Volumetric Mass Transfer Coefficient, kLa

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

Many correlations allow estimation of the gas-liquid volumetric mass transfer coefficient kLa in mechanically stirred tank reactors. The following intends not to provide a comprehensive review but rather a critical evaluation of selected correlations adapted to hydrogenations [Eqs. (40) to (43)] [25, 51-53]. 

Liquid-side volumetric mass transfer coefficient kLa = 0.078ug (s ). 

Earlier studies in mass transfer between the gas-liquid phase reported the volumetric mass-transfer coefficient kLa. Since kLa is the combination of two experimental parameters, mass-transfer coefficient and mterfacial area, it is difficult to identify which parameter is responsible for the change of kLa when we change the operating condition of a fermenter. Calderbank and Moo-Young (1961) separated kta by measuring interfacial area and correlated mass-transfer coefficients in gas-liquid dispersions in mixing vessels, and sieve and sintered plate column, as follows ... 

Akita and Yoshida (1973) correlated the volumetric mass-transfer coefficient kLa for the absorption of oxygen in various aqueous solutions in bubble columns, as follows ... 

For the scale-up of the gas-liquid contactor, the volumetric mass-transfer coefficient kLa can be used as a scale-up criterion. In general, the volumetric mass-transfer coefficient is approximately correlated to the power per volume. Therefore, constant power per volume can mean a constant kLa. 

Overall Mass-Transfer Coefficient In systems with relatively sparing soluble gases, where the gas-phase resistance is negligible, the mass-transfer rate can be determined by using the concept of an overall volumetric mass-transfer coefficient kLa as follows ... 

Some of this theoretical thinking may be utilized in reactor analysis and design. Illustrations of gas-liquid reactors are shown in Fig. 19-26. Unfortunately, some of the parameter values required to undertake a rigorous analysis often are not available. As discussed in Sec. 7, the intrinsic rate constant kc for a liquid-phase reaction without the complications of diffusional resistances may be estimated from properly designed laboratory experiments. Gas- and liquid-phase holdups may be estimated from correlations or measured. The interfacial area per unit reactor volume a may be estimated from correlations or measurements that utilize techniques of transmission or reflection of light, though these are limited to small diameters. The combined volumetric mass-transfer coefficient kLa, can be also directly measured in reactive or nonreactive systems (see, e.g., Char-pentier, Advances in Chemical Engineering, vol. 11, Academic Press, 1981, pp. 2-135). Mass-transfer coefficients, interfacial areas, and liquid holdup typical for various gas-liquid reactors are provided in Tables 19-10 and 19-11. 

The determination of volumetric mass transfer coefficients, kLa, usually requires additional knowledge on the residence time distribution of the phases. Only in large diameter columns the assumption is justified that both phases are completely mixed. In tall and smaller diameter bubble columns the determination of kLa should be based on concentration profiles measured along the length of the column and evaluated with the axial dispersed plug flow model ( 5,. ... 

Tribe, L.A., Briens, C.L., and Margaritis, A. (1995), Determination of the volumetric mass transfer coefficient (kLa) using the dynamic gas out-gas in method Analysis of errors caused by dissolved oxygen probes, Biotechnology and Bioengineering, 46(4) 388-392. 

The volumetric mass transfer coefficients (kLa) were determined from Eq (6.2.4) during plug flow at different initial nitric acid concentrations and residence times at flow rate ratio from 0.25 to 1 for the three different types of TBP/IL mixtures (30 %, v/v). In Fig. 6.12 the mass transfer coefficients in the 0.5 mm ID channel are shown as a function of initial nitric acid concentration for experiments performed in the shortest (10 cm long) channel. The total volumetric flow rate was Qmix = 14.6 cm h and the flow rate ratio was equal to 1. The mass transfer... 

Calculated conversions of butynediol (B) and hydrogen (A) with different sizes of catalyst particles are given in Fig. 8 with Dp as a parameter. The calculations are performed with a fixed value of the volumetric mass transfer coefficient, kLa, but including the liquid-solid and the intraparticle mass transfer resistances. 

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. 

Henry Law coefficient (bar m3/kmol) kLa = Gas-liquid volumetric mass transfer coefficient (s-1) ks = Liquid-solid mass transfer coefficient (m/s)... 

This simplified description of molecular transfer of hydrogen from the gas phase into the bulk of the liquid phase will be used extensively to describe the coupling of mass transfer with the catalytic reaction. Beside the Henry coefficient (which will be described in Section 45.2.2.2 and is a thermodynamic constant independent of the reactor used), the key parameters governing the mass transfer process are the mass transfer coefficient kL and the specific contact area a. Correlations used for the estimation of these parameters or their product (i.e., the volumetric mass transfer coefficient kLo) will be presented in Section 45.3 on industrial reactors and scale-up issues. Note that the reciprocal of the latter coefficient has a dimension of time and is the characteristic time for the diffusion mass transfer process tdifl-GL=l/kLa (s). 

