Axial Dispersion and Flow Maldistribution

For pluglike extract flow through fixed beds, Y should satisfy the following equation when ( z/K t/. 

In steady-state continuous countercunent extraction, when both the solid and extract flow are pluglike, 

At unsteady-state conditions A (BYlBt) and A l — (XBX/Bt) should be added to the right-hand side of (10.12-2). Axial dispersion will reduce extraction efficiency unless is negligibly small, that is, Pe Yo/D is veiy large. Pe is used to characterize the magnitude of axial-dispeision-induced effects. 

FIGURE 10.10-2 Log (Y IMX ) versus t and 9 when using upflow of solute-free water to leach infused sucrose from 4.67 mm diameter, porous alumina spheres in a bed initially filled with extract in equilibrium with the spheres. 

Marked axial dispersion in both the liquid and solid phases has been observed in continuous countercurrent leaching systems. The solid-phase dispersion is probably caused by nonuniform conveying and by backmixing caused by the baffles which are used to prevent solid beds from turning en masse. VnliD n values of 16.1 m and 20 m, respectively, have b n repotted for sugar beet extraction in tower and slope extractors. Local fiow nonuniformity and larger-scale flow maldistribution are the primary factors that cause axial dispersion in the extract. 

FIGURE 10.18 3 Log varsus i and 9 when using downflow of solute-free water to teach infused 

FIGURE 10.10-2 Log versus t and 9 when using upflow of solute-free water to leach infused 

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An issue that is not adequately addressed by most models (EQ and NEQ) is that of vapor and liquid flow patterns on distillation trays or maldistribution in packed columns. Since reaction rates and chemical equilibrium constants are dependent on the local concentrations and temperature, they may vary along the flow path of liquid on a tray, or from side to side of a packed column. For such systems the residence time distribution could be very important, as well as a proper description of mass transfer. On distillation trays, vapor will rise more or less in plug flow through a layer of froth. The liquid will flow along the tray more or less in plug flow, with some axial dispersion caused by the vapor jets and bubbles. In packed sections, maldistribution of internal vapor and liquid flows over the cross-sectional area of the column can lead to loss of interfacial area. 

FSL solutions have been developed for continuous countercurrent extractions in which the effects of flow maldistribution and axial dispersion are negligibly small. These solutions involve the following infinite series ... 

Radial density gradients in FCC and other large-diameter pneumatic transfer risers reflect gas—soHd maldistributions and reduce product yields. Cold-flow units are used to measure the transverse catalyst profiles as functions of gas velocity, catalyst flux, and inlet design. Impacts of measured flow distributions have been evaluated using a simple four lump kinetic model and assuming dispersed catalyst clusters where all the reactions are assumed to occur coupled with a continuous gas phase. A 3 wt % conversion advantage is determined for injection feed around the riser circumference as compared with an axial injection design (28). 

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