaller pellets, and FT synthesis rates and selectivity are more likely to be influenced by the rate of mass transfer across the gas-liquid interface as a gas bubble traverses the reactor (59,61,62). 

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