Mass transfer coefficient interpretation

As mentioned in Section 11.1.2, fundamental theory is insufficient to predict mass transfer coefficients from first principles. However, existing results do provide a framework for interpreting and sometimes extrapolating experimental results. 

Requirements regarding laboratory liquid-liquid reactors are very similar to those for gas-liquid reactors. To interpret laboratory data properly, knowledge of the interfacial area, mass-transfer coefficients, effect of contaminants on mass-transport processes, ionic characteristics of the system, etc. is needed. Commonly used liquid-liquid reactors have been discussed by Doraiswamy and Sharma (1984). 

Each of the mass transfer coefficients klA and k2A can be interpreted as a molecular diffusion coefficient, D, divided by a film thickness, z, for the gas phase and the water phase, respectively, i.e., k=D/z. However, this interpretation has no meaning in practice because of the lack of knowledge on the thickness of the two films. 

Pigford s solution may be interpreted in terms of the liquid-phase mass transfer coefficient, that is, by means of Eq. (171) in which v0 is replaced by For short contact times the substitution of Eq. (176) into the second expression for let in Eq. (171) gives... 

For a resolution of question (3), either MASC or the simpler SSHTZ program was run under both isothermal and adiabatic conditions, with effective mass transfer coefficients chosen to simulate the stable portion of the sorption fronts. Fortunately, in most cases described below, the programs predicted that the steady-state MTZ lengths did not change by more than 10Z or so between the two extremes. Thus, an extensive analysis of the wall effects in the various columns was not required for proper interpretation of MTZ data. 

The aim of this paper is to make measurements with liquids of various physical properties in order to define the effect of the liquid properties and operating conditions on the parameter /q, and the limits of validity of the literature models for the interpretation of mass transfer coefficients in bubble dispersions. The method, which is used for the measurements, was verified in Part I to minimize misinterpretations. 

V. Linek, M. Fujasova, M. Kordae, T. Moucha, Gas-liquid mass transfer coefficient in stirred tank interpreted through models of idealized eddy structure of turbulence in the bubble vicinity, Chem. Eng. Proc. (in press). 

The researchers interpreted the mass transfer coefficient with the mass transfer model for absorption, and the resulting empirical relationships represent the Sherwood number Sh as a function of Reynolds number Re. For details, the reader may refer to Ref. [25]. It is clear that the items included in the relationships they obtained are related closely to the reactor structure. 

Interpretation of available data is frustrated by lack of knowledge of certain fundamental quantities such as Interfacial area, mass transfer coefficients, solubility data, diffusion coefficients, bubble sizes, etc.. Existing equations for almost all of these variables have been developed on the basis of experiments conducted at atmospheric pressure and around room temperature. Use of such predictive equations at the reacting conditions involves large extrapolation, and the combined errors would make the analysis of kinetic data very suspect. In spite of this, most work reported in the literature does use such correlations. 

Equations (10-6) and (10-7) show that for the intermediate case the observed rate is a function of both the rate-of-reaction constant, ic and.. the mass-transfer coefficient k. In a design problem k and k would be known, so that Eqs. (10-6) and (10-7) give the global rate in terms of Cj. Alternately, in interpreting laboratory kinetic data k would be measured. If k is known, k can be calculated from Eq. (10-7). In the event that the reaction is not first order Eqs. (10-1) and (10-2) cannot be combined easily to eliminate C. The preferred approach is to utilize the mass-transfer coefficient to evaluate Q and then apply Eq. (10-2) to determine the order of the reaction n and the numerical value of k. One example of this approach is described by Olson et al. ... 

Both in data interpretation and in equipment design, must be evaluated from known or estimated mass-transfer coefficients or diffusivi-... 

We now recognize k as the ratio of kf to the steady-state mass-transfer coefficient niQ = DoIrQ. When k 1, the interfacial rate constant for reduction is very small compared to the effective mass-transfer rate constant, so that diffusion imposes no limitation on the current. At the opposite limit, where k >> 1, the rate constant for interfacial electron transfer greatly exceeds the effective rate constant for mass transfer, but the interpretation of this fact depends on whether k is also large. ... 

Breakthrough curves obtained in a fixed-bed ion exchange process by Pansini et al. (1996) were interpreted by means of the model, the only parameters of which are a solid-liquid and an intra-particle mass transfer coefficient. The experimental results were obtained using a... 

The Wheeler-Jonas equation has been used extensively in the case of pure physisorption on granular carbons. But recently, it has been demonstrated it can be equally well applied in a number of very divergent cases. The first extension is on the type of adsorbent, especially new types. The validly of the Wheeler-Jonas equation has been demonstrated [117,118] for both activated carbon fibres (ACF) and activated carbon monoliths (ACM). The equation itself and the calculation of the capacity IFe remain unchanged. As for the estimation of the overall mass transfer coefficient, the normal equation stays valid, providing a correct interpretation of the equivalent diameter of the particles . For ACFs, dp has been calculated fiom the total external surface. Given their small diameter, dp is essentially related to the length of the fibres [ 119]. For ACMs, dp seems to be related to the internal diameter of the channels. 

Chapters 7 and 8 present models and data for mass transfer and reaction in gas-liquid and gas-liquid-solid systems. Many diagrams are used to illustrate the concentration profiles for gas absorption plus reaction and to explain the controlling steps for different cases. Published correlations for mass transfer in bubble columns and stirred tanks are reviewed, with recommendations for design or interpretation of laboratory results. The data for slurry reactors and trickle-bed reactors are also reviewed and shown to fit relatively simple models. However, scaleup can be a problem because of changes in gas velocity and uncertainty in the mass transfer coefficients. The advantages of a scaledown approach are discussed. 

The mass transfer resistances strongly depend on the nature of the hydrodynamics in the contacting device and the mode of operation. Many devices have been used to study two-phase mass transfer at or near the liquid-liquid interface. Hence, the hydrodynamic characteristics of ion transport through a membrane were presented to evaluate the feasibility that this permeation system can be calibrated as a standardized liquid-liquid system for studying the membrane-moderated PT-catalyzed reaction. The individual mass transfer coefficients and diffusivities for the aqueous phase, organic phase, and membrane phase were determined and then correlated in terms of the conventional Sh-Re-Sc relationship. The transfer time of quaternary salt across the membrane and the thickness of the hydrodynamic diffusion boundary layer are calculated and then the effect of environmental flow conditions on the rate of membrane permeation can be accurately interpreted [127]. 

Experiment c required a number of steps to eventually find the mass transfer coefficient k This is invariably the case since k is not a directly measured variable but depends upon interpretation of the data using a model. Once k was obtained, we have a single data point to conpare to the correlation Eq. (17-3Za). They disagreed. You maybe tenpted to use the correlation and ignore the data point. However, mass transfer correlations are not very accurate. They usually predict the trends well (such as the effect of Reynolds and Schmidt numbers), but the absolute value predicted can be significantly off. A single data point can be used to adjust the constant in the correlation for application to this particular system If more data were available, we could check the entire correlation. 

Where is the heavy If your plot uses the same scale for all three conponents, it will be difficult to see the heavy. To find it set up the plot with a separate scale for heavy concentration. Note that the heavy has an initial peak and then a main, very broad peak (all at low concentrations). The initial peak occurs because with the low mass transfer coefficient some of the heavy exits the column without ever entering the packing material. This is called bypassing or instantaneous breakthrough and is obviously undesirable. Check to see if Eq. f 18-661 is satisfied, and interpret your results. 

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