Packed beds stagnant fluid

We further mention that at low values of the Reynolds number (that is at very low fluid velocities or for very small particles) for flow through packed beds the Sherwood number for the mass transfer can become lower than Sh = 2, found for a single particle stagnant relative to the fluid [5]. We refer to the relevant papers. For the practice of catalytic reactors this is not of interest at too low velocities the danger of particle runaway (see Section 4.3) becomes too large and this should be avoided, for very small particles suspension or fluid bed reactors have to be applied instead of packed beds. For small particles in large packed beds the pressure drop become prohibitive. Only for fluid bed reactors, like in catalytic cracking, may Sh approach a value of 2. 

Individual adsorbent particles within a packed bed are surrounded by a boundary layer, which is looked upon as a stagnant liquid film of the fluid phase. The thickness of the film depends on the fluid distribution in the bulk phase of the packed bed. 

One of the most important cases is when there are two (or more) distinct regions within the reactor. This might be a packed bed of porous solids, two fluid phases, partially stagnant regions, or other complicated flows through a vessel that can basically be described by an axial dispersion type model. Transport balances can be made for each phase, per unit reactor volume ... 

In Chapter 2, the design of the so-called ideal reactors was discussed. The reactor ideahty was based on defined hydrodynamic behavior. We had assumedtwo flow patterns plug flow (piston type) where axial dispersion is excluded and completely mixed flow achieved in ideal stirred tank reactors. These flow patterns are often used for reactor design because the mass and heat balances are relatively simple to treat. But real equipment often deviates from that of the ideal flow pattern. In tubular reactors radial velocity and concentration profiles may develop in laminar flow. In turbulent flow, velocity fluctuations can lead to an axial dispersion. In catalytic packed bed reactors, irregular flow with the formation of channels may occur while stagnant fluid zones (dead zones) may develop in other parts of the reactor. Incompletely mixed zones and thus inhomogeneity can also be observed in CSTR, especially in the cases of viscous media. 

Happel (1958) introduced the interesting concept of a stagnant voidage, a part of the voidage in the packed bed that is occupied by the wake of the particles and is thus not available for the fluid flow. The concept is primarily employed in the discrete particle model but may be useful for other modeling effort. 

For the mass transfer coefficient in a stagnant fluid system, 5A,ug = 2 is used in the case of mass transfer from a single particle. In multi-particle systems such as packed beds, however, Shmg takes a different value for the reason noted in Chapter S, and is given as a function of void fraction in the packed bed, c, as shown in Fig. 5.11 (Suzuki,... 

Here 3 is the fraction of fluid volume that is stagnant and Pe = Re Sc. Perturbation theory has been applied to the fundamental equations for fluid flow in packed beds in order to generate the axial and radial dispersion coefficients. A recent study (101) suggests the following value for the dispersion coefficients at large Peclet numbers ... 

ETC is an important parameter describing the thermal behavior of packed beds with a stagnant or dynamic fluid and has been extensively investigated experimentally and theoretically in the past. Various mathematical models, including continumn models and microscopic models, have been proposed to help solve this problem, but they are often limited by the homogeneity assumption in a continuum model (Wakao and Kaguei, 1982 Zehner and Schliinder, 1970) or the simple assumptions in a microscopic model... 

Glaser and Litt (G4) have proposed, in an extension of the above study, a model for gas-liquid flow through a b d of porous particles. The bed is assumed to consist of two basic structures which influence the fluid flow patterns (1) Void channels external to the packing, with which are associated dead-ended pockets that can hold stagnant pools of liquid and (2) pore channels and pockets, i.e., continuous and dead-ended pockets in the interior of the particles. On this basis, a theoretical model of liquid-phase dispersion in mixed-phase flow is developed. The model uses three bed parameters for the description of axial dispersion (1) Dispersion due to the mixing of streams from various channels of different residence times (2) dispersion from axial diffusion in the void channels and (3) dispersion from diffusion into the pores. The model is not applicable to turbulent flow nor to such low flow rates that molecular diffusion is comparable to Taylor diffusion. The latter region is unlikely to be of practical interest. The model predicts that the reciprocal Peclet number should be directly proportional to nominal liquid velocity, a prediction that has been confirmed by a few determinations of residence-time distribution for a wax desulfurization pilot reactor of 1-in. diameter packed with 10-14 mesh particles. 

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