Flow with a Stationary Bed

Fi = Is the Durand factor based on grain size and volume concentration 1 3 = the critical transition velocity between flow with a stationary bed and a heterogeneous flow... 

Velocity of the upper layer in the two-layer model of Shook and Roco Velocity for which flow with a stationary bed is started Velocity for which flow with a moving bed is started Deposition velocity or velocity above which solids start to move Velocity above which aU solids move as a pseudohomogeneous mixture Velocity at 50% stratification Wetted perimeter... 

One of the most common catalytic reactors is the fixed-bed type, in which the reaction mixture flows continuously through a tube filled with a stationary bed of catalyst pellets. Because of its importance, and because considerable information is available on its performance, most attention will be given to this reactor type. Fluidized-bed and slurry reactors are also considered later in the chapter. Some of the design methods given are applicable also to fluid-solid noncatalytic reactions. The global rate and integrated conversion-time relationships for noncatalytic gas-solid reactions will be considered in Chap. 14. 

In Reprint C in Chapter 7, the behavior of a tracer pulse in a stream flowing through a packed bed and exchanging heat or matter with the particles is studied. It is shown that the diffusion in the particles makes a contribution to the apparent dispersion coefficient that is proportional to v2 fi/D. The constant of proportionality has one part that is a function of the kinematic wave speed fi, but otherwise only a factor that depends on the shape of the particle (see p. 145 and in equation (42) ignore all except the last term and even the suffixes of this e, being unsuitable as special notation, will be replaced by A. e is defined in the middle of p. 143 of Chapter 7). In this equation, we should not be surprised to find a term of the same form as the Taylor dispersion coefficient, for it is diffusion across streams of different speeds that causes the dispersion in that case just as it is the diffusion into stationary particles that causes the dispersion in this.7 What is surprising is that the isothermal diffusion and reaction equation should come up, for A is defined by... 

Gel permeation chromatography (GPC) is essentially a process for the separation of polymer molecules according to their size. The separation occurs as the solute molecules in a flowing liquid move through a stationary bed of porous particles. The method has been used extensively in biochemistry to separate biological polymer molecules from small molecule contaminants (with the use of Sephadex column). Application of the method to synthetic polymer chemistry in the 1970s has revolutionized the procedures for polymer characterization and molecular weight determination. 

If shutdown occurs while pumping a heterogeneous slurry, solids will deposit in a stationary bed along the pipe bottom. To resume the operation of the slurry pipeline, it becomes necessary to resuspend these solids to remove them from the pipe. If the fluid flow rate over the settled solids is gradually increased, a response similar to curve A of Figure 1 is obtained. With increasing shear rate, the wall shear stress decreases until a minimum is reached. The fluid velocity that corresponds to this minimum shear stress is the critical resuspension velocity, Vs (7). 

In a packed or fixed-bed reactor, with both names used interchangeably, the reactants flow through catalysts that remain stationary. Typically, an area of the reactor tube of a PFR is filled with catalysts in the form of small pellets that are held in place in a stationary bed and can range in size from millimeters to centimeters. The reactants flow through this bed. If... 

For example, a hypothetical situation of a stationary bed filling half the pipe with all panicles above it flowing at (he same velocity is illustrated in Figure 2. 

This equation passes through a minimum which, for a small molecule and a well packed column, is found to occur at a value for h of about 2. For a conventional 4.6 mm i.d. column filled with a 5 micron reversed-phase packing in methanol/water mixtures the flow-rate of this minimum is about 0.5 ml/min, and v of the order 3—5. The A term describes the contribution to dispersion due to tortuous flow through a packed bed, and is a measure of how well the column is packed. The B term describes the effects of axial diffusion (in the direction of flow) on dispersion at normal flow-rates the influence of this term is relatively unimportant. The C term is concerned with the effects of slow equilibration between the mobile and stationary regions due to, for instance, the diffusion of solute into and out of the particle and the kinetics of adsorption and desorption. For a well packed column and a small solute A < I, B 2 and C S 0.1. 

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