Mass transfer coefficients volumetric

Substituting Vs and VL into the above equation determines the volumetric mass transfer coefficient. Volumetric mass transfer coefficient is calculated as ... 

Estimate the film thickness, mass transfer coefficient, volumetric mass transfer coefficient, and specific interfacial area for a vertically placed falling film MSR with the dimensions W = 600 pm 1 mm, H = 200 pm, L = 100 mm. The liquid flow rate is fixed to = 0.1 cm min 0.1 ml/min. 

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 ji is an apparent value because it is determined on the basis of an uncorrected. A tme 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... 

K a Overall volumetric liquid-pbase mass-transfer coefficient kmoP[(s-m )(mole-fraction (lbmol)/[(h-tt )(mole-traction... 

Volumetric Mass-Transfer Coefficients and Kia Experimental determinations of the individual mass-transfer coefficients /cg and /cl and of the effective interfacial area a involve the use of extremely difficult techniques, and therefore such data are not plentiful. More often, column experimental data are reported in terms of overall volumetric coefficients, which normally are defined as follows ... 

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. 

Traditional Design Method The traditionally employed conventional procedure for designing packed-tower gas-absorption systems involving chemical reactions makes use of overall volumetric mass-transfer coefficients as defined by the equation... 

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. 

The mass-transfer coefficient of Eq. (14-139) is carried as a product with interfacial area (giving a volumetric mass transfer coefficient) ... 

Interfacial Area This consideration in agitated vessels has been reviewed and summarized by Tatterson (op. cit.). Predictive methods for interfacial area are not presented here because correlations are given for the overall volumetric mass transfer coefficient liquid phase controlhng mass transfer. 

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

FIG. 17-14 Biihhling-hed model of Kunii and Levenspiel. dy = effective hiih-ble diameter, = concentration of A in hiihhle, = concentration of A in cloud, = concentration of A in emulsion, y = volumetric gas flow into or out of hiihhle, ky,- = mass-transfer coefficient between bubble and cloud, and k,. = mass-transfer coefficient between cloud and emulsion. (From Kunii and Leoen-spiel, Fluidization Engineering, Wiley, New York, 1.96.9, and Ktieger, Malahar, Fla., 1977.)... 

Oxygen transfer rate (OTR) The product of volumetric oxygen transfer rate kj a and the oxygen concentration driving force (C - Cl), (ML T ), where Tl is the mass transfer coefficient based on liquid phase resistance to mass transfer (LT ), a is the air bubble surface area per unit volume (L ), and C and Cl are oxygen solubility and dissolved oxygen concentration, respectively. All the terms of OTR refer to the time average values of a dynamic situation. 

Volumetric mass transfer coefficient, kLa The proportionality coefficient reflecting both molecular diffusion, turbulent mass transfer, and specific area for mass transfer. 

The plot of the rate of disappearance of CO per volume of liquid in the serum bottles versus partial pressure of CO in the gas phase based on (3.14.4.14) could give the constant slope value of KLa/H. Henry s constant is independent of the acetate concentration but it is only dependent on temperature. The overall volumetric mass transfer coefficient can be calculated based on the above assumption. The data for various acetate concentrations and different parameters were plotted to calculate the mass transfer coefficient. 

KLa is the volumetric oxygen mass transfer coefficient, owing to the oxygen transfer from the gas phase or air, c, the surface of the cells, cx or to the transfer of oxygen dissolved in water to the surface of the cells. 

The mass transfer coefficient for non-coalescing air bubbled in the fermentation broth in turbulent regime is frequently discussed in the literature.6 The volumetric mass transfer coefficient is defined by the following correlation ... 

Yoshida and Akita (Yl) determined volumetric mass-transfer coefficients for the absorption of oxygen by aqueous sodium sulfite solutions in counter-current-ffow bubble-columns. Columns of various diameters (from 7.7 to 60.0 cm) and liquid heights (from 90 to 350 cm) were used in order to examine the effects of equipment size. The volumetric absorption coefficient reportedly increases with increasing gas velocity over the entire range investigated (up to approximately 30 cm/sec nominal velocity), and with increasing column diameter, but is independent of liquid height. These observations are somewhat at variance with those of other workers. 

K, Mass transfer coefficient g0 Volumetric void fraction of dry... 

Another approach to the design problem is to determine empirical correlations based on experimental work and to adopt these correlations for scale-up. In many of the published works the latter approach is investigated. The correlations are such that the volumetric mass-transfer coefficient is generally reported as a function of one or more of the equipment, system, or operating variables cited above. Empirical correlations can be used confidently for scale-up only for equipment that has complete geometrical similarity to the... 

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. 

In evaluating their results they assumed the film theory, and, because the oxygen is sparingly soluble and the chemical reaction rate high, they also assumed that the liquid film is the controlling resistance. The results were calculated as a volumetric mass-transfer coefficient based, however, on the gas film. They found that the volumetric mass-transfer coefficient increased with power input and superficial gas velocity. Their results can be expressed as follows ... 

Empirical Correlations of Volumetric Mass-Transfer Coefficient Ks and Specific Interfacial Area s ... 

A summary of a number of correlations proposed for volumetric mass-transfer coefficients and specific interfacial area is presented in Table II, which includes data additional to those of Westerterp et al. (W4). It is apparent that disagreement exists as to the numerical values for the exponents. This is due, in part, to the lack of geometric similarity in the equipment used. In addition, variation in operating factors such as the purity of the system (surfactants), kind of chemical system, temperature, etc., also contribute to the discrepancies. To summarize Table II ... 

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