Mass transfer between phases

4 MASS TRANSFER BETWEEN PHASES 10.4A Introduction and Equilibrium Relations 

Introduction to interphase mass transfer. In Chapter 7 we considered mass transfer from a fluid phase to another phase, which was primarily a solid phase. The solute A was usually transferred from the fluid phase by convective mass transfer and through the solid by diffusion. In the present section we shall be concerned with the mass transfer of solute A from one fluid phase by convection and then through a second fluid phase by convection. For example, the solute may diffuse through a gas phase and then diffuse through and be absorbed in an adjacent and immiscible liquid phase. This occurs in the case of absorption of ammonia from air by water. 

The two phases are in direct contact with each other, such as in a packed, tray, or spray-type tower, and the interfacial area between the phases is usually not well defined. In two-phase mass transfer, a concentration gradient will exist in each phase, causing mass transfer to occur. At the interface between the two fluid phases, equilibrium exists in most cases. 

Equilibrium relations. Even when mass transfer is occurring equilibrium relations are important to determine concentration profiles for predicting rates of mass transfer. In Section 10.2 the equilibrium relation in a gas-liquid system and Henry s law were discussed. In Section 7.1C a discussion covered equilibrium distribution coefficients between two phases. These equilibrium relations will be used in discussion of mass transfer between phases in this section. 

In the majority of mass-transfer systems, two phases, which are essentially immiscible in each other, are present and also an interface between these two phases. Assuming the solute A is diffusing from the bulk gas phase G to the liquid phase L, it must pass through phase G, through the interface, and then into phase L in series. A concentration gradient 

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Chemical reaction always enhances the rate of mass transfer between phases. The possible magnitudes of such enhancements are indicated in Tables 23-6 and 23-7. They are no more predictable than are specific rates of chemical reactions and must be found experimentally for each case, or in the relatively sparse literature on the subject. 

Mass Transfer Mass transfer in plate and packed gas-liquid contactors has been covered earHer in this subsection. Attention nere will be limited to deep-bed contactors (bubble columns and agitated vessels). Theory underlying mass transfer between phases is discussed in Sec. 5 of this handbook. 

Coalescence The coalescence of droplets can occur whenever two or more droplets collide and remain in contact long enough for the continuous-phase film to become so thin that a hole develops and allows the liquid to become one body. A clean system with a high interfacial tension will generally coalesce quite rapidly. Particulates and polymeric films tend to accumulate at droplet surfaces and reduce the rate of coalescence. This can lead to the ouildup of a rag layer at the liquid-hquid interface in an extractor. Rapid drop breakup and rapid coalescence can significantly enhance the rate of mass transfer between phases. 

An impeller with a high fluid head is one with high peripheral velocity and discharge velocity. Such impellers are useful for (I) rapid reduction of concentration differences in the impeller discharge stream (rapid mixing), (2) production of large interfacial area and small droplets in gas-hquid and immiscible-liquid systems, (3) sohds deagglomeration, and (4) promotion of mass transfer between phases. 

Rushton (R11) in 1954 presented a graph showing contacting efficiency as a function of impeller diameter at constant power input. He found that the rate of mass transfer between phases increased to a maximum and then decreased as the impeller diameter increased. The optimum occurred at a ratio of impeller to tank diameter of about 0.25, a ratio which is much smaller than that found for liquid blending. 

The role of mixing in heterogeneous reactions is obvious. In multiphase processes mixing imposed by a stirrer or an external pump is necessary to increase the interface through which reactants pass to meet their partner in the other phase and/or to intensify mass transfer between phases. Mixing can also play a significant role in the case of homogeneous reactions. Chemical reactions occur at the molecular level. Reactant molecules introduced into a reactor encounter the environment in the vicinity of the inlet. The composition of the mixture there is obviously... 

Annular flow, smooth interface (Henry et al., 1969) Since the interface is relatively small compared to dispersed flow and assumed to be smooth, there is no significant momentum transfer or mass transfer between phases. Under such conditions, the change of slip ratio with pressure is... 

Mist flow, one component In a one-component system with finely dispersed drops in the mist flow, the mass transfer between phases over a large interfacial area has to be considered. For the compression wave the frozen state can be assumed to be subcooled liquid, superheated vapor conditions generated by the wave are fairly stable, and the expressions for the two-component system are valid (Henry, 1971) ... 

Sherwood TK, Woertz BB. The role of eddy diffusion in mass transfer between phases. Trans Am Inst Chem Eng 1939 35 517-540. 

Since mass transfer between phases occurs for all time t, the mass and volumes of each phase are non-constant in the interval between initial and final reaction times [tospectroscopic results and data analysis, particularly when calculating moles present. 

In Chapter 17 we pointed out that the treatment of heterogeneous reaction required the consideration of two factors in addition to those normally encountered in homogeneous reactions the modification of the kinetic expressions resulting from the mass transfer between phases and the contacting patterns of the reacting phases. 

