True mass transfer coefficient

This chapter will first provide some basics on ozone mass transfer, including theoretical background on the (two-) film theory of gas absorption and the definition of over-all mass transfer coefficients KLa (Section B 3.1) as well as an overview of the main parameters of influence (Section B 3.2). Empirical correction factors for mass transfer coefficients will also be presented in Section B 3.2. These basics will be followed by a description of the common methods for the determination of ozone mass transfer coefficients (Section B 3.3) including practical advice for the performance of the appropriate experiments. Emphasis is laid on the design of the experiments so that true mass transfer coefficients are obtained. 

The empirical correction factors are developed from comparing two mass transfer coefficients, thus, it is essential that both are measured correctly. Brown and Baillod (1982) point out that the a value from the ratio of two incorrectly measured mass transfer coefficients, apparent mass transfer coefficients, is different from the a of true mass transfer coefficients. 

A systematic study of mass transfer in bubble columns by Mashelkar and Sharma (M8, M9, S23) is summarized in Fig. 23. Increasing the superficial gas velocity increases the gas holdup a, the volumetric mass-transfer coefficients, and the interfacial area per unit volume of dispersion, but not the true mass-transfer coefficients. Correlations proposed for ki, seem too specific to be extended to practical systems (H13, FI, A3). Sharma and Mashelkar (S21) found good agreement between their experimental values of and the values from Geddes stagnant sphere model equation (G3) ... 

Chemical methods have moreover been successfully used to measure interfacial area and true mass transfer coefficients for various equipments under different conditions (34,35). However, in many cases, there are still very few data to predict even the most essential parameters (36). 

The true mass transfer coefficients were evaluated and the Sherwood numbers correlated with the Reynolds numbers of the continuous phase, the coefficients being obtained by regression as below ... 

Figure 10 Effect of mass transfer coefficient on deviation of simulated concentration profiles from experimental data. The minima correspond to the best fitting curves and the corresponding coefficients are considered to be the true mass transfer coefficients for the given experimental condition. (Actual measurements with the MIBK/water/acetic acid system are shown).

In majority of experimental investigations, overall volumetric mass transfer coefficients comprising the true mass transfer coefficient and the interfacial area are reported. To obtain the true mass transfer coefficient from such data, knowledge of the interfacial area is required. There is a wide variation in bubble/drop sizes in a... 

Constants in Eqnations 6.8 and 6.9 True mass transfer coefficient (m/s)... 

Finally, if a mass-transfer coefficient looks too good to be true, it probably is incorrect. 

Mass transfer. It is not yet possible to predict the mass transfer coefficient with a high degree of accuracy because the mechanisms of solute transfer are but imperfectly understood as discussed Light and Conway(14), Coulson and Skinner(15) and Garner and Hale 16 1. In addition, the flow in spray towers is not strictly countercurrent due to recirculation of the continuous phase, and consequently the effective overall driving force for mass transfer is not the same as that for true countercurrent flow. 

We see that, in principle, the overall reaction rate can be expressed in terms of coefficients such as the reaction rate constant and the mass transfer coefficient. To be of any use for design purposes, however, we must have knowledge of these parameters. By measuring the kinetic constant in the absence of mass transfer effects and using correlations to estimate the mass transfer coefficient we are really implying that these estimated parameters are independent of one another. This would only be true if each element of external surface behaved kinetically as all other surface elements. Such conditions are only fulfilled if the surface is uniformly accessible. It is fortuitous, however, that predictions of overall rates based on such assumptions are often within the accuracy of the kinetic information, and for this reason values of k and hD obtained independently are frequently employed for substitution into overall rate expressions. 

The LDF model is a realistic representation of the system with a surface barrier. Otherwise, k can be treated as an apparent mass transfer coefficient irrespective of the true transport mechanism which can be directly used in the design and optimization of adsorbers. This concept has been successfully used to analyze column breakthrough data for practical non-isothermal systems [18-20]. It substantially... 

The True Gas-Liquid Specific Contact Area (a) and the Liquid-Side Mass Transfer Coefficient (ki)... 

From the above it follows that in most practical situations a model, that takes into account only an intraparticle mass and an interparticle heat transfer resistance will give good results. However, in experimental laboratory reactors, which usually operate at low gas flow rates, this may not be true. In the above criteria the heat and mass transfer coefficients for interparticle transport also have to be known. These were amply discussed in Section 4.2. 

The value of the saturation concentration,, is the spatial average of the value determined from a clean water performance test and is not corrected for gas-side oxygen depletion therefore K ais an apparent value because it is determined on the basis of an uncorrected C/.,. A true volumetric mass transfer coefficient can be evaluated by correcting for the gas-side oxygen depletion. However, for design purposes, can be estimated from the surface saturation concentration and effective saturation depth by... 

Just as with the gas holdup, gas-liquid interfacial area should also be divided into two parts. The literature, however, gives a unified correlation. The same is true for volumetric gas-liquid mass transfer coefficients and mixing parameters for both gas and liquid phases. The fundamental r.echanism for inter-phase mass transfer and mixing for large bubbles is expected to be different from the one for small bubbles. Future work should develop a two phase model for the bubble column analogous to the two phase model for fluidized beds. 

Fig. 13. Interfacial areas (a) and true liquid-side mass-transfer coefficients (b) in countercurrent packed columns. (See tabulation on p. 71.)...

The true liquid-side mass-transfer coefficients /cl all lie between 4 X 10 and 2 x 10 cm/sec (Fig. 13) and may be considered independent of Mq. The most representative relationship for the liquid-side mass-transfer coefficient, accurate within a range of 20%, is probably the one contributed by Mohunta et al. (Ml7) ... 

The literature on measurement of mass transfer in vertical tubular reactors is very sparse. Kasturi and Stepanek (K3, K4) have presented data for a, ki a, and kca measured under identical conditions in the case of annular flow, annular spray flow, and slug flow. For the aqueous systems used (COj, air, NaOH) they have proposed the following correlation for the interfacial area fl = 0.23[(l - a)/QJ(AP/Z)i( whereQt is incm /sec and AP/Z is in N/m . Correlations for true liquid-side and gas-side mass-transfer coefficients by the same authors are difficult to generalize, as viscosity and surface tension were not varied. 

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