Hydrodynamics axial dispersion

Micromixing Models. Hydrodynamic models have intrinsic levels of micromixing. Examples include laminar flow with or without diffusion and the axial dispersion model. Predictions from such models are used directly without explicit concern for micromixing. The residence time distribution corresponding to the models could be associated with a range of micromixing, but this would be inconsistent with the physical model. 

The UASB tractor was modeled by the dispensed plug flow model, considering decomposition reactions for VFA componaits, axial dispersion of liquid and hydrodynamics. The difierential mass balance equations based on the dispersed plug flow model are described for multiple VFA substrate components considaed... 

The effect could be elucidated by ad tional axial dispersion characterization of GPC 1. An alternate approach is to utilize only THF in botii GPC 1 and 2 and to observe whether slices exit at the expected hydrodynamic volume. 

Concerning the hydrodynamics and the dimensioning of the test reactor, some rules of thumb are a valuable aid for the experimentalist. It is important that the reactor is operated under plug-flow conditions in order to avoid axial dispersion and diffusion limitation phenomena. Again, it has to be made clear that in many cases testing of monolithic bodies such as metal gauzes, foam ceramics, or monoliths used for environmental catalysis, often needs to be performed in the laminar flow regime. 

In Fig. 1.1 (d) the hydrodynamic behaviour is simplified in order to explain the mixing process. Let us assume that there is no axial dispersion and that radial dispersion is complete when the sampler reaches the detector. The volume of the sample zone is thus 200pl after the merging point (lOOpl sample+lOOpl-reagent as flow rates are equal). The total flow rate is 2.0ml min-1. Simple mathematics then gives a residence time of 6s for the sample in the detector flow cell. In reality, response curves reflect... 

Modeling of hydrodynamics in gas/vapor/liquid-liquid contactors includes an appropriate description of axial dispersion, liquid holdup, and pressure drop. The correlations giving such a description have been published in numerous papers and are collected in several reviews and textbooks (e.g., Refs. 65 and 66). Nevertheless, there is still a need for a better description of the hydrodynamics in catalytic column internals this is being reflected by research activities in progress (67). 

Reactive absorption processes present essentially a combination of transport phenomena and reactions taking place in a two-phase system with an interface. Because of their multicomponent nature, reactive absorption processes are affected by a complex thermodynamic and diffusional coupling which, in turn, is accompanied by simultaneous chemical reactions [14—16], Generally, the reaction has to be considered both in the bulk and in the film region. Modeling of hydrodynamics in gas-liquid contactors includes an appropriate description of axial dispersion, liquid hold-up and pressure drop. 

Nienow and Chiba (1981), and finally well summarized by the latter authors (1985). Misek (1971) described the hydrodynamics, entrainment, and partial flooding of fluidized systems consisting of nonuniform particles. Kennedy and Bretton (1966) studied the axial dispersion of nonuniform spheres fluidized with liquids, followed by investigations on size segregation carried out by Al-Dibouni and Garside (1979). 

Determinations of Peclet number were carried out by comparison between experimental residence time distribution curves and the plug flow model with axial dispersion. Hold-up and axial dispersion coefficient, for the gas and liquid phases are then obtained as a function of pressure. In the range from 0.1-1.3 MPa, the obtained results show that the hydrodynamic behaviour of the liquid phase is independant of pressure. The influence of pressure on the axial dispersion coefficient in the gas phase is demonstrated for a constant gas flow velocity maintained at 0.037 m s. 

This study, which contributes towards the understanding of hydrodynamic behaviour of gas-liquid reactors at elevated pressure, has shown the influence of pressure on the gas flow in a packed column through the axial dispersion coefficient. The gas flow diverges from plug flow when the pressure increases. As for the gas hold-up, an important parameter for the calculation of the reactional volume of a reactor, the pressure has no effect on this parameter in the studied range. This result allows to extrapolate gas hold-up values obtained... 

The elimination or estimation of the axial dispersion contribution presents a more difficult problem. Established correlations for the axial dispersion coefficient are notoriously unreliable for small particles at low Reynolds number(17,18) and it has recently been shown that dispersion in a column packed with porous particles may be much greater than for inert non-porous particles under similar hydrodynamic conditions(19>20). one method which has proved useful is to make measurements over a range of velocities and plot (cj2/2y ) (L/v) vs l/v2. It follows from eqn. 6 that in the low Reynolds number region where Dj. is essentially constant, such a plot should be linear with slope Dj, and intercept equal to the mass transfer resistance term. Representative data for several systems are shown plotted in this way in figure 2(21). CF4 and iC io molecules are too large to penetrate the 4A zeolite and the intercepts correspond only to the external film and macropore diffusion resistance which varies little with temperature. 

