Packed beds correlations

The void fraction should be the total void fraction including the pore volume. We now distinguish Stotai from the superficial void fraction used in the Ergun equation and in the packed-bed correlations of Chapter 9. The pore volume is accessible to gas molecules and can constitute a substantial fraction of the gas-phase volume. It is included in reaction rate calculations through the use of the total void fraction. The superficial void fraction ignores the pore volume. It is the appropriate parameter for the hydrodynamic calculations because fluid velocities go to zero at the external surface of the catalyst particles. The pore volume is accessible by diffusion, not bulk flow. 

The void fraction used in this equation and in Equation 9.1 should be the total void fraction that includes pore volume. We now distinguish it from the supeificial void fraction used in the Ergun equation and in the packed-bed correlations of Chapter... 

From packed bed correlation for D. and liquid phase region of graph. 

Wakao N, Kaguei S, Funazkri T. Effect of fluid dispersion coefficients on particle-to-fluid heat transfer coefficients in packed beds. Correlation of nusselt numbers. Chemical Engineering Science 1979 34(3) 325-336. 

These dimensionless groups have been used ever since as the basis for the pipe flow analogy in almost all packed bed correlations. 

To determine the mass-transfer rate, one needs the interfacial area in addition to the mass-transfer coefficient. For the simpler geometries, determining the interfacial area is straightforward. For packed beds of particles a, the interfacial area per volume can be estimated as shown in Table 5-27-A. For packed beds in distillation, absorption, and so on in Table 5-28, the interfacial area per volume is included with the mass-transfer coefficient in the correlations for HTU. For agitated liquid-liquid systems, the interfacial area can be estimated... 

S] Correlates large amount of published data. Compares number of correlations, v,. = relative velocity, uVs. In packed bed, v,. = i>s pe,./e. 

Porous Media Packed beds of granular solids are one type of the general class referred to as porous media, which include geological formations such as petroleum reservoirs and aquifers, manufactured materials such as sintered metals and porous catalysts, burning coal or char particles, and textile fabrics, to name a few. Pressure drop for incompressible flow across a porous medium has the same quahtative behavior as that given by Leva s correlation in the preceding. At low Reynolds numbers, viscous forces dominate and pressure drop is proportional to fluid viscosity and superficial velocity, and at high Reynolds numbers, pressure drop is proportional to fluid density and to the square of superficial velocity. 

Dispersion In tubes, and particiilarly in packed beds, the flow pattern is disturbed by eddies diose effect is taken into account by a dispersion coefficient in Fick s diffusion law. A PFR has a dispersion coefficient of 0 and a CSTR of oo. Some rough correlations of the Peclet number uL/D in terms of Reynolds and Schmidt numbers are Eqs. (23-47) to (23-49). There is also a relation between the Peclet number and the value of n of the RTD equation, Eq. (7-111). The dispersion model is sometimes said to be an adequate representation of a reaclor with a small deviation from phig ffow, without specifying the magnitude ol small. As a point of superiority to the RTD model, the dispersion model does have the empirical correlations that have been cited and can therefore be used for design purposes within the limits of those correlations. 

Glaser and Thodos [Am. Jn.st. Chem. Eng. J., 4, 63 (1958)] give a correlation involving individual particle shape and bed porosity. Kunii and Suzuki [Jnt. ]. Heat Mass Tran.sfer, 10, 845 (1967)] discuss heat and mass transfer in packed beds of fine particles. 

Calvert (R-12) has tested the correlation in cross-flow packed beds, which tend to give better drainage than countercurrent beds, and has found the effect of gas-flow orientation insignificant. However, the onset of reentrainment was somewhat lower in a bed of 2.5-cm... 

FIG. 16"10 Sherwood mimher correlations for external mass-transfer coefficients in packed beds for e = 0.4 (adapted from Siiziild, gen. refs.). 

TABLE 16-10 Coefficients for Axial Dispersion Correlations in Packed Beds Based on Eq (16-79)... 

Gas/Liquid Mass Transfer This topic has been widely investigated for gas absorption in packed beds, usually countercurrent. One correlation for cocurrent flow in catalyst beds is by Sato et al. (First Pacific Chemical Engineering Congre.s.s, Pergamon, 1972, p. 187) ... 

For packed beds Gamson et al (1943) developed Colburn-type correlation for heat and mass from many experimental measurements for Rep >350 as ... 

However, on die basis of the relation between pressure drop and die minimum fluidisation velocity of particles, the point of transition between a packed bed and a fluidised bed has been correlated by Ergun41 using (17.7.2.3). This is obtained by summing the pressure drop terms for laminar and turbulent flow regions. 

Experimental results for fixed packed beds are very sensitive to the structure of the bed which may be strongly influenced by its method of formation. GUPTA and Thodos157 have studied both heat transfer and mass transfer in fixed beds and have shown that the results for both processes may be correlated by similar equations based on. / -factors (see Section 10.8.1). Re-arrangement of the terms in the mass transfer equation, permits the results for the Sherwood number (Sh1) to be expressed as a function of the Reynolds (Re,) and Schmidt numbers (Sc) ... 

Correlations for E are not widely available. The more accurate model given in Section 9.1 is preferred for nonisothermal reactions in packed-beds. However, as discussed previously, this model degenerates to piston flow for an adiabatic reaction. The nonisothermal axial dispersion model is a conservative design methodology available for adiabatic reactions in packed beds and for nonisothermal reactions in turbulent pipeline flows. The fact that E >D provides some basis for estimating E. Recognize that the axial dispersion model is a correction to what would otherwise be treated as piston flow. Thus, even setting E=D should improve the accuracy of the predictions. 

What models should be used, either for scaleup or to correlate pilot-plant data Section 9.1 gives the preferred models for nonisothermal reactions in packed beds. These models have a reasonable experimental basis even though... 

Correlations for heat transfer in packed-beds are still being developed. The current state of the art is represented by... 

The central difficulty in applying Equations (11.42) and (11.43) is the usual one of estimating parameters. Order-of-magnitude values for the liquid holdup and kiA are given for packed beds in Table 11.3. Empirical correlations are unusually difficult for trickle beds. Vaporization of the liquid phase is common. From a formal viewpoint, this effect can be accounted for through the mass transfer term in Equation (11.42) and (11.43). In practice, results are specific to a particular chemical system and operating mode. Most models are proprietary. 

The errors that result from the use of average transport coefficients are not particularly serious. The correlations that are normally employed to predict these parameters are themselves determined from experimental data on packed beds. Therefore, the applications of the correlations and the data on which they are based correspond to similar physical configurations. 

Correlations for Mass Transfer Factors (jD) in Packed Beds... 

Other useful correlations of heat transfer coefficients in packed beds have been proposed. Among these is a simple relation of Calderbank and Pogorski (104)... 

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