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The limiting capacity of the cocurrent tray arises from either liquid entrainment in the collection zone, or downcomer flow limitation, or both. At some very high vapour flow rate, re-entrainment from the collector device becomes a problem. And, as just mentioned, there is some high flow rate at which downcomer backup constrains liquid flow capacity. The tests described in this paper include data on maximum capacity, except at a pressure of 414 kPa, where reboiler capacity was found to be limiting. However, at maximum heat input, the trays performed well at rates well in excess of those found for conventional trays.
Figure 1. Sketches of cocurrent tray. (a) Three-tray section (b) Collector detail.
Three adjacent trays are included in Figure 1 to enable visualization of the reverse-flow aspect of the net downward flow of liquid in the distillation or absorption column under consideration. Further elaboration of the tray contacting action is included with the description of the model development.
MODEL DEVELOPMENT EFFICIENCY
The efficiency model for the cocurrent tray is based entirely on the expected mechanisms of gas-liquid contacting. For each part of the model there is documentation in the form of previous research. The general concept is that as gas enters a tray it atomizes liquid emerging from the downcomer (see Figure 1). The gas flows through the tray in plug fashion, whereas the liquid is recirculated, alternately coalescing and re-atomizing. The time of contact between gas and liquid is not limited to the vertical distance from the tray floor to the bottom of the first row of entrainment collectors; there is continued phase contacting in the collector elements. The portion of the liquid not removed from the gas in the collector zone represents a recycle that increases the net flow of liquid to the tray (thus slightly increasing the interfacial area) but which decreases the overall efficiency of the tray.
On the above basis, some key design parameters emerge:
• Velocity of gas through the inlet distributor
• Area and width of the slots
• Height of the contacting zone.
In addition, there are the expected flow and physical property variables and geometric variables associated with the collector zone. The gas-liquid mixture in the contacting zone is treated as a uniform spray, and for mass transfer purposes the needed characteristic dimension of the spray drops is the Sauter mean diameter D32. This is the average drop size that has the same volume/surface ratio as the entire collection of drops, which in reality comprises a range of drop sizes.
Figure 2. Droplet Sauter mean diameter D_32^, as a function of the hole Ffactor (Pinczewski and Fell, 1977)3 .
For research on the characterization of this two-phase mixture, one may turn to the extensive studies by Fell and coworkers at the University of New South Wales in Australia. Measurements of air-water sprays on sieve trays have been reported by Pinczewski and Fell, 1977 and correlated as shown in Figure 2. For tray spacings in the range of 0.15 to 0.45 m, D32 was found to be a function of the velocity of gas emerging from the tray floor orifices. The curve in Figure 2 can be expressed as
D_(32,air-water)=exp[-0.287F_h+8.061] (1)
with the prime on diameter indicating micron units. The air-water diameter from equation (1) can be converted to other systems by the relationship developed by Mugele and Evans(1951):
D_(32,system)=2317D_(32,air-water) [ρ_W/ρ_L ]^0.35 [μ_L/μ_W ]^0.18 [σ/σ_L ]^0.20 (2)
where the equivalent properties of water are indicated by the subscript w.
The gas residence time in the contacting zone must be based on some mean value between the slot velocity and the velocity approaching the collector zone. Velocity profiles for gases flowing under similar circumstances have been reported by Chen et al., 19824 in terms of point values as a function of initial velocity and distance from initial dispersers (slots). The point values have been converted to average values in the contacting zone: