Mass transfer coefficients, typical values

Here, designates the mass transfer coefficient. Its value depends on the diffusion coefficient and on convection (Section 4.3). In aqueous solutions, typically has a... 

The mass-transfer coefficients are typically between 10 to 100 p.m/s, depending on hydrodynamic conditions and the values of D. 

There are a number of different types of experimental laboratory units that could be used to develop design data for chemically reacting systems. Charpentier [ACS Symp. Sen, 72, 223-261 (1978)] has summarized the state of the art with respect to methods of scaUng up lab-oratoiy data and tabulated typical values of the mass-transfer coefficients, interfacial areas, and contact times to be found in various commercial gas absorbers as well as in currently available laboratoiy units. 

Speed-up of mixing is known not only for mixing of miscible liquids, but also for multi-phase systems the mass-transfer efficiency can be improved. As an example, for a gas/liquid micro reactor, a mini packed-bed, values of the mass-transfer coefficient K a were determined to be 5-15 s [2]. This is two orders of magnitude larger than for typical conventional reactors having K a of 0.01-0.08 s . Using the same reactor filled with 50 pm catalyst particles for gas/Hquid/solid reactions, a 100-fold increase in the surface-to-volume ratio compared with the dimensions of laboratory trickle-bed catalyst particles (4-8 mm) is foimd. 

Gas-Liquid Mass Transfer. Gas-liquid mass transfer within the three-phase fluidized bed bioreactor is dependent on the interfacial area available for mass transfer, a the gas-liquid mass transfer coefficient, kx, and the driving force that results from the concentration difference between the bulk liquid and the bulk gas. The latter can be easily controlled by varying the inlet gas concentration. Because estimations of the interfacial area available for mass transfer depends on somewhat challenging measurements of bubble size and bubble size distribution, much of the research on increasing mass transfer rates has concentrated on increasing the overall mass transfer coefficient, kxa, though several studies look at the influence of various process conditions on the individual parameters. Typical values of kxa reported in the literature are listed in Table 19. 

In this case it is assumed that a pure gas A is being absorbed in a solvent eontaining a chemically inert component B. Both the solvent and B are not volatile and the fraction of A in the liquid bulk equals zero. The binary mass transfer coefficient Kij between A and the solvent in eq. (4) is given a typical value of 1 X lO" m/s, whereas the total concentration of the liquid Cr is set to 1 x 10 mol/m, also a typical value. Parameters to be chosen are the solubility of A, x i, the fraction of B in the solvent Xg, the mass transfer coefficient between A and B, K/ g and the mass transfer coefficient between B and the solvent, Kg. The results of the calculations are presented in Table 1. Since both the solvent and component B possess a zero flux. Kgs has no influence on the mass transfer process and has therefore been omitted. The computed absorption rate has been compared with the absorption rate obtained from analytical solutions for the following cases. 

Here, the particle Reynolds number is based on the slip velocity. If terminal velocity is used, then the above correlation gives the minimum value for the mass transfer coefficient. Minimum mass transfer coefficients further depend on the density difference between solid particles and solvent. For the typical case of water, the approximate values presented in Table 3.7 can be used (Harriot, 1962). 

The observed values of the mass transfer coefficient- in three-phase systems between solid and liquid for the conventional impellers and a typical baffled vessel (e.g. Rushton turbine, propeller) are between the values predicted by Hiraoka (liquid-liquid dispersion, eq. (3.267)) and Levins and Glastonbuty (solid-liquid dispersion, eq. (3.118)) correlations. However, as an approximation, the Levins and Glastonbuty correlation could be used for three-phase systems (Smith, 1981). 

The next parameter required is the diffusion coefficient of phenol in water (/)lg). Here, we can assume the typical value of 10 m2/s. Then, the resulting mass transfer coefficient is 0.23 s-1. Subsequently,... 

Transfer coefficients in catalytic monolith for automotive applications typically exhibit a maximum at the channel inlet and then decrease relatively fast (within the length of several millimeters) to the limit values for fully developed concentration and temperature profiles in laminar flow. Proper heat and mass transfer coefficients are important for correct prediction of cold-start behavior and catalyst light-off. The basic issue is to obtain accurate asymptotic Nu and Sh numbers for particular shape of the channel and washcoat layer (Hayes et al., 2004 Ramanathan et al., 2003). Even if different correlations provide different kc and profiles at the inlet region of the monolith, these differences usually have minor influence on the computed outlet values of concentrations and temperature under typical operating conditions. 

In Fig. 42, the full-width at half maximum of the (narrower) exchange propagator provides an estimate of the effective diffusion coefficient of water molecules moving between the pore space of the catalyst and the inter-particle space of the bed. In this example, the value is 2 x lO- m s which gives a lower limit to the value for the mass transfer coefficient of 4x 10 ms This value was obtained by defining a mass transfer coefficient as Djd where d is a typical distance traveled to the surface of the catalyst that we estimate as half a typical bead dimension (approximately 500 pm). This value of the mass transfer coefficient is consistent with the reaction occurring under conditions of kinetic as opposed to mass transfer control. 

In the cases above, a two-parameter model well represents the data. A model with more parameters would be more flexible, but by using a partition constant, K, or a desorption rate constant ka and k, , for the mass-transfer coefficients, the data are well described (see Figs. 3.4-15 and 3.4-13). While K would be a value experimentally determined, kp can be estimated from eqn. (3.4-97) with the external mass-transfer coefficient, km, estimated from the correlation of Stiiber et al. [25] or from that of Tan et al. [27], and the effective diffusivity from the Wakao Smith model [36], Typical values of kp obtained by fitting the data of Tan and Liou are shown in Fig. 3.4-16. As expected, they are below the usual mass-transfer correlations, because internal resistance diminishes the global mass transfer coefficient. These data correspond to the regeneration of spent activated carbon loaded with ethyl acetate, using high-pressure carbon dioxide, published by Tan and Liou [45]. 

Mass transfer coefficients (kw and fca) have been empirically defined based on experimental studies using tracer gases [71-77] and converted to values for PAHs using differences in diffusivities. The magnitude of K0i for individual PAHs typically ranges from 0.05 to 0.7 m/d (e.g. [78]). 

The film thickness is not directly accessible, and the term D/S, which has units cm s 1, is referred to as the mass transfer coefficient, ki. In solid/liquid and liquid/liquid systems, values of kL are typically 1-2 x 10 3 cm s-1 with values of D typically 5 x 10 6 to 2 x 10-5 cm2 s 1, corresponding to diffusion film thicknesses of 50-100 pm and film diffusion times of around 5 seconds. 

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. 

During a typical batch electrolysis, the minimal COD value can be estimated (CODfe min = 4.25mmol dm-3 or 136ppm) by assuming a typical value of minimal hydroxyl production current density (iu,mm = 5.0mA cm-2), and a characteristics value of mass-transfer coefficient (km = 3 x 10 s m s ). The obtained minimal COD value is higher than the final treatment value that is usually required (CODf). Consequently, it can be stated that the electrochemical treatment loses a part of electric charge supplied in secondary reactions in this final step... 

Typical values for the mass transfer coefficient lie around 10-3 m mf2 s 1 which is sufficiently high to allow neglect of the effects of mass transfer from the bulk of the liquid to the external pellet surface on the measured rates. In order to verify this it is sufficient to substitute the calculated mass transfer coefficient in Eqn. 7.74 for the Carberry number, bearing Eqn. 7.75 in mind. 

Correlation 7.181 should be used with care at low Reynolds numbers. Typical values for gas-solid transfer are 1 m mi"2 s 1 for the mass transfer coefficient and 102 W m-2 K-1 for the heat transfer coefficient. 

The mass transfer coefficient,, for a sphere can be determined from the Sherwood number, Sh (= K JD g, where is the molecular diffusion coefficient of the solvent. A, in drying gas, B typical values are 10 -10 cm /sec) and the following engineering correlation [15]... 

While the above criteria are useful for diagnosing the effects of transport limitations on reaction rates of heterogeneous catalytic reactions, they require knowledge of many physical characteristics of the reacting system. Experimental properties like effective diffusivity in catalyst pores, heat and mass transfer coefficients at the fluid-particle interface, and the thermal conductivity of the catalyst are needed to utilize Equations (6.5.1) through (6.5.5). However, it is difficult to obtain accurate values of those critical parameters. For example, the diffusional characteristics of a catalyst may vary throughout a pellet because of the compression procedures used to form the final catalyst pellets. The accuracy of the heat transfer coefficient obtained from known correlations is also questionable because of the low flow rates and small particle sizes typically used in laboratory packed bed reactors. 

Our objective here is to try to answer the following questions For a proposed type of gas-liquid contactor compatible with the properties and flow rates of the phases and with the reaction type, what are the likely values of the specific interfacial area and the gas and liquid mass-transfer coefficients by which the contact performance can be predicted And what is the expected accuracy of these values Table XVIII gives typical values of these parameters in typical contactors shown in Fig. 12 for fluids with properties not very different from those of air and water (especially, liquid viscosity under 5 cP where the liquid is nonfoaming). Because this review is especially concerned with the chemical method of determining these parameters, experimental data obtained by this method will be given in subsequent tables and figures. 

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