Condensing heat-transfer rates

When a vapor condenses to a liquid, we say that the latent heat of condensation of the vapor is liberated. In a steam reboiler, this liberated heat is used to reboil the distillation tower. When a vapor, or more commonly a liquid, cools, we say that its sensible heat is reduced. For a small or slight temperature change, the change in latent heat might be large, while the change in sensible heat will be very small. 

Heat exchange provided by sensible-heat transfer is improved when velocities are higher. Especially when the heating fluid is on the tube side of an exchanger, sensible-heat-transfer rates are always increased by high velocity. 

This improved heat-transfer rate, promoted by low velocity, applies not only for condensing steam but also for condensing other pure-component vapors. And since condensation rates are favored by low velocity, this permits the engineer to design the steam side of reboilers and condensers in general for low-pressure drops. For example, if we measured the pressure above the channel head pass partition baffle shown in Fig. 12.1, we would observe a pressure of 100 psig. The pressure below the chaimel head pass partition baffle would typically be 99 psig. 

What would happen to a steam reboiler if the float in the steam trap became stuck in a partly closed position, or if the steam trap were too small Water—that is, steam condensate—would start to back up into 

Meanwhile, the tubes covered with stagnant water would begin to cool. The steam condensate submerging these tubes would cool. This cooled water would be colder than the saturation temperature of the condensing steam. The tubes would then be said to be submerged in subcooled water. 

What would happen to a steam reboiler if the float in the steam trap became stuck in a partly closed position, or if the steam trap were too small Water—that is, steam condensate—would start to back up into the channel head of the reboiler, as shown in Fig. 11.3. The bottom tubes of the reboiler bundle would become covered with water. The number of tubes exposed to the condensing steam would decrease. 

This would reduce the rate of steam condensation and also the reboiler heat duty. 

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The presence of even a small amount of noncondensable gas in the condensing mixture can significantly reduce the condensing heat transfer rates and needs to be recognized. See Figure 10-85. 

Effect of Noncondensable Gas. As shown in Fig. 14.3, the presence of a noncondensable gas creates an additional thermal resistance to condensation heat transfer due to the required diffusion of the vapor molecules through a gas-rich layer near the surface of the condensate. This additional resistance can reduce the condensation heat transfer rate substantially. 

The heat transfer mode for subcooling liquid is that of sensible heat exchange. Subcooling heat transfer rates are much lower than condensation heat transfer rates for two reasons. First, sensible heat transfer coeflicients are much lower than condensation coeflicients and second, as the liquid subcools, the temperature difference between the... 

Condensate removal. If condensate is removed at an insufficient rate, or if the condenser traps condensate, heat transfer area will become flooded. This will lower condenser heat transfer rates, as described in Sec. 15.10. Numerous case histories of troublesome condensate removal have been reported (134, 290, 381). 

In Figure 8.22, feed flow rate is increased to 10%. If condenser duty is fixed (fixed QC), no additional heat transfer occurs in the condenser, so there are large increases in the flow rate of the vapor distillate (DV) and in the reflux-drum temperature. These responses are muealistic because the increase in the flow rate of the overhead vapor into the condenser should change the condenser heat-transfer rate. 

Second, the velocities are also reduced because of bypassing. The reduced velocities may result in excessive fouling from solids deposition or from high tube-wall temperatures. Third, venting of noncondensables may not be properly achieved with resultant reduction of condensation heat transfer rates. 

Air-cooled condensers are used mostly in air-conditioning and for smaller-refrigeration capacities. The main advantage is avauability of cooling medium (air) but heat-transfer rates for the air side are far below values when water is used as a coohng medium. Condensation always occurs inside tubes, while the air side uses extended surface (fiusy... 

To nelp consei ve steam economy, venting is usually done from the steam chest of one effecl to the steam chest of the next. In this way, excess vapor in one vent does useful evaporation at a steam economy only about one less than the overall steam economy. Only when there are large amounts of noncondensable gases present, as in beet-sugar evaporation, is it desirable to pass the vents directly to the condenser to avoid serious losses in heat-transfer rates. In such cases, it can be worthwhile to recover heat from the vents in separate heat exchangers, which preheat the entering feed. 

As shown in Fig. 13-92, methods of providing column reflux include (a) conventional top-tray reflux, (b) pump-back reflux from side-cut strippers, and (c) pump-around reflux. The latter two methods essentially function as intercondenser schemes that reduce the top-tray-refliix requirement. As shown in Fig. 13-93 for the example being considered, the internal-reflux flow rate decreases rapidly from the top tray to the feed-flash zone for case a. The other two cases, particularly case c, result in better balancing of the column-refliix traffic. Because of this and the opportunity provided to recover energy at a moderate- to high-temperature level, pump-around reflirx is the most commonly used technique. However, not indicated in Fig. 13-93 is the fact that in cases h and c the smaller quantity of reflux present in the upper portion of the column increases the tray requirements. Furthermore, the pump-around circuits, which extend over three trays each, are believed to be equivalent for mass-transfer purposes to only one tray each. Bepresentative tray requirements for the three cases are included in Fig. 13-92. In case c heat-transfer rates associated with the two pump-around circuits account for approximately 40 percent of the total heat removed in the overhead condenser and from the two pump-around circuits combined. 

Compute condenser and reboiler heat-transfer rates from Eqs. (13-159) and (13-160). 

In work with the hydrogen chloride-air-water system, Dobratz, Moore, Barnard, and Mever [Chem. Eng. Prog., 49, 611 (1953)] using a cociirrent-flowsystem found that /cg (Eig. 14-77) instead of the 0.8 power as indicated by the Gilliland equation. Heat-transfer coefficients were also determined in this study. The radical increase in heat-transfer rate in the range of G = 30 kg/(s m ) [20,000 lb/(h fH)] was similar to that obsei ved by Tepe and Mueller [Chem. Eng. Prog., 43, 267 (1947)] in condensation inside tubes. 

Cooling water inlet and outlet temperatures are 80 and lOS F, respectively. The condenser heat transfer area is 1000 ft. The cooling water pressure drop through the condenser at design rate is 5 psi. A linear-trim control valve is installed in the cooling water line. The pressure drop over the valve is 30 psi at design with the valve half open. 

The effect of condensation upon transfer rates with application to flue-gas washing plants and cooling towers are discussed. Theoretical models were developed for determining the rate of heat and mass transfer under conditions where fog formation prevails. Derived relationships are functions of the vapor and liquid equilibria and local heat and mass transfer of driving forces. They were used for a numerical study of the amount of fog formation as a function of the operational variables of a flue-gas washing plant in which the inlet gas temperature is typically... 

Where Q = Heat-Transfer Rate Fs = Steam Mass Flow AHs = Latent Heat of Vaporization F = Feed Rate Cp = Heat Capacity of Feed T0 = Steam Supply Temperature Pt = Steam Supply Pressure P2 = Steam Valve Outlet Pressure Ps = Condensing Pressure Tj = Inlet Temperature T2 = Outlet Temperature A Tm = Log Mean Temperature Difference Ts = Condensing Steam Temperature... 

The basic assumption inherent to heat transfer limited pyrolysis models is that heat transfer rates, rather than decomposition kinetics, control the pyrolysis rate. Consequently, thermal decomposition kinetics do not come into play, other than indirectly through specification of Tp. This approximation is often justified on the basis of high activation energies typical of condensed-phase pyrolysis reactions, i.e., the reaction rate is very small below Tj, but then increases rapidly with temperature in the vicinity of Tp owing to the Arrhenius nature, and the high activation energy, of the pyrolysis reaction. 

In kinetically limited models, the pyrolysis rate is no longer calculated solely from a heat balance at the pyrolysis front. Instead, the rate at which the condensed-phase is volatilized depends on its temperature. This gives a local volumetric reaction rate (kg/m3-s) by assuming that all volatiles escape instantaneously to the exterior gas-phase with no internal resistance, the fuel mass flux is obtained by integrating this volumetric reaction rate in depth. One consequence is that the pyrolysis reaction is distributed spatially rather than confined to a thin front as with heat transfer limited models and the thickness of the pyrolysis front is controlled by decomposition kinetics and heat transfer rates. For a pyrolysis reaction with high activation energy or for very high heat transfer rates, the pyrolysis zone becomes thin, and kinetically limited models tend toward heat transfer limited models. 

The way in jvhich the condensate forms on the surface, i.e., in the form of a continuous film or in the form of discrete droplets, has a strong influence on the heat transfer rate. In film condensation, the latent heat released by the vapor must be... 

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