Literature correlations

Example 11.8 With highly reactive absorbents, the mass transfer resistance in the gas phase can be controlling. Determine the number of trays needed to reduce the CO2 concentration in a methane stream from 5% to 100 ppm (by volume), assuming the liquid mass transfer and reaction steps are fast. A 0.9-m diameter column is to be operated at 8 atm and 50°C with a gas feed rate of 0.2m /s. The trays are bubble caps operated with a 0.1-m liquid level. Literature correlations suggest = 0.002 m/s and A, = 20m per square meter of tray area. 

Hence, both Cp and U can be evaluated for the physical and geometrical system under consideration instead of using literature correlations with an accuracy of 30 %. For a single reaction the rate of heat generation qp is the product of the reaction rate, the volume of the reaction mixture, and the heat of reaction, which for a batch apparatus can be written as ... 

The validation of CFD codes using pressure drop is most reliable when actual experimental data are taken in equipment identical to the situation that is being simulated. Existing literature correlations such as the Ergun equation are known to have shortcomings with respect to wall effects, particle shape effects, application to ordered beds and validity at high Re. The applicability of literature correlations to typical CFD simulation geometries needs to be examined critically before fruitful comparisons can be made. 

About 800 of these rules were chosen by testing all the IR correlations we could find in the literature,(30-32) mostly for condensed phases, against the EPA gas-phase library of 2300 compounds. (33-34) About 30% of the literature correlations were not generally satisfied by the library spectra, and were discarded. Another 200 rules were discovered by searching for patterns in compound classes in the library which could reasonably be attributed to expected vibrational modes of those classes. Statistics were generated for the probability that each of the IR rules would be satisfied for compounds which contained, or did not contain, the substructure specified by the rule. These statistics were used to compute two confidence levels for each rule, corresponding to the confidence in the two propositions a) and b) implied by the rule. 

The contraction of the exhaust gas at the entrance of the inlet channels and its expansion at the exit of the outlet channels causes inertial losses. It has been shown in Konstandopoulos et al. (2001) that CFD calculations or experiments are the only means to evaluate these losses, since estimations on literature correlations (which are not specifically developed for the honeycomb structure of the DPF) are not sufficiently accurate for such evaluations. Moreover, the influence of the soot cake on these losses has never before been studied in a thorough fashion. To improve the inclusion of such phenomena in DPF... 

Modern commercial software provides powerful capability to deploy literature correlations and to customize models for specific applications. 

The two parameters are determined experimentally by measuring the bed void volume at different linear velocities and a double-log plot of evsU.n and Ut are found as slope and intercept of a linear regression of experimental data in this plot. Additionally the parameters may be evaluated from literature correlations, which give a good estimate of the range of flow rates applicable for the fluidization of a certain matrix. Martin et al. [19] used two dimensionless... 

Much of the literature correlations for solids suspension are based on the so-called critical impeller speed. Attempts to duplicate experiments between various investigators often yield deviations of 30-50% from the critical speed shown by other investigators. Because power is proportional to speed cubed, power varies on the order of 2 to 3 times, which is not sufficiently accurate for industrial full-scale design. Therefore, many approximate, conservative estimates have been made in the literature as general guidelines for choosing mixers for solids suspension. Table IV is one such guideline for solid particles of a closely sized nature. 

The objective of the following model is to investigate the extent to which Computational Fluid Mixing (CFM) models can be used as a tool in the design of industrial reactors. The commercially available program, Fluent , is used to calculate the flow pattern and the transport and reaction of chemical species in stirred tanks. The blend time predictions are compared with a literature correlation for blend time. The product distribution for a pair of competing chemical reactions is compared with experimental data from the literature. 

Pressure Drop, Mass and Heat Transfer Pressure drop is more important in reactor design than in analysis or simulation. The size of the compressor is dictated by pressure drop across the reactor, especially in the case of gas recycle. Compressor costs can be significant and can influence the aspect ratio of a packed or trickle bed reactor. Pressure drop correlations often may depend on the geometry, the scale, and the fluids used in data generation. Prior to using literature correlations, it often is advisable to validate the correlation with measurements on a similar system at a relevant scale. 

The static contribution l. , incorporates heat transfer by conduction and radiation in the fluid present in the pores, conduction through particles, at the particle contact points and through stagnant fluid zones in the particles, and radiation from particle to particle. Figure 19-20 compares various literature correlations for the effective thermal conductivity and wall heat-transfer coefficient in fixed beds [Yagi and Kunii, AlC hE J. 3 373(1957)]. 

About fifteen years ago I was applying a leading and very well known literature correlation as part of my graduate thesis. 1 punched in keys and the computer printed out results. For some reason the results did not look right. Upon investigation, I discovered the unbelievable the correlation just did not work for my case. Not that the correlation was bad over many years, it gained a very healthy reputation. It just happened that it had limitations, just like every other correlation. The limitations of this correlation were fairly well explored, but a quarter of a century after it was derived, I found the hard way that it had one more limitation which remained hidden over all these years. 

Mechanical agitation and gas-liquid mass transfer are very important in viscous fermentation media. Most recently, Lim and Yoo (1989) and Lee and Wang (1989) have examined mixing effects in the fermentation of Xanthan gum. Aunins-cf al. (1989) evaluated the effects of paddle geometry on power input and mass transfer in small-scale animal cell culture, 500 mL Corning spinner vessels. The results indicate that power dissipation dependency differs from literature correlations and may compromise scale-up at constant power input from these vessels. 

Hence, several definitions of the molar refraction have been proposed in the literature, correlating the refractive index with the chemical structure of electrically insulating materials. Resuming ... 

Hence, the overall resistance to the mass transfer predicted by this variant of the BAMcomb model is the sum of the resistance in the liquid film and the resistance in the pore fluid. The value of the liquid film mass transfer coefficient Kf can be calculated from literature correlations,400,407,408 while the method for the estimation of the apparent pore liquid mass transfer coefficient Kp can be derived from Eq. (163). The surface interaction between the protein and the immobilized ligand at the internal particle surface can be treated in the same way as for nonporous particles, i.e.,... 

Figure 3 shows the results obtained when the above correlations developed using the more active 2.5% Pd catalyst are applied to data obtained on the less active 0.5% Pd catalyst. It can be seen that the agreement between the model predictions and experimental values is of lesser quality than the previous case. The deviations are especially noticeable with increasing L/us or decreasing external contacting efficiency since the predicted lines cross each other at an intermediate value which is opposite to the data. On a positive note, the predictions are more accurate than those that would be obtained using the literature correlations as shown earlier in Figure 1. Further work is needed to determine the underlying reason for this behavior, however.

Literature correlations to estimate heat and mass transfer coefficients are generally of the form Sh=a Re 0).ln general, they do not take into account the scale factors dp/D and dp/L which should be important, especially in the case of fluidized beds, given the complex hydrodynamics of these systems. 

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