Lwhc where hc is calculated from the Hofhuis and Zuiderweg equation [Eq. i.6.67)]. A close inspection of the experimental data correlated (85) shows that this too is a gradual transition, which occurs over a range of values rather than at a sharp point.

Valve trays. The amount of work reported thus far on valve tray regime transition is small and entirely based on air-water tests. Correlations proposed to date require the knowledge of liquid holdup at transition, which is generally not available, and are therefore of limited application for commercial columns.

An early study (91) reports that a correlation derived by Barber and Wijn for sieve tray froth-to-spray transition is also applicable to valve trays. A more recent study by Dhulesia (112) disagrees, and reports that valve trays have a stronger tendency to operate in the froth regime than sieve trays. Dhulesia proposed an alternative froth-spray transition correlation for valve trays, but this correlation is based on air-water data from a single type of valve tray, and its extension to other situations has not been tested.

6.4.4 Implications of the spray regime for design and operation

While the classical hydraulic model provides a reasonable approximation for the froth and emulsion regimes, different mechanisms determine the hydraulics and mass transfer in the spray regime. The transition from froth to spray is gradual, and so is the change in the hydraulic and mass transfer behavior (110,111,113,114).

Flow across the tray. The classical hydraulic model implies that liquid flows across the tray by building up a liquid head on the tray, and when this head exceeds the weir height it overflows it. This mechanism is valid in principle when liquid is the continuous phase, but in the spray regime, vapor is the continuous phase and the liquid is present as drops in the vapor space (Figs. 6.25d, 6.26c, and 6.276). In the spray regime, liquid is transported by a "jumping" mechanism (104,113,115) (Fig. 6.28c).

Outlet weir. While in the classical model the weir height determines the liquid level (or the clear liquid height) on the tray, in the spray regime the weir plays a minor role. Clear liquid height shows a small, if any, dependence on weir height in the spray regime (89,90,92). Liquid enters the downcomer by jumping high over the weir and not by flowing across it (Fig. 6.28c). Therefore, the Francis weir formula does not apply to trays operating in the spray regime (85,104).

Close to the outlet weir, droplets that have been unsuccessful in crossing the weir form a liquid pool (113). This pool sends liquid back along the tray floor to the orifices close to the outlet weir for reatom-ization. When the pool is too shallow (e.g., about zero-in weirs), atom-ization may grow fiercer, producing more entrainment (36,40).

Pressure drop. Wet pressure drop on the tray is determined by the resistance of the aerated mass to vapor flow (Sec. 6.3.3). As the nature of the dispersion is different, one would expect a different mechanism to cause pressure drop in the spray regime. This has been confirmed by experiments (88,114). To date, not enough is known about the nature of this mechanism.

Entrainment. Different mechanisms generate entrainment in the spray and froth regimes (Sec. 6.2.11). In the spray regime much more entrainment is produced and a larger amount of liquid resides at higher elevations (Fig. 6.28f>). Low tray spacing is not suitable for spray regime operation; generally a tray spacing of at least 18 in, and preferably 24 in or more, is recommended (108). Using high tray spacing has been a common practice in vacuum towers, which often operate in the spray regime.

Mass transfer. According to the classical model, mass transfer takes place by vapor-liquid contact in the froth. In the spray regime, mass transfer takes place on the surface of the drops (116). In order to appreciate the differences in mass transfer between the regimes, distillation systems have been classified into three types:

1. Positive-surface-tension systems (a+) where surface tension increases as liquid flows down the column.

2. Negative-surface-tension systems (a-) where surface tension drops as liquid flows down the column.

3. Neutral systems, where surface tension is unchanged.

It has been shown (116) that u- gives smaller drops, thus providing more mass transfer surface in the spray regime. This is why o— gives higher efficiency in the spra. regime while <r+ gives higher efficiency in the froth regime (108,116,117). It has been proposed (108) that for negative systems, columns should be designed to operate in the spray regime in order to improve tray efficiency. However, this is seldom practical. Columns are designed to suit the required vapor and liquids loads and the process conditions, giving the tray designer very limited freedom for choosing a desired flow regime.

Some evidence has been presented to suggest that the degree of back mixing of liquid on the tray is smaller in the spray than in the froth regime (113). Much of the back mixing in the spray regime has been attributed to reatomization of the liquid from the pool near the outlet weir (113). The lower degree of back mixing tends to enhance efficiency in the spray regime.

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