ConstantvelocityspG A3p1 pGf5 a15

(Here E is the mass of entrainment per mass of vapor and Af is the fractional open area on the tray.)

When flooding is defined as the condition that gives E of 1, the flood velocity is estimated by Eq. (14-203).

FIG. 14-89 Mechanism of the burst of an air bubble on the surface of water. [Newitt, Dombrowski, and Knellman, Trans. Inst. Chem. Eng., 32, 244 (1954). ]

FIG. 14-89 Mechanism of the burst of an air bubble on the surface of water. [Newitt, Dombrowski, and Knellman, Trans. Inst. Chem. Eng., 32, 244 (1954). ]

11 p0G1.5

The relationship is dimensionally consistent; any set of consistent units on the right-hand side yields velocity units on the left-hand side. It is similar in form to Eq. (14-168) and provides a conceptual framework for understanding the ultimate distillation column capacity concept.

"Upper Limit" Flooding in Vertical Tubes If, instead of a gas jet being injected into a liquid as in distillation, the liquid runs down the walls and the gas moves up the center of the tube, higher velocities can be achieved than shown by Eq. (14-168) or (14-203). This application is important in the design of vertical condensers.

Maharudrayya and Jayanti [AIChE J., 48(2), 212-220 (2002)] show that peak pressure drop in a 25-mm vertical tube occurs at a value close to that predicted by Eq. (14-168) or (14-203). At this velocity about 20 percent of the injected liquid is being entrained out the top of the tube. However, the condition where essentially all liquid was entrained didn't occur until a velocity over twice the value estimated from Eq. (14-168) and Eq. (14-203).

The higher velocities at modest entrainment observed by Maharu-drayya and Jayanti were obtained with special smooth entry of gas (and exit of liquid) at the bottom of the tube. Hewitt (Handbook of Heat Exchanger Design, pp. 2.3.2-23, 1992) suggests that these values should be derated by at least 35 percent for more typical sharp heat exchanger tube entry. Similar to the smooth entry effect, other data suggest that countercurrent capacity can be increased by providing an extension of the tube below the tube sheet, with the bottom of the extension cut on a steep angle (>60°) to the horizontal. The tapered extension facilitates drainage of liquid.

An extensive data bank correlated by Diehl and Koppany [Chem. Eng. Prog. Symp. Ser., 65, 77-83 (1965)] also gave higher allowable entry velocities than Eq. (14-168) or (14-203). Dielhl and Koppany's correlation [Eq. (14-204)] is dimensional, and appears to give a much higher dependence on c than the more recent work. However, for many fluids, C is essentially the same as the combination c 01875(p( - pg)03125 that appears in Eq. (14-203). Hence Eq. (14-204) gives a similar physical property dependence.

where Uf = flooding gas velocity, m/s F = 1.22 when 3.2 d/c > 1.0

= 1.22 (3.2 d/c)0-4 when 3.2 d/c < 1.0 F = (G/L)025 G/L = gas-liquid mass ratio di = inside diameter of column, mm c = surface tension, mN/m (dyn/cm) pg = gas density, kg/m3

The primary reason for citing Eq. (14-204) is the large successful experience base in practical applications. Note that the reduction in allowable gas velocity for smalldiameters given by the factor is conceptually the same as the effect of using smaller-diameter packing in distillation. Note also that over the range of G/L between 1 and 0.1, the Maharudrayya and Jayanti data show a similar reduction in allowable gas rate to the F2 factor in Eq. (14-204). The phenomenon behind this is that a thicker liquid film on the tube wall is more easily entrained.

While the limiting phenomenon of upper limit flooding in a vertical pipe is similar to ultimate capacity in distillation, there is a distinct difference. Upper limit in a vertical pipe applies to a design where a conscious effort should be made to minimize gas-liquid contact. Carried to extremes, it would involve separate tubes for liquid flowing down and vapor going up. In contrast, ultimate capacity in a distillation column corresponds to the condition where effective mass transfer disappears due to high entrainment. One could force more vapor up through the contactor, but fractionation would be poor.

Fog Condensation—The Other Way to Make Little Droplets For a variety of reasons, a gas or vapor can become supersaturated with a condensable component. Surface tension and mass transfer impose barriers on immediate condensation, so growth of fog particles lags behind what equilibrium predicts. Droplets formed by fog condensation are usually much finer (0.1 to 10 |m) than those formed by mechanical breakup and hence more difficult to collect. Sometimes fog can be a serious problem, as in the atmospheric discharge of a valuable or a hazardous material. More commonly, fog is a curiosity rather than a dominating element in chemical processing.

Fog particles grow because of excess saturation in the gas. Usually this means that the gas is supersaturated (i.e., it is below its dew point). Sometimes, fog can also grow on soluble foreign nuclei at partial pressures below saturation. Increased saturation can occur through a variety of routes:

1. Mixing of two saturated streams at different temperatures. This is commonly seen in the plume from a stack. Since vapor pressure is an exponential function of temperature, the resultant mixture of two saturated streams will be supersaturated at the mixed temperature. Uneven flow patterns and cooling in heat exchangers make this route to supersaturation difficult to prevent.

2. Increased partial pressure due to reaction. An example is the reaction of SO3 and H2O to yield H2SO4, which has much lower vapor pressure than its components.

3. Isoentropic expansion (cooling) of a gas, as in a steam nozzle.

4. Cooling of a gas containing a condensable vapor. Here the problem is that the gas cools faster than condensable vapor can be removed by mass transfer.

These mechanisms can be observed in many common situations. For example, fog via mixing can be seen in the discharge of breath on a cold day. Fog via adiabatic expansion can be seen in the low-pressure area over the wing of an airplane landing on a humid summer day; and fog via condensation can be seen in the exhaust from an automobile air conditioner (if you follow closely enough behind another car to pick up the ions or NO molecules needed for nucleation). All of these occur at a very low supersaturation and appear to be keyed to an abundance of foreign nuclei. All of these fogs also quickly dissipate as heat or unsaturated gas is added.

The supersaturation in condensers arises for two reasons. First, the condensable vapor is generally of higher molecular weight than the noncondensable gas. This means that the molecular diffusivity of the vapor will be much less than the thermal diffusivity of the gas. Restated, the ratio of NSc/NPr is greater than 1. The result is that a condenser yields more heat-transfer units dTgJ(Tg — Tt) than mass-transfer units dYg/(Yg — Y,). Second, both transfer processes derive their driving force from the temperature difference between the gas Tg and the interface Ti. Each incremental decrease in interface temperature

TABLE 14-21 Simulation of Three Heat Exchangers with Varying Foreign Nuclei

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