Liquid gradient

As the liquid or froth moves across the tray, a liquid head develops to overcome resistance to flow caused by friction between the froth on the one hand and the tray and rising vapor on the other. The result is a liquid gradient with the liquid height at the bottom of the downcomer apron greater than that at the downflow weir. 

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Figure 8-103. Effect of liquid gradient on vapor distribution with 0.5 vapor distribution ratio. Used by permission, Bolies, W. L., Pet. Processing, Feb. thru May (1956).

Y = ratio of distance between caps to cap diameter A r = liquid gradient per row of caps, uncorrected, in. hj = depth of clear liquid on tray, in. 

The values of liquid gradient read from these charts are uncorrected for vapor flow. This correction is a multiplier read from Figure 8-113. 

Figure 8-113. Correction of liquid gradient for vapor load. Used by permission, The American Chemical Society, Davies, J. A., Ind. and Eng. Cham, V. 39, (1947) p. 774.

Capacity factor based on tower area, ft/sec Capacity fector at flood, ft/sec Liquid gradient vapor load correction factor or Discharge coefficient (see accompanying table) or Gas phase loading factor, ft/sec. Equation 8-281 Eddy loss coefficient, dimensionless. Table 8-22 Wet cap pressure drop correction factor. Figure 8-115... 

Aeration factor (usually = 1.0) or Friction factor for firoth cross flow. Equation 8-255 Friction factor for liquid gradient, cross-flow for sieve trays... 

Aeration factor, f, dimensionless k = Slope of equilibrium line/slope of operating line A = Liquid gradient (corrected) for tray or tray section, in. 

A = Uncorrected liquid gradient for tray or tray section, in. 

At high liquid flowrates, the liquid gradient on the tray can become excessive and lead to poor vapour distribution across the plate. This problem may be overcome by the shortening of the liquid flow-path as in the case of the double-pass and cascade trays. The whole design process is discussed in Volume 6. 

Escarpa, A., Perez-Cabrera, C., and Gonzalez, M.C., Optimization and validation of a fast liquid gradient for determination of prominent flavan-3-ols and flavonols in fresh vegetables, J. High Resolut. Chromatogr., 23, 637, 2000. 

A factor that is of concern with bubblecap trays is the development of a liquid gradient from inlet to outlet which results in corresponding variation in vapor flow across the cross section and usually to degradation of the efficiency. With other kinds of trays this effect rarely is serious. Data and procedures for analysis of this behavior are summarized by Bolles (in Smith, 1963, Chap. 14). There also are formulas and a numerical example of the design of all features of bubblecap trays. Although, as mentioned, new installations of such trays are infrequent, many older ones still are in operation and may need to be studied for changed conditions. 

Cross-sectional view of bubble-cap tower showing effect of excessive liquid gradient. 

PRESSURE DROP DUE TO LIQUID HEAD ABOVE SLOTS, SIEVE HOLES, OR VALVE OPENINGS. Reference to Fig. 16-10 shows that the total head above bubble-cap slots for an average cap is the sum of static submergence Sm, height of liquid crest above weir ha, and average liquid gradient 0.5hg. The same... 

The liquid gradient across the tray (hg) can be approximated by use of the following equation developed by Davies. ... 

All the variables in Eq. (14) except the liquid gradient are fixed by the tray design and the operating conditions, and the value of hg can be determined by a trial-and-error or graphical procedure. Equation (14) is based on the assump-... 

Plot for evaluation of liquid-gradient factor CD and correction factor Fc in Eq. (14). 

Because liquid gradient is very small in most sieve tray towers, the last term in Eq. (16) is often dropped. 

Pressure drop across tray based on clear-liquid density (A/>r) By Eq. (16), liquid head equivalent to the pressure drop across the tray [assuming liquid gradient (hg) is negligible] is... 

Liquid head in downcomer (H) By Eq. (18), neglecting liquid gradient,... 

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