Solid-liquid systems, mass transfer rate

In catalytic gas-liquid-solid systems mass transfer is more complex. The catalyst particles are present in the liquid phase. The expression for the rate of mass transfer from the gas to the liquid is identical to that for systems without a solid catalyst (Eqn. 5.4-67). However, now also mass transfer from the liquid to the solid surface (external mass transfer) and inside the particle (internal mass transfer) have to be considered. 

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. 

Gas holdup is an important hydrodynamic parameter in stirred reactors, because it determines the gas-liquid interfacial area and hence the mass transfer rate. Several studies on gas holdup in agitated gas-liquid systems have been reported, and a number of correlations have been proposed. These are summarized in Table VIII. For a slurry system, only a few studies have been reported (Kurten and Zehner, 1979 Wiedmann et al, 1980). In general, the gas holdup depends on superficial gas velocity, power consumption, surface tension and viscosity of liquids, and the solid concentration. The dependence of gas holdup on gas velocity, power consumption, and surface tension of the liquid can be described as... 

The absorption rate depends upon the gas-liquid interfacial area, the gas residence time, and the gas-liquid mass-transfer coefficient. The gas residence time is lower and the gas-liquid mass-transfer coefficient is higher (due to higher Reynolds number) in a three-phase fluidized-bed system compared to a bubble-column with no solids present. It is the first factor (i.e., gas-liquid interfacial area) that plays an important and complex role on the mass-transfer rate in the three-phase fluidized-bed system. 

Experimental gas-solid mass transfer data are presented for the well defined supercritical CO 2-naphthalene system at 10-200 atm and 35 C. These data are compared with low pressure gas-solid and liquid-solid systems. It has been found that both natural and forced convection are important under these conditions and that mass transfer rates at near-critical conditions are higher than at lower or higher pressure. 

At 35 C, the gas-solid mass transfer coefficient increases dramatically near the critical point, has its maximum value near 100 atm, and then decreases gradually as pressure increases. The mass transfer rate under supercritical conditions is much higher than at standard conditions (1 atm and 25 C) for liquid-solid and gas-solid systems, due to strong natural convection effects. Both natural and forced convection are important for supercritical mass transfer. 

It is imperative to know the S-L-V equilibrium compositions for the ternary (C02-solvent-solid) system, for these give the concentrations at the interface, which are needed for calculating the two-way mass transfer rates of CO2 and solvent in the antisolvent crystallization processes and for the selection of operating conditions for the desired crystallization pathways. Three kinds of data are usually generated for ternary (solute-solvent-antisolvent) systems (a) the liquid phase compositions for S-L equilibrium at a fixed... 

This leads to the concept of mass transfer calculation techniques in scaleup. Figure 36 shows the concept of mass transfer from the gas-liquid step as well as the mass transfer step to liquid-solid and/or a chemical reaction. Inherent in all these mass transfer calculations is the concept of dissolved oxygen level and the driving force between the phases. In aerobic fermentation, it is normally the case that the gas-liquid mass transfer step from gas to liquid is the most important. Usually the gas-liquid mass transfer rate is measured, a driving force between the gas and the liquid calculated, and the mass transfer coefficient, KqO or t a obtained. Correlation techniques use the data shown in Fig. 37 as typical in which KqO is correlated versus power level and gas rate for the particular system studied. 

The most common extraction techniques for semivolatile and nonvolatile compounds from solid samples that can be coupled on-line with chromatography are liquid-solid extractions enhanced by microwaves, ultrasound sonication or with elevated temperature and pressures, and extraction with supercritical fluid. Elevated temperatures and the associated high mass-transfer rates are often essential when the goal is quantitative and reproducible extraction. In the case of volatile compounds, the sample pretreatment is typically easier, and solvent-free extraction methods, such as head-space extraction and thermal desorption/extraction cmi be applied. In on-line systems, the extraction can be performed in either static or dynamic mode, as long as the extraction system allows the on-line transfer of the extract to the chromatographic system. Most applications utilize dynamic extraction. However, dynamic extraction is advantageous in many respects, since the analytes are removed as soon as they are transferred from the sample to the extractant (solvent, fluid or gas) and the sample is continuously exposed to fresh solvent favouring further transfer of analytes from the sample matrix to the solvent. 

The concept of a circulating flow reactor was further developed in the Buss reactor technology (Figure 1.26). Large quantities of reaction gas are introduced via a mixer to create a well dispersed mixture. This mixture is rapidly circulated by a special pump at high gas/liquid ratios throughout the volume of the loop and permits the maximum possible mass transfer rates. A heal exchanger in the external loop allows for independent optimisation of heat transfer. For continuous operation, the product is separated by an in-line cross-flow filter which retains the suspended solid catalyst within the loop. Such a system can operate in batch, semi-continuous and continuous mode. 

