Vaporization single-component

There are various expressions for the Sherwood and Nusselt numbers if the relative drop-gas velocity is nonzero, i.e., for forced convection. Widely used correlations are those by Ranz and Marshall [20]. These were obtained from experiments of vaporizing single-component drops at atmospheric pressure and moderate ambient temperatures with low transfer rates, that is, when B = B kQ and, therefore, Nmo = 5/jo = 2. These correlations are given by... 

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. 

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. 

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. 

Diffusion through a stagnant film, as in absorption or stripping processes involving the transfer of a single component between liquid and vapor phases. Since there is a concentration gradient... 

Next consider the triple point of the single-component system at which the solid, liquid, and vapor phases are at equilibrium. The description of the surfaces and tangent planes at this point are applicable to any triple point of the system. At the triple point we have three surfaces, one for each phase. For each surface there is a plane tangent to the surface at the point where the entire system exists in that phase but at the temperature and pressure of the triple point. There would thus seem to be three tangent planes. The principal slopes of these planes are identical, because the temperatures of the three phases and the pressures of the three phases must be the same at equilibrium. The three planes are then parallel. The last condition of equilibrium requires that the chemical potential of the component must be the same in all three phases. At each point of tangency all of the component must be in that phase. Consequently, the condition... 

As an illustration consider a single-component, two-phase system in a potential field. Let the phases be a gas and a liquid phase. Such a system has one degree of freedom, and we then choose the temperature, volume, and moles of the component to be the variables that define the state of the system. The cross section of the container, A, is uniform. Let the bottom of the container be at the position rt in the field. Figure 14.2 illustrates this system where r0 is the position of the phase boundary. With knowledge of the volume of the system and the cross section of the container, (r2 — rt) is known. The unknown quantities are r0 and the moles of the component in each phase. The pressure at the phase boundary is the vapor pressure of the liquid at the chosen temperature. Then the number of moles of the component in the gas phase is... 

Having identified discrete components as our criterion, the next problem is how to define the equilibrium of three components. In Chap. 2, for example, the vapor-liquid equilibrium of a flash—a single component transfer between two phases—was derived. A certain quantity of a component, called the y fraction, is vaporized into the vapor phase as an equal amount of the same component, called the x fraction, is dissolved in the liquid phase. The K value (the equilibrium constant of K=y/x) is used to determine the component distribution results. This same logic may be used here. Although we cannot use these same K values, as they do not apply, we can apply another database. 

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