In this chapter, we review the reported studies on the hydrodynamics, holdups, and RTD of the various phases (or axial dispersion in various phases), as well as the mass-transfer (gas-liquid, liquid-solid, and slurry-wall), and heat-transfer characteristics of these types of reactors. It should be noted that the three-phase slurry reactor is presently a subject of considerable research investigation. In some cases, the work performed in two-phase (either gas-liquid or liquid-solid) reactors is applicable to three-phase reactors however, this type of extrapolation is kept to a minimum. Details of the equivalent two-phase reactors are considered to be outside the scope of this chapter. 

In ideal size-exclusion chromatography (SEC), fractionation is exclusively by hydrodynamic volume. Due to axial dispersion, however, a whole distribution of hydrodynamic volumes (and, therefore, of molecular weights) is instantaneously present in the detector cell. Under these conditions, it is assumed that the mass chromatogram w(V) (i.e., the instantaneous mass w versus the elution time or elution volume V) is a broadened version of a true (or corrected) mass chromatogram w V), as follows [1] ... 

At the heart of these processes is the absorber or the reactor of a particular configuration best suited to the chemical absorption or reaction being carried out. Its selection, design, sizing, and performance depend on the hydrodynamics and axial dispersion, mass and heat transfer, and reaction kinetics. 

Gas-solid contacting and axial dispersion of both gas and particles depend on the particle properties, operating conditions, column geometry, and scale, all of which affect the motion of gas and solids, commonly referred to as hydrodynamics. For extensive coverage of hydrodynamics may be consulted. Here we summarize the key features that affect the performance of gas-solid-fluidized beds as chemical reactors. 

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. 

Silebi CA, Dosramos JG. Axial dispersion of submicron particles in capillary hydrodynamic fractionation. AIChE J 1989 35 1351-1364. 

Exelus has developed a novel structured catalytic system that allows one to meet all four criteria in a single catalytic system Hydrodynamic tests reveal that the HyperCat has similar gas hold-up as a slurry bubble column reactor but with a much lower liquid axial-dispersion coefficient. Cold-flow studies appear to indicate that the heat-transfer coefficient of this new system is similar to a bubble column reactor. Catalyst performance tests reveal that the performance of the HyperCat is similar to that of a powder catalyst when used in a plug-flow reactor. 

In microstructured channels, laminar flow can be considered when the hydrodynamic entrance length remains short compared to the channel length. Therefore, the axial dispersion coefficient can be estimated with a relation developed by Aris [20] and Taylor [21] ... 

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. 

The change of scale or volume averaging between the particle and bed scales is ruled by the percolation process i.e., by the velocity distribution defined by Eq.5. The averaging formula depends on the nature of the hydrodynamic quantity which has to be averaged. Applications presented hereafter will concern the bed scale averaging of extensive quantities and of the axial dispersion coefficient... 

The increase of L when decreasing the particle wettability shows clearly that this hydrodynamic parameter characterizes the particle wettability. An increase of the wettability causes the Bodenstein number to increase as indicated in figure 13. Consequently, it seems that this wettability should be accounted for when deriving correlations for the axial dispersion coefficient. ... 

Dynamic analysis of a trickle bed reactor is carried out with a soluble tracer. The impulse response of the tracer is given at the inlet of the column to the gas phase and the tracer concentration distributions are obtained at the effluent both from the gas phase and the liquid phase simultaneously. The overall rate process consists the rates of mass transfer between the phases, the rate of diffusion through the catalyst pores and the rate of adsorption on the solid surface. The theoretical expressions of the zero reduced and first absolute moments which are obtained for plug flow model are compared with the expressions obtained for two different liquid phase hydrodynamic models such as cross flow model and axially dispersed plug flow model. The effect of liquid phase hydrodynamic model parameters on the estimation of intraparticle and interphase transport rates by moment analysis technique are discussed. 

Dynamic analysis of TBR by sitimules response technique has been succesfully applied to determine the extent of liquid axial mixing. There are number of learning and predictive models proposed in literature 2. Among them the ones having less number of parameters such as cross-flow model and axially dispersed plug flow ADPF model are the most adequate ones. A more realistic model profound for a TBR can be the one which includes the simultaneous effect of interphase and intraparticle transport rates, and the adequate hydrodynamic model, to minimize the relative importance of liquid mixing on these rates. 

The design, scaleup and performance prediction of slurry reactors require models which must consider not only the hydrodynamic and mixing behavior of the three phases, but also the mass transfer between the phases along with the intrinsic kinetics. In the DCL and FTS processes, an axial dispersion model is applicable, with the solid phase assumed to follow sedimentation or dispersed flow model. However, in the CCC, where the solid particles take part in the reaction, dispersion model is no longer applicable. 

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