Modeling and Prediction Maldistribution may drastically reduce packing efficiency. HETP may increase by a factor as high as 2 or 3 due to maldistribution. Shariat and Kunesh [Ind. Eng. Chem. Res., 34(4), 1273 (1995)] provide a good demonstration.
Early models [Mullins, Ind. Chem. Mfr., 33, 408 (1957); Manning and Cannon, Ind. Eng. Chem. 49(3), 347 (1957)] expressed the effect of liquid maldistribution on packing efficiency in terms of a simple channeling model. A portion of the liquid bypasses the bed, undergoing negligible mass transfer, and then rejoins and contaminates the rest of the liquid. Huber et al. [Chem. Ing. Tech. 39, 797 (1967); Chem. Eng. Sci. 21,819 (1966)] and Zuiderweg et al. [IChemE Symp. Ser. 104, A217 (1987)] replaced the simple bypassing by variations in the local L/V ratios. The overirrigated parts have a high L/V ratio, the underirrigated parts a low L/V ratio. Regions with low L/V ratios experience pinching, and, therefore, produce poor separation.
Huber et al. (loc. cit.) and Yuan and Spiegel [Chem. Ing. Tech. 54, 774 (1982)] added lateral mixing to the model. Lateral deflection of liquid by the packing particles tends to homogenize the liquid, thus counteracting the channeling and pinching effect.
A third factor is the nonuniformity of the flow profile through the packing. This nonuniformity was observed as far back as 1935 [Baker, Chilton, and Vernon, Trans. Instn. Chem. Engrs. 31, 296 (1935)] and was first modeled by Cihla and Schmidt [Coll. Czech. Chem. Commun., 22, 896 (1957)]. Hoek (Ph.D. Thesis, The University of Delft, The Netherlands, 1983) combined all three factors into a single model, leading to the zone-stage model below.
The Zone-Stage Model Zuiderweg et al. [IChemE Symp. Ser. 104, A217, A233 (1987)] extended Hoek's work combining the effects of local L/V ratio, lateral mixing, and flow profile into a model describing the effect of liquid maldistribution on packing efficiency. This work was performed at Fractionation Research Inc. (FRI) and at The University of Delft in The Netherlands. The model postulates that, in the absence of maldistribution, there is a "basic" (or "true" or "inherent") HETP which is a function of the packing and the system only. This HETP can be inferred from data for small towers, in which lateral mixing is strong enough to offset any pinching. For a given initial liquid distribution, the model uses a diffusion-type equation to characterize the splitting and recombining of liquid streams in the horizontal and vertical directions. The mass transfer is then calculated by integrating the liquid flow distribution at each elevation and the basic HETP. Kunesh et al. successfully applied the model to predict measured effects of maldistribution on packing efficiency. However, this model is difficult to use and has not gained industrywide acceptance.
Empirical Prediction Moore and Rukovena [Chemical Plants and Processing (European edition), p. 11, August 1987] proposed the empirical correlation in Fig. 14-64 for efficiency loss due to liquid maldistribution in packed towers containing Pall® rings or Metal Intalox® packing. This correlation was shown to work well for several case studies (Fig. 14-64), is simple to use, and is valuable, at least as a preliminary guide.
To quantify the quality of liquid irrigation, the correlation uses the distribution quality rating index. Typical indexes are 10 to 70 percent for most standard commercial distributors, 75 to 90 percent for intermediate-quality distributors, and over 90 percent for high-performance distributors. Moore and Rukovena present a method for calculating a distribution-quality rating index from distributor geometry. Their method is described in detail in their paper as well as in Kister's book (Distillation Operation, McGraw-Hill, New York, 1990).
Maximum Liquid Maldistribution Fraction fmax. To characterize the sensitivity of packed beds to maldistribution, Lockett and
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