Dynamic holdup, mass transfer

In general, it can be concluded that substantial progresses have been made in the experimental and theoretical analysis of trickle-bed reactors under unsteady-state conditions. But until now these results are not sufficient for a priori design and scale-up of a periodically operated trickle-bed reactor. The mathematical reactor models, which are now available are not detailed enough to simulate all of the main transient behavior observed. For solving this problem specific correlations for specific model parameters (e.g. Hquid holdup, mass transfer gas-solid and liquid-solid, intrinsic chemical kinetic, etc.) determined under dynamic conditions are required. The available correlations for important hydrodynamic, mass-and heat-transfer parameters for periodically operated trickle-bed reactors leave a lot to be desired. Indeed, work for unsteady-state conditions on a larger scale may also be necessary. 

In concurrent downward-flow trickle beds of 1 meter in height and with diameters of respectively 5, 10 and 20 cm, filled with different types of packing material, gas-continuous as well as pulsing flow was realized. Residence time distribution measurements gave information about the liquid holdup, its two composing parts the dynamic and stagnant holdup and the mass transfer rate between the two. 

Relations of the rate of mass transfer between gas and liquid and the influence of the stagnant and dynamic holdup were not researched intensively, until the present work, although papers on the general subject have been presented (3-6). Lately an interesting paper about mass transfer from liquid to solid in pulsing flow was presented by Luss and co-workers (7 ). 

Mass transfer between stagnant and dynamic holdup... 

Residence time distribution measurements, together with a theoretical model, provide a method to calculate the rate of mass transfer between the liquid flowing through the column, the dynamic holdup, and the stagnant pockets of liquid in between the particles. We have chosen the cross flow model (10). It has to be noted that the model starts from the assumption that the flow pattern has a steady-state character, which is in conflict with reality. Nevertheless, average values of the number of mass transfer units can be calculated as well as the part of the liquid being in the stagnant situation. 

The following developments will be restricted to laminar liquid flow with weak gas-liquid interactions. However, this is not a limitation of the proposed methodology which could be easily applied to any other flow regime. Applications will be presented for the modelling of the irrigation rate, the dynamic liquid holdup and the apparent reaction rate in the absence of external mass transfer limitations and in the case of non volatile liquid reactants (i.e. approximatively the operating conditions of petroleum hydrotreatment). 

For a good dynamic simulation, the designer must specify the actual control system from the piping and instrumentation diagram (see Chapter 5) and also all of the vessel designs so that holdups can be calculated. Mass transfer rates and reaction rates must also be known or assumed. 

Note that all these correlations (mass transfer, gas holdup, and dynamic pressure drop) are valid only within the following operating ranges ... 

A further advantage of absorption plus reaction is the increase in the mass-transfer coefficient. Some of this increase comes from a greater effective interfacial area, since absorption can now take place in the nearly stagnant regions (static holdup) as well as in the dynamic liquid holdup. For NHj absorption in H2SO4 solutions, K a was 1.5 to 2 times the value for absorption in water.Since the gas-film resistance is controlling, this effect must be due mainly to an increase in effective area. The values of K a for NH3 absorption in acid solutions were about the same as those for vaporization of water, where all the interfacial area is also expected to be effective. The factors and... 

The time-averaged velocities and gas holdups in the compartments, as well as the fluid interactions between the zones, are first calculated by computational fluid dynamics (CFD). Then, balance equations for heat and mass transfer and for chemical reactions are evaluated and solved using appropriate software. First results from a simulation of a cumene oxidation reactor on an industrial scale were impressive, as they matched real temperature and concentration fields. 

The distribntor effect can be quite significant such that the gas-liquid mass transfer correlation can vary by up to a factor of 2 (Lau et al., 2004). The extent to which the gas distributor affects gas holdup and bubble dynamics depends on the BC geometry and snperficial gas velocity. The taller the column is, the smaller the influence of the initial bubble diameter will be on the global gas holdup. A higher superficial gas velocity increases the probability and frequency of bubble collisions and decreases the effect of the initial bubble diameter and gas distributor design. 

This review deals mainly with the discussion of various macroscopic hydro-dynamic, heat, and mass transfer characteristics of bubble columns, with occasional reference to the analogous processes in modified versions of bubble columns with a variety of internals. The hydrodynamic considerations include determination of parameters like flow patterns, holdup, mixing, liquid circulation velocities, axial dispersion coefficient, etc., which all exert strong influence on the resulting rates of heat and mass transfer and chemical reactions carried out in bubble columns. Different correlations developed for estimating the aforementioned parameters are presented and discussed in this chapter. 

Bubble dynamics and characteristics discussed above determine the hydrodynamic and heat and mass transfer behaviors in three-phase fluidization systems, which is important for better design and operation of three-phase fluidized beds. In this section, various hydrodynamic variables and transfer properties in three-phase systems are discussed. Specifically, areas discussed in the hydrodynamics section are minimum fluidization, bed contraction and moving packed bed phenomenon, flow regime transition, overall gas holdup and hydro-dynamic similarity, and bubble size distribution and the dominant role of larger bubbles. Later in this section, important topics covering transport phenomena will be discussed, which include heat and mass transfer and phase mixing. 

It is still common practice to estimate the fluid dynamic properties from empirical correlations. Such correlations are usually developed from "cold flow" measurements which are often not properly designed and evaluated. It is understood that use of empirical correlations is of limited value and their predictions may lead to serious errors. This is particularly valid for those quantities which characterize interfacial properties like mass transfer coefficients, interfacial areas and phase holdups. It is now obvious that properties like density, viscosity, and surface tension are not always sufficient to describe fluid dynamic and interfacial phenomena. 

The normal distillation models assume instantaneous heat transfer in the condenser and reboiler, and the normal default heat-transfer option is Direct Q. The basic model does not accurately represent the short-term rapid dynamic response under sevCTe conditions because the capacitance (holdup) of material and mass of equipment metal in the reboiler and condenser heat exchangers are not considered. 

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