Rate of vaporization

V Total mass rate of flow mass rate of vapor generated Wp for total kg/s IVh... 

When the heat for evaporation in the constant-rate period is supplied by a hot gas, a dynamic equilibrium establishes the rate of heat transfer to the material and the rate of vapor removal from the surface ... 

The situation becomes more complicated when the reaction is IdneticaUy controlled and does not come to complete-chemical equilibrium under the conditions of temperature, hquid holdup, and rate of vaporization in the column reactor. Venimadhavan et al. [AIChE J., 40, 1814 (1994)] and Rev [Jnd. Eng. Chem. Res., 33, 2174 (1994)] show that the existence and location of reactive azeotropes is a function of approach to equilibrium as well as the evaporation rate. 

Assume a continuous release of pressurized, hquefied cyclohexane with a vapor emission rate of 130 g moLs, 3.18 mVs at 25°C (86,644 Ib/h). (See Discharge Rates from Punctured Lines and Vessels in this sec tion for release rates of vapor.) The LFL of cyclohexane is 1.3 percent by vol., and so the maximum distance to the LFL for a wind speed of 1 iti/s (2.2 mi/h) is 260 m (853 ft), from Fig. 26-31. Thus, from Eq. (26-48), Vj 529 m 1817 kg. The volume of fuel from the LFL up to 100 percent at the moment of ignition for a continuous emission is not equal to the total quantity of vapor released that Vr volume stays the same even if the emission lasts for an extended period with the same values of meteorological variables, e.g., wind speed. For instance, in this case 9825 kg (21,661 lb) will havebeen emitted during a 15-min period, which is considerablv more than the 1817 kg (4005 lb) of cyclohexane in the vapor cloud above LFL. (A different approach is required for an instantaneous release, i.e., when a vapor cloud is explosively dispersed.) The equivalent weight of TNT may be estimated by... 

The rate of vapor generation during refueling is a major parameter affecting the design of carbon canisters to meet ORVR requirements. 

For liquid vaporization conditions at or above the critical point, the rate of vapor discharge depends on the rate at which the fluid will expand. For such situations a latent heat of 116 kJ/kg can be used. 

M = Rate of vaporization and burning of liquid, kg/hr (selected as equal to the rate of flashed liquid entering the pit)... 

Ref [33a] in Appendix C cautions that if the vapor pressure of the fluid at the temperature is greater than the relief set/design pressure that the valve must be capable of handling the rate of vapor generation. Other situations should be examined as the thermal relief by itself may be insufficient for total relief. 

For tanks with a capacity of 20,000 barrels or more, the requirements for the vacuum condition are very close to the theoretically computed value of 2 cubic feet of air per hour per square foot of total shell and roof area. For tanks with a capacity of less than 20.000 barrels, the requirements for the vacuum condition have been based on 1 cubic foot of free air per hour for each barrel of tank capacity. This is substantially equivalent to a mean rate of vapor-space-temperature change of 1(X)F per hour. 

Tray efficiency is as high as for bubble caps and almost as high as sieve trays. It is higher than bubble caps in some systems. Performance indicates a close similarity to sieve trays, since the mechanism of bubble formation is almost identical. The real point of concern is that the efficiency falls off quickly as the flow rate of vapor through the holes is reduced close to the minimum values represented by the dump point, or point of plate initial activation. Efficiency increases as the tray spacing increases for a given throughput. 

The recirculation ratio for a unit is the lb rate of liquid leaving the outlet compared to the lb rate of vapor leaving. The liquid recirculation flow rate entering the unit is set by the differential pressure driving the system. 

Commercial propane and butane often contain substantial proportions of the corresponding unsaturated analogues and smaller amounts of near-related hydrocarbons, as well as these hydrocarbons themselves. Figure 20.1 shows vapor pressure/temperature curves for commercial propane and commercial butane. Due to its lower boiling point, higher rates of vaporization for substantial periods are obtainable from propane than from butane, and at the same time, appreciable pressures are maintained even at low ambient temperatures. 