A schematic diagram of the unit cell for a vapor-Uquid-porous catalyst system is shown in Fig. 9.9. Each cell is modeled essentially using the NEQ model for heterogeneous systems described above. The bulk fluid phases are assumed to be completely mixed. Mass-transfer resistances are located in films near the vapor-liquid and liquid-solid interfaces, and the Maxwell-Stefan equations are used for calculation of the mass-transfer rates through each film. Thermodynamic equilibrium is assumed only at the vapor-liquid interface. Mass transfer inside the porous catalyst may be described with the dusty fluid model described above. 

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). 

Many correlations have been suggested to estimate mass transfer coefficients in two-phase systems for various types of physical scenarios. Oldshue (1983) gives a summary of available correlations for liquid-solid, liquid-liquid, and gas-liquid mass transfer, as well as an estimate of the mass transfer rate of a G-L-S system—namely, the oxidation of sodium sulfite in water. Cussler (1997) gives... 

The most pertinent effects of ultrasound in solid-liquid reactions are mechanical, which are attributed to symmetrical and/or asymmetrical cavitation. Symmetrical cavitation (the type encountered in homogeneous systems) leads to localized areas of high temperatures and pressures and also to shock waves that can create microscopic turbulence (Elder, 1959). As a result, mass transfer rates are considerably enhanced. For example, Hagenson and Doraiswamy (1998) observed a twofold increase in the intrinsic mass transfer coefficient in the reaction between benzyl chloride (liquid) and sodium sulfide (solid). In addition, a decrease in particle size and therefore an increase in the interfacial surface area appears to be a common feature of ultrasound-assisted solid-liquid reactions (Suslick et al., 1987 Ratoarinoro et al., 1992, 1995 Hagenson and Doraiswamy, 1998). 

The fact that micelles are molecular aggregates of sizes typically in the radius range of 10-30 A suggests that they may be treated as microparticles that would enhance mass transfer rates in liquid-liquid or solid-liquid systems. Rate enhancements by microparticles in general has been treated in some detail in Chapter 23. Similar situations can arise in micellar reactions, where the micelles themselves act as microparticles (see Janakiraman and Sharma, 1985). 

The Kolmogoroff theory can account for the increase in mass transfer rate with increasing system turbulence and power input, but it does not take into consideration the important effects of the system physical properties. The weakness of the slip velocity theory is the fact that the relationship between terminal velocity and the actual slip velocity in a turbulent system is really unknown. Nevertheless, on balance, the slip velocity theory appears to be the more successful for solid-liquid mass transfer in agitated vessels. 

In a multi-phase catalytic reactor, the catalyst is usually a solid phase in contact with the liquid phase. Figure 4.1 shows a typical multi-phase catalytic system, where one fluid phase (gas or liquid) is dispersed in a liquid phase which contains porous catalyst particles. The reactants need to diffuse from their respective phases to the catalytic site where reaction products are formed and then they can diffuse back to one or both fluid phases. The overall reaction rate of the process will be affected by the inter-phase mass transfer rates near the gas-hquid and the liquid-solid interfaces, as well as by the intra-phase mass transfer rate competing with the intrinsic reaction rate inside the catalyst structure. 

Cini et al. (1991b) proposed the use of a tubular Pd/AljOj mesoporous membrane for the hydrogenation of a-methylstyrene to cumene. A comparison between the tubular catalyst and a fully-wetted pellet revealed a rate increase by up to a factor of 20. From that study, several other theoretical (Torres et al, 1994) and experimental ones confirmed that a three-phase membrane reactor can improve the mass transfer rate of gas-liquid-solid systems. 

We shall now apply the methods developed in the previous chapters to model PTC reactions in liquid-liquid and solid-liquid systems, including solid-supported systems. For a more detailed account of these methods, reference may be made to the articles, among others, of Naik and Doraiswamy (1998), and Yadav and collaborators (1995,2004). The rate of the overall PTC cycle is dependent on the relative rates of the different steps in the PTC cycle. Thus, when the basic conservation equations for mass balance are written for a PTC system, the individual steps that comprise the PTC cycle must be accounted for. These steps are the ion-exchange reaction, interphase mass transfer of both inactive and active forms of the phase transfer (PT) catalyst, partitioning of the catalyst between the two phases (in liquid-liquid systems), and the main organic phase reaction. When these are considered, the normal assumption of pseudo-first-order kinetics (Equation 16.1) is no longer valid. 

Liquid/Solid Mass Transfer The dissolved gas and the solvent react in contact with the surface of the catalyst. For studying the rate of transfer to the surface, an often-used system was benzoic acid or naphthalene in contact with water. A correlation of Dharwadkar and Sylvester (AJChE Journal, 23, 376 [1977]) that agrees well with some others is... 

---