Liquid deviation from plug flow

A few reactor models have recently been proposed (30-31) for prediction of integral trickle-bed reactor performance when the gaseous reactant is limiting. Common features or assumptions include i) gas-to-liquid and liquid-to-solid external mass transfer resistances are present, ii) internal particle diffusion resistance is present, iii) catalyst particles are completely externally and internally wetted, iv) gas solubility can be described by Henry s law, v) isothermal operation, vi) the axial-dispersion model can be used to describe deviations from plug-flow, and vii) the intrinsic reaction kinetics exhibit first-order behavior. A few others have used similar assumptions except were developed for nonlinear kinetics (27—28). Only in a couple of instances (7,13, 29) was incomplete external catalyst wetting accounted for. 

The parameters in the correlations were obtained using nonlinear parameter estimation software and by minimizing the sum of the relative errors between experimental and predicted conversions for the 2.5% Pd catalyst. A comparison between predicted and experimental values of conversion for both solvents is given in Figure 2. The agreement between the two is seen to be satisfactory except for hexane at the highest conversion where deviations of the liquid-phase from plug flow may influence the result. 

Axial Dispersion and the Peclet Niunber Peclet numbers are measures of deviation from plug flow. They may be calculated from residence time distributions found by tracer tests. Their values in trickle beds are Wi to Ve those of flow of liquid alone at the same Reynolds numbers. A correlation by Michell and Furzer (Chem. Eng. J, 4, 53 [1972]) is... 

Advantages of three-phase fluidized beds over trickle beds and other fixed bed systems are temperature uniformity, high heat transfer, ability to add and remove catalyst particles continuously, and limited mass transfer resistances (both external to the particles and bubbles, because of turbulence and limited bubble size, and inside the particles owing to relatively small particle diameters). Disadvantages include substantial axial dispersion (of gas, liquid, and particles), causing substantial deviations from plug flow, and lack of predictability because of the complex hydrodynamics. There are two major applications of gas-liquid-solid-fluidized beds biochemical processes and hydrocarbon processing. 

The dispersion coefficients Dq and Di are included to account for deviations from plug flow in both gas and liquid phases, as mentioned above. Equations (8-191) and (8-192) include all possibihties (or at least as many as we are willing to consider at this point), so we can now look at individual cases of interest by chipping away the particular parts that do not apply. 

The following two models are frequently used to account for partial macromixing the dispersion model and the tanks-in-series model. In the dispersion model, deviation from plug flow is expressed in terms of a dispersion or effective axial diffusion coefficient. This model was anticipated in Chapter 12, and the governing equations for mass and heat are listed in Table 12.2 of that chapter. The derivation is similar to that for plug flow except that now a term is included for diffusive flow in addition to that for bulk flow. This term appears as -D ( d[A]/d ), where is the effective axial diffusion coefficient. When the equation is nondimensionalized, the diffusion coefficient appears as part of the Peclet number defined as = itd/D. A number of correlations for predicting the Peclet number for both liquids and gases in fixed and fluidized beds are available and have been reviewed by Wen and Fan (1975). 

The main reason for the deficiencies of the present state of the art is, however, the maldistribution of gas and liquid in packed beds. Many studies reveal that there exist large deviations from plug flow of gas and in particular of hquid within the bed. (Hoek et al. 1986 Kammermaier 2008). The degree of maldistribution as well as its effect on mass transfer are unknown and, in turn, not accounted for in existing mass transfer models. Thus the pubhshed data for interfacial area and mass transfer coefficients comprise the maldistribution in an undefined manner. The data are not true but pseudo values which are not predictable within the plug flow model. 

Finally, it should be noted that more sophisticated models have been developed, either on a stagewise basis [62], similar to the Deans-Lapidus model for single phase fixed bed reactors, or on a stochastic respectively propabilistic basics [67,66]. Using data from laboratory and full-scale reactors, Schwarz and Roberts [44] have carried out parametric studies to evaluate the accuracy of the axial dispersion model. Their simulation showed that in case of first-order kinetics, dispersion in the liquid phase is frequently not of major importance. Deviations from plug flow become important only for short reactors and a high degree of conversion. 

One of the chief drawbacks of the fluid-bed reactor is deviation from plug flow. This is also a feature of other reactor types such as for gas-liquid... 

Discussion of the concepts and procedures involved in designing packed gas absorption systems shall first be confined to simple gas absorption processes without complications isothermal absorption of a solute from a mixture containing an inert gas into a nonvolatile solvent without chemical reaction. Gas and liquid are assumed to move through the packing in a plug-flow fashion. Deviations such as nonisothermal operation, multicomponent mass transfer effects, and departure from plug flow are treated in later sections. 

In a sparged reactor, the behavior of the liquid and gas phase deviates significantly from plug flow, particularly at high gas and low liquid velocities. This deviation is generally accounted for by the axial dispersion coefficient, D. Deckwer (1992) has discussed this matter in detail outlining the various approaches used to quantify axial dispersion. Tables 10.3 and 10.4 list some of the correlations available in the hterature for estimating the liquid- and gas-phase axial dispersion coefficient, and D, respectively. 

In Sect. 3.2, the development of the design equation for the tubular reactor with plug flow was based on the assumption that velocity and concentration gradients do not exist in the direction perpendiculeir to fluid flow. In industrial tubular reactors, turbulent flow is usually desirable since it is accompanied by effective heat and mass transfer and when turbulent flow takes place, the deviation from true plug flow is not great. However, especially in dealing with liquids of high viscosity, it may not be possible to achieve turbulent flow with a reasonable pressure drop and laminar flow must then be tolerated. 

Deviation from the ideal plug flow can be described by the dispersion model, which uses the axial eddy diffusivity (m s ) as an indicator of the degree of mixing in the flow direction. If the flow in a tube is plug flow, the axial dispersion is zero. On the other hand, if the fluid in a tube is perfectly mixed, the axial dispersion is infinity. For turbulent flow in a tube, the dimensionless Peclet number (Pe) deflned by the tube diameter (v dlE-Q is correlated as a function of the Reynolds number, as shown in Figure 10.3 [3] dz is the axial eddy diffusivity, d is the tube diameter, and v is the velocity of liquid averaged over the cross section of the flow channel. 

The horizontal liquid flow pattern is very complicated due to the mixing by vapor, dispersion, and the round cross section of the column. On single-pass trays, the latter results in the flow path, which first expands and then contracts. A rigorous modeling of this flow pattern is very difficult, and usually the situation is simplified by assuming that the liquid flow is unidirectional and the major deviation from the plug flow is the turbulent mixing or eddy diffusion. In [80], two different models, the eddy-diffusion model and the mixed pool model were developed and tested in the context of the rate-based approach for RD trays. The details of these models can be found in [81]. 

Cellular and diffusion models are usually used to calculate the efficiency of longitudinal mixing (turbulence) in a reactor and the related degree of deviation of the liquid flow hydrodynamic structure from perfect mixing and plug flow modes [4, 38,121-123]. 

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