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Mass transfer Higbie model

Average rates of mass transfer can be obtained, as previously, by using either the Higbie or the Danckwerts model for surface renewal. [Pg.613]

Given that, from the penetration theory for mass transfer across an interface, the instantaneous rale ol mass transfer is inversely proportional to the square root of the time of exposure, obtain a relationship between exposure lime in the Higbie mode and surface renewal rate in the Danckwerts model which will give the same average mass transfer rate. The age distribution function and average mass transfer rate from the Danckwerts theory must be deri ved from first principles. [Pg.857]

In calculating Ihe mass transfer rate from the penetration theory, two models for the age distribution of the surface elements are commonly used — those due to Higbie and to Danckwerts, Explain the difference between the two models and give examples of situations in which each of them would be appropriate. [Pg.857]

The point of view based on a physical model started with the 1935 paper of Higbie [30], While the main problem treated by Higbie was that of the mass transfer from a bubble to a liquid, it appears that he had recognized the utility of his representation for both packed beds and turbulent motion. The basic idea is that an element of liquid remains in contact with the other phase for a time A and during this time, absorption takes place in that element as in the unsteady diffusion in a semiinfinite solid. The mass transfer coefficient k should therefore depend on the diffusion coefficient D and on the time A. Dimensional analysis leads in this case to the expression... [Pg.84]

Penetration theory (Higbie, 1935)assumes that turbulent eddies travel from the bulk of the phase to the interface where they remain for a constant exposure time te. The solute is assumed to penetrate into a given eddy during its stay at the interface by a process of unsteady-state molecular diffusion. This model predicts that the mass-transfer coefficient is directly proportional to the square root of molecular diffusivity... [Pg.228]

Given that the instantaneous mass transfer rate = Kt 1/ 2, then for the Higbie model, the average mass transfer rate for an exposure time te is given by ... [Pg.250]

The mass-transfer coefficient in each film is expected to depend upon molecular diffusivity, and this behavior often is represented by a power-law function k . For two-film theory, n = 1 as discussed above [(Eq. (15-62)]. Subsequent theories introduced by Higbie [Trans. AIChE, 31, p. 365 (1935)] and by Dankwerts [Ind. Eng. Chem., 43, pp. 1460-1467 (1951)] allow for surface renewal or penetration of the stagnant film. These theories indicate a 0.5 power-law relationship. Numerous models have been developed since then where 0.5 < n < 1.0 the results depend upon such things as whether the dispersed drop is treated as a rigid sphere, as a sphere with internal circulation, or as oscillating drops. These theories are discussed by Skelland [ Tnterphase Mass Transfer, Chap. 2 in Science and Practice of Liquid-Liquid Extraction, vol. 1, Thornton, ed. (Oxford, 1992)]. [Pg.1734]

With the age distribution function for the classic Higbie model (Eq. 9.1.5), the average mass transfer coefficient is... [Pg.223]

The matrix [/c] in Eq. 9.3.30 is the matrix of mass transfer coeflicients at any time t. The matrix of time-averaged zero-flux mass transfer coeflicients is given for the Higbie model by... [Pg.232]

The addition of various surfactants and micelle forming agents on the biphasic hydroformylation of olefins was also considered as a tool for enhancement of the reaction rate. The relation between the extent of emulsification of the reaction mixture and the performance of hydroformylation reaction was also investigated. Mass transfer effects in biphasic hydroformylation of 1-octene in the presence of cetyltri-methylammoniumbromide (CTAB), was studied by Lekhal etal. [33], A mass-transfer model based on the Higbie s penetration theory was proposed to predict the rate of hydroformylation in a heterogeneous gas-liquid-liquid system under... [Pg.372]

In Chapter 7 we discussed the basics of the theory concerned with the influence of diffusion on gas-liquid reactions via the Hatta theory for flrst-order irreversible reactions, the case for rapid second-order reactions, and the generalization of the second-order theory by Van Krevelen and Hofitjzer. Those results were presented in terms of classical two-film theory, employing an enhancement factor to account for reaction effects on diffusion via a simple multiple of the mass-transfer coefficient in the absence of reaction. By and large this approach will be continued here however, alternative and more descriptive mass transfer theories such as the penetration model of Higbie and the surface-renewal theory of Danckwerts merit some attention as was done in Chapter 7. [Pg.608]

Given that the instantaneous mass transfer rate = then for the Higbie model, the... [Pg.250]

