Mass-transfer coefficients data interpretation

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). 

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. 

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-... 

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. 

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. 

Interpretation of Data. Operating data may be interpreted in terms of either mass-transfer coefficients, HTU s or H.E.T.S. s, depending upon which of the methods of Chap. 8 it is planned to use later in design. The determination of the values of H.E.T.S. from such data requires no particular explanation. In the case of the others, under ordinary circumstances the experimental data lead to over-all values of coefficients or transfer units, and these should be expressed in terms of the phase where the principal resistance to diffusion lies, as explained in Chap. 5. Over-all HTU s and Ka 8 can be converted, one into the other, through Eqs. (8.12) and (8.14). 

Hunter, et al. (28, 78) studied the extraction of phenol from kerosene as a core-liquid, with water as a wall-liquid, both liquids in turbulent flow. The data were interpreted by an equation similar to Eq. (10.12), and it was concluded that, over the limited range studied, the wall-liquid did not influence the mass-transfer coefficient for the core. Working with the liquids benzene and water over a wide range of flow rates for each, with acetic acid as the diffu- ini solute, Treybal and Work (82) showed that an equation at least as complex as Eq. (10.11) was necessary to describe the results and were therefore unable to determine the value of the constants. These observations reinforced the conclusions respecting the influence of each rate of flow on the degree of turbulence in both liquids. 

Comings and Briggs (20) studied the extraction of several solutes between benzene and water. For the extraction of benzoic acid, where the distribution favors the benzene, the major resistance to diffusion lay in the water phase. Addition of sodium hydroxide to the water reduced this resistance by causing a rapid chemical reaction, increased the mass-transfer coefficient, and made the effect of benzene rate on the over-all coefficient more pronounced, as would be expected. Similar experiences were obtained in the case of extraction of aniline, but in the case of acetic acid results were contrary to what was expected. The data apparently could be interpreted in terms of Eq. (10.11), with = 0.45 — 0.55,7 = 0 — 0.1, ri = 0.40 — 0.55, T = 0.45 — 0.55. Brinsmade and Bliss (13) extracted acetic acid from methyl isobutyl ketone (core) by water (w all). By making measurements at several temperatures, they were able to investigate the influence of Schmidt number on the rates and by graphical treatment of the data obtained values of the constants of Eq. (10.11) as follows j8 = 1, = 7 = 0,... 

For relatively slow reactions (

interpreting experimental fmdings. When the concentration of B is measured at various moments in time, both the chemical rate constant and the volumetric mass transfer coefficient can be determined. In principle, two measurements are sufficient, but a series of data will give more accurate results. 

CFaT riverine models were presented for both the water column and bed sediment. They were then simplified to focus onto the non-flow resuspension soluble fraction using the quasi-steady state assumption to isolate the key water-side and sediment-side process elements. Field evidence of soluble release based on CFaT model derived data was reviewed for three rivers. Both the traditional particle background resuspension process and more recent soluble fraction process algorithms data interpretation were covered. Numerical field calibrated resuspension velocities and soluble mass-transfer coefficients were presented. Candidate water-side and sediment-side transport processes, selected from the literature were reviewed. Those that provided the best theoretical explanation and contained laboratory and/or field data support were selected. Finally, the flux and the overall transport coefficient which captures the essential features of the framework were presented. Following this the theoretical mass-transfer coefficients were applied to a site on the Fox River below De Pere Dam. Numerical calculations were made for the transport coefficients for both individual and combined processes. 

The effects of physical transport processes on the overall adsorption on porous solids are discussed. Quantitative models are presented by which these effects can be taken into account in designing adsorption equipment or in interpreting observed data. Intraparticle processes are often of major importance in adsorption kinetics, particularly for liquid systems. The diffusivities which describe intraparticle transfer are complex, even for gaseous adsorbates. More than a single rate coefficient is commonly necessary to represent correctly the mass transfer in the interior of the adsorbent. 

Unfortunately the theory, when used for data interpretation, is based on many simplifications that are not always valid. The success of the method depends on the significance of the axial dispersion and the interfacial mass transfer and on the accuracy of the description of these effects. A comparative study of different measuring technique by [25] has shown, for the chromatographic method, that experimental uncertainties may lead to significantly broader confidence limits for the diffusion coefficients than for measurements in single pellets in a diffusion cell. 

The study of a particular adsorption process requires the knowledge of equilibrium data and adsorption kinetics [4]. Equilibrium data are obtained firom adsorption isotherms and are used to evaluate the capacity of activated carbons to adsorb a particular molecule. They constitute the first experimental information that is generally used as a tool to discriminate among different activated carbons and thereby choose the most appropriate one for a particular application. Statistically, adsorption from dilute solutions is simple because the solvent can be interpreted as primitive, that is to say as a structureless continuum [3]. Therefore, all equations derived firom monolayer gas adsorption remain vafid. Some of these equations, such as the Langmuir and Dubinin—Astakhov, are widely used to determine the adsorption capacity of activated carbons. Batch equilibrium tests are often complemented by kinetics studies, to determine the external mass transfer resistance and the effective diffusion coefficient, and by dynamic column studies. These column studies are used to determine system size requirements, contact time, and carbon usage rates. These parameters can be obtained from the breakthrough curves. In this chapter, I shall deal mainly with equilibrium data in the adsorption of organic solutes. 

The calculation of drying processes requires a knowledge of a number of characteristics of drying techniques, such as the characteristics of the material, the coefficients of conductivity and transfer, and the characteristics of shrinkage. In most cases these characteristics cannot be calculated by analysis, and it is emphasized in the description of mathematical models of the physical process that the so-called global conductivity and transfer coefficients, which reflect the total effect on the partial processes, must frequently be interpreted as experimental characteristics. Consequently, these characteristics can be determined only by adequate experiments. With experimental data it is possible to apply analytical or numerical solutions of simultaneous heat and mass transfer to practical calculations. 

Patience and Chaouki [98] adopted the two-phase model of Brereton et al. [96] to interpret their gas RTD data obtained with a radioactive tracer gas. The two model parameters, crossflow coefficient, k, and (ratio between core and riser cross-sections), were evaluated by fitting the model to the experimental data. They found that the crossflow coefficients varied between 0.03 to 0.1 m/s, and varied from 0.98, at high gas velocities, to 0.5, at low velocities. They attributed gas crossflow between core and annulus by supposing that solids drag gas to the annulus as they condense along the wall and then carry it downward for a certain distance. Solids are reintroduced into the core as they are stripped off the wall and re-entrained into the core gas flow. They developed a correlation for describing this gas mass transfer based on the analogy with wetted wall towers, as ... 

In this chapter the aspects of model selection/discrimination and parameter estimation and the experimental acquisition of kinetic data are not dealt with, since they fall fell outside its scope. Moreover, in interpreting the observed temperature dependency of the rate coefficients in this chapter it was assumed that we are dealing with intrinsic kinetic data. As will be shown in a Chapter 7, other, parasitic, phenomena of mass and heat transfer may interfere, disguising the intrinsic kinetics. Criteria will be presented there, however, to avoid this experimental problem. 

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