Mass transfer coefficients experimental determination

To this end, experimental heat and mass transfer coefficients were determined in a fluidized bed. Nusselt and Sherwood numbers were obtained in terms of Reynolds number and aspect ratios dp/L and dp/D. The results are also analyzed in terms of the Kato and Wen(5) and Nelson and Galloway(6) models. 

Many inert turbulence promoters are available and only a few have been mentioned. (See also Example 2.4.) Our correlations are specific to one material or system and should not be extrapolated to other types of parameters. This is particularly true for meshes and cloths the only safe procedure is to determine mass transfer coefficients experimentally using the limiting current technique described in Section 2.3.4. 

The growth rate of a KDP crystal in a pure solution was measured as a function of flow velocity at constant activity-based supersaturation, Aa/a =0.037. At each condition the steady level of growth was achieved during experiments. The experimental results indicate that the growth process is diffusion-controlled at the flow velocity lower than 0.033 m/s. Thus, the flow velocity, v= 0.005 m/s, was chosen for the growth measurements in the ternary system. The mass transfer coefficients were determined by applying the binary Maxwell-Stefan equations to the measured growth rates and subsequently the boundary layer thickness was obtained at different flow velocities. 

The liquid side volumetric physical mass transfer coefficient was determined from the desorption rate of oxygen. Detailed description of the experimental set up, procedure and analysis of data is given by Tosyali [30]. Methods of estimating the interfacial CO2 concentration, diffusivities of CO2 and OH in the liquid phase, reaction rate constant, which are all required in data analysis, can be found elsewhere [31, 32]. ... 

Lorbach and Man (19) simplified the system of model equations by the use of the typical facilitated transport assumption of a constant sum of the free and complexed carrier concentrations. They further simplified their stem of equations with constant pH in their external phase and they eliminated the resistance for the peripheral thin membrane layer. Their model has become the state-of-the-art model for Type 2 frcilitation. However, they used 4 reaction parameters, i.e., 2 reaction rate constants for forward and backward reactions and 2 apparent equilibrium constants for extraction and stripping. The two apparent equilibrium constants were different. In addition, they determined the external phase mass transfer coefficient experimentally and used the effective difiiisivity as an adjustable parameter. In principle, the reaction rate constants should be sufficient to define the reaction and equilibrium constants. Thus, accurate reaction rate constants are crucial to the success of the modeling. The external phase mass transfer coefficient may be estimated reasonably accurately or it may be eliminated since the external mass transfer resistance is generally negligible for typical ELM systems (2,7). Effective diffusivity may also be estimated (2,7). These appear to be the areas of improvement that can be made to the modeling. 

Equations 1.2-4 and 1.2-5 are equivalent, and they share the same successes and shortcomings. In the former, we must determine the mass transfer coefficient experimentally in the latter, we determine instead the thickness 1. Those who like a scientific veneer prefer to measure /, for it genuflects toward Pick s law of diffusion. Those who are more pragmatic prefer explicitly recognizing the empirical nature of the mass transfer coefficient. 

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 ... 

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. 

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... 

It was shown later that a mass transfer rate sufficiently high to measure the rate constant of potassium transfer [reaction (10a)] under steady-state conditions can be obtained using nanometer-sized pipettes (r < 250 nm) [8a]. Assuming uniform accessibility of the ITIES, the standard rate constant (k°) and transfer coefficient (a) were found by fitting the experimental data to Eq. (7) (Fig. 8). (Alternatively, the kinetic parameters of the interfacial reaction can be evaluated by the three-point method, i.e., the half-wave potential, iii/2, and two quartile potentials, and ii3/4 [8a,27].) A number of voltam-mograms obtained at 5-250 nm pipettes yielded similar values of kinetic parameters, = 1.3 0.6 cm/s, and a = 0.4 0.1. Importantly, no apparent correlation was found between the measured rate constant and the pipette size. The mass transfer coefficient for a 10 nm-radius pipette is > 10 cm/s (assuming D = 10 cm /s). Thus the upper limit for the determinable heterogeneous rate constant is at least 50 cm/s. 

Their correlations were based on a large amount of data on gas absorption and distillation with a variety of packings, which included Pall rings and Berl saddles. Their method for estimating the effective area of packing can also be used with experimentally determined values of the mass-transfer coefficients, and values predicted using other correlations. 

In many types of equipment used for gas—liquid reactions, the interfacial area available for mass transfer cannot be determined. The experimentally determined rates of mass transfer are therefore usually reported in terms of transfer coefficients based on unit volume of apparatus rather than on unit interfacial area. These volumetric coefficients are denoted by Kia, Kia, k fi and k[a where a is the interfacial area per unit volume of the equipment. 

A list of mass transfer coefficient relations provided in Table 4.2 illustrates the types of experimentally determined relations that exist. They are typically of the form of equation (E4.5.4), although some deviations occur due to a theoretical analysis of mass transfer. Theoretical and experimental analyses have shown that Sh for an interface that acts like a fluid and Sh for an interface that acts like a solid. 

In what follows, the preceding evaluation procedure is employed in a somewhat different mode, the main objective now being to obtain expressions for the heat or mass transfer coefficient in complex situations on the basis of information available for some simpler asymptotic cases. The order-of-magnitude procedure replaces the convective diffusion equation by an algebraic equation whose coefficients are determined from exact solutions available in simpler limiting cases [13,14]. Various cases involving free convection, forced convection, mixed convection, diffusion with reaction, convective diffusion with reaction, turbulent mass transfer with chemical reaction, and unsteady heat transfer are examined to demonstrate the usefulness of this simple approach. There are, of course, cases, such as the one treated earlier, in which the constants cannot be obtained because exact solutions are not available even for simpler limiting cases. In such cases, the procedure is still useful to correlate experimental data if the constants are determined on the basis of those data. 

The experimental determination of the film coefficients kL and kc is very difficult. When the equilibrium distribution between the two phases is linear, over-all coefficients, which are more easily determined by experiment, can be used. Over-all coefficients can be defined from the standpoint of either the liquid phase or gas phase. Each coefficient is based on a calculated over-all driving force Ac, defined as the difference between the bulk concentration of one phase (cL or cc) and the equilibrium concentration (cL or cc ) corresponding to the bulk concentration of the other phase. When the controlling resistance is in the liquid phase, the over-all mass transfer coefficient KLa is generally used ... 

Which experimental method should be used depends on the type of reactor and how it will be operated, and if clean or process water is to be used for the measurement. Nonsteady state methods are generally simpler and faster to perform if kLa is to be determined in clean water without reaction. For processes that are operated at steady state with a reaction, determination of kLa using steady state methods are preferred, since continuous-flow processes need not be interrupted and operating conditions similar to the normal process conditions can be used. This is especially important for systems with reactions because the reaction rate is usually dependent on the concentration of the reactants present. They are thus often applied for investigations of the mass transfer coefficient under real process conditions with chemical reactions kLa(02) or biological activity kLa(02), e. g. in waste water treatment systems. 

Experimental determination of the mass transfer coefficient is based on the appropriate mass balance on the specific reactor used (Figure B 1-2). The simpler the reactor system is, the simpler the mass balance model for evaluating the experimental results can be. For example, if mixing in the reactor deviates too far from ideality, kL is no longer uniform throughout the reactor. Neither method as described below can then be used. Instead a more complicated model of the mixing zones in the reactor would be necessary (Linek, 1987 Stockinger, 1995). 

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]. 

In most types of mass-transfer equipment, the interfacial area, a, that is effective for mass transfer cannot be determined accurately. For this reason, it is customary to report experimentally observed rates of transfer in terms of mass-transfer coefficients based on a unit volume of the apparatus, rather than on a unit of interfacial area. Calculation of the overall coefficients from the individual volumetric coefficients is made practically, for example, by means of the equations ... 

The mass transfer within a rigid droplet is determined by the Maxwell-Stefan diffusion. The appropriate diffusion coefficients experimentally determined... 

For gas-solid fluidized beds, Wen and Fane (1982) suggested that the determination of the bed-to-surface mass transfer coefficient can be conducted by using the corresponding heat transfer correlations, replacing the Nusselt number with the Sherwood number, and replacing the Prandtl number by Sc(cpp)/(cpp)/(l — a). Few experimental results on bed-to-surface mass transfer are available, especially for gas-solid fluidized beds operated at relatively high gas velocities. 

Packed height is determined from the relationships in Section III. Application of these relationships requires knowledge of the liquid and gas mass transfer coefficients. It is best to obtain these from experimental data on the system if available, but caution is required when extending such data to column design, because mass transfer coefficients depend on packing geometry, liquid and gas distribution, physical properties, and gas and liquid loads, and these may vary from one contactor to another. 

The height of an absorption column depends on the feed conditions, the product purity specifications, the solvent used and the extent of separation through the absorption equilibrium relationship, but also on the rate of separation. If the rate of mass transfer of the gaseous component from the gas phase into the liquid phase is slow, then the column needs to be longer to ensure that the required amount is removed. The rate of mass transfer depends on the mass-transfer coefficient, normally denoted kG or k. The value of the mass-transfer coefficient depends on the components in the gas feed and on the solvent used and is often determined experimentally. The type of packing used in the column will also have an impact on the column height as for distillation. 

The rate-based stage model parameters describing the mass transfer and hydrodynamic behavior comprise mass transfer coefficients, specific contact area, liquid hold-up, residence time distribution characteristics and pressure drop. Usually they have to be determined by extensive and expensive experimental estimation procedures and correlated with process variables and specific internals properties. 

Real experiments for the determination of external mass transfer coefficients are used as an example for virtual experiments with CFD. Here experimental studies (Williamson et al., 1963 Wilson and Geankopolis, 1966) on the flow of two liquids, namely water and a propylene glycol-water mixture, through a packed bed of spherical particles made from solid benzoic acid are... 

With the help of relevant post-processing and using the average entrance and exit concentrations, the mass transfer coefficient and /-factor can be determined via Eqns. (1),(2). In Fig. 11, the simulation results for different particle arrangements and particle size are compared with the experimental data taken from (Williamson et al., 1963 Wilson and Geankopolis, 1966). For the experimental set Wilson (1966), a , the void fraction is estimated as 43.6 %, whereas for the experimental set Wilson (1966), bM, it is 40.1 % (Wilson and Geankopolis, 1966). In the experiments by Williamson (1963), the void fraction is equal to 43.1 % or 44.1 %, respectively. The /-factor decreases with increasing... 

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