Conversion of Mass Transfer Coefficients

In a particular application related to air flowing over a water surface, the following data were reported at T = 317 K  

Water evaporates into the dry airstream at a total pressure Pj = 101.3 kPa and is denoted by the subscript A B refers to the air component, kc is the mass 

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Example 16.5. Conversion of mass-transfer coefficients and estimation of stage efficiency in mixer... 

Flux and Conversion of Mass-Transfer Coefficient. A value of kg was experimen-... 

Conversion of Mass-Transfer Coefficients. Prove or show the following relation-... 

Also listed in Table 1.3 are conversion factors for the transformation of mass transfer coefficients from one set of units to another. These are frequently required to convert literature values of k given in a particular set of units, to one needed in a different application. This type of conversion is taken up in Illustration 1.4. Of note as well in Table 1.3 is the appearance of the term the so-called logarithmic mean, or log-mean driving force, defined by... 

OS 63] ]R 27] ]P 46] Experimental results were compared with a kinetic model taking into account liquid/liquid mass transfer resistance [117]. Calculated and experimental conversions were plotted versus residence time the corresponding dependence of the mass-transfer coefficient k,a is also given as well (Figure 4.78). 

Assuming plug flow of both phases in the trickle bed, a volumetric mass transfer coefficient, kL a, was calculated from the measurements. The same plug flow model was then used to estimate bed depth necessary for 95% S02 removal from the simulated stack gas. Conversion to sulfuric acid was handled in the same way, by calculating an apparent first-order rate constant and then estimating conversion to acid at the bed depth needed for 95% S02 removal. Pressure drop was predicted for this bed depth by multiplying... 

Figure 3. CO conversion in the reactor cell as a function of temperature, measured to determine the external mass transfer coefficient of CO. Conditions 1% CO, 5% 0 t 93.3 cm /s at 273 K and 101.3 kPa.

In a typical pulse experiment, a pulse of known size, shape and composition is introduced to a reactor, preferably one with a simple flow pattern, either plug flow or well mixed. The response to the perturbation is then measured behind the reactor. A thermal conductivity detector can be used to compare the shape of the peaks before and after the reactor. This is usually done in the case of non-reacting systems, and moment analysis of the response curve can give information on diffusivities, mass transfer coefficients and adsorption constants. The typical pulse experiment in a reacting system traditionally uses GC analysis by leading the effluent from the reactor directly into a gas chromatographic column. This method yields conversions and selectivities for the total pulse, the time coordinate is lost. 

In this cell, mechanical vibration is applied to the cell housing to enhance the transfer in the parallel plate tank cell [248]. The vibrations are transfered to the electrolyte resulting in an increase of the mass-transfer coefficient. The cell is extensively used in industry for the pretreatment of higher and high metal concentrations which is finally purified by a packed bed electrolysor if the required conversion is not too high [247],... 

VOCs), and to a decrease in production yields. Quantitation of these phenomena and determination of material balances and conversion yields remain the bases for process analysis and optimisation. Two kinds of parameters are required. The first is of thermodynamic nature, i.e. phase equilibrium, which requires the vapour pressure of each pure compound involved in the system, and its activity. The second is mass-transfer coefficients related to exchanges between all phases (gas and liquids) existing in the reaction process. 

Furthermore, a liquid-phase distributor is used on the top of the bed and the overall gas-phase mass transfer coefficient was experimentally measured as 0.153 s 1 for liquid flow rate equal to 14 X 10 5 m3/s. Under these conditions, the experimental value of sulfur dioxide conversion was approximately 18%. 

The film (individual) coefficients of mass transfer can be defined similarly to the film coefficient of heat transfer. A few different driving potentials are used today to define the film coefficients of mass transfer. Some investigators use the mole fraction or molar ratio, but often the concentration difference AC (kg or kmol m ) is used to define the liquid phase coefficient (m while the partial pressure difference A/i (atm) is used to define the gas film coefficient (kmolh m 2 atm ). However, using and A gp of different dimensions is not very convenient. In this book, except for Chapter 15, we shall use the gas phase coefficient (m h" ) and the liquid phase coefficient ki (m h ), both of which are based on the molar concentration difference AC (kmol m ). With such practice, the mass transfer coefficients for both phases have the same simple dimension (L T" ). Conversion between k and is easy, as can be seen from Example 2.4. 

To calculate the bubble-free volume needed to reach the conversion of 80 % of acetylene, we have to calculate the gas-liquid acetylene mass transfer coefficient, kL, and the specific... 

This model was applied to the same data for batch and flowthrough systems with and without acid addition as for the previous two models, and some of the xylan conversion predictions calculated from the data and concentration predictions via Eq. 8 are summarized in Figs. 5 and 6 for batch and flowthrough systems, respectively. Tables 4 and 2 present the parameters and the SSE values for the branched pore model, respectively. Overall, although some data are better matched than others, hemicellulose hydrolysis models based on mass transfer alone can predict performance in batch and flow systems as well as, if not better than, reaction-only models. In addition, the changes in mass transfer coefficient with flow are consistent with expectations for a mass transfer model but not for strictly a chemical reaction. 

External mass transfer limitations, which cause a decrease in both the reaction rate and selectivity, have to be avoided. As in the batch reactor, there is a simple experimental test in order to verify the absence of these transport limitations in isothermal operations. The mass transfer coefficient increases with the fluid velocity in the catalyst bed. Therefore, when the flow rate and amount of catalyst are simultaneously changed while keeping their ratio constant (which is proportional to the contact time), identical conversion values should be found for flow rate high enough to avoid external mass transfer limitations.[15]... 

Enantioselectivity was roughly the same for the three reactors, being 80-90 and 62-65% for the Rh/Josiphos and Rh/Diop catalysts, respectively [266]. Conversion was very different. For fixed reaction time, the batch reactor and the falling-film microreactor had higher conversions than the Caroussel reactor. This was indicative of operation under mass transfer regime in the latter. On the basis of these data, it was concluded that the mass transfer coefficients kya of the helical falling-film microreactor are in between the boundaries given by the known kta values of 1-2 s 1 for small batch reactors and about 0.01 s-1 for the Caroussel reactor. 

Figure 7.19 represents schematically a way to determine experimentally whether external mass transfer can be neglected. Transfer effects do not occur when the conversion for a given space-time does not depend on the flow rate. The test is not very sensitive, however. This is caused by the small dependence of the mass transfer coefficient on the flow rate at the low Reynolds numbers prevailing in laboratory fixed bed reactors. 

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