Reynolds number for the liquid phase

R Le --------Reynolds number for the liquid phase calculated with the... 

Reynolds number for the liquid phase, UjPidpl. i Generation/disapparition (source) for i species Time, h Temperature Molecular velocity... 

Trickle-bed models assume plug flow for both phases. Thus, it is interesting to evaluate the respective Peclet numbers. The correlations of Michell-Furzer for liquid (eq. (3.417)) and Hochman-Effron for gas (eq. (3.419)) are used and the results are shown in Table 5.15. The Reynolds number for the gas phase is 32.28. 

The next parameter of importance is the Peclet number of the liquid and the gas phase. For the specified Reynolds number, the Peclet number for the liquid phase using the Michell-Furzer correlation (eq. (3.417)) is 0.74. The minimum value of Z/dp for ethanol conversion between 0.1 and 0.9, evaluated using the Mears criterion (eq. (3.421)), is 2.84 and 62.11 respectively, much lower than the value used in the example, which is about 2500. Thus, the operation can be assumed to follow the plug-flow model. 

Concerning packed bubble bed reactors, the evaluation of the Peclet number of the liquid phase is important in order to decide if we have to use a plug- or backmixed-flow model. For the specified Reynolds number, the Peclet number for the liquid phase using the Stiegel-Shah correlation (eq. (3.422)) is 0.15, much lower than in the trickle bed, which was expected as the backmixing in the liquid phase in packed bubble bed reactors is relatively high. The liquid phase can be considered to be well mixed if (Ramachandran, and Chaudhari, 1980) (eq. (3.423))... 

An expression for fia has to be derived from experimental data, by means of a power-product equation containing the gas density, the interstitial mean gas velocity, and a film-liquid Reynolds number. They found a value of-0.37 for both the exponent of pa and of ug, indicating that fiG depends on a gas-phase Reynolds number. For the exponent of the liquid film Reynolds number the value was about zero. 

Correlations for the dynamic liquid holdup have also been developed as function of various dimensionless numbers including the liquid and gas Reynolds number, and the two-phase pressure drop [see, e.g., Ramachandran and Chaudhari, Three-Phase Catalytic Reactors, Gordon and Rreach, 1983 and Hofmann, Hydrodynamics and Hydrodynamic Models of Fixed Bed Pieactors, in Gianetto and Silveston (eds.), Multiphase Chemical Pieactors, Hemisphere 1986],... 

Just as for the liquid holdup, the correlations for the k,aL are reported in two ways. Some investigators correlated kLaL to liquid and gas velocities by either dimensional30,34,35 or dimensionless34 correlations. The dimensional correlations assumed kLaL a Ui U . The values of r and s for various types of packings reported by various invesiigators are summarized in Table 6-9. Goto and Smith34 have correlated Sherwood numbers to the liquid-phase Reynolds and Schmidt numbers. 

The results predicted by formula (6.9.8) were compared with the experimental data of [92, 292] for the liquid phase mass transfer coefficients from the absorption of nitrogen bubbles in aqueous solutions of carboxymetil cellulose and carbopol at low Reynolds numbers. The maximum error of the formula is about 5% for 0.7 n < 1.0. 

The relation between c and / and X (defined by equation 5.1) is shown in Figure 5.4, where it is seen that separate curves are given according to the nature of the flow of the two phases. This relation was developed from studies on the flow in small tubes of up to 25 mm diameter with water, oils, and hydrocarbons using air at a pressure of up to 400 kN/m . For mass flowrates per unit area of U and G for the liquid and gas, respectively, Reynolds numbers Rei L d/fii ) and Rec(G d/fia) may be used as criteria for defining the flow regime values less than 1000 to 2000, however, do not necessarily imply that the fluid is in truly laminar flow. Later experimental work showed that the total pressure has an influence and data presented by Gr1H ITH(i9) may be consulted where... 

For gas-liquid flows in Regime I, the Lockhart and Martinelli analysis described in Section I,B can be used to calculate the pressure drop, phase holdups, hydraulic diameters, and phase Reynolds numbers. Once these quantities are known, the liquid phase may be treated as a single-phase fluid flowing in an open channel, and the liquid-phase wall heat-transfer coefficient and Peclet number may be calculated in the same manner as in Section lI,B,l,a. The gas-phase Reynolds number is always larger than the liquid-phase Reynolds number, and it is probable that the gas phase is well mixed at any axial position therefore, Pei is assumed to be infinite. The dimensionless group M is easily evaluated from the operating conditions and physical properties. 

The final parameter to be evaluated is the liquid-phase Peclet number, and the graph given by Levenspiel (L10) can be used for this purpose. It must be remembered that the film Reynolds number should be used in estimating the Peclet number. 

Reynolds numbers calculated for the in vivo hydrodynamics are considerably lower than those of the corresponding in vitro numbers, both for bulk and particle-liquid Reynolds numbers. Remarkably, bulk Reynolds numbers in vivo appear to have about the same magnitude as particle-liquid Reynolds numbers characterizing the flow at the particle surface in vitro using the paddle apparatus. In other words, it appears that hydrodynamics per se play a relatively minor role in vivo compared to the in vitro dissolution. This can be attributed to physiological co-factors that greatly affect the overall dissolution in vivo but are not important in vitro (e.g., absorption and secretion processes, change of MMC phases,... 

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