Liquid-solid mass-transfer coefficient determination

C. Determination of the Liquid-Solid Mass-Transfer Coefficient... 

Sykes and Gomezplata13 determined the liquid-solid mass-transfer coefficient for 0.32-cm-diameter spherical particles suspended in stirred aqueous iodine solutions. The particle density was within 5 percent of the liquid density. The effects of impeller speed (200 through 600 rev min- ), Schmidt number (770 through 11,300), and impeller type (fan-disk turbine, propeller, and 45° paddle and turbine) on the mass-transfer coefficient were examined. The data were correlated with an average deviation of 8 percent by the following expression ... 

In case of a relatively low concentration of the liquid reactant, for example, in the rear part of the reactor or in processes like hydrodesulphurization of fuels (with a typical feed concentration of organic sulfur between 100 and 1000 ppm), the effective rate is limited by the concentration of the liquid reactant. The rate is determined by the interplay of the chemical reaction and the diffusion of the liquid reactant to and within the catalyst Depending on the type of reaction, an increase in pressure may not help to improve the reaction rate, as demonstrated here for the hydrogenation of 1-octene. Then a hquid recycle would probably decrease the rate Although the liquid-solid mass transfer coefficient is increased, this effect is more than compensated by the decrease of the liquid reactant concentration. 

A detailed compilation obtained from different literature sources of the correlations used in this model for determining oil properties, gas solubilities, and gas-liquid/liquid-solid mass-transfer coefficients at process conditions is reported in the work of Alvarez and Ancheyta (2008). 

When the reaction in the porous catalyst is very rapid, the conversion rate will be determined by gas/liquid or liquid/solid mass transfer. Particularly volumetric gas/liquid mass transfer coefficients (liquid side) are not very much different in slurry-reactors and in three phase packed beds (aU under optimum conditions). 

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. 

Laboratory reactors for studying gas-liquid processes can be classified as (1) reactors for which the hydrodynamics is well known or can easily be determined, i.e. reactors for which the interfacial area, a, and mass-transfer coefficients, ki and kc, are known (e.g. the laminar jet reactor, wetted wall-column, and rotating drum, see Fig. 5.4-21), and (2) those with a well-defined interfacial area and ill-determined hydrodynamics (e.g. the stirred-cell reactor, see Fig. 5.4-22). Reactors of these two types can be successfully used for studying intrinsic kinetics of gas-liquid processes. They can also be used for studying liquid-liquid and liquid-solid processes. 

From these results, the effective mass transfer coefficient ks [s" ] can be calculated and was found to vary from 8 10 m/s (10 rpm) to 1.2 10 m/s (40 rpm). Around 100 rpm, the system enters the kinetically limited regime (Ca=0.05). These results show that immobilized trypsin is very active and useful for determining mass transfer rates for liquid solid systems. 

The over-all resistance is then the sum of the individual resistances (see equation 3-8) and the over-all mass transfer coefficient KLa takes all of them into account. In practice, it is often not possible to determine the mass transfer coefficient for a dispersed liquid or solid... 

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... 

Gas-liquid mass transfer in the absence of solids has been widely studied (Shah et al, 1982). In these studies, both physical and chemical methods for the determination of the volumetric mass-transfer coefficient and the gas-liquid... 

The volumetric mass transfer coefficient is also determined for three-phase (gas-liquid-solid) systems using both physical and chemical methods described above. A summary of these studies is given in Table XXXII. 

The physical aspects of gas-liquid, liquid-liquid, solid-liquid, and gas-liquid-solid systems are discussed in the subsequent sections of this chapter. Using the guidelines given there, it is possible to get an estimate of local and average mass-transfer coefficients, interfacial areas, and contacting patterns. This section briefly considers the effect of reactions on mass transfer, a subject treated elsewhere in this handbook and in advanced texts [29, 30]. Note that while we will refer mostly to gas-liquid systems, the same treatment would more or less apply to liquid-liquid and liquid-solid systems. In the case of gas-liquid-solid systems, it may be possible to determine the controlling resistance and simplify the analysis to a two-phase system, as far as the reaction part is concerned. 

This case study is concerned with a three-phase gas-liquid-solid (catalytic) reaction. A systematic stepwise procedure has been described for determining the rate-controlling step, which depends on the catalyst type, particle size, operating pressure and temperature, mass transfer coefficient, and concentrations of reactants and products. As indicated, the rate-controlling step may change with location in a continuous reactor and with time in a batch reactor. 

External mass transfer, such as diffusion to particles or to the outside of pipes or cylinders, requires different correlations from those for internal mass transfer, because there is boundary-layer flow over part of the surface, and boundary-layer separation is common. The mass-transfer coefficients can be determined by studying evaporation of liquid from porous wet solids. However, it is not easy to ensure that there is no effect of internal mass-transfer resistance. Complications from diffusion in the solid are eliminated if the solid is made from a slightly soluble substance that dissolves in the liquid or sublimes into a gas. This method also permits measurement of local mass-transfer coefficients for different points on the solid particle or cylinder. 

Historically, the analysis of gas/liquid systems arose from the problem of gas absorption accompanied by chemical reaction. Since the chemical reaction in this instance tends to increase the rate of absorption (mass transfer), much of the analysis is based on exploring the effects of chemical reaction on a diffusional process. This is just the opposite of the viewpoint in the theory for gas/solid systems, where we have explored the effects of appending a diffusional process to a chemical reaction. The net result of this difference in viewpoints is that most theories of gas/liquid reactions are concerned with determining enhancement factors for the mass-transfer coefficient rather than penalty functions, such as the effectiveness factor for the reaction kinetic constant. This difference in viewpoints can be rather refreshing in pointing out the various contrasts between the two approaches. 

In the SLPTC models previously developed, film mass transfer coefficients for the organic and aqueous phases are important parameters. In Chapter 14 we saw how the coefficient for gas-liquid systems can be determined. The same method can be used for liquid-liquid systems. In all of these cases, mass transfer rates are calculated using contactors with known interfacial areas. Where a solid phase is involved, the constant area criterion can be met by using a rotating disk of solid reactant or catalyst, as the case may be (Melville and Goddard, 1985, 1988 Hammerschmidt and Richarz, 1991). 

Three phase slurry reactors are characterized by a gas-liquid (K,a) and liquid-solid (k ) mass transfer coefficient. These coefficients were determined for the rotating disc reactor at the appropriate operation conditions ... 

Madden AG, Nelson DG. (1964) A novel technique for determining mass transfer coefficients in agitated solid-liquid systems. AlCHEJ, 10 415-430. 

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