In deriving the material balance equations, the dispersed plug flow model will first be used to obtain the general form but, in the numerical calculations, the dispersion term will be omitted for simplicity. As used previously throughout, the basis for the material balances will be unit volume of the whole reactor space, i.e. gas plus liquid plus solids. Thus in the equations below, for the transfer of reactant A kLa is the volumetric mass transfer coefficient for gas-liquid transfer, and k,as is the volumetric mass transfer coefficient for liquid-solid transfer. 

The proposed catalyst loading, i.e. the ratio by volume of catalyst to aniline, is to be 0.03. Under the conditions of agitation to be used, it is estimated that the gas volume fraction in the three-phase system will be 0.15 and that the volumetric gas-liquid mass transfer coefficient kLa, 0.20 s"1 (also with respect to unit volume of the whole three-phase system). The liquid-solid mass transfer coefficient is estimated to be 2.2 x 10"3m/s and the Henry law coefficient 38 for hydrogen in aniline at 130°C, 2240 bar m /kmol. (PA = 38CA where PA is the gas-phase partial pressure and CA is the equilibrium concentration in the liquid). 

The physical absorption technique (manometric method) is suitable to determine the liquid side volumetric mass transfer coefficient as well as the gas-side one. Results show that kLa is independant of pressure and depends mainly on the system s hydrodynamics and secondly, that koa is inversely proportional to the total pressure and can be related to the liquid Reynolds number. 

Abstract—Gas-liquid interfacial areas a and volumetric liquid-side mass-transfer coefficients kLa are experimentally determined in a high pressure trickle-bed reactor up to 3.2 MPa. Fast and slow absorption of carbon dioxide in aqueous and organic diethanolamine solutions are employed as model reactions for the evaluation of a and kLa at high pressure, and various liquid viscosities and packing characteristics. A simple model to estimate a and kLa for the low interaction regime in high pressure trickle-bed reactors is proposed. 

Gas-liquid mass transfer can have a strong effect on TBR overall performance therefore its accurate evaluation is essential for achieving successful design and scale-up. In spite of the vast information available on gas-liquid mass transfer characteristics of atmospheric TBRs [1,2] only a few researchers have studied how interfacial areas, a, and volumetric liquid-side mass transfer coefficients, kLa, evolve at elevated pressures. For example, it has been reported that both a and kLa increase as gas density is rised while the gas superficial velocity is kept constant [3-5], Similar observations regarding gas hold-up and two-phase pressure drop, as well as the delay in the onset of pulsing have also been reported [6],... 

Gas-liquid interfacial areas, a, and volumetric liquid-side mass transfer coefficients, kLa, are measured in a high pressure trickle-bed reactor. Increase of a and kLa with pressure is explained by the formation of tiny bubbles in the trickling liquid film. By applying Taylor s theory, a model relating the increase in a with the increase in gas hold-up, is developed. The model accounts satisfactorily for the available experimental data. To estimate kLa, contribution due to bubbles in the liquid film has to be added to the corresponding value measured at atmospheric pressure. The mass transfer coefficient from the bubbles to the liquid is calculated as if the bubbles were in a stagnant medium. 

Volumetric Mass-Transfer Coefficients K, a and KLa Experimental determinations of the individual mass-transfer coefficients hG and hi 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 ... 

Direct bubbling with a mixture of air and C02 is used in many closed photobioreactors. The mass transfer capacity (as measured by the volumetric oxygen transfer coefficient, kLa) increases with decrease in the bubble diameters (achieved by using spargers with very small diameter pores) and with increase in the aeration rate. In vertical columns (Fig. 4), the gas transfer from the gas bubbles to the medium is high since the gas bubbles remain submerged in the broth until they exit the reactor. Thus bubble column bioreactors have been used for many biological processes. 

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 KLa is an apparent value because it is determined on the basis of an uncorrected. A true volumetric mass transfer coefficient can be evaluated by correcting for the gas-side oxygen depletion. However, for design purposes, C can be estimated from the surface saturation concentration and effective saturation depth by... 

With regards to handling data on industrial apparatus for gas-liquid mass transfer (such as packed columns, bubble columns, and stirred tanks), it is more practical to use volumetric mass transfer coefficients, such as K a and KLa, because the interfacial area a cannot be well defined and will vary with operating conditions. As noted in Section 6.7.2, the volumetric mass transfer coefficients for packed columns are defined with respect to the packed volume - that is, the sum of the volumes of gas, liquid, and packings. In contrast, volumetric mass transfer coefficients, which involve the specific gas-liquid interfacial area a (L2 IT3), for liquid-gas bubble systems (such as gassed stirred tanks and bubble columns) are defined with respect to the unit volume of gas-liquid mixture or of clear liquid volume, excluding the gas bubbles. In this book we shall use a for the specific interfacial area with respect to the clear liquid volume, and a for the specific interfacial area with respect to the total volume of gas-liquid mixture. 

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