Hgura 9.5 The zone-stage model {From F. J. Zuiderweg, P. J. Hoek, and L. Lahm, Jr., I. Chem. E. Symp. Ser. 104, p. A217,1987. Reprinted courtesy of the Institution of Chemical Engineers, UK.)

rial areas between the zones. The vertical and sideways flows, added in the next lower layer of stages, determine the flow distribution. It was shown (150a) that this distribution pattern can be derived from diffusion theory if Kx = 2/3. A higher value of Ky reflects an increase of flow near the wall.

For a given packing [i.e., inherent liquid spreading characteristics, usually characterized by a liquid spreading coefficient (1506)], and a fixed number of radial zones, the vertical height needed to achieve a fixed value of Kx is a dependent variable calculated from the diffusion equation (150a,1506). This height is generally unequal to the stage height. To bridge the two, the zone-stage model employs an interpolation procedure. Vapor is assumed to be uniformly distributed, although this assumption is not required by the model. Vapor and liquid flow through each zone-stage are constant, with all interzone bulk liquid flow occurring between stages.

Kunesh et al. (131,150a) showed good agreement between predictions from the zone-stage model and some experimental data. Zuiderweg et al. (136,150,150a) applied the model to explain published efficiency data in terms of maldistribution effects. Zuiderweg et al. (136) also applied the zone-stage model to gain insight into the effect of several variables on efficiency in the presence of maldistribution. Their results are preliminary and require experimental confirmation.

Alternative models. Stichlmair and Stemmer (146,151) model the column as a large number of parallel channels, each operated at a differ ent liquid rate and at plug flow. The degree of maldistribution is ex pressed by a maldistribution number, which is evaluated from standan deviations of concentration measurements. This maldistribution num ber is used in a chart that converts the pseudo number of transfe units (i.e., plug flow) into an actual number of transfer units (i.e., al lowing for maldistribution).

9.2.6 Empirical prediction of the effects of maldistribution

Moore and Rukovena (152) proposed the empirical correlation in Fig 9.6 to determine the efficiency loss due to liquid maldistribution in ) packed tower containing Pall® rings or Metal Intalox® packing. Thi correlation was only recently proposed, and more experience with it predictions is required before it can be generally applied with confi dence. Nevertheless, it has been shown (152) to work well for severe case studies (Fig. 9.6), is simple to use, and is valuable at least as i preliminary guide.

To quantify the quality of liquid irrigation, the correlation uses thi distribution quality rating index. Typical indexes are 10 to 70 percen for most standard commercial distributors; 75 to 90 percent for inter mediate-quality distributors, and over 90 percent for high-performano distributors. Moore and Rukovena (152) present a method for calcu lating a distribution-quality rating index from distributor geometry This method is spelled out in a companion book (40).

9.2.7 Effect o! vapor maldistribution on packing efficiency

Vapor is easier to distribute than liquid, but vapor maldistributioi can also be troublesome. The effects of vapor maldistribution havi been investigated far less than those of liquid maldistribution. Thi following findings have been reported:

1. Vapor flow through packings tends to be uniform if the initial liq uid and vapor distributions to the packings are uniform (15,66).

2. A nonuniform initial vapor profile is often generated in the columi vapor inlet and vapor redistribution regions (153-157), especially when inlet velocities are high. Vapor maldistribution was shown ti strongly depend (153,154,157) on the geometry of the vapor inle (i.e., whether tangential, radial, etc.). The use of properly designei gas distributors can largely mitigate vapor maldistributioi (23,152-157). Commercial vapor distributor designs are discuss« elsewhere (23,40,152).

3. Although vapor spreads radially through the packing quite rapidly

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