Liquid phase axial dispersion correlation

Table 3. Liquid phase axial dispersion correlations for sparged columns.

Sullivan and Treybal (1972) suggested the following correlation for the liquid-phase axial dispersion coefficient for a 0.15 m i.d., 12-stage column ... 

Here, PeL = LJLdp/EZL, Reu = dppLUL/pLi GaL = dlgpl/pl, UL is the interstitial liquid velocity, and EZL is the liquid-phase axial dispersion coefficient. Furzer and Michell28 correlated the Peclet number to the dynamic holdup by a relation... 

Stiegel and Shah34 measured the liquid-phase axial dispersion coefficient in a packed rectangular column. Some details of system conditions used in this study have been described earlier, in Sec. 7-3. The axial dispersion coefficient and the liquid-phase Peclet number were correlated to the gas and liquid Reynolds numbers by the expressions... 

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). 

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. 

Two complementai y reviews of this subject are by Shah et al. AIChE Journal, 28, 353-379 [1982]) and Deckwer (in de Lasa, ed.. Chemical Reactor Design andTechnology, Martinus Nijhoff, 1985, pp. 411-461). Useful comments are made by Doraiswamy and Sharma (Heterogeneous Reactions, Wiley, 1984). Charpentier (in Gianetto and Silveston, eds.. Multiphase Chemical Reactors, Hemisphere, 1986, pp. 104—151) emphasizes parameters of trickle bed and stirred tank reactors. Recommendations based on the literature are made for several design parameters namely, bubble diameter and velocity of rise, gas holdup, interfacial area, mass-transfer coefficients k a and /cl but not /cg, axial liquid-phase dispersion coefficient, and heat-transfer coefficient to the wall. The effect of vessel diameter on these parameters is insignificant when D > 0.15 m (0.49 ft), except for the dispersion coefficient. Application of these correlations is to (1) chlorination of toluene in the presence of FeCl,3 catalyst, (2) absorption of SO9 in aqueous potassium carbonate with arsenite catalyst, and (3) reaction of butene with sulfuric acid to butanol. 

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 ... 

Bubble size in the circulating beds increases with Ug, but decreases with Ul or solid circulation rate (Gs) bubble rising velocity increases with Ug or Ul but decreases with Gs the ffequeney of bubbles increases with Ug, Ul or Gs. The axial or radial dispersion coefficient of liquid phase (Dz or Dr) has been determined by using steady or unsteady state dispersion model. The values of Dz and D, increase with increasing Ug or Gs, but decrease (slightly) with increasing Ul- The values of Dz and Dr can be predicted by Eqs.(9) and (10) with a correlation coefficient of 0.93 and 0.95, respectively[10]. 

Figure 5. Axial dispersion in the liquid phase of a slurry column. Comparison of data of Kara et al [70] with correlations.

Methods for evaluating the axial dispersion coefficient from RTD data As mentioned earlier, the one-parameter axial-dispersion model is widely used to correlate RTD data. The nature of the RTD depends upon the nature of the tracer input and the nature of the. flow, characteristics. For the RTD shown in Fig. 3-4 o), the axial dispersion coefficients for the liquid and solid phases can be obtained by fitting the equation... 

As discussed in Chap. 3, there are a large number of models proposed to evaluate macromixing in a trickle-bed reactor. A brief summary of the reported experimental studies on the measurements of RTD in a cocurrent-downflow trickle-bed reactor is given in Table 6-7. Some of these experimental studies are described in more detail in a review by Ostergaard.94 Here we briefly review some of the correlations for the axial dispersion in gas and liquid phases based on these experimental studies. 

The experimental studies have shown that, in gas-liquid trickle-bed reactors, significant axial mixing occurs in both gas and liquid phases. When the RTD data are correlated by the single-parameter axial dispersion model, the axial dispersion coefficient (or Peclet number) for the gas phase is dependent upon both the liquid and gas flow rates and the size and nature of the packings. The axial dispersion coefficient for the liquid phase is dependent upon the liquid flow rate, liquid properties, and the nature and size of the packings, but it is essentially independent of the gas flow rate. 

Significant literature on the axiaj dispersion in gas and liquid phases for countercurrent-flow packed-bed columns have been reported. Trickle- and bubble-flow regimes have been considered. Unlike the holdup, there is quite a discrepancy in the results of various investigators. Almost all the RTD data are correlated by a single-parameter axial dispersion model. A summary of the reported axial dispersion studies in countercurrent flow through a packed bed is given in Table 8-1. 

Woodburn55 showed thai, for Re], 650, the correlations proposed by DeMaria and White, J Sater and Levenspiel,43 and Dunn et al.16 could correlate his data. However, for 650 < ReL < 1,500, the axial dispersion in the gas phase was independent of the liquid rate. Under these liquid flow conditions, the reverse gas flow induced by the counterflowing liquid was measured. Thus, he concluded that an additional dispersive mechanism associated with reverse gas flow becomes operative at ReL 650. 

In all the studies described above, only the axial dispersion was considered. Anderson et al.1 measured the radial dispersion for the dispersed water phase in an air-water system. The measurements were carried out in a 30.48-cm-diameter Lucite tube packed with 91.44 cm of 1.27-cm Raschig rings. A continuous source of tracer was used. The radial Peclet number decreased with the increase in both the gas and liquid Reynolds number. Some typical results are shown in Fig. 8-5. The measurements were carried out up to the flooding point. The entire results were correlated graphically, as shown in Fig. 8-6. In Figs. 8-5 and 8-6 the Peclet number was based on the fluid velocity through the column, the nominal packing... 

The authors determined correlation constants C and a for five common types of impellers (two axial-flow impellers and three radial-flow impellers) and four impeller locations within a standard tank configuration. The specific power requirement can then be estimated by using Eq. (15-177). The power required to disperse one liquid phase... 

Figure 5.9 (a) Correlation of axial dispersion coefficients in liquid phase fixed and fluidized beds (b) correlation of axial dispersion coefficient for gases flowing through fixed beds. 

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