These empirical correlations were originally based mainly on data obtained for isothermal horizontal flow at pressures close to atmospheric (to 50 psi), normal temperatures, and pipe diameters to one inch using air and eight different liquids. In order to apply these equations to singlecomponent two-phase flow with mass transfer between phases, Martinelli... 

For no mass transfer between phases, the acceleration loss is approximately,... 

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. 

Mathematical models of packed bed reactors can be classified into two broad categories (1) one-phase, or pseudohomogeneous, models in which the reactor bed is approximated as a quasi-homogeneous medium and (2) two-phase, or heterogeneous, models in which the catalyst and fluid phases and the heat and mass transfer between phases are treated explicitly. Although the... 

Mass transfer between phases Relative phase velocities, C, P, T Important... 

The mass transfer between phases is, of course, the very basis for most of the diffusional operations of chemical engineering. A considerable amount of experimental and empirical work has been done in connection with interphase mass transfer because of its practical importance an excellent and complete survey of this subject may be found in the text book of Sherwood and Pigford (S9, Chap. Ill), where dimensionless correlations for mass transfer coefficients in systems of various shapes are assembled. 

A short guard column containing the same stationary phase as the analytical column is placed before the analytical column to protect it from contamination with particles or irreversibly adsorbed solutes. A high-quality pump provides smooth solvent flow. The injection valve allows rapid, precise sample introduction. The column is best housed in an oven to maintain a reproducible temperature. Column efficiency increases at elevated temperature because the rate of mass transfer between phases is increased. Mass spectro-metric detection provides quantitative and qualitative information for each substance eluted from the column. Ultraviolet detection is most common and it can provide qualitative information if a photodiode array is used to record a full spectrum of each analyte. Refractive index detection has universal response but is not very sensitive. Evaporative light scattering responds to the mass of each... 

The other mixing operations of the list require individual kinds of equipment whose design in some cases is less quantified and is based largely on experience and pilot plant work. Typical equipment for such purposes will be illustrated later in this chapter. Phase mixing equipment which accomplishes primarily mass transfer between phases, such as distillation and extraction towers, also are covered elsewhere. Stirred reactors are discussed in Chapter 17. 

Continuous changes in compositions of phases flowing in contact with each other are characteristic of packed towers, spray or wetted wall columns, and some novel equipment such as the FHGEE contactor (Fig. 13.14). The theory of mass transfer between phases and separation of mixtures under such conditions is based on a two-film theory. The concept is illustrated in Figure 13.15(a). 

An overall conversion rate may depend on rates of mass transfer between phases as well as chemical rates. In the simplest case, mass transfer and chemical transformation occur in series advantage is taken of the equality of these two rates at steady state conditions to eliminate interfacial concentrations from the rate equations and thus to permit integration. Item 8 of Table 17.2 is an example. 

The fixed beds of concern here are made up of catalyst particles in the range of 2-5 mm dia. Vessels that contain inert solids with the sole purpose of improving mass transfer between phases and developing plug flow behavior are not in this category. Other uses of inert packings are for purposes of heat transfer, as in pebble heaters and induction heated granular beds—these also are covered elsewhere. 

Curve B of Figure 2 is typical of gas-liquid contacting operations. Here the rate pf mass transfer between phases increases to a maximum at small impeller diameter and then decreases as impeller diameter is increased. The significance is that more turbulence is available with the small impeller and that turbulence is more important than flow in this operation. 

A theoretical analysis is helpful for understanding the basic characteristics of impinging stream processes and the performances of the related devices. In an impinging stream device, where the residence time distribution of particles is most important is in the impingement zone, because this zone is the major active region for heat and mass transfer between phases in such a device. Unfortunately, it is basically... 

As mentioned, like any other technical method, the method of impinging streams (IS) cannot be a universal tool. On one hand, IS has the outstanding advantage of significantly enhancing heat and mass transfer between phases while on the other, it also has its intrinsic faults. From the discussions in the previous chapters, the essential characteristics of gas-continuous impinging streams can be summarized briefly as follows ... 

Its effect on enhancing heat and mass transfer between phases is very significant ... 

In principle, gas-continuous impinging streams (GIS) can be applied for the combustion of gases, powdery solids and sprayed liquids. Since gas-combustion is relatively simple and the process is essentially independent of the major feature of GIS, i.e., that it significantly enhances heat and mass transfer between phases, the discussions in this chapter will focus on the combustion of the latter two kinds of fuels. 

As mentioned earlier, in gas-continuous impinging streams heat and mass transfer between phases are enhanced efficiently mainly by the following factors (1) Very high relative velocity between phases round the impingement plane, even higher than in common devices by several tens of times (2) Oscillation movement of particles or... 

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