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Rate of mass transfer

The relationship between the compositions of a given component in the liquid and vapor phases at a given column height is determined by the mass transfer rate of that component from one phase to the other. The mass transfer rate is a function of the resistance in the vicinity of the phase boundary and the composition driving force. [Pg.536]

FIGURE 15.3 Two-film mass transfer model, (a) operating line and equilibrium curve, (b) [Pg.536]

Two more points may be defined on the equilibrium curve corresponding to the same column height as (X,Y). Point (X,Y ) represents the liquid bulk composition, X, and the vapor composition, F, that would be at equilibrium with it. Point (A, T) represents the vapor bulk composition, Y, and the liquid composition, X, that would be at equilibrium with it. Note that X and Y do not exist at the same column height as (A,T). [Pg.537]

The rate of mass transfer across a film per unit of interface area is determined by the composition gradient, diffusivity, and fihn thickness. One way of expressing this relationship is through a mass transfer coefficient that includes the effects of both diffusivity and film thickness. If the compositional driving force is represented as the difference between the component mole fraction in the bulk and at the interface, the rate of mass transfer in the liquid film is given as [Pg.537]

Equations 15.9 and 15.10 are empirical with respect to the dehnition of the mass transfer coefficients, but the form of the equations is based on molecular diffusion theory. Applying the theory to a multi-component mixture where each component has a distinct diffusivity is impractically complex and must rely on diffusivity data for all the components in the mixture. To derive usable equations from the diffusion theory, certain simplifying assumptions must be made. The basis for the derivation of Equations 15.9 and 15.10 is to assume that mass transfer takes place either as equimolar counterdiffusion or as unimolar diffusion under dilute conditions. [Pg.538]


However, a note of caution should be added. In many multiphase reaction systems, rates of mass transfer between different phases can be just as important or more important than reaction kinetics in determining the reactor volume. Mass transfer rates are generally higher in gas-phase than liquid-phase systems. In such situations, it is not so easy to judge whether gas or liquid phase is preferred. [Pg.45]

The high rate of mass transfer in SECM enables the study of fast reactions under steady-state conditions and allows the mechanism and physical localization of the interfacial reaction to be probed. It combines the usefid... [Pg.1941]

The experimentally observed rates of mass transfer are often proportional to the displacement from equiHbrium and the rate equations for the gas and Hquid films are... [Pg.20]

Rate Equations with Concentration-Independent Mass Transfer Coefficients. Except for equimolar counterdiffusion, the mass transfer coefficients appHcable to the various situations apparently depend on concentration through thej/g and factors. Instead of the classical rate equations 4 and 5, containing variable mass transfer coefficients, the rate of mass transfer can be expressed in terms of the constant coefficients for equimolar counterdiffusion using the relationships... [Pg.22]

Rate of Mass Transfer in Bubble Plates. The Murphree vapor efficiency, much like the height of a transfer unit in packed absorbers, characterizes the rate of mass transfer in the equipment. The value of the efficiency depends on a large number of parameters not normally known, and its prediction is therefore difficult and involved. Correlations have led to widely used empirical relationships, which can be used for rough estimates (109,110). The most fundamental approach for tray efficiency estimation, however, summarizing intensive research on this topic, may be found in reference 111. [Pg.42]

As illustrated ia Figure 6, a porous adsorbent ia contact with a fluid phase offers at least two and often three distinct resistances to mass transfer external film resistance and iatraparticle diffusional resistance. When the pore size distribution has a well-defined bimodal form, the latter may be divided iato macropore and micropore diffusional resistances. Depending on the particular system and the conditions, any one of these resistances maybe dominant or the overall rate of mass transfer may be determined by the combiaed effects of more than one resistance. [Pg.257]

The term dqljdt represents the overall rate of mass transfer for component / (at time t and distance averaged over a particle. This is governed by a mass transfer rate expression which may be thought of as a general functional relationship of the form... [Pg.260]

The rate of mass transfer,/, is then assumed to be proportional to the concentration differences existing within each phase, the surface area between the phases,, and a coefficient (the gas or Hquid film mass transfer coefficient, k or respectively) which relates the three. Thus... [Pg.332]

