Mass transfer coefficients, measurement

The overall volumetric mass transfer coefficients measured by pure oxygen absorption were expressed as a function of the total specific power dissipated in the liquid as follows ... 

Fig. 4. Liquid film mass transfer coefficient measured by pure oxygen absorption vs. total power dissipated in the liquid, e. Symbols and lines (see Table 1).

Fig. 9. Comparison of mass transfer coefficients measured by air absorption in pure sulphite solution and in the solution with addition of ocenol with Calderbank s model.

L liquid-side mass transfer coefficient measured by oxygen absorption, ms-1... 

Comparison between volumetric mass transfer coefficients measured in ISGLR and RPB... 

According to the data for volumetric mass transfer coefficient measured in the device on a small pilot plant scale, for a certain load of flue gas to be processed, the required total volume of the reactor under consideration would be very small, only about 1/3 that of existing wet FGD equipment. In addition, the arrangement of the internal wet cyclone shown in Fig. 7.23 enables the reactor to have simultaneously high ash-removal efficiency. The reactor is especially suitable for the wet desulfurization of flue gas with hydrated lime or dilute ammonia solution as the absorbent. The design of the large-scale reactor suitable for a power station has now been accomplished and is expected to be applied industrially in the very near future. 

Kdnig (3) reports volumetric mass transfer coefficients measured during fermentations of penicillium chrysogenum in a 20 cm (I.D.) bubble colvunn. Two typical sets of rheological parameters are given ... 

EL-Temtamy er al. [81] 150 Yeast suspensions 0.82 0.001-0.023 Liquid phase volumetric mass transfer coefficient measurements. 

Figure 4 Mass transfer coefficients between immersed isolated active particles and a fluidized bed of inert particles. (Shaded area range of particle-gas mass transfer coefficient measured in a fluidized bed of only active particles).

We would then measure the concentration ci at different velocities and calculate the mass transfer coefficients. Measurements like these are the basis of the correlations given in Tables 8.3-2 and 8.3-3. At the same time, these measurements are those giving values of k which vary too strongly with velocity. 

Moreover, because the gas oil is undiluted, C o/c is unity. Thus, from Fig. 16.5-3, the actual rate will be about 45% of that expected from reactions or mass transfer coefficients measured in dilute solution. 

Film Theory. Many theories have been put forth to explain and correlate experimentally measured mass transfer coefficients. The classical model has been the film theory (13,26) that proposes to approximate the real situation at the interface by hypothetical "effective" gas and Hquid films. The fluid is assumed to be essentially stagnant within these effective films making a sharp change to totally turbulent flow where the film is in contact with the bulk of the fluid. As a result, mass is transferred through the effective films only by steady-state molecular diffusion and it is possible to compute the concentration profile through the films by integrating Fick s law ... 

To use all of these equations, the heights of the transfer units or the mass transfer coefficients and must be known. Transfer data for packed columns are often measured and reported direcdy in terms of and and correlated in this form against and... 

Other correlations based partially on theoretical considerations but made to fit existing data also exist (71—75). A number of researchers have also attempted to separate from a by measuring the latter, sometimes in terms of the wetted area (76—78). Finally, a number of correlations for the mass transfer coefficient itself exist. These ate based on a mote fundamental theory of mass transfer in packed columns (79—82). Although certain predictions were verified by experimental evidence, these models often cannot serve as design basis because the equations contain the interfacial area as an independent variable. 

Interfacial Contact Area and Approach to Equilibrium. Experimental extraction cells such as the original Lewis stirred cell (52) are often operated with a flat Hquid—Hquid interface the area of which can easily be measured. In the single-drop apparatus, a regular sequence of drops of known diameter is released through the continuous phase (42). These units are useful for the direct calculation of the mass flux N and hence the mass-transfer coefficient for a given system. 

Mass-Transfer Coefficient Denoted by /c, K, and so on, the mass-transfer coefficient is the ratio of the flux to a concentration (or composition) difference. These coefficients generally represent rates of transfer that are much greater than those that occur by diffusion alone, as a result of convection or turbulence at the interface where mass transfer occurs. There exist several principles that relate that coefficient to the diffusivity and other fluid properties and to the intensity of motion and geometry. Examples that are outlined later are the film theoiy, the surface renewal theoiy, and the penetration the-oiy, all of which pertain to ideahzed cases. For many situations of practical interest like investigating the flow inside tubes and over flat surfaces as well as measuring external flowthrough banks of tubes, in fixed beds of particles, and the like, correlations have been developed that follow the same forms as the above theories. Examples of these are provided in the subsequent section on mass-transfer coefficient correlations. 

