Apparent J h J naj

% Error in efficient = -(% error in volatility)/lna (7.36)

Figure 7.6 is a plot of Eq. (7.36). At very low relative volatilities (a < 1.2), small errors in VLE have a huge impact on tray efficiency. For instance, at a relative volatility of 1.1, a -3 percent error in relative volatility gives a tray efficiency 40 to 50 percent higher than its true value (Fig. 7.6). Since VLE errors are seldom lower than ± 2 to 3 percent, both tray efficiencies and packing HETPs of low-volatility systems become meaningless unless accompanied by VLE data. Further, for low-volatility systems, comparing efficiencies derived from different sources is misleading unless using identical VLE. In one low-relative-volatility (a = 1.1) design check, the author used 60 percent tray efficiency. The designer used 90 percent efficiency, and came up with exactly the same number of trays. The difference was due to the designer using a relative volatility 2 to 3 percent lower than the author's.

Figure 7.6 shows that errors in relative volatility are a problem only at low relative volatilities. When relative volatility exceeds 1.5 to 2.0, VLE errors have negligible direct impact on tray efficiency.

Most efficiency data reported in the literature are obtained at total reflux. At total reflux, there are no indirect effects, and Fig. 7.6 shows the overall effect of VLE errors on column efficiency. For measurements at finite reflux ratios, the indirect effects below add to those in Fig. 7.6.

Indirect effects. Consider a case where apparent < ^rue and test data at a finite reflux are analyzed to calculate tray efficient. Due to the volatility difference i?min apparent > /?mjn true. Since the test was conducted at a fixed reflux flow rate, (7?//?min)apparenc < (i?/i?mitl)true. A calculation based on the apparent R/R^n will give more theoretical stages than a calculation based on the true R/Rmin. This means a higher apparent efficiency than the true value. This effect therefore supplements that of Fig. 7.6 and widens the gap between true and ap parent efficiency. The indirect effects are most pronounced at low relative volatility, because small errors in relative volatility lead to large errors in R/Rmirt.

The indirect effects exponentially escalate as minimum reflux is approached. Small errors in VLE or reflux ratio measurement (this includes column material balance as well as reflux rate) alter R/Rj^. Near minimum reflux, even small R/Rmin errors induce huge errors in the number of stages, and, therefore, in tray efficiency. Efficiency data obtained near minimum reflux are therefore meaningless.

Overall effect. A procedure for evaluating the overall effect (combining the direct and indirect effects on tray efficiency) was developed by Nelson, Olson, and Sandler (156). This method is based on the Fenske, Underwood, and Gilliland (Eduljee version) shortcut relationships (Sees. 3.2.1 to 3.2.5) and was shown to work well when comparing to a more rigorous procedure. An example (using an x-y diagram) in Sec. 7.3.6 demonstrates how differences between true and apparent volatility affect efficiencies calculated from test data.

7.3.2 Liquid flow patterns and maldistribution on large trays

Most popular theoretical models (such as the AIChE and the Chan and Fair models, Sec. 7.2.1) postulate that liquid crosses the tray in plug flow (Fig. 7.7a ) with superimposed backmixing, and that vapor is perfectly mixed. Increasing tray diameter promotes liquid plug flow and suppresses backmixing. This should enhance efficiency in large-diameter columns, but such enhancement has not been observed (147,148). Liquid maldistribution is the common explanation to the observation.

Liquid flow patterns. Liquid entering a single-pass tray flows in a diverging channel until reaching the tray centerline, then in a converging channel as the outlet weir is approached. The liquid has little incentive to move sideways and follow the curved walls of the column. Instead, it seeks the shortest path from inlet to outlet, and channels through the tray center (Fig. 7.76). This leaves stagnant zones near the curved walls on the side.

Liquid plug flow produces a horizontal (i.e., flat) flow profile (Fig. 7.7a). Channeling produces a U-shaped flow profile (Fig. 7.8a). The liquid moves fast at the tray center and slow near the walls. Wide stagnant zones, a steep U shape, and liquid recirculation in the stagnant zones (Fig. 7.86) signify a highly channeled flow profile. The

Drinking Patterns And RegionsHeight Liquid Over Outlet Weir
Figure 7.7 Flow patterns on distillation trays, (a) Plug flow; (6) plug flow in center, stagnant regions near wall.

stagnation point produced by the collision of liquid flow against the outlet weir wall forces liquid laterally toward the column wall. Upon collision with the column wall, this lateral flow generates backward flow in the stagnant zone. If the forward flow component is very slow, the backward component will dominate, causing recirculation.

