Solid-liquid mass transfer correlations

The solid-liquid mass transfer coefficient without aeration is a function of power consumption per unit volume of the liquid. One typical case is the Levins and Glastonbury correlation for small particles (<2 mm), fully suspended and moderate density differences (Treybal, 1980) ... 

One more correlation is that of Calderbank-Moo-Young for the solid-liquid mass transfer coefficient in stirred tanks without aeration (Kato et al., 2001)... 

Gogoi and Dutta (1996) studied the solid-liquid mass transfer in a three-phase sparged reactor. They derived the following correlation ... 

Any form of convection, of course, increases the value of Ks. In slurry operation with no liquid flow, gas flow induces convection. In an agitated slurry reactor, stirring causes convection. In a pulsating slurry reactor, pulsation of the slurry induces convection and in a three-phase fluidized bed, the movements of both gas and liquid phases cause convection. Any one or more modes of convection will increase the value of the solid-liquid mass-transfer coefficient. In broad terms, the convective liquid-solid mass-transfer coefficient is correlated by-two steady state theories. Here we briefly review and compare them. 

In catalytic slurry reactors the locale of the reaction is the catalyst surface. Hence, in addition to the mass transfer resistance at the gas-liquid interface a further transport resistance may occur at the boundary layer around the catalyst particle. This is characterized by the solid-liquid mass transfer coefficient, kg, which has been the subject of many theoretical and experimental studies. Brief reviews are given by Shah (82). In general, the liquid-solid mass transfer coefficient is correlated by expressions like... 

Gladkii(16) at the State Scientific Research Institute of Industrial and Sanitary Gas Cleaning at Moscow did work on the three-phase calcium sulfite slurry oxidation system, finding that the liquid phase oxidation (pH 3.6-6) is first order with respect to the sulfite species. He pointed out, on the basis of pH versus time data from his semi-batch reaction, that the slurry oxidation had different periods in which either reaction kinetics or solid-liquid mass transfer controlled the oxidation rate. He also presented an omnibus empirical correlation between pH, temperature, and the liquid phase saturation concentration of calcium sulfite solution for predicting the slurry oxidation rate. The catalytic effect of manganese... 

By implication, therefore, processes which are particularly dependent on turbulent eddies and their associated forces are likely to be well correlated by energy dissipation rate. Bubble formation (Chapter IS) and micromixing phenomena (Chapter 10), for instance, fall into this category. However, processes which are dependent on the anisotropic ntain flows and for which the non-homogeneous nature of stirred tanks turbulence is significant, e.g. solid suspension and solid-liquid mass transfer (Chapters 16 and 17), are not well correlated that way. 

Extensive literature is available on the gas-liquid and solid-liquid mass transfer features of MASRs, for example. Levins and Glastonbury (1972a,b), Sano et al. (1974), Yagi and Yoshida (1975), Bern et al. (1976), Teshima and Ohashi (1977), Boon-Long et al. (1978), Patil and Sharma (1984). Mills and Chaudhari (1997) recommend the following correlations of Yagi and Yoshida (1975) (Equation 17.27) and Bern et al. (1976) (Equation 17.28) for gas-liquid mass transfer ... 

Solid-liquid mass transfer coefficients can be calculated from the following correlation proposed by Sano et al. (1974) ... 

The recommended correlations for gas-liquid and solid-liquid mass transfer for the different regimes are summarized in Table 17.6. The effect of liquid back-mixing is usually unimportant. 

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. 

Other inadequacies of Kolmogorov s theory in the manner of its use by Shinnar and Church (1960) and Brian et al. (1969) to correlate solid-liquid mass transfer in stirred reactors have been dealt in some detail by Levins and Glastonbury (1972a). Stewart and Townsend (1951) have estimated the value of Re to be 1500 for the existence of the inertial subrange. Taylor (1935) estimated that for the region outside the impeller, the value of ROj. for conditions typical of stirred reactors is -144. This is much smaller than that required by Stewart and Townsend s estimated value of 1500. Therefore, the validity of Equation 6.8 outside the impeller discharge stream is doubtful. Further, the use of in Equation 6.10 for Re is not justified by... 

A.7.2 Correlations for Solid-Liquid Mass Transfer CoefBcient... 

Mass transfer In the bibliography, the sources of many proposed correlations for both gas-liquid and solid-liquid mass transfer are listed. The recommended correlations are as follows. 

Correlations are available in the literature for areas and mass transfer coefficients (gas to liquid mass transfer correlations have been reviewed by Charpentier [10], Shah [73], Hirose et al. [31], Gianetto et al. [16], [17], [18] and by Specchia et al. [79], and liquid to solid mass transfer correlations by Hirose et al. [32] and Specchia et al. [80]. 

In general, the specific impact of agitation must be determined experimentally for each system. The correlations discussed below are presented to provide a guide and insight into the expected effects of various variables on solid-liquid mass transfer. 

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. 

The gas-liquid mass transfer for organic solutions and the liquid-solid mass transfer are evaluated using the appropriate correlations (eqs. (3.427) and (3.435), respectively), while the Fogler s overall coefficient (K°A) is (eq. (3.379))... 

Munjal S, Dudukovic MP, Ramachandran P. Mass transfer in rotating packed beds— I. Development of gas-liquid and liquid-solid mass-transfer correlations. Chem Eng... 

For gas-liquid-solid systems, studies on gas-liquid and liquid-solid mass transfer in basket reactors have been rather limited. For the rotating basket reactor, gas-liquid mass-transfer coefficient data are needed. Liquid-solid mass transfer has been studied by Teshima and Ohashi (1977), and their data are correlated by... 

Just as in the case of gas-liquid mass transfer, two important parameters characterizing the liquid-solid mass transfer are the liquid-solid mass-transfer coefficient and the liquid-solid interfacial area. Various correlations for the estimation of these parameters under a variety of system conditions are discussed in Chaps. 6 through 9. The importance of liquid-solid mass transfer on the reactor performance depends, once again, on the nature of the reaction and the flow conditions. 

---