Liquid axial mixing

For the same liquids axial mixing is described by (Bibaud and Treybal, loc. cit.)... 

Axial mixing in the liquid, induced by the upflow of the gas bubbles, can be substantial in commercial-scale bubble columns, especially in the chum turbulent regime. Due to typically small particle size, the axial dispersion of the solid catalyst in slurry bubble columns is expected to follow closely that of the liquid exceptions are high-density particles. The liquid axial mixing can be represented by an axial dispersion coefficient, which typically has the form... 

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. 

When ADPF model is assumed for the liquid axial mixing in TBR, the transient mass conservation equation are for the gas phase... 

As the reactor was partially compartmentalized it could be well represented by the backflow cell model.In this case liquid axial mixing could be evaluated by the interstage backflow rate f. Following these principles backflow rates f were obtained by comparison of experimental RTD-curves with curves calculated from model equations (1) ... 

The correlation proposed by Joshi [71] was tested using about 80% of the liquid axial mixing coefficients reported in the literature by Rato et al,[46], Michelsen and Ostergaard [64], Ostergaard [67], and Vail et al. [68], For the selected data points, the model conditions of 20% dissipation of input energy, was fulfilled, A 16% deviation between the experimental values and the model predictions was observed. 

Such a model should take into account at least the following phenomena Mass transfer across gas-liquid interface, mass transfer to exterior particle surface, catalytic reaction, flow and axial mixing of gas phase, and flow and axial mixing of liquid phase. 

The two models commonly used for the analysis of processes in which axial mixing is of importance are (1) the series of perfectly mixed stages and (2) the axial-dispersion model. The latter, which will be used in the following, is based on the assumption that a diffusion process in the flow direction is superimposed upon the net flow. This model has been widely used for the analysis of single-phase flow systems, and its use for a continuous phase in a two-phase system appears justified. For a dispersed phase (for example, a bubble phase) in a two-phase system, as discussed by Miyauchi and Vermeulen, the model is applicable if all of the dispersed phase at a given level in a column is at the same concentration. Such will be the case if the bubbles coalesce and break up rapidly. However, the model is probably a useful approximation even if this condition is not fulfilled. It is assumed in the following that the model is applicable for a continuous as well as for a dispersed phase in gas-liquid-particle operations. 

Dunn et al. (D7) measured axial dispersion in the gas phase in the system referred to in Section V,A,4, using helium as tracer. The data were correlated reasonably well by the random-walk model, and reproducibility was good, characterized by a mean deviation of 10%. The degree of axial mixing increases with both gas flow rate (from 300 to 1100 lb/ft2-hr) and liquid flow rate (from 0 to 11,000 lb/ft2-hr), the following empirical correlations being proposed ... 

Kramers and Alberda (K20) have reported some data in graphical form for the residence-time distribution of water with countercurrent air flow in a column of 15-cm diameter and 66-cm height packed with 10-mm Raschig rings. It was concluded that axial mixing increased with increasing gas flow rate and decreasing liquid flow rate, and that the results were not adequately represented by the diffusion model. 

These expressions have been found valid for the range 1 < [(u,lug)NRtlNs< i] < 1000. For higher values, the axial mixing is identical to that observed for the single-phase liquid flow for which the following correlation was found for the experimental data ... 

NPei and NRtt are based on the equivalent sphere diameters and on the nominal velocities ug and which in turn are based on the holdup of gas and liquid. The Schmidt number is included in the correlation partly because the range of variables covers part of the laminar-flow region (NRei < 1) and the transition region (1 < NRtl < 100) where molecular diffusion may contribute to axial mixing, and partly because the kinematic viscosity (changes of which were found to have no effect on axial mixing) is thereby eliminated from the correlation. 

Tadaki and Maeda (Tl) examined the desorption of carbon dioxide from water in a bubble-column and analyzed the experimental results under the assumption that while the gas phase moves in piston flow, the liquid undergoes axial mixing that can be characterized by the diffusion model. (Shulman and Molstad, in contrast, assumed piston flow for both phases.) Only poor agreement was obtained between the theoretical model and the experimental... 

Siemes and Weiss (SI4) investigated axial mixing of the liquid phase in a two-phase bubble-column with no net liquid flow. Column diameter was 42 mm and the height of the liquid layer 1400 mm at zero gas flow. Water and air were the fluid media. The experiments were carried out by the injection of a pulse of electrolyte solution at one position in the bed and measurement of the concentration as a function of time at another position. The mixing phenomenon was treated mathematically as a diffusion process. Diffusion coefficients increased markedly with increasing gas velocity, from about 2 cm2/sec at a superficial gas velocity of 1 cm/sec to from 30 to 70 cm2/sec at a velocity of 7 cm/sec. The diffusion coefficient also varied with bubble size, and thus, because of coalescence, with distance from the gas distributor. 

Figure 4.23. Differential element of height, AZ, for a liquid-liquid extractor with axial mixing in both phases.

Axial mixing in liquid-liquid extraction columns 258... 

Equations (8) are based on the assumption of plug flow in each phase but one may take account of any axial mixing in each liquid phase by replacing the molecular thermal conductivities fc, and ku with the effective thermal conductivities /c, eff and kn eff in the definition of the Peclet numbers. The evaluation of these conductivity terms is discussed in Section II,B,1. The wall heat-transfer terms may be defined as... 

Dynamic Modelling of a Liquid-Liquid Extractor with Axial Mixing in Both Phases... 

At any level in the transition region, there will be a balance between the mixing effects attributable to (a) axial dispersion and to (b) the segregating effect which will depend on the difference between the interstitial velocity of the liquid and that interstitial velocity which would be required to produce a bed of the same voidage for particles of that size on their own. On this basis a model may be set up to give the vertical concentration profile of each component in terms of the axial mixing coefficients for the large and the small particles. 

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