Ind. Eng. Chem. Process Des. Dev. I 9 8 4
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Influence of the Physical Properties of the Liquid on Axial Dispersion in Packed Columns Urs von Stockar” and Plerre F. Cevey Institute of Chemicel Englneerlng, SWISSFederal Insmute of Technology, CH- 10 15 Lausanne, Switzerland
The effect of viscosity and surface tension on axial dispersion and holdup of the liquid was investigated in a 0.3-m i.d. packed column with countercurrent two-phase flow. Axial dispersion appeared to be independent both of
viscosity and of surface tension. The traditional complex form of correlating Peclet numbers as a function of interstitial Reynolds and of Galllei numbers may therefore be replaced by a much simpler form containing only a Froude number a s a correlating variable for the liquid phase. Axial dispersion depended slightly on the gas flow rate. Owing to a novel experimental technique permitting point measurements at various locations in the packing, differences in axial dispersion and holdup were observed as a function of radial position.
Introduction In designing packed columns for separation processes involving gas-liquid contacting, such as adsorption, stripping, and distillation, the driving forces through the contactor are usually evaluated assuming ideal plug flow for both phases. In reality, considerable departure from ideal flow exists, which is usually referred to as “axial dispersion”. I t counteracts the countercurrent contacting scheme for which the column is designed and thus lowers the driving forces throughout the packed bed. Neglect of this effect results in an overestimation of the driving forces and, respectively, in an underestimation of the number of transfer units needed and may therefore lead to an unsafe design. The relationship between the apparent value of NTU, as computed in the traditional way on the basis of the ideal plug flow assumption and the actually needed NTU, is shown in Figure 1 for the special case when the concentration varies only slightly in one of the phases, so that but the axial dispersion of the other phase is important. The calculation is based on the solution of the axial dispersion model (“diffusion model”) for a tubular reactor with first-order kinetics (Wehner and Wilhelm, 1956; Danckwerts, 1953; Miyauchi and Vermeulen, 1963). In order to avoid the need for iteration, the solution is given graphically in terms of a Peclet parameter which contains the true height of a transfer unit as a characteristic length instead of the usual column length, which is unknown at the beginning of design calculations. Determination of the HTU from pilot plant data is also affected by axial dispersion. Neglecting it will yield high values for HTU. For the special case just discussed, Sherwood et al. (1975) have presented an explicit chart similar to Figure 1 which can be used to correct the apparent values of HTU to their true counterparts. Several experimental studies show that the (Pe)HTu parameter for the liquid phase may be as low as between 1 and 3. Therefore the actually needed NTU might exceed the value obtained by classical design procedures by as much as 50%. Although in some cases this error and the overestimation of HTU tend to compensate, a serious risk of underdesign persists, especially when mass transfer measurements made in shallow beds are to be scaled up to a large number of transfer units. Literature In order to account properly for axial dispersion in design calculations, one must be able to estimate some model
parameter characterizing the effect, such as the Peclet number. Several studies of axial dispersion of the liquid phase in countercurrent packed columns exist. Most authors have either described the effect in terms of the simple model of axial dispersion or in terms of a more complex model which also contained an axial dispersion term. Many have come up with correlations of liquid phase Peclet numbers for use in design calculations (Chung and Wen, 1968; Shah et al., 1978). Some of the more typical correlations are summarized in Table I. Their general form is often
Pe = AReBGaC(ad)D (1) The Reynolds number as correlating variable simply reflects the dependence of Pe on the liquid flow rates. The Galilei number and a geometrical factor ad have been included by some authors in analogy to a correlating equation for liquid operating holdup, which was first introduced by Otake and Okada (1953) and successfully used by various authors [Michell and Furzer, 1972; Turek et al., 1979; Farid and Gunn, 1979; Mohunita and Laddha, 1965)
Ho= AReBGaC(ad)D
(2)
As may be seen from Table I, some authors have based the Reynolds number on the interstitial liquid velocity (Re,) rather than on the superficial velocity (ReL). In order to use these correlations, one needs to estimate the interstitial velocity beforehand. To enable this estimation, the authors usually determined the mean residence time t of the liquid from RTD measurements and correlated this information as liquid holdup in the form of eq 2. Concerning the type of results which are available, one may make the following remarks. (1) With some exceptions (Michell and Furzer, 1972; Kramers and Alberda, 1953; Dunn et al., 1977; Hoogendorn and Lips, 1965; Pham Co and Ribaud, 1971; Richter, 1978; Groenhof, 1977), the results have been obtained in laboratory columns with a diameter below 0.2 m. Some of these might not be very representative for industrial applications due to the small scale packing used (e.g., 6.4-mm Raschig rings). Others used larger packing material but their results may have suffered from wall effects due to an insufficient column diameter to packing size ratio. (2) Equations 1 and 2 are essentially the result of dimensional analysis. Although values have been assigned to the exponents C and D by several authors (Table I), the experimental evidence accumulated thus far does not suffice to justify or to reject the general form of the Peclet
0 1984 American Chemical Society 0196-4305/a4/1 123-o717~0~.5010
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984
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Table I. Correlations for Predicting Axial Dispersion packing type" authors and size, mm Michell and Furzer (1972), compilation from literature; eq 4 was taken from Otake and Okada (1953)
RR, BS, SP
