Packings flow regimes

Note that the abscissa in Figure 2.4 starts at a value of 0.4, which corresponds to the voidage of a randomly packed bed. Equation 2.44 is valid for the extremes of flow regimes but strictly requires correction for the intermediate case (Khan and Richardson, 1990 Di Felice, 1994). 

In deriving expressions for the packed bed friction factor, three separate flow regimes are normally considered (see Figure 2.11) as follows. 

Very refined measurements at various positions of the packed bed were made by Jolls and Hanratty (J6), who used an active sphere (electrode) in a packed bed consisting of 1-inch inert spheres. The overall mass-transfer data for the turbulent flow regime suggest a dependence of... 

C. Packed Bed CFD Simulation Issues 1. Packed Bed Flow Regimes... 

The research on the flow regimes in packed tubes suggests that laminar flow CFD simulations should be reasonable for Re <100 approximately, and turbulent simulations for Re >600, also approximately. Just as RANS models provide steady solutions that are regarded as time averages of the real time-dependent turbulent flow, it may be suggested that CFD simulations in the unsteady laminar inertial range 100 time-averaged picture of the flow field. As with wall functions, comparisons with experimental data and an improved assessment of what information is really needed from the simulations will inform us as to how to proceed in these areas. 

The value of the permeability coefficient is frequently used to give an indication of the ease with which a fluid will flow through a bed of particles or a filter medium. Some values of B for various packings, taken from Eisenklam(2), are shown in Table 4.1, and it can be seen that B can vary over a wide range of values. It should be noted that these values of B apply only to the laminar flow regime. 

By hydrodynamics, we mean the movements of L and G phases through the S packing or with the S particles inside the reactor it deals with " firstly the flow regime... 

For the fluidized bed process the bed expansion as a consequence of an increase in linear flow rate has to be considered. In a simplified picture diffusive transport takes place in a boundary layer around the matrix particle which is frequently renewed, this frequency being dependent on velocity and voidage, as long as convective effects, e.g. the movement of particles are neglected. Rowe [74] has included these considerations into his correlation for kf in fluidized beds, which is applicable for a wide range of Reynolds numbers, including the laminar flow regime where fluidized bed adsorption of proteins takes place (Eq. 19). The exponent m is set to 1 for a liquid fluidized bed, a represents the proportionality factor in the correlation for packed beds (Eq. 18) and is assumed as 1.45. 

In the absence of suspended solutes or colloids, the pure solvent flux through an ultrafiltration membrane is directly proportional to the applied pressure difference and inversely proportional to the viscosity of the solvent and the membrane thickness. Transport within the pores occurs in the creeping flow regime, since kinematic viscosities of liquids are sufficient to make Re < C 1 for practical pore sizes. In the simplest case, the membrane can be considered to be a packed array of straight, equal diameter nonintersecting capillary tubes. The observed volumetric flux, nAvA (cc/sec cm2), equals the product of the mass flux of solvent based on the total membrane area, nA... 

CSTR for most reactions. These conditions are best met for short residence times where velocity profiles in the tubes can be maintained in the turbulent flow regime. In an empty tube this requires high flow rates for packed columns the flow rates need not be as high. Noncatalytic reactions performed in PFRs include high-pressure polymerization of ethylene and naphtha conversion to ethylene. A gas-liquid noncatalytic PFR is used for adipinic nitrile production. A gas-solid PFR is a packed-bed reactor (Section IV). An example of a noncatalytic gas-solid PFR is the convertor for steel production. Catalytic PFRs are used for sulfur dioxide combustion and ammonia synthesis. 

A number of flow regime maps are available for packed bubble columns [see, e.g., Fukushima and Lusaka, J. Chem. Eng. Japan, 12 296 (1979)]. Correlations for the various hydrodynamic parameters can be found in Shah (Gas-Liquid-Solid Reactor Design, McGraw-Hill, 1979), Ramachandran and Chaudhari (Three-Phase Catalytic Reactors, Gordon and Breach, 1983), and Shah and Sharma [Gas-Liquid-Solid Reactors in Carberry and Varma (eds.), Chemical Reaction and Reactor Engineering, Marcel Dekker, 1987]. 

It is shown, that the performance of a pulsing packed column can be split up into its two component parts, the pulses and the zones in between pulses. The pulses can be described as parts of the bed already in the dispersed bubble flow regime the zones-in between the pulses as parts of the bed still in the gas-continuous regime. The pulse frequency is linearly dependent upon the real liquid velocity. The properties of the pulse, like holdup, velocity and height are quite independent upon all the parameters except gas flow rate. 

S.2 Packing Hydraulics 8.2.1 Pressure drop flow regimes... 

In slurry reactors, an attempt is made to realize intensive and intimate contact between a gas-phase component, usually to be dissolved in the liquid phase, a liquid-phase component and a finely dispersed solid. In this respect, slurry reactors are related to packed-bed reactors with the various gas/liquid flow regimes that can be realized (such as trickle flow, pulsed flow and dispersed bubble flow). Also, there is much similarity with three-phase fluidized beds. 

A more detailed explanation about the use of tracer methods to evaluate contacting efficiency, the relationships needed to interpret tracer response data, the experimental methodology, and various results are given by Mills and Dudukovic (41). It suffices to say here that the following correlations based upon Reynolds and Galileo numbers were determined by El-Hisnawi to represent the available data on small porous packings in the trickle-flow regime ... 

It is worth emphasizing that Eqs. (13-61) to (13-68) hold regardless of the models used to calculate the interphase transport rates and EJ. With a mechanistic model of sufficient complexity it is possible, at least in principle, to account for mass transfer from bubbles in the froth on a tray as well as to entrained droplets in a spray, as well as transport between the phases flowing over and through the elements of packing in a packed column. However, a completely comprehensive model for estimating mass-transfer rates in all the possible flow regimes does not exist at present, and simpler approaches are used. 

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