With complicated geometries, the product of the interfacial area per volume and the mass-transfer coefficient is required. Correlations of kop or of HTU are more accurate than individual correlations of k and since the measurements are simpler to determine the produc t kop or HTU. 

Extrapolation of KgO data for absorption and stripping to conditions other than those for which the origin measurements were made can be extremely risky, especially in systems involving chemical reactions in the liquid phase. One therefore would be wise to restrict the use of overall volumetric mass-transfer-coefficient data to conditions not too far removed from those employed in the actual tests. The most reh-able data for this purpose would be those obtained from an operating commercial unit of similar design. 

According to this method, it is not necessaiy to investigate the kinetics of the chemical reactions in detail, nor is it necessary to determine the solubihties or the diffusivities of the various reactants in their unreacted forms. To use the method for scaling up, it is necessaiy independently to obtain data on the values of the interfacial area per unit volume a and the physical mass-transfer coefficient /c for the commercial packed tower. Once these data have been measured and tabulated, they can be used directly for scahng up the experimental laboratory data for any new chemic ly reac ting system. 

Note that the product of the mass-transfer coefficient and the interfacial area is a volumetric coefficient and obviates the need for a value of the interfacial area. While areas for mass transfer on plates have been measured, the experimental contacting equipment cuffered significantly from that used for commercial distillation or gas absorption, and the reported areas are considered unreliable for design purposes. 

Measurements simply of the extent of extrac tion in an agitated vessel lead to the overall Volumetric mass-transfer coefficients, Kca, or... 

Pore diffusion limitation was studied on a very porous catalyst at the operating conditions of a commercial reactor. The aim of the experiments was to measure the effective diffiisivity in the porous catalyst and the mass transfer coefficient at operating conditions. Few experimental results were published before 1970, but some important mathematical analyses had already been presented. Publications of Clements and Schnelle (1963) and Turner (1967) gave some advice. 

This is the most accurate method of measuring the mass transfer coefficient and it can be used in the actual fermentation system. It depends on accurate oxygen analyses and... 

The mass transfer coefficient is expected to relate gas power per unit volume and gas terminal velocity. Measurement of gas bubble velocity is troublesome in the experimental stage of aeration. Extensive research has been conducted for an explanation of the above correlation. Gas-liquid mass transfer in low viscosity fluids in agitated vessels has been reviewed and summarised as stated in (3.5.1.7)—(3.6.2) 3... 

Later publications have been concerned with mass transfer in systems containing no suspended solids. Calderbank measured and correlated gas-liquid interfacial areas (Cl), and evaluated the gas and liquid mass-transfer coefficients for gas-liquid contacting equipment with and without mechanical agitation (C2). It was found that gas film resistance was negligible compared to liquid film resistance, and that the latter was largely independent of bubble size and bubble velocity. He concluded that the effect of mechanical agitation on absorber performance is due to an increase of interfacial gas-liquid area corresponding to a decrease of bubble size. 

In spite of its wide application, the mechanisms of this reaction remain obscure. Many diverse arguments have been published since the reaction was first investigated in 1897 (Bl, C5, C9, F7, J6, M5, P9, R2, S5, W2, W4, Yl, Y4). Cooper et al. (C9) introduced this method as a yardstick for the measurement of volumetric mass-transfer coefficients in gas-liquid contacting. Karow et al. (Kl) later concluded that the sulfite oxidation is suitable for fermentation process scale-up studies. Cooper et al. established that the reaction proceeds at a rate independent of sulfite ion concentration over wide concentration ranges. In their work they considered the sulfite oxidation to be of zero order with respect to both sulfite and sulfate concentration. 

Gal-Or and Hoelscher (G5) have recently developed a fast and simple transient-response method for the measurement of concentration and volumetric mass-transfer coefficients in gas-liquid dispersions. The method involves the use of a transient response to a step change in the composition of the feed gas. The resulting change in the composition of the liquid phase of the dispersion is measured by means of a Clark electrode, which permits the rapid and accurate analysis of oxygen or carbon dioxide concentrations in a gas, in blood, or in any liquid mixture. 

Cooper et al. (C9) were the first to determine mass-transfer coefficients by measuring the oxidation rate of sodium sulfite in an aqueous solution catalyzed by cupric ions. Their data were taken for a vaned-disk agitator with 16 blades and for a flat paddle. The ratio of agitator-to-tank diameter was 0.4, and the ratio of paddle to tank diameter was 0.25. The tank was equipped with four baffles, with baffle-width to tank diameter ratio of 0.1. 

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