All of us are familiar with the process of vaporization, in which a liquid is converted to a gas, commonly referred to as a vapor. In an open container, evaporation continues until all the liquid is gone. If the container is closed, the situation is quite different. At first, the movement of molecules is primarily in one direction, from liquid to vapor. Here, however, the vapor molecules cannot escape from the container. Some of them collide with the surface and reenter the liquid. As time passes and the concentration of molecules in the vapor increases, so does the rate of condensation. When the rate of condensation becomes equal to the rate of vaporization, the liquid and vapor are in a state of dynamic equilibrium ... 

In an effort to rationalize the basic mechanism, Brown and Jensen (B12) have solved the dynamic energy- and mass-flow equations, allowing for a finite rate of vaporization of the injected fluid. The results of these calculations have shown that both mechanisms can be important. For propellants which require relatively low depressurization rates (such as polyurethane types), the evaporative-cooling mechanism can develop sufficient depressurization rates. For PBAN propellants, direct surface-cooling is the only mechanism whereby estinguishment can be accomplished. 

Chemically similar substances have comparable vaporization coefficients, so that rates of vaporization, J, can be predicted from determined using equilibrium data. Beruto and Searcy [121] have suggested the similar use of the decomposition coefficient providing that due consideration is given to the occurrence of unstable intermediates. 

Chapter 10 deals with laminar flow in heated capillaries where the meniscus position and the liquid velocity at the inlet are unknown in advance. The approach to calculate the general parameters of such flow is considered in detail. A brief discussion of the effect of operating parameters on the rate of vaporization, the position of the meniscus, and the regimes of flow, is also presented. 

It is shown that an increase in the heat flux is accompanied by an increase in the liquid and vapor velocities, the meniscus displacement towards the outlet cross-section, as well as growth of vapor to liquid forces ratio and heat losses. When is large enough, the difference between the intensity of heat transfer and heat losses are limited by some final value, which determines the maximum rate of vaporization. Accordingly, when is large all characteristic parameters are practically invariable. 

By comparing Eqs. (71) and (72) to the non-phase-change equations in Section II,A,2, it can be seen that the only additional parameters to be evaluated are rv and rcl, the absolute rates of vaporization and condensation at the gas-liquid interface. The methods for evaluating all parameters in these model equations are given in Section III,D,2. 

The absolute rates of vaporization and condensation are evaluated by using the rate expressions discussed in Section III,B. The net rate of phase change at the bubble interface or equivalently the rate of bubble growth, has been widely studied for single bubbles in stationary systems. Bankoff (B2) has reviewed the results of these studies. Ruckenstein (R2) has analyzed bubble growth in flowing systems. 

The absolute rates of vaporization and condensation are evaluated from the rate expressions given in Section III,B. In the past, the rate of mass transfer (which is the net rate of phase change) has not been calculated from an understanding of the physics of the phase-change process at the interface. The rate is generally evaluated by applying some simplifying assumptions to the process, rather than from an expression in terms of the dependent variables of the model equations. 

From the design viewpoint, Eq. (78) could be coupled with Eq. (71) to obtain an approximation of the system performance and if the liquid temperature profile can be estimated, the same procedure can be followed with Eq. (80). However, in general the design engineer needs to use analytical expressions for the absolute rates of vaporization and condensation, so that with a knowledge of the rate terms and the other parameters, Eqs. (71) and (72) could be solved for the temperature and mass flow-rate profiles. 

It was shown that in heat transfer with phase change it is necessary to understand the phase-change phenomenon on the molecular level to model effectively the mass- and heat-transfer processes. An analytical expression for the rates of vaporization and condensation was developed. It was also shown that the assumption of a saturated vapor phase greatly simplified the calculation without a significant loss in accuracy for given examples. However, experimental verification of this simplified assumption is currently lacking. 

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