The Zone-Stage Model

Zuiderweg, Kunesh et al. (131,136,160,150o) combined the effects of local LIV ratio, lateral mixing, and liquid q read into a single model that describes the effect of liquid maldistribution on packing effi ciency. The work leading up to this model was performed at Fractionation Research Inc. (FIU) and at Delft University in The Netherlands. The model is still undergoing development. 

The model postulates th t in the al nce of maldistribution, there is a basic (or true or inherent ) HETP which is a function of the packing and the stem only. This HETP can be inferred from data for small towers, in which lateral mixing is strong enou to compensate for any pinching (Sec. 9.2.3). 

A fraction of the liquid stream in every stage flows downward into the next lower stage. The balance (i.e., 1 - Ki) flows sideways into the adjacent zones and splits according to the ratio of the inter - 

Re-prinied courted cfihe Inatitutian of Chemical Engineere, UK) 

Alternative models. Stichlmair and Stemmer (146,151) model the column as a large number of parallel channels, each operated at a differ- 

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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, lnstn. Chem. Engrs. 31, 296 (1935)] and was first modeled by Cihla and Schmidt [Coll. Czech. Chem. Com-mun., 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. 

Using the zone-stage model (Sec. 9.2.5), Zuiderw et al. (136) pre cted a sli t effect of bed depth on HETP for larger packings, but a laige effect for smaller packings. 

In the first stage of the solution process, the advective control model seeks a pumping scheme in which the capture zone fully encompasses all control points representing the contaminant plume. The capture zone is simulated by tracking particles from extraction wells backwards through the velocity field. To represent the plume capture constraints numerically, a distance measure is used in which the minimum distance between each plume control point and all particles (see Figure 1) is constrained. When the distance between a control point and particle pathline equals zero then the plume control point lies within the capture zone. To ensure capture of the entire plume, the constraint function must equal zero for all control points. The reverse tracking formulation is stated as... 

It is shown that the mechanism of gas-solid noncatalytic reactions can be understood better by following the variations in pore structure of the solid during the reaction. By the investigation of the pore structures of the limestone particles at different extents of calcination, it has been shown that the mechanism of this particular system can be successfully represented by a two stage zone reaction model below 1000 °C. It has also been observed that the mechanism changes from zone reaction to unreacted core model at higher temperatures. 

These information from the pore structure data show that a simple two-stage zone reaction model can be successfully used to describe the mechanism of the calcination of this particular limestone and it is not necessary to consider much more complex models such as three-zone and particle-pellet models. 

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