The total pressure drop across a tray is the sum of the pressure drop across the disperser unit, hd (dry hole for sieve trays; dry valve for valve trays), and the pressure drop through the aerated mass hh i.e., h, = hd + ht (6.41)
6.3.2 Dry pressure drop
The diy pressure drop across the disperser unit [hd in Eq. (6.41)] is given by a variation of the orifice equation
Sieve trays. K in Eq. (6.42) is given by (4,5,18,30,31)
The prime variables affecting the orifice coefficient, Cv) are the fractional hole area and the ratio of tray thickness to hole diameter. More than 20 published correlations are available for evaluating Cv (12). Fair et al. (18) and Van Winkle (5) recommend the correlation by Liebson et al. (48; Fig. 6.21a). The Hughmark and O'Connell correlation (66) is preferred by Ludwig (4) and Chase (30).
Valve trays. Figure 6.216 illustrates the dry pressure drop of a typical valve tray as a function of vapor velocity. At low vapor velocities, all valves are closed (i.e., seated on the tray deck). Vapor rises through the crevices between the valves and the tray deck, and friction losses through these crevices constitute the dry pressure drop. Once the closed balance point (CBP) is reached, there is sufficient force in the rising vapor to open some valves. A further increase in vapor velocity opens more valves. Since vapor flow area increases as valves open, pressure drop remains constant until all valves open. This occurs at the open balance point (OBP). Further increases of vapor velocity cause the dry pressure drop to escalate in a similar manner to a sieve tray. When two weights of valves are used in alternate rows on the tray, a similar behavior applies to each valve type. The result is the pressure drop-vapor velocity relationship in Fig. 6.19«.
K in Eq. (6.42) depends on whether the valves are fully open and also on the shape and weight of the valves. These are best obtained from manufacturer literature (7-9), but can also be calculated from Bolles' (71), Lockett's (12), or Klein's (80) methods. Klein's method was derived from and fine-tunes the Bolles' model, was tested against a wide data base, and gives
■ For all valves fully closed (below the closed balance point)
■ For all valves fully open (above the open balance point)
■ Between the closed and open balance points, the dry pressure drop is constant (Fig. 6.216), and equals the pressure drop at either the closed or open balance points. Therefore, Eq. (6.44a) can be used, with uh in Eq. (6.42) set equal to the velocity at the closed balance point, uuh CBP. Alternatively, Eq. (6.446) can be used with uh in Eq. (6.42) set equal to the velocity at the open balance point, uvh QVf. Note that between the open and closed balance points the hole velocity at the relevant balance point, and not the actual gas velocity of gas through the holes, is used as uh in Eq. (6.42).
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