The Driving Force for Mass Transfer. The rate of mass transfer increases as the driving force, (7 — (7, is increased. can be enhanced as follows. From Dalton s law of partial pressures... [Pg.333]

Oxygen transfer rate (OTR) is estimated by the foUowiag standard procedure (12), where the rate of mass transfer per unit volume of Hquid is taken to be directly proportional to the driving force of the system... [Pg.342]

If condensation requires gas stream cooling of more than 40—50°C, the rate of heat transfer may appreciably exceed the rate of mass transfer and a condensate fog may form. Fog seldom occurs in direct-contact condensers because of the close proximity of the bulk of the gas to the cold-Hquid droplets. When fog formation is unavoidable, it may be removed with a high efficiency mist collector designed for 0.5—5-p.m droplets. Collectors using Brownian diffusion are usually quite economical. If atmospheric condensation and a visible plume are to be avoided, the condenser must cool the gas sufftciendy to preclude further condensation in the atmosphere. [Pg.389]

The rate of mass transfer (qv) depends on the interfacial contact area and on the rate of mass transfer per unit interfacial area, ie, the mass flux. The mass flux very close to the Hquid—Hquid interface is determined by molecular diffusion in accordance with Pick s first law ... [Pg.62]

In many types of contactors, such as stirred tanks, rotary agitated columns, and pulsed columns, mechanical energy is appHed externally in order to reduce the drop si2e far below the values estimated from equations 36 and 37 and thereby increase the rate of mass transfer. The theory of local isotropic turbulence can be appHed to the breakup of a large drop into smaller ones (66), resulting in an expression of the form... [Pg.69]

Mass Transfer and Kinetics in Rotary Kilns. The rates of mass transfer of gases and vapors to and from the sohds iu any thermal treatment process are critical to determining how long the waste must be treated. Oxygen must be transferred to the sohds. However, mass transfer occurs iu the context of a number of other processes as well. The complexity of the processes and the parallel nature of steps 2, 3, 4, and 5 of Figure 2, require that the parameters necessary for modeling the system be determined empirically. In this discussion the focus is on rotary kilns. [Pg.50]

In addition to electrode kinetics, the rate of an electrochemical reaction can be limited by the rate of mass transfer of reactants to and from the electrode surface. In dilute solutions, four principal equations are used. The flux of species i is... [Pg.65]

For systems in which the solute concentrations in the gas and hquid phases are dilute, the rate of transfer may be expressed by equations which predic t that the rate of mass transfer is proportional to the difference between the bulk concentration and the concentration at the gas-liquid interface. Thus... [Pg.600]

Experimentally observed rates of mass transfer often are expressed in terms of overall transfer coefficients even when the eqmlibrium lines are curved. This procedure is empirical, since the theory indicates that in such cases the rates of transfer may not vary in direct proportion to the overall bulk concentration differences y — y°) and (x° — x) at all concentration levels even though the rates may be proportional to the concentration difference in each phase taken separately, i.e., Xi — x) and y — y ). [Pg.602]

For the special case of steady-state unidirectional diffusion of a component through an inert-gas film in an ideal-gas system, the rate of mass transfer is derived as... [Pg.604]

Effects of Total Pressure on Uq and The influence of total system pressure on the rate of mass transfer from a gas to a licniid or to a solid has been shown to be the same as would be predicted from stagnant-film theory as defined in Eq. (5-285), where... [Pg.607]

When reactants are distributed between several phases, migration between phases ordinarily will occur with gas/liquid, from the gas to the liquid] with fluid/sohd, from the fluid to the solid between hquids, possibly both ways because reactions can occur in either or both phases. The case of interest is at steady state, where the rate of mass transfer equals the rate of reaction in the destined phase. Take a hyperbohc rate equation for the reaction on a surface. Then,... [Pg.691]

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. [Pg.706]

Wet-bulb temperature is the dynamic equilibrium temperature attained by a water surface when the rate of heat transfer to the surface by convection equals the rate of mass transfer away from the surface. At equilibrium, if neghgible change in the dry-bulb temperature is assumed, a heat balance on the surface is... [Pg.1151]