Tray flow profiles have been investigated in large-diameter simulators using dye injection, photography, fiber optics, floating Ping-Pong balls, local temperature measurements, and other techniques. The following observations have been made:

Flow Over Distillation Trays

Figure 7.8 Experimentally measured residence time profiles on large distillation trays, showing stagnant zones, (a) U-shaped flow profile with stagnant zones, 8-ft tray; <b sharp U-shaped flow profile with wide stagnant zones and recirculation in stagnant zones, 8-ft tray; (c) replenishment of liquid in the stagnant regions by mixing from the active region. (Pari a, from Richard L, Bell, AIChE J. 18 (3), p. 498, May 1972. Reprinted courtesy of the American Institute of Chemical Engineers. Part b from T. Yanagi and B. D. Scott, paper presented at the AIChE National Meeting, New Orleans, Louisiana. Reprinted courtesy of Fractionation Research Inc. Part c, from M. J. Lockett, Distillation Tray Fundamentals, Cambridge University Press, Cambridge. Reprinted courtesy of Cambridge University Press.)

Figure 7.8 Experimentally measured residence time profiles on large distillation trays, showing stagnant zones, (a) U-shaped flow profile with stagnant zones, 8-ft tray; <b sharp U-shaped flow profile with wide stagnant zones and recirculation in stagnant zones, 8-ft tray; (c) replenishment of liquid in the stagnant regions by mixing from the active region. (Pari a, from Richard L, Bell, AIChE J. 18 (3), p. 498, May 1972. Reprinted courtesy of the American Institute of Chemical Engineers. Part b from T. Yanagi and B. D. Scott, paper presented at the AIChE National Meeting, New Orleans, Louisiana. Reprinted courtesy of Fractionation Research Inc. Part c, from M. J. Lockett, Distillation Tray Fundamentals, Cambridge University Press, Cambridge. Reprinted courtesy of Cambridge University Press.)

1. Low liquid rates favor channeling (141,157,158). The following are observations on single-pass sieve trays operating at high vapor rates (about 40 to 70 percent of flood). At low liquid flow rates (<2 gpm/in of outlet weir), flow profiles are U-shaped {157-160 with regions near the wall either stagnant or having liquid recirculation (Fig. 7.86). These stagnant regions widen as liquid flow rate is lowered (141,157). At higher liquid flow rates (about 3 gpm/in of outlet weir), the U shape is flattened (almost like plug flow) or is replaced by large recirculation zones. In one test series (157), there was one recirculation zone near each sidewall, another at the central tray outlet region, and another at the cen tral tray inlet region. At high liquid flow rates (6 to 7 gpm/in of outlet weir) the pattern turned into a multitude of recirculation zones, with a confused flow profile (157).

2. Higher gas flow rates flatten the U shape, narrow the stagnant regions, and reduce liquid recirculation in the stagnant regions (158,159,161). For single-pass sieve trays operating at liquid rates 3 to 7 gpm/in of outlet weir and at more than about 50 percent of flood, observed U shapes were quite flat (157,158). At the same liquid rates, steep U shapes were observed when vapor velocities fell below about 40 percent of flood.

3. At low and moderate gas rates, a major portion of the gas flow bubbles through the stagnant zones, contacting only a small fraction of the liquid flow. Froth formation in the central zone of the tray becomes relatively weak at low vapor rates (161). Solari et al. (158,161) estimate the stagnant zones to occupy between 5 and 60 percent of the tray bubbling area.

4. Lowering weir height flattens the U shape, narrows the stagnant regions, and reduces liquid circulation in the stagnant regions (141,161). With no outlet weir, the effects of liquid and gas flows on the flow pattern appear to be the converse of those described in items 1 and 2 above (161,162).

5. At low liquid rates (~ 1 gpm/in of weir), the tray liquid flow profile strongly depends on the liquid distribution at the tray inlet (e.g., inlet weir) but is practically independent even of magor disturbances at the outlet weir (163). The importance of liquid distribution at tray inlet was also noted by others (159,160,164,165).

6. Small ratios of outlet weir length to column diameter (i.e., small downcomers) widen the stagnant zones and intensify recirculation in the stagnant zones (161,166).

7. Liquid channeling on two-pass trays is far less pronounced than on a single-pass tray (159,166,167). Liquid velocity profiles remain nonuniform, but stagnant regions are small, often nonexistent. At low liquid rates, the velocity profile often skews toward one wall, forming a stagnant region near the opposite wall (159). For a center-to-side (converging) flow, stagnant zones sire absent (166,167) except with skewed profiles (159). For a side-to-center (diverging) flow, stagnant regions form near the corners of the outlet weirs (159) or occupy the small area near the wall (167), and are widened by skewed profiles (159).

8. Tray tilt affects the liquid flow pattern and the boundaries between the regions (148).

9. Liquid channels less when gas emerges sideways from the tray openings. Liquid-channeling on bubble-cap (163) and valve trays (168) is far smaller than on sieve trays. On sieve trays, channeling decreases as hole diameter increases, presumably due to widening of the cone angle of the gas jet (157).

10. Properly positioned baffles can improve the flow profiles (160,162-165,169,170).

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