Lekhal et al. [6] proposed a pseudo-homogeneous gas-liquid-liquid model based on the Higbie penetration theory to account for simultaneous absorption of two gases into the liquid phases. Because of the assumption of rapid liquid-liquid mass transfer of reactants leading to the equilibrium between two liquid phases, the model was simplified greatly and the detail of phase dispersion and distribution and multiphase flow was avoided. Reasonable success was achieved and the results of analysis suggested that the only limitation to the conversion of hydroformylation of 1-octene was the gas-liquid mass transfer of CO and H2. [Pg.111]

The Higbie penetration model for mass transfer compensates for transient behavior. It assumes that mass transfer occurs during brief phase contacts that do not allow enough time for steady-state conditions. In other words, the phases collide but do not have a definitive and continuous interface with respect to time. The mass transfer is prompted by turbulence that refreshes the interface, and the refresh rate is the limiting step in mass transfer. Eddies approach the surface at which point mass transfer by molecular diffiision is initiated and is described by Azbel (1981) ... [Pg.13]

However, the absence of any parameter related to the channel size limits the application of the model to different two-phase systems. Van Baten and Krishna (2004) and Irandoust and Andersson (1989) included in their models the contributions of both bubble caps and film (Eq. 2.2.34). Van Baten and Krishna (2004) evaluated the contribution of the caps according to the Higbie penetration theory (Eq. 2.2.35), whilst the transfer through the film was obtained based on mass transfer in a falling film in laminar flow (Eqs. 2.2.36 and 2.2.37). [Pg.31]

A relatively simple model to describe the gas-liquid mass transfer in circular channels with slug flow pattern was proposed by van Eaten and Krishna [47]. For their fundamental model the authors considered an idealized geometry of the Taylor bubbles as shown in Figure 7.12. The bubbles consist of two hemispherical caps and a cylindrical body. The Higbie penetration model was applied to describe the mass transfer process of a compound from the gas phase to the liquid (Equation 7.8). For a rising bubble, the liquid will flow along the bubble surface of the cap. The average distance... [Pg.287]

The gas-phase mass transfer is described by the stagnant film model whilst for the liquid phase Higbie s penetration model was used. The process of diffusion and simultaneous reaction in the liquid-phase penetration zone is given by the following balances [4] ... [Pg.359]

Penetration theory can also be applied to turbulent conditions by assuming the turbulence spectrum to consist of large eddies, capable of surface renewal, and small eddies responsible for the presence of eddy diffusivity The small eddies are damped when an element of liquid reaches the interface so that, during its residence time there, mass transfer occurs in accordance with the assumptions of the penetration theory If all the eddies stay at the interface for the same interval of time we talk about penetration theory with regular surface renewal or the Higbie model If there is random distribution of residence times with an age-independent fractional rate of surface renewal, s, the term penetration theory with random surface renewal, or the Danckwerts nK)del, is employed In the case of the Higbie model, the mass transfer coefficient is the same as that given by eqn (18). For the Danckwerts model it takes the form... [Pg.624]

The enhancement of mass transfer due to chemical reaction depends on the order of the reaction as well as its rate. Order is defined as the sum of all the exponents to which the concentrations in the rate equation are raised. In elementary reactions, this number is equal to the number of molecules involved in the reaction however, this is only true if the correct reaction path has been assumed. Danckwerts presents a review of many cases of importance in gas absorption operations. He compares the results of using the film model and the Higbie and Danckweits surface-renewal models and concludes that, in general, the predictions based on the three models are quite similar. Mass transfer rate equations for a few of the cases encountered in a gas absorption operation are summarized in the following paragraphs, which are based primarily on discussions presented by Danckweits. ... [Pg.395]

Seminal work on segmented flow mass transfer was conducted by Higbie [38], who used experiments at < tp to prove the now well-established but then new penetration theory, i.e. that More recently, Irandoust et al. [39] modeled gas... [Pg.311]

More recently, Kawase and co-workers have presented semi-analytical framework for the estimation of the volumetric mass transfer coefflcient in bubble column reactors with and without an internal draft tube [51,62,67]. They have essentially combined the Higbie s penetration model with the isotropic turbulence to deduce the following expression for gas-liquid mass transfer with power law liquids ... [Pg.563]


See other pages where Mass transfer Higbie model is mentioned: [Pg.252]    [Pg.57]    [Pg.91]    [Pg.94]    [Pg.81]    [Pg.539]    [Pg.369]    [Pg.213]    [Pg.81]    [Pg.364]    [Pg.395]    [Pg.9]    [Pg.296]    [Pg.364]    [Pg.367]    [Pg.519]    [Pg.116]   
See also in sourсe #XX -- [ Pg.602 ]




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