Experimental Validation of Column Models

After all parameters for the plant (Section 6.5.5) and column (Sections 6.5.6-6.5.S) models are determined, either from experimental data or from empirical correlations, the validity of a model should be checked using different experiments than those analyzed during parameter determination. In particular, the correctness of predicting the positions of the adsorption and desorption fronts is an important indicator for the reliability of a model. 

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Known scale-up correlations thus may allow scale-up even when laboratory or pilot plant experience is minimal. The fundamental approach to process scaling involves mathematical modeling of the manufacturing process and experimental validation of the model at different scale-up ratios. In a paper on fluid dynamics in bubble column reactors, Lubbert and coworkers (54) noted ... 

The preceding section deals with the experimental validation of column profiles in rectifying CSs. However, it is just as important to be able to model stripping sections, as these operating conditions may shift topology inside the MBT in ways that... 

Bertola F, Grundseth J, Hagesaether L, Dorao C, Luo H, Hjarbo KW, Svend-sen HF, Vanni M, Baldi G, Jakobsen HA (2005) Numerical Analysis and Experimental Validation of Bubble Size Distribution in Two-Phase Bubble Column Reactors. Multiphase Science Technology 17(1-2) 123-145 Breim G, Braeske H, Durst F (2002) Investigation of the unsteady two-phase flow with small bubbles in a model bubble column using phase-Doppler anemometry. Chem Eng Sci 57(24) 5143-5159... 

FIGURE 4.6 Experimental validation of rectifying column profiles for the benzene/diethyl ether/methanol system with the reflux ratio r== 3 and x/> = X d = [0.694, 0.066] using the NRTL thermodynamic model at P=0.825 atm. 

FIGURE 4.10 Experimental validation of stripping column profiles for the acetone/ ethanol/methanol system with the reflux ratios R/ = 3 and 5, and X b = [0.05, 0.80]. Theoretical profiles were generated using the NRTL model at 0.825 atm. 

The most important validation of the model will be the comparison of the experimental and numerical force-displacement curves. If the numerical model is simulating the behavior of the knitted stmcture correctly, then the shapes of these curves should be very similar and the only difference should be the scale of force since the numerical simulation uses fewer filaments. Visual checks can also be used, e.g., comparison of loop height and width or wale/course density given as number of vertical/horizontal columns/rows of loops per cm for both the experimental and numerical case. 

In order to test the validity of this model to predict the frictional force in sphere particles in bubble column and fluidized bed, the experimental apparatus is then designed (figure 3). 

CFD has also been applied to analyze the flow patterns in a special counter-current solvent extraction column (Angelov et al, 1990). They used a singlephase flow representation and a k- turbulence model to compute the flow patterns in a periodic structure of the column. Validation of the computational results was achieved by applying LDA to obtain experimental data on the velocity profiles. CFD is a very useful tool here because the optimization of the performance of the extraction column from a geometrical point of view can be achieved with relative ease in comparison with a pure empirical strategy. 

The recent progress in experimental techniques and applications of DNS and LES for turbulent multiphase flows may lead to new insights necessary to develop better computational models to simulate dispersed multiphase flows with wide particle size distribution in turbulent regimes. Until then, the simulations of such complex turbulent multiphase flow processes have to be accompanied by careful validation (to assess errors due to modeling) and error estimation (due to numerical issues) exercise. Applications of these models to simulate multiphase stirred reactors, bubble column reactors and fluidized bed reactors, are discussed in Part IV of this book. 

Here c ( ), csim ( ) are the experimental and simulated responses at time t. When the experimental and simulated elution profiles coincide perfectly the overlap is 100% and when they are totally separated the overlap is 0%. In papers III-VI, the accuracy of the parameters was validated by calculating the overlap. We suggest that an overlap of more than 90% could be considered as good. A high overlap validates that both right isotherm model and right column model have been chosen. 

The agreement that was observed between the experimental results and the prediction of a competitive Langmuir model based on the use of single-component Langmuir isotherms in the case of the adsorption of enantiomeric derivatives of amino acids on immobilized serum albumin [26] is imusual. It demonstrates the validity of the competitive Langmuir model based on the use of the parameters of the single-component Langmuir model. However, as explained before, the experimental conditions are exceptionally favorable since the column saturation capacities for the two enantiomers are equal. Nevertheless, Zhou et ah have shown that it is possible, in certain favorable cases, to derive the equilibrium isotherms of the pure enantiomers and to calculate isotherm equilibrium data for any mixture of... 

Seshadri and Deming [44] have used the Craig model to calculate band profiles in chromatographic systems. However, they selected an unrealistic isotherm, (Ji = ( j + biCj)Ci, i.e., an isotherm which, for each component i, is linear in respect to its concentration, but with a retention factor that is a linear function of the other component concentration. There is little physical basis for this model, and this prevented them from deriving any useful conclusions. More recently, Eble et al. [45] have used the Craig model to calculate band profiles in isocratic elution and to develop general correlations between the sample size on the one hand and the apparent retention factor and the column efficiency on the other. Experimental data confirm the approximate validity of the relationships obtained [24,25] (Eig-ure 10.3). The use of such empirical relationships allowed an estimation of the band shape on a personal computer for column efficiencies not exceeding a few hxmdred theoretical plates. 

Based on these observations [93] proposed a modified model containing two time constants, one for the liquid shear induced turbulence and a second one for the bubble induced turbulence. The basic assumption made in this model development is that the shear-induced turbulent kinetic energy and the bubble-induced turbulent kinetic energy may be linearly superposed in accordance with the hypothesis of [128, 129]. Note, however, that [82] observed experimentally that this assumption is only valid for void fractions less than 1 %, whereas for higher values there is an amplification in the turbulence attributed to the interactions between the bubbles. The application of this model to the high void fraction flows occurring in operating multiphase chemical reactors like stirred tanks and bubble columns is thus questionable. 

There are two general experimental methods for estimating the extracolumn band broadening of a chromatographic instrament. The linear extrapolation method is relatively straightforward to perform and interpret but rests on the validity of Eq. (1.34) and the model used to calculate the contribution for the column variance. A plot of a T against tR, Vr or (1 + k) for a series of homologous compounds will be linear. The true column efficiency can be obtained from the slope of the line and o ext from the intercept on the vertical axis [162,167,168]. The assumption that the individual... 

It must be realized that a state must be reached where experiments and theory go hand in hand, leading to the development of better (more realistic) models, and acquisition of critical tracer data. In the absence of a knowledge of the processes involved, models employed often yield very erroneous results. Thus, whereas even a few tracer data are quite informative (since a few data points can be treated only with zero order models), any attempts to understand oceanic processes in detail pose a serious challenge. A few examples are considered here, where tracer data have contributed to the development of realistic models. As mentioned earlier, simple one-dimensional models were developed earlier on using two parameters K and w, to consider vertical transfer of tracers through an oceanic column. Even today these are used, in the absence of better alternatives, and in reality, because of a lack of tracer data in the three-dimensional space. The result is that as yet the general validity of the K-w models in space is not known or their dependence on climate. The latter arises because there are experimental tracer data for ocean waters only during the Holocene. 

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