Mass transfer rate parameters

Many of the near-critical extraction processes in use at the present time (e.g. decaffeination of coffee (chapter 5), hop extraction (chapter 4) and the extraction of flavour essences (chapter 6) involve leaching materials from a solid matrix. It is not surprising therefore that many of the mass transfer rate studies reported in the literature are for the extraction of components from a bed of solids. 

If existing mass transfer rate data are to be extended or scale-up calculations are to be carried out with a view to obtaining a preliminary costing for a proposed process, it is useful to obtain a mathematical model of the mass transfer process. 

---

In addition to the fundamental parameters of selectivity, capacity, and mass-transfer rate, other more practical factors, namely, pressure drop characteristics and adsorbent life, play an important part in the commercial viabiUty of a practical adsorbent. 

Reactor Configuration. The horizontal cross-sectional area of a reactor is a critical parameter with respect to oxygen mass-transfer effects in LPO since it influences the degree of interaction of the two types of zones. Reactions with high intrinsic rates, such as aldehyde oxidations, are largely mass-transfer rate-limited under common operating conditions. Such reactions can be conducted effectively in reactors with small horizontal cross sections. Slower reactions, however, may require larger horizontal cross sections for stable operation. 

Normally there must be a way of determining whether the mass-transfer rate with the solids is the key controlling parameter or the gas-liquid mass transfer rate. 

For many laboratoiy studies, a suitable reactor is a cell with independent agitation of each phase and an undisturbed interface of known area, like the item shown in Fig. 23-29d, Whether a rate process is controlled by a mass-transfer rate or a chemical reaction rate sometimes can be identified by simple parameters. When agitation is sufficient to produce a homogeneous dispersion and the rate varies with further increases of agitation, mass-transfer rates are likely to be significant. The effect of change in temperature is a major criterion-, a rise of 10°C (18°F) normally raises the rate of a chemical reaction by a factor of 2 to 3, but the mass-transfer rate by much less. There may be instances, however, where the combined effect on chemical equilibrium, diffusivity, viscosity, and surface tension also may give a comparable enhancement. 

Comparison of Eq. (184) with Eq. (183) shows the effect of size distribution for the case of fast chemical reaction with simultaneous diffusion. This serves to emphasize the error that may arise when one applies uniform-drop-size assumptions to drop populations. Quantitatively the error is small, because 1 — is small in comparison with the second term in the brackets [i.e., kL (kD)112). Consequently, Eq. (184) and Eq. (183) actually give about the same result. In general, the total average mass-transfer rate in the disperser has been evaluated in this model as a function of the following parameters ... 

Typical Values. Table 11.3 shows typical parameter values for mechanically agitated tanks and other gas-liquid contacting devices. Not shown are values for kgAj since these are usually so large that they have no influence on the mass transfer rate. 

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. 

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. 

Both the mass transfer kinetic parameters (diffusion in the phases, D, D j, surface renewal frequency, s) and chemical reaction rate constants (kg, kj) strongly influence enhancement of the absorption rate. The particle size, dp, the dispersed liquid holdup, e and the partition coefficient, H can also strongly alter the absorption rate [42-44,46,48]. Similarly, the distance of the first particle from the gas-liquid interface, 6q is an essential factor. Because the diffusion conditions are much better in the dispersed phase (larger solubility and, in most cases, larger diffusivity, as well) the absorption rate should increase with the decrease of the (5g value. 

The model provides a good approach for the biotransformation system and highlights the main parameters involved. However, prediction of mass transfer effects on the outcome of the process, through evaluation of changes in the mass transfer coefficients, is rather difficult. A similar mass transfer reaction model, but based on the two-film model for mass transfer for a transformation occurring in the bulk aqueous phase as shown in Figure 8.3, could prove quite useful. Each of the films presents a resistance to mass transfer, but concentrations in the two fluids are in equilibrium at the interface, an assumption that holds provided surfactants do not accumulate at the interface and mass transfer rates are extremely high [36]. 

Many parameters affect the mass transfer between two phases. As we discussed above, the concentration gradient between the two phases is the driving force for the transfer and this, together with the over-all mass transfer coefficient, determines the mass transfer rate. The influence of process parameters (e. g. flow rates, energy input) and physical parameters (e. g. density, viscosity, surface tension) as well as reactor geometry are summed up in the mass transfer coefficient. The important parameters for Kta in stirred tank reactors are ... 

Furthermore, it is almost impossible to use ozone for fc, -measurements when organic substances are present that are (easily) oxidized by molecular ozone. Mass transfer enhancement will occur during such measurements, so that the mass transfer coefficient based on only the physical process cannot be determined. In this case, the oxygen mass transfer coefficient kLa 02) should be determined to assess the mass transfer rate without reaction. The enhanced mass transfer due to reaction should be considered separately, because it is not only dependent on the parameters listed above in equation 3-10, but also dependent on the concentration of the reactants. 

Generally the oxidation of compounds with ozone is considered to be second order, which means first order with respect to the oxidant (03 or OH°) and to the pollutant M (Hoigne and Bader, 1983 a, b). A requirement for the experimental determination of the reaction order with respect to the pollutant is that the ozone concentration in the bulk liquid remains constant. A further requirement for determining kinetic parameters in general, is that the reaction rate should be independent of the mass transfer rate. These are easy to achieve for (very) slow reactions by using a continuously sparged semi-batch reactor. Such a reaction... 

Whereas current-producing reactions occur at the electrode surface, they also occur at considerable depth below the surface in porous electrodes. Porous electrodes offer enhanced performance through increased surface area for the electrode reacdon and through increased mass-transfer rates from shorter diffusion path lengths. The key parameters in determining the reaction distribution include the ratio of the volume conductivity of the electrolyte to the volume conductivity of the electrode matrix, the exchange current, the diffusion characteristics of reactants and products, and the total current flow. The porosity, pore size, and tortuosity of the electrode all play a role. 

The overall specific resistance for heat or mass transfer is the reciprocal of the heat or mass transfer coefficient, U or K, where U and K are the common parameters characterizing heat and mass transfer rates, respectively, defined as... 

---