Equations (13-111) to (13-114), (13-118) and (13-119), contain terms, Njj, for rates of mass transfer of components from the vapor phase to the liquid phase (rates are negative if transfer is from the liquid phase to the vapor phase). These rates are estimated from diffusive and bulk-flow contributions, where the former are based on interfacial area, average mole-fraction driving forces, and mass-... [Pg.1291]

Mass Transfer Relationships for calculating rates of mass transfer between gas and liquid in packed absorbers, strippers, and distillation columns may be found in Sec. 5 and are summarized in Table, 5-28. The two-resistance approach is used, with rates expressed as transfer units ... [Pg.1398]

Wetted-waU or falhng-film columns have found application in mass-transfer problems when high-heat-transfer-rate requirements are concomitant with the absorption process. Large areas of open surface are available for heat transfer for a given rate of mass transfer in this type of equipment because of the low mass-transfer rate inherent in wetted-waU equipment. In addition, this type of equipment lends itself to annular-type coohng devices. [Pg.1402]

Note that the group on the left side of Eq. (14-182) is dimensionless. When turbulence promoters are used at the inlet-gas seclion, an improvement in gas mass-transfer coefficient for absorption of water vapor by sulfuric acid was obsei ved by Greenewalt [Ind. Eng. Chem., 18, 1291 (1926)]. A falhug off of the rate of mass transfer below that indicated in Eq. (14-182) was obsei ved by Cogan and Cogan (thesis, Massachusetts Institute of Technology, 1932) when a cauTiiug zone preceded the gas inlet in ammonia absorption (Fig. 14-76). [Pg.1402]

The rate of mass transfer in the liquid phase in wetted-waU columns is highly dependent on surface conditions. When laminar-flow conditions prevail without the presence of wave formation, the laminar-penetration theory prevails. When, however, ripples form at the surface, and they may occur at a Reynolds number exceeding 4, a significant rate of surface regeneration develops, resulting in an increase in mass-transfer rate. [Pg.1402]

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. [Pg.1470]

Pulsed Spray Columns Billerbeck et al. [Jnd. Eng. Chem., 48, 183 (1956)] applied pulsing to a laboratoiy [3.8-cm- (1.5-in-) diameter] column. At pulse amplitude 1.11 cm 6 in), rates of mass transfer improved slightly with increased frequency up to 400 cycies/min, but the effecl was relatively small. Shirotsuka [Kagaku Kogaku, 22, 687 (1958)] provides additional data. There is not believed to be commercial application. [Pg.1489]

The dominant mechanism of purification for column ciystallization of sohd-solution systems is reciystallization. The rate of mass transfer resulting from reciystallization is related to the concentrations of the solid phase and free hquid which are in intimate contac t. A model based on height-of-transfer-unit (HTU) concepts representing the composition profQe in the purification sec tion for the high-melting component of a binaiy solid-solution system has been reported by Powers et al. (in Zief and Wilcox, op. cit., p. 363) for total-reflux operation. Typical data for the purification of a solid-solution system, azobenzene-stilbene, are shown in Fig. 22-10. The column ciystallizer was operated... [Pg.1993]

Reaction between an absorbed solute and a reagent reduces the equilibrium partial pressure of the solute, thus increasing the rate of mass transfer. The mass-transfer coefficient hkewise is enhanced, which contributes further to increased absorption rates. Extensive theoretical analyses of these effects have been made, but rather less experimental work and design guidehnes. [Pg.2105]

The rate of mass transfer aeross a phase boundary or interfaee ean be expressed by N=K.A(AC) ... [Pg.50]


See other pages where Rate of mass transfer is mentioned: [Pg.232]    [Pg.19]    [Pg.23]    [Pg.66]    [Pg.52]    [Pg.169]    [Pg.602]    [Pg.1180]    [Pg.1241]    [Pg.1290]    [Pg.1291]    [Pg.1403]    [Pg.1445]    [Pg.1466]    [Pg.1637]    [Pg.1639]    [Pg.405]    [Pg.263]    [Pg.271]   
See also in sourсe #XX -- [ Pg.168 ]




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