Transfer coefficients estimation

This part of Sec. 5 provides a concise guide to solving problems in situations commonly encountered by chemical engineers. It deals with diffusivity and mass-transfer coefficient estimation and common flux equations, although material balances are also presented in typical coordinate systems to permit a wide range of problems to be formulated and solved. 

The binary mass transfer coefficients estimated from these correlations and analogies are the low flux coefficients and, therefore, need to be corrected for the effects of finite transfer rates before use in design calculations. 

In Example 10.3.1 we considered the calculation of the mass transfer coefficient in the gas phase of a thin-film sulfonator. A schematic diagram of a sulfonation reactor was provided by Figure 10.5. Now, in the modeling of the reactor, the estimation of the temperature profiles along the reactor tube is very important. An important parameter in the determination of the temperature profiles is the gas-phase heat transfer coefficient. Estimate this heat transfer coefficient at the entrance to the reactor for the same set of operating conditions as specified in Example 10.3.1. 

Although the method of Bravo and Fair makes use of Onda s equations for k and k, it should be noted that the liquid-phase mass transfer coefficients estimated from the two procedures will be different since Eq. 12.3.29 for k depends on the interfacial area density (through the liquid-phase Reynolds number). 

Figure 11 shows the effect of the volumetric mass transfer coefficient estimated by the simulation in SBCR without liquid circulation. Methanol production increases 6.5 mol/kgcat-hr for the volumetric mass transfer coefficient of 0.75 and then the methanol production is no longer limited by volumetric mass transfer coefficient. This trend matched with that given in the Viking (10) report. The estimated volumetric mass transfer coefficient has a good agreement with experimental values shown in literatures (10, 43, and 44). 

The kinetic theory model was extended to include the effect of the mass transfer coefficient between the liquid and the gas and the water gas shift reaction in the slurry bubble column reactor. The computed granular temperature was around 30 cm /sec and the computed catalyst viscosity was closed to 1.0 cp. The volumetric mass transfer coefficient estimated by the simulation has a good agreement with experimental values shown in the literature. The optimum particle size was determined for maximum methanol production in a SBCR. The size was about 60 - 70 microns, found for maximum granular temperature. This particle size is similar to FCC particle used in petroleum refining. 

Similar discrepancies were noted by Blatt et al32 for colloidal suspensions such as skimmed milk, casein, polymer latexes, and clay suspensions. Actual ultrafiltration fluxes are far higher than would be predicted by the mass transfer coefficients estimated by conventional equations, with the assumption that the proper diffusion coefficients are the Stokes-Einstein diffusivities for the primary particles. Blatt concluded that either (a) the "back diffusion flux" is substantially augmented over that expected to occur by Brownian motion or (b) the transmembrane flux is not limited by the hydraulic resistance of the polarized layer. He favored the latter possibility, arguing that closely packed cakes of colloidal particles have quite high permeabilities. However, this is not a plausible hypothesis for the following reasons ... 

The sea-air CO2 flux estimated above is subject to three sources of error (1) biases in sea-air ApC02 values interpolated from relatively sparse observations, (2) the skin temperature effect, and(3) uncertainties in the gas transfer coefficient estimated on the basis of the wind speed dependence. Possible... 

Using Dextran for mass transfer coefficient estimation probably results in an overestimate of concentration polarisation, due to the larger size of Dextran compared to humic substances and calcium. However the diffusion characteristics of humic acid, calcium-humate complexes, and even calcium in the highly viscous boundary layer are not known, and Dextran is probably a conservative assumption. Corrections for calcium and HA (molecular weight 1 and 10 kDa) were performed using... 

The reason for this is the higher concentration of large molecular weight compounds in the boundarjf layer, which is evident from mass transfer coefficient estimations. The ks increases significantly with a decreasing size of the solute, and, therefore, the concentration polarisation in the boundary layer is significantly lower for smaller compounds. 

Volumetric mass transfer coefficient estimated with the empirical equation (Equation 7.14) [26] ... 

Table 2.6 Relationships between structure features and mass transfer coefficient estimated for commercial polymeric membranes...

Internal Cooling Channel Heat Transfer Coefficient Estimation... 

The hybrid solution procedure described in the previous section is computationally more demanding than one that does not rely on the CFD package to predict the heat transfer from the exhaust gas. In fact, this simpler approach was adopted in die early stages of the project, the heat transfer process was modelled using a mean heat transfer coefficient estimated from correlations for convective heat transfer in annuli. However, it was soon realized that this method has a high degree of uncertainty when the heat transfer process takes place under unsteady-state conditions and when the thermal entry length spreads over an appreciable extent of the domain. These conditions are always met in the application under study. 

If a heat transfer tube of a 2.9 cm diameter is submerged horizontally within the fluidized medium at the above operating conditions, what would be the surface heat transfer coefficient estimated by various empirical correlations ... 

If the streams in Problem 18 have the following film heat transfer coefficients, estimate the optimum minimum approach temperature for this problem. 

Gas mixing in laboratory internal recycle reactors used for gas-solid catalytic studies may be assessed from pressure drop (Berty, 1974 Berty, 1979), temperature drop measurements across the bed (Mahoney, 1984), or from mass transfer coefficient estimations (Caldwell, 1983). For a given impeller speed, the first method involves comparing the bed pressure drop of the recycle reactor v/iih pressure drop of a calibrated fixed catalyst bed conducted in a separate unit. Then knowing the fluid velocity versus pressure drop for the calibrated bed, the impeller speed versus fluid velocity can be drawn. The recycle rate can also be determined from thermodynamics based on the ratio of the adiabatic temperature change and the measured temperature difference. This method requires the measurements of temperatures across the bed and the mass flow rate. 

Microreactors proved to be much more eflicient for the phase transfer reactions (23). The two-phase reactions proceed on the phase boundary. As a result of mass transfer coefficient estimation, it can be ascertained that the application of microtechnology for the two-phase liquid reactions promotes instantaneous mixing and intensifies the interfusion of reagents, which is not to be assumed in standard reactors. By slow reactions due to increase in interfacial area, the reaction can be shifted from diffusion to kinetic control. Thus, Dan C 1, which means that there is no mass transfer limitation and the plug flow reactor model can be used to describe such a reaction (see Section 12.2). 

Heat generated by the adsorption of a component in the gas or liquid phase by the porous solid has to be transported not only between solid and fluid in an operating column, but is subsequently dissipated by transport from fluid to vessel wall and thence to the surrounding environment. A correlation due to Leva (1949) may be used to assess the resistance to heat transfer between fluid and vessel wall. A film heat transfer coefficient estimated from a correlation described by McAdams (1954) enables the evaluation of heat transfer resistance from the vessel wall to the surroundings. 

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