Single-Component Vaporizer

Consider the vaporizer sketched in Fig. 3.6. Liquefied petroleum gas (LPG) is fed into a pressurized tank to hold the liquid level in the tank. We will assume that LPG is a pure component propane. Vaporization of mixtures of components is discussed in Sec. 3.8. 

The liquid in the tank is assumed perfectly mixed. Heat is added at a rate Q to hold the desired pressure in the tank by vaporizing the liquid at a rate W (mass per time). Heat losses and the mass of the tank walls are assumed negligible. Gas is drawn off the top of the tank at a volumetric flow rate F . F is the forcing function or load disturbance. 

STEADYSTATE MODEL. The simplest model would neglect the dynamics of both vapor and liquid phases and relate the gas rate to the heat input by 

LIQUID-PHASE DYNAMICS MODEL. A somewhat more realistic model is obtained if we assume that the volume of the vapor phase is small enough to make its dynamics negligible. If only a few moles of Uquid have to be vaporized to change the pressure in the vapor phase, we can assume that this pressure is always equal to the vapor pressure of the liquid at any temperature (P = P and = p F ). An energy equation for the liquid phase gives the temperature (as a function of time), and the vapor-pressure relationship gives the pressure in the vaporizer at that temperature. 

A total continuity equation for the liquid phase is also needed, plus the two controller equations relating pressure to heat input and liquid level to feed flow rate Fq. These feedback controller relationships will be expressed here simply as functions. In later parts of this book we will iscuss these fhnctions in detail. 

---

Shell-Side Arrangements The one-pass shell (Fig. 11-35E) is the most commonly used arrangement. Condensers from single component vapors often have the nozzles moved to the center of the shell for vacuum and steam sei vices. 

SCV - Single-component vapor MCV - Multicomponent vapor SC - Subcooled condensate Ap - Pressure drop C - Coolant. Acceptability G - good F - fair P - poor X - not acceptable or not recommended. 

Configurational-bias Monte Carlo in the Gibbs ensemble has been successfully applied to the calculations of single-component vapor-liquid phase equilibria of linear and branched alkanes [61,63-67], alcohols [68,69], and a fatty-acid Langmuir monolayer [70]. The extension to multicomponent mixtures introduces a case in which the smaller molecules (members of a homologous series) have a considerably higher acceptance rate in the swap move than do larger molecules. In recent simulations for alkane mixtures... 

Vertical in-shell condensers. This is a common condensation mode in reboilers but not in overhead condensers. Vapor flows downward, (Figs. 15.1a, c, and 15.10a). The shell can be baffled (Fig. 15.10a), but often it is not for a single-component vapor. 

For the case of single-component vapor-to-liquid nucleation the above equation, in conjunction with (23), yields... 

FIG. 5 Single-component vapor-liquid equilibrium imder the capillary pressure difference. (From Ref. 25.)... 

There are no concentration differences across either the gas film or the liquid film for a single component vapor. The main resistance to condensation is the thermal gradient across the liquid film. Thus, the heat transfer coefficient primarily is a function of the thermal conductivity of the liquid, similar to the performance of vertical condenser tubes as described by Nusselt [7]. The thermal conductivity of most liquids decreases as the temperature increases however, some liquids exhibit a maximum value of thermal conductivity at a particular temperature [8]. 

Because this type of operation essentially involves the Nusselt theory with enhanced liquid flow, a heat transfer coefficient approach is used for calculative purposes, rather than transfer units. Temperature differences are calculated as if a surface condenser were being used. If a single-component vapor is condensing at a constant pressure, the temperature difference at the liquid coolant inlet is T — q. Similarly, the temperature difference at the liquid coolant outlet is Ti — to- This is true because the vapor temperature remains constant from the first drop of condensate to the last drop. Thus, the logarithmic mean temperature driving force is ... 

Single-component vapor— Vapor phase that contains but one chemical substance. 

Evaporation processes usually separate a single component (typically water) from a nonvolatile material. As such, it is good enough in most cases to assume that the vaporization and condensation processes take place at constant temperatures. 

This equation applies to vaporization of single components, but can be used for close boiling mixtures without too much error. Coefficients for wide boiling mixtures will be overestimated. 

Since the pressure drop in two-phase flow is closely related to the flow pattern, most investigations have been concerned with local pressure drop in well-characterized two-phase flow patterns. In reality, the desired pressure drop prediction is usually over the entire flow channel length and covers various flow patterns when diabatic condition exist. Thus, a summation of local Ap values is necessary, assuming the phases are in thermodynamic equilibrium. The addition of heat in the case of single-component flow causes a phase change along the channel consequently, the vapor void increases and the phase (also velocity) distribution as well as the momentum of the flow vary accordingly. 

This section describes the phase change process for a single component on a molecular level, with both vaporization and condensation occurring simultaneously. Molecules escape from the liquid surface and enter the bulk vapor phase, whereas other molecules leave the bulk vapor phase by becoming attached to the liquid surface. Analytical expressions are developed for the absolute rates of condensation and vaporization in one-component systems. The net rate of phase change, which is defined as the difference between the absolute rates of vaporization and condensation, represents the rate of mass... 

Near the critical region, the property ratio can be replaced by T(dP/dT)sat via the Clapeyron relation since both hfg and tyg are approaching zero. Here (dP/dT)sat is the slope of the vapor-pressure curve and has units of Pa/K. For multicomponent fluids, Eq. (23-93) is evaluated for each major component (> 10 % wt), and the largest single-component venting requirement is used. Refer to CCPS Guidelines (1998) for more complex schemes. 

Note that Eq. (23-94) is implicit in W a trial-and-error solution method is required. This equation is applicable for single-component or pseudo-one-component systems. For the latter, hfg is defined to be the enthalpy (heat) required to vaporize a unit mass of liquid at equilibrium vapor composition. 

Two-phase flow systems may be classified initially by composition, as containing a single component (a pure liquid and its vapor), or two or more components with any one component present in both phases or only essentially in one or the other phase. Systems may further be described as involving transfer of mass between phases, or otherwise and as isothermal, or adiabatic, or as having some intermediate temperature behavior. 

The basic assumptions implied in the homogeneous model, which is most frequently applied to single-component two-phase flow at high velocities (with annular and mist flow-patterns) are that (a) the velocities of the two phases are equal (b) if vaporization or condensation occurs, physical equilibrium is approached at all points and (c) a single-phase friction factor can be applied to the mixture if the Reynolds number is properly defined. The first assumption is true only if the bulk of the liquid is present as a dispersed spray. The second assumption (which is also implied in the Lockhart-Martinelli and Chenoweth-Martin models) seems to be reasonably justified from the very limited evidence available. 

In the case of single-component two-phase flow, such as in vaporizing water, physical equilibrium is commonly assumed and seems to yield reasonable results, even though it might seem that supersaturation could occur. The rate of mass transfer between phases, therefore, is not a limiting process for single component flow. 

Critical temperature, sometimes used in this discussion, is not to be confused with critical solution temperature. Critical temperature has its usual meaning of maximum temperature for equilibrium of liquid and vapor phases, usually of a single component, under pressure. 

---