Mass Transfer in Agitated Solid-Liquid Systems

10-4 MASS TRANSFER IN AGITATED SOLID-LIQUID SYSTEMS 

As noted earlier, with the exception of the purely physical process of producing a slurry, unit operations involving solid-liquid mixing are mass transfer processes. These include  

Mass transfer between a solid and the liquid is discussed in great detail by Doraiswamy and Sharma (1984) and in other books devoted to a particular mass transfer operation, such as crystallization (Mullins, 1993). In the following sections we highlight several important aspects. 

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

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... 

In reactive solid-liquid systems, the process can be dominated by one or more of the following mechanisms 1) external (extraparticle) mass transfer 2) internal (intraparticle) mass transfer or 3) chemical reaction (at the surface, below the surface, or in the liquid). The agitation speed only affects the interfacial area available for mass transfer (if N < as described above), and the external mass transfer coefficient... 

Crystallization and dissolution data obtained from agitated vessel studies may be analysed by the methods discussed above, but a survey of the literature related to the subject of solid-liquid mass transfer in agitated vessels shows that there is an extremely wide divergence of results, correlations and theories. The difficulty is the extremely large number of variables that can affect transfer rates, the physical properties and geometry of the system and the complex liquid-solid-agitator interactions. 

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. 

Mass Transfer Regimes in Mechanically Agitated Solid-Liquid Systems... 

Morris (M9) has recently reviewed a number of studies of mass transfer across the gas-liquid interface in mechanically agitated systems containing suspended solid particles. These studies [Hixon and Gaden (H7), Eckenfelder... 

Later publications have been concerned with mass transfer in systems containing no suspended solids. Calderbank measured and correlated gas-liquid interfacial areas (Cl), and evaluated the gas and liquid mass-transfer coefficients for gas-liquid contacting equipment with and without mechanical agitation (C2). It was found that gas film resistance was negligible compared to liquid film resistance, and that the latter was largely independent of bubble size and bubble velocity. He concluded that the effect of mechanical agitation on absorber performance is due to an increase of interfacial gas-liquid area corresponding to a decrease of bubble size. 

Mass transfer across the liquid-solid interface in mechanically agitated liquids containing suspended solid particles has been the subject of much research, and the data obtained for these systems are probably to some extent applicable to systems containing, in addition, a dispersed gas phase. Liquid-solid mass transfer in such systems has apparently not been studied separately. Recently published studies include papers by Calderbank and Jones (C3), Barker and Treybal (B5), Harriott (H4), and Marangozis and Johnson (M3, M4). Satterfield and Sherwood (S2) have reviewed this subject with specific reference to applications in slurry-reactor analysis and design. 

In connection with solid-liquid systems agitated so as to achieve interphase mass transfer or heterogeneous chemical reaction it may be noted that various workers have begun to consider the combined fluid dynamic, mass-transfer, and chemical kinetic problem in which a fluid moves past a solid with which it reacts chemically. The paper by Acrivos and Chambr6 (Al) is an example of this approach. 

Blasinski H, Pyc KW. (1975) Mass transfer in chemically reacting solid-liquid systems subjected to agitation in baffles mixed tanks. Int. Chem. Eng., 15 73-79. 

Nagata S, Yamaguchi J, Yabuta S, Harada M. (1960) Mass transfer in solid-liquid agitation systems. Soc. Chem. Eng. Jpn., 24 618-624. 

Mass transfer between a liquid and suspended solids in mechanically agitated systems has been widely studied, and a number of important investigations will be referred to in Section V,D,2. 

The proposed catalyst loading, that is the ratio by volume of catalyst to aniline, is to be 0.03. Under the conditions of agitation to be used, it is estimated that the gas volume fraction in the three-phase system will be 0.15 and that the volumetric gas-liquid mass transfer coefficient (also with respect to unit volume of the whole three-phase system) kLa, 0.20 s-1. The liquid-solid mass transfer coefficient is estimated to be 2.2 x 10-3 m/s and the Henry s law coefficient M = PA/CA for hydrogen in aniline at 403 K (130°C) = 2240 barm3/kmol where PA is the partial pressure in the gas phase and CA is the equilibrium concentration in the liquid. 

Hixson, A. W. and Baum, S. J. Ind. Eng. Chem. 33 (1941) 478, 1433. Agitation mass transfer coefficients in liquid-solid agitated systems. Agitation heat and mass transfer coefficients in liquid-solid systems. 

The liquid-solid mass-transfer coefficient depends mainly on the agitation speed, the particle size, and the physical properties of the system. While ks oc N°-2 this relationship may depend on the particle size (Sano et al., 1974). In a dimensionless form, Sh oc RemSc0 5 however, the value of m changes at some critical Reynolds number when all particles are suspended. The most generalized relationship is given by Eq. (3.34), and its use is recommended. 

For a conventional mechanically agitated biological reactor, the information provided for aqueous gas-liquid and gas-liquid-solid systems in Sections II, III, and VII is applicable here. For power consumption, the most noteworthy works are those by Hughmark (1980) (see Eqs. (6.15) and (6.16)) and Schiigerl (1981). For gas-liquid mass transfer, the relationship kLaL = (P/V, ug) is applicable for biological systems. The relationships (6.19) and (6.20) are also valuable, and their use is recommended. The most generalized relation for kLaL is provided by Eq. (6.18). The intrinsic gas-liquid mass transfer coefficient is best estimated by Eq. (6.23). For liquid-solid mass transfer, the use of the study by Calderbank and Moo-Young (1961) (Eqs. (6.24)-(6.26)) is recommended. For viscous fluids, Eq. (6.27) should be used. 

The ways in which reaction parameters affect a two phase batch reaction are similar to those considered above for the three phase systems. Since there is no gas phase, agitation only serves to keep the catalyst suspended making it more accessible to the dissolved reactants so it only has a secondary effect on mass transfer processes. Substrate concentration and catalyst quantity are the two most important reaction variables in such reactions since both have an influence on the rate of migration of the reactants through the liquid/solid interface. Also of significant importance are the factors involved in minimizing pore diffusion factors the size of the catalyst particles and their pore structure. 

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