Liquid-phase axial mixing

In the homogeneous bubble flow regime, the gas phase is generally assumed to move in plug flow and the liquid phase axial mixing is characterized by the axial dispersion coefficient. The axial dispersion coefficient is dependent upon gas velocity and column diameter according to (26,41,42)... 

It is instructive to compare gas-liquid reactors (from all the classes) on the basis of capacity, turndown ratio (L/G), liquid-phase axial mixing, gas-side pressure drop, mass transfer coefficient, effective interfacial area, heat transfer coefficient, and the number of theoretical stages. Table 11.26 presents such a comparison using ratings 1 to 5 (poor to excellent). This table should be useful to design engineers. 

Lorenz, O., Schumpe, A., Ekambara, K., and Joshi, J.B. (2005), Liquid phase axial mixing in bubble columns operated at high pressures, Chemical Engineering Science, 60(13) 3573. 

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... 

The liquid phase axial dispersion in bubble colunm reactors is very high making them effectively back-mixed reactors for industrial-scale systems. 

Unlike in MASRs, where liquid mixing is always considered complete, in this case allowance must be made for partial mixing. Thus it may often be necessary to use the dispersion model given by Equation 17.25. The liquid-phase axial diffusion coefficient for estimating the Peclet number in this equation may be calculated from the correlations of Hikita and Kikukawa (1975) or Mangartz and Pilhofer (1981). 

Godfrey, J. C. Houlton, D. A. Mariey, S. T Marrochelh, A. Slater, M. J. Continuous phase axial mixing in pulsed sieve plate liquid-liquid extraction columns, Chem. Eng. Res. Des. 66 (1988), p. 445/457... 

Dunn et al. [202] developed empirical Peclet munber correlation not only for the gas phase axial mixing but dso for the axial mixing in the liquid phase. It is found that the liquid Pedet number is proportional to the liquid superficial velocity and it is independent of the gas velocity. This independency is taken a priori 1 other investigators in this field for the area under the loadmg point, when the forces between the gas and the liquid phase can be neglect. ... 

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 ... 

Glaser and Litt (G4) have proposed, in an extension of the above study, a model for gas-liquid flow through a b d of porous particles. The bed is assumed to consist of two basic structures which influence the fluid flow patterns (1) Void channels external to the packing, with which are associated dead-ended pockets that can hold stagnant pools of liquid and (2) pore channels and pockets, i.e., continuous and dead-ended pockets in the interior of the particles. On this basis, a theoretical model of liquid-phase dispersion in mixed-phase flow is developed. The model uses three bed parameters for the description of axial dispersion (1) Dispersion due to the mixing of streams from various channels of different residence times (2) dispersion from axial diffusion in the void channels and (3) dispersion from diffusion into the pores. The model is not applicable to turbulent flow nor to such low flow rates that molecular diffusion is comparable to Taylor diffusion. The latter region is unlikely to be of practical interest. The model predicts that the reciprocal Peclet number should be directly proportional to nominal liquid velocity, a prediction that has been confirmed by a few determinations of residence-time distribution for a wax desulfurization pilot reactor of 1-in. diameter packed with 10-14 mesh particles. 

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 ... 

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.

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... 

For gas-liquid flows in Regime I, the Lockhart and Martinelli analysis described in Section I,B can be used to calculate the pressure drop, phase holdups, hydraulic diameters, and phase Reynolds numbers. Once these quantities are known, the liquid phase may be treated as a single-phase fluid flowing in an open channel, and the liquid-phase wall heat-transfer coefficient and Peclet number may be calculated in the same manner as in Section lI,B,l,a. The gas-phase Reynolds number is always larger than the liquid-phase Reynolds number, and it is probable that the gas phase is well mixed at any axial position therefore, Pei is assumed to be infinite. The dimensionless group M is easily evaluated from the operating conditions and physical properties. 

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

Fig. 47. In silu study of a-methylstyrene hydrogenation in a fixed bed of Pd/ALO catalyst, (a) Schematic representation of the bed and the chosen axial bar. (b) A mixed spatial-spectral 2-D map which corresponds to that axial bar. (c) The distribution of the liquid phase along the axial bar obtained as an integral projection of (b) on its vertical (coordinate) axis, (d f) NMR spectra of the liquid phase at various heights along the bar obtained as horizontal cross-sections of the map in (b). The location of these cross-sections is indicated in (b,c) with horizontal lines. Each spectrum corresponds to a volume of 0.66mmx 1.3mmx 2mm. The two vertical dotted lines are drawn to show the differences in relative positions of the external peaks in the spectra. Reprinted from reference (69) with permission from Elserier, Copyright (2004).

The liquid and solid phases are often supposed to be well-mixed, and a perfect mixing model can be applied to model the species-concentration profile. However, many expressions for the description of axial dispersion in the liquid phase in a BSCR are given in the literature [37,38]. 

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